2 Stockfish, a UCI chess playing engine derived from Glaurung 2.1
3 Copyright (C) 2004-2022 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/>.
22 #include <cstring> // For std::memset
36 #include "syzygy/tbprobe.h"
45 namespace Tablebases {
53 namespace TB = Tablebases;
57 using namespace Search;
61 // Different node types, used as a template parameter
62 enum NodeType { NonPV, PV, Root };
65 Value futility_margin(Depth d, bool improving) {
66 return Value(214 * (d - improving));
69 // Reductions lookup table, initialized at startup
70 int Reductions[MAX_MOVES]; // [depth or moveNumber]
72 Depth reduction(bool i, Depth d, int mn, Value delta, Value rootDelta) {
73 int r = Reductions[d] * Reductions[mn];
74 return (r + 1358 - int(delta) * 1024 / int(rootDelta)) / 1024 + (!i && r > 904);
77 constexpr int futility_move_count(bool improving, Depth depth) {
78 return (3 + depth * depth) / (2 - improving);
81 // History and stats update bonus, based on depth
82 int stat_bonus(Depth d) {
83 return std::min((6 * d + 229) * d - 215 , 2000);
86 // Add a small random component to draw evaluations to avoid 3-fold blindness
87 Value value_draw(Thread* thisThread) {
88 return VALUE_DRAW + Value(2 * (thisThread->nodes & 1) - 1);
91 // Check if the current thread is in a search explosion
92 ExplosionState search_explosion(Thread* thisThread) {
94 uint64_t nodesNow = thisThread->nodes;
95 bool explosive = thisThread->doubleExtensionAverage[WHITE].is_greater(2, 100)
96 || thisThread->doubleExtensionAverage[BLACK].is_greater(2, 100);
99 thisThread->nodesLastExplosive = nodesNow;
101 thisThread->nodesLastNormal = nodesNow;
104 && thisThread->state == EXPLOSION_NONE
105 && nodesNow - thisThread->nodesLastNormal > 6000000)
106 thisThread->state = MUST_CALM_DOWN;
108 if ( thisThread->state == MUST_CALM_DOWN
109 && nodesNow - thisThread->nodesLastExplosive > 6000000)
110 thisThread->state = EXPLOSION_NONE;
112 return thisThread->state;
115 // Skill structure is used to implement strength limit. If we have an uci_elo then
116 // we convert it to a suitable fractional skill level using anchoring to CCRL Elo
117 // (goldfish 1.13 = 2000) and a fit through Ordo derived Elo for match (TC 60+0.6)
118 // results spanning a wide range of k values.
120 Skill(int skill_level, int uci_elo) {
122 level = std::clamp(std::pow((uci_elo - 1346.6) / 143.4, 1 / 0.806), 0.0, 20.0);
124 level = double(skill_level);
126 bool enabled() const { return level < 20.0; }
127 bool time_to_pick(Depth depth) const { return depth == 1 + int(level); }
128 Move pick_best(size_t multiPV);
131 Move best = MOVE_NONE;
134 template <NodeType nodeType>
135 Value search(Position& pos, Stack* ss, Value alpha, Value beta, Depth depth, bool cutNode);
137 template <NodeType nodeType>
138 Value qsearch(Position& pos, Stack* ss, Value alpha, Value beta, Depth depth = 0);
140 Value value_to_tt(Value v, int ply);
141 Value value_from_tt(Value v, int ply, int r50c);
142 void update_pv(Move* pv, Move move, Move* childPv);
143 void update_continuation_histories(Stack* ss, Piece pc, Square to, int bonus);
144 void update_quiet_stats(const Position& pos, Stack* ss, Move move, int bonus);
145 void update_all_stats(const Position& pos, Stack* ss, Move bestMove, Value bestValue, Value beta, Square prevSq,
146 Move* quietsSearched, int quietCount, Move* capturesSearched, int captureCount, Depth depth);
148 // perft() is our utility to verify move generation. All the leaf nodes up
149 // to the given depth are generated and counted, and the sum is returned.
151 uint64_t perft(Position& pos, Depth depth) {
154 ASSERT_ALIGNED(&st, Eval::NNUE::CacheLineSize);
156 uint64_t cnt, nodes = 0;
157 const bool leaf = (depth == 2);
159 for (const auto& m : MoveList<LEGAL>(pos))
161 if (Root && depth <= 1)
166 cnt = leaf ? MoveList<LEGAL>(pos).size() : perft<false>(pos, depth - 1);
171 sync_cout << UCI::move(m, pos.is_chess960()) << ": " << cnt << sync_endl;
179 /// Search::init() is called at startup to initialize various lookup tables
181 void Search::init() {
183 for (int i = 1; i < MAX_MOVES; ++i)
184 Reductions[i] = int((21.9 + std::log(Threads.size()) / 2) * std::log(i));
188 /// Search::clear() resets search state to its initial value
190 void Search::clear() {
192 Threads.main()->wait_for_search_finished();
194 Time.availableNodes = 0;
197 Tablebases::init(Options["SyzygyPath"]); // Free mapped files
201 /// MainThread::search() is started when the program receives the UCI 'go'
202 /// 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)
228 Threads.start_searching(); // start non-main threads
229 Thread::search(); // main thread start searching
232 // When we reach the maximum depth, we can arrive here without a raise of
233 // Threads.stop. However, if we are pondering or in an infinite search,
234 // the UCI protocol states that we shouldn't print the best move before the
235 // GUI sends a "stop" or "ponderhit" command. We therefore simply wait here
236 // until the GUI sends one of those commands.
238 while (!Threads.stop && (ponder || Limits.infinite))
239 {} // Busy wait for a stop or a ponder reset
241 // Stop the threads if not already stopped (also raise the stop if
242 // "ponderhit" just reset Threads.ponder).
245 // Wait until all threads have finished
246 Threads.wait_for_search_finished();
248 // When playing in 'nodes as time' mode, subtract the searched nodes from
249 // the available ones before exiting.
251 Time.availableNodes += Limits.inc[us] - Threads.nodes_searched();
253 Thread* bestThread = this;
254 Skill skill = Skill(Options["Skill Level"], Options["UCI_LimitStrength"] ? int(Options["UCI_Elo"]) : 0);
256 if ( int(Options["MultiPV"]) == 1
259 && rootMoves[0].pv[0] != MOVE_NONE)
260 bestThread = Threads.get_best_thread();
262 bestPreviousScore = bestThread->rootMoves[0].score;
263 bestPreviousAverageScore = bestThread->rootMoves[0].averageScore;
265 // Send again PV info if we have a new best thread
266 if (bestThread != this)
267 sync_cout << UCI::pv(bestThread->rootPos, bestThread->completedDepth, -VALUE_INFINITE, VALUE_INFINITE) << sync_endl;
269 sync_cout << "bestmove " << UCI::move(bestThread->rootMoves[0].pv[0], rootPos.is_chess960());
271 if (bestThread->rootMoves[0].pv.size() > 1 || bestThread->rootMoves[0].extract_ponder_from_tt(rootPos))
272 std::cout << " ponder " << UCI::move(bestThread->rootMoves[0].pv[1], rootPos.is_chess960());
274 std::cout << sync_endl;
278 /// Thread::search() is the main iterative deepening loop. It calls search()
279 /// repeatedly with increasing depth until the allocated thinking time has been
280 /// consumed, the user stops the search, or the maximum search depth is reached.
282 void Thread::search() {
284 // To allow access to (ss-7) up to (ss+2), the stack must be oversized.
285 // The former is needed to allow update_continuation_histories(ss-1, ...),
286 // which accesses its argument at ss-6, also near the root.
287 // The latter is needed for statScore and killer initialization.
288 Stack stack[MAX_PLY+10], *ss = stack+7;
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--)
300 (ss-i)->continuationHistory = &this->continuationHistory[0][0][NO_PIECE][0]; // Use as a sentinel
302 for (int i = 0; i <= MAX_PLY + 2; ++i)
307 bestValue = delta = alpha = -VALUE_INFINITE;
308 beta = 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 doubleExtensionAverage[WHITE].set(0, 100); // initialize the running average at 0%
331 doubleExtensionAverage[BLACK].set(0, 100); // initialize the running average at 0%
333 nodesLastExplosive = nodes;
334 nodesLastNormal = nodes;
335 state = EXPLOSION_NONE;
337 optimism[ us] = Value(25);
338 optimism[~us] = -optimism[us];
340 int searchAgainCounter = 0;
342 // Iterative deepening loop until requested to stop or the target depth is reached
343 while ( ++rootDepth < MAX_PLY
345 && !(Limits.depth && mainThread && rootDepth > Limits.depth))
347 // Age out PV variability metric
349 totBestMoveChanges /= 2;
351 // Save the last iteration's scores before first PV line is searched and
352 // all the move scores except the (new) PV are set to -VALUE_INFINITE.
353 for (RootMove& rm : rootMoves)
354 rm.previousScore = rm.score;
359 if (!Threads.increaseDepth)
360 searchAgainCounter++;
362 // MultiPV loop. We perform a full root search for each PV line
363 for (pvIdx = 0; pvIdx < multiPV && !Threads.stop; ++pvIdx)
368 for (pvLast++; pvLast < rootMoves.size(); pvLast++)
369 if (rootMoves[pvLast].tbRank != rootMoves[pvFirst].tbRank)
373 // Reset UCI info selDepth for each depth and each PV line
376 // Reset aspiration window starting size
379 Value prev = rootMoves[pvIdx].averageScore;
380 delta = Value(17) + int(prev) * prev / 16384;
381 alpha = std::max(prev - delta,-VALUE_INFINITE);
382 beta = std::min(prev + delta, VALUE_INFINITE);
384 // Adjust trend and optimism based on root move's previousScore
385 int tr = sigmoid(prev, 0, 0, 147, 113, 1);
386 trend = (us == WHITE ? make_score(tr, tr / 2)
387 : -make_score(tr, tr / 2));
389 int opt = sigmoid(prev, 0, 25, 147, 14464, 256);
390 optimism[ us] = Value(opt);
391 optimism[~us] = -optimism[us];
394 // Start with a small aspiration window and, in the case of a fail
395 // high/low, re-search with a bigger window until we don't fail
397 int failedHighCnt = 0;
400 Depth adjustedDepth = std::max(1, rootDepth - failedHighCnt - searchAgainCounter);
401 bestValue = Stockfish::search<Root>(rootPos, ss, alpha, beta, adjustedDepth, false);
403 // Bring the best move to the front. It is critical that sorting
404 // is done with a stable algorithm because all the values but the
405 // first and eventually the new best one are set to -VALUE_INFINITE
406 // and we want to keep the same order for all the moves except the
407 // new PV that goes to the front. Note that in case of MultiPV
408 // search the already searched PV lines are preserved.
409 std::stable_sort(rootMoves.begin() + pvIdx, rootMoves.begin() + pvLast);
411 // If search has been stopped, we break immediately. Sorting is
412 // safe because RootMoves is still valid, although it refers to
413 // the previous iteration.
417 // When failing high/low give some update (without cluttering
418 // the UI) before a re-search.
421 && (bestValue <= alpha || bestValue >= beta)
422 && Time.elapsed() > 3000)
423 sync_cout << UCI::pv(rootPos, rootDepth, alpha, beta) << sync_endl;
425 // In case of failing low/high increase aspiration window and
426 // re-search, otherwise exit the loop.
427 if (bestValue <= alpha)
429 beta = (alpha + beta) / 2;
430 alpha = std::max(bestValue - delta, -VALUE_INFINITE);
434 mainThread->stopOnPonderhit = false;
436 else if (bestValue >= beta)
438 beta = std::min(bestValue + delta, VALUE_INFINITE);
444 delta += delta / 4 + 5;
446 assert(alpha >= -VALUE_INFINITE && beta <= VALUE_INFINITE);
449 // Sort the PV lines searched so far and update the GUI
450 std::stable_sort(rootMoves.begin() + pvFirst, rootMoves.begin() + pvIdx + 1);
453 && (Threads.stop || pvIdx + 1 == multiPV || Time.elapsed() > 3000))
454 sync_cout << UCI::pv(rootPos, rootDepth, alpha, beta) << sync_endl;
458 completedDepth = rootDepth;
460 if (rootMoves[0].pv[0] != lastBestMove) {
461 lastBestMove = rootMoves[0].pv[0];
462 lastBestMoveDepth = rootDepth;
465 // Have we found a "mate in x"?
467 && bestValue >= VALUE_MATE_IN_MAX_PLY
468 && VALUE_MATE - bestValue <= 2 * Limits.mate)
474 // If skill level is enabled and time is up, pick a sub-optimal best move
475 if (skill.enabled() && skill.time_to_pick(rootDepth))
476 skill.pick_best(multiPV);
478 // Use part of the gained time from a previous stable move for the current move
479 for (Thread* th : Threads)
481 totBestMoveChanges += th->bestMoveChanges;
482 th->bestMoveChanges = 0;
485 // Do we have time for the next iteration? Can we stop searching now?
486 if ( Limits.use_time_management()
488 && !mainThread->stopOnPonderhit)
490 double fallingEval = (142 + 12 * (mainThread->bestPreviousAverageScore - bestValue)
491 + 6 * (mainThread->iterValue[iterIdx] - bestValue)) / 825.0;
492 fallingEval = std::clamp(fallingEval, 0.5, 1.5);
494 // If the bestMove is stable over several iterations, reduce time accordingly
495 timeReduction = lastBestMoveDepth + 9 < completedDepth ? 1.92 : 0.95;
496 double reduction = (1.47 + mainThread->previousTimeReduction) / (2.32 * timeReduction);
497 double bestMoveInstability = 1.073 + std::max(1.0, 2.25 - 9.9 / rootDepth)
498 * totBestMoveChanges / Threads.size();
499 double totalTime = Time.optimum() * fallingEval * reduction * bestMoveInstability;
501 // Cap used time in case of a single legal move for a better viewer experience in tournaments
502 // yielding correct scores and sufficiently fast moves.
503 if (rootMoves.size() == 1)
504 totalTime = std::min(500.0, totalTime);
506 // Stop the search if we have exceeded the totalTime
507 if (Time.elapsed() > totalTime)
509 // If we are allowed to ponder do not stop the search now but
510 // keep pondering until the GUI sends "ponderhit" or "stop".
511 if (mainThread->ponder)
512 mainThread->stopOnPonderhit = true;
516 else if ( Threads.increaseDepth
517 && !mainThread->ponder
518 && Time.elapsed() > totalTime * 0.58)
519 Threads.increaseDepth = false;
521 Threads.increaseDepth = true;
524 mainThread->iterValue[iterIdx] = bestValue;
525 iterIdx = (iterIdx + 1) & 3;
531 mainThread->previousTimeReduction = timeReduction;
533 // If skill level is enabled, swap best PV line with the sub-optimal one
535 std::swap(rootMoves[0], *std::find(rootMoves.begin(), rootMoves.end(),
536 skill.best ? skill.best : skill.pick_best(multiPV)));
542 // search<>() is the main search function for both PV and non-PV nodes
544 template <NodeType nodeType>
545 Value search(Position& pos, Stack* ss, Value alpha, Value beta, Depth depth, bool cutNode) {
547 Thread* thisThread = pos.this_thread();
549 // Step 0. Limit search explosion
551 && search_explosion(thisThread) == MUST_CALM_DOWN
552 && depth > (ss-1)->depth)
553 depth = (ss-1)->depth;
555 constexpr bool PvNode = nodeType != NonPV;
556 constexpr bool rootNode = nodeType == Root;
557 const Depth maxNextDepth = rootNode ? depth : depth + 1;
559 // Check if we have an upcoming move which draws by repetition, or
560 // if the opponent had an alternative move earlier to this position.
562 && pos.rule50_count() >= 3
563 && alpha < VALUE_DRAW
564 && pos.has_game_cycle(ss->ply))
566 alpha = value_draw(pos.this_thread());
571 // Dive into quiescence search when the depth reaches zero
573 return qsearch<PvNode ? PV : NonPV>(pos, ss, alpha, beta);
575 assert(-VALUE_INFINITE <= alpha && alpha < beta && beta <= VALUE_INFINITE);
576 assert(PvNode || (alpha == beta - 1));
577 assert(0 < depth && depth < MAX_PLY);
578 assert(!(PvNode && cutNode));
580 Move pv[MAX_PLY+1], capturesSearched[32], quietsSearched[64];
582 ASSERT_ALIGNED(&st, Eval::NNUE::CacheLineSize);
586 Move ttMove, move, excludedMove, bestMove;
587 Depth extension, newDepth;
588 Value bestValue, value, ttValue, eval, maxValue, probCutBeta;
589 bool givesCheck, improving, didLMR, priorCapture;
590 bool captureOrPromotion, doFullDepthSearch, moveCountPruning, ttCapture;
592 int moveCount, captureCount, quietCount, bestMoveCount, improvement;
594 // Step 1. Initialize node
595 ss->inCheck = pos.checkers();
596 priorCapture = pos.captured_piece();
597 Color us = pos.side_to_move();
598 moveCount = bestMoveCount = captureCount = quietCount = ss->moveCount = 0;
599 bestValue = -VALUE_INFINITE;
600 maxValue = VALUE_INFINITE;
602 // Check for the available remaining time
603 if (thisThread == Threads.main())
604 static_cast<MainThread*>(thisThread)->check_time();
606 // Used to send selDepth info to GUI (selDepth counts from 1, ply from 0)
607 if (PvNode && thisThread->selDepth < ss->ply + 1)
608 thisThread->selDepth = ss->ply + 1;
612 // Step 2. Check for aborted search and immediate draw
613 if ( Threads.stop.load(std::memory_order_relaxed)
614 || pos.is_draw(ss->ply)
615 || ss->ply >= MAX_PLY)
616 return (ss->ply >= MAX_PLY && !ss->inCheck) ? evaluate(pos)
617 : value_draw(pos.this_thread());
619 // Step 3. Mate distance pruning. Even if we mate at the next move our score
620 // would be at best mate_in(ss->ply+1), but if alpha is already bigger because
621 // a shorter mate was found upward in the tree then there is no need to search
622 // because we will never beat the current alpha. Same logic but with reversed
623 // signs applies also in the opposite condition of being mated instead of giving
624 // mate. In this case return a fail-high score.
625 alpha = std::max(mated_in(ss->ply), alpha);
626 beta = std::min(mate_in(ss->ply+1), beta);
631 thisThread->rootDelta = beta - alpha;
633 assert(0 <= ss->ply && ss->ply < MAX_PLY);
635 (ss+1)->ttPv = false;
636 (ss+1)->excludedMove = bestMove = MOVE_NONE;
637 (ss+2)->killers[0] = (ss+2)->killers[1] = MOVE_NONE;
638 ss->doubleExtensions = (ss-1)->doubleExtensions;
640 Square prevSq = to_sq((ss-1)->currentMove);
642 // Update the running average statistics for double extensions
643 thisThread->doubleExtensionAverage[us].update(ss->depth > (ss-1)->depth);
645 // Initialize statScore to zero for the grandchildren of the current position.
646 // So statScore is shared between all grandchildren and only the first grandchild
647 // starts with statScore = 0. Later grandchildren start with the last calculated
648 // statScore of the previous grandchild. This influences the reduction rules in
649 // LMR which are based on the statScore of parent position.
651 (ss+2)->statScore = 0;
653 // Step 4. Transposition table lookup. We don't want the score of a partial
654 // search to overwrite a previous full search TT value, so we use a different
655 // position key in case of an excluded move.
656 excludedMove = ss->excludedMove;
657 posKey = excludedMove == MOVE_NONE ? pos.key() : pos.key() ^ make_key(excludedMove);
658 tte = TT.probe(posKey, ss->ttHit);
659 ttValue = ss->ttHit ? value_from_tt(tte->value(), ss->ply, pos.rule50_count()) : VALUE_NONE;
660 ttMove = rootNode ? thisThread->rootMoves[thisThread->pvIdx].pv[0]
661 : ss->ttHit ? tte->move() : MOVE_NONE;
662 ttCapture = ttMove && pos.capture_or_promotion(ttMove);
664 ss->ttPv = PvNode || (ss->ttHit && tte->is_pv());
666 // At non-PV nodes we check for an early TT cutoff
669 && tte->depth() > depth - (thisThread->id() % 2 == 1)
670 && ttValue != VALUE_NONE // Possible in case of TT access race
671 && (ttValue >= beta ? (tte->bound() & BOUND_LOWER)
672 : (tte->bound() & BOUND_UPPER)))
674 // If ttMove is quiet, update move sorting heuristics on TT hit (~1 Elo)
679 // Bonus for a quiet ttMove that fails high (~3 Elo)
681 update_quiet_stats(pos, ss, ttMove, stat_bonus(depth));
683 // Extra penalty for early quiet moves of the previous ply (~0 Elo)
684 if ((ss-1)->moveCount <= 2 && !priorCapture)
685 update_continuation_histories(ss-1, pos.piece_on(prevSq), prevSq, -stat_bonus(depth + 1));
687 // Penalty for a quiet ttMove that fails low (~1 Elo)
690 int penalty = -stat_bonus(depth);
691 thisThread->mainHistory[us][from_to(ttMove)] << penalty;
692 update_continuation_histories(ss, pos.moved_piece(ttMove), to_sq(ttMove), penalty);
696 // Partial workaround for the graph history interaction problem
697 // For high rule50 counts don't produce transposition table cutoffs.
698 if (pos.rule50_count() < 90)
702 // Step 5. Tablebases probe
703 if (!rootNode && TB::Cardinality)
705 int piecesCount = pos.count<ALL_PIECES>();
707 if ( piecesCount <= TB::Cardinality
708 && (piecesCount < TB::Cardinality || depth >= TB::ProbeDepth)
709 && pos.rule50_count() == 0
710 && !pos.can_castle(ANY_CASTLING))
713 TB::WDLScore wdl = Tablebases::probe_wdl(pos, &err);
715 // Force check of time on the next occasion
716 if (thisThread == Threads.main())
717 static_cast<MainThread*>(thisThread)->callsCnt = 0;
719 if (err != TB::ProbeState::FAIL)
721 thisThread->tbHits.fetch_add(1, std::memory_order_relaxed);
723 int drawScore = TB::UseRule50 ? 1 : 0;
725 // use the range VALUE_MATE_IN_MAX_PLY to VALUE_TB_WIN_IN_MAX_PLY to score
726 value = wdl < -drawScore ? VALUE_MATED_IN_MAX_PLY + ss->ply + 1
727 : wdl > drawScore ? VALUE_MATE_IN_MAX_PLY - ss->ply - 1
728 : VALUE_DRAW + 2 * wdl * drawScore;
730 Bound b = wdl < -drawScore ? BOUND_UPPER
731 : wdl > drawScore ? BOUND_LOWER : BOUND_EXACT;
733 if ( b == BOUND_EXACT
734 || (b == BOUND_LOWER ? value >= beta : value <= alpha))
736 tte->save(posKey, value_to_tt(value, ss->ply), ss->ttPv, b,
737 std::min(MAX_PLY - 1, depth + 6),
738 MOVE_NONE, VALUE_NONE);
745 if (b == BOUND_LOWER)
746 bestValue = value, alpha = std::max(alpha, bestValue);
754 CapturePieceToHistory& captureHistory = thisThread->captureHistory;
756 // Step 6. Static evaluation of the position
759 // Skip early pruning when in check
760 ss->staticEval = eval = VALUE_NONE;
767 // Never assume anything about values stored in TT
768 ss->staticEval = eval = tte->eval();
769 if (eval == VALUE_NONE)
770 ss->staticEval = eval = evaluate(pos);
772 // Randomize draw evaluation
773 if (eval == VALUE_DRAW)
774 eval = value_draw(thisThread);
776 // ttValue can be used as a better position evaluation (~4 Elo)
777 if ( ttValue != VALUE_NONE
778 && (tte->bound() & (ttValue > eval ? BOUND_LOWER : BOUND_UPPER)))
783 ss->staticEval = eval = evaluate(pos);
785 // Save static evaluation into transposition table
787 tte->save(posKey, VALUE_NONE, ss->ttPv, BOUND_NONE, DEPTH_NONE, MOVE_NONE, eval);
790 // Use static evaluation difference to improve quiet move ordering (~3 Elo)
791 if (is_ok((ss-1)->currentMove) && !(ss-1)->inCheck && !priorCapture)
793 int bonus = std::clamp(-16 * int((ss-1)->staticEval + ss->staticEval), -2000, 2000);
794 thisThread->mainHistory[~us][from_to((ss-1)->currentMove)] << bonus;
797 // Set up the improvement variable, which is the difference between the current
798 // static evaluation and the previous static evaluation at our turn (if we were
799 // in check at our previous move we look at the move prior to it). The improvement
800 // margin and the improving flag are used in various pruning heuristics.
801 improvement = (ss-2)->staticEval != VALUE_NONE ? ss->staticEval - (ss-2)->staticEval
802 : (ss-4)->staticEval != VALUE_NONE ? ss->staticEval - (ss-4)->staticEval
805 improving = improvement > 0;
807 // Step 7. Futility pruning: child node (~25 Elo).
808 // The depth condition is important for mate finding.
811 && eval - futility_margin(depth, improving) >= beta
812 && eval < 15000) // 50% larger than VALUE_KNOWN_WIN, but smaller than TB wins.
815 // Step 8. Null move search with verification search (~22 Elo)
817 && (ss-1)->currentMove != MOVE_NULL
818 && (ss-1)->statScore < 23767
820 && eval >= ss->staticEval
821 && ss->staticEval >= beta - 20 * depth - improvement / 15 + 204
823 && pos.non_pawn_material(us)
824 && (ss->ply >= thisThread->nmpMinPly || us != thisThread->nmpColor))
826 assert(eval - beta >= 0);
828 // Null move dynamic reduction based on depth and value
829 Depth R = std::min(int(eval - beta) / 205, 3) + depth / 3 + 4;
831 ss->currentMove = MOVE_NULL;
832 ss->continuationHistory = &thisThread->continuationHistory[0][0][NO_PIECE][0];
834 pos.do_null_move(st);
836 Value nullValue = -search<NonPV>(pos, ss+1, -beta, -beta+1, depth-R, !cutNode);
838 pos.undo_null_move();
840 if (nullValue >= beta)
842 // Do not return unproven mate or TB scores
843 if (nullValue >= VALUE_TB_WIN_IN_MAX_PLY)
846 if (thisThread->nmpMinPly || (abs(beta) < VALUE_KNOWN_WIN && depth < 14))
849 assert(!thisThread->nmpMinPly); // Recursive verification is not allowed
851 // Do verification search at high depths, with null move pruning disabled
852 // for us, until ply exceeds nmpMinPly.
853 thisThread->nmpMinPly = ss->ply + 3 * (depth-R) / 4;
854 thisThread->nmpColor = us;
856 Value v = search<NonPV>(pos, ss, beta-1, beta, depth-R, false);
858 thisThread->nmpMinPly = 0;
865 probCutBeta = beta + 209 - 44 * improving;
867 // Step 9. ProbCut (~4 Elo)
868 // If we have a good enough capture and a reduced search returns a value
869 // much above beta, we can (almost) safely prune the previous move.
872 && abs(beta) < VALUE_TB_WIN_IN_MAX_PLY
873 // if value from transposition table is lower than probCutBeta, don't attempt probCut
874 // there and in further interactions with transposition table cutoff depth is set to depth - 3
875 // because probCut search has depth set to depth - 4 but we also do a move before it
876 // so effective depth is equal to depth - 3
878 && tte->depth() >= depth - 3
879 && ttValue != VALUE_NONE
880 && ttValue < probCutBeta))
882 assert(probCutBeta < VALUE_INFINITE);
884 MovePicker mp(pos, ttMove, probCutBeta - ss->staticEval, &captureHistory);
885 bool ttPv = ss->ttPv;
888 while ((move = mp.next_move()) != MOVE_NONE)
889 if (move != excludedMove && pos.legal(move))
891 assert(pos.capture_or_promotion(move));
894 captureOrPromotion = true;
896 ss->currentMove = move;
897 ss->continuationHistory = &thisThread->continuationHistory[ss->inCheck]
899 [pos.moved_piece(move)]
902 pos.do_move(move, st);
904 // Perform a preliminary qsearch to verify that the move holds
905 value = -qsearch<NonPV>(pos, ss+1, -probCutBeta, -probCutBeta+1);
907 // If the qsearch held, perform the regular search
908 if (value >= probCutBeta)
909 value = -search<NonPV>(pos, ss+1, -probCutBeta, -probCutBeta+1, depth - 4, !cutNode);
913 if (value >= probCutBeta)
915 // if transposition table doesn't have equal or more deep info write probCut data into it
917 && tte->depth() >= depth - 3
918 && ttValue != VALUE_NONE))
919 tte->save(posKey, value_to_tt(value, ss->ply), ttPv,
921 depth - 3, move, ss->staticEval);
928 // Step 10. If the position is not in TT, decrease depth by 2 or 1 depending on node type (~3 Elo)
939 moves_loop: // When in check, search starts here
941 // Step 11. A small Probcut idea, when we are in check (~0 Elo)
942 probCutBeta = beta + 409;
947 && (tte->bound() & BOUND_LOWER)
948 && tte->depth() >= depth - 3
949 && ttValue >= probCutBeta
950 && abs(ttValue) <= VALUE_KNOWN_WIN
951 && abs(beta) <= VALUE_KNOWN_WIN
956 const PieceToHistory* contHist[] = { (ss-1)->continuationHistory, (ss-2)->continuationHistory,
957 nullptr , (ss-4)->continuationHistory,
958 nullptr , (ss-6)->continuationHistory };
960 Move countermove = thisThread->counterMoves[pos.piece_on(prevSq)][prevSq];
962 MovePicker mp(pos, ttMove, depth, &thisThread->mainHistory,
969 moveCountPruning = false;
971 // Indicate PvNodes that will probably fail low if the node was searched
972 // at a depth equal or greater than the current depth, and the result of this search was a fail low.
973 bool likelyFailLow = PvNode
975 && (tte->bound() & BOUND_UPPER)
976 && tte->depth() >= depth;
978 // Step 12. Loop through all pseudo-legal moves until no moves remain
979 // or a beta cutoff occurs.
980 while ((move = mp.next_move(moveCountPruning)) != MOVE_NONE)
984 if (move == excludedMove)
987 // At root obey the "searchmoves" option and skip moves not listed in Root
988 // Move List. As a consequence any illegal move is also skipped. In MultiPV
989 // mode we also skip PV moves which have been already searched and those
990 // of lower "TB rank" if we are in a TB root position.
991 if (rootNode && !std::count(thisThread->rootMoves.begin() + thisThread->pvIdx,
992 thisThread->rootMoves.begin() + thisThread->pvLast, move))
995 // Check for legality
996 if (!rootNode && !pos.legal(move))
999 ss->moveCount = ++moveCount;
1001 if (rootNode && thisThread == Threads.main() && Time.elapsed() > 3000)
1002 sync_cout << "info depth " << depth
1003 << " currmove " << UCI::move(move, pos.is_chess960())
1004 << " currmovenumber " << moveCount + thisThread->pvIdx << sync_endl;
1006 (ss+1)->pv = nullptr;
1009 captureOrPromotion = pos.capture_or_promotion(move);
1010 movedPiece = pos.moved_piece(move);
1011 givesCheck = pos.gives_check(move);
1013 // Calculate new depth for this move
1014 newDepth = depth - 1;
1016 Value delta = beta - alpha;
1018 // Step 13. Pruning at shallow depth (~98 Elo). Depth conditions are important for mate finding.
1020 && pos.non_pawn_material(us)
1021 && bestValue > VALUE_TB_LOSS_IN_MAX_PLY)
1023 // Skip quiet moves if movecount exceeds our FutilityMoveCount threshold (~7 Elo)
1024 moveCountPruning = moveCount >= futility_move_count(improving, depth);
1026 // Reduced depth of the next LMR search
1027 int lmrDepth = std::max(newDepth - reduction(improving, depth, moveCount, delta, thisThread->rootDelta), 0);
1029 if ( captureOrPromotion
1032 // Futility pruning for captures (~0 Elo)
1033 if ( !pos.empty(to_sq(move))
1038 && ss->staticEval + 342 + 238 * lmrDepth + PieceValue[EG][pos.piece_on(to_sq(move))]
1039 + captureHistory[movedPiece][to_sq(move)][type_of(pos.piece_on(to_sq(move)))] / 8 < alpha)
1042 // SEE based pruning (~9 Elo)
1043 if (!pos.see_ge(move, Value(-218) * depth))
1048 int history = (*contHist[0])[movedPiece][to_sq(move)]
1049 + (*contHist[1])[movedPiece][to_sq(move)]
1050 + (*contHist[3])[movedPiece][to_sq(move)];
1052 // Continuation history based pruning (~2 Elo)
1054 && history < -3000 * depth + 3000)
1057 history += thisThread->mainHistory[us][from_to(move)];
1059 // Futility pruning: parent node (~9 Elo)
1062 && ss->staticEval + 142 + 139 * lmrDepth + history / 64 <= alpha)
1065 // Prune moves with negative SEE (~3 Elo)
1066 if (!pos.see_ge(move, Value(-21 * lmrDepth * lmrDepth - 21 * lmrDepth)))
1071 // Step 14. Extensions (~66 Elo)
1073 // Singular extension search (~58 Elo). If all moves but one fail low on a
1074 // search of (alpha-s, beta-s), and just one fails high on (alpha, beta),
1075 // then that move is singular and should be extended. To verify this we do
1076 // a reduced search on all the other moves but the ttMove and if the
1077 // result is lower than ttValue minus a margin, then we will extend the ttMove.
1079 && depth >= 6 + 2 * (PvNode && tte->is_pv())
1081 && !excludedMove // Avoid recursive singular search
1082 /* && ttValue != VALUE_NONE Already implicit in the next condition */
1083 && abs(ttValue) < VALUE_KNOWN_WIN
1084 && (tte->bound() & BOUND_LOWER)
1085 && tte->depth() >= depth - 3)
1087 Value singularBeta = ttValue - 3 * depth;
1088 Depth singularDepth = (depth - 1) / 2;
1090 ss->excludedMove = move;
1091 value = search<NonPV>(pos, ss, singularBeta - 1, singularBeta, singularDepth, cutNode);
1092 ss->excludedMove = MOVE_NONE;
1094 if (value < singularBeta)
1098 // Avoid search explosion by limiting the number of double extensions
1100 && value < singularBeta - 75
1101 && ss->doubleExtensions <= 6)
1105 // Multi-cut pruning
1106 // Our ttMove is assumed to fail high, and now we failed high also on a reduced
1107 // search without the ttMove. So we assume this expected Cut-node is not singular,
1108 // that multiple moves fail high, and we can prune the whole subtree by returning
1110 else if (singularBeta >= beta)
1111 return singularBeta;
1113 // If the eval of ttMove is greater than beta, we reduce it (negative extension)
1114 else if (ttValue >= beta)
1118 // Check extensions (~1 Elo)
1119 else if ( givesCheck
1121 && abs(ss->staticEval) > 100)
1124 // Quiet ttMove extensions (~0 Elo)
1127 && move == ss->killers[0]
1128 && (*contHist[0])[movedPiece][to_sq(move)] >= 10000)
1131 // Add extension to new depth
1132 newDepth += extension;
1133 ss->doubleExtensions = (ss-1)->doubleExtensions + (extension == 2);
1135 // Speculative prefetch as early as possible
1136 prefetch(TT.first_entry(pos.key_after(move)));
1138 // Update the current move (this must be done after singular extension search)
1139 ss->currentMove = move;
1140 ss->continuationHistory = &thisThread->continuationHistory[ss->inCheck]
1141 [captureOrPromotion]
1145 // Step 15. Make the move
1146 pos.do_move(move, st, givesCheck);
1148 bool doDeeperSearch = false;
1150 // Step 16. Late moves reduction / extension (LMR, ~98 Elo)
1151 // We use various heuristics for the sons of a node after the first son has
1152 // been searched. In general we would like to reduce them, but there are many
1153 // cases where we extend a son if it has good chances to be "interesting".
1155 && moveCount > 1 + 2 * rootNode
1157 || !captureOrPromotion
1158 || (cutNode && (ss-1)->moveCount > 1)))
1160 Depth r = reduction(improving, depth, moveCount, delta, thisThread->rootDelta);
1162 // Decrease reduction at some PvNodes (~2 Elo)
1164 && bestMoveCount <= 3)
1167 // Decrease reduction if position is or has been on the PV
1168 // and node is not likely to fail low. (~3 Elo)
1173 // Decrease reduction if opponent's move count is high (~1 Elo)
1174 if ((ss-1)->moveCount > 13)
1177 // Increase reduction for cut nodes (~3 Elo)
1178 if (cutNode && move != ss->killers[0])
1181 // Increase reduction if ttMove is a capture (~3 Elo)
1185 ss->statScore = thisThread->mainHistory[us][from_to(move)]
1186 + (*contHist[0])[movedPiece][to_sq(move)]
1187 + (*contHist[1])[movedPiece][to_sq(move)]
1188 + (*contHist[3])[movedPiece][to_sq(move)]
1191 // Decrease/increase reduction for moves with a good/bad history (~30 Elo)
1192 r -= ss->statScore / 14721;
1194 // In general we want to cap the LMR depth search at newDepth. But if reductions
1195 // are really negative and movecount is low, we allow this move to be searched
1196 // deeper than the first move (this may lead to hidden double extensions).
1197 int deeper = r >= -1 ? 0
1198 : moveCount <= 5 ? 2
1199 : PvNode && depth > 6 ? 1
1200 : cutNode && moveCount <= 7 ? 1
1203 Depth d = std::clamp(newDepth - r, 1, newDepth + deeper);
1205 value = -search<NonPV>(pos, ss+1, -(alpha+1), -alpha, d, true);
1207 // If the son is reduced and fails high it will be re-searched at full depth
1208 doFullDepthSearch = value > alpha && d < newDepth;
1209 doDeeperSearch = value > (alpha + 62 + 20 * (newDepth - d));
1214 doFullDepthSearch = !PvNode || moveCount > 1;
1218 // Step 17. Full depth search when LMR is skipped or fails high
1219 if (doFullDepthSearch)
1221 value = -search<NonPV>(pos, ss+1, -(alpha+1), -alpha, newDepth + doDeeperSearch, !cutNode);
1223 // If the move passed LMR update its stats
1224 if (didLMR && !captureOrPromotion)
1226 int bonus = value > alpha ? stat_bonus(newDepth)
1227 : -stat_bonus(newDepth);
1229 update_continuation_histories(ss, movedPiece, to_sq(move), bonus);
1233 // For PV nodes only, do a full PV search on the first move or after a fail
1234 // high (in the latter case search only if value < beta), otherwise let the
1235 // parent node fail low with value <= alpha and try another move.
1236 if (PvNode && (moveCount == 1 || (value > alpha && (rootNode || value < beta))))
1239 (ss+1)->pv[0] = MOVE_NONE;
1241 value = -search<PV>(pos, ss+1, -beta, -alpha,
1242 std::min(maxNextDepth, newDepth), false);
1245 // Step 18. Undo move
1246 pos.undo_move(move);
1248 assert(value > -VALUE_INFINITE && value < VALUE_INFINITE);
1250 // Step 19. Check for a new best move
1251 // Finished searching the move. If a stop occurred, the return value of
1252 // the search cannot be trusted, and we return immediately without
1253 // updating best move, PV and TT.
1254 if (Threads.stop.load(std::memory_order_relaxed))
1259 RootMove& rm = *std::find(thisThread->rootMoves.begin(),
1260 thisThread->rootMoves.end(), move);
1262 rm.averageScore = rm.averageScore != -VALUE_INFINITE ? (2 * value + rm.averageScore) / 3 : value;
1264 // PV move or new best move?
1265 if (moveCount == 1 || value > alpha)
1268 rm.selDepth = thisThread->selDepth;
1273 for (Move* m = (ss+1)->pv; *m != MOVE_NONE; ++m)
1274 rm.pv.push_back(*m);
1276 // We record how often the best move has been changed in each iteration.
1277 // This information is used for time management. In MultiPV mode,
1278 // we must take care to only do this for the first PV line.
1280 && !thisThread->pvIdx)
1281 ++thisThread->bestMoveChanges;
1284 // All other moves but the PV are set to the lowest value: this
1285 // is not a problem when sorting because the sort is stable and the
1286 // move position in the list is preserved - just the PV is pushed up.
1287 rm.score = -VALUE_INFINITE;
1290 if (value > bestValue)
1298 if (PvNode && !rootNode) // Update pv even in fail-high case
1299 update_pv(ss->pv, move, (ss+1)->pv);
1301 if (PvNode && value < beta) // Update alpha! Always alpha < beta
1308 assert(value >= beta); // Fail high
1314 // If the move is worse than some previously searched move, remember it to update its stats later
1315 if (move != bestMove)
1317 if (captureOrPromotion && captureCount < 32)
1318 capturesSearched[captureCount++] = move;
1320 else if (!captureOrPromotion && quietCount < 64)
1321 quietsSearched[quietCount++] = move;
1325 // The following condition would detect a stop only after move loop has been
1326 // completed. But in this case bestValue is valid because we have fully
1327 // searched our subtree, and we can anyhow save the result in TT.
1333 // Step 20. Check for mate and stalemate
1334 // All legal moves have been searched and if there are no legal moves, it
1335 // must be a mate or a stalemate. If we are in a singular extension search then
1336 // return a fail low score.
1338 assert(moveCount || !ss->inCheck || excludedMove || !MoveList<LEGAL>(pos).size());
1341 bestValue = excludedMove ? alpha :
1342 ss->inCheck ? mated_in(ss->ply)
1345 // If there is a move which produces search value greater than alpha we update stats of searched moves
1347 update_all_stats(pos, ss, bestMove, bestValue, beta, prevSq,
1348 quietsSearched, quietCount, capturesSearched, captureCount, depth);
1350 // Bonus for prior countermove that caused the fail low
1351 else if ( (depth >= 3 || PvNode)
1354 //Assign extra bonus if current node is PvNode or cutNode
1355 //or fail low was really bad
1356 bool extraBonus = PvNode
1358 || bestValue < alpha - 94 * depth;
1360 update_continuation_histories(ss-1, pos.piece_on(prevSq), prevSq, stat_bonus(depth) * (1 + extraBonus));
1364 bestValue = std::min(bestValue, maxValue);
1366 // If no good move is found and the previous position was ttPv, then the previous
1367 // opponent move is probably good and the new position is added to the search tree.
1368 if (bestValue <= alpha)
1369 ss->ttPv = ss->ttPv || ((ss-1)->ttPv && depth > 3);
1370 // Otherwise, a counter move has been found and if the position is the last leaf
1371 // in the search tree, remove the position from the search tree.
1373 ss->ttPv = ss->ttPv && (ss+1)->ttPv;
1375 // Write gathered information in transposition table
1376 if (!excludedMove && !(rootNode && thisThread->pvIdx))
1377 tte->save(posKey, value_to_tt(bestValue, ss->ply), ss->ttPv,
1378 bestValue >= beta ? BOUND_LOWER :
1379 PvNode && bestMove ? BOUND_EXACT : BOUND_UPPER,
1380 depth, bestMove, ss->staticEval);
1382 assert(bestValue > -VALUE_INFINITE && bestValue < VALUE_INFINITE);
1388 // qsearch() is the quiescence search function, which is called by the main search
1389 // function with zero depth, or recursively with further decreasing depth per call.
1390 template <NodeType nodeType>
1391 Value qsearch(Position& pos, Stack* ss, Value alpha, Value beta, Depth depth) {
1393 static_assert(nodeType != Root);
1394 constexpr bool PvNode = nodeType == PV;
1396 assert(alpha >= -VALUE_INFINITE && alpha < beta && beta <= VALUE_INFINITE);
1397 assert(PvNode || (alpha == beta - 1));
1402 ASSERT_ALIGNED(&st, Eval::NNUE::CacheLineSize);
1406 Move ttMove, move, bestMove;
1408 Value bestValue, value, ttValue, futilityValue, futilityBase;
1409 bool pvHit, givesCheck, captureOrPromotion;
1415 ss->pv[0] = MOVE_NONE;
1418 Thread* thisThread = pos.this_thread();
1419 bestMove = MOVE_NONE;
1420 ss->inCheck = pos.checkers();
1423 // Check for an immediate draw or maximum ply reached
1424 if ( pos.is_draw(ss->ply)
1425 || ss->ply >= MAX_PLY)
1426 return (ss->ply >= MAX_PLY && !ss->inCheck) ? evaluate(pos) : VALUE_DRAW;
1428 assert(0 <= ss->ply && ss->ply < MAX_PLY);
1430 // Decide whether or not to include checks: this fixes also the type of
1431 // TT entry depth that we are going to use. Note that in qsearch we use
1432 // only two types of depth in TT: DEPTH_QS_CHECKS or DEPTH_QS_NO_CHECKS.
1433 ttDepth = ss->inCheck || depth >= DEPTH_QS_CHECKS ? DEPTH_QS_CHECKS
1434 : DEPTH_QS_NO_CHECKS;
1435 // Transposition table lookup
1437 tte = TT.probe(posKey, ss->ttHit);
1438 ttValue = ss->ttHit ? value_from_tt(tte->value(), ss->ply, pos.rule50_count()) : VALUE_NONE;
1439 ttMove = ss->ttHit ? tte->move() : MOVE_NONE;
1440 pvHit = ss->ttHit && tte->is_pv();
1444 && tte->depth() >= ttDepth
1445 && ttValue != VALUE_NONE // Only in case of TT access race
1446 && (ttValue >= beta ? (tte->bound() & BOUND_LOWER)
1447 : (tte->bound() & BOUND_UPPER)))
1450 // Evaluate the position statically
1453 ss->staticEval = VALUE_NONE;
1454 bestValue = futilityBase = -VALUE_INFINITE;
1460 // Never assume anything about values stored in TT
1461 if ((ss->staticEval = bestValue = tte->eval()) == VALUE_NONE)
1462 ss->staticEval = bestValue = evaluate(pos);
1464 // ttValue can be used as a better position evaluation (~7 Elo)
1465 if ( ttValue != VALUE_NONE
1466 && (tte->bound() & (ttValue > bestValue ? BOUND_LOWER : BOUND_UPPER)))
1467 bestValue = ttValue;
1470 // In case of null move search use previous static eval with a different sign
1471 ss->staticEval = bestValue =
1472 (ss-1)->currentMove != MOVE_NULL ? evaluate(pos)
1473 : -(ss-1)->staticEval;
1475 // Stand pat. Return immediately if static value is at least beta
1476 if (bestValue >= beta)
1478 // Save gathered info in transposition table
1480 tte->save(posKey, value_to_tt(bestValue, ss->ply), false, BOUND_LOWER,
1481 DEPTH_NONE, MOVE_NONE, ss->staticEval);
1486 if (PvNode && bestValue > alpha)
1489 futilityBase = bestValue + 155;
1492 const PieceToHistory* contHist[] = { (ss-1)->continuationHistory, (ss-2)->continuationHistory,
1493 nullptr , (ss-4)->continuationHistory,
1494 nullptr , (ss-6)->continuationHistory };
1496 // Initialize a MovePicker object for the current position, and prepare
1497 // to search the moves. Because the depth is <= 0 here, only captures,
1498 // queen promotions, and other checks (only if depth >= DEPTH_QS_CHECKS)
1499 // will be generated.
1500 Square prevSq = to_sq((ss-1)->currentMove);
1501 MovePicker mp(pos, ttMove, depth, &thisThread->mainHistory,
1502 &thisThread->captureHistory,
1506 // Loop through the moves until no moves remain or a beta cutoff occurs
1507 while ((move = mp.next_move()) != MOVE_NONE)
1509 assert(is_ok(move));
1511 // Check for legality
1512 if (!pos.legal(move))
1515 givesCheck = pos.gives_check(move);
1516 captureOrPromotion = pos.capture_or_promotion(move);
1520 // Futility pruning and moveCount pruning (~5 Elo)
1521 if ( bestValue > VALUE_TB_LOSS_IN_MAX_PLY
1523 && to_sq(move) != prevSq
1524 && futilityBase > -VALUE_KNOWN_WIN
1525 && type_of(move) != PROMOTION)
1531 futilityValue = futilityBase + PieceValue[EG][pos.piece_on(to_sq(move))];
1533 if (futilityValue <= alpha)
1535 bestValue = std::max(bestValue, futilityValue);
1539 if (futilityBase <= alpha && !pos.see_ge(move, VALUE_ZERO + 1))
1541 bestValue = std::max(bestValue, futilityBase);
1546 // Do not search moves with negative SEE values (~5 Elo)
1547 if ( bestValue > VALUE_TB_LOSS_IN_MAX_PLY
1548 && !pos.see_ge(move))
1551 // Speculative prefetch as early as possible
1552 prefetch(TT.first_entry(pos.key_after(move)));
1554 ss->currentMove = move;
1555 ss->continuationHistory = &thisThread->continuationHistory[ss->inCheck]
1556 [captureOrPromotion]
1557 [pos.moved_piece(move)]
1560 // Continuation history based pruning (~2 Elo)
1561 if ( !captureOrPromotion
1562 && bestValue > VALUE_TB_LOSS_IN_MAX_PLY
1563 && (*contHist[0])[pos.moved_piece(move)][to_sq(move)] < CounterMovePruneThreshold
1564 && (*contHist[1])[pos.moved_piece(move)][to_sq(move)] < CounterMovePruneThreshold)
1567 // Make and search the move
1568 pos.do_move(move, st, givesCheck);
1569 value = -qsearch<nodeType>(pos, ss+1, -beta, -alpha, depth - 1);
1570 pos.undo_move(move);
1572 assert(value > -VALUE_INFINITE && value < VALUE_INFINITE);
1574 // Check for a new best move
1575 if (value > bestValue)
1583 if (PvNode) // Update pv even in fail-high case
1584 update_pv(ss->pv, move, (ss+1)->pv);
1586 if (PvNode && value < beta) // Update alpha here!
1594 // All legal moves have been searched. A special case: if we're in check
1595 // and no legal moves were found, it is checkmate.
1596 if (ss->inCheck && bestValue == -VALUE_INFINITE)
1598 assert(!MoveList<LEGAL>(pos).size());
1600 return mated_in(ss->ply); // Plies to mate from the root
1603 // Save gathered info in transposition table
1604 tte->save(posKey, value_to_tt(bestValue, ss->ply), pvHit,
1605 bestValue >= beta ? BOUND_LOWER : BOUND_UPPER,
1606 ttDepth, bestMove, ss->staticEval);
1608 assert(bestValue > -VALUE_INFINITE && bestValue < VALUE_INFINITE);
1614 // value_to_tt() adjusts a mate or TB score from "plies to mate from the root" to
1615 // "plies to mate from the current position". Standard scores are unchanged.
1616 // The function is called before storing a value in the transposition table.
1618 Value value_to_tt(Value v, int ply) {
1620 assert(v != VALUE_NONE);
1622 return v >= VALUE_TB_WIN_IN_MAX_PLY ? v + ply
1623 : v <= VALUE_TB_LOSS_IN_MAX_PLY ? v - ply : v;
1627 // value_from_tt() is the inverse of value_to_tt(): it adjusts a mate or TB score
1628 // from the transposition table (which refers to the plies to mate/be mated from
1629 // current position) to "plies to mate/be mated (TB win/loss) from the root". However,
1630 // for mate scores, to avoid potentially false mate scores related to the 50 moves rule
1631 // and the graph history interaction, we return an optimal TB score instead.
1633 Value value_from_tt(Value v, int ply, int r50c) {
1635 if (v == VALUE_NONE)
1638 if (v >= VALUE_TB_WIN_IN_MAX_PLY) // TB win or better
1640 if (v >= VALUE_MATE_IN_MAX_PLY && VALUE_MATE - v > 99 - r50c)
1641 return VALUE_MATE_IN_MAX_PLY - 1; // do not return a potentially false mate score
1646 if (v <= VALUE_TB_LOSS_IN_MAX_PLY) // TB loss or worse
1648 if (v <= VALUE_MATED_IN_MAX_PLY && VALUE_MATE + v > 99 - r50c)
1649 return VALUE_MATED_IN_MAX_PLY + 1; // do not return a potentially false mate score
1658 // update_pv() adds current move and appends child pv[]
1660 void update_pv(Move* pv, Move move, Move* childPv) {
1662 for (*pv++ = move; childPv && *childPv != MOVE_NONE; )
1668 // update_all_stats() updates stats at the end of search() when a bestMove is found
1670 void update_all_stats(const Position& pos, Stack* ss, Move bestMove, Value bestValue, Value beta, Square prevSq,
1671 Move* quietsSearched, int quietCount, Move* capturesSearched, int captureCount, Depth depth) {
1674 Color us = pos.side_to_move();
1675 Thread* thisThread = pos.this_thread();
1676 CapturePieceToHistory& captureHistory = thisThread->captureHistory;
1677 Piece moved_piece = pos.moved_piece(bestMove);
1678 PieceType captured = type_of(pos.piece_on(to_sq(bestMove)));
1680 bonus1 = stat_bonus(depth + 1);
1681 bonus2 = bestValue > beta + PawnValueMg ? bonus1 // larger bonus
1682 : stat_bonus(depth); // smaller bonus
1684 if (!pos.capture_or_promotion(bestMove))
1686 // Increase stats for the best move in case it was a quiet move
1687 update_quiet_stats(pos, ss, bestMove, bonus2);
1689 // Decrease stats for all non-best quiet moves
1690 for (int i = 0; i < quietCount; ++i)
1692 thisThread->mainHistory[us][from_to(quietsSearched[i])] << -bonus2;
1693 update_continuation_histories(ss, pos.moved_piece(quietsSearched[i]), to_sq(quietsSearched[i]), -bonus2);
1697 // Increase stats for the best move in case it was a capture move
1698 captureHistory[moved_piece][to_sq(bestMove)][captured] << bonus1;
1700 // Extra penalty for a quiet early move that was not a TT move or
1701 // main killer move in previous ply when it gets refuted.
1702 if ( ((ss-1)->moveCount == 1 + (ss-1)->ttHit || ((ss-1)->currentMove == (ss-1)->killers[0]))
1703 && !pos.captured_piece())
1704 update_continuation_histories(ss-1, pos.piece_on(prevSq), prevSq, -bonus1);
1706 // Decrease stats for all non-best capture moves
1707 for (int i = 0; i < captureCount; ++i)
1709 moved_piece = pos.moved_piece(capturesSearched[i]);
1710 captured = type_of(pos.piece_on(to_sq(capturesSearched[i])));
1711 captureHistory[moved_piece][to_sq(capturesSearched[i])][captured] << -bonus1;
1716 // update_continuation_histories() updates histories of the move pairs formed
1717 // by moves at ply -1, -2, -4, and -6 with current move.
1719 void update_continuation_histories(Stack* ss, Piece pc, Square to, int bonus) {
1721 for (int i : {1, 2, 4, 6})
1723 // Only update first 2 continuation histories if we are in check
1724 if (ss->inCheck && i > 2)
1726 if (is_ok((ss-i)->currentMove))
1727 (*(ss-i)->continuationHistory)[pc][to] << bonus;
1732 // update_quiet_stats() updates move sorting heuristics
1734 void update_quiet_stats(const Position& pos, Stack* ss, Move move, int bonus) {
1737 if (ss->killers[0] != move)
1739 ss->killers[1] = ss->killers[0];
1740 ss->killers[0] = move;
1743 Color us = pos.side_to_move();
1744 Thread* thisThread = pos.this_thread();
1745 thisThread->mainHistory[us][from_to(move)] << bonus;
1746 update_continuation_histories(ss, pos.moved_piece(move), to_sq(move), bonus);
1748 // Update countermove history
1749 if (is_ok((ss-1)->currentMove))
1751 Square prevSq = to_sq((ss-1)->currentMove);
1752 thisThread->counterMoves[pos.piece_on(prevSq)][prevSq] = move;
1756 // When playing with strength handicap, choose best move among a set of RootMoves
1757 // using a statistical rule dependent on 'level'. Idea by Heinz van Saanen.
1759 Move Skill::pick_best(size_t multiPV) {
1761 const RootMoves& rootMoves = Threads.main()->rootMoves;
1762 static PRNG rng(now()); // PRNG sequence should be non-deterministic
1764 // RootMoves are already sorted by score in descending order
1765 Value topScore = rootMoves[0].score;
1766 int delta = std::min(topScore - rootMoves[multiPV - 1].score, PawnValueMg);
1767 int maxScore = -VALUE_INFINITE;
1768 double weakness = 120 - 2 * level;
1770 // Choose best move. For each move score we add two terms, both dependent on
1771 // weakness. One is deterministic and bigger for weaker levels, and one is
1772 // random. Then we choose the move with the resulting highest score.
1773 for (size_t i = 0; i < multiPV; ++i)
1775 // This is our magic formula
1776 int push = int(( weakness * int(topScore - rootMoves[i].score)
1777 + delta * (rng.rand<unsigned>() % int(weakness))) / 128);
1779 if (rootMoves[i].score + push >= maxScore)
1781 maxScore = rootMoves[i].score + push;
1782 best = rootMoves[i].pv[0];
1792 /// MainThread::check_time() is used to print debug info and, more importantly,
1793 /// to detect when we are out of available time and thus stop the search.
1795 void MainThread::check_time() {
1800 // When using nodes, ensure checking rate is not lower than 0.1% of nodes
1801 callsCnt = Limits.nodes ? std::min(1024, int(Limits.nodes / 1024)) : 1024;
1803 static TimePoint lastInfoTime = now();
1805 TimePoint elapsed = Time.elapsed();
1806 TimePoint tick = Limits.startTime + elapsed;
1808 if (tick - lastInfoTime >= 1000)
1810 lastInfoTime = tick;
1814 // We should not stop pondering until told so by the GUI
1818 if ( (Limits.use_time_management() && (elapsed > Time.maximum() - 10 || stopOnPonderhit))
1819 || (Limits.movetime && elapsed >= Limits.movetime)
1820 || (Limits.nodes && Threads.nodes_searched() >= (uint64_t)Limits.nodes))
1821 Threads.stop = true;
1825 /// UCI::pv() formats PV information according to the UCI protocol. UCI requires
1826 /// that all (if any) unsearched PV lines are sent using a previous search score.
1828 string UCI::pv(const Position& pos, Depth depth, Value alpha, Value beta) {
1830 std::stringstream ss;
1831 TimePoint elapsed = Time.elapsed() + 1;
1832 const RootMoves& rootMoves = pos.this_thread()->rootMoves;
1833 size_t pvIdx = pos.this_thread()->pvIdx;
1834 size_t multiPV = std::min((size_t)Options["MultiPV"], rootMoves.size());
1835 uint64_t nodesSearched = Threads.nodes_searched();
1836 uint64_t tbHits = Threads.tb_hits() + (TB::RootInTB ? rootMoves.size() : 0);
1838 for (size_t i = 0; i < multiPV; ++i)
1840 bool updated = rootMoves[i].score != -VALUE_INFINITE;
1842 if (depth == 1 && !updated && i > 0)
1845 Depth d = updated ? depth : std::max(1, depth - 1);
1846 Value v = updated ? rootMoves[i].score : rootMoves[i].previousScore;
1848 if (v == -VALUE_INFINITE)
1851 bool tb = TB::RootInTB && abs(v) < VALUE_MATE_IN_MAX_PLY;
1852 v = tb ? rootMoves[i].tbScore : v;
1854 if (ss.rdbuf()->in_avail()) // Not at first line
1859 << " seldepth " << rootMoves[i].selDepth
1860 << " multipv " << i + 1
1861 << " score " << UCI::value(v);
1863 if (Options["UCI_ShowWDL"])
1864 ss << UCI::wdl(v, pos.game_ply());
1866 if (!tb && i == pvIdx)
1867 ss << (v >= beta ? " lowerbound" : v <= alpha ? " upperbound" : "");
1869 ss << " nodes " << nodesSearched
1870 << " nps " << nodesSearched * 1000 / elapsed;
1872 if (elapsed > 1000) // Earlier makes little sense
1873 ss << " hashfull " << TT.hashfull();
1875 ss << " tbhits " << tbHits
1876 << " time " << elapsed
1879 for (Move m : rootMoves[i].pv)
1880 ss << " " << UCI::move(m, pos.is_chess960());
1887 /// RootMove::extract_ponder_from_tt() is called in case we have no ponder move
1888 /// before exiting the search, for instance, in case we stop the search during a
1889 /// fail high at root. We try hard to have a ponder move to return to the GUI,
1890 /// otherwise in case of 'ponder on' we have nothing to think on.
1892 bool RootMove::extract_ponder_from_tt(Position& pos) {
1895 ASSERT_ALIGNED(&st, Eval::NNUE::CacheLineSize);
1899 assert(pv.size() == 1);
1901 if (pv[0] == MOVE_NONE)
1904 pos.do_move(pv[0], st);
1905 TTEntry* tte = TT.probe(pos.key(), ttHit);
1909 Move m = tte->move(); // Local copy to be SMP safe
1910 if (MoveList<LEGAL>(pos).contains(m))
1914 pos.undo_move(pv[0]);
1915 return pv.size() > 1;
1918 void Tablebases::rank_root_moves(Position& pos, Search::RootMoves& rootMoves) {
1921 UseRule50 = bool(Options["Syzygy50MoveRule"]);
1922 ProbeDepth = int(Options["SyzygyProbeDepth"]);
1923 Cardinality = int(Options["SyzygyProbeLimit"]);
1924 bool dtz_available = true;
1926 // Tables with fewer pieces than SyzygyProbeLimit are searched with
1927 // ProbeDepth == DEPTH_ZERO
1928 if (Cardinality > MaxCardinality)
1930 Cardinality = MaxCardinality;
1934 if (Cardinality >= popcount(pos.pieces()) && !pos.can_castle(ANY_CASTLING))
1936 // Rank moves using DTZ tables
1937 RootInTB = root_probe(pos, rootMoves);
1941 // DTZ tables are missing; try to rank moves using WDL tables
1942 dtz_available = false;
1943 RootInTB = root_probe_wdl(pos, rootMoves);
1949 // Sort moves according to TB rank
1950 std::stable_sort(rootMoves.begin(), rootMoves.end(),
1951 [](const RootMove &a, const RootMove &b) { return a.tbRank > b.tbRank; } );
1953 // Probe during search only if DTZ is not available and we are winning
1954 if (dtz_available || rootMoves[0].tbScore <= VALUE_DRAW)
1959 // Clean up if root_probe() and root_probe_wdl() have failed
1960 for (auto& m : rootMoves)
1965 } // namespace Stockfish