/*

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

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 <algorithm>

#include <cassert>

#include "bitboard.h"

#include "bitcount.h"

#include "endgame.h"

#include "movegen.h"

using std::string;

namespace {

// Table used to drive the king towards the edge of the board

// in KX vs K and KQ vs KR endgames.

const int PushToEdges[SQUARE_NB] = {

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 king towards a corner square of the

// right color in KBN vs K endgames.

const int PushToCorners[SQUARE_NB] = {

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

};

// Tables used to drive a piece towards or away from another piece

const int PushClose[8] = { 0, 0, 100, 80, 60, 40, 20, 10 };

const int PushAway [8] = { 0, 5, 20, 40, 60, 80, 90, 100 };

// Pawn Rank based scaling factors used in KRPPKRP endgame

const int KRPPKRPScaleFactors[RANK_NB] = { 0, 9, 10, 14, 21, 44, 0, 0 };

#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 = Square(sq ^ 7); // Mirror SQ_H1 -> SQ_A1

if (strongSide == BLACK)

sq = ~sq;

return sq;

}

// Get the material key of Position out of the given endgame key code

// like "KBPKN". The trick here is to first forge an ad-hoc FEN string

// and then let a Position object do the work for us.

Key key(const string& code, Color c) {

assert(code.length() > 0 && code.length() < 8);

assert(code[0] == 'K');

string sides[] = { code.substr(code.find('K', 1)), // Weak

code.substr(0, code.find('K', 1)) }; // Strong

std::transform(sides[c].begin(), sides[c].end(), sides[c].begin(), tolower);

string fen = sides[0] + char(8 - sides[0].length() + '0') + "/8/8/8/8/8/8/"

+ sides[1] + char(8 - sides[1].length() + '0') + " w - - 0 10";

return Position(fen, false, nullptr).material_key();

}

} // namespace

/// Endgames members definitions

Endgames::Endgames() {

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<KNPK>("KNPK");

add<KNPKB>("KNPKB");

add<KRPKR>("KRPKR");

add<KRPKB>("KRPKB");

add<KBPKB>("KBPKB");

add<KBPKN>("KBPKN");

add<KBPPKB>("KBPPKB");

add<KRPPKRP>("KRPPKRP");

}

template<EndgameType E, typename T>

void Endgames::add(const string& code) {

map<T>()[key(code, WHITE)] = std::unique_ptr<EndgameBase<T>>(new Endgame<E>(WHITE));

map<T>()[key(code, BLACK)] = std::unique_ptr<EndgameBase<T>>(new Endgame<E>(BLACK));

}

/// 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 winnerKSq = pos.square<KING>(strongSide);

Square loserKSq = pos.square<KING>(weakSide);

Value result = pos.non_pawn_material(strongSide)

+ pos.count<PAWN>(strongSide) * PawnValueEg

+ PushToEdges[loserKSq]

+ PushClose[distance(winnerKSq, loserKSq)];

if ( pos.count<QUEEN>(strongSide)

|| pos.count<ROOK>(strongSide)

||(pos.count<BISHOP>(strongSide) && pos.count<KNIGHT>(strongSide))

||(pos.count<BISHOP>(strongSide) > 1 && opposite_colors(pos.squares<BISHOP>(strongSide)[0],

pos.squares<BISHOP>(strongSide)[1])))

result += VALUE_KNOWN_WIN;

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 of the right color.

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 winnerKSq = pos.square<KING>(strongSide);

Square loserKSq = pos.square<KING>(weakSide);

Square bishopSq = pos.square<BISHOP>(strongSide);

// kbnk_mate_table() tries to drive toward corners A1 or H8. If we have a

// bishop that cannot reach the above squares, we flip the kings in order

// to drive the enemy toward corners A8 or H1.

if (opposite_colors(bishopSq, SQ_A1))

{

winnerKSq = ~winnerKSq;

loserKSq = ~loserKSq;

}

Value result = VALUE_KNOWN_WIN

+ PushClose[distance(winnerKSq, loserKSq)]

+ PushToCorners[loserKSq];

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 wksq = normalize(pos, strongSide, pos.square<KING>(strongSide));

Square bksq = normalize(pos, strongSide, pos.square<KING>(weakSide));

Square psq = normalize(pos, strongSide, pos.square<PAWN>(strongSide));

Color us = strongSide == pos.side_to_move() ? WHITE : BLACK;

if (!Bitbases::probe(wksq, psq, bksq, us))

return VALUE_DRAW;

Value result = VALUE_KNOWN_WIN + PawnValueEg + Value(rank_of(psq));

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 wksq = relative_square(strongSide, pos.square<KING>(strongSide));

Square bksq = relative_square(strongSide, pos.square<KING>(weakSide));

Square rsq = relative_square(strongSide, pos.square<ROOK>(strongSide));

Square psq = relative_square(strongSide, pos.square<PAWN>(weakSide));

Square queeningSq = make_square(file_of(psq), RANK_1);

Value result;

// If the stronger side's king is in front of the pawn, it's a win

if (wksq < psq && file_of(wksq) == file_of(psq))

result = RookValueEg - distance(wksq, psq);

// If the weaker side's king is too far from the pawn and the rook,

// it's a win.

else if ( distance(bksq, psq) >= 3 + (pos.side_to_move() == weakSide)

&& distance(bksq, rsq) >= 3)

result = RookValueEg - distance(wksq, psq);

// If the pawn is far advanced and supported by the defending king,

// the position is drawish

else if ( rank_of(bksq) <= RANK_3

&& distance(bksq, psq) == 1

&& rank_of(wksq) >= RANK_4

&& distance(wksq, psq) > 2 + (pos.side_to_move() == strongSide))

result = Value(80) - 8 * distance(wksq, psq);

else

result = Value(200) - 8 * ( distance(wksq, psq + DELTA_S)

- distance(bksq, psq + DELTA_S)

- distance(psq, queeningSq));

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(PushToEdges[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 bksq = pos.square<KING>(weakSide);

Square bnsq = pos.square<KNIGHT>(weakSide);

Value result = Value(PushToEdges[bksq] + PushAway[distance(bksq, bnsq)]);

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 winnerKSq = pos.square<KING>(strongSide);

Square loserKSq = pos.square<KING>(weakSide);

Square pawnSq = pos.square<PAWN>(weakSide);

Value result = Value(PushClose[distance(winnerKSq, loserKSq)]);

if ( relative_rank(weakSide, pawnSq) != RANK_7

|| distance(loserKSq, pawnSq) != 1

|| !((FileABB | FileCBB | FileFBB | FileHBB) & pawnSq))

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 winnerKSq = pos.square<KING>(strongSide);

Square loserKSq = pos.square<KING>(weakSide);

Value result = QueenValueEg

- RookValueEg

+ PushToEdges[loserKSq]

+ PushClose[distance(winnerKSq, loserKSq)];

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 pawns = pos.pieces(strongSide, PAWN);

File pawnsFile = file_of(lsb(pawns));

// All pawns are on a single rook file?

if ( (pawnsFile == FILE_A || pawnsFile == FILE_H)

&& !(pawns & ~file_bb(pawnsFile)))

{

Square bishopSq = pos.square<BISHOP>(strongSide);

Square queeningSq = relative_square(strongSide, make_square(pawnsFile, RANK_8));

Square kingSq = pos.square<KING>(weakSide);

if ( opposite_colors(queeningSq, bishopSq)

&& distance(queeningSq, kingSq) <= 1)

return SCALE_FACTOR_DRAW;

}

// If all the pawns are on the same B or G file, then it's potentially a draw

if ( (pawnsFile == FILE_B || pawnsFile == FILE_G)

&& !(pos.pieces(PAWN) & ~file_bb(pawnsFile))

&& pos.non_pawn_material(weakSide) == 0

&& pos.count<PAWN>(weakSide) >= 1)

{

// Get weakSide pawn that is closest to the home rank

Square weakPawnSq = backmost_sq(weakSide, pos.pieces(weakSide, PAWN));

Square strongKingSq = pos.square<KING>(strongSide);

Square weakKingSq = pos.square<KING>(weakSide);

Square bishopSq = pos.square<BISHOP>(strongSide);

// 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, weakPawnSq) == RANK_7

&& (pos.pieces(strongSide, PAWN) & (weakPawnSq + pawn_push(weakSide)))

&& (opposite_colors(bishopSq, weakPawnSq) || pos.count<PAWN>(strongSide) == 1))

{

int strongKingDist = distance(weakPawnSq, strongKingSq);

int weakKingDist = distance(weakPawnSq, weakKingSq);

// 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, weakKingSq) >= 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 kingSq = pos.square<KING>(weakSide);

Square rsq = pos.square<ROOK>(weakSide);

if ( relative_rank(weakSide, kingSq) <= RANK_2

&& relative_rank(weakSide, pos.square<KING>(strongSide)) >= RANK_4

&& relative_rank(weakSide, rsq) == RANK_3

&& ( pos.pieces(weakSide, PAWN)

& pos.attacks_from<KING>(kingSq)

& pos.attacks_from<PAWN>(rsq, strongSide)))

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 wksq = normalize(pos, strongSide, pos.square<KING>(strongSide));

Square bksq = normalize(pos, strongSide, pos.square<KING>(weakSide));

Square wrsq = normalize(pos, strongSide, pos.square<ROOK>(strongSide));

Square wpsq = normalize(pos, strongSide, pos.square<PAWN>(strongSide));

Square brsq = normalize(pos, strongSide, pos.square<ROOK>(weakSide));

File f = file_of(wpsq);

Rank r = rank_of(wpsq);

Square queeningSq = make_square(f, 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 ( r <= RANK_5

&& distance(bksq, queeningSq) <= 1

&& wksq <= SQ_H5

&& (rank_of(brsq) == RANK_6 || (r <= RANK_3 && rank_of(wrsq) != 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 ( r == RANK_6

&& distance(bksq, queeningSq) <= 1

&& rank_of(wksq) + tempo <= RANK_6

&& (rank_of(brsq) == RANK_1 || (!tempo && distance<File>(brsq, wpsq) >= 3)))

return SCALE_FACTOR_DRAW;

if ( r >= RANK_6

&& bksq == queeningSq

&& rank_of(brsq) == RANK_1

&& (!tempo || distance(wksq, wpsq) >= 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 ( wpsq == SQ_A7

&& wrsq == SQ_A8

&& (bksq == SQ_H7 || bksq == SQ_G7)

&& file_of(brsq) == FILE_A

&& (rank_of(brsq) <= RANK_3 || file_of(wksq) >= FILE_D || rank_of(wksq) <= 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 ( r <= RANK_5

&& bksq == wpsq + DELTA_N

&& distance(wksq, wpsq) - tempo >= 2

&& distance(wksq, brsq) - 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 ( r == RANK_7

&& f != FILE_A

&& file_of(wrsq) == f

&& wrsq != queeningSq

&& (distance(wksq, queeningSq) < distance(bksq, queeningSq) - 2 + tempo)

&& (distance(wksq, queeningSq) < distance(bksq, wrsq) + tempo))

return ScaleFactor(SCALE_FACTOR_MAX - 2 * distance(wksq, queeningSq));

// Similar to the above, but with the pawn further back

if ( f != FILE_A

&& file_of(wrsq) == f

&& wrsq < wpsq

&& (distance(wksq, queeningSq) < distance(bksq, queeningSq) - 2 + tempo)

&& (distance(wksq, wpsq + DELTA_N) < distance(bksq, wpsq + DELTA_N) - 2 + tempo)

&& ( distance(bksq, wrsq) + tempo >= 3

|| ( distance(wksq, queeningSq) < distance(bksq, wrsq) + tempo

&& (distance(wksq, wpsq + DELTA_N) < distance(bksq, wrsq) + tempo))))

return ScaleFactor( SCALE_FACTOR_MAX

- 8 * distance(wpsq, queeningSq)

- 2 * 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 (file_of(bksq) == file_of(wpsq))

return ScaleFactor(10);

if ( distance<File>(bksq, wpsq) == 1

&& distance(wksq, bksq) > 2)

return ScaleFactor(24 - 2 * distance(wksq, bksq));

}

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 ksq = pos.square<KING>(weakSide);

Square bsq = pos.square<BISHOP>(weakSide);

Square psq = pos.square<PAWN>(strongSide);

Rank rk = relative_rank(strongSide, psq);

Square 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 (rk == RANK_5 && !opposite_colors(bsq, psq))

{

int d = distance(psq + 3 * push, ksq);

if (d <= 2 && !(d == 0 && ksq == pos.square<KING>(strongSide) + 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 ( rk == RANK_6

&& distance(psq + 2 * push, ksq) <= 1

&& (PseudoAttacks[BISHOP][bsq] & (psq + push))

&& distance<File>(bsq, psq) >= 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 wpsq1 = pos.squares<PAWN>(strongSide)[0];

Square wpsq2 = pos.squares<PAWN>(strongSide)[1];

Square bksq = pos.square<KING>(weakSide);

// Does the stronger side have a passed pawn?

if (pos.pawn_passed(strongSide, wpsq1) || pos.pawn_passed(strongSide, wpsq2))

return SCALE_FACTOR_NONE;

Rank r = std::max(relative_rank(strongSide, wpsq1), relative_rank(strongSide, wpsq2));

if ( distance<File>(bksq, wpsq1) <= 1

&& distance<File>(bksq, wpsq2) <= 1

&& relative_rank(strongSide, bksq) > r)

{

assert(r > RANK_1 && r < RANK_7);

return ScaleFactor(KRPPKRPScaleFactors[r]);

}

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 ksq = pos.square<KING>(weakSide);

Bitboard pawns = pos.pieces(strongSide, PAWN);

// If all pawns are ahead of the king, on a single rook file and

// the king is within one file of the pawns, it's a draw.

if ( !(pawns & ~in_front_bb(weakSide, rank_of(ksq)))

&& !((pawns & ~FileABB) && (pawns & ~FileHBB))

&& distance<File>(ksq, lsb(pawns)) <= 1)

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 pawnSq = pos.square<PAWN>(strongSide);

Square strongBishopSq = pos.square<BISHOP>(strongSide);

Square weakBishopSq = pos.square<BISHOP>(weakSide);

Square weakKingSq = pos.square<KING>(weakSide);

// Case 1: Defending king blocks the pawn, and cannot be driven away

if ( file_of(weakKingSq) == file_of(pawnSq)

&& relative_rank(strongSide, pawnSq) < relative_rank(strongSide, weakKingSq)

&& ( opposite_colors(weakKingSq, strongBishopSq)

|| relative_rank(strongSide, weakKingSq) <= RANK_6))

return SCALE_FACTOR_DRAW;

// Case 2: Opposite colored bishops

if (opposite_colors(strongBishopSq, weakBishopSq))

{

// 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(strongSide, pawnSq) <= RANK_5)

return SCALE_FACTOR_DRAW;

else

{

Bitboard path = forward_bb(strongSide, pawnSq);

if (path & pos.pieces(weakSide, KING))

return SCALE_FACTOR_DRAW;

if ( (pos.attacks_from<BISHOP>(weakBishopSq) & path)

&& distance(weakBishopSq, pawnSq) >= 3)

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 wbsq = pos.square<BISHOP>(strongSide);

Square bbsq = pos.square<BISHOP>(weakSide);

if (!opposite_colors(wbsq, bbsq))

return SCALE_FACTOR_NONE;

Square ksq = pos.square<KING>(weakSide);

Square psq1 = pos.squares<PAWN>(strongSide)[0];

Square psq2 = pos.squares<PAWN>(strongSide)[1];

Rank r1 = rank_of(psq1);

Rank r2 = rank_of(psq2);

Square blockSq1, blockSq2;

if (relative_rank(strongSide, psq1) > relative_rank(strongSide, psq2))

{

blockSq1 = psq1 + pawn_push(strongSide);

blockSq2 = make_square(file_of(psq2), rank_of(psq1));

}

else

{

blockSq1 = psq2 + pawn_push(strongSide);

blockSq2 = make_square(file_of(psq1), rank_of(psq2));

}

switch (distance<File>(psq1, psq2))

{

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(ksq) == file_of(blockSq1)

&& relative_rank(strongSide, ksq) >= relative_rank(strongSide, blockSq1)

&& opposite_colors(ksq, wbsq))

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 ( ksq == blockSq1

&& opposite_colors(ksq, wbsq)

&& ( bbsq == blockSq2

|| (pos.attacks_from<BISHOP>(blockSq2) & pos.pieces(weakSide, BISHOP))

|| distance(r1, r2) >= 2))

return SCALE_FACTOR_DRAW;

else if ( ksq == blockSq2

&& opposite_colors(ksq, wbsq)

&& ( bbsq == blockSq1

|| (pos.attacks_from<BISHOP>(blockSq1) & 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 pawnSq = pos.square<PAWN>(strongSide);

Square strongBishopSq = pos.square<BISHOP>(strongSide);

Square weakKingSq = pos.square<KING>(weakSide);

if ( file_of(weakKingSq) == file_of(pawnSq)

&& relative_rank(strongSide, pawnSq) < relative_rank(strongSide, weakKingSq)

&& ( opposite_colors(weakKingSq, strongBishopSq)

|| relative_rank(strongSide, weakKingSq) <= RANK_6))

return SCALE_FACTOR_DRAW;

return SCALE_FACTOR_NONE;

}

/// KNP vs K. 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<KNPK>::operator()(const Position& pos) const {

assert(verify_material(pos, strongSide, KnightValueMg, 1));

assert(verify_material(pos, weakSide, VALUE_ZERO, 0));

// Assume strongSide is white and the pawn is on files A-D

Square pawnSq = normalize(pos, strongSide, pos.square<PAWN>(strongSide));

Square weakKingSq = normalize(pos, strongSide, pos.square<KING>(weakSide));

if (pawnSq == SQ_A7 && distance(SQ_A8, weakKingSq) <= 1)

return SCALE_FACTOR_DRAW;

return SCALE_FACTOR_NONE;

}

/// KNP vs KB. If knight can block bishop from taking pawn, it's a win.

/// Otherwise the position is drawn.

template<>

ScaleFactor Endgame<KNPKB>::operator()(const Position& pos) const {

Square pawnSq = pos.square<PAWN>(strongSide);

Square bishopSq = pos.square<BISHOP>(weakSide);

Square weakKingSq = pos.square<KING>(weakSide);

// King needs to get close to promoting pawn to prevent knight from blocking.

// Rules for this are very tricky, so just approximate.

if (forward_bb(strongSide, pawnSq) & pos.attacks_from<BISHOP>(bishopSq))

return ScaleFactor(distance(weakKingSq, pawnSq));

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 wksq = normalize(pos, strongSide, pos.square<KING>(strongSide));

Square bksq = normalize(pos, strongSide, pos.square<KING>(weakSide));

Square psq = 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(psq) >= RANK_5 && file_of(psq) != 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(wksq, psq, bksq, us) ? SCALE_FACTOR_NONE : SCALE_FACTOR_DRAW;

}