Simplify verification search (#1362)

1. avoid recursive call of verification.
   For the interested side to move recursion makes no sense.
   For the other side it could make sense in case of mutual zugzwang,
   but I was not able to figure out any concrete problematic position.
   Allows the removal of 2 local variables.
   
2. avoid further reduction by removing R += ONE_PLY;

Benchmark with zugzwang-suite (see #1338), max 45 secs per position:
Patch  solves 33 out of 37
Master solves 31 out of 37

STC:
LLR: 2.95 (-2.94,2.94) [-3.00,1.00]
Total: 76188 W: 13866 L: 13840 D: 48482
http://tests.stockfishchess.org/tests/view/5a5612ed0ebc590297da516c

LTC:
LLR: 2.95 (-2.94,2.94) [-3.00,1.00]
Total: 40479 W: 5247 L: 5152 D: 30080
http://tests.stockfishchess.org/tests/view/5a56f7d30ebc590299e4550e

bench: 5340015

src/search.cpp

@@ -676,7 +676,7 @@ namespace {
     if (   !PvNode
         &&  eval >= beta
         &&  ss->staticEval >= beta - 36 * depth / ONE_PLY + 225
-		&& (ss->ply >= thisThread->nmp_ply || ss->ply % 2 == thisThread->pair))
+        && (ss->ply >= thisThread->nmp_ply || ss->ply % 2 != thisThread->nmp_odd))
     {
 
         assert(eval - beta >= 0);
@@ -698,21 +698,18 @@ namespace {
             if (nullValue >= VALUE_MATE_IN_MAX_PLY)
                 nullValue = beta;
 
-            if (depth < 12 * ONE_PLY && abs(beta) < VALUE_KNOWN_WIN)
+            if (abs(beta) < VALUE_KNOWN_WIN && (depth < 12 * ONE_PLY || thisThread->nmp_ply))
                 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;
+            thisThread->nmp_odd = ss->ply % 2;
 
             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;
+
+            thisThread->nmp_odd = thisThread->nmp_ply = 0;
 
             if (v >= beta)
                 return nullValue;

src/thread.cpp

@@ -187,12 +187,10 @@ void ThreadPool::start_thinking(Position& pos, StateListPtr& states,
 
   for (Thread* th : *this)
   {
-      th->nodes = th->tbHits = 0;
+      th->nodes = th->tbHits = th->nmp_ply = th->nmp_odd = 0;
       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 @@ class Thread {
   Material::Table materialTable;
   Endgames endgames;
   size_t PVIdx;
-  int selDepth, nmp_ply, pair;
+  int selDepth, nmp_ply, nmp_odd;
   std::atomic<uint64_t> nodes, tbHits;
 
   Position rootPos;