Restore "fail-low of reduced" and close regression

This reverts "Threat Extensions" and is the last of
this revert series.

In single-thread tests we should now be on par with 2.3.1

src/search.cpp

@@ -99,6 +99,7 @@ namespace {
   Value value_to_tt(Value v, int ply);
   Value value_from_tt(Value v, int ply);
   bool check_is_dangerous(Position& pos, Move move, Value futilityBase, Value beta);
+  bool allows_move(const Position& pos, Move first, Move second);
   bool prevents_move(const Position& pos, Move first, Move second);
   string uci_pv(const Position& pos, int depth, Value alpha, Value beta);
 
@@ -692,9 +693,21 @@ namespace {
                 return nullValue;
         }
         else
+        {
             // The null move failed low, which means that we may be faced with
-            // some kind of threat.
+            // some kind of threat. If the previous move was reduced, check if
+            // the move that refuted the null move was somehow connected to the
+            // move which was reduced. If a connection is found, return a fail
+            // low score (which will cause the reduced move to fail high in the
+            // parent node, which will trigger a re-search with full depth).
             threatMove = (ss+1)->currentMove;
+
+            if (   depth < 5 * ONE_PLY
+                && (ss-1)->reduction
+                && threatMove != MOVE_NONE
+                && allows_move(pos, (ss-1)->currentMove, threatMove))
+                return beta - 1;
+        }
     }
 
     // Step 9. ProbCut (is omitted in PV nodes)
@@ -847,12 +860,13 @@ split_point_start: // At split points actual search starts from here
           && !inCheck
           && !dangerous
           &&  move != ttMove
-          && (!threatMove || !prevents_move(pos, move, threatMove))
           && (bestValue > VALUE_MATED_IN_MAX_PLY || (   bestValue == -VALUE_INFINITE
                                                      && alpha > VALUE_MATED_IN_MAX_PLY)))
       {
           // Move count based pruning
-          if (depth < 16 * ONE_PLY && moveCount >= FutilityMoveCounts[depth])
+          if (   depth < 16 * ONE_PLY
+              && moveCount >= FutilityMoveCounts[depth]
+              && (!threatMove || !prevents_move(pos, move, threatMove)))
           {
               if (SpNode)
                   sp->mutex.lock();
@@ -1352,6 +1366,47 @@ split_point_start: // At split points actual search starts from here
   }
 
 
+  // allows_move() tests whether the move at previous ply (first) somehow makes a
+  // second move possible, for instance if the moving piece is the same in both
+  // moves. Normally the second move is the threat move (the best move returned
+  // from a null search that fails low).
+
+  bool allows_move(const Position& pos, Move first, Move second) {
+
+    assert(is_ok(first));
+    assert(is_ok(second));
+    assert(color_of(pos.piece_on(from_sq(second))) == ~pos.side_to_move());
+    assert(color_of(pos.piece_on(to_sq(first))) == ~pos.side_to_move());
+
+    Square m1from = from_sq(first);
+    Square m2from = from_sq(second);
+    Square m1to = to_sq(first);
+    Square m2to = to_sq(second);
+
+    // The piece is the same or second's destination was vacated by the first move
+    if (m1to == m2from || m2to == m1from)
+        return true;
+
+    // Second one moves through the square vacated by first one
+    if (between_bb(m2from, m2to) & m1from)
+      return true;
+
+    // Second's destination is defended by the first move's piece
+    Bitboard m1att = pos.attacks_from(pos.piece_on(m1to), m1to, pos.pieces() ^ m2from);
+    if (m1att & m2to)
+        return true;
+
+    // Second move gives a discovered check through the first's checking piece
+    if (m1att & pos.king_square(pos.side_to_move()))
+    {
+        assert(between_bb(m1to, pos.king_square(pos.side_to_move())) & m2from);
+        return true;
+    }
+
+    return false;
+  }
+
+
   // prevents_move() tests whether a move (first) is able to defend against an
   // opponent's move (second). In this case will not be pruned. Normally the
   // second move is the threat move (the best move returned from a null search