Moved DroidFish project to trunk/

DroidFish/jni/stockfish/endgame.cpp

@@ -0,0 +1,939 @@
+/*
+  Stockfish, a UCI chess playing engine derived from Glaurung 2.1
+  Copyright (C) 2004-2008 Tord Romstad (Glaurung author)
+  Copyright (C) 2008-2010 Marco Costalba, Joona Kiiski, 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 "bitcount.h"
+#include "endgame.h"
+#include "pawns.h"
+
+using std::string;
+
+extern uint32_t probe_kpk_bitbase(Square wksq, Square wpsq, Square bksq, Color stm);
+
+namespace {
+
+  // Table used to drive the defending king towards the edge of the board
+  // in KX vs K and KQ vs KR endgames.
+  const int MateTable[64] = {
+    100, 90, 80, 70, 70, 80, 90, 100,
+     90, 70, 60, 50, 50, 60, 70,  90,
+     80, 60, 40, 30, 30, 40, 60,  80,
+     70, 50, 30, 20, 20, 30, 50,  70,
+     70, 50, 30, 20, 20, 30, 50,  70,
+     80, 60, 40, 30, 30, 40, 60,  80,
+     90, 70, 60, 50, 50, 60, 70,  90,
+    100, 90, 80, 70, 70, 80, 90, 100,
+  };
+
+  // Table used to drive the defending king towards a corner square of the
+  // right color in KBN vs K endgames.
+  const int KBNKMateTable[64] = {
+    200, 190, 180, 170, 160, 150, 140, 130,
+    190, 180, 170, 160, 150, 140, 130, 140,
+    180, 170, 155, 140, 140, 125, 140, 150,
+    170, 160, 140, 120, 110, 140, 150, 160,
+    160, 150, 140, 110, 120, 140, 160, 170,
+    150, 140, 125, 140, 140, 155, 170, 180,
+    140, 130, 140, 150, 160, 170, 180, 190,
+    130, 140, 150, 160, 170, 180, 190, 200
+  };
+
+  // The attacking side is given a descending bonus based on distance between
+  // the two kings in basic endgames.
+  const int DistanceBonus[8] = { 0, 0, 100, 80, 60, 40, 20, 10 };
+
+  // Penalty for big distance between king and knight for the defending king
+  // and knight in KR vs KN endgames.
+  const int KRKNKingKnightDistancePenalty[8] = { 0, 0, 4, 10, 20, 32, 48, 70 };
+
+  // Build corresponding key code for the opposite color: "KBPKN" -> "KNKBP"
+  const string swap_colors(const string& keyCode) {
+
+    size_t idx = keyCode.find('K', 1);
+    return keyCode.substr(idx) + keyCode.substr(0, idx);
+  }
+
+  // Get the material key of a position out of the given endgame key code
+  // like "KBPKN". The trick here is to first build up a FEN string and then
+  // let a Position object to do the work for us. Note that the FEN string
+  // could correspond to an illegal position.
+  Key mat_key(const string& keyCode) {
+
+    assert(keyCode.length() > 0 && keyCode.length() < 8);
+    assert(keyCode[0] == 'K');
+
+    string fen;
+    size_t i = 0;
+
+    // First add white and then black pieces
+    do fen += keyCode[i];                while (keyCode[++i] != 'K');
+    do fen += char(tolower(keyCode[i])); while (++i < keyCode.length());
+
+    // Add file padding and remaining empty ranks
+    fen += string(1, '0' + int(8 - keyCode.length())) + "/8/8/8/8/8/8/8 w - -";
+
+    // Build a Position out of the fen string and get its material key
+    return Position(fen, false, 0).get_material_key();
+  }
+
+  typedef EndgameBase<Value> EF;
+  typedef EndgameBase<ScaleFactor> SF;
+
+} // namespace
+
+
+/// Endgames member definitions
+
+template<> const Endgames::EFMap& Endgames::get<EF>() const { return maps.first; }
+template<> const Endgames::SFMap& Endgames::get<SF>() const { return maps.second; }
+
+Endgames::Endgames() {
+
+  add<Endgame<Value, KNNK>  >("KNNK");
+  add<Endgame<Value, KPK>   >("KPK");
+  add<Endgame<Value, KBNK>  >("KBNK");
+  add<Endgame<Value, KRKP>  >("KRKP");
+  add<Endgame<Value, KRKB>  >("KRKB");
+  add<Endgame<Value, KRKN>  >("KRKN");
+  add<Endgame<Value, KQKR>  >("KQKR");
+  add<Endgame<Value, KBBKN> >("KBBKN");
+
+  add<Endgame<ScaleFactor, KNPK>    >("KNPK");
+  add<Endgame<ScaleFactor, KRPKR>   >("KRPKR");
+  add<Endgame<ScaleFactor, KBPKB>   >("KBPKB");
+  add<Endgame<ScaleFactor, KBPPKB>  >("KBPPKB");
+  add<Endgame<ScaleFactor, KBPKN>   >("KBPKN");
+  add<Endgame<ScaleFactor, KRPPKRP> >("KRPPKRP");
+}
+
+Endgames::~Endgames() {
+
+  for (EFMap::const_iterator it = get<EF>().begin(); it != get<EF>().end(); ++it)
+      delete it->second;
+
+  for (SFMap::const_iterator it = get<SF>().begin(); it != get<SF>().end(); ++it)
+      delete it->second;
+}
+
+template<class T>
+void Endgames::add(const string& keyCode) {
+
+  typedef typename T::Base F;
+  typedef std::map<Key, F*> M;
+
+  const_cast<M&>(get<F>()).insert(std::pair<Key, F*>(mat_key(keyCode), new T(WHITE)));
+  const_cast<M&>(get<F>()).insert(std::pair<Key, F*>(mat_key(swap_colors(keyCode)), new T(BLACK)));
+}
+
+template<class T>
+T* Endgames::get(Key key) const {
+
+  typename std::map<Key, T*>::const_iterator it = get<T>().find(key);
+  return it != get<T>().end() ? it->second : NULL;
+}
+
+// Explicit template instantiations
+template EF* Endgames::get<EF>(Key key) const;
+template SF* Endgames::get<SF>(Key key) const;
+
+
+/// 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<Value, KXK>::apply(const Position& pos) const {
+
+  assert(pos.non_pawn_material(weakerSide) == VALUE_ZERO);
+  assert(pos.piece_count(weakerSide, PAWN) == VALUE_ZERO);
+
+  Square winnerKSq = pos.king_square(strongerSide);
+  Square loserKSq = pos.king_square(weakerSide);
+
+  Value result =   pos.non_pawn_material(strongerSide)
+                 + pos.piece_count(strongerSide, PAWN) * PawnValueEndgame
+                 + MateTable[loserKSq]
+                 + DistanceBonus[square_distance(winnerKSq, loserKSq)];
+
+  if (   pos.piece_count(strongerSide, QUEEN)
+      || pos.piece_count(strongerSide, ROOK)
+      || pos.piece_count(strongerSide, BISHOP) > 1)
+      // TODO: check for two equal-colored bishops!
+      result += VALUE_KNOWN_WIN;
+
+  return strongerSide == 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 of the right color.
+template<>
+Value Endgame<Value, KBNK>::apply(const Position& pos) const {
+
+  assert(pos.non_pawn_material(weakerSide) == VALUE_ZERO);
+  assert(pos.piece_count(weakerSide, PAWN) == VALUE_ZERO);
+  assert(pos.non_pawn_material(strongerSide) == KnightValueMidgame + BishopValueMidgame);
+  assert(pos.piece_count(strongerSide, BISHOP) == 1);
+  assert(pos.piece_count(strongerSide, KNIGHT) == 1);
+  assert(pos.piece_count(strongerSide, PAWN) == 0);
+
+  Square winnerKSq = pos.king_square(strongerSide);
+  Square loserKSq = pos.king_square(weakerSide);
+  Square bishopSquare = pos.piece_list(strongerSide, BISHOP, 0);
+
+  // kbnk_mate_table() tries to drive toward corners A1 or H8,
+  // if we have a bishop that cannot reach the above squares we
+  // mirror the kings so to drive enemy toward corners A8 or H1.
+  if (opposite_color_squares(bishopSquare, SQ_A1))
+  {
+      winnerKSq = flop_square(winnerKSq);
+      loserKSq = flop_square(loserKSq);
+  }
+
+  Value result =  VALUE_KNOWN_WIN
+                + DistanceBonus[square_distance(winnerKSq, loserKSq)]
+                + KBNKMateTable[loserKSq];
+
+  return strongerSide == pos.side_to_move() ? result : -result;
+}
+
+
+/// KP vs K. This endgame is evaluated with the help of a bitbase.
+template<>
+Value Endgame<Value, KPK>::apply(const Position& pos) const {
+
+  assert(pos.non_pawn_material(strongerSide) == VALUE_ZERO);
+  assert(pos.non_pawn_material(weakerSide) == VALUE_ZERO);
+  assert(pos.piece_count(strongerSide, PAWN) == 1);
+  assert(pos.piece_count(weakerSide, PAWN) == 0);
+
+  Square wksq, bksq, wpsq;
+  Color stm;
+
+  if (strongerSide == WHITE)
+  {
+      wksq = pos.king_square(WHITE);
+      bksq = pos.king_square(BLACK);
+      wpsq = pos.piece_list(WHITE, PAWN, 0);
+      stm = pos.side_to_move();
+  }
+  else
+  {
+      wksq = flip_square(pos.king_square(BLACK));
+      bksq = flip_square(pos.king_square(WHITE));
+      wpsq = flip_square(pos.piece_list(BLACK, PAWN, 0));
+      stm = opposite_color(pos.side_to_move());
+  }
+
+  if (square_file(wpsq) >= FILE_E)
+  {
+      wksq = flop_square(wksq);
+      bksq = flop_square(bksq);
+      wpsq = flop_square(wpsq);
+  }
+
+  if (!probe_kpk_bitbase(wksq, wpsq, bksq, stm))
+      return VALUE_DRAW;
+
+  Value result =  VALUE_KNOWN_WIN
+                + PawnValueEndgame
+                + Value(square_rank(wpsq));
+
+  return strongerSide == 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<Value, KRKP>::apply(const Position& pos) const {
+
+  assert(pos.non_pawn_material(strongerSide) == RookValueMidgame);
+  assert(pos.piece_count(strongerSide, PAWN) == 0);
+  assert(pos.non_pawn_material(weakerSide) == 0);
+  assert(pos.piece_count(weakerSide, PAWN) == 1);
+
+  Square wksq, wrsq, bksq, bpsq;
+  int tempo = (pos.side_to_move() == strongerSide);
+
+  wksq = pos.king_square(strongerSide);
+  wrsq = pos.piece_list(strongerSide, ROOK, 0);
+  bksq = pos.king_square(weakerSide);
+  bpsq = pos.piece_list(weakerSide, PAWN, 0);
+
+  if (strongerSide == BLACK)
+  {
+      wksq = flip_square(wksq);
+      wrsq = flip_square(wrsq);
+      bksq = flip_square(bksq);
+      bpsq = flip_square(bpsq);
+  }
+
+  Square queeningSq = make_square(square_file(bpsq), RANK_1);
+  Value result;
+
+  // If the stronger side's king is in front of the pawn, it's a win
+  if (wksq < bpsq && square_file(wksq) == square_file(bpsq))
+      result = RookValueEndgame - Value(square_distance(wksq, bpsq));
+
+  // If the weaker side's king is too far from the pawn and the rook,
+  // it's a win
+  else if (   square_distance(bksq, bpsq) - (tempo ^ 1) >= 3
+           && square_distance(bksq, wrsq) >= 3)
+      result = RookValueEndgame - Value(square_distance(wksq, bpsq));
+
+  // If the pawn is far advanced and supported by the defending king,
+  // the position is drawish
+  else if (   square_rank(bksq) <= RANK_3
+           && square_distance(bksq, bpsq) == 1
+           && square_rank(wksq) >= RANK_4
+           && square_distance(wksq, bpsq) - tempo > 2)
+      result = Value(80 - square_distance(wksq, bpsq) * 8);
+
+  else
+      result =  Value(200)
+              - Value(square_distance(wksq, bpsq + DELTA_S) * 8)
+              + Value(square_distance(bksq, bpsq + DELTA_S) * 8)
+              + Value(square_distance(bpsq, queeningSq) * 8);
+
+  return strongerSide == 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<Value, KRKB>::apply(const Position& pos) const {
+
+  assert(pos.non_pawn_material(strongerSide) == RookValueMidgame);
+  assert(pos.piece_count(strongerSide, PAWN) == 0);
+  assert(pos.non_pawn_material(weakerSide) == BishopValueMidgame);
+  assert(pos.piece_count(weakerSide, PAWN) == 0);
+  assert(pos.piece_count(weakerSide, BISHOP) == 1);
+
+  Value result = Value(MateTable[pos.king_square(weakerSide)]);
+  return strongerSide == 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<Value, KRKN>::apply(const Position& pos) const {
+
+  assert(pos.non_pawn_material(strongerSide) == RookValueMidgame);
+  assert(pos.piece_count(strongerSide, PAWN) == 0);
+  assert(pos.non_pawn_material(weakerSide) == KnightValueMidgame);
+  assert(pos.piece_count(weakerSide, PAWN) == 0);
+  assert(pos.piece_count(weakerSide, KNIGHT) == 1);
+
+  Square defendingKSq = pos.king_square(weakerSide);
+  Square nSq = pos.piece_list(weakerSide, KNIGHT, 0);
+
+  int d = square_distance(defendingKSq, nSq);
+  Value result =   Value(10)
+                 + MateTable[defendingKSq]
+                 + KRKNKingKnightDistancePenalty[d];
+
+  return strongerSide == 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 be
+/// able to win KQ vs KR.
+template<>
+Value Endgame<Value, KQKR>::apply(const Position& pos) const {
+
+  assert(pos.non_pawn_material(strongerSide) == QueenValueMidgame);
+  assert(pos.piece_count(strongerSide, PAWN) == 0);
+  assert(pos.non_pawn_material(weakerSide) == RookValueMidgame);
+  assert(pos.piece_count(weakerSide, PAWN) == 0);
+
+  Square winnerKSq = pos.king_square(strongerSide);
+  Square loserKSq = pos.king_square(weakerSide);
+
+  Value result =  QueenValueEndgame
+                - RookValueEndgame
+                + MateTable[loserKSq]
+                + DistanceBonus[square_distance(winnerKSq, loserKSq)];
+
+  return strongerSide == pos.side_to_move() ? result : -result;
+}
+
+template<>
+Value Endgame<Value, KBBKN>::apply(const Position& pos) const {
+
+  assert(pos.piece_count(strongerSide, BISHOP) == 2);
+  assert(pos.non_pawn_material(strongerSide) == 2*BishopValueMidgame);
+  assert(pos.piece_count(weakerSide, KNIGHT) == 1);
+  assert(pos.non_pawn_material(weakerSide) == KnightValueMidgame);
+  assert(pos.pieces(PAWN) == EmptyBoardBB);
+
+  Value result = BishopValueEndgame;
+  Square wksq = pos.king_square(strongerSide);
+  Square bksq = pos.king_square(weakerSide);
+  Square nsq = pos.piece_list(weakerSide, KNIGHT, 0);
+
+  // Bonus for attacking king close to defending king
+  result += Value(DistanceBonus[square_distance(wksq, bksq)]);
+
+  // Bonus for driving the defending king and knight apart
+  result += Value(square_distance(bksq, nsq) * 32);
+
+  // Bonus for restricting the knight's mobility
+  result += Value((8 - count_1s<CNT32_MAX15>(pos.attacks_from<KNIGHT>(nsq))) * 8);
+
+  return strongerSide == pos.side_to_move() ? result : -result;
+}
+
+
+/// K and two minors vs K and one or two minors or K and two knights against
+/// king alone are always draw.
+template<>
+Value Endgame<Value, KmmKm>::apply(const Position&) const {
+  return VALUE_DRAW;
+}
+
+template<>
+Value Endgame<Value, KNNK>::apply(const Position&) const {
+  return VALUE_DRAW;
+}
+
+/// KBPKScalingFunction scales endgames where the stronger side has king,
+/// bishop and one or more pawns. It checks for draws with rook pawns and a
+/// bishop of the wrong color. If such a draw is detected, SCALE_FACTOR_ZERO is
+/// returned. If not, the return value is SCALE_FACTOR_NONE, i.e. no scaling
+/// will be used.
+template<>
+ScaleFactor Endgame<ScaleFactor, KBPsK>::apply(const Position& pos) const {
+
+  assert(pos.non_pawn_material(strongerSide) == BishopValueMidgame);
+  assert(pos.piece_count(strongerSide, BISHOP) == 1);
+  assert(pos.piece_count(strongerSide, PAWN) >= 1);
+
+  // No assertions about the material of weakerSide, because we want draws to
+  // be detected even when the weaker side has some pawns.
+
+  Bitboard pawns = pos.pieces(PAWN, strongerSide);
+  File pawnFile = square_file(pos.piece_list(strongerSide, PAWN, 0));
+
+  // All pawns are on a single rook file ?
+  if (   (pawnFile == FILE_A || pawnFile == FILE_H)
+      && (pawns & ~file_bb(pawnFile)) == EmptyBoardBB)
+  {
+      Square bishopSq = pos.piece_list(strongerSide, BISHOP, 0);
+      Square queeningSq = relative_square(strongerSide, make_square(pawnFile, RANK_8));
+      Square kingSq = pos.king_square(weakerSide);
+
+      if (   opposite_color_squares(queeningSq, bishopSq)
+          && abs(square_file(kingSq) - pawnFile) <= 1)
+      {
+          // The bishop has the wrong color, and the defending king is on the
+          // file of the pawn(s) or the neighboring file. Find the rank of the
+          // frontmost pawn.
+          Rank rank;
+          if (strongerSide == WHITE)
+          {
+              for (rank = RANK_7; (rank_bb(rank) & pawns) == EmptyBoardBB; rank--) {}
+              assert(rank >= RANK_2 && rank <= RANK_7);
+          }
+          else
+          {
+              for (rank = RANK_2; (rank_bb(rank) & pawns) == EmptyBoardBB; rank++) {}
+              rank = Rank(rank ^ 7);  // HACK to get the relative rank
+              assert(rank >= RANK_2 && rank <= RANK_7);
+          }
+          // If the defending king has distance 1 to the promotion square or
+          // is placed somewhere in front of the pawn, it's a draw.
+          if (   square_distance(kingSq, queeningSq) <= 1
+              || relative_rank(strongerSide, kingSq) >= rank)
+              return SCALE_FACTOR_ZERO;
+      }
+  }
+  return SCALE_FACTOR_NONE;
+}
+
+
+/// KQKRPScalingFunction scales endgames where the stronger side has only
+/// king and queen, while the weaker side has at least a rook and a pawn.
+/// It tests for fortress draws with a rook on the third rank defended by
+/// a pawn.
+template<>
+ScaleFactor Endgame<ScaleFactor, KQKRPs>::apply(const Position& pos) const {
+
+  assert(pos.non_pawn_material(strongerSide) == QueenValueMidgame);
+  assert(pos.piece_count(strongerSide, QUEEN) == 1);
+  assert(pos.piece_count(strongerSide, PAWN) == 0);
+  assert(pos.piece_count(weakerSide, ROOK) == 1);
+  assert(pos.piece_count(weakerSide, PAWN) >= 1);
+
+  Square kingSq = pos.king_square(weakerSide);
+  if (   relative_rank(weakerSide, kingSq) <= RANK_2
+      && relative_rank(weakerSide, pos.king_square(strongerSide)) >= RANK_4
+      && (pos.pieces(ROOK, weakerSide) & rank_bb(relative_rank(weakerSide, RANK_3)))
+      && (pos.pieces(PAWN, weakerSide) & rank_bb(relative_rank(weakerSide, RANK_2)))
+      && (pos.attacks_from<KING>(kingSq) & pos.pieces(PAWN, weakerSide)))
+  {
+      Square rsq = pos.piece_list(weakerSide, ROOK, 0);
+      if (pos.attacks_from<PAWN>(rsq, strongerSide) & pos.pieces(PAWN, weakerSide))
+          return SCALE_FACTOR_ZERO;
+  }
+  return SCALE_FACTOR_NONE;
+}
+
+
+/// KRPKRScalingFunction scales KRP vs KR endgames. 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 not very pretty.
+template<>
+ScaleFactor Endgame<ScaleFactor, KRPKR>::apply(const Position& pos) const {
+
+  assert(pos.non_pawn_material(strongerSide) == RookValueMidgame);
+  assert(pos.piece_count(strongerSide, PAWN) == 1);
+  assert(pos.non_pawn_material(weakerSide) == RookValueMidgame);
+  assert(pos.piece_count(weakerSide, PAWN) == 0);
+
+  Square wksq = pos.king_square(strongerSide);
+  Square wrsq = pos.piece_list(strongerSide, ROOK, 0);
+  Square wpsq = pos.piece_list(strongerSide, PAWN, 0);
+  Square bksq = pos.king_square(weakerSide);
+  Square brsq = pos.piece_list(weakerSide, ROOK, 0);
+
+  // Orient the board in such a way that the stronger side is white, and the
+  // pawn is on the left half of the board.
+  if (strongerSide == BLACK)
+  {
+      wksq = flip_square(wksq);
+      wrsq = flip_square(wrsq);
+      wpsq = flip_square(wpsq);
+      bksq = flip_square(bksq);
+      brsq = flip_square(brsq);
+  }
+  if (square_file(wpsq) > FILE_D)
+  {
+      wksq = flop_square(wksq);
+      wrsq = flop_square(wrsq);
+      wpsq = flop_square(wpsq);
+      bksq = flop_square(bksq);
+      brsq = flop_square(brsq);
+  }
+
+  File f = square_file(wpsq);
+  Rank r = square_rank(wpsq);
+  Square queeningSq = make_square(f, RANK_8);
+  int tempo = (pos.side_to_move() == strongerSide);
+
+  // If the pawn is not too far advanced and the defending king defends the
+  // queening square, use the third-rank defence.
+  if (   r <= RANK_5
+      && square_distance(bksq, queeningSq) <= 1
+      && wksq <= SQ_H5
+      && (square_rank(brsq) == RANK_6 || (r <= RANK_3 && square_rank(wrsq) != RANK_6)))
+      return SCALE_FACTOR_ZERO;
+
+  // 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 (   r == RANK_6
+      && square_distance(bksq, queeningSq) <= 1
+      && square_rank(wksq) + tempo <= RANK_6
+      && (square_rank(brsq) == RANK_1 || (!tempo && abs(square_file(brsq) - f) >= 3)))
+      return SCALE_FACTOR_ZERO;
+
+  if (   r >= RANK_6
+      && bksq == queeningSq
+      && square_rank(brsq) == RANK_1
+      && (!tempo || square_distance(wksq, wpsq) >= 2))
+      return SCALE_FACTOR_ZERO;
+
+  // 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 (   wpsq == SQ_A7
+      && wrsq == SQ_A8
+      && (bksq == SQ_H7 || bksq == SQ_G7)
+      && square_file(brsq) == FILE_A
+      && (square_rank(brsq) <= RANK_3 || square_file(wksq) >= FILE_D || square_rank(wksq) <= RANK_5))
+      return SCALE_FACTOR_ZERO;
+
+  // If the defending king blocks the pawn and the attacking king is too far
+  // away, it's a draw.
+  if (   r <= RANK_5
+      && bksq == wpsq + DELTA_N
+      && square_distance(wksq, wpsq) - tempo >= 2
+      && square_distance(wksq, brsq) - tempo >= 2)
+      return SCALE_FACTOR_ZERO;
+
+  // 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 (   r == RANK_7
+      && f != FILE_A
+      && square_file(wrsq) == f
+      && wrsq != queeningSq
+      && (square_distance(wksq, queeningSq) < square_distance(bksq, queeningSq) - 2 + tempo)
+      && (square_distance(wksq, queeningSq) < square_distance(bksq, wrsq) + tempo))
+      return ScaleFactor(SCALE_FACTOR_MAX - 2 * square_distance(wksq, queeningSq));
+
+  // Similar to the above, but with the pawn further back
+  if (   f != FILE_A
+      && square_file(wrsq) == f
+      && wrsq < wpsq
+      && (square_distance(wksq, queeningSq) < square_distance(bksq, queeningSq) - 2 + tempo)
+      && (square_distance(wksq, wpsq + DELTA_N) < square_distance(bksq, wpsq + DELTA_N) - 2 + tempo)
+      && (  square_distance(bksq, wrsq) + tempo >= 3
+          || (    square_distance(wksq, queeningSq) < square_distance(bksq, wrsq) + tempo
+              && (square_distance(wksq, wpsq + DELTA_N) < square_distance(bksq, wrsq) + tempo))))
+      return ScaleFactor(  SCALE_FACTOR_MAX
+                         - 8 * square_distance(wpsq, queeningSq)
+                         - 2 * square_distance(wksq, queeningSq));
+
+  // If the pawn is not far advanced, and the defending king is somewhere in
+  // the pawn's path, it's probably a draw.
+  if (r <= RANK_4 && bksq > wpsq)
+  {
+      if (square_file(bksq) == square_file(wpsq))
+          return ScaleFactor(10);
+      if (   abs(square_file(bksq) - square_file(wpsq)) == 1
+          && square_distance(wksq, bksq) > 2)
+          return ScaleFactor(24 - 2 * square_distance(wksq, bksq));
+  }
+  return SCALE_FACTOR_NONE;
+}
+
+
+/// KRPPKRPScalingFunction scales KRPP vs KRP endgames. There is only a
+/// single pattern: If the stronger side has no pawns and the defending king
+/// is actively placed, the position is drawish.
+template<>
+ScaleFactor Endgame<ScaleFactor, KRPPKRP>::apply(const Position& pos) const {
+
+  assert(pos.non_pawn_material(strongerSide) == RookValueMidgame);
+  assert(pos.piece_count(strongerSide, PAWN) == 2);
+  assert(pos.non_pawn_material(weakerSide) == RookValueMidgame);
+  assert(pos.piece_count(weakerSide, PAWN) == 1);
+
+  Square wpsq1 = pos.piece_list(strongerSide, PAWN, 0);
+  Square wpsq2 = pos.piece_list(strongerSide, PAWN, 1);
+  Square bksq = pos.king_square(weakerSide);
+
+  // Does the stronger side have a passed pawn?
+  if (   pos.pawn_is_passed(strongerSide, wpsq1)
+      || pos.pawn_is_passed(strongerSide, wpsq2))
+      return SCALE_FACTOR_NONE;
+
+  Rank r = Max(relative_rank(strongerSide, wpsq1), relative_rank(strongerSide, wpsq2));
+
+  if (   file_distance(bksq, wpsq1) <= 1
+      && file_distance(bksq, wpsq2) <= 1
+      && relative_rank(strongerSide, bksq) > r)
+  {
+      switch (r) {
+      case RANK_2: return ScaleFactor(10);
+      case RANK_3: return ScaleFactor(10);
+      case RANK_4: return ScaleFactor(15);
+      case RANK_5: return ScaleFactor(20);
+      case RANK_6: return ScaleFactor(40);
+      default: assert(false);
+      }
+  }
+  return SCALE_FACTOR_NONE;
+}
+
+
+/// KPsKScalingFunction scales endgames with king and two or more pawns
+/// against king. 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<ScaleFactor, KPsK>::apply(const Position& pos) const {
+
+  assert(pos.non_pawn_material(strongerSide) == VALUE_ZERO);
+  assert(pos.piece_count(strongerSide, PAWN) >= 2);
+  assert(pos.non_pawn_material(weakerSide) == VALUE_ZERO);
+  assert(pos.piece_count(weakerSide, PAWN) == 0);
+
+  Square ksq = pos.king_square(weakerSide);
+  Bitboard pawns = pos.pieces(PAWN, strongerSide);
+
+  // Are all pawns on the 'a' file?
+  if ((pawns & ~FileABB) == EmptyBoardBB)
+  {
+      // Does the defending king block the pawns?
+      if (   square_distance(ksq, relative_square(strongerSide, SQ_A8)) <= 1
+          || (   square_file(ksq) == FILE_A
+              && (in_front_bb(strongerSide, ksq) & pawns) == EmptyBoardBB))
+          return SCALE_FACTOR_ZERO;
+  }
+  // Are all pawns on the 'h' file?
+  else if ((pawns & ~FileHBB) == EmptyBoardBB)
+  {
+    // Does the defending king block the pawns?
+    if (   square_distance(ksq, relative_square(strongerSide, SQ_H8)) <= 1
+        || (   square_file(ksq) == FILE_H
+            && (in_front_bb(strongerSide, ksq) & pawns) == EmptyBoardBB))
+        return SCALE_FACTOR_ZERO;
+  }
+  return SCALE_FACTOR_NONE;
+}
+
+
+/// KBPKBScalingFunction scales KBP vs KB endgames. 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<ScaleFactor, KBPKB>::apply(const Position& pos) const {
+
+  assert(pos.non_pawn_material(strongerSide) == BishopValueMidgame);
+  assert(pos.piece_count(strongerSide, BISHOP) == 1);
+  assert(pos.piece_count(strongerSide, PAWN) == 1);
+  assert(pos.non_pawn_material(weakerSide) == BishopValueMidgame);
+  assert(pos.piece_count(weakerSide, BISHOP) == 1);
+  assert(pos.piece_count(weakerSide, PAWN) == 0);
+
+  Square pawnSq = pos.piece_list(strongerSide, PAWN, 0);
+  Square strongerBishopSq = pos.piece_list(strongerSide, BISHOP, 0);
+  Square weakerBishopSq = pos.piece_list(weakerSide, BISHOP, 0);
+  Square weakerKingSq = pos.king_square(weakerSide);
+
+  // Case 1: Defending king blocks the pawn, and cannot be driven away
+  if (   square_file(weakerKingSq) == square_file(pawnSq)
+      && relative_rank(strongerSide, pawnSq) < relative_rank(strongerSide, weakerKingSq)
+      && (   opposite_color_squares(weakerKingSq, strongerBishopSq)
+          || relative_rank(strongerSide, weakerKingSq) <= RANK_6))
+      return SCALE_FACTOR_ZERO;
+
+  // Case 2: Opposite colored bishops
+  if (opposite_color_squares(strongerBishopSq, weakerBishopSq))
+  {
+      // We assume that the position is drawn in the following three situations:
+      //
+      //   a. The pawn is on rank 5 or further back.
+      //   b. The defending king is somewhere in the pawn's path.
+      //   c. The defending bishop attacks some square along the pawn's path,
+      //      and is at least three squares away from the pawn.
+      //
+      // These rules are probably not perfect, but in practice they work
+      // reasonably well.
+
+      if (relative_rank(strongerSide, pawnSq) <= RANK_5)
+          return SCALE_FACTOR_ZERO;
+      else
+      {
+          Bitboard path = squares_in_front_of(strongerSide, pawnSq);
+
+          if (path & pos.pieces(KING, weakerSide))
+              return SCALE_FACTOR_ZERO;
+
+          if (  (pos.attacks_from<BISHOP>(weakerBishopSq) & path)
+              && square_distance(weakerBishopSq, pawnSq) >= 3)
+              return SCALE_FACTOR_ZERO;
+      }
+  }
+  return SCALE_FACTOR_NONE;
+}
+
+
+/// KBPPKBScalingFunction scales KBPP vs KB endgames. It detects a few basic
+/// draws with opposite-colored bishops.
+template<>
+ScaleFactor Endgame<ScaleFactor, KBPPKB>::apply(const Position& pos) const {
+
+  assert(pos.non_pawn_material(strongerSide) == BishopValueMidgame);
+  assert(pos.piece_count(strongerSide, BISHOP) == 1);
+  assert(pos.piece_count(strongerSide, PAWN) == 2);
+  assert(pos.non_pawn_material(weakerSide) == BishopValueMidgame);
+  assert(pos.piece_count(weakerSide, BISHOP) == 1);
+  assert(pos.piece_count(weakerSide, PAWN) == 0);
+
+  Square wbsq = pos.piece_list(strongerSide, BISHOP, 0);
+  Square bbsq = pos.piece_list(weakerSide, BISHOP, 0);
+
+  if (!opposite_color_squares(wbsq, bbsq))
+      return SCALE_FACTOR_NONE;
+
+  Square ksq = pos.king_square(weakerSide);
+  Square psq1 = pos.piece_list(strongerSide, PAWN, 0);
+  Square psq2 = pos.piece_list(strongerSide, PAWN, 1);
+  Rank r1 = square_rank(psq1);
+  Rank r2 = square_rank(psq2);
+  Square blockSq1, blockSq2;
+
+  if (relative_rank(strongerSide, psq1) > relative_rank(strongerSide, psq2))
+  {
+      blockSq1 = psq1 + pawn_push(strongerSide);
+      blockSq2 = make_square(square_file(psq2), square_rank(psq1));
+  }
+  else
+  {
+      blockSq1 = psq2 + pawn_push(strongerSide);
+      blockSq2 = make_square(square_file(psq1), square_rank(psq2));
+  }
+
+  switch (file_distance(psq1, psq2))
+  {
+  case 0:
+    // Both pawns are on the same file. Easy draw if defender firmly controls
+    // some square in the frontmost pawn's path.
+    if (   square_file(ksq) == square_file(blockSq1)
+        && relative_rank(strongerSide, ksq) >= relative_rank(strongerSide, blockSq1)
+        && opposite_color_squares(ksq, wbsq))
+        return SCALE_FACTOR_ZERO;
+    else
+        return SCALE_FACTOR_NONE;
+
+  case 1:
+    // Pawns on neighboring files. Draw if 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 (   ksq == blockSq1
+        && opposite_color_squares(ksq, wbsq)
+        && (   bbsq == blockSq2
+            || (pos.attacks_from<BISHOP>(blockSq2) & pos.pieces(BISHOP, weakerSide))
+            || abs(r1 - r2) >= 2))
+        return SCALE_FACTOR_ZERO;
+
+    else if (   ksq == blockSq2
+             && opposite_color_squares(ksq, wbsq)
+             && (   bbsq == blockSq1
+                 || (pos.attacks_from<BISHOP>(blockSq1) & pos.pieces(BISHOP, weakerSide))))
+        return SCALE_FACTOR_ZERO;
+    else
+        return SCALE_FACTOR_NONE;
+
+  default:
+    // The pawns are not on the same file or adjacent files. No scaling.
+    return SCALE_FACTOR_NONE;
+  }
+}
+
+
+/// KBPKNScalingFunction scales KBP vs KN endgames. 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<ScaleFactor, KBPKN>::apply(const Position& pos) const {
+
+  assert(pos.non_pawn_material(strongerSide) == BishopValueMidgame);
+  assert(pos.piece_count(strongerSide, BISHOP) == 1);
+  assert(pos.piece_count(strongerSide, PAWN) == 1);
+  assert(pos.non_pawn_material(weakerSide) == KnightValueMidgame);
+  assert(pos.piece_count(weakerSide, KNIGHT) == 1);
+  assert(pos.piece_count(weakerSide, PAWN) == 0);
+
+  Square pawnSq = pos.piece_list(strongerSide, PAWN, 0);
+  Square strongerBishopSq = pos.piece_list(strongerSide, BISHOP, 0);
+  Square weakerKingSq = pos.king_square(weakerSide);
+
+  if (   square_file(weakerKingSq) == square_file(pawnSq)
+      && relative_rank(strongerSide, pawnSq) < relative_rank(strongerSide, weakerKingSq)
+      && (   opposite_color_squares(weakerKingSq, strongerBishopSq)
+          || relative_rank(strongerSide, weakerKingSq) <= RANK_6))
+      return SCALE_FACTOR_ZERO;
+
+  return SCALE_FACTOR_NONE;
+}
+
+
+/// KNPKScalingFunction scales KNP vs K endgames. There is a single rule:
+/// If the pawn is a rook pawn on the 7th rank and the defending king prevents
+/// the pawn from advancing, the position is drawn.
+template<>
+ScaleFactor Endgame<ScaleFactor, KNPK>::apply(const Position& pos) const {
+
+  assert(pos.non_pawn_material(strongerSide) == KnightValueMidgame);
+  assert(pos.piece_count(strongerSide, KNIGHT) == 1);
+  assert(pos.piece_count(strongerSide, PAWN) == 1);
+  assert(pos.non_pawn_material(weakerSide) == VALUE_ZERO);
+  assert(pos.piece_count(weakerSide, PAWN) == 0);
+
+  Square pawnSq = pos.piece_list(strongerSide, PAWN, 0);
+  Square weakerKingSq = pos.king_square(weakerSide);
+
+  if (   pawnSq == relative_square(strongerSide, SQ_A7)
+      && square_distance(weakerKingSq, relative_square(strongerSide, SQ_A8)) <= 1)
+      return SCALE_FACTOR_ZERO;
+
+  if (   pawnSq == relative_square(strongerSide, SQ_H7)
+      && square_distance(weakerKingSq, relative_square(strongerSide, SQ_H8)) <= 1)
+      return SCALE_FACTOR_ZERO;
+
+  return SCALE_FACTOR_NONE;
+}
+
+
+/// KPKPScalingFunction scales KP vs KP endgames. 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, she 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<ScaleFactor, KPKP>::apply(const Position& pos) const {
+
+  assert(pos.non_pawn_material(strongerSide) == VALUE_ZERO);
+  assert(pos.non_pawn_material(weakerSide) == VALUE_ZERO);
+  assert(pos.piece_count(WHITE, PAWN) == 1);
+  assert(pos.piece_count(BLACK, PAWN) == 1);
+
+  Square wksq, bksq, wpsq;
+  Color stm;
+
+  if (strongerSide == WHITE)
+  {
+      wksq = pos.king_square(WHITE);
+      bksq = pos.king_square(BLACK);
+      wpsq = pos.piece_list(WHITE, PAWN, 0);
+      stm = pos.side_to_move();
+  }
+  else
+  {
+      wksq = flip_square(pos.king_square(BLACK));
+      bksq = flip_square(pos.king_square(WHITE));
+      wpsq = flip_square(pos.piece_list(BLACK, PAWN, 0));
+      stm = opposite_color(pos.side_to_move());
+  }
+
+  if (square_file(wpsq) >= FILE_E)
+  {
+      wksq = flop_square(wksq);
+      bksq = flop_square(bksq);
+      wpsq = flop_square(wpsq);
+  }
+
+  // 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 (   square_rank(wpsq) >= RANK_5
+      && square_file(wpsq) != 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 probe_kpk_bitbase(wksq, wpsq, bksq, stm) ? SCALE_FACTOR_NONE : SCALE_FACTOR_ZERO;
+}