2 Stockfish, a UCI chess playing engine derived from Glaurung 2.1
3 Copyright (C) 2004-2023 The Stockfish developers (see AUTHORS file)
5 Stockfish is free software: you can redistribute it and/or modify
6 it under the terms of the GNU General Public License as published by
7 the Free Software Foundation, either version 3 of the License, or
8 (at your option) any later version.
10 Stockfish is distributed in the hope that it will be useful,
11 but WITHOUT ANY WARRANTY; without even the implied warranty of
12 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
13 GNU General Public License for more details.
15 You should have received a copy of the GNU General Public License
16 along with this program. If not, see <http://www.gnu.org/licenses/>.
28 #include <initializer_list>
39 #include "nnue/evaluate_nnue.h"
40 #include "nnue/nnue_common.h"
42 #include "syzygy/tbprobe.h"
55 namespace Tablebases {
63 namespace TB = Tablebases;
67 using namespace Search;
71 // Different node types, used as a template parameter
72 enum NodeType { NonPV, PV, Root };
75 Value futility_margin(Depth d, bool noTtCutNode, bool improving) {
76 return Value((126 - 42 * noTtCutNode) * (d - improving));
79 // Reductions lookup table initialized at startup
80 int Reductions[MAX_MOVES]; // [depth or moveNumber]
82 Depth reduction(bool i, Depth d, int mn, Value delta, Value rootDelta) {
83 int reductionScale = Reductions[d] * Reductions[mn];
84 return (reductionScale + 1560 - int(delta) * 945 / int(rootDelta)) / 1024
85 + (!i && reductionScale > 791);
88 constexpr int futility_move_count(bool improving, Depth depth) {
89 return improving ? (3 + depth * depth)
90 : (3 + depth * depth) / 2;
93 // History and stats update bonus, based on depth
94 int stat_bonus(Depth d) {
95 return std::min(334 * d - 531, 1538);
98 // Add a small random component to draw evaluations to avoid 3-fold blindness
99 Value value_draw(const Thread* thisThread) {
100 return VALUE_DRAW - 1 + Value(thisThread->nodes & 0x2);
103 // Skill structure is used to implement strength limit.
104 // If we have a UCI_Elo, we convert it to an appropriate skill level, anchored to the Stash engine.
105 // This method is based on a fit of the Elo results for games played between the master at various
106 // skill levels and various versions of the Stash engine, all ranked at CCRL.
107 // Skill 0 .. 19 now covers CCRL Blitz Elo from 1320 to 3190, approximately
108 // Reference: https://github.com/vondele/Stockfish/commit/a08b8d4e9711c20acedbfe17d618c3c384b339ec
110 Skill(int skill_level, int uci_elo) {
113 double e = double(uci_elo - 1320) / (3190 - 1320);
114 level = std::clamp((((37.2473 * e - 40.8525) * e + 22.2943) * e - 0.311438), 0.0, 19.0);
117 level = double(skill_level);
119 bool enabled() const { return level < 20.0; }
120 bool time_to_pick(Depth depth) const { return depth == 1 + int(level); }
121 Move pick_best(size_t multiPV);
124 Move best = MOVE_NONE;
127 template <NodeType nodeType>
128 Value search(Position& pos, Stack* ss, Value alpha, Value beta, Depth depth, bool cutNode);
130 template <NodeType nodeType>
131 Value qsearch(Position& pos, Stack* ss, Value alpha, Value beta, Depth depth = 0);
133 Value value_to_tt(Value v, int ply);
134 Value value_from_tt(Value v, int ply, int r50c);
135 void update_pv(Move* pv, Move move, const Move* childPv);
136 void update_continuation_histories(Stack* ss, Piece pc, Square to, int bonus);
137 void update_quiet_stats(const Position& pos, Stack* ss, Move move, int bonus);
138 void update_all_stats(const Position& pos, Stack* ss, Move bestMove, Value bestValue, Value beta, Square prevSq,
139 Move* quietsSearched, int quietCount, Move* capturesSearched, int captureCount, Depth depth);
141 // perft() is our utility to verify move generation. All the leaf nodes up
142 // to the given depth are generated and counted, and the sum is returned.
144 uint64_t perft(Position& pos, Depth depth) {
147 ASSERT_ALIGNED(&st, Eval::NNUE::CacheLineSize);
149 uint64_t cnt, nodes = 0;
150 const bool leaf = (depth == 2);
152 for (const auto& m : MoveList<LEGAL>(pos))
154 if (Root && depth <= 1)
159 cnt = leaf ? MoveList<LEGAL>(pos).size() : perft<false>(pos, depth - 1);
164 sync_cout << UCI::move(m, pos.is_chess960()) << ": " << cnt << sync_endl;
172 /// Search::init() is called at startup to initialize various lookup tables
174 void Search::init() {
176 for (int i = 1; i < MAX_MOVES; ++i)
177 Reductions[i] = int((20.37 + std::log(Threads.size()) / 2) * std::log(i));
181 /// Search::clear() resets search state to its initial value
183 void Search::clear() {
185 Threads.main()->wait_for_search_finished();
187 Time.availableNodes = 0;
190 Tablebases::init(Options["SyzygyPath"]); // Free mapped files
194 /// MainThread::search() is started when the program receives the UCI 'go'
195 /// command. It searches from the root position and outputs the "bestmove".
197 void MainThread::search() {
201 nodes = perft<true>(rootPos, Limits.perft);
202 sync_cout << "\nNodes searched: " << nodes << "\n" << sync_endl;
206 Color us = rootPos.side_to_move();
207 Time.init(Limits, us, rootPos.game_ply());
210 Eval::NNUE::verify();
212 if (rootMoves.empty())
214 rootMoves.emplace_back(MOVE_NONE);
215 sync_cout << "info depth 0 score "
216 << UCI::value(rootPos.checkers() ? -VALUE_MATE : VALUE_DRAW)
221 Threads.start_searching(); // start non-main threads
222 Thread::search(); // main thread start searching
225 // When we reach the maximum depth, we can arrive here without a raise of
226 // Threads.stop. However, if we are pondering or in an infinite search,
227 // the UCI protocol states that we shouldn't print the best move before the
228 // GUI sends a "stop" or "ponderhit" command. We therefore simply wait here
229 // until the GUI sends one of those commands.
231 while (!Threads.stop && (ponder || Limits.infinite))
232 {} // Busy wait for a stop or a ponder reset
234 // Stop the threads if not already stopped (also raise the stop if
235 // "ponderhit" just reset Threads.ponder).
238 // Wait until all threads have finished
239 Threads.wait_for_search_finished();
241 // When playing in 'nodes as time' mode, subtract the searched nodes from
242 // the available ones before exiting.
244 Time.availableNodes += Limits.inc[us] - Threads.nodes_searched();
246 Thread* bestThread = this;
247 Skill skill = Skill(Options["Skill Level"], Options["UCI_LimitStrength"] ? int(Options["UCI_Elo"]) : 0);
249 if ( int(Options["MultiPV"]) == 1
252 && rootMoves[0].pv[0] != MOVE_NONE)
253 bestThread = Threads.get_best_thread();
255 bestPreviousScore = bestThread->rootMoves[0].score;
256 bestPreviousAverageScore = bestThread->rootMoves[0].averageScore;
258 // Send again PV info if we have a new best thread
259 if (bestThread != this)
260 sync_cout << UCI::pv(bestThread->rootPos, bestThread->completedDepth) << sync_endl;
262 sync_cout << "bestmove " << UCI::move(bestThread->rootMoves[0].pv[0], rootPos.is_chess960());
264 if (bestThread->rootMoves[0].pv.size() > 1 || bestThread->rootMoves[0].extract_ponder_from_tt(rootPos))
265 std::cout << " ponder " << UCI::move(bestThread->rootMoves[0].pv[1], rootPos.is_chess960());
267 std::cout << sync_endl;
271 /// Thread::search() is the main iterative deepening loop. It calls search()
272 /// repeatedly with increasing depth until the allocated thinking time has been
273 /// consumed, the user stops the search, or the maximum search depth is reached.
275 void Thread::search() {
277 // Allocate stack with extra size to allow access from (ss-7) to (ss+2)
278 // (ss-7) is needed for update_continuation_histories(ss-1, ...) which accesses (ss-6)
279 // (ss+2) is needed for initialization of statScore and killers
280 Stack stack[MAX_PLY+10], *ss = stack+7;
282 Value alpha, beta, delta;
283 Move lastBestMove = MOVE_NONE;
284 Depth lastBestMoveDepth = 0;
285 MainThread* mainThread = (this == Threads.main() ? Threads.main() : nullptr);
286 double timeReduction = 1, totBestMoveChanges = 0;
287 Color us = rootPos.side_to_move();
290 std::memset(ss-7, 0, 10 * sizeof(Stack));
291 for (int i = 7; i > 0; --i)
293 (ss-i)->continuationHistory = &this->continuationHistory[0][0][NO_PIECE][0]; // Use as a sentinel
294 (ss-i)->staticEval = VALUE_NONE;
297 for (int i = 0; i <= MAX_PLY + 2; ++i)
302 bestValue = -VALUE_INFINITE;
306 if (mainThread->bestPreviousScore == VALUE_INFINITE)
307 for (int i = 0; i < 4; ++i)
308 mainThread->iterValue[i] = VALUE_ZERO;
310 for (int i = 0; i < 4; ++i)
311 mainThread->iterValue[i] = mainThread->bestPreviousScore;
314 size_t multiPV = size_t(Options["MultiPV"]);
315 Skill skill(Options["Skill Level"], Options["UCI_LimitStrength"] ? int(Options["UCI_Elo"]) : 0);
317 // When playing with strength handicap enable MultiPV search that we will
318 // use behind-the-scenes to retrieve a set of possible moves.
320 multiPV = std::max(multiPV, size_t(4));
322 multiPV = std::min(multiPV, rootMoves.size());
324 int searchAgainCounter = 0;
326 // Iterative deepening loop until requested to stop or the target depth is reached
327 while ( ++rootDepth < MAX_PLY
329 && !(Limits.depth && mainThread && rootDepth > Limits.depth))
331 // Age out PV variability metric
333 totBestMoveChanges /= 2;
335 // Save the last iteration's scores before the first PV line is searched and
336 // all the move scores except the (new) PV are set to -VALUE_INFINITE.
337 for (RootMove& rm : rootMoves)
338 rm.previousScore = rm.score;
343 if (!Threads.increaseDepth)
344 searchAgainCounter++;
346 // MultiPV loop. We perform a full root search for each PV line
347 for (pvIdx = 0; pvIdx < multiPV && !Threads.stop; ++pvIdx)
352 for (pvLast++; pvLast < rootMoves.size(); pvLast++)
353 if (rootMoves[pvLast].tbRank != rootMoves[pvFirst].tbRank)
357 // Reset UCI info selDepth for each depth and each PV line
360 // Reset aspiration window starting size
361 Value prev = rootMoves[pvIdx].averageScore;
362 delta = Value(10) + int(prev) * prev / 17470;
363 alpha = std::max(prev - delta,-VALUE_INFINITE);
364 beta = std::min(prev + delta, VALUE_INFINITE);
366 // Adjust optimism based on root move's previousScore (~4 Elo)
367 int opt = 113 * prev / (std::abs(prev) + 109);
368 optimism[ us] = Value(opt);
369 optimism[~us] = -optimism[us];
371 // Start with a small aspiration window and, in the case of a fail
372 // high/low, re-search with a bigger window until we don't fail
374 int failedHighCnt = 0;
377 // Adjust the effective depth searched, but ensure at least one effective increment for every
378 // four searchAgain steps (see issue #2717).
379 Depth adjustedDepth = std::max(1, rootDepth - failedHighCnt - 3 * (searchAgainCounter + 1) / 4);
380 bestValue = Stockfish::search<Root>(rootPos, ss, alpha, beta, adjustedDepth, false);
382 // Bring the best move to the front. It is critical that sorting
383 // is done with a stable algorithm because all the values but the
384 // first and eventually the new best one is set to -VALUE_INFINITE
385 // and we want to keep the same order for all the moves except the
386 // new PV that goes to the front. Note that in the case of MultiPV
387 // search the already searched PV lines are preserved.
388 std::stable_sort(rootMoves.begin() + pvIdx, rootMoves.begin() + pvLast);
390 // If search has been stopped, we break immediately. Sorting is
391 // safe because RootMoves is still valid, although it refers to
392 // the previous iteration.
396 // When failing high/low give some update (without cluttering
397 // the UI) before a re-search.
400 && (bestValue <= alpha || bestValue >= beta)
401 && Time.elapsed() > 3000)
402 sync_cout << UCI::pv(rootPos, rootDepth) << sync_endl;
404 // In case of failing low/high increase aspiration window and
405 // re-search, otherwise exit the loop.
406 if (bestValue <= alpha)
408 beta = (alpha + beta) / 2;
409 alpha = std::max(bestValue - delta, -VALUE_INFINITE);
413 mainThread->stopOnPonderhit = false;
415 else if (bestValue >= beta)
417 beta = std::min(bestValue + delta, VALUE_INFINITE);
425 assert(alpha >= -VALUE_INFINITE && beta <= VALUE_INFINITE);
428 // Sort the PV lines searched so far and update the GUI
429 std::stable_sort(rootMoves.begin() + pvFirst, rootMoves.begin() + pvIdx + 1);
432 && (Threads.stop || pvIdx + 1 == multiPV || Time.elapsed() > 3000))
433 sync_cout << UCI::pv(rootPos, rootDepth) << sync_endl;
437 completedDepth = rootDepth;
439 if (rootMoves[0].pv[0] != lastBestMove)
441 lastBestMove = rootMoves[0].pv[0];
442 lastBestMoveDepth = rootDepth;
445 // Have we found a "mate in x"?
447 && bestValue >= VALUE_MATE_IN_MAX_PLY
448 && VALUE_MATE - bestValue <= 2 * Limits.mate)
454 // If the skill level is enabled and time is up, pick a sub-optimal best move
455 if (skill.enabled() && skill.time_to_pick(rootDepth))
456 skill.pick_best(multiPV);
458 // Use part of the gained time from a previous stable move for the current move
459 for (Thread* th : Threads)
461 totBestMoveChanges += th->bestMoveChanges;
462 th->bestMoveChanges = 0;
465 // Do we have time for the next iteration? Can we stop searching now?
466 if ( Limits.use_time_management()
468 && !mainThread->stopOnPonderhit)
470 double fallingEval = (69 + 13 * (mainThread->bestPreviousAverageScore - bestValue)
471 + 6 * (mainThread->iterValue[iterIdx] - bestValue)) / 619.6;
472 fallingEval = std::clamp(fallingEval, 0.5, 1.5);
474 // If the bestMove is stable over several iterations, reduce time accordingly
475 timeReduction = lastBestMoveDepth + 8 < completedDepth ? 1.57 : 0.65;
476 double reduction = (1.4 + mainThread->previousTimeReduction) / (2.08 * timeReduction);
477 double bestMoveInstability = 1 + 1.8 * totBestMoveChanges / Threads.size();
479 double totalTime = Time.optimum() * fallingEval * reduction * bestMoveInstability;
481 // Cap used time in case of a single legal move for a better viewer experience in tournaments
482 // yielding correct scores and sufficiently fast moves.
483 if (rootMoves.size() == 1)
484 totalTime = std::min(500.0, totalTime);
486 // Stop the search if we have exceeded the totalTime
487 if (Time.elapsed() > totalTime)
489 // If we are allowed to ponder do not stop the search now but
490 // keep pondering until the GUI sends "ponderhit" or "stop".
491 if (mainThread->ponder)
492 mainThread->stopOnPonderhit = true;
496 else if ( !mainThread->ponder
497 && Time.elapsed() > totalTime * 0.50)
498 Threads.increaseDepth = false;
500 Threads.increaseDepth = true;
503 mainThread->iterValue[iterIdx] = bestValue;
504 iterIdx = (iterIdx + 1) & 3;
510 mainThread->previousTimeReduction = timeReduction;
512 // If the skill level is enabled, swap the best PV line with the sub-optimal one
514 std::swap(rootMoves[0], *std::find(rootMoves.begin(), rootMoves.end(),
515 skill.best ? skill.best : skill.pick_best(multiPV)));
521 // search<>() is the main search function for both PV and non-PV nodes
523 template <NodeType nodeType>
524 Value search(Position& pos, Stack* ss, Value alpha, Value beta, Depth depth, bool cutNode) {
526 constexpr bool PvNode = nodeType != NonPV;
527 constexpr bool rootNode = nodeType == Root;
529 // Dive into quiescence search when the depth reaches zero
531 return qsearch<PvNode ? PV : NonPV>(pos, ss, alpha, beta);
533 // Check if we have an upcoming move that draws by repetition, or
534 // if the opponent had an alternative move earlier to this position.
536 && alpha < VALUE_DRAW
537 && pos.has_game_cycle(ss->ply))
539 alpha = value_draw(pos.this_thread());
544 assert(-VALUE_INFINITE <= alpha && alpha < beta && beta <= VALUE_INFINITE);
545 assert(PvNode || (alpha == beta - 1));
546 assert(0 < depth && depth < MAX_PLY);
547 assert(!(PvNode && cutNode));
549 Move pv[MAX_PLY+1], capturesSearched[32], quietsSearched[32];
551 ASSERT_ALIGNED(&st, Eval::NNUE::CacheLineSize);
555 Move ttMove, move, excludedMove, bestMove;
556 Depth extension, newDepth;
557 Value bestValue, value, ttValue, eval, maxValue, probCutBeta;
558 bool givesCheck, improving, priorCapture, singularQuietLMR;
559 bool capture, moveCountPruning, ttCapture;
561 int moveCount, captureCount, quietCount;
563 // Step 1. Initialize node
564 Thread* thisThread = pos.this_thread();
565 ss->inCheck = pos.checkers();
566 priorCapture = pos.captured_piece();
567 Color us = pos.side_to_move();
568 moveCount = captureCount = quietCount = ss->moveCount = 0;
569 bestValue = -VALUE_INFINITE;
570 maxValue = VALUE_INFINITE;
572 // Check for the available remaining time
573 if (thisThread == Threads.main())
574 static_cast<MainThread*>(thisThread)->check_time();
576 // Used to send selDepth info to GUI (selDepth counts from 1, ply from 0)
577 if (PvNode && thisThread->selDepth < ss->ply + 1)
578 thisThread->selDepth = ss->ply + 1;
582 // Step 2. Check for aborted search and immediate draw
583 if ( Threads.stop.load(std::memory_order_relaxed)
584 || pos.is_draw(ss->ply)
585 || ss->ply >= MAX_PLY)
586 return (ss->ply >= MAX_PLY && !ss->inCheck) ? evaluate(pos)
587 : value_draw(pos.this_thread());
589 // Step 3. Mate distance pruning. Even if we mate at the next move our score
590 // would be at best mate_in(ss->ply+1), but if alpha is already bigger because
591 // a shorter mate was found upward in the tree then there is no need to search
592 // because we will never beat the current alpha. Same logic but with reversed
593 // signs apply also in the opposite condition of being mated instead of giving
594 // mate. In this case, return a fail-high score.
595 alpha = std::max(mated_in(ss->ply), alpha);
596 beta = std::min(mate_in(ss->ply+1), beta);
601 thisThread->rootDelta = beta - alpha;
603 assert(0 <= ss->ply && ss->ply < MAX_PLY);
605 (ss+1)->excludedMove = bestMove = MOVE_NONE;
606 (ss+2)->killers[0] = (ss+2)->killers[1] = MOVE_NONE;
607 (ss+2)->cutoffCnt = 0;
608 ss->doubleExtensions = (ss-1)->doubleExtensions;
609 Square prevSq = is_ok((ss-1)->currentMove) ? to_sq((ss-1)->currentMove) : SQ_NONE;
612 // Step 4. Transposition table lookup.
613 excludedMove = ss->excludedMove;
615 tte = TT.probe(posKey, ss->ttHit);
616 ttValue = ss->ttHit ? value_from_tt(tte->value(), ss->ply, pos.rule50_count()) : VALUE_NONE;
617 ttMove = rootNode ? thisThread->rootMoves[thisThread->pvIdx].pv[0]
618 : ss->ttHit ? tte->move() : MOVE_NONE;
619 ttCapture = ttMove && pos.capture_stage(ttMove);
621 // At this point, if excluded, skip straight to step 6, static eval. However,
622 // to save indentation, we list the condition in all code between here and there.
624 ss->ttPv = PvNode || (ss->ttHit && tte->is_pv());
626 // At non-PV nodes we check for an early TT cutoff
629 && tte->depth() > depth
630 && ttValue != VALUE_NONE // Possible in case of TT access race or if !ttHit
631 && (tte->bound() & (ttValue >= beta ? BOUND_LOWER : BOUND_UPPER)))
633 // If ttMove is quiet, update move sorting heuristics on TT hit (~2 Elo)
638 // Bonus for a quiet ttMove that fails high (~2 Elo)
640 update_quiet_stats(pos, ss, ttMove, stat_bonus(depth));
642 // Extra penalty for early quiet moves of the previous ply (~0 Elo on STC, ~2 Elo on LTC)
643 if (prevSq != SQ_NONE && (ss-1)->moveCount <= 2 && !priorCapture)
644 update_continuation_histories(ss-1, pos.piece_on(prevSq), prevSq, -stat_bonus(depth + 1));
646 // Penalty for a quiet ttMove that fails low (~1 Elo)
649 int penalty = -stat_bonus(depth);
650 thisThread->mainHistory[us][from_to(ttMove)] << penalty;
651 update_continuation_histories(ss, pos.moved_piece(ttMove), to_sq(ttMove), penalty);
655 // Partial workaround for the graph history interaction problem
656 // For high rule50 counts don't produce transposition table cutoffs.
657 if (pos.rule50_count() < 90)
661 // Step 5. Tablebases probe
662 if (!rootNode && !excludedMove && TB::Cardinality)
664 int piecesCount = pos.count<ALL_PIECES>();
666 if ( piecesCount <= TB::Cardinality
667 && (piecesCount < TB::Cardinality || depth >= TB::ProbeDepth)
668 && pos.rule50_count() == 0
669 && !pos.can_castle(ANY_CASTLING))
672 TB::WDLScore wdl = Tablebases::probe_wdl(pos, &err);
674 // Force check of time on the next occasion
675 if (thisThread == Threads.main())
676 static_cast<MainThread*>(thisThread)->callsCnt = 0;
678 if (err != TB::ProbeState::FAIL)
680 thisThread->tbHits.fetch_add(1, std::memory_order_relaxed);
682 int drawScore = TB::UseRule50 ? 1 : 0;
684 // use the range VALUE_MATE_IN_MAX_PLY to VALUE_TB_WIN_IN_MAX_PLY to score
685 value = wdl < -drawScore ? VALUE_MATED_IN_MAX_PLY + ss->ply + 1
686 : wdl > drawScore ? VALUE_MATE_IN_MAX_PLY - ss->ply - 1
687 : VALUE_DRAW + 2 * wdl * drawScore;
689 Bound b = wdl < -drawScore ? BOUND_UPPER
690 : wdl > drawScore ? BOUND_LOWER : BOUND_EXACT;
692 if ( b == BOUND_EXACT
693 || (b == BOUND_LOWER ? value >= beta : value <= alpha))
695 tte->save(posKey, value_to_tt(value, ss->ply), ss->ttPv, b,
696 std::min(MAX_PLY - 1, depth + 6),
697 MOVE_NONE, VALUE_NONE);
704 if (b == BOUND_LOWER)
705 bestValue = value, alpha = std::max(alpha, bestValue);
713 CapturePieceToHistory& captureHistory = thisThread->captureHistory;
715 // Step 6. Static evaluation of the position
718 // Skip early pruning when in check
719 ss->staticEval = eval = VALUE_NONE;
723 else if (excludedMove)
725 // Providing the hint that this node's accumulator will be used often brings significant Elo gain (~13 Elo)
726 Eval::NNUE::hint_common_parent_position(pos);
727 eval = ss->staticEval;
731 // Never assume anything about values stored in TT
732 ss->staticEval = eval = tte->eval();
733 if (eval == VALUE_NONE)
734 ss->staticEval = eval = evaluate(pos);
736 Eval::NNUE::hint_common_parent_position(pos);
738 // ttValue can be used as a better position evaluation (~7 Elo)
739 if ( ttValue != VALUE_NONE
740 && (tte->bound() & (ttValue > eval ? BOUND_LOWER : BOUND_UPPER)))
745 ss->staticEval = eval = evaluate(pos);
746 // Save static evaluation into the transposition table
747 tte->save(posKey, VALUE_NONE, ss->ttPv, BOUND_NONE, DEPTH_NONE, MOVE_NONE, eval);
750 // Use static evaluation difference to improve quiet move ordering (~4 Elo)
751 if (is_ok((ss-1)->currentMove) && !(ss-1)->inCheck && !priorCapture)
753 int bonus = std::clamp(-18 * int((ss-1)->staticEval + ss->staticEval), -1812, 1812);
754 thisThread->mainHistory[~us][from_to((ss-1)->currentMove)] << bonus;
757 // Set up the improving flag, which is true if current static evaluation is
758 // bigger than the previous static evaluation at our turn (if we were in
759 // check at our previous move we look at static evaluation at move prior to it
760 // and if we were in check at move prior to it flag is set to true) and is
761 // false otherwise. The improving flag is used in various pruning heuristics.
762 improving = (ss-2)->staticEval != VALUE_NONE ? ss->staticEval > (ss-2)->staticEval
763 : (ss-4)->staticEval != VALUE_NONE ? ss->staticEval > (ss-4)->staticEval
766 // Step 7. Razoring (~1 Elo)
767 // If eval is really low check with qsearch if it can exceed alpha, if it can't,
768 // return a fail low.
769 // Adjust razor margin according to cutoffCnt. (~1 Elo)
770 if (eval < alpha - 492 - (257 - 200 * ((ss+1)->cutoffCnt > 3)) * depth * depth)
772 value = qsearch<NonPV>(pos, ss, alpha - 1, alpha);
777 // Step 8. Futility pruning: child node (~40 Elo)
778 // The depth condition is important for mate finding.
781 && eval - futility_margin(depth, cutNode && !ss->ttHit, improving) - (ss-1)->statScore / 321 >= beta
783 && eval < 29462 // smaller than TB wins
786 && thisThread->mainHistory[us][from_to(ttMove)] < 989))
789 // Step 9. Null move search with verification search (~35 Elo)
791 && (ss-1)->currentMove != MOVE_NULL
792 && (ss-1)->statScore < 17257
794 && eval >= ss->staticEval
795 && ss->staticEval >= beta - 24 * depth + 281
797 && pos.non_pawn_material(us)
798 && ss->ply >= thisThread->nmpMinPly
799 && beta > VALUE_TB_LOSS_IN_MAX_PLY)
801 assert(eval - beta >= 0);
803 // Null move dynamic reduction based on depth and eval
804 Depth R = std::min(int(eval - beta) / 152, 6) + depth / 3 + 4;
806 ss->currentMove = MOVE_NULL;
807 ss->continuationHistory = &thisThread->continuationHistory[0][0][NO_PIECE][0];
809 pos.do_null_move(st);
811 Value nullValue = -search<NonPV>(pos, ss+1, -beta, -beta+1, depth-R, !cutNode);
813 pos.undo_null_move();
815 if (nullValue >= beta)
817 // Do not return unproven mate or TB scores
818 nullValue = std::min(nullValue, VALUE_TB_WIN_IN_MAX_PLY-1);
820 if (thisThread->nmpMinPly || depth < 14)
823 assert(!thisThread->nmpMinPly); // Recursive verification is not allowed
825 // Do verification search at high depths, with null move pruning disabled
826 // until ply exceeds nmpMinPly.
827 thisThread->nmpMinPly = ss->ply + 3 * (depth-R) / 4;
829 Value v = search<NonPV>(pos, ss, beta-1, beta, depth-R, false);
831 thisThread->nmpMinPly = 0;
838 // Step 10. If the position doesn't have a ttMove, decrease depth by 2
839 // (or by 4 if the TT entry for the current position was hit and the stored depth is greater than or equal to the current depth).
840 // Use qsearch if depth is equal or below zero (~9 Elo)
843 depth -= 2 + 2 * (ss->ttHit && tte->depth() >= depth);
846 return qsearch<PV>(pos, ss, alpha, beta);
853 probCutBeta = beta + 168 - 70 * improving;
855 // Step 11. ProbCut (~10 Elo)
856 // If we have a good enough capture (or queen promotion) and a reduced search returns a value
857 // much above beta, we can (almost) safely prune the previous move.
860 && abs(beta) < VALUE_TB_WIN_IN_MAX_PLY
861 // If value from transposition table is lower than probCutBeta, don't attempt probCut
862 // there and in further interactions with transposition table cutoff depth is set to depth - 3
863 // because probCut search has depth set to depth - 4 but we also do a move before it
864 // So effective depth is equal to depth - 3
865 && !( tte->depth() >= depth - 3
866 && ttValue != VALUE_NONE
867 && ttValue < probCutBeta))
869 assert(probCutBeta < VALUE_INFINITE);
871 MovePicker mp(pos, ttMove, probCutBeta - ss->staticEval, &captureHistory);
873 while ((move = mp.next_move()) != MOVE_NONE)
874 if (move != excludedMove && pos.legal(move))
876 assert(pos.capture_stage(move));
878 ss->currentMove = move;
879 ss->continuationHistory = &thisThread->continuationHistory[ss->inCheck]
881 [pos.moved_piece(move)]
884 pos.do_move(move, st);
886 // Perform a preliminary qsearch to verify that the move holds
887 value = -qsearch<NonPV>(pos, ss+1, -probCutBeta, -probCutBeta+1);
889 // If the qsearch held, perform the regular search
890 if (value >= probCutBeta)
891 value = -search<NonPV>(pos, ss+1, -probCutBeta, -probCutBeta+1, depth - 4, !cutNode);
895 if (value >= probCutBeta)
897 // Save ProbCut data into transposition table
898 tte->save(posKey, value_to_tt(value, ss->ply), ss->ttPv, BOUND_LOWER, depth - 3, move, ss->staticEval);
903 Eval::NNUE::hint_common_parent_position(pos);
906 moves_loop: // When in check, search starts here
908 // Step 12. A small Probcut idea, when we are in check (~4 Elo)
909 probCutBeta = beta + 416;
913 && (tte->bound() & BOUND_LOWER)
914 && tte->depth() >= depth - 4
915 && ttValue >= probCutBeta
916 && abs(ttValue) < VALUE_TB_WIN_IN_MAX_PLY
917 && abs(beta) < VALUE_TB_WIN_IN_MAX_PLY)
920 const PieceToHistory* contHist[] = { (ss-1)->continuationHistory, (ss-2)->continuationHistory,
921 (ss-3)->continuationHistory, (ss-4)->continuationHistory,
922 nullptr , (ss-6)->continuationHistory };
924 Move countermove = prevSq != SQ_NONE ? thisThread->counterMoves[pos.piece_on(prevSq)][prevSq] : MOVE_NONE;
926 MovePicker mp(pos, ttMove, depth, &thisThread->mainHistory,
933 moveCountPruning = singularQuietLMR = false;
935 // Indicate PvNodes that will probably fail low if the node was searched
936 // at a depth equal to or greater than the current depth, and the result
937 // of this search was a fail low.
938 bool likelyFailLow = PvNode
940 && (tte->bound() & BOUND_UPPER)
941 && tte->depth() >= depth;
943 // Step 13. Loop through all pseudo-legal moves until no moves remain
944 // or a beta cutoff occurs.
945 while ((move = mp.next_move(moveCountPruning)) != MOVE_NONE)
949 if (move == excludedMove)
952 // Check for legality
953 if (!pos.legal(move))
956 // At root obey the "searchmoves" option and skip moves not listed in Root
957 // Move List. In MultiPV mode we also skip PV moves that have been already
958 // searched and those of lower "TB rank" if we are in a TB root position.
959 if (rootNode && !std::count(thisThread->rootMoves.begin() + thisThread->pvIdx,
960 thisThread->rootMoves.begin() + thisThread->pvLast, move))
963 ss->moveCount = ++moveCount;
965 if (rootNode && thisThread == Threads.main() && Time.elapsed() > 3000)
966 sync_cout << "info depth " << depth
967 << " currmove " << UCI::move(move, pos.is_chess960())
968 << " currmovenumber " << moveCount + thisThread->pvIdx << sync_endl;
970 (ss+1)->pv = nullptr;
973 capture = pos.capture_stage(move);
974 movedPiece = pos.moved_piece(move);
975 givesCheck = pos.gives_check(move);
977 // Calculate new depth for this move
978 newDepth = depth - 1;
980 Value delta = beta - alpha;
982 Depth r = reduction(improving, depth, moveCount, delta, thisThread->rootDelta);
984 // Step 14. Pruning at shallow depth (~120 Elo). Depth conditions are important for mate finding.
986 && pos.non_pawn_material(us)
987 && bestValue > VALUE_TB_LOSS_IN_MAX_PLY)
989 // Skip quiet moves if movecount exceeds our FutilityMoveCount threshold (~8 Elo)
990 if (!moveCountPruning)
991 moveCountPruning = moveCount >= futility_move_count(improving, depth);
993 // Reduced depth of the next LMR search
994 int lmrDepth = newDepth - r;
999 // Futility pruning for captures (~2 Elo)
1003 && ss->staticEval + 188 + 206 * lmrDepth + PieceValue[pos.piece_on(to_sq(move))]
1004 + captureHistory[movedPiece][to_sq(move)][type_of(pos.piece_on(to_sq(move)))] / 7 < alpha)
1007 // SEE based pruning for captures and checks (~11 Elo)
1008 if (!pos.see_ge(move, Value(-185) * depth))
1013 int history = (*contHist[0])[movedPiece][to_sq(move)]
1014 + (*contHist[1])[movedPiece][to_sq(move)]
1015 + (*contHist[3])[movedPiece][to_sq(move)];
1017 // Continuation history based pruning (~2 Elo)
1019 && history < -3232 * depth)
1022 history += 2 * thisThread->mainHistory[us][from_to(move)];
1024 lmrDepth += history / 5793;
1025 lmrDepth = std::max(lmrDepth, -2);
1027 // Futility pruning: parent node (~13 Elo)
1030 && ss->staticEval + 115 + 122 * lmrDepth <= alpha)
1033 lmrDepth = std::max(lmrDepth, 0);
1035 // Prune moves with negative SEE (~4 Elo)
1036 if (!pos.see_ge(move, Value(-27 * lmrDepth * lmrDepth)))
1041 // Step 15. Extensions (~100 Elo)
1042 // We take care to not overdo to avoid search getting stuck.
1043 if (ss->ply < thisThread->rootDepth * 2)
1045 // Singular extension search (~94 Elo). If all moves but one fail low on a
1046 // search of (alpha-s, beta-s), and just one fails high on (alpha, beta),
1047 // then that move is singular and should be extended. To verify this we do
1048 // a reduced search on all the other moves but the ttMove and if the result
1049 // is lower than ttValue minus a margin, then we will extend the ttMove. Note
1050 // that depth margin and singularBeta margin are known for having non-linear
1051 // scaling. Their values are optimized to time controls of 180+1.8 and longer
1052 // so changing them requires tests at this type of time controls.
1054 && depth >= 4 - (thisThread->completedDepth > 24) + 2 * (PvNode && tte->is_pv())
1056 && !excludedMove // Avoid recursive singular search
1057 /* && ttValue != VALUE_NONE Already implicit in the next condition */
1058 && abs(ttValue) < VALUE_TB_WIN_IN_MAX_PLY
1059 && (tte->bound() & BOUND_LOWER)
1060 && tte->depth() >= depth - 3)
1062 Value singularBeta = ttValue - (64 + 57 * (ss->ttPv && !PvNode)) * depth / 64;
1063 Depth singularDepth = (depth - 1) / 2;
1065 ss->excludedMove = move;
1066 value = search<NonPV>(pos, ss, singularBeta - 1, singularBeta, singularDepth, cutNode);
1067 ss->excludedMove = MOVE_NONE;
1069 if (value < singularBeta)
1072 singularQuietLMR = !ttCapture;
1074 // Avoid search explosion by limiting the number of double extensions
1076 && value < singularBeta - 18
1077 && ss->doubleExtensions <= 11)
1080 depth += depth < 15;
1084 // Multi-cut pruning
1085 // Our ttMove is assumed to fail high, and now we failed high also on a
1086 // reduced search without the ttMove. So we assume this expected cut-node
1087 // is not singular, that multiple moves fail high, and we can prune the
1088 // whole subtree by returning a softbound.
1089 else if (singularBeta >= beta)
1090 return singularBeta;
1092 // If the eval of ttMove is greater than beta, we reduce it (negative extension) (~7 Elo)
1093 else if (ttValue >= beta)
1094 extension = -2 - !PvNode;
1096 // If we are on a cutNode, reduce it based on depth (negative extension) (~1 Elo)
1098 extension = depth < 19 ? -2 : -1;
1100 // If the eval of ttMove is less than value, we reduce it (negative extension) (~1 Elo)
1101 else if (ttValue <= value)
1105 // Check extensions (~1 Elo)
1106 else if ( givesCheck
1110 // Quiet ttMove extensions (~1 Elo)
1113 && move == ss->killers[0]
1114 && (*contHist[0])[movedPiece][to_sq(move)] >= 4194)
1118 // Add extension to new depth
1119 newDepth += extension;
1120 ss->doubleExtensions = (ss-1)->doubleExtensions + (extension == 2);
1122 // Speculative prefetch as early as possible
1123 prefetch(TT.first_entry(pos.key_after(move)));
1125 // Update the current move (this must be done after singular extension search)
1126 ss->currentMove = move;
1127 ss->continuationHistory = &thisThread->continuationHistory[ss->inCheck]
1132 // Step 16. Make the move
1133 pos.do_move(move, st, givesCheck);
1135 // Decrease reduction if position is or has been on the PV and not likely to fail low. (~3 Elo)
1136 // Decrease further on cutNodes. (~1 Elo)
1139 r -= cutNode && tte->depth() >= depth ? 3 : 2;
1141 // Decrease reduction if opponent's move count is high (~1 Elo)
1142 if ((ss-1)->moveCount > 7)
1145 // Increase reduction for cut nodes (~3 Elo)
1149 // Increase reduction if ttMove is a capture (~3 Elo)
1153 // Decrease reduction for PvNodes (~2 Elo)
1157 // Decrease reduction if ttMove has been singularly extended (~1 Elo)
1158 if (singularQuietLMR)
1161 // Increase reduction on repetition (~1 Elo)
1162 if ( move == (ss-4)->currentMove
1163 && pos.has_repeated())
1166 // Increase reduction if next ply has a lot of fail high (~5 Elo)
1167 if ((ss+1)->cutoffCnt > 3)
1170 // Decrease reduction for first generated move (ttMove)
1171 else if (move == ttMove)
1174 ss->statScore = 2 * thisThread->mainHistory[us][from_to(move)]
1175 + (*contHist[0])[movedPiece][to_sq(move)]
1176 + (*contHist[1])[movedPiece][to_sq(move)]
1177 + (*contHist[3])[movedPiece][to_sq(move)]
1180 // Decrease/increase reduction for moves with a good/bad history (~25 Elo)
1181 r -= ss->statScore / (10216 + 3855 * (depth > 5 && depth < 23));
1183 // Step 17. Late moves reduction / extension (LMR, ~117 Elo)
1184 // We use various heuristics for the sons of a node after the first son has
1185 // been searched. In general, we would like to reduce them, but there are many
1186 // cases where we extend a son if it has good chances to be "interesting".
1188 && moveCount > 1 + (PvNode && ss->ply <= 1)
1191 || (cutNode && (ss-1)->moveCount > 1)))
1193 // In general we want to cap the LMR depth search at newDepth, but when
1194 // reduction is negative, we allow this move a limited search extension
1195 // beyond the first move depth. This may lead to hidden double extensions.
1196 Depth d = std::clamp(newDepth - r, 1, newDepth + 1);
1198 value = -search<NonPV>(pos, ss+1, -(alpha+1), -alpha, d, true);
1200 // Do a full-depth search when reduced LMR search fails high
1201 if (value > alpha && d < newDepth)
1203 // Adjust full-depth search based on LMR results - if the result
1204 // was good enough search deeper, if it was bad enough search shallower
1205 const bool doDeeperSearch = value > (bestValue + 51 + 10 * (newDepth - d));
1206 const bool doEvenDeeperSearch = value > alpha + 700 && ss->doubleExtensions <= 6;
1207 const bool doShallowerSearch = value < bestValue + newDepth;
1209 ss->doubleExtensions = ss->doubleExtensions + doEvenDeeperSearch;
1211 newDepth += doDeeperSearch - doShallowerSearch + doEvenDeeperSearch;
1214 value = -search<NonPV>(pos, ss+1, -(alpha+1), -alpha, newDepth, !cutNode);
1216 int bonus = value <= alpha ? -stat_bonus(newDepth)
1217 : value >= beta ? stat_bonus(newDepth)
1220 update_continuation_histories(ss, movedPiece, to_sq(move), bonus);
1224 // Step 18. Full-depth search when LMR is skipped. If expected reduction is high, reduce its depth by 1.
1225 else if (!PvNode || moveCount > 1)
1227 // Increase reduction for cut nodes and not ttMove (~1 Elo)
1228 if (!ttMove && cutNode)
1231 value = -search<NonPV>(pos, ss+1, -(alpha+1), -alpha, newDepth - (r > 3), !cutNode);
1234 // For PV nodes only, do a full PV search on the first move or after a fail high,
1235 // otherwise let the parent node fail low with value <= alpha and try another move.
1236 if (PvNode && (moveCount == 1 || value > alpha))
1239 (ss+1)->pv[0] = MOVE_NONE;
1241 value = -search<PV>(pos, ss+1, -beta, -alpha, newDepth, false);
1244 // Step 19. Undo move
1245 pos.undo_move(move);
1247 assert(value > -VALUE_INFINITE && value < VALUE_INFINITE);
1249 // Step 20. Check for a new best move
1250 // Finished searching the move. If a stop occurred, the return value of
1251 // the search cannot be trusted, and we return immediately without
1252 // updating best move, PV and TT.
1253 if (Threads.stop.load(std::memory_order_relaxed))
1258 RootMove& rm = *std::find(thisThread->rootMoves.begin(),
1259 thisThread->rootMoves.end(), move);
1261 rm.averageScore = rm.averageScore != -VALUE_INFINITE ? (2 * value + rm.averageScore) / 3 : value;
1263 // PV move or new best move?
1264 if (moveCount == 1 || value > alpha)
1266 rm.score = rm.uciScore = value;
1267 rm.selDepth = thisThread->selDepth;
1268 rm.scoreLowerbound = rm.scoreUpperbound = false;
1272 rm.scoreLowerbound = true;
1275 else if (value <= alpha)
1277 rm.scoreUpperbound = true;
1278 rm.uciScore = alpha;
1285 for (Move* m = (ss+1)->pv; *m != MOVE_NONE; ++m)
1286 rm.pv.push_back(*m);
1288 // We record how often the best move has been changed in each iteration.
1289 // This information is used for time management. In MultiPV mode,
1290 // we must take care to only do this for the first PV line.
1292 && !thisThread->pvIdx)
1293 ++thisThread->bestMoveChanges;
1296 // All other moves but the PV, are set to the lowest value: this
1297 // is not a problem when sorting because the sort is stable and the
1298 // move position in the list is preserved - just the PV is pushed up.
1299 rm.score = -VALUE_INFINITE;
1302 if (value > bestValue)
1310 if (PvNode && !rootNode) // Update pv even in fail-high case
1311 update_pv(ss->pv, move, (ss+1)->pv);
1315 ss->cutoffCnt += 1 + !ttMove;
1316 assert(value >= beta); // Fail high
1321 // Reduce other moves if we have found at least one score improvement (~2 Elo)
1329 alpha = value; // Update alpha! Always alpha < beta
1335 // If the move is worse than some previously searched move, remember it, to update its stats later
1336 if (move != bestMove && moveCount <= 32)
1339 capturesSearched[captureCount++] = move;
1342 quietsSearched[quietCount++] = move;
1346 // The following condition would detect a stop only after move loop has been
1347 // completed. But in this case, bestValue is valid because we have fully
1348 // searched our subtree, and we can anyhow save the result in TT.
1354 // Step 21. Check for mate and stalemate
1355 // All legal moves have been searched and if there are no legal moves, it
1356 // must be a mate or a stalemate. If we are in a singular extension search then
1357 // return a fail low score.
1359 assert(moveCount || !ss->inCheck || excludedMove || !MoveList<LEGAL>(pos).size());
1362 bestValue = excludedMove ? alpha :
1363 ss->inCheck ? mated_in(ss->ply)
1366 // If there is a move that produces search value greater than alpha we update the stats of searched moves
1368 update_all_stats(pos, ss, bestMove, bestValue, beta, prevSq,
1369 quietsSearched, quietCount, capturesSearched, captureCount, depth);
1371 // Bonus for prior countermove that caused the fail low
1372 else if (!priorCapture && prevSq != SQ_NONE)
1374 int bonus = (depth > 6) + (PvNode || cutNode) + (bestValue < alpha - 653) + ((ss-1)->moveCount > 11);
1375 update_continuation_histories(ss-1, pos.piece_on(prevSq), prevSq, stat_bonus(depth) * bonus);
1376 thisThread->mainHistory[~us][from_to((ss-1)->currentMove)] << stat_bonus(depth) * bonus / 2;
1380 bestValue = std::min(bestValue, maxValue);
1382 // If no good move is found and the previous position was ttPv, then the previous
1383 // opponent move is probably good and the new position is added to the search tree. (~7 Elo)
1384 if (bestValue <= alpha)
1385 ss->ttPv = ss->ttPv || ((ss-1)->ttPv && depth > 3);
1387 // Write gathered information in transposition table
1388 if (!excludedMove && !(rootNode && thisThread->pvIdx))
1389 tte->save(posKey, value_to_tt(bestValue, ss->ply), ss->ttPv,
1390 bestValue >= beta ? BOUND_LOWER :
1391 PvNode && bestMove ? BOUND_EXACT : BOUND_UPPER,
1392 depth, bestMove, ss->staticEval);
1394 assert(bestValue > -VALUE_INFINITE && bestValue < VALUE_INFINITE);
1400 // qsearch() is the quiescence search function, which is called by the main search
1401 // function with zero depth, or recursively with further decreasing depth per call.
1403 template <NodeType nodeType>
1404 Value qsearch(Position& pos, Stack* ss, Value alpha, Value beta, Depth depth) {
1406 static_assert(nodeType != Root);
1407 constexpr bool PvNode = nodeType == PV;
1409 assert(alpha >= -VALUE_INFINITE && alpha < beta && beta <= VALUE_INFINITE);
1410 assert(PvNode || (alpha == beta - 1));
1413 // Check if we have an upcoming move that draws by repetition, or
1414 // if the opponent had an alternative move earlier to this position.
1415 if ( alpha < VALUE_DRAW
1416 && pos.has_game_cycle(ss->ply))
1418 alpha = value_draw(pos.this_thread());
1425 ASSERT_ALIGNED(&st, Eval::NNUE::CacheLineSize);
1429 Move ttMove, move, bestMove;
1431 Value bestValue, value, ttValue, futilityValue, futilityBase;
1432 bool pvHit, givesCheck, capture;
1434 Color us = pos.side_to_move();
1436 // Step 1. Initialize node
1440 ss->pv[0] = MOVE_NONE;
1443 Thread* thisThread = pos.this_thread();
1444 bestMove = MOVE_NONE;
1445 ss->inCheck = pos.checkers();
1448 // Step 2. Check for an immediate draw or maximum ply reached
1449 if ( pos.is_draw(ss->ply)
1450 || ss->ply >= MAX_PLY)
1451 return (ss->ply >= MAX_PLY && !ss->inCheck) ? evaluate(pos) : VALUE_DRAW;
1453 assert(0 <= ss->ply && ss->ply < MAX_PLY);
1455 // Decide whether or not to include checks: this fixes also the type of
1456 // TT entry depth that we are going to use. Note that in qsearch we use
1457 // only two types of depth in TT: DEPTH_QS_CHECKS or DEPTH_QS_NO_CHECKS.
1458 ttDepth = ss->inCheck || depth >= DEPTH_QS_CHECKS ? DEPTH_QS_CHECKS
1459 : DEPTH_QS_NO_CHECKS;
1461 // Step 3. Transposition table lookup
1463 tte = TT.probe(posKey, ss->ttHit);
1464 ttValue = ss->ttHit ? value_from_tt(tte->value(), ss->ply, pos.rule50_count()) : VALUE_NONE;
1465 ttMove = ss->ttHit ? tte->move() : MOVE_NONE;
1466 pvHit = ss->ttHit && tte->is_pv();
1468 // At non-PV nodes we check for an early TT cutoff
1470 && tte->depth() >= ttDepth
1471 && ttValue != VALUE_NONE // Only in case of TT access race or if !ttHit
1472 && (tte->bound() & (ttValue >= beta ? BOUND_LOWER : BOUND_UPPER)))
1475 // Step 4. Static evaluation of the position
1477 bestValue = futilityBase = -VALUE_INFINITE;
1482 // Never assume anything about values stored in TT
1483 if ((ss->staticEval = bestValue = tte->eval()) == VALUE_NONE)
1484 ss->staticEval = bestValue = evaluate(pos);
1486 // ttValue can be used as a better position evaluation (~13 Elo)
1487 if ( ttValue != VALUE_NONE
1488 && (tte->bound() & (ttValue > bestValue ? BOUND_LOWER : BOUND_UPPER)))
1489 bestValue = ttValue;
1492 // In case of null move search use previous static eval with a different sign
1493 ss->staticEval = bestValue = (ss-1)->currentMove != MOVE_NULL ? evaluate(pos)
1494 : -(ss-1)->staticEval;
1496 // Stand pat. Return immediately if static value is at least beta
1497 if (bestValue >= beta)
1499 // Save gathered info in transposition table
1501 tte->save(posKey, value_to_tt(bestValue, ss->ply), false, BOUND_LOWER,
1502 DEPTH_NONE, MOVE_NONE, ss->staticEval);
1507 if (bestValue > alpha)
1510 futilityBase = std::min(ss->staticEval, bestValue) + 200;
1513 const PieceToHistory* contHist[] = { (ss-1)->continuationHistory, (ss-2)->continuationHistory,
1514 (ss-3)->continuationHistory, (ss-4)->continuationHistory,
1515 nullptr , (ss-6)->continuationHistory };
1517 // Initialize a MovePicker object for the current position, and prepare
1518 // to search the moves. Because the depth is <= 0 here, only captures,
1519 // queen promotions, and other checks (only if depth >= DEPTH_QS_CHECKS)
1520 // will be generated.
1521 Square prevSq = is_ok((ss-1)->currentMove) ? to_sq((ss-1)->currentMove) : SQ_NONE;
1522 MovePicker mp(pos, ttMove, depth, &thisThread->mainHistory,
1523 &thisThread->captureHistory,
1527 int quietCheckEvasions = 0;
1529 // Step 5. Loop through all pseudo-legal moves until no moves remain
1530 // or a beta cutoff occurs.
1531 while ((move = mp.next_move()) != MOVE_NONE)
1533 assert(is_ok(move));
1535 // Check for legality
1536 if (!pos.legal(move))
1539 givesCheck = pos.gives_check(move);
1540 capture = pos.capture_stage(move);
1545 if (bestValue > VALUE_TB_LOSS_IN_MAX_PLY && pos.non_pawn_material(us))
1547 // Futility pruning and moveCount pruning (~10 Elo)
1549 && to_sq(move) != prevSq
1550 && futilityBase > VALUE_TB_LOSS_IN_MAX_PLY
1551 && type_of(move) != PROMOTION)
1556 futilityValue = futilityBase + PieceValue[pos.piece_on(to_sq(move))];
1558 // If static eval + value of piece we are going to capture is much lower
1559 // than alpha we can prune this move
1560 if (futilityValue <= alpha)
1562 bestValue = std::max(bestValue, futilityValue);
1566 // If static eval is much lower than alpha and move is not winning material
1567 // we can prune this move
1568 if (futilityBase <= alpha && !pos.see_ge(move, VALUE_ZERO + 1))
1570 bestValue = std::max(bestValue, futilityBase);
1574 // If static exchange evaluation is much worse than what is needed to not
1575 // fall below alpha we can prune this move
1576 if (futilityBase > alpha && !pos.see_ge(move, (alpha - futilityBase) * 4))
1583 // We prune after the second quiet check evasion move, where being 'in check' is
1584 // implicitly checked through the counter, and being a 'quiet move' apart from
1585 // being a tt move is assumed after an increment because captures are pushed ahead.
1586 if (quietCheckEvasions > 1)
1589 // Continuation history based pruning (~3 Elo)
1591 && (*contHist[0])[pos.moved_piece(move)][to_sq(move)] < 0
1592 && (*contHist[1])[pos.moved_piece(move)][to_sq(move)] < 0)
1595 // Do not search moves with bad enough SEE values (~5 Elo)
1596 if (!pos.see_ge(move, Value(-90)))
1600 // Speculative prefetch as early as possible
1601 prefetch(TT.first_entry(pos.key_after(move)));
1603 // Update the current move
1604 ss->currentMove = move;
1605 ss->continuationHistory = &thisThread->continuationHistory[ss->inCheck]
1607 [pos.moved_piece(move)]
1610 quietCheckEvasions += !capture && ss->inCheck;
1612 // Step 7. Make and search the move
1613 pos.do_move(move, st, givesCheck);
1614 value = -qsearch<nodeType>(pos, ss+1, -beta, -alpha, depth - 1);
1615 pos.undo_move(move);
1617 assert(value > -VALUE_INFINITE && value < VALUE_INFINITE);
1619 // Step 8. Check for a new best move
1620 if (value > bestValue)
1628 if (PvNode) // Update pv even in fail-high case
1629 update_pv(ss->pv, move, (ss+1)->pv);
1631 if (value < beta) // Update alpha here!
1639 // Step 9. Check for mate
1640 // All legal moves have been searched. A special case: if we're in check
1641 // and no legal moves were found, it is checkmate.
1642 if (ss->inCheck && bestValue == -VALUE_INFINITE)
1644 assert(!MoveList<LEGAL>(pos).size());
1646 return mated_in(ss->ply); // Plies to mate from the root
1649 // Save gathered info in transposition table
1650 tte->save(posKey, value_to_tt(bestValue, ss->ply), pvHit,
1651 bestValue >= beta ? BOUND_LOWER : BOUND_UPPER,
1652 ttDepth, bestMove, ss->staticEval);
1654 assert(bestValue > -VALUE_INFINITE && bestValue < VALUE_INFINITE);
1660 // value_to_tt() adjusts a mate or TB score from "plies to mate from the root" to
1661 // "plies to mate from the current position". Standard scores are unchanged.
1662 // The function is called before storing a value in the transposition table.
1664 Value value_to_tt(Value v, int ply) {
1666 assert(v != VALUE_NONE);
1668 return v >= VALUE_TB_WIN_IN_MAX_PLY ? v + ply
1669 : v <= VALUE_TB_LOSS_IN_MAX_PLY ? v - ply : v;
1673 // value_from_tt() is the inverse of value_to_tt(): it adjusts a mate or TB score
1674 // from the transposition table (which refers to the plies to mate/be mated from
1675 // current position) to "plies to mate/be mated (TB win/loss) from the root". However,
1676 // for mate scores, to avoid potentially false mate scores related to the 50 moves rule
1677 // and the graph history interaction, we return an optimal TB score instead.
1679 Value value_from_tt(Value v, int ply, int r50c) {
1681 if (v == VALUE_NONE)
1684 if (v >= VALUE_TB_WIN_IN_MAX_PLY) // TB win or better
1686 if (v >= VALUE_MATE_IN_MAX_PLY && VALUE_MATE - v > 99 - r50c)
1687 return VALUE_MATE_IN_MAX_PLY - 1; // do not return a potentially false mate score
1692 if (v <= VALUE_TB_LOSS_IN_MAX_PLY) // TB loss or worse
1694 if (v <= VALUE_MATED_IN_MAX_PLY && VALUE_MATE + v > 99 - r50c)
1695 return VALUE_MATED_IN_MAX_PLY + 1; // do not return a potentially false mate score
1704 // update_pv() adds current move and appends child pv[]
1706 void update_pv(Move* pv, Move move, const Move* childPv) {
1708 for (*pv++ = move; childPv && *childPv != MOVE_NONE; )
1714 // update_all_stats() updates stats at the end of search() when a bestMove is found
1716 void update_all_stats(const Position& pos, Stack* ss, Move bestMove, Value bestValue, Value beta, Square prevSq,
1717 Move* quietsSearched, int quietCount, Move* capturesSearched, int captureCount, Depth depth) {
1719 Color us = pos.side_to_move();
1720 Thread* thisThread = pos.this_thread();
1721 CapturePieceToHistory& captureHistory = thisThread->captureHistory;
1722 Piece moved_piece = pos.moved_piece(bestMove);
1725 int quietMoveBonus = stat_bonus(depth + 1);
1727 if (!pos.capture_stage(bestMove))
1729 int bestMoveBonus = bestValue > beta + 168 ? quietMoveBonus // larger bonus
1730 : stat_bonus(depth); // smaller bonus
1732 // Increase stats for the best move in case it was a quiet move
1733 update_quiet_stats(pos, ss, bestMove, bestMoveBonus);
1735 // Decrease stats for all non-best quiet moves
1736 for (int i = 0; i < quietCount; ++i)
1738 thisThread->mainHistory[us][from_to(quietsSearched[i])] << -bestMoveBonus;
1739 update_continuation_histories(ss, pos.moved_piece(quietsSearched[i]), to_sq(quietsSearched[i]), -bestMoveBonus);
1744 // Increase stats for the best move in case it was a capture move
1745 captured = type_of(pos.piece_on(to_sq(bestMove)));
1746 captureHistory[moved_piece][to_sq(bestMove)][captured] << quietMoveBonus;
1749 // Extra penalty for a quiet early move that was not a TT move or
1750 // main killer move in previous ply when it gets refuted.
1751 if ( prevSq != SQ_NONE
1752 && ((ss-1)->moveCount == 1 + (ss-1)->ttHit || ((ss-1)->currentMove == (ss-1)->killers[0]))
1753 && !pos.captured_piece())
1754 update_continuation_histories(ss-1, pos.piece_on(prevSq), prevSq, -quietMoveBonus);
1756 // Decrease stats for all non-best capture moves
1757 for (int i = 0; i < captureCount; ++i)
1759 moved_piece = pos.moved_piece(capturesSearched[i]);
1760 captured = type_of(pos.piece_on(to_sq(capturesSearched[i])));
1761 captureHistory[moved_piece][to_sq(capturesSearched[i])][captured] << -quietMoveBonus;
1766 // update_continuation_histories() updates histories of the move pairs formed
1767 // by moves at ply -1, -2, -4, and -6 with current move.
1769 void update_continuation_histories(Stack* ss, Piece pc, Square to, int bonus) {
1771 for (int i : {1, 2, 3, 4, 6})
1773 // Only update the first 2 continuation histories if we are in check
1774 if (ss->inCheck && i > 2)
1776 if (is_ok((ss-i)->currentMove))
1777 (*(ss-i)->continuationHistory)[pc][to] << bonus / (1 + 3 * (i == 3));
1782 // update_quiet_stats() updates move sorting heuristics
1784 void update_quiet_stats(const Position& pos, Stack* ss, Move move, int bonus) {
1787 if (ss->killers[0] != move)
1789 ss->killers[1] = ss->killers[0];
1790 ss->killers[0] = move;
1793 Color us = pos.side_to_move();
1794 Thread* thisThread = pos.this_thread();
1795 thisThread->mainHistory[us][from_to(move)] << bonus;
1796 update_continuation_histories(ss, pos.moved_piece(move), to_sq(move), bonus);
1798 // Update countermove history
1799 if (is_ok((ss-1)->currentMove))
1801 Square prevSq = to_sq((ss-1)->currentMove);
1802 thisThread->counterMoves[pos.piece_on(prevSq)][prevSq] = move;
1806 // When playing with strength handicap, choose the best move among a set of RootMoves
1807 // using a statistical rule dependent on 'level'. Idea by Heinz van Saanen.
1809 Move Skill::pick_best(size_t multiPV) {
1811 const RootMoves& rootMoves = Threads.main()->rootMoves;
1812 static PRNG rng(now()); // PRNG sequence should be non-deterministic
1814 // RootMoves are already sorted by score in descending order
1815 Value topScore = rootMoves[0].score;
1816 int delta = std::min(topScore - rootMoves[multiPV - 1].score, PawnValue);
1817 int maxScore = -VALUE_INFINITE;
1818 double weakness = 120 - 2 * level;
1820 // Choose best move. For each move score we add two terms, both dependent on
1821 // weakness. One is deterministic and bigger for weaker levels, and one is
1822 // random. Then we choose the move with the resulting highest score.
1823 for (size_t i = 0; i < multiPV; ++i)
1825 // This is our magic formula
1826 int push = int(( weakness * int(topScore - rootMoves[i].score)
1827 + delta * (rng.rand<unsigned>() % int(weakness))) / 128);
1829 if (rootMoves[i].score + push >= maxScore)
1831 maxScore = rootMoves[i].score + push;
1832 best = rootMoves[i].pv[0];
1842 /// MainThread::check_time() is used to print debug info and, more importantly,
1843 /// to detect when we are out of available time and thus stop the search.
1845 void MainThread::check_time() {
1850 // When using nodes, ensure checking rate is not lower than 0.1% of nodes
1851 callsCnt = Limits.nodes ? std::min(512, int(Limits.nodes / 1024)) : 512;
1853 static TimePoint lastInfoTime = now();
1855 TimePoint elapsed = Time.elapsed();
1856 TimePoint tick = Limits.startTime + elapsed;
1858 if (tick - lastInfoTime >= 1000)
1860 lastInfoTime = tick;
1864 // We should not stop pondering until told so by the GUI
1868 if ( (Limits.use_time_management() && (elapsed > Time.maximum() || stopOnPonderhit))
1869 || (Limits.movetime && elapsed >= Limits.movetime)
1870 || (Limits.nodes && Threads.nodes_searched() >= uint64_t(Limits.nodes)))
1871 Threads.stop = true;
1875 /// UCI::pv() formats PV information according to the UCI protocol. UCI requires
1876 /// that all (if any) unsearched PV lines are sent using a previous search score.
1878 string UCI::pv(const Position& pos, Depth depth) {
1880 std::stringstream ss;
1881 TimePoint elapsed = Time.elapsed() + 1;
1882 const RootMoves& rootMoves = pos.this_thread()->rootMoves;
1883 size_t pvIdx = pos.this_thread()->pvIdx;
1884 size_t multiPV = std::min(size_t(Options["MultiPV"]), rootMoves.size());
1885 uint64_t nodesSearched = Threads.nodes_searched();
1886 uint64_t tbHits = Threads.tb_hits() + (TB::RootInTB ? rootMoves.size() : 0);
1888 for (size_t i = 0; i < multiPV; ++i)
1890 bool updated = rootMoves[i].score != -VALUE_INFINITE;
1892 if (depth == 1 && !updated && i > 0)
1895 Depth d = updated ? depth : std::max(1, depth - 1);
1896 Value v = updated ? rootMoves[i].uciScore : rootMoves[i].previousScore;
1898 if (v == -VALUE_INFINITE)
1901 bool tb = TB::RootInTB && abs(v) < VALUE_MATE_IN_MAX_PLY;
1902 v = tb ? rootMoves[i].tbScore : v;
1904 if (ss.rdbuf()->in_avail()) // Not at first line
1909 << " seldepth " << rootMoves[i].selDepth
1910 << " multipv " << i + 1
1911 << " score " << UCI::value(v);
1913 if (Options["UCI_ShowWDL"])
1914 ss << UCI::wdl(v, pos.game_ply());
1916 if (i == pvIdx && !tb && updated) // tablebase- and previous-scores are exact
1917 ss << (rootMoves[i].scoreLowerbound ? " lowerbound" : (rootMoves[i].scoreUpperbound ? " upperbound" : ""));
1919 ss << " nodes " << nodesSearched
1920 << " nps " << nodesSearched * 1000 / elapsed
1921 << " hashfull " << TT.hashfull()
1922 << " tbhits " << tbHits
1923 << " time " << elapsed
1926 for (Move m : rootMoves[i].pv)
1927 ss << " " << UCI::move(m, pos.is_chess960());
1934 /// RootMove::extract_ponder_from_tt() is called in case we have no ponder move
1935 /// before exiting the search, for instance, in case we stop the search during a
1936 /// fail high at root. We try hard to have a ponder move to return to the GUI,
1937 /// otherwise in case of 'ponder on' we have nothing to think about.
1939 bool RootMove::extract_ponder_from_tt(Position& pos) {
1942 ASSERT_ALIGNED(&st, Eval::NNUE::CacheLineSize);
1946 assert(pv.size() == 1);
1948 if (pv[0] == MOVE_NONE)
1951 pos.do_move(pv[0], st);
1952 TTEntry* tte = TT.probe(pos.key(), ttHit);
1956 Move m = tte->move(); // Local copy to be SMP safe
1957 if (MoveList<LEGAL>(pos).contains(m))
1961 pos.undo_move(pv[0]);
1962 return pv.size() > 1;
1965 void Tablebases::rank_root_moves(Position& pos, Search::RootMoves& rootMoves) {
1968 UseRule50 = bool(Options["Syzygy50MoveRule"]);
1969 ProbeDepth = int(Options["SyzygyProbeDepth"]);
1970 Cardinality = int(Options["SyzygyProbeLimit"]);
1971 bool dtz_available = true;
1973 // Tables with fewer pieces than SyzygyProbeLimit are searched with
1974 // ProbeDepth == DEPTH_ZERO
1975 if (Cardinality > MaxCardinality)
1977 Cardinality = MaxCardinality;
1981 if (Cardinality >= popcount(pos.pieces()) && !pos.can_castle(ANY_CASTLING))
1983 // Rank moves using DTZ tables
1984 RootInTB = root_probe(pos, rootMoves);
1988 // DTZ tables are missing; try to rank moves using WDL tables
1989 dtz_available = false;
1990 RootInTB = root_probe_wdl(pos, rootMoves);
1996 // Sort moves according to TB rank
1997 std::stable_sort(rootMoves.begin(), rootMoves.end(),
1998 [](const RootMove &a, const RootMove &b) { return a.tbRank > b.tbRank; } );
2000 // Probe during search only if DTZ is not available and we are winning
2001 if (dtz_available || rootMoves[0].tbScore <= VALUE_DRAW)
2006 // Clean up if root_probe() and root_probe_wdl() have failed
2007 for (auto& m : rootMoves)
2012 } // namespace Stockfish