Introduce tropism measure in king danger

This patch adds the tropism measure as a new term in the king danger variable.
Since we then trasform this variable as a Score via a quadratic formula, the
main effect of the patch is the positive correlation of the tropism measure
with some checks and pins information already present in the king danger code.

STC:
LLR: 2.96 (-2.94,2.94) [0.00,5.00]
Total: 6805 W: 1597 L: 1431 D: 3777
http://tests.stockfishchess.org/tests/view/5b5df8d10ebc5902bdb91699

LTC:
LLR: 2.96 (-2.94,2.94) [0.00,5.00]
Total: 32872 W: 5782 L: 5523 D: 21567
http://tests.stockfishchess.org/tests/view/5b5e08d80ebc5902bdb917ee

How to continue from there?

• it may be possible to use CloseEnemies=S(7,0)
• we may want to try incorporating other strategic features in the quadratic
  king danger.

Closes #1717

Bench: 5591925

src/evaluate.cpp

@@ -413,11 +413,19 @@ namespace {
                                            : AllSquares ^ Rank1BB ^ Rank2BB ^ Rank3BB);
 
     const Square ksq = pos.square<KING>(Us);
-    Bitboard weak, b, b1, b2, safe, unsafeChecks;
+    Bitboard kingFlank, weak, b, b1, b2, safe, unsafeChecks;
 
     // King shelter and enemy pawns storm
     Score score = pe->king_safety<Us>(pos, ksq);
 
+    // Find the squares that opponent attacks in our king flank, and the squares
+    // which are attacked twice in that flank but not defended by our pawns.
+    kingFlank = KingFlank[file_of(ksq)];
+    b1 = attackedBy[Them][ALL_PIECES] & kingFlank & Camp;
+    b2 = b1 & attackedBy2[Them] & ~attackedBy[Us][PAWN];
+
+    int tropism = popcount(b1) + popcount(b2);
+
     // Main king safety evaluation
     if (kingAttackersCount[Them] > 1 - pos.count<QUEEN>(Them))
     {
@@ -470,9 +478,10 @@ namespace {
                      +  69 * kingAttacksCount[Them]
                      + 185 * popcount(kingRing[Us] & weak)
                      + 129 * popcount(pos.blockers_for_king(Us) | unsafeChecks)
+                     +   4 * tropism
                      - 873 * !pos.count<QUEEN>(Them)
                      -   6 * mg_value(score) / 8
-                     -   2 ;
+                     -   30;
 
         // Transform the kingDanger units into a Score, and subtract it from the evaluation
         if (kingDanger > 0)
@@ -483,19 +492,12 @@ namespace {
         }
     }
 
-    Bitboard kf = KingFlank[file_of(ksq)];
-
     // Penalty when our king is on a pawnless flank
-    if (!(pos.pieces(PAWN) & kf))
+    if (!(pos.pieces(PAWN) & kingFlank))
         score -= PawnlessFlank;
 
-    // Find the squares that opponent attacks in our king flank, and the squares
-    // which are attacked twice in that flank but not defended by our pawns.
-    b1 = attackedBy[Them][ALL_PIECES] & kf & Camp;
-    b2 = b1 & attackedBy2[Them] & ~attackedBy[Us][PAWN];
-
-    // King tropism, to anticipate slow motion attacks on our king
-    score -= CloseEnemies * (popcount(b1) + popcount(b2));
+    // King tropism bonus, to anticipate slow motion attacks on our king
+    score -= CloseEnemies * tropism;
 
     if (T)
         Trace::add(KING, Us, score);