Introduce king flank defenders

This patch implements what we have been trying for quite some time -
dependance of kingdanger on balance of attackers and defenders of king
flank, to avoid overestimate attacking power if the opponent has enough
defenders of king position. We already have some form of it in bishop
and knight defenders - this is further work in this direction.

What to do based on this?

1) constant 4 is arbitrary, maybe it is not optimal
2) maybe we can use quadratic formula as in kingflankattack
3) simplification into alrealy existing terms is always a possibility :)
4) overall kingdanger tuning always can be done.

passed STC:
http://tests.stockfishchess.org/tests/view/5dcf40560ebc590256325f30
LLR: 2.96 (-2.94,2.94) [-1.50,4.50]
Total: 26298 W: 5819 L: 5632 D: 14847

passed LTC:
http://tests.stockfishchess.org/tests/view/5dcfa5760ebc590256326464
LLR: 2.96 (-2.94,2.94) [0.00,3.50]
Total: 30600 W: 5042 L: 4784 D: 20774

Closes official-stockfish/Stockfish#2415

Bench: 4496847

src/evaluate.cpp

@@ -380,7 +380,7 @@ namespace {
     constexpr Bitboard Camp = (Us == WHITE ? AllSquares ^ Rank6BB ^ Rank7BB ^ Rank8BB
                                            : AllSquares ^ Rank1BB ^ Rank2BB ^ Rank3BB);
 
-    Bitboard weak, b1, b2, safe, unsafeChecks = 0;
+    Bitboard weak, b1, b2, b3, safe, unsafeChecks = 0;
     Bitboard rookChecks, queenChecks, bishopChecks, knightChecks;
     int kingDanger = 0;
     const Square ksq = pos.square<KING>(Us);
@@ -439,19 +439,22 @@ namespace {
     else
         unsafeChecks |= knightChecks;
 
-    // Find the squares that opponent attacks in our king flank, and the squares
-    // which are attacked twice in that flank.
+    // Find the squares that opponent attacks in our king flank, the squares
+    // which they attack twice in that flank, and the squares that we defend.
     b1 = attackedBy[Them][ALL_PIECES] & KingFlank[file_of(ksq)] & Camp;
     b2 = b1 & attackedBy2[Them];
+    b3 = attackedBy[Us][ALL_PIECES] & KingFlank[file_of(ksq)] & Camp;
 
-    int kingFlankAttacks = popcount(b1) + popcount(b2);
+    int kingFlankAttack = popcount(b1) + popcount(b2);
+    int kingFlankDefense = popcount(b3);
 
     kingDanger +=        kingAttackersCount[Them] * kingAttackersWeight[Them]
                  + 185 * popcount(kingRing[Us] & weak)
                  + 148 * popcount(unsafeChecks)
                  +  98 * popcount(pos.blockers_for_king(Us))
                  +  69 * kingAttacksCount[Them]
-                 +   3 * kingFlankAttacks * kingFlankAttacks / 8
+                 +   4 * (kingFlankAttack - kingFlankDefense)
+                 +   3 * kingFlankAttack * kingFlankAttack / 8
                  +       mg_value(mobility[Them] - mobility[Us])
                  - 873 * !pos.count<QUEEN>(Them)
                  - 100 * bool(attackedBy[Us][KNIGHT] & attackedBy[Us][KING])
@@ -468,7 +471,7 @@ namespace {
         score -= PawnlessFlank;
 
     // Penalty if king flank is under attack, potentially moving toward the king
-    score -= FlankAttacks * kingFlankAttacks;
+    score -= FlankAttacks * kingFlankAttack;
 
     if (T)
         Trace::add(KING, Us, score);