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((126 - 42 * 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 + 1560 - int(delta) * 945 / int(rootDelta)) / 1024
89 + (!i && reductionScale > 791);
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(334 * d - 531, 1538); }
99 // Add a small random component to draw evaluations to avoid 3-fold blindness
100 Value value_draw(const Thread* thisThread) {
101 return VALUE_DRAW - 1 + Value(thisThread->nodes & 0x2);
104 // Skill structure is used to implement strength limit. If we have a UCI_Elo,
105 // we convert it to an appropriate skill level, anchored to the Stash engine.
106 // This method is based on a fit of the Elo results for games played between
107 // Stockfish at various skill levels and various versions of the Stash engine.
108 // Skill 0 .. 19 now covers CCRL Blitz Elo from 1320 to 3190, approximately
109 // Reference: https://github.com/vondele/Stockfish/commit/a08b8d4e9711c2
111 Skill(int skill_level, int uci_elo) {
114 double e = double(uci_elo - 1320) / (3190 - 1320);
115 level = std::clamp((((37.2473 * e - 40.8525) * e + 22.2943) * e - 0.311438), 0.0, 19.0);
118 level = double(skill_level);
120 bool enabled() const { return level < 20.0; }
121 bool time_to_pick(Depth depth) const { return depth == 1 + int(level); }
122 Move pick_best(size_t multiPV);
125 Move best = MOVE_NONE;
128 template<NodeType nodeType>
129 Value search(Position& pos, Stack* ss, Value alpha, Value beta, Depth depth, bool cutNode);
131 template<NodeType nodeType>
132 Value qsearch(Position& pos, Stack* ss, Value alpha, Value beta, Depth depth = 0);
134 Value value_to_tt(Value v, int ply);
135 Value value_from_tt(Value v, int ply, int r50c);
136 void update_pv(Move* pv, Move move, const Move* childPv);
137 void update_continuation_histories(Stack* ss, Piece pc, Square to, int bonus);
138 void update_quiet_stats(const Position& pos, Stack* ss, Move move, int bonus);
139 void update_all_stats(const Position& pos,
145 Move* quietsSearched,
147 Move* capturesSearched,
151 // Utility to verify move generation. All the leaf nodes up
152 // to the given depth are generated and counted, and the sum is returned.
154 uint64_t perft(Position& pos, Depth depth) {
157 ASSERT_ALIGNED(&st, Eval::NNUE::CacheLineSize);
159 uint64_t cnt, nodes = 0;
160 const bool leaf = (depth == 2);
162 for (const auto& m : MoveList<LEGAL>(pos))
164 if (Root && depth <= 1)
169 cnt = leaf ? MoveList<LEGAL>(pos).size() : perft<false>(pos, depth - 1);
174 sync_cout << UCI::move(m, pos.is_chess960()) << ": " << cnt << sync_endl;
182 // Called at startup to initialize various lookup tables
183 void Search::init() {
185 for (int i = 1; i < MAX_MOVES; ++i)
186 Reductions[i] = int((20.37 + std::log(Threads.size()) / 2) * std::log(i));
190 // Resets search state to its initial value
191 void Search::clear() {
193 Threads.main()->wait_for_search_finished();
195 Time.availableNodes = 0;
198 Tablebases::init(Options["SyzygyPath"]); // Free mapped files
202 // Called when the program receives the UCI 'go'
203 // command. It searches from the root position and outputs the "bestmove".
204 void MainThread::search() {
208 nodes = perft<true>(rootPos, Limits.perft);
209 sync_cout << "\nNodes searched: " << nodes << "\n" << sync_endl;
213 Color us = rootPos.side_to_move();
214 Time.init(Limits, us, rootPos.game_ply());
217 Eval::NNUE::verify();
219 if (rootMoves.empty())
221 rootMoves.emplace_back(MOVE_NONE);
222 sync_cout << "info depth 0 score "
223 << UCI::value(rootPos.checkers() ? -VALUE_MATE : VALUE_DRAW) << sync_endl;
227 Threads.start_searching(); // start non-main threads
228 Thread::search(); // main thread start searching
231 // When we reach the maximum depth, we can arrive here without a raise of
232 // Threads.stop. However, if we are pondering or in an infinite search,
233 // the UCI protocol states that we shouldn't print the best move before the
234 // GUI sends a "stop" or "ponderhit" command. We therefore simply wait here
235 // until the GUI sends one of those commands.
237 while (!Threads.stop && (ponder || Limits.infinite))
238 {} // Busy wait for a stop or a ponder reset
240 // Stop the threads if not already stopped (also raise the stop if
241 // "ponderhit" just reset Threads.ponder).
244 // Wait until all threads have finished
245 Threads.wait_for_search_finished();
247 // When playing in 'nodes as time' mode, subtract the searched nodes from
248 // the available ones before exiting.
250 Time.availableNodes += Limits.inc[us] - Threads.nodes_searched();
252 Thread* bestThread = this;
254 Skill(Options["Skill Level"], Options["UCI_LimitStrength"] ? int(Options["UCI_Elo"]) : 0);
256 if (int(Options["MultiPV"]) == 1 && !Limits.depth && !skill.enabled()
257 && rootMoves[0].pv[0] != MOVE_NONE)
258 bestThread = Threads.get_best_thread();
260 bestPreviousScore = bestThread->rootMoves[0].score;
261 bestPreviousAverageScore = bestThread->rootMoves[0].averageScore;
263 // Send again PV info if we have a new best thread
264 if (bestThread != this)
265 sync_cout << UCI::pv(bestThread->rootPos, bestThread->completedDepth) << sync_endl;
267 sync_cout << "bestmove " << UCI::move(bestThread->rootMoves[0].pv[0], rootPos.is_chess960());
269 if (bestThread->rootMoves[0].pv.size() > 1
270 || bestThread->rootMoves[0].extract_ponder_from_tt(rootPos))
271 std::cout << " ponder " << UCI::move(bestThread->rootMoves[0].pv[1], rootPos.is_chess960());
273 std::cout << sync_endl;
277 // Main iterative deepening loop. It calls search()
278 // repeatedly with increasing depth until the allocated thinking time has been
279 // consumed, the user stops the search, or the maximum search depth is reached.
280 void Thread::search() {
282 // Allocate stack with extra size to allow access from (ss-7) to (ss+2):
283 // (ss-7) is needed for update_continuation_histories(ss-1) which accesses (ss-6),
284 // (ss+2) is needed for initialization of statScore and killers.
285 Stack stack[MAX_PLY + 10], *ss = stack + 7;
286 Move pv[MAX_PLY + 1];
287 Value alpha, beta, delta;
288 Move lastBestMove = MOVE_NONE;
289 Depth lastBestMoveDepth = 0;
290 MainThread* mainThread = (this == Threads.main() ? Threads.main() : nullptr);
291 double timeReduction = 1, totBestMoveChanges = 0;
292 Color us = rootPos.side_to_move();
295 std::memset(ss - 7, 0, 10 * sizeof(Stack));
296 for (int i = 7; i > 0; --i)
298 (ss - i)->continuationHistory =
299 &this->continuationHistory[0][0][NO_PIECE][0]; // Use as a sentinel
300 (ss - i)->staticEval = VALUE_NONE;
303 for (int i = 0; i <= MAX_PLY + 2; ++i)
308 bestValue = -VALUE_INFINITE;
312 if (mainThread->bestPreviousScore == VALUE_INFINITE)
313 for (int i = 0; i < 4; ++i)
314 mainThread->iterValue[i] = VALUE_ZERO;
316 for (int i = 0; i < 4; ++i)
317 mainThread->iterValue[i] = mainThread->bestPreviousScore;
320 size_t multiPV = size_t(Options["MultiPV"]);
321 Skill skill(Options["Skill Level"], Options["UCI_LimitStrength"] ? int(Options["UCI_Elo"]) : 0);
323 // When playing with strength handicap enable MultiPV search that we will
324 // use behind-the-scenes to retrieve a set of possible moves.
326 multiPV = std::max(multiPV, size_t(4));
328 multiPV = std::min(multiPV, rootMoves.size());
330 int searchAgainCounter = 0;
332 // Iterative deepening loop until requested to stop or the target depth is reached
333 while (++rootDepth < MAX_PLY && !Threads.stop
334 && !(Limits.depth && mainThread && rootDepth > Limits.depth))
336 // Age out PV variability metric
338 totBestMoveChanges /= 2;
340 // Save the last iteration's scores before the first PV line is searched and
341 // all the move scores except the (new) PV are set to -VALUE_INFINITE.
342 for (RootMove& rm : rootMoves)
343 rm.previousScore = rm.score;
348 if (!Threads.increaseDepth)
349 searchAgainCounter++;
351 // MultiPV loop. We perform a full root search for each PV line
352 for (pvIdx = 0; pvIdx < multiPV && !Threads.stop; ++pvIdx)
357 for (pvLast++; pvLast < rootMoves.size(); pvLast++)
358 if (rootMoves[pvLast].tbRank != rootMoves[pvFirst].tbRank)
362 // Reset UCI info selDepth for each depth and each PV line
365 // Reset aspiration window starting size
366 Value prev = rootMoves[pvIdx].averageScore;
367 delta = Value(10) + int(prev) * prev / 17470;
368 alpha = std::max(prev - delta, -VALUE_INFINITE);
369 beta = std::min(prev + delta, VALUE_INFINITE);
371 // Adjust optimism based on root move's previousScore (~4 Elo)
372 int opt = 113 * prev / (std::abs(prev) + 109);
373 optimism[us] = Value(opt);
374 optimism[~us] = -optimism[us];
376 // Start with a small aspiration window and, in the case of a fail
377 // high/low, re-search with a bigger window until we don't fail
379 int failedHighCnt = 0;
382 // Adjust the effective depth searched, but ensure at least one effective increment for every
383 // four searchAgain steps (see issue #2717).
384 Depth adjustedDepth =
385 std::max(1, rootDepth - failedHighCnt - 3 * (searchAgainCounter + 1) / 4);
386 bestValue = Stockfish::search<Root>(rootPos, ss, alpha, beta, adjustedDepth, false);
388 // Bring the best move to the front. It is critical that sorting
389 // is done with a stable algorithm because all the values but the
390 // first and eventually the new best one is set to -VALUE_INFINITE
391 // and we want to keep the same order for all the moves except the
392 // new PV that goes to the front. Note that in the case of MultiPV
393 // search the already searched PV lines are preserved.
394 std::stable_sort(rootMoves.begin() + pvIdx, rootMoves.begin() + pvLast);
396 // If search has been stopped, we break immediately. Sorting is
397 // safe because RootMoves is still valid, although it refers to
398 // the previous iteration.
402 // When failing high/low give some update (without cluttering
403 // the UI) before a re-search.
404 if (mainThread && multiPV == 1 && (bestValue <= alpha || bestValue >= beta)
405 && Time.elapsed() > 3000)
406 sync_cout << UCI::pv(rootPos, rootDepth) << sync_endl;
408 // In case of failing low/high increase aspiration window and
409 // re-search, otherwise exit the loop.
410 if (bestValue <= alpha)
412 beta = (alpha + beta) / 2;
413 alpha = std::max(bestValue - delta, -VALUE_INFINITE);
417 mainThread->stopOnPonderhit = false;
419 else if (bestValue >= beta)
421 beta = std::min(bestValue + delta, VALUE_INFINITE);
429 assert(alpha >= -VALUE_INFINITE && beta <= VALUE_INFINITE);
432 // Sort the PV lines searched so far and update the GUI
433 std::stable_sort(rootMoves.begin() + pvFirst, rootMoves.begin() + pvIdx + 1);
435 if (mainThread && (Threads.stop || pvIdx + 1 == multiPV || Time.elapsed() > 3000))
436 sync_cout << UCI::pv(rootPos, rootDepth) << sync_endl;
440 completedDepth = rootDepth;
442 if (rootMoves[0].pv[0] != lastBestMove)
444 lastBestMove = rootMoves[0].pv[0];
445 lastBestMoveDepth = rootDepth;
448 // Have we found a "mate in x"?
449 if (Limits.mate && bestValue >= VALUE_MATE_IN_MAX_PLY
450 && VALUE_MATE - bestValue <= 2 * Limits.mate)
456 // If the skill level is enabled and time is up, pick a sub-optimal best move
457 if (skill.enabled() && skill.time_to_pick(rootDepth))
458 skill.pick_best(multiPV);
460 // Use part of the gained time from a previous stable move for the current move
461 for (Thread* th : Threads)
463 totBestMoveChanges += th->bestMoveChanges;
464 th->bestMoveChanges = 0;
467 // Do we have time for the next iteration? Can we stop searching now?
468 if (Limits.use_time_management() && !Threads.stop && !mainThread->stopOnPonderhit)
470 double fallingEval = (69 + 13 * (mainThread->bestPreviousAverageScore - bestValue)
471 + 6 * (mainThread->iterValue[iterIdx] - bestValue))
473 fallingEval = std::clamp(fallingEval, 0.5, 1.5);
475 // If the bestMove is stable over several iterations, reduce time accordingly
476 timeReduction = lastBestMoveDepth + 8 < completedDepth ? 1.57 : 0.65;
477 double reduction = (1.4 + mainThread->previousTimeReduction) / (2.08 * timeReduction);
478 double bestMoveInstability = 1 + 1.8 * totBestMoveChanges / Threads.size();
480 double totalTime = Time.optimum() * fallingEval * reduction * bestMoveInstability;
482 // Cap used time in case of a single legal move for a better viewer experience
483 if (rootMoves.size() == 1)
484 totalTime = std::min(500.0, totalTime);
486 // Stop the search if we have exceeded the totalTime
487 if (Time.elapsed() > totalTime)
489 // If we are allowed to ponder do not stop the search now but
490 // keep pondering until the GUI sends "ponderhit" or "stop".
491 if (mainThread->ponder)
492 mainThread->stopOnPonderhit = true;
496 else if (!mainThread->ponder && Time.elapsed() > totalTime * 0.50)
497 Threads.increaseDepth = false;
499 Threads.increaseDepth = true;
502 mainThread->iterValue[iterIdx] = bestValue;
503 iterIdx = (iterIdx + 1) & 3;
509 mainThread->previousTimeReduction = timeReduction;
511 // If the skill level is enabled, swap the best PV line with the sub-optimal one
513 std::swap(rootMoves[0], *std::find(rootMoves.begin(), rootMoves.end(),
514 skill.best ? skill.best : skill.pick_best(multiPV)));
520 // Main search function for both PV and non-PV nodes
521 template<NodeType nodeType>
522 Value search(Position& pos, Stack* ss, Value alpha, Value beta, Depth depth, bool cutNode) {
524 constexpr bool PvNode = nodeType != NonPV;
525 constexpr bool rootNode = nodeType == Root;
527 // Dive into quiescence search when the depth reaches zero
529 return qsearch < PvNode ? PV : NonPV > (pos, ss, alpha, beta);
531 // Check if we have an upcoming move that draws by repetition, or
532 // if the opponent had an alternative move earlier to this position.
533 if (!rootNode && alpha < VALUE_DRAW && pos.has_game_cycle(ss->ply))
535 alpha = value_draw(pos.this_thread());
540 assert(-VALUE_INFINITE <= alpha && alpha < beta && beta <= VALUE_INFINITE);
541 assert(PvNode || (alpha == beta - 1));
542 assert(0 < depth && depth < MAX_PLY);
543 assert(!(PvNode && cutNode));
545 Move pv[MAX_PLY + 1], capturesSearched[32], quietsSearched[32];
547 ASSERT_ALIGNED(&st, Eval::NNUE::CacheLineSize);
551 Move ttMove, move, excludedMove, bestMove;
552 Depth extension, newDepth;
553 Value bestValue, value, ttValue, eval, maxValue, probCutBeta;
554 bool givesCheck, improving, priorCapture, singularQuietLMR;
555 bool capture, moveCountPruning, ttCapture;
557 int moveCount, captureCount, quietCount;
559 // Step 1. Initialize node
560 Thread* thisThread = pos.this_thread();
561 ss->inCheck = pos.checkers();
562 priorCapture = pos.captured_piece();
563 Color us = pos.side_to_move();
564 moveCount = captureCount = quietCount = ss->moveCount = 0;
565 bestValue = -VALUE_INFINITE;
566 maxValue = VALUE_INFINITE;
568 // Check for the available remaining time
569 if (thisThread == Threads.main())
570 static_cast<MainThread*>(thisThread)->check_time();
572 // Used to send selDepth info to GUI (selDepth counts from 1, ply from 0)
573 if (PvNode && thisThread->selDepth < ss->ply + 1)
574 thisThread->selDepth = ss->ply + 1;
578 // Step 2. Check for aborted search and immediate draw
579 if (Threads.stop.load(std::memory_order_relaxed) || pos.is_draw(ss->ply)
580 || ss->ply >= MAX_PLY)
581 return (ss->ply >= MAX_PLY && !ss->inCheck) ? evaluate(pos)
582 : value_draw(pos.this_thread());
584 // Step 3. Mate distance pruning. Even if we mate at the next move our score
585 // would be at best mate_in(ss->ply+1), but if alpha is already bigger because
586 // a shorter mate was found upward in the tree then there is no need to search
587 // because we will never beat the current alpha. Same logic but with reversed
588 // signs apply also in the opposite condition of being mated instead of giving
589 // mate. In this case, return a fail-high score.
590 alpha = std::max(mated_in(ss->ply), alpha);
591 beta = std::min(mate_in(ss->ply + 1), beta);
596 thisThread->rootDelta = beta - alpha;
598 assert(0 <= ss->ply && ss->ply < MAX_PLY);
600 (ss + 1)->excludedMove = bestMove = MOVE_NONE;
601 (ss + 2)->killers[0] = (ss + 2)->killers[1] = MOVE_NONE;
602 (ss + 2)->cutoffCnt = 0;
603 ss->doubleExtensions = (ss - 1)->doubleExtensions;
604 Square prevSq = is_ok((ss - 1)->currentMove) ? to_sq((ss - 1)->currentMove) : SQ_NONE;
607 // Step 4. Transposition table lookup.
608 excludedMove = ss->excludedMove;
610 tte = TT.probe(posKey, ss->ttHit);
611 ttValue = ss->ttHit ? value_from_tt(tte->value(), ss->ply, pos.rule50_count()) : VALUE_NONE;
612 ttMove = rootNode ? thisThread->rootMoves[thisThread->pvIdx].pv[0]
613 : ss->ttHit ? tte->move()
615 ttCapture = ttMove && pos.capture_stage(ttMove);
617 // At this point, if excluded, skip straight to step 6, static eval. However,
618 // to save indentation, we list the condition in all code between here and there.
620 ss->ttPv = PvNode || (ss->ttHit && tte->is_pv());
622 // At non-PV nodes we check for an early TT cutoff
623 if (!PvNode && !excludedMove && tte->depth() > depth
624 && ttValue != VALUE_NONE // Possible in case of TT access race or if !ttHit
625 && (tte->bound() & (ttValue >= beta ? BOUND_LOWER : BOUND_UPPER)))
627 // If ttMove is quiet, update move sorting heuristics on TT hit (~2 Elo)
632 // Bonus for a quiet ttMove that fails high (~2 Elo)
634 update_quiet_stats(pos, ss, ttMove, stat_bonus(depth));
636 // Extra penalty for early quiet moves of the previous ply (~0 Elo on STC, ~2 Elo on LTC)
637 if (prevSq != SQ_NONE && (ss - 1)->moveCount <= 2 && !priorCapture)
638 update_continuation_histories(ss - 1, pos.piece_on(prevSq), prevSq,
639 -stat_bonus(depth + 1));
641 // Penalty for a quiet ttMove that fails low (~1 Elo)
644 int penalty = -stat_bonus(depth);
645 thisThread->mainHistory[us][from_to(ttMove)] << penalty;
646 update_continuation_histories(ss, pos.moved_piece(ttMove), to_sq(ttMove), penalty);
650 // Partial workaround for the graph history interaction problem
651 // For high rule50 counts don't produce transposition table cutoffs.
652 if (pos.rule50_count() < 90)
656 // Step 5. Tablebases probe
657 if (!rootNode && !excludedMove && TB::Cardinality)
659 int piecesCount = pos.count<ALL_PIECES>();
661 if (piecesCount <= TB::Cardinality
662 && (piecesCount < TB::Cardinality || depth >= TB::ProbeDepth) && pos.rule50_count() == 0
663 && !pos.can_castle(ANY_CASTLING))
666 TB::WDLScore wdl = Tablebases::probe_wdl(pos, &err);
668 // Force check of time on the next occasion
669 if (thisThread == Threads.main())
670 static_cast<MainThread*>(thisThread)->callsCnt = 0;
672 if (err != TB::ProbeState::FAIL)
674 thisThread->tbHits.fetch_add(1, std::memory_order_relaxed);
676 int drawScore = TB::UseRule50 ? 1 : 0;
678 // use the range VALUE_MATE_IN_MAX_PLY to VALUE_TB_WIN_IN_MAX_PLY to score
679 value = wdl < -drawScore ? VALUE_MATED_IN_MAX_PLY + ss->ply + 1
680 : wdl > drawScore ? VALUE_MATE_IN_MAX_PLY - ss->ply - 1
681 : VALUE_DRAW + 2 * wdl * drawScore;
683 Bound b = wdl < -drawScore ? BOUND_UPPER
684 : wdl > drawScore ? BOUND_LOWER
687 if (b == BOUND_EXACT || (b == BOUND_LOWER ? value >= beta : value <= alpha))
689 tte->save(posKey, value_to_tt(value, ss->ply), ss->ttPv, b,
690 std::min(MAX_PLY - 1, depth + 6), MOVE_NONE, VALUE_NONE);
697 if (b == BOUND_LOWER)
698 bestValue = value, alpha = std::max(alpha, bestValue);
706 CapturePieceToHistory& captureHistory = thisThread->captureHistory;
708 // Step 6. Static evaluation of the position
711 // Skip early pruning when in check
712 ss->staticEval = eval = VALUE_NONE;
716 else if (excludedMove)
718 // Providing the hint that this node's accumulator will be used often brings significant Elo gain (~13 Elo)
719 Eval::NNUE::hint_common_parent_position(pos);
720 eval = ss->staticEval;
724 // Never assume anything about values stored in TT
725 ss->staticEval = eval = tte->eval();
726 if (eval == VALUE_NONE)
727 ss->staticEval = eval = evaluate(pos);
729 Eval::NNUE::hint_common_parent_position(pos);
731 // ttValue can be used as a better position evaluation (~7 Elo)
732 if (ttValue != VALUE_NONE && (tte->bound() & (ttValue > eval ? BOUND_LOWER : BOUND_UPPER)))
737 ss->staticEval = eval = evaluate(pos);
738 // Save static evaluation into the transposition table
739 tte->save(posKey, VALUE_NONE, ss->ttPv, BOUND_NONE, DEPTH_NONE, MOVE_NONE, eval);
742 // Use static evaluation difference to improve quiet move ordering (~4 Elo)
743 if (is_ok((ss - 1)->currentMove) && !(ss - 1)->inCheck && !priorCapture)
745 int bonus = std::clamp(-18 * int((ss - 1)->staticEval + ss->staticEval), -1812, 1812);
746 thisThread->mainHistory[~us][from_to((ss - 1)->currentMove)] << bonus;
749 // Set up the improving flag, which is true if current static evaluation is
750 // bigger than the previous static evaluation at our turn (if we were in
751 // check at our previous move we look at static evaluation at move prior to it
752 // and if we were in check at move prior to it flag is set to true) and is
753 // false otherwise. The improving flag is used in various pruning heuristics.
754 improving = (ss - 2)->staticEval != VALUE_NONE ? ss->staticEval > (ss - 2)->staticEval
755 : (ss - 4)->staticEval != VALUE_NONE ? ss->staticEval > (ss - 4)->staticEval
758 // Step 7. Razoring (~1 Elo)
759 // If eval is really low check with qsearch if it can exceed alpha, if it can't,
760 // return a fail low.
761 // Adjust razor margin according to cutoffCnt. (~1 Elo)
762 if (eval < alpha - 492 - (257 - 200 * ((ss + 1)->cutoffCnt > 3)) * depth * depth)
764 value = qsearch<NonPV>(pos, ss, alpha - 1, alpha);
769 // Step 8. Futility pruning: child node (~40 Elo)
770 // The depth condition is important for mate finding.
771 if (!ss->ttPv && depth < 9
772 && eval - futility_margin(depth, cutNode && !ss->ttHit, improving)
773 - (ss - 1)->statScore / 321
775 && eval >= beta && eval < 29462 // smaller than TB wins
776 && !(!ttCapture && ttMove))
779 // Step 9. Null move search with verification search (~35 Elo)
780 if (!PvNode && (ss - 1)->currentMove != MOVE_NULL && (ss - 1)->statScore < 17257 && eval >= beta
781 && eval >= ss->staticEval && ss->staticEval >= beta - 24 * depth + 281 && !excludedMove
782 && pos.non_pawn_material(us) && ss->ply >= thisThread->nmpMinPly
783 && beta > VALUE_TB_LOSS_IN_MAX_PLY)
785 assert(eval - beta >= 0);
787 // Null move dynamic reduction based on depth and eval
788 Depth R = std::min(int(eval - beta) / 152, 6) + depth / 3 + 4;
790 ss->currentMove = MOVE_NULL;
791 ss->continuationHistory = &thisThread->continuationHistory[0][0][NO_PIECE][0];
793 pos.do_null_move(st);
795 Value nullValue = -search<NonPV>(pos, ss + 1, -beta, -beta + 1, depth - R, !cutNode);
797 pos.undo_null_move();
799 // Do not return unproven mate or TB scores
800 if (nullValue >= beta && nullValue < VALUE_TB_WIN_IN_MAX_PLY)
802 if (thisThread->nmpMinPly || depth < 14)
805 assert(!thisThread->nmpMinPly); // Recursive verification is not allowed
807 // Do verification search at high depths, with null move pruning disabled
808 // until ply exceeds nmpMinPly.
809 thisThread->nmpMinPly = ss->ply + 3 * (depth - R) / 4;
811 Value v = search<NonPV>(pos, ss, beta - 1, beta, depth - R, false);
813 thisThread->nmpMinPly = 0;
820 // Step 10. If the position doesn't have a ttMove, decrease depth by 2
821 // (or by 4 if the TT entry for the current position was hit and the stored depth is greater than or equal to the current depth).
822 // Use qsearch if depth is equal or below zero (~9 Elo)
823 if (PvNode && !ttMove)
824 depth -= 2 + 2 * (ss->ttHit && tte->depth() >= depth);
827 return qsearch<PV>(pos, ss, alpha, beta);
829 if (cutNode && depth >= 8 && !ttMove)
832 probCutBeta = beta + 168 - 70 * improving;
834 // Step 11. ProbCut (~10 Elo)
835 // If we have a good enough capture (or queen promotion) and a reduced search returns a value
836 // much above beta, we can (almost) safely prune the previous move.
839 && abs(beta) < VALUE_TB_WIN_IN_MAX_PLY
840 // If value from transposition table is lower than probCutBeta, don't attempt probCut
841 // there and in further interactions with transposition table cutoff depth is set to depth - 3
842 // because probCut search has depth set to depth - 4 but we also do a move before it
843 // So effective depth is equal to depth - 3
844 && !(tte->depth() >= depth - 3 && ttValue != VALUE_NONE && ttValue < probCutBeta))
846 assert(probCutBeta < VALUE_INFINITE);
848 MovePicker mp(pos, ttMove, probCutBeta - ss->staticEval, &captureHistory);
850 while ((move = mp.next_move()) != MOVE_NONE)
851 if (move != excludedMove && pos.legal(move))
853 assert(pos.capture_stage(move));
855 ss->currentMove = move;
856 ss->continuationHistory =
858 ->continuationHistory[ss->inCheck][true][pos.moved_piece(move)][to_sq(move)];
860 pos.do_move(move, st);
862 // Perform a preliminary qsearch to verify that the move holds
863 value = -qsearch<NonPV>(pos, ss + 1, -probCutBeta, -probCutBeta + 1);
865 // If the qsearch held, perform the regular search
866 if (value >= probCutBeta)
867 value = -search<NonPV>(pos, ss + 1, -probCutBeta, -probCutBeta + 1, depth - 4,
872 if (value >= probCutBeta)
874 // Save ProbCut data into transposition table
875 tte->save(posKey, value_to_tt(value, ss->ply), ss->ttPv, BOUND_LOWER, depth - 3,
876 move, ss->staticEval);
877 return value - (probCutBeta - beta);
881 Eval::NNUE::hint_common_parent_position(pos);
884 moves_loop: // When in check, search starts here
886 // Step 12. A small Probcut idea, when we are in check (~4 Elo)
887 probCutBeta = beta + 416;
888 if (ss->inCheck && !PvNode && ttCapture && (tte->bound() & BOUND_LOWER)
889 && tte->depth() >= depth - 4 && ttValue >= probCutBeta
890 && abs(ttValue) < VALUE_TB_WIN_IN_MAX_PLY && abs(beta) < VALUE_TB_WIN_IN_MAX_PLY)
893 const PieceToHistory* contHist[] = {(ss - 1)->continuationHistory,
894 (ss - 2)->continuationHistory,
895 (ss - 3)->continuationHistory,
896 (ss - 4)->continuationHistory,
898 (ss - 6)->continuationHistory};
901 prevSq != SQ_NONE ? thisThread->counterMoves[pos.piece_on(prevSq)][prevSq] : MOVE_NONE;
903 MovePicker mp(pos, ttMove, depth, &thisThread->mainHistory, &captureHistory, contHist,
904 countermove, ss->killers);
907 moveCountPruning = singularQuietLMR = false;
909 // Indicate PvNodes that will probably fail low if the node was searched
910 // at a depth equal to or greater than the current depth, and the result
911 // of this search was a fail low.
912 bool likelyFailLow = PvNode && ttMove && (tte->bound() & BOUND_UPPER) && tte->depth() >= depth;
914 // Step 13. Loop through all pseudo-legal moves until no moves remain
915 // or a beta cutoff occurs.
916 while ((move = mp.next_move(moveCountPruning)) != MOVE_NONE)
920 if (move == excludedMove)
923 // Check for legality
924 if (!pos.legal(move))
927 // At root obey the "searchmoves" option and skip moves not listed in Root
928 // Move List. In MultiPV mode we also skip PV moves that have been already
929 // searched and those of lower "TB rank" if we are in a TB root position.
931 && !std::count(thisThread->rootMoves.begin() + thisThread->pvIdx,
932 thisThread->rootMoves.begin() + thisThread->pvLast, move))
935 ss->moveCount = ++moveCount;
937 if (rootNode && thisThread == Threads.main() && Time.elapsed() > 3000)
938 sync_cout << "info depth " << depth << " currmove "
939 << UCI::move(move, pos.is_chess960()) << " currmovenumber "
940 << moveCount + thisThread->pvIdx << sync_endl;
942 (ss + 1)->pv = nullptr;
945 capture = pos.capture_stage(move);
946 movedPiece = pos.moved_piece(move);
947 givesCheck = pos.gives_check(move);
949 // Calculate new depth for this move
950 newDepth = depth - 1;
952 Value delta = beta - alpha;
954 Depth r = reduction(improving, depth, moveCount, delta, thisThread->rootDelta);
956 // Step 14. Pruning at shallow depth (~120 Elo).
957 // Depth conditions are important for mate finding.
958 if (!rootNode && pos.non_pawn_material(us) && bestValue > VALUE_TB_LOSS_IN_MAX_PLY)
960 // Skip quiet moves if movecount exceeds our FutilityMoveCount threshold (~8 Elo)
961 if (!moveCountPruning)
962 moveCountPruning = moveCount >= futility_move_count(improving, depth);
964 // Reduced depth of the next LMR search
965 int lmrDepth = newDepth - r;
967 if (capture || givesCheck)
969 // Futility pruning for captures (~2 Elo)
970 if (!givesCheck && lmrDepth < 7 && !ss->inCheck
971 && ss->staticEval + 188 + 206 * lmrDepth + PieceValue[pos.piece_on(to_sq(move))]
972 + captureHistory[movedPiece][to_sq(move)]
973 [type_of(pos.piece_on(to_sq(move)))]
978 // SEE based pruning for captures and checks (~11 Elo)
979 if (!pos.see_ge(move, Value(-185) * depth))
984 int history = (*contHist[0])[movedPiece][to_sq(move)]
985 + (*contHist[1])[movedPiece][to_sq(move)]
986 + (*contHist[3])[movedPiece][to_sq(move)];
988 // Continuation history based pruning (~2 Elo)
989 if (lmrDepth < 6 && history < -3232 * depth)
992 history += 2 * thisThread->mainHistory[us][from_to(move)];
994 lmrDepth += history / 5793;
995 lmrDepth = std::max(lmrDepth, -2);
997 // Futility pruning: parent node (~13 Elo)
998 if (!ss->inCheck && lmrDepth < 13 && ss->staticEval + 115 + 122 * lmrDepth <= alpha)
1001 lmrDepth = std::max(lmrDepth, 0);
1003 // Prune moves with negative SEE (~4 Elo)
1004 if (!pos.see_ge(move, Value(-27 * lmrDepth * lmrDepth)))
1009 // Step 15. Extensions (~100 Elo)
1010 // We take care to not overdo to avoid search getting stuck.
1011 if (ss->ply < thisThread->rootDepth * 2)
1013 // Singular extension search (~94 Elo). If all moves but one fail low on a
1014 // search of (alpha-s, beta-s), and just one fails high on (alpha, beta),
1015 // then that move is singular and should be extended. To verify this we do
1016 // a reduced search on all the other moves but the ttMove and if the result
1017 // is lower than ttValue minus a margin, then we will extend the ttMove. Note
1018 // that depth margin and singularBeta margin are known for having non-linear
1019 // scaling. Their values are optimized to time controls of 180+1.8 and longer
1020 // so changing them requires tests at this type of time controls.
1022 && depth >= 4 - (thisThread->completedDepth > 24) + 2 * (PvNode && tte->is_pv())
1023 && move == ttMove && !excludedMove // Avoid recursive singular search
1024 && abs(ttValue) < VALUE_TB_WIN_IN_MAX_PLY && (tte->bound() & BOUND_LOWER)
1025 && tte->depth() >= depth - 3)
1027 Value singularBeta = ttValue - (64 + 57 * (ss->ttPv && !PvNode)) * depth / 64;
1028 Depth singularDepth = (depth - 1) / 2;
1030 ss->excludedMove = move;
1032 search<NonPV>(pos, ss, singularBeta - 1, singularBeta, singularDepth, cutNode);
1033 ss->excludedMove = MOVE_NONE;
1035 if (value < singularBeta)
1038 singularQuietLMR = !ttCapture;
1040 // Avoid search explosion by limiting the number of double extensions
1041 if (!PvNode && value < singularBeta - 18 && ss->doubleExtensions <= 11)
1044 depth += depth < 15;
1048 // Multi-cut pruning
1049 // Our ttMove is assumed to fail high, and now we failed high also on a
1050 // reduced search without the ttMove. So we assume this expected cut-node
1051 // is not singular, that multiple moves fail high, and we can prune the
1052 // whole subtree by returning a softbound.
1053 else if (singularBeta >= beta)
1054 return singularBeta;
1056 // If the eval of ttMove is greater than beta, we reduce it (negative extension) (~7 Elo)
1057 else if (ttValue >= beta)
1058 extension = -2 - !PvNode;
1060 // If we are on a cutNode, reduce it based on depth (negative extension) (~1 Elo)
1062 extension = depth < 19 ? -2 : -1;
1064 // If the eval of ttMove is less than value, we reduce it (negative extension) (~1 Elo)
1065 else if (ttValue <= value)
1069 // Check extensions (~1 Elo)
1070 else if (givesCheck && depth > 9)
1073 // Quiet ttMove extensions (~1 Elo)
1074 else if (PvNode && move == ttMove && move == ss->killers[0]
1075 && (*contHist[0])[movedPiece][to_sq(move)] >= 4194)
1079 // Add extension to new depth
1080 newDepth += extension;
1081 ss->doubleExtensions = (ss - 1)->doubleExtensions + (extension == 2);
1083 // Speculative prefetch as early as possible
1084 prefetch(TT.first_entry(pos.key_after(move)));
1086 // Update the current move (this must be done after singular extension search)
1087 ss->currentMove = move;
1088 ss->continuationHistory =
1089 &thisThread->continuationHistory[ss->inCheck][capture][movedPiece][to_sq(move)];
1091 // Step 16. Make the move
1092 pos.do_move(move, st, givesCheck);
1094 // Decrease reduction if position is or has been on the PV (~4 Elo)
1095 if (ss->ttPv && !likelyFailLow)
1096 r -= cutNode && tte->depth() >= depth ? 3 : 2;
1098 // Decrease reduction if opponent's move count is high (~1 Elo)
1099 if ((ss - 1)->moveCount > 7)
1102 // Increase reduction for cut nodes (~3 Elo)
1106 // Increase reduction if ttMove is a capture (~3 Elo)
1110 // Decrease reduction for PvNodes (~2 Elo)
1114 // Decrease reduction if ttMove has been singularly extended (~1 Elo)
1115 if (singularQuietLMR)
1118 // Increase reduction on repetition (~1 Elo)
1119 if (move == (ss - 4)->currentMove && pos.has_repeated())
1122 // Increase reduction if next ply has a lot of fail high (~5 Elo)
1123 if ((ss + 1)->cutoffCnt > 3)
1126 // Decrease reduction for first generated move (ttMove)
1127 else if (move == ttMove)
1130 ss->statScore = 2 * thisThread->mainHistory[us][from_to(move)]
1131 + (*contHist[0])[movedPiece][to_sq(move)]
1132 + (*contHist[1])[movedPiece][to_sq(move)]
1133 + (*contHist[3])[movedPiece][to_sq(move)] - 3848;
1135 // Decrease/increase reduction for moves with a good/bad history (~25 Elo)
1136 r -= ss->statScore / (10216 + 3855 * (depth > 5 && depth < 23));
1138 // Step 17. Late moves reduction / extension (LMR, ~117 Elo)
1139 // We use various heuristics for the sons of a node after the first son has
1140 // been searched. In general, we would like to reduce them, but there are many
1141 // cases where we extend a son if it has good chances to be "interesting".
1142 if (depth >= 2 && moveCount > 1 + (PvNode && ss->ply <= 1)
1143 && (!ss->ttPv || !capture || (cutNode && (ss - 1)->moveCount > 1)))
1145 // In general we want to cap the LMR depth search at newDepth, but when
1146 // reduction is negative, we allow this move a limited search extension
1147 // beyond the first move depth. This may lead to hidden double extensions.
1148 Depth d = std::clamp(newDepth - r, 1, newDepth + 1);
1150 value = -search<NonPV>(pos, ss + 1, -(alpha + 1), -alpha, d, true);
1152 // Do a full-depth search when reduced LMR search fails high
1153 if (value > alpha && d < newDepth)
1155 // Adjust full-depth search based on LMR results - if the result
1156 // was good enough search deeper, if it was bad enough search shallower.
1157 const bool doDeeperSearch = value > (bestValue + 51 + 10 * (newDepth - d));
1158 const bool doEvenDeeperSearch = value > alpha + 700 && ss->doubleExtensions <= 6;
1159 const bool doShallowerSearch = value < bestValue + newDepth;
1161 ss->doubleExtensions = ss->doubleExtensions + doEvenDeeperSearch;
1163 newDepth += doDeeperSearch - doShallowerSearch + doEvenDeeperSearch;
1166 value = -search<NonPV>(pos, ss + 1, -(alpha + 1), -alpha, newDepth, !cutNode);
1168 int bonus = value <= alpha ? -stat_bonus(newDepth)
1169 : value >= beta ? stat_bonus(newDepth)
1172 update_continuation_histories(ss, movedPiece, to_sq(move), bonus);
1176 // Step 18. Full-depth search when LMR is skipped
1177 else if (!PvNode || moveCount > 1)
1179 // Increase reduction for cut nodes and not ttMove (~1 Elo)
1180 if (!ttMove && cutNode)
1183 // Note that if expected reduction is high, we reduce search depth by 1 here
1184 value = -search<NonPV>(pos, ss + 1, -(alpha + 1), -alpha, newDepth - (r > 3), !cutNode);
1187 // For PV nodes only, do a full PV search on the first move or after a fail high,
1188 // otherwise let the parent node fail low with value <= alpha and try another move.
1189 if (PvNode && (moveCount == 1 || value > alpha))
1192 (ss + 1)->pv[0] = MOVE_NONE;
1194 value = -search<PV>(pos, ss + 1, -beta, -alpha, newDepth, false);
1197 // Step 19. Undo move
1198 pos.undo_move(move);
1200 assert(value > -VALUE_INFINITE && value < VALUE_INFINITE);
1202 // Step 20. Check for a new best move
1203 // Finished searching the move. If a stop occurred, the return value of
1204 // the search cannot be trusted, and we return immediately without
1205 // updating best move, PV and TT.
1206 if (Threads.stop.load(std::memory_order_relaxed))
1212 *std::find(thisThread->rootMoves.begin(), thisThread->rootMoves.end(), move);
1215 rm.averageScore != -VALUE_INFINITE ? (2 * value + rm.averageScore) / 3 : value;
1217 // PV move or new best move?
1218 if (moveCount == 1 || value > alpha)
1220 rm.score = rm.uciScore = value;
1221 rm.selDepth = thisThread->selDepth;
1222 rm.scoreLowerbound = rm.scoreUpperbound = false;
1226 rm.scoreLowerbound = true;
1229 else if (value <= alpha)
1231 rm.scoreUpperbound = true;
1232 rm.uciScore = alpha;
1237 assert((ss + 1)->pv);
1239 for (Move* m = (ss + 1)->pv; *m != MOVE_NONE; ++m)
1240 rm.pv.push_back(*m);
1242 // We record how often the best move has been changed in each iteration.
1243 // This information is used for time management. In MultiPV mode,
1244 // we must take care to only do this for the first PV line.
1245 if (moveCount > 1 && !thisThread->pvIdx)
1246 ++thisThread->bestMoveChanges;
1249 // All other moves but the PV, are set to the lowest value: this
1250 // is not a problem when sorting because the sort is stable and the
1251 // move position in the list is preserved - just the PV is pushed up.
1252 rm.score = -VALUE_INFINITE;
1255 if (value > bestValue)
1263 if (PvNode && !rootNode) // Update pv even in fail-high case
1264 update_pv(ss->pv, move, (ss + 1)->pv);
1268 ss->cutoffCnt += 1 + !ttMove;
1269 assert(value >= beta); // Fail high
1274 // Reduce other moves if we have found at least one score improvement (~2 Elo)
1275 if (depth > 2 && depth < 12 && beta < 13828 && value > -11369)
1279 alpha = value; // Update alpha! Always alpha < beta
1284 // If the move is worse than some previously searched move,
1285 // remember it, to update its stats later.
1286 if (move != bestMove && moveCount <= 32)
1289 capturesSearched[captureCount++] = move;
1292 quietsSearched[quietCount++] = move;
1296 // Step 21. Check for mate and stalemate
1297 // All legal moves have been searched and if there are no legal moves, it
1298 // must be a mate or a stalemate. If we are in a singular extension search then
1299 // return a fail low score.
1301 assert(moveCount || !ss->inCheck || excludedMove || !MoveList<LEGAL>(pos).size());
1304 bestValue = excludedMove ? alpha : ss->inCheck ? mated_in(ss->ply) : VALUE_DRAW;
1306 // If there is a move that produces search value greater than alpha we update the stats of searched moves
1308 update_all_stats(pos, ss, bestMove, bestValue, beta, prevSq, quietsSearched, quietCount,
1309 capturesSearched, captureCount, depth);
1311 // Bonus for prior countermove that caused the fail low
1312 else if (!priorCapture && prevSq != SQ_NONE)
1314 int bonus = (depth > 6) + (PvNode || cutNode) + (bestValue < alpha - 653)
1315 + ((ss - 1)->moveCount > 11);
1316 update_continuation_histories(ss - 1, pos.piece_on(prevSq), prevSq,
1317 stat_bonus(depth) * bonus);
1318 thisThread->mainHistory[~us][from_to((ss - 1)->currentMove)]
1319 << stat_bonus(depth) * bonus / 2;
1323 bestValue = std::min(bestValue, maxValue);
1325 // If no good move is found and the previous position was ttPv, then the previous
1326 // opponent move is probably good and the new position is added to the search tree. (~7 Elo)
1327 if (bestValue <= alpha)
1328 ss->ttPv = ss->ttPv || ((ss - 1)->ttPv && depth > 3);
1330 // Write gathered information in transposition table
1331 if (!excludedMove && !(rootNode && thisThread->pvIdx))
1332 tte->save(posKey, value_to_tt(bestValue, ss->ply), ss->ttPv,
1333 bestValue >= beta ? BOUND_LOWER
1334 : PvNode && bestMove ? BOUND_EXACT
1336 depth, bestMove, ss->staticEval);
1338 assert(bestValue > -VALUE_INFINITE && bestValue < VALUE_INFINITE);
1344 // Quiescence search function, which is called by the main search
1345 // function with zero depth, or recursively with further decreasing depth per call.
1347 template<NodeType nodeType>
1348 Value qsearch(Position& pos, Stack* ss, Value alpha, Value beta, Depth depth) {
1350 static_assert(nodeType != Root);
1351 constexpr bool PvNode = nodeType == PV;
1353 assert(alpha >= -VALUE_INFINITE && alpha < beta && beta <= VALUE_INFINITE);
1354 assert(PvNode || (alpha == beta - 1));
1357 // Check if we have an upcoming move that draws by repetition, or
1358 // if the opponent had an alternative move earlier to this position.
1359 if (alpha < VALUE_DRAW && pos.has_game_cycle(ss->ply))
1361 alpha = value_draw(pos.this_thread());
1366 Move pv[MAX_PLY + 1];
1368 ASSERT_ALIGNED(&st, Eval::NNUE::CacheLineSize);
1372 Move ttMove, move, bestMove;
1374 Value bestValue, value, ttValue, futilityValue, futilityBase;
1375 bool pvHit, givesCheck, capture;
1377 Color us = pos.side_to_move();
1379 // Step 1. Initialize node
1383 ss->pv[0] = MOVE_NONE;
1386 Thread* thisThread = pos.this_thread();
1387 bestMove = MOVE_NONE;
1388 ss->inCheck = pos.checkers();
1391 // Step 2. Check for an immediate draw or maximum ply reached
1392 if (pos.is_draw(ss->ply) || ss->ply >= MAX_PLY)
1393 return (ss->ply >= MAX_PLY && !ss->inCheck) ? evaluate(pos) : VALUE_DRAW;
1395 assert(0 <= ss->ply && ss->ply < MAX_PLY);
1397 // Decide whether or not to include checks: this fixes also the type of
1398 // TT entry depth that we are going to use. Note that in qsearch we use
1399 // only two types of depth in TT: DEPTH_QS_CHECKS or DEPTH_QS_NO_CHECKS.
1400 ttDepth = ss->inCheck || depth >= DEPTH_QS_CHECKS ? DEPTH_QS_CHECKS : DEPTH_QS_NO_CHECKS;
1402 // Step 3. Transposition table lookup
1404 tte = TT.probe(posKey, ss->ttHit);
1405 ttValue = ss->ttHit ? value_from_tt(tte->value(), ss->ply, pos.rule50_count()) : VALUE_NONE;
1406 ttMove = ss->ttHit ? tte->move() : MOVE_NONE;
1407 pvHit = ss->ttHit && tte->is_pv();
1409 // At non-PV nodes we check for an early TT cutoff
1410 if (!PvNode && tte->depth() >= ttDepth
1411 && ttValue != VALUE_NONE // Only in case of TT access race or if !ttHit
1412 && (tte->bound() & (ttValue >= beta ? BOUND_LOWER : BOUND_UPPER)))
1415 // Step 4. Static evaluation of the position
1417 bestValue = futilityBase = -VALUE_INFINITE;
1422 // Never assume anything about values stored in TT
1423 if ((ss->staticEval = bestValue = tte->eval()) == VALUE_NONE)
1424 ss->staticEval = bestValue = evaluate(pos);
1426 // ttValue can be used as a better position evaluation (~13 Elo)
1427 if (ttValue != VALUE_NONE
1428 && (tte->bound() & (ttValue > bestValue ? BOUND_LOWER : BOUND_UPPER)))
1429 bestValue = ttValue;
1432 // In case of null move search use previous static eval with a different sign
1433 ss->staticEval = bestValue =
1434 (ss - 1)->currentMove != MOVE_NULL ? evaluate(pos) : -(ss - 1)->staticEval;
1436 // Stand pat. Return immediately if static value is at least beta
1437 if (bestValue >= beta)
1440 tte->save(posKey, value_to_tt(bestValue, ss->ply), false, BOUND_LOWER, DEPTH_NONE,
1441 MOVE_NONE, ss->staticEval);
1446 if (bestValue > alpha)
1449 futilityBase = ss->staticEval + 200;
1452 const PieceToHistory* contHist[] = {(ss - 1)->continuationHistory,
1453 (ss - 2)->continuationHistory};
1455 // Initialize a MovePicker object for the current position, and prepare
1456 // to search the moves. Because the depth is <= 0 here, only captures,
1457 // queen promotions, and other checks (only if depth >= DEPTH_QS_CHECKS)
1458 // will be generated.
1459 Square prevSq = is_ok((ss - 1)->currentMove) ? to_sq((ss - 1)->currentMove) : SQ_NONE;
1460 MovePicker mp(pos, ttMove, depth, &thisThread->mainHistory, &thisThread->captureHistory,
1463 int quietCheckEvasions = 0;
1465 // Step 5. Loop through all pseudo-legal moves until no moves remain
1466 // or a beta cutoff occurs.
1467 while ((move = mp.next_move()) != MOVE_NONE)
1469 assert(is_ok(move));
1471 // Check for legality
1472 if (!pos.legal(move))
1475 givesCheck = pos.gives_check(move);
1476 capture = pos.capture_stage(move);
1481 if (bestValue > VALUE_TB_LOSS_IN_MAX_PLY && pos.non_pawn_material(us))
1483 // Futility pruning and moveCount pruning (~10 Elo)
1484 if (!givesCheck && to_sq(move) != prevSq && futilityBase > VALUE_TB_LOSS_IN_MAX_PLY
1485 && type_of(move) != PROMOTION)
1490 futilityValue = futilityBase + PieceValue[pos.piece_on(to_sq(move))];
1492 // If static eval + value of piece we are going to capture is much lower
1493 // than alpha we can prune this move.
1494 if (futilityValue <= alpha)
1496 bestValue = std::max(bestValue, futilityValue);
1500 // If static eval is much lower than alpha and move is not winning material
1501 // we can prune this move.
1502 if (futilityBase <= alpha && !pos.see_ge(move, VALUE_ZERO + 1))
1504 bestValue = std::max(bestValue, futilityBase);
1508 // If static exchange evaluation is much worse than what is needed to not
1509 // fall below alpha we can prune this move.
1510 if (futilityBase > alpha && !pos.see_ge(move, (alpha - futilityBase) * 4))
1517 // We prune after the second quiet check evasion move, where being 'in check' is
1518 // implicitly checked through the counter, and being a 'quiet move' apart from
1519 // being a tt move is assumed after an increment because captures are pushed ahead.
1520 if (quietCheckEvasions > 1)
1523 // Continuation history based pruning (~3 Elo)
1524 if (!capture && (*contHist[0])[pos.moved_piece(move)][to_sq(move)] < 0
1525 && (*contHist[1])[pos.moved_piece(move)][to_sq(move)] < 0)
1528 // Do not search moves with bad enough SEE values (~5 Elo)
1529 if (!pos.see_ge(move, Value(-90)))
1533 // Speculative prefetch as early as possible
1534 prefetch(TT.first_entry(pos.key_after(move)));
1536 // Update the current move
1537 ss->currentMove = move;
1538 ss->continuationHistory =
1540 ->continuationHistory[ss->inCheck][capture][pos.moved_piece(move)][to_sq(move)];
1542 quietCheckEvasions += !capture && ss->inCheck;
1544 // Step 7. Make and search the move
1545 pos.do_move(move, st, givesCheck);
1546 value = -qsearch<nodeType>(pos, ss + 1, -beta, -alpha, depth - 1);
1547 pos.undo_move(move);
1549 assert(value > -VALUE_INFINITE && value < VALUE_INFINITE);
1551 // Step 8. Check for a new best move
1552 if (value > bestValue)
1560 if (PvNode) // Update pv even in fail-high case
1561 update_pv(ss->pv, move, (ss + 1)->pv);
1563 if (value < beta) // Update alpha here!
1571 // Step 9. Check for mate
1572 // All legal moves have been searched. A special case: if we're in check
1573 // and no legal moves were found, it is checkmate.
1574 if (ss->inCheck && bestValue == -VALUE_INFINITE)
1576 assert(!MoveList<LEGAL>(pos).size());
1578 return mated_in(ss->ply); // Plies to mate from the root
1581 // Save gathered info in transposition table
1582 tte->save(posKey, value_to_tt(bestValue, ss->ply), pvHit,
1583 bestValue >= beta ? BOUND_LOWER : BOUND_UPPER, ttDepth, bestMove, ss->staticEval);
1585 assert(bestValue > -VALUE_INFINITE && bestValue < VALUE_INFINITE);
1591 // Adjusts a mate or TB score from "plies to mate from the root"
1592 // to "plies to mate from the current position". Standard scores are unchanged.
1593 // The function is called before storing a value in the transposition table.
1594 Value value_to_tt(Value v, int ply) {
1596 assert(v != VALUE_NONE);
1598 return v >= VALUE_TB_WIN_IN_MAX_PLY ? v + ply : v <= VALUE_TB_LOSS_IN_MAX_PLY ? v - ply : v;
1602 // Inverse of value_to_tt(): it adjusts a mate or TB score
1603 // from the transposition table (which refers to the plies to mate/be mated from
1604 // current position) to "plies to mate/be mated (TB win/loss) from the root".
1605 // However, to avoid potentially false mate scores related to the 50 moves rule
1606 // and the graph history interaction problem, we return an optimal TB score instead.
1607 Value value_from_tt(Value v, int ply, int r50c) {
1609 if (v == VALUE_NONE)
1612 if (v >= VALUE_TB_WIN_IN_MAX_PLY) // TB win or better
1614 if (v >= VALUE_MATE_IN_MAX_PLY && VALUE_MATE - v > 99 - r50c)
1615 return VALUE_MATE_IN_MAX_PLY - 1; // do not return a potentially false mate score
1620 if (v <= VALUE_TB_LOSS_IN_MAX_PLY) // TB loss or worse
1622 if (v <= VALUE_MATED_IN_MAX_PLY && VALUE_MATE + v > 99 - r50c)
1623 return VALUE_MATED_IN_MAX_PLY + 1; // do not return a potentially false mate score
1632 // Adds current move and appends child pv[]
1633 void update_pv(Move* pv, Move move, const Move* childPv) {
1635 for (*pv++ = move; childPv && *childPv != MOVE_NONE;)
1641 // Updates stats at the end of search() when a bestMove is found
1642 void update_all_stats(const Position& pos,
1648 Move* quietsSearched,
1650 Move* capturesSearched,
1654 Color us = pos.side_to_move();
1655 Thread* thisThread = pos.this_thread();
1656 CapturePieceToHistory& captureHistory = thisThread->captureHistory;
1657 Piece moved_piece = pos.moved_piece(bestMove);
1660 int quietMoveBonus = stat_bonus(depth + 1);
1662 if (!pos.capture_stage(bestMove))
1664 int bestMoveBonus = bestValue > beta + 168 ? quietMoveBonus // larger bonus
1665 : stat_bonus(depth); // smaller bonus
1667 // Increase stats for the best move in case it was a quiet move
1668 update_quiet_stats(pos, ss, bestMove, bestMoveBonus);
1670 // Decrease stats for all non-best quiet moves
1671 for (int i = 0; i < quietCount; ++i)
1673 thisThread->mainHistory[us][from_to(quietsSearched[i])] << -bestMoveBonus;
1674 update_continuation_histories(ss, pos.moved_piece(quietsSearched[i]),
1675 to_sq(quietsSearched[i]), -bestMoveBonus);
1680 // Increase stats for the best move in case it was a capture move
1681 captured = type_of(pos.piece_on(to_sq(bestMove)));
1682 captureHistory[moved_piece][to_sq(bestMove)][captured] << quietMoveBonus;
1685 // Extra penalty for a quiet early move that was not a TT move or
1686 // main killer move in previous ply when it gets refuted.
1687 if (prevSq != SQ_NONE
1688 && ((ss - 1)->moveCount == 1 + (ss - 1)->ttHit
1689 || ((ss - 1)->currentMove == (ss - 1)->killers[0]))
1690 && !pos.captured_piece())
1691 update_continuation_histories(ss - 1, pos.piece_on(prevSq), prevSq, -quietMoveBonus);
1693 // Decrease stats for all non-best capture moves
1694 for (int i = 0; i < captureCount; ++i)
1696 moved_piece = pos.moved_piece(capturesSearched[i]);
1697 captured = type_of(pos.piece_on(to_sq(capturesSearched[i])));
1698 captureHistory[moved_piece][to_sq(capturesSearched[i])][captured] << -quietMoveBonus;
1703 // Updates histories of the move pairs formed
1704 // by moves at ply -1, -2, -4, and -6 with current move.
1705 void update_continuation_histories(Stack* ss, Piece pc, Square to, int bonus) {
1707 for (int i : {1, 2, 3, 4, 6})
1709 // Only update the first 2 continuation histories if we are in check
1710 if (ss->inCheck && i > 2)
1712 if (is_ok((ss - i)->currentMove))
1713 (*(ss - i)->continuationHistory)[pc][to] << bonus / (1 + 3 * (i == 3));
1718 // Updates move sorting heuristics
1719 void update_quiet_stats(const Position& pos, Stack* ss, Move move, int bonus) {
1722 if (ss->killers[0] != move)
1724 ss->killers[1] = ss->killers[0];
1725 ss->killers[0] = move;
1728 Color us = pos.side_to_move();
1729 Thread* thisThread = pos.this_thread();
1730 thisThread->mainHistory[us][from_to(move)] << bonus;
1731 update_continuation_histories(ss, pos.moved_piece(move), to_sq(move), bonus);
1733 // Update countermove history
1734 if (is_ok((ss - 1)->currentMove))
1736 Square prevSq = to_sq((ss - 1)->currentMove);
1737 thisThread->counterMoves[pos.piece_on(prevSq)][prevSq] = move;
1741 // When playing with strength handicap, choose the best move among a set of RootMoves
1742 // using a statistical rule dependent on 'level'. Idea by Heinz van Saanen.
1743 Move Skill::pick_best(size_t multiPV) {
1745 const RootMoves& rootMoves = Threads.main()->rootMoves;
1746 static PRNG rng(now()); // PRNG sequence should be non-deterministic
1748 // RootMoves are already sorted by score in descending order
1749 Value topScore = rootMoves[0].score;
1750 int delta = std::min(topScore - rootMoves[multiPV - 1].score, PawnValue);
1751 int maxScore = -VALUE_INFINITE;
1752 double weakness = 120 - 2 * level;
1754 // Choose best move. For each move score we add two terms, both dependent on
1755 // weakness. One is deterministic and bigger for weaker levels, and one is
1756 // random. Then we choose the move with the resulting highest score.
1757 for (size_t i = 0; i < multiPV; ++i)
1759 // This is our magic formula
1760 int push = int((weakness * int(topScore - rootMoves[i].score)
1761 + delta * (rng.rand<unsigned>() % int(weakness)))
1764 if (rootMoves[i].score + push >= maxScore)
1766 maxScore = rootMoves[i].score + push;
1767 best = rootMoves[i].pv[0];
1777 // Used to print debug info and, more importantly,
1778 // to detect when we are out of available time and thus stop the search.
1779 void MainThread::check_time() {
1784 // When using nodes, ensure checking rate is not lower than 0.1% of nodes
1785 callsCnt = Limits.nodes ? std::min(512, int(Limits.nodes / 1024)) : 512;
1787 static TimePoint lastInfoTime = now();
1789 TimePoint elapsed = Time.elapsed();
1790 TimePoint tick = Limits.startTime + elapsed;
1792 if (tick - lastInfoTime >= 1000)
1794 lastInfoTime = tick;
1798 // We should not stop pondering until told so by the GUI
1802 if ((Limits.use_time_management() && (elapsed > Time.maximum() || stopOnPonderhit))
1803 || (Limits.movetime && elapsed >= Limits.movetime)
1804 || (Limits.nodes && Threads.nodes_searched() >= uint64_t(Limits.nodes)))
1805 Threads.stop = true;
1809 // Formats PV information according to the UCI protocol. UCI requires
1810 // that all (if any) unsearched PV lines are sent using a previous search score.
1811 string UCI::pv(const Position& pos, Depth depth) {
1813 std::stringstream ss;
1814 TimePoint elapsed = Time.elapsed() + 1;
1815 const RootMoves& rootMoves = pos.this_thread()->rootMoves;
1816 size_t pvIdx = pos.this_thread()->pvIdx;
1817 size_t multiPV = std::min(size_t(Options["MultiPV"]), rootMoves.size());
1818 uint64_t nodesSearched = Threads.nodes_searched();
1819 uint64_t tbHits = Threads.tb_hits() + (TB::RootInTB ? rootMoves.size() : 0);
1821 for (size_t i = 0; i < multiPV; ++i)
1823 bool updated = rootMoves[i].score != -VALUE_INFINITE;
1825 if (depth == 1 && !updated && i > 0)
1828 Depth d = updated ? depth : std::max(1, depth - 1);
1829 Value v = updated ? rootMoves[i].uciScore : rootMoves[i].previousScore;
1831 if (v == -VALUE_INFINITE)
1834 bool tb = TB::RootInTB && abs(v) < VALUE_MATE_IN_MAX_PLY;
1835 v = tb ? rootMoves[i].tbScore : v;
1837 if (ss.rdbuf()->in_avail()) // Not at first line
1841 << " depth " << d << " seldepth " << rootMoves[i].selDepth << " multipv " << i + 1
1842 << " score " << UCI::value(v);
1844 if (Options["UCI_ShowWDL"])
1845 ss << UCI::wdl(v, pos.game_ply());
1847 if (i == pvIdx && !tb && updated) // tablebase- and previous-scores are exact
1848 ss << (rootMoves[i].scoreLowerbound
1850 : (rootMoves[i].scoreUpperbound ? " upperbound" : ""));
1852 ss << " nodes " << nodesSearched << " nps " << nodesSearched * 1000 / elapsed
1853 << " hashfull " << TT.hashfull() << " tbhits " << tbHits << " time " << elapsed << " pv";
1855 for (Move m : rootMoves[i].pv)
1856 ss << " " << UCI::move(m, pos.is_chess960());
1863 // Called in case we have no ponder move
1864 // before exiting the search, for instance, in case we stop the search during a
1865 // fail high at root. We try hard to have a ponder move to return to the GUI,
1866 // otherwise in case of 'ponder on' we have nothing to think about.
1867 bool RootMove::extract_ponder_from_tt(Position& pos) {
1870 ASSERT_ALIGNED(&st, Eval::NNUE::CacheLineSize);
1874 assert(pv.size() == 1);
1876 if (pv[0] == MOVE_NONE)
1879 pos.do_move(pv[0], st);
1880 TTEntry* tte = TT.probe(pos.key(), ttHit);
1884 Move m = tte->move(); // Local copy to be SMP safe
1885 if (MoveList<LEGAL>(pos).contains(m))
1889 pos.undo_move(pv[0]);
1890 return pv.size() > 1;
1893 void Tablebases::rank_root_moves(Position& pos, Search::RootMoves& rootMoves) {
1896 UseRule50 = bool(Options["Syzygy50MoveRule"]);
1897 ProbeDepth = int(Options["SyzygyProbeDepth"]);
1898 Cardinality = int(Options["SyzygyProbeLimit"]);
1899 bool dtz_available = true;
1901 // Tables with fewer pieces than SyzygyProbeLimit are searched with
1902 // ProbeDepth == DEPTH_ZERO
1903 if (Cardinality > MaxCardinality)
1905 Cardinality = MaxCardinality;
1909 if (Cardinality >= popcount(pos.pieces()) && !pos.can_castle(ANY_CASTLING))
1911 // Rank moves using DTZ tables
1912 RootInTB = root_probe(pos, rootMoves);
1916 // DTZ tables are missing; try to rank moves using WDL tables
1917 dtz_available = false;
1918 RootInTB = root_probe_wdl(pos, rootMoves);
1924 // Sort moves according to TB rank
1925 std::stable_sort(rootMoves.begin(), rootMoves.end(),
1926 [](const RootMove& a, const RootMove& b) { return a.tbRank > b.tbRank; });
1928 // Probe during search only if DTZ is not available and we are winning
1929 if (dtz_available || rootMoves[0].tbScore <= VALUE_DRAW)
1934 // Clean up if root_probe() and root_probe_wdl() have failed
1935 for (auto& m : rootMoves)
1940 } // namespace Stockfish