Enhanced verify search (#1338)

by disabling null-move-pruning for the side to move for first part of
the remaining search tree. This helps to better recognize zugzwang.

STC:
LLR: 2.96 (-2.94,2.94) [-3.00,1.00]
Total: 18220 W: 3379 L: 3253 D: 11588
http://tests.stockfishchess.org/tests/view/5a2fa6460ebc590ccbb8bc2f

LTC:
LLR: 2.96 (-2.94,2.94) [-3.00,1.00]
Total: 41899 W: 5359 L: 5265 D: 31275
http://tests.stockfishchess.org/tests/view/5a2fcf440ebc590ccbb8bc47

For further detail see commit notes and discussion at 
6401a80ab9

bench: 5776193

src/search.cpp

@@ -681,7 +681,8 @@ namespace {
     // Step 8. Null move search with verification search (is omitted in PV nodes)
     if (   !PvNode
         &&  eval >= beta
-        &&  ss->staticEval >= beta - 36 * depth / ONE_PLY + 225)
+        &&  ss->staticEval >= beta - 36 * depth / ONE_PLY + 225
+		&& (ss->ply >= thisThread->nmp_ply || ss->ply % 2 == thisThread->pair))
     {
 
         assert(eval - beta >= 0);
@@ -707,8 +708,17 @@ namespace {
                 return nullValue;
 
             // Do verification search at high depths
+            R += ONE_PLY;
+            // disable null move pruning for side to move for the first part of the remaining search tree
+            int nmp_ply = thisThread->nmp_ply;
+            int pair = thisThread->pair;
+            thisThread->nmp_ply = ss->ply + 3 * (depth-R) / 4;
+            thisThread->pair = (ss->ply % 2) == 0;
+
             Value v = depth-R < ONE_PLY ? qsearch<NonPV, false>(pos, ss, beta-1, beta)
                                         :  search<NonPV>(pos, ss, beta-1, beta, depth-R, false, true);
+            thisThread->pair = pair;
+            thisThread->nmp_ply = nmp_ply;
 
             if (v >= beta)
                 return nullValue;

src/thread.cpp

@@ -187,6 +187,8 @@ void ThreadPool::start_thinking(Position& pos, StateListPtr& states,
       th->rootDepth = th->completedDepth = DEPTH_ZERO;
       th->rootMoves = rootMoves;
       th->rootPos.set(pos.fen(), pos.is_chess960(), &setupStates->back(), th);
+      th->nmp_ply = 0;
+      th->pair = -1;
   }
 
   setupStates->back() = tmp;

src/thread.h

@@ -61,7 +61,7 @@ public:
   Material::Table materialTable;
   Endgames endgames;
   size_t PVIdx;
-  int selDepth;
+  int selDepth, nmp_ply, pair;
   std::atomic<uint64_t> nodes, tbHits;
 
   Position rootPos;