2 Stockfish, a UCI chess playing engine derived from Glaurung 2.1
3 Copyright (C) 2004-2023 The Stockfish developers (see AUTHORS file)
5 Stockfish is free software: you can redistribute it and/or modify
6 it under the terms of the GNU General Public License as published by
7 the Free Software Foundation, either version 3 of the License, or
8 (at your option) any later version.
10 Stockfish is distributed in the hope that it will be useful,
11 but WITHOUT ANY WARRANTY; without even the implied warranty of
12 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
13 GNU General Public License for more details.
15 You should have received a copy of the GNU General Public License
16 along with this program. If not, see <http://www.gnu.org/licenses/>.
28 #include <initializer_list>
39 #include "nnue/evaluate_nnue.h"
40 #include "nnue/nnue_common.h"
42 #include "syzygy/tbprobe.h"
55 namespace Tablebases {
63 namespace TB = Tablebases;
67 using namespace Search;
71 // Different node types, used as a template parameter
79 Value futility_margin(Depth d, bool noTtCutNode, bool improving) {
80 return Value((116 - 44 * noTtCutNode) * (d - improving));
83 // Reductions lookup table initialized at startup
84 int Reductions[MAX_MOVES]; // [depth or moveNumber]
86 Depth reduction(bool i, Depth d, int mn, Value delta, Value rootDelta) {
87 int reductionScale = Reductions[d] * Reductions[mn];
88 return (reductionScale + 1346 - int(delta) * 896 / int(rootDelta)) / 1024
89 + (!i && reductionScale > 880);
92 constexpr int futility_move_count(bool improving, Depth depth) {
93 return improving ? (3 + depth * depth) : (3 + depth * depth) / 2;
96 // History and stats update bonus, based on depth
97 int stat_bonus(Depth d) { return std::min(268 * d - 352, 1153); }
99 // History and stats update malus, based on depth
100 int stat_malus(Depth d) { return std::min(400 * d - 354, 1201); }
102 // Add a small random component to draw evaluations to avoid 3-fold blindness
103 Value value_draw(const Thread* thisThread) {
104 return VALUE_DRAW - 1 + Value(thisThread->nodes & 0x2);
107 // Skill structure is used to implement strength limit. If we have a UCI_Elo,
108 // we convert it to an appropriate skill level, anchored to the Stash engine.
109 // This method is based on a fit of the Elo results for games played between
110 // Stockfish at various skill levels and various versions of the Stash engine.
111 // Skill 0 .. 19 now covers CCRL Blitz Elo from 1320 to 3190, approximately
112 // Reference: https://github.com/vondele/Stockfish/commit/a08b8d4e9711c2
114 Skill(int skill_level, int uci_elo) {
117 double e = double(uci_elo - 1320) / (3190 - 1320);
118 level = std::clamp((((37.2473 * e - 40.8525) * e + 22.2943) * e - 0.311438), 0.0, 19.0);
121 level = double(skill_level);
123 bool enabled() const { return level < 20.0; }
124 bool time_to_pick(Depth depth) const { return depth == 1 + int(level); }
125 Move pick_best(size_t multiPV);
128 Move best = MOVE_NONE;
131 template<NodeType nodeType>
132 Value search(Position& pos, Stack* ss, Value alpha, Value beta, Depth depth, bool cutNode);
134 template<NodeType nodeType>
135 Value qsearch(Position& pos, Stack* ss, Value alpha, Value beta, Depth depth = 0);
137 Value value_to_tt(Value v, int ply);
138 Value value_from_tt(Value v, int ply, int r50c);
139 void update_pv(Move* pv, Move move, const Move* childPv);
140 void update_continuation_histories(Stack* ss, Piece pc, Square to, int bonus);
141 void update_quiet_stats(const Position& pos, Stack* ss, Move move, int bonus);
142 void update_all_stats(const Position& pos,
148 Move* quietsSearched,
150 Move* capturesSearched,
154 // Utility to verify move generation. All the leaf nodes up
155 // to the given depth are generated and counted, and the sum is returned.
157 uint64_t perft(Position& pos, Depth depth) {
160 ASSERT_ALIGNED(&st, Eval::NNUE::CacheLineSize);
162 uint64_t cnt, nodes = 0;
163 const bool leaf = (depth == 2);
165 for (const auto& m : MoveList<LEGAL>(pos))
167 if (Root && depth <= 1)
172 cnt = leaf ? MoveList<LEGAL>(pos).size() : perft<false>(pos, depth - 1);
177 sync_cout << UCI::move(m, pos.is_chess960()) << ": " << cnt << sync_endl;
185 // Called at startup to initialize various lookup tables
186 void Search::init() {
188 for (int i = 1; i < MAX_MOVES; ++i)
189 Reductions[i] = int((20.37 + std::log(Threads.size()) / 2) * std::log(i));
193 // Resets search state to its initial value
194 void Search::clear() {
196 Threads.main()->wait_for_search_finished();
198 Time.availableNodes = 0;
201 Tablebases::init(Options["SyzygyPath"]); // Free mapped files
205 // Called when the program receives the UCI 'go'
206 // command. It searches from the root position and outputs the "bestmove".
207 void MainThread::search() {
211 nodes = perft<true>(rootPos, Limits.perft);
212 sync_cout << "\nNodes searched: " << nodes << "\n" << sync_endl;
216 Color us = rootPos.side_to_move();
217 Time.init(Limits, us, rootPos.game_ply());
220 Eval::NNUE::verify();
222 if (rootMoves.empty())
224 rootMoves.emplace_back(MOVE_NONE);
225 sync_cout << "info depth 0 score "
226 << UCI::value(rootPos.checkers() ? -VALUE_MATE : VALUE_DRAW) << sync_endl;
230 Threads.start_searching(); // start non-main threads
231 Thread::search(); // main thread start searching
234 // When we reach the maximum depth, we can arrive here without a raise of
235 // Threads.stop. However, if we are pondering or in an infinite search,
236 // the UCI protocol states that we shouldn't print the best move before the
237 // GUI sends a "stop" or "ponderhit" command. We therefore simply wait here
238 // until the GUI sends one of those commands.
240 while (!Threads.stop && (ponder || Limits.infinite))
241 {} // Busy wait for a stop or a ponder reset
243 // Stop the threads if not already stopped (also raise the stop if
244 // "ponderhit" just reset Threads.ponder).
247 // Wait until all threads have finished
248 Threads.wait_for_search_finished();
250 // When playing in 'nodes as time' mode, subtract the searched nodes from
251 // the available ones before exiting.
253 Time.availableNodes += Limits.inc[us] - Threads.nodes_searched();
255 Thread* bestThread = this;
257 Skill(Options["Skill Level"], Options["UCI_LimitStrength"] ? int(Options["UCI_Elo"]) : 0);
259 if (int(Options["MultiPV"]) == 1 && !Limits.depth && !skill.enabled()
260 && rootMoves[0].pv[0] != MOVE_NONE)
261 bestThread = Threads.get_best_thread();
263 bestPreviousScore = bestThread->rootMoves[0].score;
264 bestPreviousAverageScore = bestThread->rootMoves[0].averageScore;
266 // Send again PV info if we have a new best thread
267 if (bestThread != this)
268 sync_cout << UCI::pv(bestThread->rootPos, bestThread->completedDepth) << sync_endl;
270 sync_cout << "bestmove " << UCI::move(bestThread->rootMoves[0].pv[0], rootPos.is_chess960());
272 if (bestThread->rootMoves[0].pv.size() > 1
273 || bestThread->rootMoves[0].extract_ponder_from_tt(rootPos))
274 std::cout << " ponder " << UCI::move(bestThread->rootMoves[0].pv[1], rootPos.is_chess960());
276 std::cout << sync_endl;
280 // Main iterative deepening loop. It calls search()
281 // repeatedly with increasing depth until the allocated thinking time has been
282 // consumed, the user stops the search, or the maximum search depth is reached.
283 void Thread::search() {
285 // Allocate stack with extra size to allow access from (ss - 7) to (ss + 2):
286 // (ss - 7) is needed for update_continuation_histories(ss - 1) which accesses (ss - 6),
287 // (ss + 2) is needed for initialization of cutOffCnt and killers.
288 Stack stack[MAX_PLY + 10], *ss = stack + 7;
289 Move pv[MAX_PLY + 1];
290 Value alpha, beta, delta;
291 Move lastBestMove = MOVE_NONE;
292 Depth lastBestMoveDepth = 0;
293 MainThread* mainThread = (this == Threads.main() ? Threads.main() : nullptr);
294 double timeReduction = 1, totBestMoveChanges = 0;
295 Color us = rootPos.side_to_move();
298 std::memset(ss - 7, 0, 10 * sizeof(Stack));
299 for (int i = 7; i > 0; --i)
301 (ss - i)->continuationHistory =
302 &this->continuationHistory[0][0][NO_PIECE][0]; // Use as a sentinel
303 (ss - i)->staticEval = VALUE_NONE;
306 for (int i = 0; i <= MAX_PLY + 2; ++i)
311 bestValue = -VALUE_INFINITE;
315 if (mainThread->bestPreviousScore == VALUE_INFINITE)
316 for (int i = 0; i < 4; ++i)
317 mainThread->iterValue[i] = VALUE_ZERO;
319 for (int i = 0; i < 4; ++i)
320 mainThread->iterValue[i] = mainThread->bestPreviousScore;
323 size_t multiPV = size_t(Options["MultiPV"]);
324 Skill skill(Options["Skill Level"], Options["UCI_LimitStrength"] ? int(Options["UCI_Elo"]) : 0);
326 // When playing with strength handicap enable MultiPV search that we will
327 // use behind-the-scenes to retrieve a set of possible moves.
329 multiPV = std::max(multiPV, size_t(4));
331 multiPV = std::min(multiPV, rootMoves.size());
333 int searchAgainCounter = 0;
335 // Iterative deepening loop until requested to stop or the target depth is reached
336 while (++rootDepth < MAX_PLY && !Threads.stop
337 && !(Limits.depth && mainThread && rootDepth > Limits.depth))
339 // Age out PV variability metric
341 totBestMoveChanges /= 2;
343 // Save the last iteration's scores before the first PV line is searched and
344 // all the move scores except the (new) PV are set to -VALUE_INFINITE.
345 for (RootMove& rm : rootMoves)
346 rm.previousScore = rm.score;
351 if (!Threads.increaseDepth)
352 searchAgainCounter++;
354 // MultiPV loop. We perform a full root search for each PV line
355 for (pvIdx = 0; pvIdx < multiPV && !Threads.stop; ++pvIdx)
360 for (pvLast++; pvLast < rootMoves.size(); pvLast++)
361 if (rootMoves[pvLast].tbRank != rootMoves[pvFirst].tbRank)
365 // Reset UCI info selDepth for each depth and each PV line
368 // Reset aspiration window starting size
369 Value avg = rootMoves[pvIdx].averageScore;
370 delta = Value(9) + int(avg) * avg / 14847;
371 alpha = std::max(avg - delta, -VALUE_INFINITE);
372 beta = std::min(avg + delta, VALUE_INFINITE);
374 // Adjust optimism based on root move's averageScore (~4 Elo)
375 optimism[us] = 121 * avg / (std::abs(avg) + 109);
376 optimism[~us] = -optimism[us];
378 // Start with a small aspiration window and, in the case of a fail
379 // high/low, re-search with a bigger window until we don't fail
381 int failedHighCnt = 0;
384 // Adjust the effective depth searched, but ensure at least one effective increment
385 // for every four searchAgain steps (see issue #2717).
386 Depth adjustedDepth =
387 std::max(1, rootDepth - failedHighCnt - 3 * (searchAgainCounter + 1) / 4);
388 bestValue = Stockfish::search<Root>(rootPos, ss, alpha, beta, adjustedDepth, false);
390 // Bring the best move to the front. It is critical that sorting
391 // is done with a stable algorithm because all the values but the
392 // first and eventually the new best one is set to -VALUE_INFINITE
393 // and we want to keep the same order for all the moves except the
394 // new PV that goes to the front. Note that in the case of MultiPV
395 // search the already searched PV lines are preserved.
396 std::stable_sort(rootMoves.begin() + pvIdx, rootMoves.begin() + pvLast);
398 // If search has been stopped, we break immediately. Sorting is
399 // safe because RootMoves is still valid, although it refers to
400 // the previous iteration.
404 // When failing high/low give some update (without cluttering
405 // the UI) before a re-search.
406 if (mainThread && multiPV == 1 && (bestValue <= alpha || bestValue >= beta)
407 && Time.elapsed() > 3000)
408 sync_cout << UCI::pv(rootPos, rootDepth) << sync_endl;
410 // In case of failing low/high increase aspiration window and
411 // re-search, otherwise exit the loop.
412 if (bestValue <= alpha)
414 beta = (alpha + beta) / 2;
415 alpha = std::max(bestValue - delta, -VALUE_INFINITE);
419 mainThread->stopOnPonderhit = false;
421 else if (bestValue >= beta)
423 beta = std::min(bestValue + delta, VALUE_INFINITE);
431 assert(alpha >= -VALUE_INFINITE && beta <= VALUE_INFINITE);
434 // Sort the PV lines searched so far and update the GUI
435 std::stable_sort(rootMoves.begin() + pvFirst, rootMoves.begin() + pvIdx + 1);
437 if (mainThread && (Threads.stop || pvIdx + 1 == multiPV || Time.elapsed() > 3000))
438 sync_cout << UCI::pv(rootPos, rootDepth) << sync_endl;
442 completedDepth = rootDepth;
444 if (rootMoves[0].pv[0] != lastBestMove)
446 lastBestMove = rootMoves[0].pv[0];
447 lastBestMoveDepth = rootDepth;
450 // Have we found a "mate in x"?
451 if (Limits.mate && bestValue >= VALUE_MATE_IN_MAX_PLY
452 && VALUE_MATE - bestValue <= 2 * Limits.mate)
458 // If the skill level is enabled and time is up, pick a sub-optimal best move
459 if (skill.enabled() && skill.time_to_pick(rootDepth))
460 skill.pick_best(multiPV);
462 // Use part of the gained time from a previous stable move for the current move
463 for (Thread* th : Threads)
465 totBestMoveChanges += th->bestMoveChanges;
466 th->bestMoveChanges = 0;
469 // Do we have time for the next iteration? Can we stop searching now?
470 if (Limits.use_time_management() && !Threads.stop && !mainThread->stopOnPonderhit)
472 double fallingEval = (66 + 14 * (mainThread->bestPreviousAverageScore - bestValue)
473 + 6 * (mainThread->iterValue[iterIdx] - bestValue))
475 fallingEval = std::clamp(fallingEval, 0.5, 1.5);
477 // If the bestMove is stable over several iterations, reduce time accordingly
478 timeReduction = lastBestMoveDepth + 8 < completedDepth ? 1.56 : 0.69;
479 double reduction = (1.4 + mainThread->previousTimeReduction) / (2.03 * timeReduction);
480 double bestMoveInstability = 1 + 1.79 * totBestMoveChanges / Threads.size();
482 double totalTime = Time.optimum() * fallingEval * reduction * bestMoveInstability;
484 // Cap used time in case of a single legal move for a better viewer experience
485 if (rootMoves.size() == 1)
486 totalTime = std::min(500.0, totalTime);
488 // Stop the search if we have exceeded the totalTime
489 if (Time.elapsed() > totalTime)
491 // If we are allowed to ponder do not stop the search now but
492 // keep pondering until the GUI sends "ponderhit" or "stop".
493 if (mainThread->ponder)
494 mainThread->stopOnPonderhit = true;
498 else if (!mainThread->ponder && Time.elapsed() > totalTime * 0.50)
499 Threads.increaseDepth = false;
501 Threads.increaseDepth = true;
504 mainThread->iterValue[iterIdx] = bestValue;
505 iterIdx = (iterIdx + 1) & 3;
511 mainThread->previousTimeReduction = timeReduction;
513 // If the skill level is enabled, swap the best PV line with the sub-optimal one
515 std::swap(rootMoves[0], *std::find(rootMoves.begin(), rootMoves.end(),
516 skill.best ? skill.best : skill.pick_best(multiPV)));
522 // Main search function for both PV and non-PV nodes
523 template<NodeType nodeType>
524 Value search(Position& pos, Stack* ss, Value alpha, Value beta, Depth depth, bool cutNode) {
526 constexpr bool PvNode = nodeType != NonPV;
527 constexpr bool rootNode = nodeType == Root;
529 // Dive into quiescence search when the depth reaches zero
531 return qsearch < PvNode ? PV : NonPV > (pos, ss, alpha, beta);
533 // Check if we have an upcoming move that draws by repetition, or
534 // if the opponent had an alternative move earlier to this position.
535 if (!rootNode && alpha < VALUE_DRAW && pos.has_game_cycle(ss->ply))
537 alpha = value_draw(pos.this_thread());
542 assert(-VALUE_INFINITE <= alpha && alpha < beta && beta <= VALUE_INFINITE);
543 assert(PvNode || (alpha == beta - 1));
544 assert(0 < depth && depth < MAX_PLY);
545 assert(!(PvNode && cutNode));
547 Move pv[MAX_PLY + 1], capturesSearched[32], quietsSearched[32];
549 ASSERT_ALIGNED(&st, Eval::NNUE::CacheLineSize);
553 Move ttMove, move, excludedMove, bestMove;
554 Depth extension, newDepth;
555 Value bestValue, value, ttValue, eval, maxValue, probCutBeta;
556 bool givesCheck, improving, priorCapture, singularQuietLMR;
557 bool capture, moveCountPruning, ttCapture;
559 int moveCount, captureCount, quietCount;
561 // Step 1. Initialize node
562 Thread* thisThread = pos.this_thread();
563 ss->inCheck = pos.checkers();
564 priorCapture = pos.captured_piece();
565 Color us = pos.side_to_move();
566 moveCount = captureCount = quietCount = ss->moveCount = 0;
567 bestValue = -VALUE_INFINITE;
568 maxValue = VALUE_INFINITE;
570 // Check for the available remaining time
571 if (thisThread == Threads.main())
572 static_cast<MainThread*>(thisThread)->check_time();
574 // Used to send selDepth info to GUI (selDepth counts from 1, ply from 0)
575 if (PvNode && thisThread->selDepth < ss->ply + 1)
576 thisThread->selDepth = ss->ply + 1;
580 // Step 2. Check for aborted search and immediate draw
581 if (Threads.stop.load(std::memory_order_relaxed) || pos.is_draw(ss->ply)
582 || ss->ply >= MAX_PLY)
583 return (ss->ply >= MAX_PLY && !ss->inCheck) ? evaluate(pos)
584 : value_draw(pos.this_thread());
586 // Step 3. Mate distance pruning. Even if we mate at the next move our score
587 // would be at best mate_in(ss->ply + 1), but if alpha is already bigger because
588 // a shorter mate was found upward in the tree then there is no need to search
589 // because we will never beat the current alpha. Same logic but with reversed
590 // signs apply also in the opposite condition of being mated instead of giving
591 // mate. In this case, return a fail-high score.
592 alpha = std::max(mated_in(ss->ply), alpha);
593 beta = std::min(mate_in(ss->ply + 1), beta);
598 thisThread->rootDelta = beta - alpha;
600 assert(0 <= ss->ply && ss->ply < MAX_PLY);
602 (ss + 1)->excludedMove = bestMove = MOVE_NONE;
603 (ss + 2)->killers[0] = (ss + 2)->killers[1] = MOVE_NONE;
604 (ss + 2)->cutoffCnt = 0;
605 ss->doubleExtensions = (ss - 1)->doubleExtensions;
606 Square prevSq = is_ok((ss - 1)->currentMove) ? to_sq((ss - 1)->currentMove) : SQ_NONE;
609 // Step 4. Transposition table lookup.
610 excludedMove = ss->excludedMove;
612 tte = TT.probe(posKey, ss->ttHit);
613 ttValue = ss->ttHit ? value_from_tt(tte->value(), ss->ply, pos.rule50_count()) : VALUE_NONE;
614 ttMove = rootNode ? thisThread->rootMoves[thisThread->pvIdx].pv[0]
615 : ss->ttHit ? tte->move()
617 ttCapture = ttMove && pos.capture_stage(ttMove);
619 // At this point, if excluded, skip straight to step 6, static eval. However,
620 // to save indentation, we list the condition in all code between here and there.
622 ss->ttPv = PvNode || (ss->ttHit && tte->is_pv());
624 // At non-PV nodes we check for an early TT cutoff
625 if (!PvNode && !excludedMove && tte->depth() > depth
626 && ttValue != VALUE_NONE // Possible in case of TT access race or if !ttHit
627 && (tte->bound() & (ttValue >= beta ? BOUND_LOWER : BOUND_UPPER)))
629 // If ttMove is quiet, update move sorting heuristics on TT hit (~2 Elo)
634 // Bonus for a quiet ttMove that fails high (~2 Elo)
636 update_quiet_stats(pos, ss, ttMove, stat_bonus(depth));
638 // Extra penalty for early quiet moves of
639 // the previous ply (~0 Elo on STC, ~2 Elo on LTC).
640 if (prevSq != SQ_NONE && (ss - 1)->moveCount <= 2 && !priorCapture)
641 update_continuation_histories(ss - 1, pos.piece_on(prevSq), prevSq,
642 -stat_malus(depth + 1));
644 // Penalty for a quiet ttMove that fails low (~1 Elo)
647 int penalty = -stat_malus(depth);
648 thisThread->mainHistory[us][from_to(ttMove)] << penalty;
649 update_continuation_histories(ss, pos.moved_piece(ttMove), to_sq(ttMove), penalty);
653 // Partial workaround for the graph history interaction problem
654 // For high rule50 counts don't produce transposition table cutoffs.
655 if (pos.rule50_count() < 90)
659 // Step 5. Tablebases probe
660 if (!rootNode && !excludedMove && TB::Cardinality)
662 int piecesCount = pos.count<ALL_PIECES>();
664 if (piecesCount <= TB::Cardinality
665 && (piecesCount < TB::Cardinality || depth >= TB::ProbeDepth) && pos.rule50_count() == 0
666 && !pos.can_castle(ANY_CASTLING))
669 TB::WDLScore wdl = Tablebases::probe_wdl(pos, &err);
671 // Force check of time on the next occasion
672 if (thisThread == Threads.main())
673 static_cast<MainThread*>(thisThread)->callsCnt = 0;
675 if (err != TB::ProbeState::FAIL)
677 thisThread->tbHits.fetch_add(1, std::memory_order_relaxed);
679 int drawScore = TB::UseRule50 ? 1 : 0;
681 Value tbValue = VALUE_TB - ss->ply;
683 // use the range VALUE_TB to VALUE_TB_WIN_IN_MAX_PLY to score
684 value = wdl < -drawScore ? -tbValue
685 : wdl > drawScore ? tbValue
686 : VALUE_DRAW + 2 * wdl * drawScore;
688 Bound b = wdl < -drawScore ? BOUND_UPPER
689 : wdl > drawScore ? BOUND_LOWER
692 if (b == BOUND_EXACT || (b == BOUND_LOWER ? value >= beta : value <= alpha))
694 tte->save(posKey, value_to_tt(value, ss->ply), ss->ttPv, b,
695 std::min(MAX_PLY - 1, depth + 6), MOVE_NONE, VALUE_NONE);
702 if (b == BOUND_LOWER)
703 bestValue = value, alpha = std::max(alpha, bestValue);
711 CapturePieceToHistory& captureHistory = thisThread->captureHistory;
713 // Step 6. Static evaluation of the position
716 // Skip early pruning when in check
717 ss->staticEval = eval = VALUE_NONE;
721 else if (excludedMove)
723 // Providing the hint that this node's accumulator will be used often
724 // brings significant Elo gain (~13 Elo).
725 Eval::NNUE::hint_common_parent_position(pos);
726 eval = ss->staticEval;
730 // Never assume anything about values stored in TT
731 ss->staticEval = eval = tte->eval();
732 if (eval == VALUE_NONE)
733 ss->staticEval = eval = evaluate(pos);
735 Eval::NNUE::hint_common_parent_position(pos);
737 // ttValue can be used as a better position evaluation (~7 Elo)
738 if (ttValue != VALUE_NONE && (tte->bound() & (ttValue > eval ? BOUND_LOWER : BOUND_UPPER)))
743 ss->staticEval = eval = evaluate(pos);
744 // Save static evaluation into the transposition table
745 tte->save(posKey, VALUE_NONE, ss->ttPv, BOUND_NONE, DEPTH_NONE, MOVE_NONE, eval);
748 // Use static evaluation difference to improve quiet move ordering (~4 Elo)
749 if (is_ok((ss - 1)->currentMove) && !(ss - 1)->inCheck && !priorCapture)
751 int bonus = std::clamp(-13 * int((ss - 1)->staticEval + ss->staticEval), -1555, 1452);
752 thisThread->mainHistory[~us][from_to((ss - 1)->currentMove)] << bonus;
753 if (type_of(pos.piece_on(prevSq)) != PAWN && type_of((ss - 1)->currentMove) != PROMOTION)
754 thisThread->pawnHistory[pawn_structure(pos)][pos.piece_on(prevSq)][prevSq] << bonus / 4;
757 // Set up the improving flag, which is true if current static evaluation is
758 // bigger than the previous static evaluation at our turn (if we were in
759 // check at our previous move we look at static evaluation at move prior to it
760 // and if we were in check at move prior to it flag is set to true) and is
761 // false otherwise. The improving flag is used in various pruning heuristics.
762 improving = (ss - 2)->staticEval != VALUE_NONE ? ss->staticEval > (ss - 2)->staticEval
763 : (ss - 4)->staticEval != VALUE_NONE ? ss->staticEval > (ss - 4)->staticEval
766 // Step 7. Razoring (~1 Elo)
767 // If eval is really low check with qsearch if it can exceed alpha, if it can't,
768 // return a fail low.
769 // Adjust razor margin according to cutoffCnt. (~1 Elo)
770 if (eval < alpha - 472 - (284 - 165 * ((ss + 1)->cutoffCnt > 3)) * depth * depth)
772 value = qsearch<NonPV>(pos, ss, alpha - 1, alpha);
777 // Step 8. Futility pruning: child node (~40 Elo)
778 // The depth condition is important for mate finding.
779 if (!ss->ttPv && depth < 9
780 && eval - futility_margin(depth, cutNode && !ss->ttHit, improving)
781 - (ss - 1)->statScore / 337
783 && eval >= beta && eval < 29008 // smaller than TB wins
784 && (!ttMove || ttCapture))
785 return (eval + beta) / 2;
787 // Step 9. Null move search with verification search (~35 Elo)
788 if (!PvNode && (ss - 1)->currentMove != MOVE_NULL && (ss - 1)->statScore < 17496 && eval >= beta
789 && eval >= ss->staticEval && ss->staticEval >= beta - 23 * depth + 304 && !excludedMove
790 && pos.non_pawn_material(us) && ss->ply >= thisThread->nmpMinPly
791 && beta > VALUE_TB_LOSS_IN_MAX_PLY)
793 assert(eval - beta >= 0);
795 // Null move dynamic reduction based on depth and eval
796 Depth R = std::min(int(eval - beta) / 144, 6) + depth / 3 + 4;
798 ss->currentMove = MOVE_NULL;
799 ss->continuationHistory = &thisThread->continuationHistory[0][0][NO_PIECE][0];
801 pos.do_null_move(st);
803 Value nullValue = -search<NonPV>(pos, ss + 1, -beta, -beta + 1, depth - R, !cutNode);
805 pos.undo_null_move();
807 // Do not return unproven mate or TB scores
808 if (nullValue >= beta && nullValue < VALUE_TB_WIN_IN_MAX_PLY)
810 if (thisThread->nmpMinPly || depth < 15)
813 assert(!thisThread->nmpMinPly); // Recursive verification is not allowed
815 // Do verification search at high depths, with null move pruning disabled
816 // until ply exceeds nmpMinPly.
817 thisThread->nmpMinPly = ss->ply + 3 * (depth - R) / 4;
819 Value v = search<NonPV>(pos, ss, beta - 1, beta, depth - R, false);
821 thisThread->nmpMinPly = 0;
828 // Step 10. Internal iterative reductions (~9 Elo)
829 // For PV nodes without a ttMove, we decrease depth by 2,
830 // or by 4 if the current position is present in the TT and
831 // the stored depth is greater than or equal to the current depth.
832 // Use qsearch if depth <= 0.
833 if (PvNode && !ttMove)
834 depth -= 2 + 2 * (ss->ttHit && tte->depth() >= depth);
837 return qsearch<PV>(pos, ss, alpha, beta);
839 // For cutNodes without a ttMove, we decrease depth by 2 if depth is high enough.
840 if (cutNode && depth >= 8 && !ttMove)
843 probCutBeta = beta + 163 - 67 * improving;
845 // Step 11. ProbCut (~10 Elo)
846 // If we have a good enough capture (or queen promotion) and a reduced search returns a value
847 // much above beta, we can (almost) safely prune the previous move.
850 && abs(beta) < VALUE_TB_WIN_IN_MAX_PLY
851 // If value from transposition table is lower than probCutBeta, don't attempt probCut
852 // there and in further interactions with transposition table cutoff depth is set to depth - 3
853 // because probCut search has depth set to depth - 4 but we also do a move before it
854 // So effective depth is equal to depth - 3
855 && !(tte->depth() >= depth - 3 && ttValue != VALUE_NONE && ttValue < probCutBeta))
857 assert(probCutBeta < VALUE_INFINITE);
859 MovePicker mp(pos, ttMove, probCutBeta - ss->staticEval, &captureHistory);
861 while ((move = mp.next_move()) != MOVE_NONE)
862 if (move != excludedMove && pos.legal(move))
864 assert(pos.capture_stage(move));
866 // Prefetch the TT entry for the resulting position
867 prefetch(TT.first_entry(pos.key_after(move)));
869 ss->currentMove = move;
870 ss->continuationHistory =
872 ->continuationHistory[ss->inCheck][true][pos.moved_piece(move)][to_sq(move)];
874 pos.do_move(move, st);
876 // Perform a preliminary qsearch to verify that the move holds
877 value = -qsearch<NonPV>(pos, ss + 1, -probCutBeta, -probCutBeta + 1);
879 // If the qsearch held, perform the regular search
880 if (value >= probCutBeta)
881 value = -search<NonPV>(pos, ss + 1, -probCutBeta, -probCutBeta + 1, depth - 4,
886 if (value >= probCutBeta)
888 // Save ProbCut data into transposition table
889 tte->save(posKey, value_to_tt(value, ss->ply), ss->ttPv, BOUND_LOWER, depth - 3,
890 move, ss->staticEval);
891 return value - (probCutBeta - beta);
895 Eval::NNUE::hint_common_parent_position(pos);
898 moves_loop: // When in check, search starts here
900 // Step 12. A small Probcut idea, when we are in check (~4 Elo)
901 probCutBeta = beta + 425;
902 if (ss->inCheck && !PvNode && ttCapture && (tte->bound() & BOUND_LOWER)
903 && tte->depth() >= depth - 4 && ttValue >= probCutBeta
904 && abs(ttValue) < VALUE_TB_WIN_IN_MAX_PLY && abs(beta) < VALUE_TB_WIN_IN_MAX_PLY)
907 const PieceToHistory* contHist[] = {(ss - 1)->continuationHistory,
908 (ss - 2)->continuationHistory,
909 (ss - 3)->continuationHistory,
910 (ss - 4)->continuationHistory,
912 (ss - 6)->continuationHistory};
915 prevSq != SQ_NONE ? thisThread->counterMoves[pos.piece_on(prevSq)][prevSq] : MOVE_NONE;
917 MovePicker mp(pos, ttMove, depth, &thisThread->mainHistory, &captureHistory, contHist,
918 &thisThread->pawnHistory, countermove, ss->killers);
921 moveCountPruning = singularQuietLMR = false;
923 // Indicate PvNodes that will probably fail low if the node was searched
924 // at a depth equal to or greater than the current depth, and the result
925 // of this search was a fail low.
926 bool likelyFailLow = PvNode && ttMove && (tte->bound() & BOUND_UPPER) && tte->depth() >= depth;
928 // Step 13. Loop through all pseudo-legal moves until no moves remain
929 // or a beta cutoff occurs.
930 while ((move = mp.next_move(moveCountPruning)) != MOVE_NONE)
934 if (move == excludedMove)
937 // Check for legality
938 if (!pos.legal(move))
941 // At root obey the "searchmoves" option and skip moves not listed in Root
942 // Move List. In MultiPV mode we also skip PV moves that have been already
943 // searched and those of lower "TB rank" if we are in a TB root position.
945 && !std::count(thisThread->rootMoves.begin() + thisThread->pvIdx,
946 thisThread->rootMoves.begin() + thisThread->pvLast, move))
949 ss->moveCount = ++moveCount;
951 if (rootNode && thisThread == Threads.main() && Time.elapsed() > 3000)
952 sync_cout << "info depth " << depth << " currmove "
953 << UCI::move(move, pos.is_chess960()) << " currmovenumber "
954 << moveCount + thisThread->pvIdx << sync_endl;
956 (ss + 1)->pv = nullptr;
959 capture = pos.capture_stage(move);
960 movedPiece = pos.moved_piece(move);
961 givesCheck = pos.gives_check(move);
963 // Calculate new depth for this move
964 newDepth = depth - 1;
966 Value delta = beta - alpha;
968 Depth r = reduction(improving, depth, moveCount, delta, thisThread->rootDelta);
970 // Step 14. Pruning at shallow depth (~120 Elo).
971 // Depth conditions are important for mate finding.
972 if (!rootNode && pos.non_pawn_material(us) && bestValue > VALUE_TB_LOSS_IN_MAX_PLY)
974 // Skip quiet moves if movecount exceeds our FutilityMoveCount threshold (~8 Elo)
975 if (!moveCountPruning)
976 moveCountPruning = moveCount >= futility_move_count(improving, depth);
978 // Reduced depth of the next LMR search
979 int lmrDepth = newDepth - r;
981 if (capture || givesCheck)
983 // Futility pruning for captures (~2 Elo)
984 if (!givesCheck && lmrDepth < 7 && !ss->inCheck)
986 Piece capturedPiece = pos.piece_on(to_sq(move));
988 ss->staticEval + 238 + 305 * lmrDepth + PieceValue[capturedPiece]
989 + captureHistory[movedPiece][to_sq(move)][type_of(capturedPiece)] / 7;
990 if (futilityEval < alpha)
994 // SEE based pruning for captures and checks (~11 Elo)
995 if (!pos.see_ge(move, Value(-187) * depth))
1000 int history = (*contHist[0])[movedPiece][to_sq(move)]
1001 + (*contHist[1])[movedPiece][to_sq(move)]
1002 + (*contHist[3])[movedPiece][to_sq(move)]
1003 + thisThread->pawnHistory[pawn_structure(pos)][movedPiece][to_sq(move)];
1005 // Continuation history based pruning (~2 Elo)
1006 if (lmrDepth < 6 && history < -3752 * depth)
1009 history += 2 * thisThread->mainHistory[us][from_to(move)];
1011 lmrDepth += history / 7838;
1012 lmrDepth = std::max(lmrDepth, -1);
1014 // Futility pruning: parent node (~13 Elo)
1015 if (!ss->inCheck && lmrDepth < 14
1016 && ss->staticEval + (bestValue < ss->staticEval - 57 ? 124 : 71)
1021 lmrDepth = std::max(lmrDepth, 0);
1023 // Prune moves with negative SEE (~4 Elo)
1024 if (!pos.see_ge(move, Value(-26 * lmrDepth * lmrDepth)))
1029 // Step 15. Extensions (~100 Elo)
1030 // We take care to not overdo to avoid search getting stuck.
1031 if (ss->ply < thisThread->rootDepth * 2)
1033 // Singular extension search (~94 Elo). If all moves but one fail low on a
1034 // search of (alpha-s, beta-s), and just one fails high on (alpha, beta),
1035 // then that move is singular and should be extended. To verify this we do
1036 // a reduced search on the position excluding the ttMove and if the result
1037 // is lower than ttValue minus a margin, then we will extend the ttMove.
1039 // Note: the depth margin and singularBeta margin are known for having non-linear
1040 // scaling. Their values are optimized to time controls of 180+1.8 and longer
1041 // so changing them requires tests at these types of time controls.
1042 // Recursive singular search is avoided.
1043 if (!rootNode && move == ttMove && !excludedMove
1044 && depth >= 4 - (thisThread->completedDepth > 27) + 2 * (PvNode && tte->is_pv())
1045 && abs(ttValue) < VALUE_TB_WIN_IN_MAX_PLY && (tte->bound() & BOUND_LOWER)
1046 && tte->depth() >= depth - 3)
1048 Value singularBeta = ttValue - (66 + 58 * (ss->ttPv && !PvNode)) * depth / 64;
1049 Depth singularDepth = newDepth / 2;
1051 ss->excludedMove = move;
1053 search<NonPV>(pos, ss, singularBeta - 1, singularBeta, singularDepth, cutNode);
1054 ss->excludedMove = MOVE_NONE;
1056 if (value < singularBeta)
1059 singularQuietLMR = !ttCapture;
1061 // Avoid search explosion by limiting the number of double extensions
1062 if (!PvNode && value < singularBeta - 17 && ss->doubleExtensions <= 11)
1065 depth += depth < 15;
1069 // Multi-cut pruning
1070 // Our ttMove is assumed to fail high based on the bound of the TT entry,
1071 // and if after excluding the ttMove with a reduced search we fail high over the original beta,
1072 // we assume this expected cut-node is not singular (multiple moves fail high),
1073 // and we can prune the whole subtree by returning a softbound.
1074 else if (singularBeta >= beta)
1075 return singularBeta;
1077 // Negative extensions
1078 // If other moves failed high over (ttValue - margin) without the ttMove on a reduced search,
1079 // but we cannot do multi-cut because (ttValue - margin) is lower than the original beta,
1080 // we do not know if the ttMove is singular or can do a multi-cut,
1081 // so we reduce the ttMove in favor of other moves based on some conditions:
1083 // If the ttMove is assumed to fail high over current beta (~7 Elo)
1084 else if (ttValue >= beta)
1085 extension = -2 - !PvNode;
1087 // If we are on a cutNode but the ttMove is not assumed to fail high over current beta (~1 Elo)
1089 extension = depth < 19 ? -2 : -1;
1091 // If the ttMove is assumed to fail low over the value of the reduced search (~1 Elo)
1092 else if (ttValue <= value)
1096 // Check extensions (~1 Elo)
1097 else if (givesCheck && depth > 10)
1100 // Quiet ttMove extensions (~1 Elo)
1101 else if (PvNode && move == ttMove && move == ss->killers[0]
1102 && (*contHist[0])[movedPiece][to_sq(move)] >= 4325)
1105 // Recapture extensions (~1 Elo)
1106 else if (PvNode && move == ttMove && to_sq(move) == prevSq
1107 && captureHistory[movedPiece][to_sq(move)][type_of(pos.piece_on(to_sq(move)))]
1112 // Add extension to new depth
1113 newDepth += extension;
1114 ss->doubleExtensions = (ss - 1)->doubleExtensions + (extension == 2);
1116 // Speculative prefetch as early as possible
1117 prefetch(TT.first_entry(pos.key_after(move)));
1119 // Update the current move (this must be done after singular extension search)
1120 ss->currentMove = move;
1121 ss->continuationHistory =
1122 &thisThread->continuationHistory[ss->inCheck][capture][movedPiece][to_sq(move)];
1124 // Step 16. Make the move
1125 pos.do_move(move, st, givesCheck);
1127 // Decrease reduction if position is or has been on the PV (~4 Elo)
1128 if (ss->ttPv && !likelyFailLow)
1129 r -= cutNode && tte->depth() >= depth ? 3 : 2;
1131 // Decrease reduction if opponent's move count is high (~1 Elo)
1132 if ((ss - 1)->moveCount > 7)
1135 // Increase reduction for cut nodes (~3 Elo)
1139 // Increase reduction if ttMove is a capture (~3 Elo)
1143 // Decrease reduction for PvNodes (~2 Elo)
1147 // Decrease reduction if a quiet ttMove has been singularly extended (~1 Elo)
1148 if (singularQuietLMR)
1151 // Increase reduction on repetition (~1 Elo)
1152 if (move == (ss - 4)->currentMove && pos.has_repeated())
1155 // Increase reduction if next ply has a lot of fail high (~5 Elo)
1156 if ((ss + 1)->cutoffCnt > 3)
1159 // Set reduction to 0 for first picked move (ttMove) (~2 Elo)
1160 // Nullifies all previous reduction adjustments to ttMove and leaves only history to do them
1161 else if (move == ttMove)
1164 ss->statScore = 2 * thisThread->mainHistory[us][from_to(move)]
1165 + (*contHist[0])[movedPiece][to_sq(move)]
1166 + (*contHist[1])[movedPiece][to_sq(move)]
1167 + (*contHist[3])[movedPiece][to_sq(move)] - 3817;
1169 // Decrease/increase reduction for moves with a good/bad history (~25 Elo)
1170 r -= ss->statScore / 14767;
1172 // Step 17. Late moves reduction / extension (LMR, ~117 Elo)
1173 // We use various heuristics for the sons of a node after the first son has
1174 // been searched. In general, we would like to reduce them, but there are many
1175 // cases where we extend a son if it has good chances to be "interesting".
1176 if (depth >= 2 && moveCount > 1 + rootNode
1177 && (!ss->ttPv || !capture || (cutNode && (ss - 1)->moveCount > 1)))
1179 // In general we want to cap the LMR depth search at newDepth, but when
1180 // reduction is negative, we allow this move a limited search extension
1181 // beyond the first move depth. This may lead to hidden double extensions.
1182 // To prevent problems when the max value is less than the min value,
1183 // std::clamp has been replaced by a more robust implementation.
1184 Depth d = std::max(1, std::min(newDepth - r, newDepth + 1));
1186 value = -search<NonPV>(pos, ss + 1, -(alpha + 1), -alpha, d, true);
1188 // Do a full-depth search when reduced LMR search fails high
1189 if (value > alpha && d < newDepth)
1191 // Adjust full-depth search based on LMR results - if the result
1192 // was good enough search deeper, if it was bad enough search shallower.
1193 const bool doDeeperSearch = value > (bestValue + 53 + 2 * newDepth); // (~1 Elo)
1194 const bool doShallowerSearch = value < bestValue + newDepth; // (~2 Elo)
1196 newDepth += doDeeperSearch - doShallowerSearch;
1199 value = -search<NonPV>(pos, ss + 1, -(alpha + 1), -alpha, newDepth, !cutNode);
1201 int bonus = value <= alpha ? -stat_malus(newDepth)
1202 : value >= beta ? stat_bonus(newDepth)
1205 update_continuation_histories(ss, movedPiece, to_sq(move), bonus);
1209 // Step 18. Full-depth search when LMR is skipped
1210 else if (!PvNode || moveCount > 1)
1212 // Increase reduction if ttMove is not present (~1 Elo)
1216 // Note that if expected reduction is high, we reduce search depth by 1 here
1217 value = -search<NonPV>(pos, ss + 1, -(alpha + 1), -alpha, newDepth - (r > 3), !cutNode);
1220 // For PV nodes only, do a full PV search on the first move or after a fail high,
1221 // otherwise let the parent node fail low with value <= alpha and try another move.
1222 if (PvNode && (moveCount == 1 || value > alpha))
1225 (ss + 1)->pv[0] = MOVE_NONE;
1227 value = -search<PV>(pos, ss + 1, -beta, -alpha, newDepth, false);
1230 // Step 19. Undo move
1231 pos.undo_move(move);
1233 assert(value > -VALUE_INFINITE && value < VALUE_INFINITE);
1235 // Step 20. Check for a new best move
1236 // Finished searching the move. If a stop occurred, the return value of
1237 // the search cannot be trusted, and we return immediately without
1238 // updating best move, PV and TT.
1239 if (Threads.stop.load(std::memory_order_relaxed))
1245 *std::find(thisThread->rootMoves.begin(), thisThread->rootMoves.end(), move);
1248 rm.averageScore != -VALUE_INFINITE ? (2 * value + rm.averageScore) / 3 : value;
1250 // PV move or new best move?
1251 if (moveCount == 1 || value > alpha)
1253 rm.score = rm.uciScore = value;
1254 rm.selDepth = thisThread->selDepth;
1255 rm.scoreLowerbound = rm.scoreUpperbound = false;
1259 rm.scoreLowerbound = true;
1262 else if (value <= alpha)
1264 rm.scoreUpperbound = true;
1265 rm.uciScore = alpha;
1270 assert((ss + 1)->pv);
1272 for (Move* m = (ss + 1)->pv; *m != MOVE_NONE; ++m)
1273 rm.pv.push_back(*m);
1275 // We record how often the best move has been changed in each iteration.
1276 // This information is used for time management. In MultiPV mode,
1277 // we must take care to only do this for the first PV line.
1278 if (moveCount > 1 && !thisThread->pvIdx)
1279 ++thisThread->bestMoveChanges;
1282 // All other moves but the PV, are set to the lowest value: this
1283 // is not a problem when sorting because the sort is stable and the
1284 // move position in the list is preserved - just the PV is pushed up.
1285 rm.score = -VALUE_INFINITE;
1288 if (value > bestValue)
1296 if (PvNode && !rootNode) // Update pv even in fail-high case
1297 update_pv(ss->pv, move, (ss + 1)->pv);
1301 ss->cutoffCnt += 1 + !ttMove;
1302 assert(value >= beta); // Fail high
1307 // Reduce other moves if we have found at least one score improvement (~2 Elo)
1308 if (depth > 2 && depth < 12 && beta < 13782 && value > -11541)
1312 alpha = value; // Update alpha! Always alpha < beta
1317 // If the move is worse than some previously searched move,
1318 // remember it, to update its stats later.
1319 if (move != bestMove && moveCount <= 32)
1322 capturesSearched[captureCount++] = move;
1325 quietsSearched[quietCount++] = move;
1329 // Step 21. Check for mate and stalemate
1330 // All legal moves have been searched and if there are no legal moves, it
1331 // must be a mate or a stalemate. If we are in a singular extension search then
1332 // return a fail low score.
1334 assert(moveCount || !ss->inCheck || excludedMove || !MoveList<LEGAL>(pos).size());
1337 bestValue = excludedMove ? alpha : ss->inCheck ? mated_in(ss->ply) : VALUE_DRAW;
1339 // If there is a move that produces search value greater than alpha we update the stats of searched moves
1341 update_all_stats(pos, ss, bestMove, bestValue, beta, prevSq, quietsSearched, quietCount,
1342 capturesSearched, captureCount, depth);
1344 // Bonus for prior countermove that caused the fail low
1345 else if (!priorCapture && prevSq != SQ_NONE)
1347 int bonus = (depth > 6) + (PvNode || cutNode) + (bestValue < alpha - 656)
1348 + ((ss - 1)->moveCount > 10);
1349 update_continuation_histories(ss - 1, pos.piece_on(prevSq), prevSq,
1350 stat_bonus(depth) * bonus);
1351 thisThread->mainHistory[~us][from_to((ss - 1)->currentMove)]
1352 << stat_bonus(depth) * bonus / 2;
1356 bestValue = std::min(bestValue, maxValue);
1358 // If no good move is found and the previous position was ttPv, then the previous
1359 // opponent move is probably good and the new position is added to the search tree. (~7 Elo)
1360 if (bestValue <= alpha)
1361 ss->ttPv = ss->ttPv || ((ss - 1)->ttPv && depth > 3);
1363 // Write gathered information in transposition table
1364 if (!excludedMove && !(rootNode && thisThread->pvIdx))
1365 tte->save(posKey, value_to_tt(bestValue, ss->ply), ss->ttPv,
1366 bestValue >= beta ? BOUND_LOWER
1367 : PvNode && bestMove ? BOUND_EXACT
1369 depth, bestMove, ss->staticEval);
1371 assert(bestValue > -VALUE_INFINITE && bestValue < VALUE_INFINITE);
1377 // Quiescence search function, which is called by the main search
1378 // function with zero depth, or recursively with further decreasing depth per call.
1380 template<NodeType nodeType>
1381 Value qsearch(Position& pos, Stack* ss, Value alpha, Value beta, Depth depth) {
1383 static_assert(nodeType != Root);
1384 constexpr bool PvNode = nodeType == PV;
1386 assert(alpha >= -VALUE_INFINITE && alpha < beta && beta <= VALUE_INFINITE);
1387 assert(PvNode || (alpha == beta - 1));
1390 // Check if we have an upcoming move that draws by repetition, or
1391 // if the opponent had an alternative move earlier to this position.
1392 if (alpha < VALUE_DRAW && pos.has_game_cycle(ss->ply))
1394 alpha = value_draw(pos.this_thread());
1399 Move pv[MAX_PLY + 1];
1401 ASSERT_ALIGNED(&st, Eval::NNUE::CacheLineSize);
1405 Move ttMove, move, bestMove;
1407 Value bestValue, value, ttValue, futilityValue, futilityBase;
1408 bool pvHit, givesCheck, capture;
1410 Color us = pos.side_to_move();
1412 // Step 1. Initialize node
1416 ss->pv[0] = MOVE_NONE;
1419 Thread* thisThread = pos.this_thread();
1420 bestMove = MOVE_NONE;
1421 ss->inCheck = pos.checkers();
1424 // Used to send selDepth info to GUI (selDepth counts from 1, ply from 0)
1425 if (PvNode && thisThread->selDepth < ss->ply + 1)
1426 thisThread->selDepth = ss->ply + 1;
1428 // Step 2. Check for an immediate draw or maximum ply reached
1429 if (pos.is_draw(ss->ply) || ss->ply >= MAX_PLY)
1430 return (ss->ply >= MAX_PLY && !ss->inCheck) ? evaluate(pos) : VALUE_DRAW;
1432 assert(0 <= ss->ply && ss->ply < MAX_PLY);
1434 // Decide the replacement and cutoff priority of the qsearch TT entries
1435 ttDepth = ss->inCheck || depth >= DEPTH_QS_CHECKS ? DEPTH_QS_CHECKS : DEPTH_QS_NO_CHECKS;
1437 // Step 3. Transposition table lookup
1439 tte = TT.probe(posKey, ss->ttHit);
1440 ttValue = ss->ttHit ? value_from_tt(tte->value(), ss->ply, pos.rule50_count()) : VALUE_NONE;
1441 ttMove = ss->ttHit ? tte->move() : MOVE_NONE;
1442 pvHit = ss->ttHit && tte->is_pv();
1444 // At non-PV nodes we check for an early TT cutoff
1445 if (!PvNode && tte->depth() >= ttDepth
1446 && ttValue != VALUE_NONE // Only in case of TT access race or if !ttHit
1447 && (tte->bound() & (ttValue >= beta ? BOUND_LOWER : BOUND_UPPER)))
1450 // Step 4. Static evaluation of the position
1452 bestValue = futilityBase = -VALUE_INFINITE;
1457 // Never assume anything about values stored in TT
1458 if ((ss->staticEval = bestValue = tte->eval()) == VALUE_NONE)
1459 ss->staticEval = bestValue = evaluate(pos);
1461 // ttValue can be used as a better position evaluation (~13 Elo)
1462 if (ttValue != VALUE_NONE
1463 && (tte->bound() & (ttValue > bestValue ? BOUND_LOWER : BOUND_UPPER)))
1464 bestValue = ttValue;
1467 // In case of null move search, use previous static eval with a different sign
1468 ss->staticEval = bestValue =
1469 (ss - 1)->currentMove != MOVE_NULL ? evaluate(pos) : -(ss - 1)->staticEval;
1471 // Stand pat. Return immediately if static value is at least beta
1472 if (bestValue >= beta)
1475 tte->save(posKey, value_to_tt(bestValue, ss->ply), false, BOUND_LOWER, DEPTH_NONE,
1476 MOVE_NONE, ss->staticEval);
1481 if (bestValue > alpha)
1484 futilityBase = ss->staticEval + 182;
1487 const PieceToHistory* contHist[] = {(ss - 1)->continuationHistory,
1488 (ss - 2)->continuationHistory};
1490 // Initialize a MovePicker object for the current position, and prepare
1491 // to search the moves. Because the depth is <= 0 here, only captures,
1492 // queen promotions, and other checks (only if depth >= DEPTH_QS_CHECKS)
1493 // will be generated.
1494 Square prevSq = is_ok((ss - 1)->currentMove) ? to_sq((ss - 1)->currentMove) : SQ_NONE;
1495 MovePicker mp(pos, ttMove, depth, &thisThread->mainHistory, &thisThread->captureHistory,
1496 contHist, &thisThread->pawnHistory);
1498 int quietCheckEvasions = 0;
1500 // Step 5. Loop through all pseudo-legal moves until no moves remain
1501 // or a beta cutoff occurs.
1502 while ((move = mp.next_move()) != MOVE_NONE)
1504 assert(is_ok(move));
1506 // Check for legality
1507 if (!pos.legal(move))
1510 givesCheck = pos.gives_check(move);
1511 capture = pos.capture_stage(move);
1516 if (bestValue > VALUE_TB_LOSS_IN_MAX_PLY && pos.non_pawn_material(us))
1518 // Futility pruning and moveCount pruning (~10 Elo)
1519 if (!givesCheck && to_sq(move) != prevSq && futilityBase > VALUE_TB_LOSS_IN_MAX_PLY
1520 && type_of(move) != PROMOTION)
1525 futilityValue = futilityBase + PieceValue[pos.piece_on(to_sq(move))];
1527 // If static eval + value of piece we are going to capture is much lower
1528 // than alpha we can prune this move.
1529 if (futilityValue <= alpha)
1531 bestValue = std::max(bestValue, futilityValue);
1535 // If static eval is much lower than alpha and move is not winning material
1536 // we can prune this move.
1537 if (futilityBase <= alpha && !pos.see_ge(move, VALUE_ZERO + 1))
1539 bestValue = std::max(bestValue, futilityBase);
1543 // If static exchange evaluation is much worse than what is needed to not
1544 // fall below alpha we can prune this move.
1545 if (futilityBase > alpha && !pos.see_ge(move, (alpha - futilityBase) * 4))
1552 // We prune after the second quiet check evasion move, where being 'in check' is
1553 // implicitly checked through the counter, and being a 'quiet move' apart from
1554 // being a tt move is assumed after an increment because captures are pushed ahead.
1555 if (quietCheckEvasions > 1)
1558 // Continuation history based pruning (~3 Elo)
1559 if (!capture && (*contHist[0])[pos.moved_piece(move)][to_sq(move)] < 0
1560 && (*contHist[1])[pos.moved_piece(move)][to_sq(move)] < 0)
1563 // Do not search moves with bad enough SEE values (~5 Elo)
1564 if (!pos.see_ge(move, Value(-77)))
1568 // Speculative prefetch as early as possible
1569 prefetch(TT.first_entry(pos.key_after(move)));
1571 // Update the current move
1572 ss->currentMove = move;
1573 ss->continuationHistory =
1575 ->continuationHistory[ss->inCheck][capture][pos.moved_piece(move)][to_sq(move)];
1577 quietCheckEvasions += !capture && ss->inCheck;
1579 // Step 7. Make and search the move
1580 pos.do_move(move, st, givesCheck);
1581 value = -qsearch<nodeType>(pos, ss + 1, -beta, -alpha, depth - 1);
1582 pos.undo_move(move);
1584 assert(value > -VALUE_INFINITE && value < VALUE_INFINITE);
1586 // Step 8. Check for a new best move
1587 if (value > bestValue)
1595 if (PvNode) // Update pv even in fail-high case
1596 update_pv(ss->pv, move, (ss + 1)->pv);
1598 if (value < beta) // Update alpha here!
1606 // Step 9. Check for mate
1607 // All legal moves have been searched. A special case: if we're in check
1608 // and no legal moves were found, it is checkmate.
1609 if (ss->inCheck && bestValue == -VALUE_INFINITE)
1611 assert(!MoveList<LEGAL>(pos).size());
1613 return mated_in(ss->ply); // Plies to mate from the root
1616 // Save gathered info in transposition table
1617 tte->save(posKey, value_to_tt(bestValue, ss->ply), pvHit,
1618 bestValue >= beta ? BOUND_LOWER : BOUND_UPPER, ttDepth, bestMove, ss->staticEval);
1620 assert(bestValue > -VALUE_INFINITE && bestValue < VALUE_INFINITE);
1626 // Adjusts a mate or TB score from "plies to mate from the root"
1627 // to "plies to mate from the current position". Standard scores are unchanged.
1628 // The function is called before storing a value in the transposition table.
1629 Value value_to_tt(Value v, int ply) {
1631 assert(v != VALUE_NONE);
1633 return v >= VALUE_TB_WIN_IN_MAX_PLY ? v + ply : v <= VALUE_TB_LOSS_IN_MAX_PLY ? v - ply : v;
1637 // Inverse of value_to_tt(): it adjusts a mate or TB score
1638 // from the transposition table (which refers to the plies to mate/be mated from
1639 // current position) to "plies to mate/be mated (TB win/loss) from the root".
1640 // However, to avoid potentially false mate or TB scores related to the 50 moves rule
1641 // and the graph history interaction, we return highest non-TB score instead.
1643 Value value_from_tt(Value v, int ply, int r50c) {
1645 if (v == VALUE_NONE)
1648 // handle TB win or better
1649 if (v >= VALUE_TB_WIN_IN_MAX_PLY)
1651 // Downgrade a potentially false mate score
1652 if (v >= VALUE_MATE_IN_MAX_PLY && VALUE_MATE - v > 100 - r50c)
1653 return VALUE_TB_WIN_IN_MAX_PLY - 1;
1655 // Downgrade a potentially false TB score.
1656 if (VALUE_TB - v > 100 - r50c)
1657 return VALUE_TB_WIN_IN_MAX_PLY - 1;
1662 // handle TB loss or worse
1663 if (v <= VALUE_TB_LOSS_IN_MAX_PLY)
1665 // Downgrade a potentially false mate score.
1666 if (v <= VALUE_MATED_IN_MAX_PLY && VALUE_MATE + v > 100 - r50c)
1667 return VALUE_TB_LOSS_IN_MAX_PLY + 1;
1669 // Downgrade a potentially false TB score.
1670 if (VALUE_TB + v > 100 - r50c)
1671 return VALUE_TB_LOSS_IN_MAX_PLY + 1;
1680 // Adds current move and appends child pv[]
1681 void update_pv(Move* pv, Move move, const Move* childPv) {
1683 for (*pv++ = move; childPv && *childPv != MOVE_NONE;)
1689 // Updates stats at the end of search() when a bestMove is found
1690 void update_all_stats(const Position& pos,
1696 Move* quietsSearched,
1698 Move* capturesSearched,
1702 Color us = pos.side_to_move();
1703 Thread* thisThread = pos.this_thread();
1704 CapturePieceToHistory& captureHistory = thisThread->captureHistory;
1705 Piece moved_piece = pos.moved_piece(bestMove);
1708 int quietMoveBonus = stat_bonus(depth + 1);
1709 int quietMoveMalus = stat_malus(depth);
1711 if (!pos.capture_stage(bestMove))
1713 int bestMoveBonus = bestValue > beta + 173 ? quietMoveBonus // larger bonus
1714 : stat_bonus(depth); // smaller bonus
1716 // Increase stats for the best move in case it was a quiet move
1717 update_quiet_stats(pos, ss, bestMove, bestMoveBonus);
1718 thisThread->pawnHistory[pawn_structure(pos)][moved_piece][to_sq(bestMove)]
1721 // Decrease stats for all non-best quiet moves
1722 for (int i = 0; i < quietCount; ++i)
1724 thisThread->pawnHistory[pawn_structure(pos)][pos.moved_piece(quietsSearched[i])]
1725 [to_sq(quietsSearched[i])]
1727 thisThread->mainHistory[us][from_to(quietsSearched[i])] << -quietMoveMalus;
1728 update_continuation_histories(ss, pos.moved_piece(quietsSearched[i]),
1729 to_sq(quietsSearched[i]), -quietMoveMalus);
1734 // Increase stats for the best move in case it was a capture move
1735 captured = type_of(pos.piece_on(to_sq(bestMove)));
1736 captureHistory[moved_piece][to_sq(bestMove)][captured] << quietMoveBonus;
1739 // Extra penalty for a quiet early move that was not a TT move or
1740 // main killer move in previous ply when it gets refuted.
1741 if (prevSq != SQ_NONE
1742 && ((ss - 1)->moveCount == 1 + (ss - 1)->ttHit
1743 || ((ss - 1)->currentMove == (ss - 1)->killers[0]))
1744 && !pos.captured_piece())
1745 update_continuation_histories(ss - 1, pos.piece_on(prevSq), prevSq, -quietMoveMalus);
1747 // Decrease stats for all non-best capture moves
1748 for (int i = 0; i < captureCount; ++i)
1750 moved_piece = pos.moved_piece(capturesSearched[i]);
1751 captured = type_of(pos.piece_on(to_sq(capturesSearched[i])));
1752 captureHistory[moved_piece][to_sq(capturesSearched[i])][captured] << -quietMoveMalus;
1757 // Updates histories of the move pairs formed
1758 // by moves at ply -1, -2, -3, -4, and -6 with current move.
1759 void update_continuation_histories(Stack* ss, Piece pc, Square to, int bonus) {
1761 for (int i : {1, 2, 3, 4, 6})
1763 // Only update the first 2 continuation histories if we are in check
1764 if (ss->inCheck && i > 2)
1766 if (is_ok((ss - i)->currentMove))
1767 (*(ss - i)->continuationHistory)[pc][to] << bonus / (1 + 3 * (i == 3));
1772 // Updates move sorting heuristics
1773 void update_quiet_stats(const Position& pos, Stack* ss, Move move, int bonus) {
1776 if (ss->killers[0] != move)
1778 ss->killers[1] = ss->killers[0];
1779 ss->killers[0] = move;
1782 Color us = pos.side_to_move();
1783 Thread* thisThread = pos.this_thread();
1784 thisThread->mainHistory[us][from_to(move)] << bonus;
1785 update_continuation_histories(ss, pos.moved_piece(move), to_sq(move), bonus);
1787 // Update countermove history
1788 if (is_ok((ss - 1)->currentMove))
1790 Square prevSq = to_sq((ss - 1)->currentMove);
1791 thisThread->counterMoves[pos.piece_on(prevSq)][prevSq] = move;
1795 // When playing with strength handicap, choose the best move among a set of RootMoves
1796 // using a statistical rule dependent on 'level'. Idea by Heinz van Saanen.
1797 Move Skill::pick_best(size_t multiPV) {
1799 const RootMoves& rootMoves = Threads.main()->rootMoves;
1800 static PRNG rng(now()); // PRNG sequence should be non-deterministic
1802 // RootMoves are already sorted by score in descending order
1803 Value topScore = rootMoves[0].score;
1804 int delta = std::min(topScore - rootMoves[multiPV - 1].score, PawnValue);
1805 int maxScore = -VALUE_INFINITE;
1806 double weakness = 120 - 2 * level;
1808 // Choose best move. For each move score we add two terms, both dependent on
1809 // weakness. One is deterministic and bigger for weaker levels, and one is
1810 // random. Then we choose the move with the resulting highest score.
1811 for (size_t i = 0; i < multiPV; ++i)
1813 // This is our magic formula
1814 int push = int((weakness * int(topScore - rootMoves[i].score)
1815 + delta * (rng.rand<unsigned>() % int(weakness)))
1818 if (rootMoves[i].score + push >= maxScore)
1820 maxScore = rootMoves[i].score + push;
1821 best = rootMoves[i].pv[0];
1831 // Used to print debug info and, more importantly,
1832 // to detect when we are out of available time and thus stop the search.
1833 void MainThread::check_time() {
1838 // When using nodes, ensure checking rate is not lower than 0.1% of nodes
1839 callsCnt = Limits.nodes ? std::min(512, int(Limits.nodes / 1024)) : 512;
1841 static TimePoint lastInfoTime = now();
1843 TimePoint elapsed = Time.elapsed();
1844 TimePoint tick = Limits.startTime + elapsed;
1846 if (tick - lastInfoTime >= 1000)
1848 lastInfoTime = tick;
1852 // We should not stop pondering until told so by the GUI
1856 if ((Limits.use_time_management() && (elapsed > Time.maximum() || stopOnPonderhit))
1857 || (Limits.movetime && elapsed >= Limits.movetime)
1858 || (Limits.nodes && Threads.nodes_searched() >= uint64_t(Limits.nodes)))
1859 Threads.stop = true;
1863 // Formats PV information according to the UCI protocol. UCI requires
1864 // that all (if any) unsearched PV lines are sent using a previous search score.
1865 string UCI::pv(const Position& pos, Depth depth) {
1867 std::stringstream ss;
1868 TimePoint elapsed = Time.elapsed() + 1;
1869 const RootMoves& rootMoves = pos.this_thread()->rootMoves;
1870 size_t pvIdx = pos.this_thread()->pvIdx;
1871 size_t multiPV = std::min(size_t(Options["MultiPV"]), rootMoves.size());
1872 uint64_t nodesSearched = Threads.nodes_searched();
1873 uint64_t tbHits = Threads.tb_hits() + (TB::RootInTB ? rootMoves.size() : 0);
1875 for (size_t i = 0; i < multiPV; ++i)
1877 bool updated = rootMoves[i].score != -VALUE_INFINITE;
1879 if (depth == 1 && !updated && i > 0)
1882 Depth d = updated ? depth : std::max(1, depth - 1);
1883 Value v = updated ? rootMoves[i].uciScore : rootMoves[i].previousScore;
1885 if (v == -VALUE_INFINITE)
1888 bool tb = TB::RootInTB && abs(v) <= VALUE_TB;
1889 v = tb ? rootMoves[i].tbScore : v;
1891 if (ss.rdbuf()->in_avail()) // Not at first line
1895 << " depth " << d << " seldepth " << rootMoves[i].selDepth << " multipv " << i + 1
1896 << " score " << UCI::value(v);
1898 if (Options["UCI_ShowWDL"])
1899 ss << UCI::wdl(v, pos.game_ply());
1901 if (i == pvIdx && !tb && updated) // tablebase- and previous-scores are exact
1902 ss << (rootMoves[i].scoreLowerbound
1904 : (rootMoves[i].scoreUpperbound ? " upperbound" : ""));
1906 ss << " nodes " << nodesSearched << " nps " << nodesSearched * 1000 / elapsed
1907 << " hashfull " << TT.hashfull() << " tbhits " << tbHits << " time " << elapsed << " pv";
1909 for (Move m : rootMoves[i].pv)
1910 ss << " " << UCI::move(m, pos.is_chess960());
1917 // Called in case we have no ponder move before exiting the search,
1918 // for instance, in case we stop the search during a fail high at root.
1919 // We try hard to have a ponder move to return to the GUI,
1920 // otherwise in case of 'ponder on' we have nothing to think about.
1921 bool RootMove::extract_ponder_from_tt(Position& pos) {
1924 ASSERT_ALIGNED(&st, Eval::NNUE::CacheLineSize);
1928 assert(pv.size() == 1);
1930 if (pv[0] == MOVE_NONE)
1933 pos.do_move(pv[0], st);
1934 TTEntry* tte = TT.probe(pos.key(), ttHit);
1938 Move m = tte->move(); // Local copy to be SMP safe
1939 if (MoveList<LEGAL>(pos).contains(m))
1943 pos.undo_move(pv[0]);
1944 return pv.size() > 1;
1947 void Tablebases::rank_root_moves(Position& pos, Search::RootMoves& rootMoves) {
1950 UseRule50 = bool(Options["Syzygy50MoveRule"]);
1951 ProbeDepth = int(Options["SyzygyProbeDepth"]);
1952 Cardinality = int(Options["SyzygyProbeLimit"]);
1953 bool dtz_available = true;
1955 // Tables with fewer pieces than SyzygyProbeLimit are searched with
1956 // ProbeDepth == DEPTH_ZERO
1957 if (Cardinality > MaxCardinality)
1959 Cardinality = MaxCardinality;
1963 if (Cardinality >= popcount(pos.pieces()) && !pos.can_castle(ANY_CASTLING))
1965 // Rank moves using DTZ tables
1966 RootInTB = root_probe(pos, rootMoves);
1970 // DTZ tables are missing; try to rank moves using WDL tables
1971 dtz_available = false;
1972 RootInTB = root_probe_wdl(pos, rootMoves);
1978 // Sort moves according to TB rank
1979 std::stable_sort(rootMoves.begin(), rootMoves.end(),
1980 [](const RootMove& a, const RootMove& b) { return a.tbRank > b.tbRank; });
1982 // Probe during search only if DTZ is not available and we are winning
1983 if (dtz_available || rootMoves[0].tbScore <= VALUE_DRAW)
1988 // Clean up if root_probe() and root_probe_wdl() have failed
1989 for (auto& m : rootMoves)
1994 } // namespace Stockfish