Merge NNUE (master) in the cluster branch.

fixes minor merge conflicts, and a first quick testing looks OK:

4mpix4th vs 4th at 30+0.3s:

Score of cluster vs master: 3 - 0 - 37  [0.537] 40
Elo difference: 26.1 +/- 28.5, LOS: 95.8 %, DrawRatio: 92.5 %

No functional change.

src/uci.cpp

@@ -1,8 +1,6 @@
 /*
   Stockfish, a UCI chess playing engine derived from Glaurung 2.1
-  Copyright (C) 2004-2008 Tord Romstad (Glaurung author)
-  Copyright (C) 2008-2015 Marco Costalba, Joona Kiiski, Tord Romstad
-  Copyright (C) 2015-2020 Marco Costalba, Joona Kiiski, Gary Linscott, Tord Romstad
+  Copyright (C) 2004-2020 The Stockfish developers (see AUTHORS file)
 
   Stockfish is free software: you can redistribute it and/or modify
   it under the terms of the GNU General Public License as published by
@@ -19,6 +17,7 @@
 */
 
 #include <cassert>
+#include <cmath>
 #include <iostream>
 #include <sstream>
 #include <string>
@@ -78,6 +77,20 @@ namespace {
     }
   }
 
+  // trace_eval() prints the evaluation for the current position, consistent with the UCI
+  // options set so far.
+
+  void trace_eval(Position& pos) {
+
+    StateListPtr states(new std::deque<StateInfo>(1));
+    Position p;
+    p.set(pos.fen(), Options["UCI_Chess960"], &states->back(), Threads.main());
+
+    Eval::verify_NNUE();
+
+    sync_cout << "\n" << Eval::trace(p) << sync_endl;
+  }
+
 
   // setoption() is called when engine receives the "setoption" UCI command. The
   // function updates the UCI option ("name") to the given value ("value").
@@ -167,7 +180,7 @@ namespace {
                nodes += Threads.nodes_searched();
             }
             else if (Cluster::is_root())
-               sync_cout << "\n" << Eval::trace(pos) << sync_endl;
+               trace_eval(pos);
         }
         else if (token == "setoption")  setoption(is);
         else if (token == "position")   position(pos, is, states);
@@ -185,6 +198,28 @@ namespace {
              << "\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[] = {-8.24404295, 64.23892342, -95.73056462, 153.86478679};
+     double bs[] = {-3.37154371, 28.44489198, -56.67657741,  72.05858751};
+     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 = Utility::clamp(double(100 * v) / PawnValueEg, -1000.0, 1000.0);
+
+     // Return win rate in per mille (rounded to nearest)
+     return int(0.5 + 1000 / (1 + std::exp((a - x) / b)));
+  }
+
 } // namespace
 
 
@@ -244,7 +279,7 @@ void UCI::loop(int argc, char* argv[]) {
       else if (token == "d" && Cluster::is_root())
           sync_cout << pos << sync_endl;
       else if (token == "eval" && Cluster::is_root())
-          sync_cout << Eval::trace(pos) << sync_endl;
+          trace_eval(pos);
       else if (token == "compiler" && Cluster::is_root())
           sync_cout << compiler_info() << sync_endl;
       else if (Cluster::is_root())
@@ -276,6 +311,22 @@ string UCI::value(Value v) {
 }
 
 
+/// UCI::wdl() report WDL statistics given an evaluation and a game ply, based on
+/// data gathered for fishtest LTC games.
+
+string UCI::wdl(Value v, int ply) {
+
+  stringstream ss;
+
+  int wdl_w = win_rate_model( v, ply);
+  int wdl_l = win_rate_model(-v, ply);
+  int wdl_d = 1000 - wdl_w - wdl_l;
+  ss << " wdl " << wdl_w << " " << wdl_d << " " << wdl_l;
+
+  return ss.str();
+}
+
+
 /// UCI::square() converts a Square to a string in algebraic notation (g1, a7, etc.)
 
 std::string UCI::square(Square s) {