Verified SEE pruning for capturing and checking moves.

Patch analyzes field after SEE exchanges concluded with a recapture by
the opponent:
if opponent Queen/Rook/King results under attack after the exchanges, we
consider the move sharp and don't prune it.

Important note:
By accident I forgot to adjust 'occupied' when the king takes part in
the exchanges.
As result of this a move is considered sharp too, when opponent king
apparently can evade check by recapturing.
Surprisingly this seems contribute to patch's strength.

STC:
https://tests.stockfishchess.org/tests/view/640b16132644b62c33947397
LLR: 2.96 (-2.94,2.94) <0.00,2.00>
Total: 116400 W: 31239 L: 30817 D: 54344
Ptnml(0-2): 350, 12742, 31618, 13116, 374

LTC:
https://tests.stockfishchess.org/tests/view/640c88092644b62c3394c1c5
LLR: 2.95 (-2.94,2.94) <0.50,2.50>
Total: 177600 W: 47988 L: 47421 D: 82191
Ptnml(0-2): 62, 16905, 54317, 17436, 80

closes #4453

bench: 5012145

src/movepick.cpp

@@ -95,7 +95,7 @@ MovePicker::MovePicker(const Position& p, Move ttm, Value th, const CapturePiece
 
   stage = PROBCUT_TT + !(ttm && pos.capture_stage(ttm)
                              && pos.pseudo_legal(ttm)
-                             && pos.see_ge(ttm, threshold));
+                             && pos.see_ge(ttm, occupied, threshold));
 }
 
 /// MovePicker::score() assigns a numerical value to each move in a list, used
@@ -197,7 +197,7 @@ Move MovePicker::next_move(bool skipQuiets) {
 
   case GOOD_CAPTURE:
       if (select<Next>([&](){
-                       return pos.see_ge(*cur, Value(-cur->value)) ?
+                       return pos.see_ge(*cur, occupied, Value(-cur->value)) ?
                               // Move losing capture to endBadCaptures to be tried later
                               true : (*endBadCaptures++ = *cur, false); }))
           return *(cur - 1);
@@ -264,7 +264,7 @@ Move MovePicker::next_move(bool skipQuiets) {
       return select<Best>([](){ return true; });
 
   case PROBCUT:
-      return select<Next>([&](){ return pos.see_ge(*cur, threshold); });
+      return select<Next>([&](){ return pos.see_ge(*cur, occupied, threshold); });
 
   case QCAPTURE:
       if (select<Next>([&](){ return   depth > DEPTH_QS_RECAPTURES

src/movepick.h

@@ -150,6 +150,7 @@ class MovePicker {
   Value threshold;
   Depth depth;
   ExtMove moves[MAX_MOVES];
+  Bitboard occupied;
 };
 
 } // namespace Stockfish

src/position.cpp

@@ -1062,7 +1062,7 @@ Key Position::key_after(Move m) const {
 /// SEE value of move is greater or equal to the given threshold. We'll use an
 /// algorithm similar to alpha-beta pruning with a null window.
 
-bool Position::see_ge(Move m, Value threshold) const {
+bool Position::see_ge(Move m, Bitboard& occupied, Value threshold) const {
 
   assert(is_ok(m));
 
@@ -1081,7 +1081,7 @@ bool Position::see_ge(Move m, Value threshold) const {
       return true;
 
   assert(color_of(piece_on(from)) == sideToMove);
-  Bitboard occupied = pieces() ^ from ^ to;
+  occupied = pieces() ^ from ^ to; // xoring to is important for pinned piece logic
   Color stm = sideToMove;
   Bitboard attackers = attackers_to(to, occupied);
   Bitboard stmAttackers, bb;
@@ -1112,45 +1112,44 @@ bool Position::see_ge(Move m, Value threshold) const {
       // the bitboard 'attackers' any X-ray attackers behind it.
       if ((bb = stmAttackers & pieces(PAWN)))
       {
+          occupied ^= least_significant_square_bb(bb);
           if ((swap = PawnValueMg - swap) < res)
               break;
 
-          occupied ^= least_significant_square_bb(bb);
           attackers |= attacks_bb<BISHOP>(to, occupied) & pieces(BISHOP, QUEEN);
       }
 
       else if ((bb = stmAttackers & pieces(KNIGHT)))
       {
+          occupied ^= least_significant_square_bb(bb);
           if ((swap = KnightValueMg - swap) < res)
               break;
-
-          occupied ^= least_significant_square_bb(bb);
       }
 
       else if ((bb = stmAttackers & pieces(BISHOP)))
       {
+          occupied ^= least_significant_square_bb(bb);
           if ((swap = BishopValueMg - swap) < res)
               break;
 
-          occupied ^= least_significant_square_bb(bb);
           attackers |= attacks_bb<BISHOP>(to, occupied) & pieces(BISHOP, QUEEN);
       }
 
       else if ((bb = stmAttackers & pieces(ROOK)))
       {
+          occupied ^= least_significant_square_bb(bb);
           if ((swap = RookValueMg - swap) < res)
               break;
 
-          occupied ^= least_significant_square_bb(bb);
           attackers |= attacks_bb<ROOK>(to, occupied) & pieces(ROOK, QUEEN);
       }
 
       else if ((bb = stmAttackers & pieces(QUEEN)))
       {
+          occupied ^= least_significant_square_bb(bb);
           if ((swap = QueenValueMg - swap) < res)
               break;
 
-          occupied ^= least_significant_square_bb(bb);
           attackers |=  (attacks_bb<BISHOP>(to, occupied) & pieces(BISHOP, QUEEN))
                       | (attacks_bb<ROOK  >(to, occupied) & pieces(ROOK  , QUEEN));
       }

src/position.h

@@ -144,7 +144,7 @@ class Position {
   void undo_null_move();
 
   // Static Exchange Evaluation
-  bool see_ge(Move m, Value threshold = VALUE_ZERO) const;
+  bool see_ge(Move m, Bitboard& occupied, Value threshold = VALUE_ZERO) const;
 
   // Accessing hash keys
   Key key() const;

src/search.cpp

@@ -1019,9 +1019,27 @@ namespace {
                    + captureHistory[movedPiece][to_sq(move)][type_of(pos.piece_on(to_sq(move)))] / 7 < alpha)
                   continue;
 
+              Bitboard occupied;
               // SEE based pruning (~11 Elo)
-              if (!pos.see_ge(move, Value(-206) * depth))
-                  continue;
+              if (!pos.see_ge(move, occupied, Value(-206) * depth))
+              {
+                  if (depth < 2 - capture)
+                      continue;
+                  // don't prune move if a heavy enemy piece (KQR) is under attack after the exchanges
+                  Bitboard leftEnemies = (pos.pieces(~us, QUEEN, ROOK) | pos.pieces(~us, KING)) & occupied;
+                  Bitboard attacks = 0;
+                  occupied |= to_sq(move);
+                  while (leftEnemies && !attacks)
+                  {
+                      Square sq = pop_lsb(leftEnemies);
+                      attacks |= pos.attackers_to(sq, occupied) & pos.pieces(us) & occupied;
+                      // exclude Queen/Rook(s) which were already threatened before SEE
+                      if (attacks && (sq != pos.square<KING>(~us) && (pos.attackers_to(sq, pos.pieces()) & pos.pieces(us))))
+                          attacks = 0;
+                  }
+                  if (!attacks)
+                      continue;
+              }
           }
           else
           {
@@ -1047,8 +1065,9 @@ namespace {
 
               lmrDepth = std::max(lmrDepth, 0);
 
+              Bitboard occupied;
               // Prune moves with negative SEE (~4 Elo)
-              if (!pos.see_ge(move, Value(-24 * lmrDepth * lmrDepth - 15 * lmrDepth)))
+              if (!pos.see_ge(move, occupied, Value(-24 * lmrDepth * lmrDepth - 15 * lmrDepth)))
                   continue;
           }
       }
@@ -1533,6 +1552,7 @@ namespace {
                                       prevSq);
 
     int quietCheckEvasions = 0;
+    Bitboard occupied;
 
     // Step 5. Loop through all pseudo-legal moves until no moves remain
     // or a beta cutoff occurs.
@@ -1569,7 +1589,7 @@ namespace {
               continue;
           }
 
-          if (futilityBase <= alpha && !pos.see_ge(move, VALUE_ZERO + 1))
+          if (futilityBase <= alpha && !pos.see_ge(move, occupied, VALUE_ZERO + 1))
           {
               bestValue = std::max(bestValue, futilityBase);
               continue;
@@ -1588,7 +1608,7 @@ namespace {
           continue;
 
       // Do not search moves with bad enough SEE values (~5 Elo)
-      if (!pos.see_ge(move, Value(-110)))
+      if (!pos.see_ge(move, occupied, Value(-110)))
           continue;
     }