+ Threads.start_thinking(pos, states, limits, ponderMode);
+ }
+
+
+ // bench() is called when engine receives the "bench" command. Firstly
+ // a list of UCI commands is setup according to bench parameters, then
+ // it is run one by one printing a summary at the end.
+
+ void bench(Position& pos, istream& args, StateListPtr& states) {
+
+ string token;
+ uint64_t num, nodes = 0, cnt = 1;
+
+ vector<string> list = setup_bench(pos, args);
+ num = count_if(list.begin(), list.end(), [](string s) { return s.find("go ") == 0 || s.find("eval") == 0; });
+
+ TimePoint elapsed = now();
+
+ for (const auto& cmd : list)
+ {
+ istringstream is(cmd);
+ is >> skipws >> token;
+
+ if (token == "go" || token == "eval")
+ {
+ cerr << "\nPosition: " << cnt++ << '/' << num << " (" << pos.fen() << ")" << endl;
+ if (token == "go")
+ {
+ go(pos, is, states);
+ Threads.main()->wait_for_search_finished();
+ nodes += Threads.nodes_searched();
+ }
+ else
+ trace_eval(pos);
+ }
+ else if (token == "setoption") setoption(is);
+ else if (token == "position") position(pos, is, states);
+ else if (token == "ucinewgame") { Search::clear(); elapsed = now(); } // Search::clear() may take some while
+ }
+
+ elapsed = now() - elapsed + 1; // Ensure positivity to avoid a 'divide by zero'
+
+ dbg_print(); // Just before exiting
+
+ cerr << "\n==========================="
+ << "\nTotal time (ms) : " << elapsed
+ << "\nNodes searched : " << nodes
+ << "\nNodes/second : " << 1000 * nodes / elapsed << endl;
+ }
+
+ // The win rate model returns the probability (per mille) of winning given an eval
+ // and a game-ply. The model fits rather accurately the LTC fishtest statistics.
+ int win_rate_model(Value v, int ply) {
+
+ // The model captures only up to 240 plies, so limit input (and rescale)
+ double m = std::min(240, ply) / 64.0;
+
+ // Coefficients of a 3rd order polynomial fit based on fishtest data
+ // for two parameters needed to transform eval to the argument of a
+ // logistic function.
+ double as[] = {-3.68389304, 30.07065921, -60.52878723, 149.53378557};
+ double bs[] = {-2.0181857, 15.85685038, -29.83452023, 47.59078827};
+ double a = (((as[0] * m + as[1]) * m + as[2]) * m) + as[3];
+ double b = (((bs[0] * m + bs[1]) * m + bs[2]) * m) + bs[3];
+
+ // Transform eval to centipawns with limited range
+ double x = std::clamp(double(100 * v) / PawnValueEg, -2000.0, 2000.0);
+
+ // Return win rate in per mille (rounded to nearest)
+ return int(0.5 + 1000 / (1 + std::exp((a - x) / b)));