Fix go mate x in multithreading

Fixes two issues with master for go mate x:

- when running go mate x in losing positions, master always goes to the
  maximal depth, arguably against what the UCI protocol demands

- when running go mate x in winning positions with multiple
  threads, master may return non-mate scores from the search (this issue
  is present in stockfish since at least sf16) The issues are fixed by
  (a) also checking if score is mate -x and by (b) only letting
  mainthread stop the search for go mate x commands, and by not looking
  for a best thread but using mainthread as per the default. Related:
    niklasf/python-chess#1070

More diagnostics can be found here peregrineshahin#6 (comment)

closes #5094

No functional change

Co-Authored-By: Robert Nürnberg <[email protected]>

src/search.cpp

@@ -187,7 +187,7 @@ void Search::Worker::start_searching() {
     Skill   skill =
       Skill(options["Skill Level"], options["UCI_LimitStrength"] ? int(options["UCI_Elo"]) : 0);
 
-    if (int(options["MultiPV"]) == 1 && !limits.depth && !skill.enabled()
+    if (int(options["MultiPV"]) == 1 && !limits.depth && !limits.mate && !skill.enabled()
         && rootMoves[0].pv[0] != Move::none())
         bestThread = threads.get_best_thread()->worker.get();
 
@@ -399,14 +399,18 @@ void Search::Worker::iterative_deepening() {
             lastBestMoveDepth = rootDepth;
         }
 
-        // Have we found a "mate in x"?
-        if (limits.mate && bestValue >= VALUE_MATE_IN_MAX_PLY
-            && VALUE_MATE - bestValue <= 2 * limits.mate)
-            threads.stop = true;
-
         if (!mainThread)
             continue;
 
+        // Have we found a "mate in x"?
+        if (limits.mate && rootMoves[0].score == rootMoves[0].uciScore
+            && ((rootMoves[0].score >= VALUE_MATE_IN_MAX_PLY
+                 && VALUE_MATE - rootMoves[0].score <= 2 * limits.mate)
+                || (rootMoves[0].score != -VALUE_INFINITE
+                    && rootMoves[0].score <= VALUE_TB_LOSS_IN_MAX_PLY
+                    && VALUE_MATE + rootMoves[0].score <= 2 * limits.mate)))
+            threads.stop = true;
+
         // If the skill level is enabled and time is up, pick a sub-optimal best move
         if (skill.enabled() && skill.time_to_pick(rootDepth))
             skill.pick_best(rootMoves, multiPV);