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%
332 complexityAverage.set(232, 1);
334 nodesLastExplosive = nodes;
335 nodesLastNormal = nodes;
336 state = EXPLOSION_NONE;
338 optimism[ us] = Value(25);
339 optimism[~us] = -optimism[us];
341 int searchAgainCounter = 0;
343 // Iterative deepening loop until requested to stop or the target depth is reached
344 while ( ++rootDepth < MAX_PLY
346 && !(Limits.depth && mainThread && rootDepth > Limits.depth))
348 // Age out PV variability metric
350 totBestMoveChanges /= 2;
352 // Save the last iteration's scores before first PV line is searched and
353 // all the move scores except the (new) PV are set to -VALUE_INFINITE.
354 for (RootMove& rm : rootMoves)
355 rm.previousScore = rm.score;
360 if (!Threads.increaseDepth)
361 searchAgainCounter++;
363 // MultiPV loop. We perform a full root search for each PV line
364 for (pvIdx = 0; pvIdx < multiPV && !Threads.stop; ++pvIdx)
369 for (pvLast++; pvLast < rootMoves.size(); pvLast++)
370 if (rootMoves[pvLast].tbRank != rootMoves[pvFirst].tbRank)
374 // Reset UCI info selDepth for each depth and each PV line
377 // Reset aspiration window starting size
380 Value prev = rootMoves[pvIdx].averageScore;
381 delta = Value(17) + int(prev) * prev / 16384;
382 alpha = std::max(prev - delta,-VALUE_INFINITE);
383 beta = std::min(prev + delta, VALUE_INFINITE);
385 // Adjust trend and optimism based on root move's previousScore
386 int tr = sigmoid(prev, 0, 0, 147, 113, 1);
387 trend = (us == WHITE ? make_score(tr, tr / 2)
388 : -make_score(tr, tr / 2));
390 int opt = sigmoid(prev, 0, 25, 147, 14464, 256);
391 optimism[ us] = Value(opt);
392 optimism[~us] = -optimism[us];
395 // Start with a small aspiration window and, in the case of a fail
396 // high/low, re-search with a bigger window until we don't fail
398 int failedHighCnt = 0;
401 Depth adjustedDepth = std::max(1, rootDepth - failedHighCnt - searchAgainCounter);
402 bestValue = Stockfish::search<Root>(rootPos, ss, alpha, beta, adjustedDepth, false);
404 // Bring the best move to the front. It is critical that sorting
405 // is done with a stable algorithm because all the values but the
406 // first and eventually the new best one are set to -VALUE_INFINITE
407 // and we want to keep the same order for all the moves except the
408 // new PV that goes to the front. Note that in case of MultiPV
409 // search the already searched PV lines are preserved.
410 std::stable_sort(rootMoves.begin() + pvIdx, rootMoves.begin() + pvLast);
412 // If search has been stopped, we break immediately. Sorting is
413 // safe because RootMoves is still valid, although it refers to
414 // the previous iteration.
418 // When failing high/low give some update (without cluttering
419 // the UI) before a re-search.
422 && (bestValue <= alpha || bestValue >= beta)
423 && Time.elapsed() > 3000)
424 sync_cout << UCI::pv(rootPos, rootDepth, alpha, beta) << sync_endl;
426 // In case of failing low/high increase aspiration window and
427 // re-search, otherwise exit the loop.
428 if (bestValue <= alpha)
430 beta = (alpha + beta) / 2;
431 alpha = std::max(bestValue - delta, -VALUE_INFINITE);
435 mainThread->stopOnPonderhit = false;
437 else if (bestValue >= beta)
439 beta = std::min(bestValue + delta, VALUE_INFINITE);
445 delta += delta / 4 + 5;
447 assert(alpha >= -VALUE_INFINITE && beta <= VALUE_INFINITE);
450 // Sort the PV lines searched so far and update the GUI
451 std::stable_sort(rootMoves.begin() + pvFirst, rootMoves.begin() + pvIdx + 1);
454 && (Threads.stop || pvIdx + 1 == multiPV || Time.elapsed() > 3000))
455 sync_cout << UCI::pv(rootPos, rootDepth, alpha, beta) << sync_endl;
459 completedDepth = rootDepth;
461 if (rootMoves[0].pv[0] != lastBestMove) {
462 lastBestMove = rootMoves[0].pv[0];
463 lastBestMoveDepth = rootDepth;
466 // Have we found a "mate in x"?
468 && bestValue >= VALUE_MATE_IN_MAX_PLY
469 && VALUE_MATE - bestValue <= 2 * Limits.mate)
475 // If skill level is enabled and time is up, pick a sub-optimal best move
476 if (skill.enabled() && skill.time_to_pick(rootDepth))
477 skill.pick_best(multiPV);
479 // Use part of the gained time from a previous stable move for the current move
480 for (Thread* th : Threads)
482 totBestMoveChanges += th->bestMoveChanges;
483 th->bestMoveChanges = 0;
486 // Do we have time for the next iteration? Can we stop searching now?
487 if ( Limits.use_time_management()
489 && !mainThread->stopOnPonderhit)
491 double fallingEval = (142 + 12 * (mainThread->bestPreviousAverageScore - bestValue)
492 + 6 * (mainThread->iterValue[iterIdx] - bestValue)) / 825.0;
493 fallingEval = std::clamp(fallingEval, 0.5, 1.5);
495 // If the bestMove is stable over several iterations, reduce time accordingly
496 timeReduction = lastBestMoveDepth + 9 < completedDepth ? 1.92 : 0.95;
497 double reduction = (1.47 + mainThread->previousTimeReduction) / (2.32 * timeReduction);
498 double bestMoveInstability = 1.073 + std::max(1.0, 2.25 - 9.9 / rootDepth)
499 * totBestMoveChanges / Threads.size();
500 int complexity = mainThread->complexityAverage.value();
501 double complexPosition = std::clamp(1.0 + (complexity - 232) / 1750.0, 0.5, 1.5);
503 double totalTime = Time.optimum() * fallingEval * reduction * bestMoveInstability * complexPosition;
505 // Cap used time in case of a single legal move for a better viewer experience in tournaments
506 // yielding correct scores and sufficiently fast moves.
507 if (rootMoves.size() == 1)
508 totalTime = std::min(500.0, totalTime);
510 // Stop the search if we have exceeded the totalTime
511 if (Time.elapsed() > totalTime)
513 // If we are allowed to ponder do not stop the search now but
514 // keep pondering until the GUI sends "ponderhit" or "stop".
515 if (mainThread->ponder)
516 mainThread->stopOnPonderhit = true;
520 else if ( Threads.increaseDepth
521 && !mainThread->ponder
522 && Time.elapsed() > totalTime * 0.58)
523 Threads.increaseDepth = false;
525 Threads.increaseDepth = true;
528 mainThread->iterValue[iterIdx] = bestValue;
529 iterIdx = (iterIdx + 1) & 3;
535 mainThread->previousTimeReduction = timeReduction;
537 // If skill level is enabled, swap best PV line with the sub-optimal one
539 std::swap(rootMoves[0], *std::find(rootMoves.begin(), rootMoves.end(),
540 skill.best ? skill.best : skill.pick_best(multiPV)));
546 // search<>() is the main search function for both PV and non-PV nodes
548 template <NodeType nodeType>
549 Value search(Position& pos, Stack* ss, Value alpha, Value beta, Depth depth, bool cutNode) {
551 Thread* thisThread = pos.this_thread();
553 // Step 0. Limit search explosion
555 && search_explosion(thisThread) == MUST_CALM_DOWN
556 && depth > (ss-1)->depth)
557 depth = (ss-1)->depth;
559 constexpr bool PvNode = nodeType != NonPV;
560 constexpr bool rootNode = nodeType == Root;
561 const Depth maxNextDepth = rootNode ? depth : depth + 1;
563 // Check if we have an upcoming move which draws by repetition, or
564 // if the opponent had an alternative move earlier to this position.
566 && pos.rule50_count() >= 3
567 && alpha < VALUE_DRAW
568 && pos.has_game_cycle(ss->ply))
570 alpha = value_draw(pos.this_thread());
575 // Dive into quiescence search when the depth reaches zero
577 return qsearch<PvNode ? PV : NonPV>(pos, ss, alpha, beta);
579 assert(-VALUE_INFINITE <= alpha && alpha < beta && beta <= VALUE_INFINITE);
580 assert(PvNode || (alpha == beta - 1));
581 assert(0 < depth && depth < MAX_PLY);
582 assert(!(PvNode && cutNode));
584 Move pv[MAX_PLY+1], capturesSearched[32], quietsSearched[64];
586 ASSERT_ALIGNED(&st, Eval::NNUE::CacheLineSize);
590 Move ttMove, move, excludedMove, bestMove;
591 Depth extension, newDepth;
592 Value bestValue, value, ttValue, eval, maxValue, probCutBeta;
593 bool givesCheck, improving, didLMR, priorCapture;
594 bool captureOrPromotion, doFullDepthSearch, moveCountPruning, ttCapture;
596 int moveCount, captureCount, quietCount, bestMoveCount, improvement, complexity;
598 // Step 1. Initialize node
599 ss->inCheck = pos.checkers();
600 priorCapture = pos.captured_piece();
601 Color us = pos.side_to_move();
602 moveCount = bestMoveCount = captureCount = quietCount = ss->moveCount = 0;
603 bestValue = -VALUE_INFINITE;
604 maxValue = VALUE_INFINITE;
606 // Check for the available remaining time
607 if (thisThread == Threads.main())
608 static_cast<MainThread*>(thisThread)->check_time();
610 // Used to send selDepth info to GUI (selDepth counts from 1, ply from 0)
611 if (PvNode && thisThread->selDepth < ss->ply + 1)
612 thisThread->selDepth = ss->ply + 1;
616 // Step 2. Check for aborted search and immediate draw
617 if ( Threads.stop.load(std::memory_order_relaxed)
618 || pos.is_draw(ss->ply)
619 || ss->ply >= MAX_PLY)
620 return (ss->ply >= MAX_PLY && !ss->inCheck) ? evaluate(pos)
621 : value_draw(pos.this_thread());
623 // Step 3. Mate distance pruning. Even if we mate at the next move our score
624 // would be at best mate_in(ss->ply+1), but if alpha is already bigger because
625 // a shorter mate was found upward in the tree then there is no need to search
626 // because we will never beat the current alpha. Same logic but with reversed
627 // signs applies also in the opposite condition of being mated instead of giving
628 // mate. In this case return a fail-high score.
629 alpha = std::max(mated_in(ss->ply), alpha);
630 beta = std::min(mate_in(ss->ply+1), beta);
635 thisThread->rootDelta = beta - alpha;
637 assert(0 <= ss->ply && ss->ply < MAX_PLY);
639 (ss+1)->ttPv = false;
640 (ss+1)->excludedMove = bestMove = MOVE_NONE;
641 (ss+2)->killers[0] = (ss+2)->killers[1] = MOVE_NONE;
642 ss->doubleExtensions = (ss-1)->doubleExtensions;
644 Square prevSq = to_sq((ss-1)->currentMove);
646 // Update the running average statistics for double extensions
647 thisThread->doubleExtensionAverage[us].update(ss->depth > (ss-1)->depth);
649 // Initialize statScore to zero for the grandchildren of the current position.
650 // So statScore is shared between all grandchildren and only the first grandchild
651 // starts with statScore = 0. Later grandchildren start with the last calculated
652 // statScore of the previous grandchild. This influences the reduction rules in
653 // LMR which are based on the statScore of parent position.
655 (ss+2)->statScore = 0;
657 // Step 4. Transposition table lookup. We don't want the score of a partial
658 // search to overwrite a previous full search TT value, so we use a different
659 // position key in case of an excluded move.
660 excludedMove = ss->excludedMove;
661 posKey = excludedMove == MOVE_NONE ? pos.key() : pos.key() ^ make_key(excludedMove);
662 tte = TT.probe(posKey, ss->ttHit);
663 ttValue = ss->ttHit ? value_from_tt(tte->value(), ss->ply, pos.rule50_count()) : VALUE_NONE;
664 ttMove = rootNode ? thisThread->rootMoves[thisThread->pvIdx].pv[0]
665 : ss->ttHit ? tte->move() : MOVE_NONE;
666 ttCapture = ttMove && pos.capture_or_promotion(ttMove);
668 ss->ttPv = PvNode || (ss->ttHit && tte->is_pv());
670 // At non-PV nodes we check for an early TT cutoff
673 && tte->depth() > depth - (thisThread->id() % 2 == 1)
674 && ttValue != VALUE_NONE // Possible in case of TT access race
675 && (ttValue >= beta ? (tte->bound() & BOUND_LOWER)
676 : (tte->bound() & BOUND_UPPER)))
678 // If ttMove is quiet, update move sorting heuristics on TT hit (~1 Elo)
683 // Bonus for a quiet ttMove that fails high (~3 Elo)
685 update_quiet_stats(pos, ss, ttMove, stat_bonus(depth));
687 // Extra penalty for early quiet moves of the previous ply (~0 Elo)
688 if ((ss-1)->moveCount <= 2 && !priorCapture)
689 update_continuation_histories(ss-1, pos.piece_on(prevSq), prevSq, -stat_bonus(depth + 1));
691 // Penalty for a quiet ttMove that fails low (~1 Elo)
694 int penalty = -stat_bonus(depth);
695 thisThread->mainHistory[us][from_to(ttMove)] << penalty;
696 update_continuation_histories(ss, pos.moved_piece(ttMove), to_sq(ttMove), penalty);
700 // Partial workaround for the graph history interaction problem
701 // For high rule50 counts don't produce transposition table cutoffs.
702 if (pos.rule50_count() < 90)
706 // Step 5. Tablebases probe
707 if (!rootNode && TB::Cardinality)
709 int piecesCount = pos.count<ALL_PIECES>();
711 if ( piecesCount <= TB::Cardinality
712 && (piecesCount < TB::Cardinality || depth >= TB::ProbeDepth)
713 && pos.rule50_count() == 0
714 && !pos.can_castle(ANY_CASTLING))
717 TB::WDLScore wdl = Tablebases::probe_wdl(pos, &err);
719 // Force check of time on the next occasion
720 if (thisThread == Threads.main())
721 static_cast<MainThread*>(thisThread)->callsCnt = 0;
723 if (err != TB::ProbeState::FAIL)
725 thisThread->tbHits.fetch_add(1, std::memory_order_relaxed);
727 int drawScore = TB::UseRule50 ? 1 : 0;
729 // use the range VALUE_MATE_IN_MAX_PLY to VALUE_TB_WIN_IN_MAX_PLY to score
730 value = wdl < -drawScore ? VALUE_MATED_IN_MAX_PLY + ss->ply + 1
731 : wdl > drawScore ? VALUE_MATE_IN_MAX_PLY - ss->ply - 1
732 : VALUE_DRAW + 2 * wdl * drawScore;
734 Bound b = wdl < -drawScore ? BOUND_UPPER
735 : wdl > drawScore ? BOUND_LOWER : BOUND_EXACT;
737 if ( b == BOUND_EXACT
738 || (b == BOUND_LOWER ? value >= beta : value <= alpha))
740 tte->save(posKey, value_to_tt(value, ss->ply), ss->ttPv, b,
741 std::min(MAX_PLY - 1, depth + 6),
742 MOVE_NONE, VALUE_NONE);
749 if (b == BOUND_LOWER)
750 bestValue = value, alpha = std::max(alpha, bestValue);
758 CapturePieceToHistory& captureHistory = thisThread->captureHistory;
760 // Step 6. Static evaluation of the position
763 // Skip early pruning when in check
764 ss->staticEval = eval = VALUE_NONE;
772 // Never assume anything about values stored in TT
773 ss->staticEval = eval = tte->eval();
774 if (eval == VALUE_NONE)
775 ss->staticEval = eval = evaluate(pos);
777 // Randomize draw evaluation
778 if (eval == VALUE_DRAW)
779 eval = value_draw(thisThread);
781 // ttValue can be used as a better position evaluation (~4 Elo)
782 if ( ttValue != VALUE_NONE
783 && (tte->bound() & (ttValue > eval ? BOUND_LOWER : BOUND_UPPER)))
788 ss->staticEval = eval = evaluate(pos);
790 // Save static evaluation into transposition table
792 tte->save(posKey, VALUE_NONE, ss->ttPv, BOUND_NONE, DEPTH_NONE, MOVE_NONE, eval);
795 // Use static evaluation difference to improve quiet move ordering (~3 Elo)
796 if (is_ok((ss-1)->currentMove) && !(ss-1)->inCheck && !priorCapture)
798 int bonus = std::clamp(-16 * int((ss-1)->staticEval + ss->staticEval), -2000, 2000);
799 thisThread->mainHistory[~us][from_to((ss-1)->currentMove)] << bonus;
802 // Set up the improvement variable, which is the difference between the current
803 // static evaluation and the previous static evaluation at our turn (if we were
804 // in check at our previous move we look at the move prior to it). The improvement
805 // margin and the improving flag are used in various pruning heuristics.
806 improvement = (ss-2)->staticEval != VALUE_NONE ? ss->staticEval - (ss-2)->staticEval
807 : (ss-4)->staticEval != VALUE_NONE ? ss->staticEval - (ss-4)->staticEval
810 improving = improvement > 0;
811 complexity = abs(ss->staticEval - (us == WHITE ? eg_value(pos.psq_score()) : -eg_value(pos.psq_score())));
813 thisThread->complexityAverage.update(complexity);
815 // Step 7. Futility pruning: child node (~25 Elo).
816 // The depth condition is important for mate finding.
819 && eval - futility_margin(depth, improving) >= beta
820 && eval < 15000) // 50% larger than VALUE_KNOWN_WIN, but smaller than TB wins.
823 // Step 8. Null move search with verification search (~22 Elo)
825 && (ss-1)->currentMove != MOVE_NULL
826 && (ss-1)->statScore < 23767
828 && eval >= ss->staticEval
829 && ss->staticEval >= beta - 20 * depth - improvement / 15 + 204 + complexity / 25
831 && pos.non_pawn_material(us)
832 && (ss->ply >= thisThread->nmpMinPly || us != thisThread->nmpColor))
834 assert(eval - beta >= 0);
836 // Null move dynamic reduction based on depth and value
837 Depth R = std::min(int(eval - beta) / 205, 3) + depth / 3 + 4;
839 ss->currentMove = MOVE_NULL;
840 ss->continuationHistory = &thisThread->continuationHistory[0][0][NO_PIECE][0];
842 pos.do_null_move(st);
844 Value nullValue = -search<NonPV>(pos, ss+1, -beta, -beta+1, depth-R, !cutNode);
846 pos.undo_null_move();
848 if (nullValue >= beta)
850 // Do not return unproven mate or TB scores
851 if (nullValue >= VALUE_TB_WIN_IN_MAX_PLY)
854 if (thisThread->nmpMinPly || (abs(beta) < VALUE_KNOWN_WIN && depth < 14))
857 assert(!thisThread->nmpMinPly); // Recursive verification is not allowed
859 // Do verification search at high depths, with null move pruning disabled
860 // for us, until ply exceeds nmpMinPly.
861 thisThread->nmpMinPly = ss->ply + 3 * (depth-R) / 4;
862 thisThread->nmpColor = us;
864 Value v = search<NonPV>(pos, ss, beta-1, beta, depth-R, false);
866 thisThread->nmpMinPly = 0;
873 probCutBeta = beta + 209 - 44 * improving;
875 // Step 9. ProbCut (~4 Elo)
876 // If we have a good enough capture and a reduced search returns a value
877 // much above beta, we can (almost) safely prune the previous move.
880 && abs(beta) < VALUE_TB_WIN_IN_MAX_PLY
881 // if value from transposition table is lower than probCutBeta, don't attempt probCut
882 // there and in further interactions with transposition table cutoff depth is set to depth - 3
883 // because probCut search has depth set to depth - 4 but we also do a move before it
884 // so effective depth is equal to depth - 3
886 && tte->depth() >= depth - 3
887 && ttValue != VALUE_NONE
888 && ttValue < probCutBeta))
890 assert(probCutBeta < VALUE_INFINITE);
892 MovePicker mp(pos, ttMove, probCutBeta - ss->staticEval, &captureHistory);
893 bool ttPv = ss->ttPv;
896 while ((move = mp.next_move()) != MOVE_NONE)
897 if (move != excludedMove && pos.legal(move))
899 assert(pos.capture_or_promotion(move));
902 captureOrPromotion = true;
904 ss->currentMove = move;
905 ss->continuationHistory = &thisThread->continuationHistory[ss->inCheck]
907 [pos.moved_piece(move)]
910 pos.do_move(move, st);
912 // Perform a preliminary qsearch to verify that the move holds
913 value = -qsearch<NonPV>(pos, ss+1, -probCutBeta, -probCutBeta+1);
915 // If the qsearch held, perform the regular search
916 if (value >= probCutBeta)
917 value = -search<NonPV>(pos, ss+1, -probCutBeta, -probCutBeta+1, depth - 4, !cutNode);
921 if (value >= probCutBeta)
923 // if transposition table doesn't have equal or more deep info write probCut data into it
925 && tte->depth() >= depth - 3
926 && ttValue != VALUE_NONE))
927 tte->save(posKey, value_to_tt(value, ss->ply), ttPv,
929 depth - 3, move, ss->staticEval);
936 // Step 10. If the position is not in TT, decrease depth by 2 or 1 depending on node type (~3 Elo)
947 moves_loop: // When in check, search starts here
949 // Step 11. A small Probcut idea, when we are in check (~0 Elo)
950 probCutBeta = beta + 409;
955 && (tte->bound() & BOUND_LOWER)
956 && tte->depth() >= depth - 3
957 && ttValue >= probCutBeta
958 && abs(ttValue) <= VALUE_KNOWN_WIN
959 && abs(beta) <= VALUE_KNOWN_WIN
964 const PieceToHistory* contHist[] = { (ss-1)->continuationHistory, (ss-2)->continuationHistory,
965 nullptr , (ss-4)->continuationHistory,
966 nullptr , (ss-6)->continuationHistory };
968 Move countermove = thisThread->counterMoves[pos.piece_on(prevSq)][prevSq];
970 MovePicker mp(pos, ttMove, depth, &thisThread->mainHistory,
977 moveCountPruning = false;
979 // Indicate PvNodes that will probably fail low if the node was searched
980 // at a depth equal or greater than the current depth, and the result of this search was a fail low.
981 bool likelyFailLow = PvNode
983 && (tte->bound() & BOUND_UPPER)
984 && tte->depth() >= depth;
986 // Step 12. Loop through all pseudo-legal moves until no moves remain
987 // or a beta cutoff occurs.
988 while ((move = mp.next_move(moveCountPruning)) != MOVE_NONE)
992 if (move == excludedMove)
995 // At root obey the "searchmoves" option and skip moves not listed in Root
996 // Move List. As a consequence any illegal move is also skipped. In MultiPV
997 // mode we also skip PV moves which have been already searched and those
998 // of lower "TB rank" if we are in a TB root position.
999 if (rootNode && !std::count(thisThread->rootMoves.begin() + thisThread->pvIdx,
1000 thisThread->rootMoves.begin() + thisThread->pvLast, move))
1003 // Check for legality
1004 if (!rootNode && !pos.legal(move))
1007 ss->moveCount = ++moveCount;
1009 if (rootNode && thisThread == Threads.main() && Time.elapsed() > 3000)
1010 sync_cout << "info depth " << depth
1011 << " currmove " << UCI::move(move, pos.is_chess960())
1012 << " currmovenumber " << moveCount + thisThread->pvIdx << sync_endl;
1014 (ss+1)->pv = nullptr;
1017 captureOrPromotion = pos.capture_or_promotion(move);
1018 movedPiece = pos.moved_piece(move);
1019 givesCheck = pos.gives_check(move);
1021 // Calculate new depth for this move
1022 newDepth = depth - 1;
1024 Value delta = beta - alpha;
1026 // Step 13. Pruning at shallow depth (~98 Elo). Depth conditions are important for mate finding.
1028 && pos.non_pawn_material(us)
1029 && bestValue > VALUE_TB_LOSS_IN_MAX_PLY)
1031 // Skip quiet moves if movecount exceeds our FutilityMoveCount threshold (~7 Elo)
1032 moveCountPruning = moveCount >= futility_move_count(improving, depth);
1034 // Reduced depth of the next LMR search
1035 int lmrDepth = std::max(newDepth - reduction(improving, depth, moveCount, delta, thisThread->rootDelta), 0);
1037 if ( captureOrPromotion
1040 // Futility pruning for captures (~0 Elo)
1041 if ( !pos.empty(to_sq(move))
1046 && ss->staticEval + 342 + 238 * lmrDepth + PieceValue[EG][pos.piece_on(to_sq(move))]
1047 + captureHistory[movedPiece][to_sq(move)][type_of(pos.piece_on(to_sq(move)))] / 8 < alpha)
1050 // SEE based pruning (~9 Elo)
1051 if (!pos.see_ge(move, Value(-217) * depth))
1056 int history = (*contHist[0])[movedPiece][to_sq(move)]
1057 + (*contHist[1])[movedPiece][to_sq(move)]
1058 + (*contHist[3])[movedPiece][to_sq(move)];
1060 // Continuation history based pruning (~2 Elo)
1062 && history < -3875 * (depth - 1))
1065 history += thisThread->mainHistory[us][from_to(move)];
1067 // Futility pruning: parent node (~9 Elo)
1070 && ss->staticEval + 138 + 137 * lmrDepth + history / 64 <= alpha)
1073 // Prune moves with negative SEE (~3 Elo)
1074 if (!pos.see_ge(move, Value(-21 * lmrDepth * lmrDepth - 21 * lmrDepth)))
1079 // Step 14. Extensions (~66 Elo)
1081 // Singular extension search (~58 Elo). If all moves but one fail low on a
1082 // search of (alpha-s, beta-s), and just one fails high on (alpha, beta),
1083 // then that move is singular and should be extended. To verify this we do
1084 // a reduced search on all the other moves but the ttMove and if the
1085 // result is lower than ttValue minus a margin, then we will extend the ttMove.
1087 && depth >= 6 + 2 * (PvNode && tte->is_pv())
1089 && !excludedMove // Avoid recursive singular search
1090 /* && ttValue != VALUE_NONE Already implicit in the next condition */
1091 && abs(ttValue) < VALUE_KNOWN_WIN
1092 && (tte->bound() & BOUND_LOWER)
1093 && tte->depth() >= depth - 3)
1095 Value singularBeta = ttValue - 3 * depth;
1096 Depth singularDepth = (depth - 1) / 2;
1098 ss->excludedMove = move;
1099 value = search<NonPV>(pos, ss, singularBeta - 1, singularBeta, singularDepth, cutNode);
1100 ss->excludedMove = MOVE_NONE;
1102 if (value < singularBeta)
1106 // Avoid search explosion by limiting the number of double extensions
1108 && value < singularBeta - 75
1109 && ss->doubleExtensions <= 6)
1113 // Multi-cut pruning
1114 // Our ttMove is assumed to fail high, and now we failed high also on a reduced
1115 // search without the ttMove. So we assume this expected Cut-node is not singular,
1116 // that multiple moves fail high, and we can prune the whole subtree by returning
1118 else if (singularBeta >= beta)
1119 return singularBeta;
1121 // If the eval of ttMove is greater than beta, we reduce it (negative extension)
1122 else if (ttValue >= beta)
1126 // Check extensions (~1 Elo)
1127 else if ( givesCheck
1129 && abs(ss->staticEval) > 100)
1132 // Quiet ttMove extensions (~0 Elo)
1135 && move == ss->killers[0]
1136 && (*contHist[0])[movedPiece][to_sq(move)] >= 10000)
1139 // Add extension to new depth
1140 newDepth += extension;
1141 ss->doubleExtensions = (ss-1)->doubleExtensions + (extension == 2);
1143 // Speculative prefetch as early as possible
1144 prefetch(TT.first_entry(pos.key_after(move)));
1146 // Update the current move (this must be done after singular extension search)
1147 ss->currentMove = move;
1148 ss->continuationHistory = &thisThread->continuationHistory[ss->inCheck]
1149 [captureOrPromotion]
1153 // Step 15. Make the move
1154 pos.do_move(move, st, givesCheck);
1156 bool doDeeperSearch = false;
1158 // Step 16. Late moves reduction / extension (LMR, ~98 Elo)
1159 // We use various heuristics for the sons of a node after the first son has
1160 // been searched. In general we would like to reduce them, but there are many
1161 // cases where we extend a son if it has good chances to be "interesting".
1163 && moveCount > 1 + 2 * rootNode
1165 || !captureOrPromotion
1166 || (cutNode && (ss-1)->moveCount > 1)))
1168 Depth r = reduction(improving, depth, moveCount, delta, thisThread->rootDelta);
1170 // Decrease reduction at some PvNodes (~2 Elo)
1172 && bestMoveCount <= 3)
1175 // Decrease reduction if position is or has been on the PV
1176 // and node is not likely to fail low. (~3 Elo)
1181 // Decrease reduction if opponent's move count is high (~1 Elo)
1182 if ((ss-1)->moveCount > 13)
1185 // Increase reduction for cut nodes (~3 Elo)
1186 if (cutNode && move != ss->killers[0])
1189 // Increase reduction if ttMove is a capture (~3 Elo)
1193 ss->statScore = thisThread->mainHistory[us][from_to(move)]
1194 + (*contHist[0])[movedPiece][to_sq(move)]
1195 + (*contHist[1])[movedPiece][to_sq(move)]
1196 + (*contHist[3])[movedPiece][to_sq(move)]
1199 // Decrease/increase reduction for moves with a good/bad history (~30 Elo)
1200 r -= ss->statScore / 14721;
1202 // In general we want to cap the LMR depth search at newDepth. But if reductions
1203 // are really negative and movecount is low, we allow this move to be searched
1204 // deeper than the first move (this may lead to hidden double extensions).
1205 int deeper = r >= -1 ? 0
1206 : moveCount <= 5 ? 2
1207 : PvNode && depth > 6 ? 1
1208 : cutNode && moveCount <= 7 ? 1
1211 Depth d = std::clamp(newDepth - r, 1, newDepth + deeper);
1213 value = -search<NonPV>(pos, ss+1, -(alpha+1), -alpha, d, true);
1215 // If the son is reduced and fails high it will be re-searched at full depth
1216 doFullDepthSearch = value > alpha && d < newDepth;
1217 doDeeperSearch = value > (alpha + 62 + 20 * (newDepth - d));
1222 doFullDepthSearch = !PvNode || moveCount > 1;
1226 // Step 17. Full depth search when LMR is skipped or fails high
1227 if (doFullDepthSearch)
1229 value = -search<NonPV>(pos, ss+1, -(alpha+1), -alpha, newDepth + doDeeperSearch, !cutNode);
1231 // If the move passed LMR update its stats
1232 if (didLMR && !captureOrPromotion)
1234 int bonus = value > alpha ? stat_bonus(newDepth)
1235 : -stat_bonus(newDepth);
1237 update_continuation_histories(ss, movedPiece, to_sq(move), bonus);
1241 // For PV nodes only, do a full PV search on the first move or after a fail
1242 // high (in the latter case search only if value < beta), otherwise let the
1243 // parent node fail low with value <= alpha and try another move.
1244 if (PvNode && (moveCount == 1 || (value > alpha && (rootNode || value < beta))))
1247 (ss+1)->pv[0] = MOVE_NONE;
1249 value = -search<PV>(pos, ss+1, -beta, -alpha,
1250 std::min(maxNextDepth, newDepth), false);
1253 // Step 18. Undo move
1254 pos.undo_move(move);
1256 assert(value > -VALUE_INFINITE && value < VALUE_INFINITE);
1258 // Step 19. Check for a new best move
1259 // Finished searching the move. If a stop occurred, the return value of
1260 // the search cannot be trusted, and we return immediately without
1261 // updating best move, PV and TT.
1262 if (Threads.stop.load(std::memory_order_relaxed))
1267 RootMove& rm = *std::find(thisThread->rootMoves.begin(),
1268 thisThread->rootMoves.end(), move);
1270 rm.averageScore = rm.averageScore != -VALUE_INFINITE ? (2 * value + rm.averageScore) / 3 : value;
1272 // PV move or new best move?
1273 if (moveCount == 1 || value > alpha)
1276 rm.selDepth = thisThread->selDepth;
1281 for (Move* m = (ss+1)->pv; *m != MOVE_NONE; ++m)
1282 rm.pv.push_back(*m);
1284 // We record how often the best move has been changed in each iteration.
1285 // This information is used for time management. In MultiPV mode,
1286 // we must take care to only do this for the first PV line.
1288 && !thisThread->pvIdx)
1289 ++thisThread->bestMoveChanges;
1292 // All other moves but the PV are set to the lowest value: this
1293 // is not a problem when sorting because the sort is stable and the
1294 // move position in the list is preserved - just the PV is pushed up.
1295 rm.score = -VALUE_INFINITE;
1298 if (value > bestValue)
1306 if (PvNode && !rootNode) // Update pv even in fail-high case
1307 update_pv(ss->pv, move, (ss+1)->pv);
1309 if (PvNode && value < beta) // Update alpha! Always alpha < beta
1316 assert(value >= beta); // Fail high
1322 // If the move is worse than some previously searched move, remember it to update its stats later
1323 if (move != bestMove)
1325 if (captureOrPromotion && captureCount < 32)
1326 capturesSearched[captureCount++] = move;
1328 else if (!captureOrPromotion && quietCount < 64)
1329 quietsSearched[quietCount++] = move;
1333 // The following condition would detect a stop only after move loop has been
1334 // completed. But in this case bestValue is valid because we have fully
1335 // searched our subtree, and we can anyhow save the result in TT.
1341 // Step 20. Check for mate and stalemate
1342 // All legal moves have been searched and if there are no legal moves, it
1343 // must be a mate or a stalemate. If we are in a singular extension search then
1344 // return a fail low score.
1346 assert(moveCount || !ss->inCheck || excludedMove || !MoveList<LEGAL>(pos).size());
1349 bestValue = excludedMove ? alpha :
1350 ss->inCheck ? mated_in(ss->ply)
1353 // If there is a move which produces search value greater than alpha we update stats of searched moves
1355 update_all_stats(pos, ss, bestMove, bestValue, beta, prevSq,
1356 quietsSearched, quietCount, capturesSearched, captureCount, depth);
1358 // Bonus for prior countermove that caused the fail low
1359 else if ( (depth >= 3 || PvNode)
1362 //Assign extra bonus if current node is PvNode or cutNode
1363 //or fail low was really bad
1364 bool extraBonus = PvNode
1366 || bestValue < alpha - 94 * depth;
1368 update_continuation_histories(ss-1, pos.piece_on(prevSq), prevSq, stat_bonus(depth) * (1 + extraBonus));
1372 bestValue = std::min(bestValue, maxValue);
1374 // If no good move is found and the previous position was ttPv, then the previous
1375 // opponent move is probably good and the new position is added to the search tree.
1376 if (bestValue <= alpha)
1377 ss->ttPv = ss->ttPv || ((ss-1)->ttPv && depth > 3);
1378 // Otherwise, a counter move has been found and if the position is the last leaf
1379 // in the search tree, remove the position from the search tree.
1381 ss->ttPv = ss->ttPv && (ss+1)->ttPv;
1383 // Write gathered information in transposition table
1384 if (!excludedMove && !(rootNode && thisThread->pvIdx))
1385 tte->save(posKey, value_to_tt(bestValue, ss->ply), ss->ttPv,
1386 bestValue >= beta ? BOUND_LOWER :
1387 PvNode && bestMove ? BOUND_EXACT : BOUND_UPPER,
1388 depth, bestMove, ss->staticEval);
1390 assert(bestValue > -VALUE_INFINITE && bestValue < VALUE_INFINITE);
1396 // qsearch() is the quiescence search function, which is called by the main search
1397 // function with zero depth, or recursively with further decreasing depth per call.
1398 template <NodeType nodeType>
1399 Value qsearch(Position& pos, Stack* ss, Value alpha, Value beta, Depth depth) {
1401 static_assert(nodeType != Root);
1402 constexpr bool PvNode = nodeType == PV;
1404 assert(alpha >= -VALUE_INFINITE && alpha < beta && beta <= VALUE_INFINITE);
1405 assert(PvNode || (alpha == beta - 1));
1410 ASSERT_ALIGNED(&st, Eval::NNUE::CacheLineSize);
1414 Move ttMove, move, bestMove;
1416 Value bestValue, value, ttValue, futilityValue, futilityBase;
1417 bool pvHit, givesCheck, captureOrPromotion;
1423 ss->pv[0] = MOVE_NONE;
1426 Thread* thisThread = pos.this_thread();
1427 bestMove = MOVE_NONE;
1428 ss->inCheck = pos.checkers();
1431 // Check for an immediate draw or maximum ply reached
1432 if ( pos.is_draw(ss->ply)
1433 || ss->ply >= MAX_PLY)
1434 return (ss->ply >= MAX_PLY && !ss->inCheck) ? evaluate(pos) : VALUE_DRAW;
1436 assert(0 <= ss->ply && ss->ply < MAX_PLY);
1438 // Decide whether or not to include checks: this fixes also the type of
1439 // TT entry depth that we are going to use. Note that in qsearch we use
1440 // only two types of depth in TT: DEPTH_QS_CHECKS or DEPTH_QS_NO_CHECKS.
1441 ttDepth = ss->inCheck || depth >= DEPTH_QS_CHECKS ? DEPTH_QS_CHECKS
1442 : DEPTH_QS_NO_CHECKS;
1443 // Transposition table lookup
1445 tte = TT.probe(posKey, ss->ttHit);
1446 ttValue = ss->ttHit ? value_from_tt(tte->value(), ss->ply, pos.rule50_count()) : VALUE_NONE;
1447 ttMove = ss->ttHit ? tte->move() : MOVE_NONE;
1448 pvHit = ss->ttHit && tte->is_pv();
1452 && tte->depth() >= ttDepth
1453 && ttValue != VALUE_NONE // Only in case of TT access race
1454 && (ttValue >= beta ? (tte->bound() & BOUND_LOWER)
1455 : (tte->bound() & BOUND_UPPER)))
1458 // Evaluate the position statically
1461 ss->staticEval = VALUE_NONE;
1462 bestValue = futilityBase = -VALUE_INFINITE;
1468 // Never assume anything about values stored in TT
1469 if ((ss->staticEval = bestValue = tte->eval()) == VALUE_NONE)
1470 ss->staticEval = bestValue = evaluate(pos);
1472 // ttValue can be used as a better position evaluation (~7 Elo)
1473 if ( ttValue != VALUE_NONE
1474 && (tte->bound() & (ttValue > bestValue ? BOUND_LOWER : BOUND_UPPER)))
1475 bestValue = ttValue;
1478 // In case of null move search use previous static eval with a different sign
1479 ss->staticEval = bestValue =
1480 (ss-1)->currentMove != MOVE_NULL ? evaluate(pos)
1481 : -(ss-1)->staticEval;
1483 // Stand pat. Return immediately if static value is at least beta
1484 if (bestValue >= beta)
1486 // Save gathered info in transposition table
1488 tte->save(posKey, value_to_tt(bestValue, ss->ply), false, BOUND_LOWER,
1489 DEPTH_NONE, MOVE_NONE, ss->staticEval);
1494 if (PvNode && bestValue > alpha)
1497 futilityBase = bestValue + 155;
1500 const PieceToHistory* contHist[] = { (ss-1)->continuationHistory, (ss-2)->continuationHistory,
1501 nullptr , (ss-4)->continuationHistory,
1502 nullptr , (ss-6)->continuationHistory };
1504 // Initialize a MovePicker object for the current position, and prepare
1505 // to search the moves. Because the depth is <= 0 here, only captures,
1506 // queen promotions, and other checks (only if depth >= DEPTH_QS_CHECKS)
1507 // will be generated.
1508 Square prevSq = to_sq((ss-1)->currentMove);
1509 MovePicker mp(pos, ttMove, depth, &thisThread->mainHistory,
1510 &thisThread->captureHistory,
1514 // Loop through the moves until no moves remain or a beta cutoff occurs
1515 while ((move = mp.next_move()) != MOVE_NONE)
1517 assert(is_ok(move));
1519 // Check for legality
1520 if (!pos.legal(move))
1523 givesCheck = pos.gives_check(move);
1524 captureOrPromotion = pos.capture_or_promotion(move);
1528 // Futility pruning and moveCount pruning (~5 Elo)
1529 if ( bestValue > VALUE_TB_LOSS_IN_MAX_PLY
1531 && to_sq(move) != prevSq
1532 && futilityBase > -VALUE_KNOWN_WIN
1533 && type_of(move) != PROMOTION)
1539 futilityValue = futilityBase + PieceValue[EG][pos.piece_on(to_sq(move))];
1541 if (futilityValue <= alpha)
1543 bestValue = std::max(bestValue, futilityValue);
1547 if (futilityBase <= alpha && !pos.see_ge(move, VALUE_ZERO + 1))
1549 bestValue = std::max(bestValue, futilityBase);
1554 // Do not search moves with negative SEE values (~5 Elo)
1555 if ( bestValue > VALUE_TB_LOSS_IN_MAX_PLY
1556 && !pos.see_ge(move))
1559 // Speculative prefetch as early as possible
1560 prefetch(TT.first_entry(pos.key_after(move)));
1562 ss->currentMove = move;
1563 ss->continuationHistory = &thisThread->continuationHistory[ss->inCheck]
1564 [captureOrPromotion]
1565 [pos.moved_piece(move)]
1568 // Continuation history based pruning (~2 Elo)
1569 if ( !captureOrPromotion
1570 && bestValue > VALUE_TB_LOSS_IN_MAX_PLY
1571 && (*contHist[0])[pos.moved_piece(move)][to_sq(move)] < CounterMovePruneThreshold
1572 && (*contHist[1])[pos.moved_piece(move)][to_sq(move)] < CounterMovePruneThreshold)
1575 // Make and search the move
1576 pos.do_move(move, st, givesCheck);
1577 value = -qsearch<nodeType>(pos, ss+1, -beta, -alpha, depth - 1);
1578 pos.undo_move(move);
1580 assert(value > -VALUE_INFINITE && value < VALUE_INFINITE);
1582 // Check for a new best move
1583 if (value > bestValue)
1591 if (PvNode) // Update pv even in fail-high case
1592 update_pv(ss->pv, move, (ss+1)->pv);
1594 if (PvNode && value < beta) // Update alpha here!
1602 // All legal moves have been searched. A special case: if we're in check
1603 // and no legal moves were found, it is checkmate.
1604 if (ss->inCheck && bestValue == -VALUE_INFINITE)
1606 assert(!MoveList<LEGAL>(pos).size());
1608 return mated_in(ss->ply); // Plies to mate from the root
1611 // Save gathered info in transposition table
1612 tte->save(posKey, value_to_tt(bestValue, ss->ply), pvHit,
1613 bestValue >= beta ? BOUND_LOWER : BOUND_UPPER,
1614 ttDepth, bestMove, ss->staticEval);
1616 assert(bestValue > -VALUE_INFINITE && bestValue < VALUE_INFINITE);
1622 // value_to_tt() adjusts a mate or TB score from "plies to mate from the root" to
1623 // "plies to mate from the current position". Standard scores are unchanged.
1624 // The function is called before storing a value in the transposition table.
1626 Value value_to_tt(Value v, int ply) {
1628 assert(v != VALUE_NONE);
1630 return v >= VALUE_TB_WIN_IN_MAX_PLY ? v + ply
1631 : v <= VALUE_TB_LOSS_IN_MAX_PLY ? v - ply : v;
1635 // value_from_tt() is the inverse of value_to_tt(): it adjusts a mate or TB score
1636 // from the transposition table (which refers to the plies to mate/be mated from
1637 // current position) to "plies to mate/be mated (TB win/loss) from the root". However,
1638 // for mate scores, to avoid potentially false mate scores related to the 50 moves rule
1639 // and the graph history interaction, we return an optimal TB score instead.
1641 Value value_from_tt(Value v, int ply, int r50c) {
1643 if (v == VALUE_NONE)
1646 if (v >= VALUE_TB_WIN_IN_MAX_PLY) // TB win or better
1648 if (v >= VALUE_MATE_IN_MAX_PLY && VALUE_MATE - v > 99 - r50c)
1649 return VALUE_MATE_IN_MAX_PLY - 1; // do not return a potentially false mate score
1654 if (v <= VALUE_TB_LOSS_IN_MAX_PLY) // TB loss or worse
1656 if (v <= VALUE_MATED_IN_MAX_PLY && VALUE_MATE + v > 99 - r50c)
1657 return VALUE_MATED_IN_MAX_PLY + 1; // do not return a potentially false mate score
1666 // update_pv() adds current move and appends child pv[]
1668 void update_pv(Move* pv, Move move, Move* childPv) {
1670 for (*pv++ = move; childPv && *childPv != MOVE_NONE; )
1676 // update_all_stats() updates stats at the end of search() when a bestMove is found
1678 void update_all_stats(const Position& pos, Stack* ss, Move bestMove, Value bestValue, Value beta, Square prevSq,
1679 Move* quietsSearched, int quietCount, Move* capturesSearched, int captureCount, Depth depth) {
1682 Color us = pos.side_to_move();
1683 Thread* thisThread = pos.this_thread();
1684 CapturePieceToHistory& captureHistory = thisThread->captureHistory;
1685 Piece moved_piece = pos.moved_piece(bestMove);
1686 PieceType captured = type_of(pos.piece_on(to_sq(bestMove)));
1688 bonus1 = stat_bonus(depth + 1);
1689 bonus2 = bestValue > beta + PawnValueMg ? bonus1 // larger bonus
1690 : stat_bonus(depth); // smaller bonus
1692 if (!pos.capture_or_promotion(bestMove))
1694 // Increase stats for the best move in case it was a quiet move
1695 update_quiet_stats(pos, ss, bestMove, bonus2);
1697 // Decrease stats for all non-best quiet moves
1698 for (int i = 0; i < quietCount; ++i)
1700 thisThread->mainHistory[us][from_to(quietsSearched[i])] << -bonus2;
1701 update_continuation_histories(ss, pos.moved_piece(quietsSearched[i]), to_sq(quietsSearched[i]), -bonus2);
1705 // Increase stats for the best move in case it was a capture move
1706 captureHistory[moved_piece][to_sq(bestMove)][captured] << bonus1;
1708 // Extra penalty for a quiet early move that was not a TT move or
1709 // main killer move in previous ply when it gets refuted.
1710 if ( ((ss-1)->moveCount == 1 + (ss-1)->ttHit || ((ss-1)->currentMove == (ss-1)->killers[0]))
1711 && !pos.captured_piece())
1712 update_continuation_histories(ss-1, pos.piece_on(prevSq), prevSq, -bonus1);
1714 // Decrease stats for all non-best capture moves
1715 for (int i = 0; i < captureCount; ++i)
1717 moved_piece = pos.moved_piece(capturesSearched[i]);
1718 captured = type_of(pos.piece_on(to_sq(capturesSearched[i])));
1719 captureHistory[moved_piece][to_sq(capturesSearched[i])][captured] << -bonus1;
1724 // update_continuation_histories() updates histories of the move pairs formed
1725 // by moves at ply -1, -2, -4, and -6 with current move.
1727 void update_continuation_histories(Stack* ss, Piece pc, Square to, int bonus) {
1729 for (int i : {1, 2, 4, 6})
1731 // Only update first 2 continuation histories if we are in check
1732 if (ss->inCheck && i > 2)
1734 if (is_ok((ss-i)->currentMove))
1735 (*(ss-i)->continuationHistory)[pc][to] << bonus;
1740 // update_quiet_stats() updates move sorting heuristics
1742 void update_quiet_stats(const Position& pos, Stack* ss, Move move, int bonus) {
1745 if (ss->killers[0] != move)
1747 ss->killers[1] = ss->killers[0];
1748 ss->killers[0] = move;
1751 Color us = pos.side_to_move();
1752 Thread* thisThread = pos.this_thread();
1753 thisThread->mainHistory[us][from_to(move)] << bonus;
1754 update_continuation_histories(ss, pos.moved_piece(move), to_sq(move), bonus);
1756 // Update countermove history
1757 if (is_ok((ss-1)->currentMove))
1759 Square prevSq = to_sq((ss-1)->currentMove);
1760 thisThread->counterMoves[pos.piece_on(prevSq)][prevSq] = move;
1764 // When playing with strength handicap, choose best move among a set of RootMoves
1765 // using a statistical rule dependent on 'level'. Idea by Heinz van Saanen.
1767 Move Skill::pick_best(size_t multiPV) {
1769 const RootMoves& rootMoves = Threads.main()->rootMoves;
1770 static PRNG rng(now()); // PRNG sequence should be non-deterministic
1772 // RootMoves are already sorted by score in descending order
1773 Value topScore = rootMoves[0].score;
1774 int delta = std::min(topScore - rootMoves[multiPV - 1].score, PawnValueMg);
1775 int maxScore = -VALUE_INFINITE;
1776 double weakness = 120 - 2 * level;
1778 // Choose best move. For each move score we add two terms, both dependent on
1779 // weakness. One is deterministic and bigger for weaker levels, and one is
1780 // random. Then we choose the move with the resulting highest score.
1781 for (size_t i = 0; i < multiPV; ++i)
1783 // This is our magic formula
1784 int push = int(( weakness * int(topScore - rootMoves[i].score)
1785 + delta * (rng.rand<unsigned>() % int(weakness))) / 128);
1787 if (rootMoves[i].score + push >= maxScore)
1789 maxScore = rootMoves[i].score + push;
1790 best = rootMoves[i].pv[0];
1800 /// MainThread::check_time() is used to print debug info and, more importantly,
1801 /// to detect when we are out of available time and thus stop the search.
1803 void MainThread::check_time() {
1808 // When using nodes, ensure checking rate is not lower than 0.1% of nodes
1809 callsCnt = Limits.nodes ? std::min(1024, int(Limits.nodes / 1024)) : 1024;
1811 static TimePoint lastInfoTime = now();
1813 TimePoint elapsed = Time.elapsed();
1814 TimePoint tick = Limits.startTime + elapsed;
1816 if (tick - lastInfoTime >= 1000)
1818 lastInfoTime = tick;
1822 // We should not stop pondering until told so by the GUI
1826 if ( (Limits.use_time_management() && (elapsed > Time.maximum() - 10 || stopOnPonderhit))
1827 || (Limits.movetime && elapsed >= Limits.movetime)
1828 || (Limits.nodes && Threads.nodes_searched() >= (uint64_t)Limits.nodes))
1829 Threads.stop = true;
1833 /// UCI::pv() formats PV information according to the UCI protocol. UCI requires
1834 /// that all (if any) unsearched PV lines are sent using a previous search score.
1836 string UCI::pv(const Position& pos, Depth depth, Value alpha, Value beta) {
1838 std::stringstream ss;
1839 TimePoint elapsed = Time.elapsed() + 1;
1840 const RootMoves& rootMoves = pos.this_thread()->rootMoves;
1841 size_t pvIdx = pos.this_thread()->pvIdx;
1842 size_t multiPV = std::min((size_t)Options["MultiPV"], rootMoves.size());
1843 uint64_t nodesSearched = Threads.nodes_searched();
1844 uint64_t tbHits = Threads.tb_hits() + (TB::RootInTB ? rootMoves.size() : 0);
1846 for (size_t i = 0; i < multiPV; ++i)
1848 bool updated = rootMoves[i].score != -VALUE_INFINITE;
1850 if (depth == 1 && !updated && i > 0)
1853 Depth d = updated ? depth : std::max(1, depth - 1);
1854 Value v = updated ? rootMoves[i].score : rootMoves[i].previousScore;
1856 if (v == -VALUE_INFINITE)
1859 bool tb = TB::RootInTB && abs(v) < VALUE_MATE_IN_MAX_PLY;
1860 v = tb ? rootMoves[i].tbScore : v;
1862 if (ss.rdbuf()->in_avail()) // Not at first line
1867 << " seldepth " << rootMoves[i].selDepth
1868 << " multipv " << i + 1
1869 << " score " << UCI::value(v);
1871 if (Options["UCI_ShowWDL"])
1872 ss << UCI::wdl(v, pos.game_ply());
1874 if (!tb && i == pvIdx)
1875 ss << (v >= beta ? " lowerbound" : v <= alpha ? " upperbound" : "");
1877 ss << " nodes " << nodesSearched
1878 << " nps " << nodesSearched * 1000 / elapsed;
1880 if (elapsed > 1000) // Earlier makes little sense
1881 ss << " hashfull " << TT.hashfull();
1883 ss << " tbhits " << tbHits
1884 << " time " << elapsed
1887 for (Move m : rootMoves[i].pv)
1888 ss << " " << UCI::move(m, pos.is_chess960());
1895 /// RootMove::extract_ponder_from_tt() is called in case we have no ponder move
1896 /// before exiting the search, for instance, in case we stop the search during a
1897 /// fail high at root. We try hard to have a ponder move to return to the GUI,
1898 /// otherwise in case of 'ponder on' we have nothing to think on.
1900 bool RootMove::extract_ponder_from_tt(Position& pos) {
1903 ASSERT_ALIGNED(&st, Eval::NNUE::CacheLineSize);
1907 assert(pv.size() == 1);
1909 if (pv[0] == MOVE_NONE)
1912 pos.do_move(pv[0], st);
1913 TTEntry* tte = TT.probe(pos.key(), ttHit);
1917 Move m = tte->move(); // Local copy to be SMP safe
1918 if (MoveList<LEGAL>(pos).contains(m))
1922 pos.undo_move(pv[0]);
1923 return pv.size() > 1;
1926 void Tablebases::rank_root_moves(Position& pos, Search::RootMoves& rootMoves) {
1929 UseRule50 = bool(Options["Syzygy50MoveRule"]);
1930 ProbeDepth = int(Options["SyzygyProbeDepth"]);
1931 Cardinality = int(Options["SyzygyProbeLimit"]);
1932 bool dtz_available = true;
1934 // Tables with fewer pieces than SyzygyProbeLimit are searched with
1935 // ProbeDepth == DEPTH_ZERO
1936 if (Cardinality > MaxCardinality)
1938 Cardinality = MaxCardinality;
1942 if (Cardinality >= popcount(pos.pieces()) && !pos.can_castle(ANY_CASTLING))
1944 // Rank moves using DTZ tables
1945 RootInTB = root_probe(pos, rootMoves);
1949 // DTZ tables are missing; try to rank moves using WDL tables
1950 dtz_available = false;
1951 RootInTB = root_probe_wdl(pos, rootMoves);
1957 // Sort moves according to TB rank
1958 std::stable_sort(rootMoves.begin(), rootMoves.end(),
1959 [](const RootMove &a, const RootMove &b) { return a.tbRank > b.tbRank; } );
1961 // Probe during search only if DTZ is not available and we are winning
1962 if (dtz_available || rootMoves[0].tbScore <= VALUE_DRAW)
1967 // Clean up if root_probe() and root_probe_wdl() have failed
1968 for (auto& m : rootMoves)
1973 } // namespace Stockfish