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/>.
22 #include <cstring> // For std::memset
36 #include "syzygy/tbprobe.h"
37 #include "nnue/evaluate_nnue.h"
46 namespace Tablebases {
54 namespace TB = Tablebases;
58 using namespace Search;
62 // Different node types, used as a template parameter
63 enum NodeType { NonPV, PV, Root };
66 Value futility_margin(Depth d, bool improving) {
67 return Value(154 * (d - improving));
70 // Reductions lookup table, initialized at startup
71 int Reductions[MAX_MOVES]; // [depth or moveNumber]
73 Depth reduction(bool i, Depth d, int mn, Value delta, Value rootDelta) {
74 int r = Reductions[d] * Reductions[mn];
75 return (r + 1449 - int(delta) * 937 / int(rootDelta)) / 1024 + (!i && r > 941);
78 constexpr int futility_move_count(bool improving, Depth depth) {
79 return improving ? (3 + depth * depth)
80 : (3 + depth * depth) / 2;
83 // History and stats update bonus, based on depth
84 int stat_bonus(Depth d) {
85 return std::min(341 * d - 470, 1710);
88 // Add a small random component to draw evaluations to avoid 3-fold blindness
89 Value value_draw(const Thread* thisThread) {
90 return VALUE_DRAW - 1 + Value(thisThread->nodes & 0x2);
93 // Skill structure is used to implement strength limit. If we have an uci_elo then
94 // we convert it to a suitable fractional skill level using anchoring to CCRL Elo
95 // (goldfish 1.13 = 2000) and a fit through Ordo derived Elo for match (TC 60+0.6)
96 // results spanning a wide range of k values.
98 Skill(int skill_level, int uci_elo) {
101 double e = double(uci_elo - 1320) / (3190 - 1320);
102 level = std::clamp((((37.2473 * e - 40.8525) * e + 22.2943) * e - 0.311438), 0.0, 19.0);
105 level = double(skill_level);
107 bool enabled() const { return level < 20.0; }
108 bool time_to_pick(Depth depth) const { return depth == 1 + int(level); }
109 Move pick_best(size_t multiPV);
112 Move best = MOVE_NONE;
115 template <NodeType nodeType>
116 Value search(Position& pos, Stack* ss, Value alpha, Value beta, Depth depth, bool cutNode);
118 template <NodeType nodeType>
119 Value qsearch(Position& pos, Stack* ss, Value alpha, Value beta, Depth depth = 0);
121 Value value_to_tt(Value v, int ply);
122 Value value_from_tt(Value v, int ply, int r50c);
123 void update_pv(Move* pv, Move move, const Move* childPv);
124 void update_continuation_histories(Stack* ss, Piece pc, Square to, int bonus);
125 void update_quiet_stats(const Position& pos, Stack* ss, Move move, int bonus);
126 void update_all_stats(const Position& pos, Stack* ss, Move bestMove, Value bestValue, Value beta, Square prevSq,
127 Move* quietsSearched, int quietCount, Move* capturesSearched, int captureCount, Depth depth);
129 // perft() is our utility to verify move generation. All the leaf nodes up
130 // to the given depth are generated and counted, and the sum is returned.
132 uint64_t perft(Position& pos, Depth depth) {
135 ASSERT_ALIGNED(&st, Eval::NNUE::CacheLineSize);
137 uint64_t cnt, nodes = 0;
138 const bool leaf = (depth == 2);
140 for (const auto& m : MoveList<LEGAL>(pos))
142 if (Root && depth <= 1)
147 cnt = leaf ? MoveList<LEGAL>(pos).size() : perft<false>(pos, depth - 1);
152 sync_cout << UCI::move(m, pos.is_chess960()) << ": " << cnt << sync_endl;
160 /// Search::init() is called at startup to initialize various lookup tables
162 void Search::init() {
164 for (int i = 1; i < MAX_MOVES; ++i)
165 Reductions[i] = int((19.47 + std::log(Threads.size()) / 2) * std::log(i));
169 /// Search::clear() resets search state to its initial value
171 void Search::clear() {
173 Threads.main()->wait_for_search_finished();
175 Time.availableNodes = 0;
178 Tablebases::init(Options["SyzygyPath"]); // Free mapped files
182 /// MainThread::search() is started when the program receives the UCI 'go'
183 /// command. It searches from the root position and outputs the "bestmove".
185 void MainThread::search() {
189 nodes = perft<true>(rootPos, Limits.perft);
190 sync_cout << "\nNodes searched: " << nodes << "\n" << sync_endl;
194 Color us = rootPos.side_to_move();
195 Time.init(Limits, us, rootPos.game_ply());
198 Eval::NNUE::verify();
200 if (rootMoves.empty())
202 rootMoves.emplace_back(MOVE_NONE);
203 sync_cout << "info depth 0 score "
204 << UCI::value(rootPos.checkers() ? -VALUE_MATE : VALUE_DRAW)
209 Threads.start_searching(); // start non-main threads
210 Thread::search(); // main thread start searching
213 // When we reach the maximum depth, we can arrive here without a raise of
214 // Threads.stop. However, if we are pondering or in an infinite search,
215 // the UCI protocol states that we shouldn't print the best move before the
216 // GUI sends a "stop" or "ponderhit" command. We therefore simply wait here
217 // until the GUI sends one of those commands.
219 while (!Threads.stop && (ponder || Limits.infinite))
220 {} // Busy wait for a stop or a ponder reset
222 // Stop the threads if not already stopped (also raise the stop if
223 // "ponderhit" just reset Threads.ponder).
226 // Wait until all threads have finished
227 Threads.wait_for_search_finished();
229 // When playing in 'nodes as time' mode, subtract the searched nodes from
230 // the available ones before exiting.
232 Time.availableNodes += Limits.inc[us] - Threads.nodes_searched();
234 Thread* bestThread = this;
235 Skill skill = Skill(Options["Skill Level"], Options["UCI_LimitStrength"] ? int(Options["UCI_Elo"]) : 0);
237 if ( int(Options["MultiPV"]) == 1
240 && rootMoves[0].pv[0] != MOVE_NONE)
241 bestThread = Threads.get_best_thread();
243 bestPreviousScore = bestThread->rootMoves[0].score;
244 bestPreviousAverageScore = bestThread->rootMoves[0].averageScore;
246 // Send again PV info if we have a new best thread
247 if (bestThread != this)
248 sync_cout << UCI::pv(bestThread->rootPos, bestThread->completedDepth) << sync_endl;
250 sync_cout << "bestmove " << UCI::move(bestThread->rootMoves[0].pv[0], rootPos.is_chess960());
252 if (bestThread->rootMoves[0].pv.size() > 1 || bestThread->rootMoves[0].extract_ponder_from_tt(rootPos))
253 std::cout << " ponder " << UCI::move(bestThread->rootMoves[0].pv[1], rootPos.is_chess960());
255 std::cout << sync_endl;
259 /// Thread::search() is the main iterative deepening loop. It calls search()
260 /// repeatedly with increasing depth until the allocated thinking time has been
261 /// consumed, the user stops the search, or the maximum search depth is reached.
263 void Thread::search() {
265 // To allow access to (ss-7) up to (ss+2), the stack must be oversized.
266 // The former is needed to allow update_continuation_histories(ss-1, ...),
267 // which accesses its argument at ss-6, also near the root.
268 // The latter is needed for statScore and killer initialization.
269 Stack stack[MAX_PLY+10], *ss = stack+7;
271 Value alpha, beta, delta;
272 Move lastBestMove = MOVE_NONE;
273 Depth lastBestMoveDepth = 0;
274 MainThread* mainThread = (this == Threads.main() ? Threads.main() : nullptr);
275 double timeReduction = 1, totBestMoveChanges = 0;
276 Color us = rootPos.side_to_move();
279 std::memset(ss-7, 0, 10 * sizeof(Stack));
280 for (int i = 7; i > 0; --i)
282 (ss-i)->continuationHistory = &this->continuationHistory[0][0][NO_PIECE][0]; // Use as a sentinel
283 (ss-i)->staticEval = VALUE_NONE;
286 for (int i = 0; i <= MAX_PLY + 2; ++i)
291 bestValue = -VALUE_INFINITE;
295 if (mainThread->bestPreviousScore == VALUE_INFINITE)
296 for (int i = 0; i < 4; ++i)
297 mainThread->iterValue[i] = VALUE_ZERO;
299 for (int i = 0; i < 4; ++i)
300 mainThread->iterValue[i] = mainThread->bestPreviousScore;
303 size_t multiPV = size_t(Options["MultiPV"]);
304 Skill skill(Options["Skill Level"], Options["UCI_LimitStrength"] ? int(Options["UCI_Elo"]) : 0);
306 // When playing with strength handicap enable MultiPV search that we will
307 // use behind the scenes to retrieve a set of possible moves.
309 multiPV = std::max(multiPV, (size_t)4);
311 multiPV = std::min(multiPV, rootMoves.size());
313 int searchAgainCounter = 0;
315 // Iterative deepening loop until requested to stop or the target depth is reached
316 while ( ++rootDepth < MAX_PLY
318 && !(Limits.depth && mainThread && rootDepth > Limits.depth))
320 // Age out PV variability metric
322 totBestMoveChanges /= 2;
324 // Save the last iteration's scores before first PV line is searched and
325 // all the move scores except the (new) PV are set to -VALUE_INFINITE.
326 for (RootMove& rm : rootMoves)
327 rm.previousScore = rm.score;
332 if (!Threads.increaseDepth)
333 searchAgainCounter++;
335 // MultiPV loop. We perform a full root search for each PV line
336 for (pvIdx = 0; pvIdx < multiPV && !Threads.stop; ++pvIdx)
341 for (pvLast++; pvLast < rootMoves.size(); pvLast++)
342 if (rootMoves[pvLast].tbRank != rootMoves[pvFirst].tbRank)
346 // Reset UCI info selDepth for each depth and each PV line
349 // Reset aspiration window starting size
350 Value prev = rootMoves[pvIdx].averageScore;
351 delta = Value(10) + int(prev) * prev / 16502;
352 alpha = std::max(prev - delta,-VALUE_INFINITE);
353 beta = std::min(prev + delta, VALUE_INFINITE);
355 // Adjust optimism based on root move's previousScore
356 int opt = 102 * prev / (std::abs(prev) + 147);
357 optimism[ us] = Value(opt);
358 optimism[~us] = -optimism[us];
360 // Start with a small aspiration window and, in the case of a fail
361 // high/low, re-search with a bigger window until we don't fail
363 int failedHighCnt = 0;
366 // Adjust the effective depth searched, but ensuring at least one effective increment for every
367 // four searchAgain steps (see issue #2717).
368 Depth adjustedDepth = std::max(1, rootDepth - failedHighCnt - 3 * (searchAgainCounter + 1) / 4);
369 bestValue = Stockfish::search<Root>(rootPos, ss, alpha, beta, adjustedDepth, false);
371 // Bring the best move to the front. It is critical that sorting
372 // is done with a stable algorithm because all the values but the
373 // first and eventually the new best one are set to -VALUE_INFINITE
374 // and we want to keep the same order for all the moves except the
375 // new PV that goes to the front. Note that in case of MultiPV
376 // search the already searched PV lines are preserved.
377 std::stable_sort(rootMoves.begin() + pvIdx, rootMoves.begin() + pvLast);
379 // If search has been stopped, we break immediately. Sorting is
380 // safe because RootMoves is still valid, although it refers to
381 // the previous iteration.
385 // When failing high/low give some update (without cluttering
386 // the UI) before a re-search.
389 && (bestValue <= alpha || bestValue >= beta)
390 && Time.elapsed() > 3000)
391 sync_cout << UCI::pv(rootPos, rootDepth) << sync_endl;
393 // In case of failing low/high increase aspiration window and
394 // re-search, otherwise exit the loop.
395 if (bestValue <= alpha)
397 beta = (alpha + beta) / 2;
398 alpha = std::max(bestValue - delta, -VALUE_INFINITE);
402 mainThread->stopOnPonderhit = false;
404 else if (bestValue >= beta)
406 beta = std::min(bestValue + delta, VALUE_INFINITE);
412 delta += delta / 4 + 2;
414 assert(alpha >= -VALUE_INFINITE && beta <= VALUE_INFINITE);
417 // Sort the PV lines searched so far and update the GUI
418 std::stable_sort(rootMoves.begin() + pvFirst, rootMoves.begin() + pvIdx + 1);
421 && (Threads.stop || pvIdx + 1 == multiPV || Time.elapsed() > 3000))
422 sync_cout << UCI::pv(rootPos, rootDepth) << sync_endl;
426 completedDepth = rootDepth;
428 if (rootMoves[0].pv[0] != lastBestMove)
430 lastBestMove = rootMoves[0].pv[0];
431 lastBestMoveDepth = rootDepth;
434 // Have we found a "mate in x"?
436 && bestValue >= VALUE_MATE_IN_MAX_PLY
437 && VALUE_MATE - bestValue <= 2 * Limits.mate)
443 // If skill level is enabled and time is up, pick a sub-optimal best move
444 if (skill.enabled() && skill.time_to_pick(rootDepth))
445 skill.pick_best(multiPV);
447 // Use part of the gained time from a previous stable move for the current move
448 for (Thread* th : Threads)
450 totBestMoveChanges += th->bestMoveChanges;
451 th->bestMoveChanges = 0;
454 // Do we have time for the next iteration? Can we stop searching now?
455 if ( Limits.use_time_management()
457 && !mainThread->stopOnPonderhit)
459 double fallingEval = (69 + 13 * (mainThread->bestPreviousAverageScore - bestValue)
460 + 6 * (mainThread->iterValue[iterIdx] - bestValue)) / 619.6;
461 fallingEval = std::clamp(fallingEval, 0.5, 1.5);
463 // If the bestMove is stable over several iterations, reduce time accordingly
464 timeReduction = lastBestMoveDepth + 8 < completedDepth ? 1.57 : 0.65;
465 double reduction = (1.4 + mainThread->previousTimeReduction) / (2.08 * timeReduction);
466 double bestMoveInstability = 1 + 1.8 * totBestMoveChanges / Threads.size();
468 double totalTime = Time.optimum() * fallingEval * reduction * bestMoveInstability;
470 // Cap used time in case of a single legal move for a better viewer experience in tournaments
471 // yielding correct scores and sufficiently fast moves.
472 if (rootMoves.size() == 1)
473 totalTime = std::min(500.0, totalTime);
475 // Stop the search if we have exceeded the totalTime
476 if (Time.elapsed() > totalTime)
478 // If we are allowed to ponder do not stop the search now but
479 // keep pondering until the GUI sends "ponderhit" or "stop".
480 if (mainThread->ponder)
481 mainThread->stopOnPonderhit = true;
485 else if ( !mainThread->ponder
486 && Time.elapsed() > totalTime * 0.50)
487 Threads.increaseDepth = false;
489 Threads.increaseDepth = true;
492 mainThread->iterValue[iterIdx] = bestValue;
493 iterIdx = (iterIdx + 1) & 3;
499 mainThread->previousTimeReduction = timeReduction;
501 // If skill level is enabled, swap best PV line with the sub-optimal one
503 std::swap(rootMoves[0], *std::find(rootMoves.begin(), rootMoves.end(),
504 skill.best ? skill.best : skill.pick_best(multiPV)));
510 // search<>() is the main search function for both PV and non-PV nodes
512 template <NodeType nodeType>
513 Value search(Position& pos, Stack* ss, Value alpha, Value beta, Depth depth, bool cutNode) {
515 constexpr bool PvNode = nodeType != NonPV;
516 constexpr bool rootNode = nodeType == Root;
518 // Check if we have an upcoming move which draws by repetition, or
519 // if the opponent had an alternative move earlier to this position.
521 && pos.rule50_count() >= 3
522 && alpha < VALUE_DRAW
523 && pos.has_game_cycle(ss->ply))
525 alpha = value_draw(pos.this_thread());
530 // Dive into quiescence search when the depth reaches zero
532 return qsearch<PvNode ? PV : NonPV>(pos, ss, alpha, beta);
534 assert(-VALUE_INFINITE <= alpha && alpha < beta && beta <= VALUE_INFINITE);
535 assert(PvNode || (alpha == beta - 1));
536 assert(0 < depth && depth < MAX_PLY);
537 assert(!(PvNode && cutNode));
539 Move pv[MAX_PLY+1], capturesSearched[32], quietsSearched[64];
541 ASSERT_ALIGNED(&st, Eval::NNUE::CacheLineSize);
545 Move ttMove, move, excludedMove, bestMove;
546 Depth extension, newDepth;
547 Value bestValue, value, ttValue, eval, maxValue, probCutBeta;
548 bool givesCheck, improving, priorCapture, singularQuietLMR;
549 bool capture, moveCountPruning, ttCapture;
551 int moveCount, captureCount, quietCount, improvement;
553 // Step 1. Initialize node
554 Thread* thisThread = pos.this_thread();
555 ss->inCheck = pos.checkers();
556 priorCapture = pos.captured_piece();
557 Color us = pos.side_to_move();
558 moveCount = captureCount = quietCount = ss->moveCount = 0;
559 bestValue = -VALUE_INFINITE;
560 maxValue = VALUE_INFINITE;
562 // Check for the available remaining time
563 if (thisThread == Threads.main())
564 static_cast<MainThread*>(thisThread)->check_time();
566 // Used to send selDepth info to GUI (selDepth counts from 1, ply from 0)
567 if (PvNode && thisThread->selDepth < ss->ply + 1)
568 thisThread->selDepth = ss->ply + 1;
572 // Step 2. Check for aborted search and immediate draw
573 if ( Threads.stop.load(std::memory_order_relaxed)
574 || pos.is_draw(ss->ply)
575 || ss->ply >= MAX_PLY)
576 return (ss->ply >= MAX_PLY && !ss->inCheck) ? evaluate(pos)
577 : value_draw(pos.this_thread());
579 // Step 3. Mate distance pruning. Even if we mate at the next move our score
580 // would be at best mate_in(ss->ply+1), but if alpha is already bigger because
581 // a shorter mate was found upward in the tree then there is no need to search
582 // because we will never beat the current alpha. Same logic but with reversed
583 // signs applies also in the opposite condition of being mated instead of giving
584 // mate. In this case return a fail-high score.
585 alpha = std::max(mated_in(ss->ply), alpha);
586 beta = std::min(mate_in(ss->ply+1), beta);
591 thisThread->rootDelta = beta - alpha;
593 assert(0 <= ss->ply && ss->ply < MAX_PLY);
595 (ss+1)->excludedMove = bestMove = MOVE_NONE;
596 (ss+2)->killers[0] = (ss+2)->killers[1] = MOVE_NONE;
597 (ss+2)->cutoffCnt = 0;
598 ss->doubleExtensions = (ss-1)->doubleExtensions;
599 Square prevSq = is_ok((ss-1)->currentMove) ? to_sq((ss-1)->currentMove) : SQ_NONE;
602 // Step 4. Transposition table lookup.
603 excludedMove = ss->excludedMove;
605 tte = TT.probe(posKey, ss->ttHit);
606 ttValue = ss->ttHit ? value_from_tt(tte->value(), ss->ply, pos.rule50_count()) : VALUE_NONE;
607 ttMove = rootNode ? thisThread->rootMoves[thisThread->pvIdx].pv[0]
608 : ss->ttHit ? tte->move() : MOVE_NONE;
609 ttCapture = ttMove && pos.capture_stage(ttMove);
611 // At this point, if excluded, skip straight to step 6, static eval. However,
612 // to save indentation, we list the condition in all code between here and there.
614 ss->ttPv = PvNode || (ss->ttHit && tte->is_pv());
616 // At non-PV nodes we check for an early TT cutoff
620 && tte->depth() > depth - (tte->bound() == BOUND_EXACT)
621 && ttValue != VALUE_NONE // Possible in case of TT access race
622 && (tte->bound() & (ttValue >= beta ? BOUND_LOWER : BOUND_UPPER)))
624 // If ttMove is quiet, update move sorting heuristics on TT hit (~2 Elo)
629 // Bonus for a quiet ttMove that fails high (~2 Elo)
631 update_quiet_stats(pos, ss, ttMove, stat_bonus(depth));
633 // Extra penalty for early quiet moves of the previous ply (~0 Elo on STC, ~2 Elo on LTC)
634 if (prevSq != SQ_NONE && (ss-1)->moveCount <= 2 && !priorCapture)
635 update_continuation_histories(ss-1, pos.piece_on(prevSq), prevSq, -stat_bonus(depth + 1));
637 // Penalty for a quiet ttMove that fails low (~1 Elo)
640 int penalty = -stat_bonus(depth);
641 thisThread->mainHistory[us][from_to(ttMove)] << penalty;
642 update_continuation_histories(ss, pos.moved_piece(ttMove), to_sq(ttMove), penalty);
646 // Partial workaround for the graph history interaction problem
647 // For high rule50 counts don't produce transposition table cutoffs.
648 if (pos.rule50_count() < 90)
652 // Step 5. Tablebases probe
653 if (!rootNode && !excludedMove && TB::Cardinality)
655 int piecesCount = pos.count<ALL_PIECES>();
657 if ( piecesCount <= TB::Cardinality
658 && (piecesCount < TB::Cardinality || depth >= TB::ProbeDepth)
659 && pos.rule50_count() == 0
660 && !pos.can_castle(ANY_CASTLING))
663 TB::WDLScore wdl = Tablebases::probe_wdl(pos, &err);
665 // Force check of time on the next occasion
666 if (thisThread == Threads.main())
667 static_cast<MainThread*>(thisThread)->callsCnt = 0;
669 if (err != TB::ProbeState::FAIL)
671 thisThread->tbHits.fetch_add(1, std::memory_order_relaxed);
673 int drawScore = TB::UseRule50 ? 1 : 0;
675 // use the range VALUE_MATE_IN_MAX_PLY to VALUE_TB_WIN_IN_MAX_PLY to score
676 value = wdl < -drawScore ? VALUE_MATED_IN_MAX_PLY + ss->ply + 1
677 : wdl > drawScore ? VALUE_MATE_IN_MAX_PLY - ss->ply - 1
678 : VALUE_DRAW + 2 * wdl * drawScore;
680 Bound b = wdl < -drawScore ? BOUND_UPPER
681 : wdl > drawScore ? BOUND_LOWER : BOUND_EXACT;
683 if ( b == BOUND_EXACT
684 || (b == BOUND_LOWER ? value >= beta : value <= alpha))
686 tte->save(posKey, value_to_tt(value, ss->ply), ss->ttPv, b,
687 std::min(MAX_PLY - 1, depth + 6),
688 MOVE_NONE, VALUE_NONE);
695 if (b == BOUND_LOWER)
696 bestValue = value, alpha = std::max(alpha, bestValue);
704 CapturePieceToHistory& captureHistory = thisThread->captureHistory;
706 // Step 6. Static evaluation of the position
709 // Skip early pruning when in check
710 ss->staticEval = eval = VALUE_NONE;
715 else if (excludedMove)
717 // Providing the hint that this node's accumulator will be used often brings significant Elo gain (13 Elo)
718 Eval::NNUE::hint_common_parent_position(pos);
719 eval = ss->staticEval;
723 // Never assume anything about values stored in TT
724 ss->staticEval = eval = tte->eval();
725 if (eval == VALUE_NONE)
726 ss->staticEval = eval = evaluate(pos);
730 Eval::NNUE::hint_common_parent_position(pos);
733 // ttValue can be used as a better position evaluation (~7 Elo)
734 if ( ttValue != VALUE_NONE
735 && (tte->bound() & (ttValue > eval ? BOUND_LOWER : BOUND_UPPER)))
740 ss->staticEval = eval = evaluate(pos);
741 // Save static evaluation into transposition table
742 tte->save(posKey, VALUE_NONE, ss->ttPv, BOUND_NONE, DEPTH_NONE, MOVE_NONE, eval);
745 // Use static evaluation difference to improve quiet move ordering (~4 Elo)
746 if (is_ok((ss-1)->currentMove) && !(ss-1)->inCheck && !priorCapture)
748 int bonus = std::clamp(-19 * int((ss-1)->staticEval + ss->staticEval), -1920, 1920);
749 thisThread->mainHistory[~us][from_to((ss-1)->currentMove)] << bonus;
752 // Set up the improvement variable, which is the difference between the current
753 // static evaluation and the previous static evaluation at our turn (if we were
754 // in check at our previous move we look at the move prior to it). The improvement
755 // margin and the improving flag are used in various pruning heuristics.
756 improvement = (ss-2)->staticEval != VALUE_NONE ? ss->staticEval - (ss-2)->staticEval
757 : (ss-4)->staticEval != VALUE_NONE ? ss->staticEval - (ss-4)->staticEval
759 improving = improvement > 0;
761 // Step 7. Razoring (~1 Elo).
762 // If eval is really low check with qsearch if it can exceed alpha, if it can't,
763 // return a fail low.
764 if (eval < alpha - 426 - 256 * depth * depth)
766 value = qsearch<NonPV>(pos, ss, alpha - 1, alpha);
771 // Step 8. Futility pruning: child node (~40 Elo).
772 // The depth condition is important for mate finding.
775 && eval - futility_margin(depth, improving) - (ss-1)->statScore / 280 >= beta
777 && eval < 25128) // larger than VALUE_KNOWN_WIN, but smaller than TB wins
780 // Step 9. Null move search with verification search (~35 Elo)
782 && (ss-1)->currentMove != MOVE_NULL
783 && (ss-1)->statScore < 18755
785 && eval >= ss->staticEval
786 && ss->staticEval >= beta - 20 * depth - improvement / 13 + 253
788 && pos.non_pawn_material(us)
789 && (ss->ply >= thisThread->nmpMinPly))
791 assert(eval - beta >= 0);
793 // Null move dynamic reduction based on depth and eval
794 Depth R = std::min(int(eval - beta) / 172, 6) + depth / 3 + 4;
796 ss->currentMove = MOVE_NULL;
797 ss->continuationHistory = &thisThread->continuationHistory[0][0][NO_PIECE][0];
799 pos.do_null_move(st);
801 Value nullValue = -search<NonPV>(pos, ss+1, -beta, -beta+1, depth-R, !cutNode);
803 pos.undo_null_move();
805 if (nullValue >= beta)
807 // Do not return unproven mate or TB scores
808 if (nullValue >= VALUE_TB_WIN_IN_MAX_PLY)
811 if (thisThread->nmpMinPly || (abs(beta) < VALUE_KNOWN_WIN && depth < 14))
814 assert(!thisThread->nmpMinPly); // Recursive verification is not allowed
816 // Do verification search at high depths, with null move pruning disabled
817 // until ply exceeds nmpMinPly.
818 thisThread->nmpMinPly = ss->ply + 3 * (depth-R) / 4;
820 Value v = search<NonPV>(pos, ss, beta-1, beta, depth-R, false);
822 thisThread->nmpMinPly = 0;
829 probCutBeta = beta + 186 - 54 * improving;
831 // Step 10. ProbCut (~10 Elo)
832 // If we have a good enough capture (or queen promotion) and a reduced search returns a value
833 // much above beta, we can (almost) safely prune the previous move.
836 && abs(beta) < VALUE_TB_WIN_IN_MAX_PLY
837 // if value from transposition table is lower than probCutBeta, don't attempt probCut
838 // there and in further interactions with transposition table cutoff depth is set to depth - 3
839 // because probCut search has depth set to depth - 4 but we also do a move before it
840 // so effective depth is equal to depth - 3
842 && tte->depth() >= depth - 3
843 && ttValue != VALUE_NONE
844 && ttValue < probCutBeta))
846 assert(probCutBeta < VALUE_INFINITE);
848 MovePicker mp(pos, ttMove, probCutBeta - ss->staticEval, &captureHistory);
850 while ((move = mp.next_move()) != MOVE_NONE)
851 if (move != excludedMove && pos.legal(move))
853 assert(pos.capture_stage(move));
855 ss->currentMove = move;
856 ss->continuationHistory = &thisThread->continuationHistory[ss->inCheck]
858 [pos.moved_piece(move)]
861 pos.do_move(move, st);
863 // Perform a preliminary qsearch to verify that the move holds
864 value = -qsearch<NonPV>(pos, ss+1, -probCutBeta, -probCutBeta+1);
866 // If the qsearch held, perform the regular search
867 if (value >= probCutBeta)
868 value = -search<NonPV>(pos, ss+1, -probCutBeta, -probCutBeta+1, depth - 4, !cutNode);
872 if (value >= probCutBeta)
874 // Save ProbCut data into transposition table
875 tte->save(posKey, value_to_tt(value, ss->ply), ss->ttPv, BOUND_LOWER, depth - 3, move, ss->staticEval);
880 Eval::NNUE::hint_common_parent_position(pos);
883 // Step 11. If the position is not in TT, decrease depth by 2 (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).
884 // Use qsearch if depth is equal or below zero (~9 Elo)
887 depth -= 2 + 2 * (ss->ttHit && tte->depth() >= depth);
890 return qsearch<PV>(pos, ss, alpha, beta);
897 moves_loop: // When in check, search starts here
899 // Step 12. A small Probcut idea, when we are in check (~4 Elo)
900 probCutBeta = beta + 391;
905 && (tte->bound() & BOUND_LOWER)
906 && tte->depth() >= depth - 3
907 && ttValue >= probCutBeta
908 && abs(ttValue) <= VALUE_KNOWN_WIN
909 && abs(beta) <= VALUE_KNOWN_WIN)
912 const PieceToHistory* contHist[] = { (ss-1)->continuationHistory, (ss-2)->continuationHistory,
913 nullptr , (ss-4)->continuationHistory,
914 nullptr , (ss-6)->continuationHistory };
916 Move countermove = prevSq != SQ_NONE ? thisThread->counterMoves[pos.piece_on(prevSq)][prevSq] : MOVE_NONE;
918 MovePicker mp(pos, ttMove, depth, &thisThread->mainHistory,
925 moveCountPruning = singularQuietLMR = false;
927 // Indicate PvNodes that will probably fail low if the node was searched
928 // at a depth equal or greater than the current depth, and the result of this search was a fail low.
929 bool likelyFailLow = PvNode
931 && (tte->bound() & BOUND_UPPER)
932 && tte->depth() >= depth;
934 // Step 13. Loop through all pseudo-legal moves until no moves remain
935 // or a beta cutoff occurs.
936 while ((move = mp.next_move(moveCountPruning)) != MOVE_NONE)
940 if (move == excludedMove)
943 // At root obey the "searchmoves" option and skip moves not listed in Root
944 // Move List. As a consequence any illegal move is also skipped. In MultiPV
945 // mode we also skip PV moves which have been already searched and those
946 // of lower "TB rank" if we are in a TB root position.
947 if (rootNode && !std::count(thisThread->rootMoves.begin() + thisThread->pvIdx,
948 thisThread->rootMoves.begin() + thisThread->pvLast, move))
951 // Check for legality
952 if (!rootNode && !pos.legal(move))
955 ss->moveCount = ++moveCount;
957 if (rootNode && thisThread == Threads.main() && Time.elapsed() > 3000)
958 sync_cout << "info depth " << depth
959 << " currmove " << UCI::move(move, pos.is_chess960())
960 << " currmovenumber " << moveCount + thisThread->pvIdx << sync_endl;
962 (ss+1)->pv = nullptr;
965 capture = pos.capture_stage(move);
966 movedPiece = pos.moved_piece(move);
967 givesCheck = pos.gives_check(move);
969 // Calculate new depth for this move
970 newDepth = depth - 1;
972 Value delta = beta - alpha;
974 Depth r = reduction(improving, depth, moveCount, delta, thisThread->rootDelta);
976 // Step 14. Pruning at shallow depth (~120 Elo). Depth conditions are important for mate finding.
978 && pos.non_pawn_material(us)
979 && bestValue > VALUE_TB_LOSS_IN_MAX_PLY)
981 // Skip quiet moves if movecount exceeds our FutilityMoveCount threshold (~8 Elo)
982 moveCountPruning = moveCount >= futility_move_count(improving, depth);
984 // Reduced depth of the next LMR search
985 int lmrDepth = std::max(newDepth - r, 0);
990 // Futility pruning for captures (~2 Elo)
994 && ss->staticEval + 182 + 230 * lmrDepth + PieceValue[EG][pos.piece_on(to_sq(move))]
995 + captureHistory[movedPiece][to_sq(move)][type_of(pos.piece_on(to_sq(move)))] / 7 < alpha)
999 // SEE based pruning (~11 Elo)
1000 if (!pos.see_ge(move, occupied, Value(-206) * depth))
1002 if (depth < 2 - capture)
1004 // Don't prune the move if opp. King/Queen/Rook gets a discovered attack during or after the exchanges
1005 Bitboard leftEnemies = pos.pieces(~us, KING, QUEEN, ROOK);
1006 Bitboard attacks = 0;
1007 occupied |= to_sq(move);
1008 while (leftEnemies && !attacks)
1010 Square sq = pop_lsb(leftEnemies);
1011 attacks = pos.attackers_to(sq, occupied) & pos.pieces(us) & occupied;
1012 // Exclude Queen/Rook(s) which were already threatened before SEE (opp King can't be in check when it's our turn)
1013 if (attacks && sq != pos.square<KING>(~us) && (pos.attackers_to(sq, pos.pieces()) & pos.pieces(us)))
1022 int history = (*contHist[0])[movedPiece][to_sq(move)]
1023 + (*contHist[1])[movedPiece][to_sq(move)]
1024 + (*contHist[3])[movedPiece][to_sq(move)];
1026 // Continuation history based pruning (~2 Elo)
1028 && history < -4405 * (depth - 1))
1031 history += 2 * thisThread->mainHistory[us][from_to(move)];
1033 lmrDepth += history / 7278;
1034 lmrDepth = std::max(lmrDepth, -2);
1036 // Futility pruning: parent node (~13 Elo)
1039 && ss->staticEval + 103 + 138 * lmrDepth <= alpha)
1042 lmrDepth = std::max(lmrDepth, 0);
1044 // Prune moves with negative SEE (~4 Elo)
1045 if (!pos.see_ge(move, Value(-24 * lmrDepth * lmrDepth - 16 * lmrDepth)))
1050 // Step 15. Extensions (~100 Elo)
1051 // We take care to not overdo to avoid search getting stuck.
1052 if (ss->ply < thisThread->rootDepth * 2)
1054 // Singular extension search (~94 Elo). If all moves but one fail low on a
1055 // search of (alpha-s, beta-s), and just one fails high on (alpha, beta),
1056 // then that move is singular and should be extended. To verify this we do
1057 // a reduced search on all the other moves but the ttMove and if the
1058 // result is lower than ttValue minus a margin, then we will extend the ttMove.
1060 && depth >= 4 - (thisThread->completedDepth > 21) + 2 * (PvNode && tte->is_pv())
1062 && !excludedMove // Avoid recursive singular search
1063 /* && ttValue != VALUE_NONE Already implicit in the next condition */
1064 && abs(ttValue) < VALUE_KNOWN_WIN
1065 && (tte->bound() & BOUND_LOWER)
1066 && tte->depth() >= depth - 3)
1068 Value singularBeta = ttValue - (3 + 2 * (ss->ttPv && !PvNode)) * depth / 2;
1069 Depth singularDepth = (depth - 1) / 2;
1071 ss->excludedMove = move;
1072 value = search<NonPV>(pos, ss, singularBeta - 1, singularBeta, singularDepth, cutNode);
1073 ss->excludedMove = MOVE_NONE;
1075 if (value < singularBeta)
1078 singularQuietLMR = !ttCapture;
1080 // Avoid search explosion by limiting the number of double extensions
1082 && value < singularBeta - 25
1083 && ss->doubleExtensions <= 10)
1086 depth += depth < 13;
1090 // Multi-cut pruning
1091 // Our ttMove is assumed to fail high, and now we failed high also on a reduced
1092 // search without the ttMove. So we assume this expected Cut-node is not singular,
1093 // that multiple moves fail high, and we can prune the whole subtree by returning
1095 else if (singularBeta >= beta)
1096 return singularBeta;
1098 // If the eval of ttMove is greater than beta, we reduce it (negative extension) (~7 Elo)
1099 else if (ttValue >= beta)
1100 extension = -2 - !PvNode;
1102 // If the eval of ttMove is less than value, we reduce it (negative extension) (~1 Elo)
1103 else if (ttValue <= value)
1106 // If the eval of ttMove is less than alpha, we reduce it (negative extension) (~1 Elo)
1107 else if (ttValue <= alpha)
1111 // Check extensions (~1 Elo)
1112 else if ( givesCheck
1114 && abs(ss->staticEval) > 88)
1117 // Quiet ttMove extensions (~1 Elo)
1120 && move == ss->killers[0]
1121 && (*contHist[0])[movedPiece][to_sq(move)] >= 5705)
1125 // Add extension to new depth
1126 newDepth += extension;
1127 ss->doubleExtensions = (ss-1)->doubleExtensions + (extension == 2);
1129 // Speculative prefetch as early as possible
1130 prefetch(TT.first_entry(pos.key_after(move)));
1132 // Update the current move (this must be done after singular extension search)
1133 ss->currentMove = move;
1134 ss->continuationHistory = &thisThread->continuationHistory[ss->inCheck]
1139 // Step 16. Make the move
1140 pos.do_move(move, st, givesCheck);
1142 // Decrease reduction if position is or has been on the PV
1143 // and node is not likely to fail low. (~3 Elo)
1144 // Decrease further on cutNodes. (~1 Elo)
1147 r -= cutNode && tte->depth() >= depth + 3 ? 3 : 2;
1149 // Decrease reduction if opponent's move count is high (~1 Elo)
1150 if ((ss-1)->moveCount > 7)
1153 // Increase reduction for cut nodes (~3 Elo)
1157 // Increase reduction if ttMove is a capture (~3 Elo)
1161 // Decrease reduction for PvNodes based on depth (~2 Elo)
1163 r -= 1 + 12 / (3 + depth);
1165 // Decrease reduction if ttMove has been singularly extended (~1 Elo)
1166 if (singularQuietLMR)
1169 // Increase reduction if next ply has a lot of fail high (~5 Elo)
1170 if ((ss+1)->cutoffCnt > 3)
1173 else if (move == ttMove)
1176 ss->statScore = 2 * thisThread->mainHistory[us][from_to(move)]
1177 + (*contHist[0])[movedPiece][to_sq(move)]
1178 + (*contHist[1])[movedPiece][to_sq(move)]
1179 + (*contHist[3])[movedPiece][to_sq(move)]
1182 // Decrease/increase reduction for moves with a good/bad history (~25 Elo)
1183 r -= ss->statScore / (11079 + 4626 * (depth > 6 && depth < 19));
1185 // Step 17. Late moves reduction / extension (LMR, ~117 Elo)
1186 // We use various heuristics for the sons of a node after the first son has
1187 // been searched. In general we would like to reduce them, but there are many
1188 // cases where we extend a son if it has good chances to be "interesting".
1190 && moveCount > 1 + (PvNode && ss->ply <= 1)
1193 || (cutNode && (ss-1)->moveCount > 1)))
1195 // In general we want to cap the LMR depth search at newDepth, but when
1196 // reduction is negative, we allow this move a limited search extension
1197 // beyond the first move depth. This may lead to hidden double extensions.
1198 Depth d = std::clamp(newDepth - r, 1, newDepth + 1);
1200 value = -search<NonPV>(pos, ss+1, -(alpha+1), -alpha, d, true);
1202 // Do full depth search when reduced LMR search fails high
1203 if (value > alpha && d < newDepth)
1205 // Adjust full depth search based on LMR results - if result
1206 // was good enough search deeper, if it was bad enough search shallower
1207 const bool doDeeperSearch = value > (alpha + 58 + 12 * (newDepth - d));
1208 const bool doEvenDeeperSearch = value > alpha + 588 && ss->doubleExtensions <= 5;
1209 const bool doShallowerSearch = value < bestValue + newDepth;
1211 ss->doubleExtensions = ss->doubleExtensions + doEvenDeeperSearch;
1213 newDepth += doDeeperSearch - doShallowerSearch + doEvenDeeperSearch;
1216 value = -search<NonPV>(pos, ss+1, -(alpha+1), -alpha, newDepth, !cutNode);
1218 int bonus = value <= alpha ? -stat_bonus(newDepth)
1219 : value >= beta ? stat_bonus(newDepth)
1222 update_continuation_histories(ss, movedPiece, to_sq(move), bonus);
1226 // Step 18. Full depth search when LMR is skipped. If expected reduction is high, reduce its depth by 1.
1227 else if (!PvNode || moveCount > 1)
1229 // Increase reduction for cut nodes and not ttMove (~1 Elo)
1230 if (!ttMove && cutNode)
1233 value = -search<NonPV>(pos, ss+1, -(alpha+1), -alpha, newDepth - (r > 4), !cutNode);
1236 // For PV nodes only, do a full PV search on the first move or after a fail
1237 // high (in the latter case search only if value < beta), otherwise let the
1238 // parent node fail low with value <= alpha and try another move.
1239 if (PvNode && (moveCount == 1 || (value > alpha && (rootNode || value < beta))))
1242 (ss+1)->pv[0] = MOVE_NONE;
1244 value = -search<PV>(pos, ss+1, -beta, -alpha, newDepth, false);
1247 // Step 19. Undo move
1248 pos.undo_move(move);
1250 assert(value > -VALUE_INFINITE && value < VALUE_INFINITE);
1252 // Step 20. Check for a new best move
1253 // Finished searching the move. If a stop occurred, the return value of
1254 // the search cannot be trusted, and we return immediately without
1255 // updating best move, PV and TT.
1256 if (Threads.stop.load(std::memory_order_relaxed))
1261 RootMove& rm = *std::find(thisThread->rootMoves.begin(),
1262 thisThread->rootMoves.end(), move);
1264 rm.averageScore = rm.averageScore != -VALUE_INFINITE ? (2 * value + rm.averageScore) / 3 : value;
1266 // PV move or new best move?
1267 if (moveCount == 1 || value > alpha)
1269 rm.score = rm.uciScore = value;
1270 rm.selDepth = thisThread->selDepth;
1271 rm.scoreLowerbound = rm.scoreUpperbound = false;
1275 rm.scoreLowerbound = true;
1278 else if (value <= alpha)
1280 rm.scoreUpperbound = true;
1281 rm.uciScore = alpha;
1288 for (Move* m = (ss+1)->pv; *m != MOVE_NONE; ++m)
1289 rm.pv.push_back(*m);
1291 // We record how often the best move has been changed in each iteration.
1292 // This information is used for time management. In MultiPV mode,
1293 // we must take care to only do this for the first PV line.
1295 && !thisThread->pvIdx)
1296 ++thisThread->bestMoveChanges;
1299 // All other moves but the PV are set to the lowest value: this
1300 // is not a problem when sorting because the sort is stable and the
1301 // move position in the list is preserved - just the PV is pushed up.
1302 rm.score = -VALUE_INFINITE;
1305 if (value > bestValue)
1313 if (PvNode && !rootNode) // Update pv even in fail-high case
1314 update_pv(ss->pv, move, (ss+1)->pv);
1316 if (PvNode && value < beta) // Update alpha! Always alpha < beta
1318 // Reduce other moves if we have found at least one score improvement (~1 Elo)
1330 assert(value >= beta); // Fail high
1337 // If the move is worse than some previously searched move, remember it to update its stats later
1338 if (move != bestMove)
1340 if (capture && captureCount < 32)
1341 capturesSearched[captureCount++] = move;
1343 else if (!capture && quietCount < 64)
1344 quietsSearched[quietCount++] = move;
1348 // The following condition would detect a stop only after move loop has been
1349 // completed. But in this case bestValue is valid because we have fully
1350 // searched our subtree, and we can anyhow save the result in TT.
1356 // Step 21. Check for mate and stalemate
1357 // All legal moves have been searched and if there are no legal moves, it
1358 // must be a mate or a stalemate. If we are in a singular extension search then
1359 // return a fail low score.
1361 assert(moveCount || !ss->inCheck || excludedMove || !MoveList<LEGAL>(pos).size());
1364 bestValue = excludedMove ? alpha :
1365 ss->inCheck ? mated_in(ss->ply)
1368 // If there is a move which produces search value greater than alpha we update stats of searched moves
1370 update_all_stats(pos, ss, bestMove, bestValue, beta, prevSq,
1371 quietsSearched, quietCount, capturesSearched, captureCount, depth);
1373 // Bonus for prior countermove that caused the fail low
1374 else if (!priorCapture && prevSq != SQ_NONE)
1376 int bonus = (depth > 5) + (PvNode || cutNode) + (bestValue < alpha - 97 * depth) + ((ss-1)->moveCount > 10);
1377 update_continuation_histories(ss-1, pos.piece_on(prevSq), prevSq, stat_bonus(depth) * bonus);
1381 bestValue = std::min(bestValue, maxValue);
1383 // If no good move is found and the previous position was ttPv, then the previous
1384 // opponent move is probably good and the new position is added to the search tree. (~7 Elo)
1385 if (bestValue <= alpha)
1386 ss->ttPv = ss->ttPv || ((ss-1)->ttPv && depth > 3);
1388 // Write gathered information in transposition table
1389 if (!excludedMove && !(rootNode && thisThread->pvIdx))
1390 tte->save(posKey, value_to_tt(bestValue, ss->ply), ss->ttPv,
1391 bestValue >= beta ? BOUND_LOWER :
1392 PvNode && bestMove ? BOUND_EXACT : BOUND_UPPER,
1393 depth, bestMove, ss->staticEval);
1395 assert(bestValue > -VALUE_INFINITE && bestValue < VALUE_INFINITE);
1401 // qsearch() is the quiescence search function, which is called by the main search
1402 // function with zero depth, or recursively with further decreasing depth per call.
1404 template <NodeType nodeType>
1405 Value qsearch(Position& pos, Stack* ss, Value alpha, Value beta, Depth depth) {
1407 static_assert(nodeType != Root);
1408 constexpr bool PvNode = nodeType == PV;
1410 assert(alpha >= -VALUE_INFINITE && alpha < beta && beta <= VALUE_INFINITE);
1411 assert(PvNode || (alpha == beta - 1));
1416 ASSERT_ALIGNED(&st, Eval::NNUE::CacheLineSize);
1420 Move ttMove, move, bestMove;
1422 Value bestValue, value, ttValue, futilityValue, futilityBase;
1423 bool pvHit, givesCheck, capture;
1426 // Step 1. Initialize node
1430 ss->pv[0] = MOVE_NONE;
1433 Thread* thisThread = pos.this_thread();
1434 bestMove = MOVE_NONE;
1435 ss->inCheck = pos.checkers();
1438 // Step 2. Check for an immediate draw or maximum ply reached
1439 if ( pos.is_draw(ss->ply)
1440 || ss->ply >= MAX_PLY)
1441 return (ss->ply >= MAX_PLY && !ss->inCheck) ? evaluate(pos) : VALUE_DRAW;
1443 assert(0 <= ss->ply && ss->ply < MAX_PLY);
1445 // Decide whether or not to include checks: this fixes also the type of
1446 // TT entry depth that we are going to use. Note that in qsearch we use
1447 // only two types of depth in TT: DEPTH_QS_CHECKS or DEPTH_QS_NO_CHECKS.
1448 ttDepth = ss->inCheck || depth >= DEPTH_QS_CHECKS ? DEPTH_QS_CHECKS
1449 : DEPTH_QS_NO_CHECKS;
1451 // Step 3. Transposition table lookup
1453 tte = TT.probe(posKey, ss->ttHit);
1454 ttValue = ss->ttHit ? value_from_tt(tte->value(), ss->ply, pos.rule50_count()) : VALUE_NONE;
1455 ttMove = ss->ttHit ? tte->move() : MOVE_NONE;
1456 pvHit = ss->ttHit && tte->is_pv();
1458 // At non-PV nodes we check for an early TT cutoff
1461 && tte->depth() >= ttDepth
1462 && ttValue != VALUE_NONE // Only in case of TT access race
1463 && (tte->bound() & (ttValue >= beta ? BOUND_LOWER : BOUND_UPPER)))
1466 // Step 4. Static evaluation of the position
1469 ss->staticEval = VALUE_NONE;
1470 bestValue = futilityBase = -VALUE_INFINITE;
1476 // Never assume anything about values stored in TT
1477 if ((ss->staticEval = bestValue = tte->eval()) == VALUE_NONE)
1478 ss->staticEval = bestValue = evaluate(pos);
1480 // ttValue can be used as a better position evaluation (~13 Elo)
1481 if ( ttValue != VALUE_NONE
1482 && (tte->bound() & (ttValue > bestValue ? BOUND_LOWER : BOUND_UPPER)))
1483 bestValue = ttValue;
1486 // In case of null move search use previous static eval with a different sign
1487 ss->staticEval = bestValue =
1488 (ss-1)->currentMove != MOVE_NULL ? evaluate(pos)
1489 : -(ss-1)->staticEval;
1491 // Stand pat. Return immediately if static value is at least beta
1492 if (bestValue >= beta)
1494 // Save gathered info in transposition table
1496 tte->save(posKey, value_to_tt(bestValue, ss->ply), false, BOUND_LOWER,
1497 DEPTH_NONE, MOVE_NONE, ss->staticEval);
1502 if (PvNode && bestValue > alpha)
1505 futilityBase = bestValue + 168;
1508 const PieceToHistory* contHist[] = { (ss-1)->continuationHistory, (ss-2)->continuationHistory,
1509 nullptr , (ss-4)->continuationHistory,
1510 nullptr , (ss-6)->continuationHistory };
1512 // Initialize a MovePicker object for the current position, and prepare
1513 // to search the moves. Because the depth is <= 0 here, only captures,
1514 // queen promotions, and other checks (only if depth >= DEPTH_QS_CHECKS)
1515 // will be generated.
1516 Square prevSq = (ss-1)->currentMove != MOVE_NULL ? to_sq((ss-1)->currentMove) : SQ_NONE;
1517 MovePicker mp(pos, ttMove, depth, &thisThread->mainHistory,
1518 &thisThread->captureHistory,
1522 int quietCheckEvasions = 0;
1524 // Step 5. Loop through all pseudo-legal moves until no moves remain
1525 // or a beta cutoff occurs.
1526 while ((move = mp.next_move()) != MOVE_NONE)
1528 assert(is_ok(move));
1530 // Check for legality
1531 if (!pos.legal(move))
1534 givesCheck = pos.gives_check(move);
1535 capture = pos.capture_stage(move);
1540 if (bestValue > VALUE_TB_LOSS_IN_MAX_PLY)
1542 // Futility pruning and moveCount pruning (~10 Elo)
1544 && to_sq(move) != prevSq
1545 && futilityBase > -VALUE_KNOWN_WIN
1546 && type_of(move) != PROMOTION)
1551 futilityValue = futilityBase + PieceValue[EG][pos.piece_on(to_sq(move))];
1553 if (futilityValue <= alpha)
1555 bestValue = std::max(bestValue, futilityValue);
1559 if (futilityBase <= alpha && !pos.see_ge(move, VALUE_ZERO + 1))
1561 bestValue = std::max(bestValue, futilityBase);
1566 // We prune after 2nd quiet check evasion where being 'in check' is implicitly checked through the counter
1567 // and being a 'quiet' apart from being a tt move is assumed after an increment because captures are pushed ahead.
1568 if (quietCheckEvasions > 1)
1571 // Continuation history based pruning (~3 Elo)
1573 && (*contHist[0])[pos.moved_piece(move)][to_sq(move)] < 0
1574 && (*contHist[1])[pos.moved_piece(move)][to_sq(move)] < 0)
1577 // Do not search moves with bad enough SEE values (~5 Elo)
1578 if (!pos.see_ge(move, Value(-110)))
1582 // Speculative prefetch as early as possible
1583 prefetch(TT.first_entry(pos.key_after(move)));
1585 // Update the current move
1586 ss->currentMove = move;
1587 ss->continuationHistory = &thisThread->continuationHistory[ss->inCheck]
1589 [pos.moved_piece(move)]
1592 quietCheckEvasions += !capture && ss->inCheck;
1594 // Step 7. Make and search the move
1595 pos.do_move(move, st, givesCheck);
1596 value = -qsearch<nodeType>(pos, ss+1, -beta, -alpha, depth - 1);
1597 pos.undo_move(move);
1599 assert(value > -VALUE_INFINITE && value < VALUE_INFINITE);
1601 // Step 8. Check for a new best move
1602 if (value > bestValue)
1610 if (PvNode) // Update pv even in fail-high case
1611 update_pv(ss->pv, move, (ss+1)->pv);
1613 if (PvNode && value < beta) // Update alpha here!
1621 // Step 9. Check for mate
1622 // All legal moves have been searched. A special case: if we're in check
1623 // and no legal moves were found, it is checkmate.
1624 if (ss->inCheck && bestValue == -VALUE_INFINITE)
1626 assert(!MoveList<LEGAL>(pos).size());
1628 return mated_in(ss->ply); // Plies to mate from the root
1631 // Save gathered info in transposition table
1632 tte->save(posKey, value_to_tt(bestValue, ss->ply), pvHit,
1633 bestValue >= beta ? BOUND_LOWER : BOUND_UPPER,
1634 ttDepth, bestMove, ss->staticEval);
1636 assert(bestValue > -VALUE_INFINITE && bestValue < VALUE_INFINITE);
1642 // value_to_tt() adjusts a mate or TB score from "plies to mate from the root" to
1643 // "plies to mate from the current position". Standard scores are unchanged.
1644 // The function is called before storing a value in the transposition table.
1646 Value value_to_tt(Value v, int ply) {
1648 assert(v != VALUE_NONE);
1650 return v >= VALUE_TB_WIN_IN_MAX_PLY ? v + ply
1651 : v <= VALUE_TB_LOSS_IN_MAX_PLY ? v - ply : v;
1655 // value_from_tt() is the inverse of value_to_tt(): it adjusts a mate or TB score
1656 // from the transposition table (which refers to the plies to mate/be mated from
1657 // current position) to "plies to mate/be mated (TB win/loss) from the root". However,
1658 // for mate scores, to avoid potentially false mate scores related to the 50 moves rule
1659 // and the graph history interaction, we return an optimal TB score instead.
1661 Value value_from_tt(Value v, int ply, int r50c) {
1663 if (v == VALUE_NONE)
1666 if (v >= VALUE_TB_WIN_IN_MAX_PLY) // TB win or better
1668 if (v >= VALUE_MATE_IN_MAX_PLY && VALUE_MATE - v > 99 - r50c)
1669 return VALUE_MATE_IN_MAX_PLY - 1; // do not return a potentially false mate score
1674 if (v <= VALUE_TB_LOSS_IN_MAX_PLY) // TB loss or worse
1676 if (v <= VALUE_MATED_IN_MAX_PLY && VALUE_MATE + v > 99 - r50c)
1677 return VALUE_MATED_IN_MAX_PLY + 1; // do not return a potentially false mate score
1686 // update_pv() adds current move and appends child pv[]
1688 void update_pv(Move* pv, Move move, const Move* childPv) {
1690 for (*pv++ = move; childPv && *childPv != MOVE_NONE; )
1696 // update_all_stats() updates stats at the end of search() when a bestMove is found
1698 void update_all_stats(const Position& pos, Stack* ss, Move bestMove, Value bestValue, Value beta, Square prevSq,
1699 Move* quietsSearched, int quietCount, Move* capturesSearched, int captureCount, Depth depth) {
1701 Color us = pos.side_to_move();
1702 Thread* thisThread = pos.this_thread();
1703 CapturePieceToHistory& captureHistory = thisThread->captureHistory;
1704 Piece moved_piece = pos.moved_piece(bestMove);
1707 int bonus1 = stat_bonus(depth + 1);
1709 if (!pos.capture_stage(bestMove))
1711 int bonus2 = bestValue > beta + 153 ? bonus1 // larger bonus
1712 : stat_bonus(depth); // smaller bonus
1714 // Increase stats for the best move in case it was a quiet move
1715 update_quiet_stats(pos, ss, bestMove, bonus2);
1717 // Decrease stats for all non-best quiet moves
1718 for (int i = 0; i < quietCount; ++i)
1720 thisThread->mainHistory[us][from_to(quietsSearched[i])] << -bonus2;
1721 update_continuation_histories(ss, pos.moved_piece(quietsSearched[i]), to_sq(quietsSearched[i]), -bonus2);
1726 // Increase stats for the best move in case it was a capture move
1727 captured = type_of(pos.piece_on(to_sq(bestMove)));
1728 captureHistory[moved_piece][to_sq(bestMove)][captured] << bonus1;
1731 // Extra penalty for a quiet early move that was not a TT move or
1732 // main killer move in previous ply when it gets refuted.
1733 if ( prevSq != SQ_NONE
1734 && ((ss-1)->moveCount == 1 + (ss-1)->ttHit || ((ss-1)->currentMove == (ss-1)->killers[0]))
1735 && !pos.captured_piece())
1736 update_continuation_histories(ss-1, pos.piece_on(prevSq), prevSq, -bonus1);
1738 // Decrease stats for all non-best capture moves
1739 for (int i = 0; i < captureCount; ++i)
1741 moved_piece = pos.moved_piece(capturesSearched[i]);
1742 captured = type_of(pos.piece_on(to_sq(capturesSearched[i])));
1743 captureHistory[moved_piece][to_sq(capturesSearched[i])][captured] << -bonus1;
1748 // update_continuation_histories() updates histories of the move pairs formed
1749 // by moves at ply -1, -2, -4, and -6 with current move.
1751 void update_continuation_histories(Stack* ss, Piece pc, Square to, int bonus) {
1753 for (int i : {1, 2, 4, 6})
1755 // Only update first 2 continuation histories if we are in check
1756 if (ss->inCheck && i > 2)
1758 if (is_ok((ss-i)->currentMove))
1759 (*(ss-i)->continuationHistory)[pc][to] << bonus;
1764 // update_quiet_stats() updates move sorting heuristics
1766 void update_quiet_stats(const Position& pos, Stack* ss, Move move, int bonus) {
1769 if (ss->killers[0] != move)
1771 ss->killers[1] = ss->killers[0];
1772 ss->killers[0] = move;
1775 Color us = pos.side_to_move();
1776 Thread* thisThread = pos.this_thread();
1777 thisThread->mainHistory[us][from_to(move)] << bonus;
1778 update_continuation_histories(ss, pos.moved_piece(move), to_sq(move), bonus);
1780 // Update countermove history
1781 if (is_ok((ss-1)->currentMove))
1783 Square prevSq = to_sq((ss-1)->currentMove);
1784 thisThread->counterMoves[pos.piece_on(prevSq)][prevSq] = move;
1788 // When playing with strength handicap, choose best move among a set of RootMoves
1789 // using a statistical rule dependent on 'level'. Idea by Heinz van Saanen.
1791 Move Skill::pick_best(size_t multiPV) {
1793 const RootMoves& rootMoves = Threads.main()->rootMoves;
1794 static PRNG rng(now()); // PRNG sequence should be non-deterministic
1796 // RootMoves are already sorted by score in descending order
1797 Value topScore = rootMoves[0].score;
1798 int delta = std::min(topScore - rootMoves[multiPV - 1].score, PawnValueMg);
1799 int maxScore = -VALUE_INFINITE;
1800 double weakness = 120 - 2 * level;
1802 // Choose best move. For each move score we add two terms, both dependent on
1803 // weakness. One is deterministic and bigger for weaker levels, and one is
1804 // random. Then we choose the move with the resulting highest score.
1805 for (size_t i = 0; i < multiPV; ++i)
1807 // This is our magic formula
1808 int push = int(( weakness * int(topScore - rootMoves[i].score)
1809 + delta * (rng.rand<unsigned>() % int(weakness))) / 128);
1811 if (rootMoves[i].score + push >= maxScore)
1813 maxScore = rootMoves[i].score + push;
1814 best = rootMoves[i].pv[0];
1824 /// MainThread::check_time() is used to print debug info and, more importantly,
1825 /// to detect when we are out of available time and thus stop the search.
1827 void MainThread::check_time() {
1832 // When using nodes, ensure checking rate is not lower than 0.1% of nodes
1833 callsCnt = Limits.nodes ? std::min(1024, int(Limits.nodes / 1024)) : 1024;
1835 static TimePoint lastInfoTime = now();
1837 TimePoint elapsed = Time.elapsed();
1838 TimePoint tick = Limits.startTime + elapsed;
1840 if (tick - lastInfoTime >= 1000)
1842 lastInfoTime = tick;
1846 // We should not stop pondering until told so by the GUI
1850 if ( (Limits.use_time_management() && (elapsed > Time.maximum() - 10 || stopOnPonderhit))
1851 || (Limits.movetime && elapsed >= Limits.movetime)
1852 || (Limits.nodes && Threads.nodes_searched() >= (uint64_t)Limits.nodes))
1853 Threads.stop = true;
1857 /// UCI::pv() formats PV information according to the UCI protocol. UCI requires
1858 /// that all (if any) unsearched PV lines are sent using a previous search score.
1860 string UCI::pv(const Position& pos, Depth depth) {
1862 std::stringstream ss;
1863 TimePoint elapsed = Time.elapsed() + 1;
1864 const RootMoves& rootMoves = pos.this_thread()->rootMoves;
1865 size_t pvIdx = pos.this_thread()->pvIdx;
1866 size_t multiPV = std::min((size_t)Options["MultiPV"], rootMoves.size());
1867 uint64_t nodesSearched = Threads.nodes_searched();
1868 uint64_t tbHits = Threads.tb_hits() + (TB::RootInTB ? rootMoves.size() : 0);
1870 for (size_t i = 0; i < multiPV; ++i)
1872 bool updated = rootMoves[i].score != -VALUE_INFINITE;
1874 if (depth == 1 && !updated && i > 0)
1877 Depth d = updated ? depth : std::max(1, depth - 1);
1878 Value v = updated ? rootMoves[i].uciScore : rootMoves[i].previousScore;
1880 if (v == -VALUE_INFINITE)
1883 bool tb = TB::RootInTB && abs(v) < VALUE_MATE_IN_MAX_PLY;
1884 v = tb ? rootMoves[i].tbScore : v;
1886 if (ss.rdbuf()->in_avail()) // Not at first line
1891 << " seldepth " << rootMoves[i].selDepth
1892 << " multipv " << i + 1
1893 << " score " << UCI::value(v);
1895 if (Options["UCI_ShowWDL"])
1896 ss << UCI::wdl(v, pos.game_ply());
1898 if (i == pvIdx && !tb && updated) // tablebase- and previous-scores are exact
1899 ss << (rootMoves[i].scoreLowerbound ? " lowerbound" : (rootMoves[i].scoreUpperbound ? " upperbound" : ""));
1901 ss << " nodes " << nodesSearched
1902 << " nps " << nodesSearched * 1000 / elapsed
1903 << " hashfull " << TT.hashfull()
1904 << " tbhits " << tbHits
1905 << " time " << elapsed
1908 for (Move m : rootMoves[i].pv)
1909 ss << " " << UCI::move(m, pos.is_chess960());
1916 /// RootMove::extract_ponder_from_tt() is called in case we have no ponder move
1917 /// before exiting the search, for instance, in case we stop the search during a
1918 /// fail high at root. We try hard to have a ponder move to return to the GUI,
1919 /// otherwise in case of 'ponder on' we have nothing to think on.
1921 bool RootMove::extract_ponder_from_tt(Position& pos) {
1924 ASSERT_ALIGNED(&st, Eval::NNUE::CacheLineSize);
1928 assert(pv.size() == 1);
1930 if (pv[0] == MOVE_NONE)
1933 pos.do_move(pv[0], st);
1934 TTEntry* tte = TT.probe(pos.key(), ttHit);
1938 Move m = tte->move(); // Local copy to be SMP safe
1939 if (MoveList<LEGAL>(pos).contains(m))
1943 pos.undo_move(pv[0]);
1944 return pv.size() > 1;
1947 void Tablebases::rank_root_moves(Position& pos, Search::RootMoves& rootMoves) {
1950 UseRule50 = bool(Options["Syzygy50MoveRule"]);
1951 ProbeDepth = int(Options["SyzygyProbeDepth"]);
1952 Cardinality = int(Options["SyzygyProbeLimit"]);
1953 bool dtz_available = true;
1955 // Tables with fewer pieces than SyzygyProbeLimit are searched with
1956 // ProbeDepth == DEPTH_ZERO
1957 if (Cardinality > MaxCardinality)
1959 Cardinality = MaxCardinality;
1963 if (Cardinality >= popcount(pos.pieces()) && !pos.can_castle(ANY_CASTLING))
1965 // Rank moves using DTZ tables
1966 RootInTB = root_probe(pos, rootMoves);
1970 // DTZ tables are missing; try to rank moves using WDL tables
1971 dtz_available = false;
1972 RootInTB = root_probe_wdl(pos, rootMoves);
1978 // Sort moves according to TB rank
1979 std::stable_sort(rootMoves.begin(), rootMoves.end(),
1980 [](const RootMove &a, const RootMove &b) { return a.tbRank > b.tbRank; } );
1982 // Probe during search only if DTZ is not available and we are winning
1983 if (dtz_available || rootMoves[0].tbScore <= VALUE_DRAW)
1988 // Clean up if root_probe() and root_probe_wdl() have failed
1989 for (auto& m : rootMoves)
1994 } // namespace Stockfish