Remove Tempo

The Tempo variable was introduced 10 years ago in our search because the
classical evaluation function was antisymmetrical in White and Black by design
to gain speed:

    Eval(White to play) = -Eval(Black to play)

Nowadays our neural networks know which side is to play in a position when
they evaluate a position and are trained on real games, so the neural network
encodes the advantage of moving as an output of search. This patch shows that
the Tempo variable is not necessary anymore.

STC:
LLR: 2.94 (-2.94,2.94) <-2.50,0.50>
Total: 33512 W: 2805 L: 2709 D: 27998
Ptnml(0-2): 80, 2209, 12095, 2279, 93
https://tests.stockfishchess.org/tests/view/60a44ceace8ea25a3ef03d30

LTC:
LLR: 2.95 (-2.94,2.94) <-2.50,0.50>
Total: 53920 W: 1807 L: 1760 D: 50353
Ptnml(0-2): 16, 1617, 23650, 1658, 19
https://tests.stockfishchess.org/tests/view/60a477f0ce8ea25a3ef03d49

We also tried a match (20000 games) at STC using purely classical, result was neutral:
https://tests.stockfishchess.org/tests/view/60a4eebcce8ea25a3ef03db5

Note: there are two locations left in search.cpp where we assume antisymmetry
of evaluation (in relation with a speed optimization for null moves in lines
770 and 1439), but as the values are just used for heuristic pruning this
approximation should not hurt too much because the order of magnitude is still
true most of the time.

closes https://github.com/official-stockfish/Stockfish/pull/3481

Bench: 4015864

src/evaluate.cpp

@@ -1058,7 +1058,7 @@ make_v:
     v = (v / 16) * 16;
 
     // Side to move point of view
-    v = (pos.side_to_move() == WHITE ? v : -v) + Tempo;
+    v = (pos.side_to_move() == WHITE ? v : -v);
 
     return v;
   }
@@ -1119,7 +1119,7 @@ Value Eval::evaluate(const Position& pos) {
 
          int scale = 903 + 28 * pos.count<PAWN>() + 28 * pos.non_pawn_material() / 1024;
 
-         Value nnue = NNUE::evaluate(pos) * scale / 1024 + Time.tempoNNUE;
+         Value nnue = NNUE::evaluate(pos) * scale / 1024;
 
          if (pos.is_chess960())
              nnue += fix_FRC(pos);

src/search.cpp

@@ -767,7 +767,7 @@ namespace {
         if ((ss-1)->currentMove != MOVE_NULL)
             ss->staticEval = eval = evaluate(pos);
         else
-            ss->staticEval = eval = -(ss-1)->staticEval + 2 * Tempo;
+            ss->staticEval = eval = -(ss-1)->staticEval;
 
         // Save static evaluation into transposition table
         tte->save(posKey, VALUE_NONE, ss->ttPv, BOUND_NONE, DEPTH_NONE, MOVE_NONE, eval);
@@ -776,7 +776,7 @@ namespace {
     // Use static evaluation difference to improve quiet move ordering
     if (is_ok((ss-1)->currentMove) && !(ss-1)->inCheck && !priorCapture)
     {
-        int bonus = std::clamp(-depth * 4 * int((ss-1)->staticEval + ss->staticEval - 2 * Tempo), -1000, 1000);
+        int bonus = std::clamp(-depth * 4 * int((ss-1)->staticEval + ss->staticEval), -1000, 1000);
         thisThread->mainHistory[~us][from_to((ss-1)->currentMove)] << bonus;
     }
 
@@ -1436,7 +1436,7 @@ moves_loop: // When in check, search starts from here
             // and addition of two tempos
             ss->staticEval = bestValue =
             (ss-1)->currentMove != MOVE_NULL ? evaluate(pos)
-                                             : -(ss-1)->staticEval + 2 * Tempo;
+                                             : -(ss-1)->staticEval;
 
         // Stand pat. Return immediately if static value is at least beta
         if (bestValue >= beta)

src/timeman.cpp

@@ -94,14 +94,6 @@ void TimeManagement::init(Search::LimitsType& limits, Color us, int ply) {
   optimumTime = TimePoint(optScale * timeLeft);
   maximumTime = TimePoint(std::min(0.8 * limits.time[us] - moveOverhead, maxScale * optimumTime));
 
-  if (Stockfish::Search::Limits.use_time_management())
-  {
-      int strength = std::log( std::max(1, int(optimumTime * Threads.size() / 10))) * 60;
-      tempoNNUE = std::clamp( (strength + 264) / 24, 18, 30);
-  }
-  else
-      tempoNNUE = 28; // default for no time given
-
   if (Options["Ponder"])
       optimumTime += optimumTime / 4;
 }

src/timeman.h

@@ -37,7 +37,6 @@ public:
                                      TimePoint(Threads.nodes_searched()) : now() - startTime; }
 
   int64_t availableNodes; // When in 'nodes as time' mode
-  int tempoNNUE;
 
 private:
   TimePoint startTime;

src/types.h

@@ -191,7 +191,6 @@ enum Value : int {
   BishopValueMg = 825,   BishopValueEg = 915,
   RookValueMg   = 1276,  RookValueEg   = 1380,
   QueenValueMg  = 2538,  QueenValueEg  = 2682,
-  Tempo = 28,
 
   MidgameLimit  = 15258, EndgameLimit  = 3915
 };