Skip quiet moves based on moveCount pruning threshold and history stats

If we can moveCountPrune and next quiet move has negative stats,
then go directly to the next move stage (Bad_Captures).

Reduction formula is tweaked to compensate for the decrease in move count that is used in LMR.

STC:
LLR: 2.96 (-2.94,2.94) [0.00,5.00]
Total: 6847 W: 1276 L: 1123 D: 4448

LTC:
LLR: 2.95 (-2.94,2.94) [0.00,5.00]
Total: 48687 W: 6503 L: 6226 D: 35958

Bench: 5919519

Closes #1036

src/movepick.cpp

@@ -175,7 +175,7 @@ void MovePicker::score<EVASIONS>() {
 /// left. It picks the move with the biggest value from a list of generated moves
 /// taking care not to return the ttMove if it has already been searched.
 
-Move MovePicker::next_move() {
+Move MovePicker::next_move(bool skipQuiets) {
 
   Move move;
 
@@ -248,9 +248,11 @@ Move MovePicker::next_move() {
       ++stage;
 
   case QUIET:
-      while (cur < endMoves)
+      while (    cur < endMoves
+             && (!skipQuiets || cur->value >= VALUE_ZERO))
       {
           move = *cur++;
+
           if (   move != ttMove
               && move != ss->killers[0]
               && move != ss->killers[1]

src/movepick.h

@@ -95,7 +95,7 @@ public:
   MovePicker(const Position&, Move, Depth, Square);
   MovePicker(const Position&, Move, Depth, Search::Stack*);
 
-  Move next_move();
+  Move next_move(bool skipQuiets = false);
 
 private:
   template<GenType> void score();

src/search.cpp

@@ -163,7 +163,7 @@ void Search::init() {
       for (int d = 1; d < 64; ++d)
           for (int mc = 1; mc < 64; ++mc)
           {
-              double r = log(d) * log(mc) / 2;
+              double r = log(d) * log(mc) / 1.95;
 
               Reductions[NonPV][imp][d][mc] = int(std::round(r));
               Reductions[PV][imp][d][mc] = std::max(Reductions[NonPV][imp][d][mc] - 1, 0);
@@ -542,7 +542,7 @@ namespace {
     Depth extension, newDepth;
     Value bestValue, value, ttValue, eval;
     bool ttHit, inCheck, givesCheck, singularExtensionNode, improving;
-    bool captureOrPromotion, doFullDepthSearch, moveCountPruning;
+    bool captureOrPromotion, doFullDepthSearch, moveCountPruning, skipQuiets;
     Piece moved_piece;
     int moveCount, quietCount;
 
@@ -829,10 +829,11 @@ moves_loop: // When in check search starts from here
                            && !excludedMove // Recursive singular search is not allowed
                            && (tte->bound() & BOUND_LOWER)
                            &&  tte->depth() >= depth - 3 * ONE_PLY;
+    skipQuiets = false;
 
     // Step 11. Loop through moves
     // Loop through all pseudo-legal moves until no moves remain or a beta cutoff occurs
-    while ((move = mp.next_move()) != MOVE_NONE)
+    while ((move = mp.next_move(skipQuiets)) != MOVE_NONE)
     {
       assert(is_ok(move));
 
@@ -906,8 +907,10 @@ moves_loop: // When in check search starts from here
               && (!pos.advanced_pawn_push(move) || pos.non_pawn_material() >= 5000))
           {
               // Move count based pruning
-              if (moveCountPruning)
+              if (moveCountPruning) {
+                  skipQuiets = true;
                   continue;
+              }
 
               // Reduced depth of the next LMR search
               int lmrDepth = std::max(newDepth - reduction<PvNode>(improving, depth, moveCount), DEPTH_ZERO) / ONE_PLY;