Remove use of half-ply reductions from LMR, Null-move, IID and

Singular extensions.

STC:
ELO: 3.80 +-3.1 (95%) LOS: 99.2%
Total: 19727 W: 4190 L: 3974 D: 11563

LTC:
LLR: 2.96 (-2.94,2.94) [-3.00,1.00]
Total: 7647 W: 1356 L: 1214 D: 5077

Bench: 6545733

Resolves #55

Author: uriblass

src/search.cpp

@@ -127,17 +127,14 @@ void Search::init() {
   {
       double    pvRed = 0.00 + log(double(hd)) * log(double(mc)) / 3.00;
       double nonPVRed = 0.33 + log(double(hd)) * log(double(mc)) / 2.25;
-      Reductions[1][1][hd][mc] = int8_t(   pvRed >= 1.0 ?    pvRed * int(ONE_PLY) : 0);
-      Reductions[0][1][hd][mc] = int8_t(nonPVRed >= 1.0 ? nonPVRed * int(ONE_PLY) : 0);
+      Reductions[1][1][hd][mc] = int8_t(   pvRed >= 1.0 ?    pvRed+0.5: 0)*int(ONE_PLY);
+      Reductions[0][1][hd][mc] = int8_t(nonPVRed >= 1.0 ? nonPVRed+0.5: 0)*int(ONE_PLY);
 
       Reductions[1][0][hd][mc] = Reductions[1][1][hd][mc];
       Reductions[0][0][hd][mc] = Reductions[0][1][hd][mc];
 
-      if (Reductions[0][0][hd][mc] > 2 * ONE_PLY)
+      if (Reductions[0][0][hd][mc] >= 2 * ONE_PLY)
           Reductions[0][0][hd][mc] += ONE_PLY;
-
-      else if (Reductions[0][0][hd][mc] > 1 * ONE_PLY)
-          Reductions[0][0][hd][mc] += ONE_PLY / 2;
   }
 
   // Init futility move count array
@@ -565,8 +562,7 @@ namespace {
         assert(eval - beta >= 0);
 
         // Null move dynamic reduction based on depth and value
-        Depth R =  3 * ONE_PLY
-                 + depth / 4
+        Depth R = (3 + (depth / 8 )) * ONE_PLY
                  + std::min(int(eval - beta) / PawnValueMg, 3) * ONE_PLY;
 
         pos.do_null_move(st);
@@ -633,7 +629,7 @@ namespace {
         && (PvNode || ss->staticEval + 256 >= beta))
     {
         Depth d = depth - 2 * ONE_PLY - (PvNode ? DEPTH_ZERO : depth / 4);
-
+        d = (d / 2) * 2;  // Round to nearest full-ply
         ss->skipNullMove = true;
         search<PvNode ? PV : NonPV, false>(pos, ss, alpha, beta, d, true);
         ss->skipNullMove = false;
@@ -735,7 +731,7 @@ namespace {
           Value rBeta = ttValue - int(depth);
           ss->excludedMove = move;
           ss->skipNullMove = true;
-          value = search<NonPV, false>(pos, ss, rBeta - 1, rBeta, depth / 2, cutNode);
+          value = search<NonPV, false>(pos, ss, rBeta - 1, rBeta, (depth / 4) * 2, cutNode);
           ss->skipNullMove = false;
           ss->excludedMove = MOVE_NONE;