Introducing NodeType Root

We transform rootNode into constexpr by adding a new NodeType `Root`,
which causes a speed up.

Local test:
```
Build Tester: 1.4.7.0
Windows 10 (Version 10.0, Build 0, 64-bit Edition)
Intel(R) Core(TM) i7-8750H CPU @ 2.20GHz
SafeMode: No
Running In VM: No
HyperThreading Enabled: Yes
CPU Warmup: Yes
Command Line: bench
Tests per Build: 25
ANOVA: n/a

                Engine# (NPS)                     Speedup     Sp     Conf. 95%    S.S.
patch  (920.179,4) ---> master  (906.329,2)  --->  1,528%  20.336,5     Yes        No
```

---------

STC:
LLR: 2.94 (-2.94,2.94) <-0.50,2.50>
Total: 98216 W: 8348 L: 8102 D: 81766
Ptnml(0-2): 295, 6357, 35549, 6621, 286
https://tests.stockfishchess.org/tests/view/60b797e2457376eb8bcaa0ab

Yellow LTC:
LLR: -2.95 (-2.94,2.94) <0.50,3.50>
Total: 76936 W: 2651 L: 2626 D: 71659
Ptnml(0-2): 29, 2233, 33916, 2264, 26
https://tests.stockfishchess.org/tests/view/60b80d6d457376eb8bcaa145

closes https://github.com/official-stockfish/Stockfish/pull/3522

No functional change

src/search.cpp

@@ -59,7 +59,7 @@ using namespace Search;
 namespace {
 
   // Different node types, used as a template parameter
-  enum NodeType { NonPV, PV };
+  enum NodeType { NonPV, PV, Root };
 
   constexpr uint64_t TtHitAverageWindow     = 4096;
   constexpr uint64_t TtHitAverageResolution = 1024;
@@ -102,10 +102,10 @@ namespace {
     Move best = MOVE_NONE;
   };
 
-  template <NodeType NT>
+  template <NodeType nodeType>
   Value search(Position& pos, Stack* ss, Value alpha, Value beta, Depth depth, bool cutNode);
 
-  template <NodeType NT>
+  template <NodeType nodeType>
   Value qsearch(Position& pos, Stack* ss, Value alpha, Value beta, Depth depth = 0);
 
   Value value_to_tt(Value v, int ply);
@@ -384,7 +384,7 @@ void Thread::search() {
           while (true)
           {
               Depth adjustedDepth = std::max(1, rootDepth - failedHighCnt - searchAgainCounter);
-              bestValue = Stockfish::search<PV>(rootPos, ss, alpha, beta, adjustedDepth, false);
+              bestValue = Stockfish::search<Root>(rootPos, ss, alpha, beta, adjustedDepth, false);
 
               // Bring the best move to the front. It is critical that sorting
               // is done with a stable algorithm because all the values but the
@@ -527,18 +527,18 @@ namespace {
 
   // search<>() is the main search function for both PV and non-PV nodes
 
-  template <NodeType NT>
+  template <NodeType nodeType>
   Value search(Position& pos, Stack* ss, Value alpha, Value beta, Depth depth, bool cutNode) {
 
-    constexpr bool PvNode = NT == PV;
-    const bool rootNode = PvNode && ss->ply == 0;
+    constexpr bool PvNode = nodeType != NonPV;
+    constexpr bool rootNode = nodeType == Root;
     const Depth maxNextDepth = rootNode ? depth : depth + 1;
 
     // Check if we have an upcoming move which draws by repetition, or
     // if the opponent had an alternative move earlier to this position.
-    if (   pos.rule50_count() >= 3
+    if (   !rootNode
+        && pos.rule50_count() >= 3
         && alpha < VALUE_DRAW
-        && !rootNode
         && pos.has_game_cycle(ss->ply))
     {
         alpha = value_draw(pos.this_thread());
@@ -548,7 +548,7 @@ namespace {
 
     // Dive into quiescence search when the depth reaches zero
     if (depth <= 0)
-        return qsearch<NT>(pos, ss, alpha, beta);
+        return qsearch<PvNode ? PV : NonPV>(pos, ss, alpha, beta);
 
     assert(-VALUE_INFINITE <= alpha && alpha < beta && beta <= VALUE_INFINITE);
     assert(PvNode || (alpha == beta - 1));
@@ -1054,9 +1054,9 @@ moves_loop: // When in check, search starts from here
       // then that move is singular and should be extended. To verify this we do
       // a reduced search on all the other moves but the ttMove and if the
       // result is lower than ttValue minus a margin, then we will extend the ttMove.
-      if (    depth >= 7
+      if (   !rootNode
+          &&  depth >= 7
           &&  move == ttMove
-          && !rootNode
           && !excludedMove // Avoid recursive singular search
        /* &&  ttValue != VALUE_NONE Already implicit in the next condition */
           &&  abs(ttValue) < VALUE_KNOWN_WIN
@@ -1351,10 +1351,11 @@ moves_loop: // When in check, search starts from here
 
   // qsearch() is the quiescence search function, which is called by the main search
   // function with zero depth, or recursively with further decreasing depth per call.
-  template <NodeType NT>
+  template <NodeType nodeType>
   Value qsearch(Position& pos, Stack* ss, Value alpha, Value beta, Depth depth) {
 
-    constexpr bool PvNode = NT == PV;
+    static_assert(nodeType != Root);
+    constexpr bool PvNode = nodeType == PV;
 
     assert(alpha >= -VALUE_INFINITE && alpha < beta && beta <= VALUE_INFINITE);
     assert(PvNode || (alpha == beta - 1));
@@ -1532,7 +1533,7 @@ moves_loop: // When in check, search starts from here
 
       // Make and search the move
       pos.do_move(move, st, givesCheck);
-      value = -qsearch<NT>(pos, ss+1, -beta, -alpha, depth - 1);
+      value = -qsearch<nodeType>(pos, ss+1, -beta, -alpha, depth - 1);
       pos.undo_move(move);
 
       assert(value > -VALUE_INFINITE && value < VALUE_INFINITE);