Change tempo with time and threads

Introduce variable tempo for nnue depending on logarithm of estimated
strength, where strength is the product of time and number of threads.

The original idea here was that NNUE is best with a slightly different
tempo value to classical, since its style of play is slightly different.
It turns out that the best tempo for NNUE varies with strength of play,
so a formula is used which gives about 19 for STC and 24 for LTC under
current fishtest settings.

STC 10+0.1:
LLR: 2.94 (-2.94,2.94) {-0.20,1.10}
Total: 120816 W: 11155 L: 10861 D: 98800
Ptnml(0-2): 406, 8728, 41933, 8848, 493
https://tests.stockfishchess.org/tests/view/60735b3a8141753378960534

LTC 60+0.6:
LLR: 2.94 (-2.94,2.94) {0.20,0.90}
Total: 35688 W: 1392 L: 1234 D: 33062
Ptnml(0-2): 23, 1079, 15473, 1255, 14
https://tests.stockfishchess.org/tests/view/6073ffbc814175337896057f

Passed non-regression SMP test at LTC 20+0.2 (8 threads):
LLR: 2.95 (-2.94,2.94) {-0.70,0.20}
Total: 11008 W: 317 L: 267 D: 10424
Ptnml(0-2): 2, 245, 4962, 291, 4
https://tests.stockfishchess.org/tests/view/60749ea881417533789605a4

closes https://github.com/official-stockfish/Stockfish/pull/3426

Bench 4075325

src/evaluate.cpp

@@ -33,6 +33,7 @@
 #include "misc.h"
 #include "pawns.h"
 #include "thread.h"
+#include "timeman.h"
 #include "uci.h"
 #include "incbin/incbin.h"
 
@@ -1096,7 +1097,7 @@ Value Eval::evaluate(const Position& pos) {
                     + material / 32
                     - 4 * pos.rule50_count();
 
-         Value nnue = NNUE::evaluate(pos) * scale / 1024 + Tempo;
+         Value nnue = NNUE::evaluate(pos) * scale / 1024 + Time.tempoNNUE;
 
          if (pos.is_chess960())
              nnue += fix_FRC(pos);

src/timeman.cpp

@@ -94,6 +94,14 @@ 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

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