Introduce Triple Extensions

This replaces singularquietLMR with triple instead of double extending non-capture ttmoves that have value far below singularBeta. This threshold value is initially set to 200, there is scope for more scaling by reducing it as occured with double extensions.

Passed STC:
https://tests.stockfishchess.org/tests/view/65b683b8c865510db0274074
LLR: 2.95 (-2.94,2.94) <0.00,2.00>
Total: 222912 W: 58141 L: 57535 D: 107236
Ptnml(0-2): 1063, 26244, 56154, 27014, 981

Passed LTC:
https://tests.stockfishchess.org/tests/view/65bae6d4c865510db0278eb5
LLR: 2.94 (-2.94,2.94) <0.50,2.50>
Total: 66306 W: 16825 L: 16440 D: 33041
Ptnml(0-2): 40, 7374, 17952, 7735, 52

closes official-stockfish#5027

bench 1394701

src/search.cpp

@@ -522,7 +522,7 @@ Value Search::Worker::search(
     Move     ttMove, move, excludedMove, bestMove;
     Depth    extension, newDepth;
     Value    bestValue, value, ttValue, eval, maxValue, probCutBeta;
-    bool     givesCheck, improving, priorCapture, singularQuietLMR;
+    bool     givesCheck, improving, priorCapture;
     bool     capture, moveCountPruning, ttCapture;
     Piece    movedPiece;
     int      moveCount, captureCount, quietCount;
@@ -900,7 +900,7 @@ Value Search::Worker::search(
                   contHist, &thisThread->pawnHistory, countermove, ss->killers);
 
     value            = bestValue;
-    moveCountPruning = singularQuietLMR = false;
+    moveCountPruning = false;
 
     // Step 13. Loop through all pseudo-legal moves until no moves remain
     // or a beta cutoff occurs.
@@ -1035,13 +1035,12 @@ Value Search::Worker::search(
 
                 if (value < singularBeta)
                 {
-                    extension        = 1;
-                    singularQuietLMR = !ttCapture;
+                    extension = 1;
 
                     // Avoid search explosion by limiting the number of double extensions
-                    if (!PvNode && value < singularBeta - 2 && ss->doubleExtensions <= 12)
+                    if (!PvNode && value < singularBeta - 2 && ss->doubleExtensions <= 15)
                     {
-                        extension = 2;
+                        extension = 2 + (value < singularBeta - 200 && !ttCapture);
                         depth += depth < 15;
                     }
                 }
@@ -1092,7 +1091,7 @@ Value Search::Worker::search(
 
         // Add extension to new depth
         newDepth += extension;
-        ss->doubleExtensions = (ss - 1)->doubleExtensions + (extension == 2);
+        ss->doubleExtensions = (ss - 1)->doubleExtensions + (extension >= 2);
 
         // Speculative prefetch as early as possible
         prefetch(tt.first_entry(pos.key_after(move)));
@@ -1126,10 +1125,6 @@ Value Search::Worker::search(
         if (PvNode && tte->bound() != BOUND_UPPER)
             r--;
 
-        // Decrease reduction if a quiet ttMove has been singularly extended (~1 Elo)
-        if (singularQuietLMR)
-            r--;
-
         // Increase reduction on repetition (~1 Elo)
         if (move == (ss - 4)->currentMove && pos.has_repeated())
             r += 2;