Use node counting to early stop search

This introduces a form of node counting which can
be used to further tweak the usage of our search
time.
The current approach stops the search when almost
all nodes are searched on a single move.

The idea originally came from Koivisto, but the
implemention is a bit different, Koivisto scales
the optimal time by the nodes effort and then
determines if the search should be stopped.
We just scale down the `totalTime` and stop the
search if we exceed it and the effort is large
enough.

Passed STC:
https://tests.stockfishchess.org/tests/view/65c8e0661d8e83c78bfcd5ec
LLR: 2.97 (-2.94,2.94) <0.00,2.00>
Total: 88672 W: 22907 L: 22512 D: 43253
Ptnml(0-2): 310, 10163, 23041, 10466, 356

Passed LTC:
https://tests.stockfishchess.org/tests/view/65ca632b1d8e83c78bfcf554
LLR: 2.95 (-2.94,2.94) <0.50,2.50>
Total: 170856 W: 42910 L: 42320 D: 85626
Ptnml(0-2): 104, 18337, 47960, 18919, 108

closes https://github.com/official-stockfish/Stockfish/pull/5053

Bench: 1198939

src/search.cpp

@@ -23,6 +23,7 @@
 #include <atomic>
 #include <cassert>
 #include <cmath>
+#include <cstdint>
 #include <cstdlib>
 #include <initializer_list>
 #include <iostream>
@@ -418,6 +419,10 @@ void Search::Worker::iterative_deepening() {
         // Do we have time for the next iteration? Can we stop searching now?
         if (limits.use_time_management() && !threads.stop && !mainThread->stopOnPonderhit)
         {
+            auto bestmove    = rootMoves[0].pv[0];
+            int  nodesEffort = effort[bestmove.from_sq()][bestmove.to_sq()] * 100
+                            / std::max(size_t(1), size_t(nodes));
+
             double fallingEval = (66 + 14 * (mainThread->bestPreviousAverageScore - bestValue)
                                   + 6 * (mainThread->iterValue[iterIdx] - bestValue))
                                / 616.6;
@@ -435,6 +440,13 @@ void Search::Worker::iterative_deepening() {
             if (rootMoves.size() == 1)
                 totalTime = std::min(500.0, totalTime);
 
+            if (completedDepth >= 10 && nodesEffort >= 95
+                && mainThread->tm.elapsed(threads.nodes_searched()) > totalTime * 3 / 4
+                && !mainThread->ponder)
+            {
+                threads.stop = true;
+            }
+
             // Stop the search if we have exceeded the totalTime
             if (mainThread->tm.elapsed(threads.nodes_searched()) > totalTime)
             {
@@ -1087,6 +1099,8 @@ moves_loop:  // When in check, search starts here
         ss->continuationHistory =
           &thisThread->continuationHistory[ss->inCheck][capture][movedPiece][move.to_sq()];
 
+        uint64_t nodeCount = rootNode ? uint64_t(nodes) : 0;
+
         // Step 16. Make the move
         thisThread->nodes.fetch_add(1, std::memory_order_relaxed);
         pos.do_move(move, st, givesCheck);
@@ -1186,6 +1200,9 @@ moves_loop:  // When in check, search starts here
         // Step 19. Undo move
         pos.undo_move(move);
 
+        if (rootNode)
+            effort[move.from_sq()][move.to_sq()] += nodes - nodeCount;
+
         assert(value > -VALUE_INFINITE && value < VALUE_INFINITE);
 
         // Step 20. Check for a new best move

src/search.h

@@ -219,6 +219,8 @@ class Worker {
         return static_cast<SearchManager*>(manager.get());
     }
 
+    std::array<std::array<uint64_t, SQUARE_NB>, SQUARE_NB> effort;
+
     LimitsType limits;
 
     size_t                pvIdx, pvLast;

src/thread.cpp

@@ -24,6 +24,7 @@
 #include <memory>
 #include <unordered_map>
 #include <utility>
+#include <array>
 
 #include "misc.h"
 #include "movegen.h"
@@ -203,6 +204,7 @@ void ThreadPool::start_thinking(const OptionsMap&  options,
         th->worker->rootPos.set(pos.fen(), pos.is_chess960(), &th->worker->rootState);
         th->worker->rootState = setupStates->back();
         th->worker->tbConfig  = tbConfig;
+        th->worker->effort    = {};
     }
 
     main_thread()->start_searching();