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((140 - 40 * 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 + 1372 - int(delta) * 1073 / int(rootDelta)) / 1024
85 + (!i && reductionScale > 936);
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(336 * d - 547, 1561);
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. If we have an uci_elo then
104 // we convert it to a suitable fractional skill level using anchoring to CCRL Elo
105 // (goldfish 1.13 = 2000) and a fit through Ordo derived Elo for a match (TC 60+0.6)
106 // results spanning a wide range of k values.
108 Skill(int skill_level, int uci_elo) {
111 double e = double(uci_elo - 1320) / (3190 - 1320);
112 level = std::clamp((((37.2473 * e - 40.8525) * e + 22.2943) * e - 0.311438), 0.0, 19.0);
115 level = double(skill_level);
117 bool enabled() const { return level < 20.0; }
118 bool time_to_pick(Depth depth) const { return depth == 1 + int(level); }
119 Move pick_best(size_t multiPV);
122 Move best = MOVE_NONE;
125 template <NodeType nodeType>
126 Value search(Position& pos, Stack* ss, Value alpha, Value beta, Depth depth, bool cutNode);
128 template <NodeType nodeType>
129 Value qsearch(Position& pos, Stack* ss, Value alpha, Value beta, Depth depth = 0);
131 Value value_to_tt(Value v, int ply);
132 Value value_from_tt(Value v, int ply, int r50c);
133 void update_pv(Move* pv, Move move, const Move* childPv);
134 void update_continuation_histories(Stack* ss, Piece pc, Square to, int bonus);
135 void update_quiet_stats(const Position& pos, Stack* ss, Move move, int bonus);
136 void update_all_stats(const Position& pos, Stack* ss, Move bestMove, Value bestValue, Value beta, Square prevSq,
137 Move* quietsSearched, int quietCount, Move* capturesSearched, int captureCount, Depth depth);
139 // perft() is our utility to verify move generation. All the leaf nodes up
140 // to the given depth are generated and counted, and the sum is returned.
142 uint64_t perft(Position& pos, Depth depth) {
145 ASSERT_ALIGNED(&st, Eval::NNUE::CacheLineSize);
147 uint64_t cnt, nodes = 0;
148 const bool leaf = (depth == 2);
150 for (const auto& m : MoveList<LEGAL>(pos))
152 if (Root && depth <= 1)
157 cnt = leaf ? MoveList<LEGAL>(pos).size() : perft<false>(pos, depth - 1);
162 sync_cout << UCI::move(m, pos.is_chess960()) << ": " << cnt << sync_endl;
170 /// Search::init() is called at startup to initialize various lookup tables
172 void Search::init() {
174 for (int i = 1; i < MAX_MOVES; ++i)
175 Reductions[i] = int((20.57 + std::log(Threads.size()) / 2) * std::log(i));
179 /// Search::clear() resets search state to its initial value
181 void Search::clear() {
183 Threads.main()->wait_for_search_finished();
185 Time.availableNodes = 0;
188 Tablebases::init(Options["SyzygyPath"]); // Free mapped files
192 /// MainThread::search() is started when the program receives the UCI 'go'
193 /// command. It searches from the root position and outputs the "bestmove".
195 void MainThread::search() {
199 nodes = perft<true>(rootPos, Limits.perft);
200 sync_cout << "\nNodes searched: " << nodes << "\n" << sync_endl;
204 Color us = rootPos.side_to_move();
205 Time.init(Limits, us, rootPos.game_ply());
208 Eval::NNUE::verify();
210 if (rootMoves.empty())
212 rootMoves.emplace_back(MOVE_NONE);
213 sync_cout << "info depth 0 score "
214 << UCI::value(rootPos.checkers() ? -VALUE_MATE : VALUE_DRAW)
219 Threads.start_searching(); // start non-main threads
220 Thread::search(); // main thread start searching
223 // When we reach the maximum depth, we can arrive here without a raise of
224 // Threads.stop. However, if we are pondering or in an infinite search,
225 // the UCI protocol states that we shouldn't print the best move before the
226 // GUI sends a "stop" or "ponderhit" command. We therefore simply wait here
227 // until the GUI sends one of those commands.
229 while (!Threads.stop && (ponder || Limits.infinite))
230 {} // Busy wait for a stop or a ponder reset
232 // Stop the threads if not already stopped (also raise the stop if
233 // "ponderhit" just reset Threads.ponder).
236 // Wait until all threads have finished
237 Threads.wait_for_search_finished();
239 // When playing in 'nodes as time' mode, subtract the searched nodes from
240 // the available ones before exiting.
242 Time.availableNodes += Limits.inc[us] - Threads.nodes_searched();
244 Thread* bestThread = this;
245 Skill skill = Skill(Options["Skill Level"], Options["UCI_LimitStrength"] ? int(Options["UCI_Elo"]) : 0);
247 if ( int(Options["MultiPV"]) == 1
250 && rootMoves[0].pv[0] != MOVE_NONE)
251 bestThread = Threads.get_best_thread();
253 bestPreviousScore = bestThread->rootMoves[0].score;
254 bestPreviousAverageScore = bestThread->rootMoves[0].averageScore;
256 // Send again PV info if we have a new best thread
257 if (bestThread != this)
258 sync_cout << UCI::pv(bestThread->rootPos, bestThread->completedDepth) << sync_endl;
260 sync_cout << "bestmove " << UCI::move(bestThread->rootMoves[0].pv[0], rootPos.is_chess960());
262 if (bestThread->rootMoves[0].pv.size() > 1 || bestThread->rootMoves[0].extract_ponder_from_tt(rootPos))
263 std::cout << " ponder " << UCI::move(bestThread->rootMoves[0].pv[1], rootPos.is_chess960());
265 std::cout << sync_endl;
269 /// Thread::search() is the main iterative deepening loop. It calls search()
270 /// repeatedly with increasing depth until the allocated thinking time has been
271 /// consumed, the user stops the search, or the maximum search depth is reached.
273 void Thread::search() {
275 // To allow access to (ss-7) up to (ss+2), the stack must be oversized.
276 // The former is needed to allow update_continuation_histories(ss-1, ...),
277 // which accesses its argument at ss-6, also near the root.
278 // The latter is needed for statScore and killer initialization.
279 Stack stack[MAX_PLY+10], *ss = stack+7;
281 Value alpha, beta, delta;
282 Move lastBestMove = MOVE_NONE;
283 Depth lastBestMoveDepth = 0;
284 MainThread* mainThread = (this == Threads.main() ? Threads.main() : nullptr);
285 double timeReduction = 1, totBestMoveChanges = 0;
286 Color us = rootPos.side_to_move();
289 std::memset(ss-7, 0, 10 * sizeof(Stack));
290 for (int i = 7; i > 0; --i)
292 (ss-i)->continuationHistory = &this->continuationHistory[0][0][NO_PIECE][0]; // Use as a sentinel
293 (ss-i)->staticEval = VALUE_NONE;
296 for (int i = 0; i <= MAX_PLY + 2; ++i)
301 bestValue = -VALUE_INFINITE;
305 if (mainThread->bestPreviousScore == VALUE_INFINITE)
306 for (int i = 0; i < 4; ++i)
307 mainThread->iterValue[i] = VALUE_ZERO;
309 for (int i = 0; i < 4; ++i)
310 mainThread->iterValue[i] = mainThread->bestPreviousScore;
313 size_t multiPV = size_t(Options["MultiPV"]);
314 Skill skill(Options["Skill Level"], Options["UCI_LimitStrength"] ? int(Options["UCI_Elo"]) : 0);
316 // When playing with strength handicap enable MultiPV search that we will
317 // use behind-the-scenes to retrieve a set of possible moves.
319 multiPV = std::max(multiPV, size_t(4));
321 multiPV = std::min(multiPV, rootMoves.size());
323 int searchAgainCounter = 0;
325 // Iterative deepening loop until requested to stop or the target depth is reached
326 while ( ++rootDepth < MAX_PLY
328 && !(Limits.depth && mainThread && rootDepth > Limits.depth))
330 // Age out PV variability metric
332 totBestMoveChanges /= 2;
334 // Save the last iteration's scores before the first PV line is searched and
335 // all the move scores except the (new) PV are set to -VALUE_INFINITE.
336 for (RootMove& rm : rootMoves)
337 rm.previousScore = rm.score;
342 if (!Threads.increaseDepth)
343 searchAgainCounter++;
345 // MultiPV loop. We perform a full root search for each PV line
346 for (pvIdx = 0; pvIdx < multiPV && !Threads.stop; ++pvIdx)
351 for (pvLast++; pvLast < rootMoves.size(); pvLast++)
352 if (rootMoves[pvLast].tbRank != rootMoves[pvFirst].tbRank)
356 // Reset UCI info selDepth for each depth and each PV line
359 // Reset aspiration window starting size
360 Value prev = rootMoves[pvIdx].averageScore;
361 delta = Value(10) + int(prev) * prev / 15799;
362 alpha = std::max(prev - delta,-VALUE_INFINITE);
363 beta = std::min(prev + delta, VALUE_INFINITE);
365 // Adjust optimism based on root move's previousScore
366 int opt = 109 * prev / (std::abs(prev) + 141);
367 optimism[ us] = Value(opt);
368 optimism[~us] = -optimism[us];
370 // Start with a small aspiration window and, in the case of a fail
371 // high/low, re-search with a bigger window until we don't fail
373 int failedHighCnt = 0;
376 // Adjust the effective depth searched, but ensure at least one effective increment for every
377 // four searchAgain steps (see issue #2717).
378 Depth adjustedDepth = std::max(1, rootDepth - failedHighCnt - 3 * (searchAgainCounter + 1) / 4);
379 bestValue = Stockfish::search<Root>(rootPos, ss, alpha, beta, adjustedDepth, false);
381 // Bring the best move to the front. It is critical that sorting
382 // is done with a stable algorithm because all the values but the
383 // first and eventually the new best one is set to -VALUE_INFINITE
384 // and we want to keep the same order for all the moves except the
385 // new PV that goes to the front. Note that in the case of MultiPV
386 // search the already searched PV lines are preserved.
387 std::stable_sort(rootMoves.begin() + pvIdx, rootMoves.begin() + pvLast);
389 // If search has been stopped, we break immediately. Sorting is
390 // safe because RootMoves is still valid, although it refers to
391 // the previous iteration.
395 // When failing high/low give some update (without cluttering
396 // the UI) before a re-search.
399 && (bestValue <= alpha || bestValue >= beta)
400 && Time.elapsed() > 3000)
401 sync_cout << UCI::pv(rootPos, rootDepth) << sync_endl;
403 // In case of failing low/high increase aspiration window and
404 // re-search, otherwise exit the loop.
405 if (bestValue <= alpha)
407 beta = (alpha + beta) / 2;
408 alpha = std::max(bestValue - delta, -VALUE_INFINITE);
412 mainThread->stopOnPonderhit = false;
414 else if (bestValue >= beta)
416 beta = std::min(bestValue + delta, VALUE_INFINITE);
424 assert(alpha >= -VALUE_INFINITE && beta <= VALUE_INFINITE);
427 // Sort the PV lines searched so far and update the GUI
428 std::stable_sort(rootMoves.begin() + pvFirst, rootMoves.begin() + pvIdx + 1);
431 && (Threads.stop || pvIdx + 1 == multiPV || Time.elapsed() > 3000))
432 sync_cout << UCI::pv(rootPos, rootDepth) << sync_endl;
436 completedDepth = rootDepth;
438 if (rootMoves[0].pv[0] != lastBestMove)
440 lastBestMove = rootMoves[0].pv[0];
441 lastBestMoveDepth = rootDepth;
444 // Have we found a "mate in x"?
446 && bestValue >= VALUE_MATE_IN_MAX_PLY
447 && VALUE_MATE - bestValue <= 2 * Limits.mate)
453 // If the skill level is enabled and time is up, pick a sub-optimal best move
454 if (skill.enabled() && skill.time_to_pick(rootDepth))
455 skill.pick_best(multiPV);
457 // Use part of the gained time from a previous stable move for the current move
458 for (Thread* th : Threads)
460 totBestMoveChanges += th->bestMoveChanges;
461 th->bestMoveChanges = 0;
464 // Do we have time for the next iteration? Can we stop searching now?
465 if ( Limits.use_time_management()
467 && !mainThread->stopOnPonderhit)
469 double fallingEval = (69 + 13 * (mainThread->bestPreviousAverageScore - bestValue)
470 + 6 * (mainThread->iterValue[iterIdx] - bestValue)) / 619.6;
471 fallingEval = std::clamp(fallingEval, 0.5, 1.5);
473 // If the bestMove is stable over several iterations, reduce time accordingly
474 timeReduction = lastBestMoveDepth + 8 < completedDepth ? 1.57 : 0.65;
475 double reduction = (1.4 + mainThread->previousTimeReduction) / (2.08 * timeReduction);
476 double bestMoveInstability = 1 + 1.8 * totBestMoveChanges / Threads.size();
478 double totalTime = Time.optimum() * fallingEval * reduction * bestMoveInstability;
480 // Cap used time in case of a single legal move for a better viewer experience in tournaments
481 // yielding correct scores and sufficiently fast moves.
482 if (rootMoves.size() == 1)
483 totalTime = std::min(500.0, totalTime);
485 // Stop the search if we have exceeded the totalTime
486 if (Time.elapsed() > totalTime)
488 // If we are allowed to ponder do not stop the search now but
489 // keep pondering until the GUI sends "ponderhit" or "stop".
490 if (mainThread->ponder)
491 mainThread->stopOnPonderhit = true;
495 else if ( !mainThread->ponder
496 && Time.elapsed() > totalTime * 0.50)
497 Threads.increaseDepth = false;
499 Threads.increaseDepth = true;
502 mainThread->iterValue[iterIdx] = bestValue;
503 iterIdx = (iterIdx + 1) & 3;
509 mainThread->previousTimeReduction = timeReduction;
511 // If the skill level is enabled, swap the best PV line with the sub-optimal one
513 std::swap(rootMoves[0], *std::find(rootMoves.begin(), rootMoves.end(),
514 skill.best ? skill.best : skill.pick_best(multiPV)));
520 // search<>() is the main search function for both PV and non-PV nodes
522 template <NodeType nodeType>
523 Value search(Position& pos, Stack* ss, Value alpha, Value beta, Depth depth, bool cutNode) {
525 constexpr bool PvNode = nodeType != NonPV;
526 constexpr bool rootNode = nodeType == Root;
528 // Dive into quiescence search when the depth reaches zero
530 return qsearch<PvNode ? PV : NonPV>(pos, ss, alpha, beta);
532 // Check if we have an upcoming move that draws by repetition, or
533 // if the opponent had an alternative move earlier to this position.
535 && alpha < VALUE_DRAW
536 && pos.has_game_cycle(ss->ply))
538 alpha = value_draw(pos.this_thread());
543 assert(-VALUE_INFINITE <= alpha && alpha < beta && beta <= VALUE_INFINITE);
544 assert(PvNode || (alpha == beta - 1));
545 assert(0 < depth && depth < MAX_PLY);
546 assert(!(PvNode && cutNode));
548 Move pv[MAX_PLY+1], capturesSearched[32], quietsSearched[64];
550 ASSERT_ALIGNED(&st, Eval::NNUE::CacheLineSize);
554 Move ttMove, move, excludedMove, bestMove;
555 Depth extension, newDepth;
556 Value bestValue, value, ttValue, eval, maxValue, probCutBeta;
557 bool givesCheck, improving, priorCapture, singularQuietLMR;
558 bool capture, moveCountPruning, ttCapture;
560 int moveCount, captureCount, quietCount;
562 // Step 1. Initialize node
563 Thread* thisThread = pos.this_thread();
564 ss->inCheck = pos.checkers();
565 priorCapture = pos.captured_piece();
566 Color us = pos.side_to_move();
567 moveCount = captureCount = quietCount = ss->moveCount = 0;
568 bestValue = -VALUE_INFINITE;
569 maxValue = VALUE_INFINITE;
571 // Check for the available remaining time
572 if (thisThread == Threads.main())
573 static_cast<MainThread*>(thisThread)->check_time();
575 // Used to send selDepth info to GUI (selDepth counts from 1, ply from 0)
576 if (PvNode && thisThread->selDepth < ss->ply + 1)
577 thisThread->selDepth = ss->ply + 1;
581 // Step 2. Check for aborted search and immediate draw
582 if ( Threads.stop.load(std::memory_order_relaxed)
583 || pos.is_draw(ss->ply)
584 || ss->ply >= MAX_PLY)
585 return (ss->ply >= MAX_PLY && !ss->inCheck) ? evaluate(pos)
586 : value_draw(pos.this_thread());
588 // Step 3. Mate distance pruning. Even if we mate at the next move our score
589 // would be at best mate_in(ss->ply+1), but if alpha is already bigger because
590 // a shorter mate was found upward in the tree then there is no need to search
591 // because we will never beat the current alpha. Same logic but with reversed
592 // signs apply also in the opposite condition of being mated instead of giving
593 // mate. In this case, return a fail-high score.
594 alpha = std::max(mated_in(ss->ply), alpha);
595 beta = std::min(mate_in(ss->ply+1), beta);
600 thisThread->rootDelta = beta - alpha;
602 assert(0 <= ss->ply && ss->ply < MAX_PLY);
604 (ss+1)->excludedMove = bestMove = MOVE_NONE;
605 (ss+2)->killers[0] = (ss+2)->killers[1] = MOVE_NONE;
606 (ss+2)->cutoffCnt = 0;
607 ss->doubleExtensions = (ss-1)->doubleExtensions;
608 Square prevSq = is_ok((ss-1)->currentMove) ? to_sq((ss-1)->currentMove) : SQ_NONE;
611 // Step 4. Transposition table lookup.
612 excludedMove = ss->excludedMove;
614 tte = TT.probe(posKey, ss->ttHit);
615 ttValue = ss->ttHit ? value_from_tt(tte->value(), ss->ply, pos.rule50_count()) : VALUE_NONE;
616 ttMove = rootNode ? thisThread->rootMoves[thisThread->pvIdx].pv[0]
617 : ss->ttHit ? tte->move() : MOVE_NONE;
618 ttCapture = ttMove && pos.capture_stage(ttMove);
620 // At this point, if excluded, skip straight to step 6, static eval. However,
621 // to save indentation, we list the condition in all code between here and there.
623 ss->ttPv = PvNode || (ss->ttHit && tte->is_pv());
625 // At non-PV nodes we check for an early TT cutoff
628 && tte->depth() > depth
629 && ttValue != VALUE_NONE // Possible in case of TT access race or if !ttHit
630 && (tte->bound() & (ttValue >= beta ? BOUND_LOWER : BOUND_UPPER)))
632 // If ttMove is quiet, update move sorting heuristics on TT hit (~2 Elo)
637 // Bonus for a quiet ttMove that fails high (~2 Elo)
639 update_quiet_stats(pos, ss, ttMove, stat_bonus(depth));
641 // Extra penalty for early quiet moves of the previous ply (~0 Elo on STC, ~2 Elo on LTC)
642 if (prevSq != SQ_NONE && (ss-1)->moveCount <= 2 && !priorCapture)
643 update_continuation_histories(ss-1, pos.piece_on(prevSq), prevSq, -stat_bonus(depth + 1));
645 // Penalty for a quiet ttMove that fails low (~1 Elo)
648 int penalty = -stat_bonus(depth);
649 thisThread->mainHistory[us][from_to(ttMove)] << penalty;
650 update_continuation_histories(ss, pos.moved_piece(ttMove), to_sq(ttMove), penalty);
654 // Partial workaround for the graph history interaction problem
655 // For high rule50 counts don't produce transposition table cutoffs.
656 if (pos.rule50_count() < 90)
660 // Step 5. Tablebases probe
661 if (!rootNode && !excludedMove && TB::Cardinality)
663 int piecesCount = pos.count<ALL_PIECES>();
665 if ( piecesCount <= TB::Cardinality
666 && (piecesCount < TB::Cardinality || depth >= TB::ProbeDepth)
667 && pos.rule50_count() == 0
668 && !pos.can_castle(ANY_CASTLING))
671 TB::WDLScore wdl = Tablebases::probe_wdl(pos, &err);
673 // Force check of time on the next occasion
674 if (thisThread == Threads.main())
675 static_cast<MainThread*>(thisThread)->callsCnt = 0;
677 if (err != TB::ProbeState::FAIL)
679 thisThread->tbHits.fetch_add(1, std::memory_order_relaxed);
681 int drawScore = TB::UseRule50 ? 1 : 0;
683 // use the range VALUE_MATE_IN_MAX_PLY to VALUE_TB_WIN_IN_MAX_PLY to score
684 value = wdl < -drawScore ? VALUE_MATED_IN_MAX_PLY + ss->ply + 1
685 : wdl > drawScore ? VALUE_MATE_IN_MAX_PLY - ss->ply - 1
686 : VALUE_DRAW + 2 * wdl * drawScore;
688 Bound b = wdl < -drawScore ? BOUND_UPPER
689 : wdl > drawScore ? BOUND_LOWER : BOUND_EXACT;
691 if ( b == BOUND_EXACT
692 || (b == BOUND_LOWER ? value >= beta : value <= alpha))
694 tte->save(posKey, value_to_tt(value, ss->ply), ss->ttPv, b,
695 std::min(MAX_PLY - 1, depth + 6),
696 MOVE_NONE, VALUE_NONE);
703 if (b == BOUND_LOWER)
704 bestValue = value, alpha = std::max(alpha, bestValue);
712 CapturePieceToHistory& captureHistory = thisThread->captureHistory;
714 // Step 6. Static evaluation of the position
717 // Skip early pruning when in check
718 ss->staticEval = eval = VALUE_NONE;
722 else if (excludedMove)
724 // Providing the hint that this node's accumulator will be used often brings significant Elo gain (13 Elo)
725 Eval::NNUE::hint_common_parent_position(pos);
726 eval = ss->staticEval;
730 // Never assume anything about values stored in TT
731 ss->staticEval = eval = tte->eval();
732 if (eval == VALUE_NONE)
733 ss->staticEval = eval = evaluate(pos);
735 Eval::NNUE::hint_common_parent_position(pos);
737 // ttValue can be used as a better position evaluation (~7 Elo)
738 if ( ttValue != VALUE_NONE
739 && (tte->bound() & (ttValue > eval ? BOUND_LOWER : BOUND_UPPER)))
744 ss->staticEval = eval = evaluate(pos);
745 // Save static evaluation into the transposition table
746 tte->save(posKey, VALUE_NONE, ss->ttPv, BOUND_NONE, DEPTH_NONE, MOVE_NONE, eval);
749 // Use static evaluation difference to improve quiet move ordering (~4 Elo)
750 if (is_ok((ss-1)->currentMove) && !(ss-1)->inCheck && !priorCapture)
752 int bonus = std::clamp(-18 * int((ss-1)->staticEval + ss->staticEval), -1817, 1817);
753 thisThread->mainHistory[~us][from_to((ss-1)->currentMove)] << bonus;
756 // Set up the improving flag, which is true if current static evaluation is
757 // bigger than the previous static evaluation at our turn (if we were in
758 // check at our previous move we look at static evaluation at move prior to it
759 // and if we were in check at move prior to it flag is set to true) and is
760 // false otherwise. The improving flag is used in various pruning heuristics.
761 improving = (ss-2)->staticEval != VALUE_NONE ? ss->staticEval > (ss-2)->staticEval
762 : (ss-4)->staticEval != VALUE_NONE ? ss->staticEval > (ss-4)->staticEval
765 // Step 7. Razoring (~1 Elo).
766 // If eval is really low check with qsearch if it can exceed alpha, if it can't,
767 // return a fail low.
768 if (eval < alpha - 456 - 252 * depth * depth)
770 value = qsearch<NonPV>(pos, ss, alpha - 1, alpha);
775 // Step 8. Futility pruning: child node (~40 Elo).
776 // The depth condition is important for mate finding.
779 && eval - futility_margin(depth, cutNode && !ss->ttHit, improving) - (ss-1)->statScore / 306 >= beta
781 && eval < 24923) // larger than VALUE_KNOWN_WIN, but smaller than TB wins
784 // Step 9. Null move search with verification search (~35 Elo)
786 && (ss-1)->currentMove != MOVE_NULL
787 && (ss-1)->statScore < 17329
789 && eval >= ss->staticEval
790 && ss->staticEval >= beta - 21 * depth + 258
792 && pos.non_pawn_material(us)
793 && ss->ply >= thisThread->nmpMinPly
794 && beta > VALUE_TB_LOSS_IN_MAX_PLY)
796 assert(eval - beta >= 0);
798 // Null move dynamic reduction based on depth and eval
799 Depth R = std::min(int(eval - beta) / 173, 6) + depth / 3 + 4;
801 ss->currentMove = MOVE_NULL;
802 ss->continuationHistory = &thisThread->continuationHistory[0][0][NO_PIECE][0];
804 pos.do_null_move(st);
806 Value nullValue = -search<NonPV>(pos, ss+1, -beta, -beta+1, depth-R, !cutNode);
808 pos.undo_null_move();
810 if (nullValue >= beta)
812 // Do not return unproven mate or TB scores
813 nullValue = std::min(nullValue, VALUE_TB_WIN_IN_MAX_PLY-1);
815 if (thisThread->nmpMinPly || depth < 14)
818 assert(!thisThread->nmpMinPly); // Recursive verification is not allowed
820 // Do verification search at high depths, with null move pruning disabled
821 // until ply exceeds nmpMinPly.
822 thisThread->nmpMinPly = ss->ply + 3 * (depth-R) / 4;
824 Value v = search<NonPV>(pos, ss, beta-1, beta, depth-R, false);
826 thisThread->nmpMinPly = 0;
833 // Step 10. If the position doesn't have a ttMove, decrease depth by 2
834 // (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).
835 // Use qsearch if depth is equal or below zero (~9 Elo)
838 depth -= 2 + 2 * (ss->ttHit && tte->depth() >= depth);
841 return qsearch<PV>(pos, ss, alpha, beta);
848 probCutBeta = beta + 168 - 61 * improving;
850 // Step 11. ProbCut (~10 Elo)
851 // If we have a good enough capture (or queen promotion) and a reduced search returns a value
852 // much above beta, we can (almost) safely prune the previous move.
855 && abs(beta) < VALUE_TB_WIN_IN_MAX_PLY
856 // If value from transposition table is lower than probCutBeta, don't attempt probCut
857 // there and in further interactions with transposition table cutoff depth is set to depth - 3
858 // because probCut search has depth set to depth - 4 but we also do a move before it
859 // So effective depth is equal to depth - 3
860 && !( tte->depth() >= depth - 3
861 && ttValue != VALUE_NONE
862 && ttValue < probCutBeta))
864 assert(probCutBeta < VALUE_INFINITE);
866 MovePicker mp(pos, ttMove, probCutBeta - ss->staticEval, &captureHistory);
868 while ((move = mp.next_move()) != MOVE_NONE)
869 if (move != excludedMove && pos.legal(move))
871 assert(pos.capture_stage(move));
873 ss->currentMove = move;
874 ss->continuationHistory = &thisThread->continuationHistory[ss->inCheck]
876 [pos.moved_piece(move)]
879 pos.do_move(move, st);
881 // Perform a preliminary qsearch to verify that the move holds
882 value = -qsearch<NonPV>(pos, ss+1, -probCutBeta, -probCutBeta+1);
884 // If the qsearch held, perform the regular search
885 if (value >= probCutBeta)
886 value = -search<NonPV>(pos, ss+1, -probCutBeta, -probCutBeta+1, depth - 4, !cutNode);
890 if (value >= probCutBeta)
892 // Save ProbCut data into transposition table
893 tte->save(posKey, value_to_tt(value, ss->ply), ss->ttPv, BOUND_LOWER, depth - 3, move, ss->staticEval);
898 Eval::NNUE::hint_common_parent_position(pos);
901 moves_loop: // When in check, search starts here
903 // Step 12. A small Probcut idea, when we are in check (~4 Elo)
904 probCutBeta = beta + 413;
908 && (tte->bound() & BOUND_LOWER)
909 && tte->depth() >= depth - 4
910 && ttValue >= probCutBeta
911 && abs(ttValue) <= VALUE_KNOWN_WIN
912 && abs(beta) <= VALUE_KNOWN_WIN)
915 const PieceToHistory* contHist[] = { (ss-1)->continuationHistory, (ss-2)->continuationHistory,
916 nullptr , (ss-4)->continuationHistory,
917 nullptr , (ss-6)->continuationHistory };
919 Move countermove = prevSq != SQ_NONE ? thisThread->counterMoves[pos.piece_on(prevSq)][prevSq] : MOVE_NONE;
921 MovePicker mp(pos, ttMove, depth, &thisThread->mainHistory,
928 moveCountPruning = singularQuietLMR = false;
930 // Indicate PvNodes that will probably fail low if the node was searched
931 // at a depth equal to or greater than the current depth, and the result
932 // of this search was a fail low.
933 bool likelyFailLow = PvNode
935 && (tte->bound() & BOUND_UPPER)
936 && tte->depth() >= depth;
938 // Step 13. Loop through all pseudo-legal moves until no moves remain
939 // or a beta cutoff occurs.
940 while ((move = mp.next_move(moveCountPruning)) != MOVE_NONE)
944 if (move == excludedMove)
947 // At root obey the "searchmoves" option and skip moves not listed in Root
948 // Move List. As a consequence, any illegal move is also skipped. In MultiPV
949 // mode we also skip PV moves that have been already searched and those
950 // of lower "TB rank" if we are in a TB root position.
951 if (rootNode && !std::count(thisThread->rootMoves.begin() + thisThread->pvIdx,
952 thisThread->rootMoves.begin() + thisThread->pvLast, move))
955 // Check for legality
956 if (!rootNode && !pos.legal(move))
959 ss->moveCount = ++moveCount;
961 if (rootNode && thisThread == Threads.main() && Time.elapsed() > 3000)
962 sync_cout << "info depth " << depth
963 << " currmove " << UCI::move(move, pos.is_chess960())
964 << " currmovenumber " << moveCount + thisThread->pvIdx << sync_endl;
966 (ss+1)->pv = nullptr;
969 capture = pos.capture_stage(move);
970 movedPiece = pos.moved_piece(move);
971 givesCheck = pos.gives_check(move);
973 // Calculate new depth for this move
974 newDepth = depth - 1;
976 Value delta = beta - alpha;
978 Depth r = reduction(improving, depth, moveCount, delta, thisThread->rootDelta);
980 // Step 14. Pruning at shallow depth (~120 Elo). Depth conditions are important for mate finding.
982 && pos.non_pawn_material(us)
983 && bestValue > VALUE_TB_LOSS_IN_MAX_PLY)
985 // Skip quiet moves if movecount exceeds our FutilityMoveCount threshold (~8 Elo)
986 moveCountPruning = moveCount >= futility_move_count(improving, depth);
988 // Reduced depth of the next LMR search
989 int lmrDepth = newDepth - r;
994 // Futility pruning for captures (~2 Elo)
998 && ss->staticEval + 197 + 248 * lmrDepth + PieceValue[pos.piece_on(to_sq(move))]
999 + captureHistory[movedPiece][to_sq(move)][type_of(pos.piece_on(to_sq(move)))] / 7 < alpha)
1002 // SEE based pruning for captures and checks (~11 Elo)
1003 if (!pos.see_ge(move, Value(-205) * depth))
1008 int history = (*contHist[0])[movedPiece][to_sq(move)]
1009 + (*contHist[1])[movedPiece][to_sq(move)]
1010 + (*contHist[3])[movedPiece][to_sq(move)];
1012 // Continuation history based pruning (~2 Elo)
1014 && history < -3832 * depth)
1017 history += 2 * thisThread->mainHistory[us][from_to(move)];
1019 lmrDepth += history / 7011;
1020 lmrDepth = std::max(lmrDepth, -2);
1022 // Futility pruning: parent node (~13 Elo)
1025 && ss->staticEval + 112 + 138 * lmrDepth <= alpha)
1028 lmrDepth = std::max(lmrDepth, 0);
1030 // Prune moves with negative SEE (~4 Elo)
1031 if (!pos.see_ge(move, Value(-31 * lmrDepth * lmrDepth)))
1036 // Step 15. Extensions (~100 Elo)
1037 // We take care to not overdo to avoid search getting stuck.
1038 if (ss->ply < thisThread->rootDepth * 2)
1040 // Singular extension search (~94 Elo). If all moves but one fail low on a
1041 // search of (alpha-s, beta-s), and just one fails high on (alpha, beta),
1042 // then that move is singular and should be extended. To verify this we do
1043 // a reduced search on all the other moves but the ttMove and if the result
1044 // is lower than ttValue minus a margin, then we will extend the ttMove. Note
1045 // that depth margin and singularBeta margin are known for having non-linear
1046 // scaling. Their values are optimized to time controls of 180+1.8 and longer
1047 // so changing them requires tests at this type of time controls.
1049 && depth >= 4 - (thisThread->completedDepth > 22) + 2 * (PvNode && tte->is_pv())
1051 && !excludedMove // Avoid recursive singular search
1052 /* && ttValue != VALUE_NONE Already implicit in the next condition */
1053 && abs(ttValue) < VALUE_KNOWN_WIN
1054 && (tte->bound() & BOUND_LOWER)
1055 && tte->depth() >= depth - 3)
1057 Value singularBeta = ttValue - (82 + 65 * (ss->ttPv && !PvNode)) * depth / 64;
1058 Depth singularDepth = (depth - 1) / 2;
1060 ss->excludedMove = move;
1061 value = search<NonPV>(pos, ss, singularBeta - 1, singularBeta, singularDepth, cutNode);
1062 ss->excludedMove = MOVE_NONE;
1064 if (value < singularBeta)
1067 singularQuietLMR = !ttCapture;
1069 // Avoid search explosion by limiting the number of double extensions
1071 && value < singularBeta - 21
1072 && ss->doubleExtensions <= 11)
1075 depth += depth < 13;
1079 // Multi-cut pruning
1080 // Our ttMove is assumed to fail high, and now we failed high also on a
1081 // reduced search without the ttMove. So we assume this expected cut-node
1082 // is not singular, that multiple moves fail high, and we can prune the
1083 // whole subtree by returning a softbound.
1084 else if (singularBeta >= beta)
1085 return singularBeta;
1087 // If the eval of ttMove is greater than beta, we reduce it (negative extension) (~7 Elo)
1088 else if (ttValue >= beta)
1089 extension = -2 - !PvNode;
1091 // If we are on a cutNode, reduce it based on depth (negative extension) (~1 Elo)
1093 extension = depth < 17 ? -3 : -1;
1095 // If the eval of ttMove is less than value, we reduce it (negative extension) (~1 Elo)
1096 else if (ttValue <= value)
1100 // Check extensions (~1 Elo)
1101 else if ( givesCheck
1105 // Quiet ttMove extensions (~1 Elo)
1108 && move == ss->killers[0]
1109 && (*contHist[0])[movedPiece][to_sq(move)] >= 5168)
1113 // Add extension to new depth
1114 newDepth += extension;
1115 ss->doubleExtensions = (ss-1)->doubleExtensions + (extension == 2);
1117 // Speculative prefetch as early as possible
1118 prefetch(TT.first_entry(pos.key_after(move)));
1120 // Update the current move (this must be done after singular extension search)
1121 ss->currentMove = move;
1122 ss->continuationHistory = &thisThread->continuationHistory[ss->inCheck]
1127 // Step 16. Make the move
1128 pos.do_move(move, st, givesCheck);
1130 // Decrease reduction if position is or has been on the PV and not likely to fail low. (~3 Elo)
1131 // Decrease further on cutNodes. (~1 Elo)
1134 r -= cutNode && tte->depth() >= depth ? 3 : 2;
1136 // Decrease reduction if opponent's move count is high (~1 Elo)
1137 if ((ss-1)->moveCount > 8)
1140 // Increase reduction for cut nodes (~3 Elo)
1144 // Increase reduction if ttMove is a capture (~3 Elo)
1148 // Decrease reduction for PvNodes (~2 Elo)
1152 // Decrease reduction if ttMove has been singularly extended (~1 Elo)
1153 if (singularQuietLMR)
1156 // Increase reduction on repetition (~1 Elo)
1157 if ( move == (ss-4)->currentMove
1158 && pos.has_repeated())
1161 // Increase reduction if next ply has a lot of fail high (~5 Elo)
1162 if ((ss+1)->cutoffCnt > 3)
1165 // Decrease reduction for first generated move (ttMove)
1166 else if (move == ttMove)
1169 ss->statScore = 2 * thisThread->mainHistory[us][from_to(move)]
1170 + (*contHist[0])[movedPiece][to_sq(move)]
1171 + (*contHist[1])[movedPiece][to_sq(move)]
1172 + (*contHist[3])[movedPiece][to_sq(move)]
1175 // Decrease/increase reduction for moves with a good/bad history (~25 Elo)
1176 r -= ss->statScore / (11124 + 4740 * (depth > 5 && depth < 22));
1178 // Step 17. Late moves reduction / extension (LMR, ~117 Elo)
1179 // We use various heuristics for the sons of a node after the first son has
1180 // been searched. In general, we would like to reduce them, but there are many
1181 // cases where we extend a son if it has good chances to be "interesting".
1183 && moveCount > 1 + (PvNode && ss->ply <= 1)
1186 || (cutNode && (ss-1)->moveCount > 1)))
1188 // In general we want to cap the LMR depth search at newDepth, but when
1189 // reduction is negative, we allow this move a limited search extension
1190 // beyond the first move depth. This may lead to hidden double extensions.
1191 Depth d = std::clamp(newDepth - r, 1, newDepth + 1);
1193 value = -search<NonPV>(pos, ss+1, -(alpha+1), -alpha, d, true);
1195 // Do a full-depth search when reduced LMR search fails high
1196 if (value > alpha && d < newDepth)
1198 // Adjust full-depth search based on LMR results - if the result
1199 // was good enough search deeper, if it was bad enough search shallower
1200 const bool doDeeperSearch = value > (bestValue + 64 + 11 * (newDepth - d));
1201 const bool doEvenDeeperSearch = value > alpha + 711 && ss->doubleExtensions <= 6;
1202 const bool doShallowerSearch = value < bestValue + newDepth;
1204 ss->doubleExtensions = ss->doubleExtensions + doEvenDeeperSearch;
1206 newDepth += doDeeperSearch - doShallowerSearch + doEvenDeeperSearch;
1209 value = -search<NonPV>(pos, ss+1, -(alpha+1), -alpha, newDepth, !cutNode);
1211 int bonus = value <= alpha ? -stat_bonus(newDepth)
1212 : value >= beta ? stat_bonus(newDepth)
1215 update_continuation_histories(ss, movedPiece, to_sq(move), bonus);
1219 // Step 18. Full-depth search when LMR is skipped. If expected reduction is high, reduce its depth by 1.
1220 else if (!PvNode || moveCount > 1)
1222 // Increase reduction for cut nodes and not ttMove (~1 Elo)
1223 if (!ttMove && cutNode)
1226 value = -search<NonPV>(pos, ss+1, -(alpha+1), -alpha, newDepth - (r > 3), !cutNode);
1229 // For PV nodes only, do a full PV search on the first move or after a fail high,
1230 // otherwise let the parent node fail low with value <= alpha and try another move.
1231 if (PvNode && (moveCount == 1 || value > alpha))
1234 (ss+1)->pv[0] = MOVE_NONE;
1236 value = -search<PV>(pos, ss+1, -beta, -alpha, newDepth, false);
1239 // Step 19. Undo move
1240 pos.undo_move(move);
1242 assert(value > -VALUE_INFINITE && value < VALUE_INFINITE);
1244 // Step 20. Check for a new best move
1245 // Finished searching the move. If a stop occurred, the return value of
1246 // the search cannot be trusted, and we return immediately without
1247 // updating best move, PV and TT.
1248 if (Threads.stop.load(std::memory_order_relaxed))
1253 RootMove& rm = *std::find(thisThread->rootMoves.begin(),
1254 thisThread->rootMoves.end(), move);
1256 rm.averageScore = rm.averageScore != -VALUE_INFINITE ? (2 * value + rm.averageScore) / 3 : value;
1258 // PV move or new best move?
1259 if (moveCount == 1 || value > alpha)
1261 rm.score = rm.uciScore = value;
1262 rm.selDepth = thisThread->selDepth;
1263 rm.scoreLowerbound = rm.scoreUpperbound = false;
1267 rm.scoreLowerbound = true;
1270 else if (value <= alpha)
1272 rm.scoreUpperbound = true;
1273 rm.uciScore = alpha;
1280 for (Move* m = (ss+1)->pv; *m != MOVE_NONE; ++m)
1281 rm.pv.push_back(*m);
1283 // We record how often the best move has been changed in each iteration.
1284 // This information is used for time management. In MultiPV mode,
1285 // we must take care to only do this for the first PV line.
1287 && !thisThread->pvIdx)
1288 ++thisThread->bestMoveChanges;
1291 // All other moves but the PV, are set to the lowest value: this
1292 // is not a problem when sorting because the sort is stable and the
1293 // move position in the list is preserved - just the PV is pushed up.
1294 rm.score = -VALUE_INFINITE;
1297 if (value > bestValue)
1305 if (PvNode && !rootNode) // Update pv even in fail-high case
1306 update_pv(ss->pv, move, (ss+1)->pv);
1310 ss->cutoffCnt += 1 + !ttMove;
1311 assert(value >= beta); // Fail high
1316 // Reduce other moves if we have found at least one score improvement (~2 Elo)
1324 alpha = value; // Update alpha! Always alpha < beta
1330 // If the move is worse than some previously searched move, remember it, to update its stats later
1331 if (move != bestMove)
1333 if (capture && captureCount < 32)
1334 capturesSearched[captureCount++] = move;
1336 else if (!capture && quietCount < 64)
1337 quietsSearched[quietCount++] = move;
1341 // The following condition would detect a stop only after move loop has been
1342 // completed. But in this case, bestValue is valid because we have fully
1343 // searched our subtree, and we can anyhow save the result in TT.
1349 // Step 21. Check for mate and stalemate
1350 // All legal moves have been searched and if there are no legal moves, it
1351 // must be a mate or a stalemate. If we are in a singular extension search then
1352 // return a fail low score.
1354 assert(moveCount || !ss->inCheck || excludedMove || !MoveList<LEGAL>(pos).size());
1357 bestValue = excludedMove ? alpha :
1358 ss->inCheck ? mated_in(ss->ply)
1361 // If there is a move that produces search value greater than alpha we update the stats of searched moves
1363 update_all_stats(pos, ss, bestMove, bestValue, beta, prevSq,
1364 quietsSearched, quietCount, capturesSearched, captureCount, depth);
1366 // Bonus for prior countermove that caused the fail low
1367 else if (!priorCapture && prevSq != SQ_NONE)
1369 int bonus = (depth > 5) + (PvNode || cutNode) + (bestValue < alpha - 800) + ((ss-1)->moveCount > 12);
1370 update_continuation_histories(ss-1, pos.piece_on(prevSq), prevSq, stat_bonus(depth) * bonus);
1371 thisThread->mainHistory[~us][from_to((ss-1)->currentMove)] << stat_bonus(depth) * bonus / 2;
1375 bestValue = std::min(bestValue, maxValue);
1377 // If no good move is found and the previous position was ttPv, then the previous
1378 // opponent move is probably good and the new position is added to the search tree. (~7 Elo)
1379 if (bestValue <= alpha)
1380 ss->ttPv = ss->ttPv || ((ss-1)->ttPv && depth > 3);
1382 // Write gathered information in transposition table
1383 if (!excludedMove && !(rootNode && thisThread->pvIdx))
1384 tte->save(posKey, value_to_tt(bestValue, ss->ply), ss->ttPv,
1385 bestValue >= beta ? BOUND_LOWER :
1386 PvNode && bestMove ? BOUND_EXACT : BOUND_UPPER,
1387 depth, bestMove, ss->staticEval);
1389 assert(bestValue > -VALUE_INFINITE && bestValue < VALUE_INFINITE);
1395 // qsearch() is the quiescence search function, which is called by the main search
1396 // function with zero depth, or recursively with further decreasing depth per call.
1398 template <NodeType nodeType>
1399 Value qsearch(Position& pos, Stack* ss, Value alpha, Value beta, Depth depth) {
1401 static_assert(nodeType != Root);
1402 constexpr bool PvNode = nodeType == PV;
1404 assert(alpha >= -VALUE_INFINITE && alpha < beta && beta <= VALUE_INFINITE);
1405 assert(PvNode || (alpha == beta - 1));
1408 // Check if we have an upcoming move that draws by repetition, or
1409 // if the opponent had an alternative move earlier to this position.
1410 if ( alpha < VALUE_DRAW
1411 && pos.has_game_cycle(ss->ply))
1413 alpha = value_draw(pos.this_thread());
1420 ASSERT_ALIGNED(&st, Eval::NNUE::CacheLineSize);
1424 Move ttMove, move, bestMove;
1426 Value bestValue, value, ttValue, futilityValue, futilityBase;
1427 bool pvHit, givesCheck, capture;
1430 // Step 1. Initialize node
1434 ss->pv[0] = MOVE_NONE;
1437 Thread* thisThread = pos.this_thread();
1438 bestMove = MOVE_NONE;
1439 ss->inCheck = pos.checkers();
1442 // Step 2. Check for an immediate draw or maximum ply reached
1443 if ( pos.is_draw(ss->ply)
1444 || ss->ply >= MAX_PLY)
1445 return (ss->ply >= MAX_PLY && !ss->inCheck) ? evaluate(pos) : VALUE_DRAW;
1447 assert(0 <= ss->ply && ss->ply < MAX_PLY);
1449 // Decide whether or not to include checks: this fixes also the type of
1450 // TT entry depth that we are going to use. Note that in qsearch we use
1451 // only two types of depth in TT: DEPTH_QS_CHECKS or DEPTH_QS_NO_CHECKS.
1452 ttDepth = ss->inCheck || depth >= DEPTH_QS_CHECKS ? DEPTH_QS_CHECKS
1453 : DEPTH_QS_NO_CHECKS;
1455 // Step 3. Transposition table lookup
1457 tte = TT.probe(posKey, ss->ttHit);
1458 ttValue = ss->ttHit ? value_from_tt(tte->value(), ss->ply, pos.rule50_count()) : VALUE_NONE;
1459 ttMove = ss->ttHit ? tte->move() : MOVE_NONE;
1460 pvHit = ss->ttHit && tte->is_pv();
1462 // At non-PV nodes we check for an early TT cutoff
1464 && tte->depth() >= ttDepth
1465 && ttValue != VALUE_NONE // Only in case of TT access race or if !ttHit
1466 && (tte->bound() & (ttValue >= beta ? BOUND_LOWER : BOUND_UPPER)))
1469 // Step 4. Static evaluation of the position
1471 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 = (ss-1)->currentMove != MOVE_NULL ? evaluate(pos)
1488 : -(ss-1)->staticEval;
1490 // Stand pat. Return immediately if static value is at least beta
1491 if (bestValue >= beta)
1493 // Save gathered info in transposition table
1495 tte->save(posKey, value_to_tt(bestValue, ss->ply), false, BOUND_LOWER,
1496 DEPTH_NONE, MOVE_NONE, ss->staticEval);
1501 if (bestValue > alpha)
1504 futilityBase = std::min(ss->staticEval, bestValue) + 200;
1507 const PieceToHistory* contHist[] = { (ss-1)->continuationHistory, (ss-2)->continuationHistory,
1508 nullptr , (ss-4)->continuationHistory,
1509 nullptr , (ss-6)->continuationHistory };
1511 // Initialize a MovePicker object for the current position, and prepare
1512 // to search the moves. Because the depth is <= 0 here, only captures,
1513 // queen promotions, and other checks (only if depth >= DEPTH_QS_CHECKS)
1514 // will be generated.
1515 Square prevSq = is_ok((ss-1)->currentMove) ? to_sq((ss-1)->currentMove) : SQ_NONE;
1516 MovePicker mp(pos, ttMove, depth, &thisThread->mainHistory,
1517 &thisThread->captureHistory,
1521 int quietCheckEvasions = 0;
1523 // Step 5. Loop through all pseudo-legal moves until no moves remain
1524 // or a beta cutoff occurs.
1525 while ((move = mp.next_move()) != MOVE_NONE)
1527 assert(is_ok(move));
1529 // Check for legality
1530 if (!pos.legal(move))
1533 givesCheck = pos.gives_check(move);
1534 capture = pos.capture_stage(move);
1539 if (bestValue > VALUE_TB_LOSS_IN_MAX_PLY)
1541 // Futility pruning and moveCount pruning (~10 Elo)
1543 && to_sq(move) != prevSq
1544 && futilityBase > -VALUE_KNOWN_WIN
1545 && type_of(move) != PROMOTION)
1550 futilityValue = futilityBase + PieceValue[pos.piece_on(to_sq(move))];
1552 // If static eval + value of piece we are going to capture is much lower
1553 // than alpha we can prune this move
1554 if (futilityValue <= alpha)
1556 bestValue = std::max(bestValue, futilityValue);
1560 // If static eval is much lower than alpha and move is not winning material
1561 // we can prune this move
1562 if (futilityBase <= alpha && !pos.see_ge(move, VALUE_ZERO + 1))
1564 bestValue = std::max(bestValue, futilityBase);
1568 // If static exchange evaluation is much worse than what is needed to not
1569 // fall below alpha we can prune this move
1570 if (futilityBase > alpha && !pos.see_ge(move, (alpha - futilityBase) * 4))
1577 // We prune after the second quiet check evasion move, where being 'in check' is
1578 // implicitly checked through the counter, and being a 'quiet move' apart from
1579 // being a tt move is assumed after an increment because captures are pushed ahead.
1580 if (quietCheckEvasions > 1)
1583 // Continuation history based pruning (~3 Elo)
1585 && (*contHist[0])[pos.moved_piece(move)][to_sq(move)] < 0
1586 && (*contHist[1])[pos.moved_piece(move)][to_sq(move)] < 0)
1589 // Do not search moves with bad enough SEE values (~5 Elo)
1590 if (!pos.see_ge(move, Value(-95)))
1594 // Speculative prefetch as early as possible
1595 prefetch(TT.first_entry(pos.key_after(move)));
1597 // Update the current move
1598 ss->currentMove = move;
1599 ss->continuationHistory = &thisThread->continuationHistory[ss->inCheck]
1601 [pos.moved_piece(move)]
1604 quietCheckEvasions += !capture && ss->inCheck;
1606 // Step 7. Make and search the move
1607 pos.do_move(move, st, givesCheck);
1608 value = -qsearch<nodeType>(pos, ss+1, -beta, -alpha, depth - 1);
1609 pos.undo_move(move);
1611 assert(value > -VALUE_INFINITE && value < VALUE_INFINITE);
1613 // Step 8. Check for a new best move
1614 if (value > bestValue)
1622 if (PvNode) // Update pv even in fail-high case
1623 update_pv(ss->pv, move, (ss+1)->pv);
1625 if (value < beta) // Update alpha here!
1633 // Step 9. Check for mate
1634 // All legal moves have been searched. A special case: if we're in check
1635 // and no legal moves were found, it is checkmate.
1636 if (ss->inCheck && bestValue == -VALUE_INFINITE)
1638 assert(!MoveList<LEGAL>(pos).size());
1640 return mated_in(ss->ply); // Plies to mate from the root
1643 // Save gathered info in transposition table
1644 tte->save(posKey, value_to_tt(bestValue, ss->ply), pvHit,
1645 bestValue >= beta ? BOUND_LOWER : BOUND_UPPER,
1646 ttDepth, bestMove, ss->staticEval);
1648 assert(bestValue > -VALUE_INFINITE && bestValue < VALUE_INFINITE);
1654 // value_to_tt() adjusts a mate or TB score from "plies to mate from the root" to
1655 // "plies to mate from the current position". Standard scores are unchanged.
1656 // The function is called before storing a value in the transposition table.
1658 Value value_to_tt(Value v, int ply) {
1660 assert(v != VALUE_NONE);
1662 return v >= VALUE_TB_WIN_IN_MAX_PLY ? v + ply
1663 : v <= VALUE_TB_LOSS_IN_MAX_PLY ? v - ply : v;
1667 // value_from_tt() is the inverse of value_to_tt(): it adjusts a mate or TB score
1668 // from the transposition table (which refers to the plies to mate/be mated from
1669 // current position) to "plies to mate/be mated (TB win/loss) from the root". However,
1670 // for mate scores, to avoid potentially false mate scores related to the 50 moves rule
1671 // and the graph history interaction, we return an optimal TB score instead.
1673 Value value_from_tt(Value v, int ply, int r50c) {
1675 if (v == VALUE_NONE)
1678 if (v >= VALUE_TB_WIN_IN_MAX_PLY) // TB win or better
1680 if (v >= VALUE_MATE_IN_MAX_PLY && VALUE_MATE - v > 99 - r50c)
1681 return VALUE_MATE_IN_MAX_PLY - 1; // do not return a potentially false mate score
1686 if (v <= VALUE_TB_LOSS_IN_MAX_PLY) // TB loss or worse
1688 if (v <= VALUE_MATED_IN_MAX_PLY && VALUE_MATE + v > 99 - r50c)
1689 return VALUE_MATED_IN_MAX_PLY + 1; // do not return a potentially false mate score
1698 // update_pv() adds current move and appends child pv[]
1700 void update_pv(Move* pv, Move move, const Move* childPv) {
1702 for (*pv++ = move; childPv && *childPv != MOVE_NONE; )
1708 // update_all_stats() updates stats at the end of search() when a bestMove is found
1710 void update_all_stats(const Position& pos, Stack* ss, Move bestMove, Value bestValue, Value beta, Square prevSq,
1711 Move* quietsSearched, int quietCount, Move* capturesSearched, int captureCount, Depth depth) {
1713 Color us = pos.side_to_move();
1714 Thread* thisThread = pos.this_thread();
1715 CapturePieceToHistory& captureHistory = thisThread->captureHistory;
1716 Piece moved_piece = pos.moved_piece(bestMove);
1719 int quietMoveBonus = stat_bonus(depth + 1);
1721 if (!pos.capture_stage(bestMove))
1723 int bestMoveBonus = bestValue > beta + 145 ? quietMoveBonus // larger bonus
1724 : stat_bonus(depth); // smaller bonus
1726 // Increase stats for the best move in case it was a quiet move
1727 update_quiet_stats(pos, ss, bestMove, bestMoveBonus);
1729 // Decrease stats for all non-best quiet moves
1730 for (int i = 0; i < quietCount; ++i)
1732 thisThread->mainHistory[us][from_to(quietsSearched[i])] << -bestMoveBonus;
1733 update_continuation_histories(ss, pos.moved_piece(quietsSearched[i]), to_sq(quietsSearched[i]), -bestMoveBonus);
1738 // Increase stats for the best move in case it was a capture move
1739 captured = type_of(pos.piece_on(to_sq(bestMove)));
1740 captureHistory[moved_piece][to_sq(bestMove)][captured] << quietMoveBonus;
1743 // Extra penalty for a quiet early move that was not a TT move or
1744 // main killer move in previous ply when it gets refuted.
1745 if ( prevSq != SQ_NONE
1746 && ((ss-1)->moveCount == 1 + (ss-1)->ttHit || ((ss-1)->currentMove == (ss-1)->killers[0]))
1747 && !pos.captured_piece())
1748 update_continuation_histories(ss-1, pos.piece_on(prevSq), prevSq, -quietMoveBonus);
1750 // Decrease stats for all non-best capture moves
1751 for (int i = 0; i < captureCount; ++i)
1753 moved_piece = pos.moved_piece(capturesSearched[i]);
1754 captured = type_of(pos.piece_on(to_sq(capturesSearched[i])));
1755 captureHistory[moved_piece][to_sq(capturesSearched[i])][captured] << -quietMoveBonus;
1760 // update_continuation_histories() updates histories of the move pairs formed
1761 // by moves at ply -1, -2, -4, and -6 with current move.
1763 void update_continuation_histories(Stack* ss, Piece pc, Square to, int bonus) {
1765 for (int i : {1, 2, 4, 6})
1767 // Only update the first 2 continuation histories if we are in check
1768 if (ss->inCheck && i > 2)
1770 if (is_ok((ss-i)->currentMove))
1771 (*(ss-i)->continuationHistory)[pc][to] << bonus;
1776 // update_quiet_stats() updates move sorting heuristics
1778 void update_quiet_stats(const Position& pos, Stack* ss, Move move, int bonus) {
1781 if (ss->killers[0] != move)
1783 ss->killers[1] = ss->killers[0];
1784 ss->killers[0] = move;
1787 Color us = pos.side_to_move();
1788 Thread* thisThread = pos.this_thread();
1789 thisThread->mainHistory[us][from_to(move)] << bonus;
1790 update_continuation_histories(ss, pos.moved_piece(move), to_sq(move), bonus);
1792 // Update countermove history
1793 if (is_ok((ss-1)->currentMove))
1795 Square prevSq = to_sq((ss-1)->currentMove);
1796 thisThread->counterMoves[pos.piece_on(prevSq)][prevSq] = move;
1800 // When playing with strength handicap, choose the best move among a set of RootMoves
1801 // using a statistical rule dependent on 'level'. Idea by Heinz van Saanen.
1803 Move Skill::pick_best(size_t multiPV) {
1805 const RootMoves& rootMoves = Threads.main()->rootMoves;
1806 static PRNG rng(now()); // PRNG sequence should be non-deterministic
1808 // RootMoves are already sorted by score in descending order
1809 Value topScore = rootMoves[0].score;
1810 int delta = std::min(topScore - rootMoves[multiPV - 1].score, PawnValue);
1811 int maxScore = -VALUE_INFINITE;
1812 double weakness = 120 - 2 * level;
1814 // Choose best move. For each move score we add two terms, both dependent on
1815 // weakness. One is deterministic and bigger for weaker levels, and one is
1816 // random. Then we choose the move with the resulting highest score.
1817 for (size_t i = 0; i < multiPV; ++i)
1819 // This is our magic formula
1820 int push = int(( weakness * int(topScore - rootMoves[i].score)
1821 + delta * (rng.rand<unsigned>() % int(weakness))) / 128);
1823 if (rootMoves[i].score + push >= maxScore)
1825 maxScore = rootMoves[i].score + push;
1826 best = rootMoves[i].pv[0];
1836 /// MainThread::check_time() is used to print debug info and, more importantly,
1837 /// to detect when we are out of available time and thus stop the search.
1839 void MainThread::check_time() {
1844 // When using nodes, ensure checking rate is not lower than 0.1% of nodes
1845 callsCnt = Limits.nodes ? std::min(512, int(Limits.nodes / 1024)) : 512;
1847 static TimePoint lastInfoTime = now();
1849 TimePoint elapsed = Time.elapsed();
1850 TimePoint tick = Limits.startTime + elapsed;
1852 if (tick - lastInfoTime >= 1000)
1854 lastInfoTime = tick;
1858 // We should not stop pondering until told so by the GUI
1862 if ( (Limits.use_time_management() && (elapsed > Time.maximum() || stopOnPonderhit))
1863 || (Limits.movetime && elapsed >= Limits.movetime)
1864 || (Limits.nodes && Threads.nodes_searched() >= uint64_t(Limits.nodes)))
1865 Threads.stop = true;
1869 /// UCI::pv() formats PV information according to the UCI protocol. UCI requires
1870 /// that all (if any) unsearched PV lines are sent using a previous search score.
1872 string UCI::pv(const Position& pos, Depth depth) {
1874 std::stringstream ss;
1875 TimePoint elapsed = Time.elapsed() + 1;
1876 const RootMoves& rootMoves = pos.this_thread()->rootMoves;
1877 size_t pvIdx = pos.this_thread()->pvIdx;
1878 size_t multiPV = std::min(size_t(Options["MultiPV"]), rootMoves.size());
1879 uint64_t nodesSearched = Threads.nodes_searched();
1880 uint64_t tbHits = Threads.tb_hits() + (TB::RootInTB ? rootMoves.size() : 0);
1882 for (size_t i = 0; i < multiPV; ++i)
1884 bool updated = rootMoves[i].score != -VALUE_INFINITE;
1886 if (depth == 1 && !updated && i > 0)
1889 Depth d = updated ? depth : std::max(1, depth - 1);
1890 Value v = updated ? rootMoves[i].uciScore : rootMoves[i].previousScore;
1892 if (v == -VALUE_INFINITE)
1895 bool tb = TB::RootInTB && abs(v) < VALUE_MATE_IN_MAX_PLY;
1896 v = tb ? rootMoves[i].tbScore : v;
1898 if (ss.rdbuf()->in_avail()) // Not at first line
1903 << " seldepth " << rootMoves[i].selDepth
1904 << " multipv " << i + 1
1905 << " score " << UCI::value(v);
1907 if (Options["UCI_ShowWDL"])
1908 ss << UCI::wdl(v, pos.game_ply());
1910 if (i == pvIdx && !tb && updated) // tablebase- and previous-scores are exact
1911 ss << (rootMoves[i].scoreLowerbound ? " lowerbound" : (rootMoves[i].scoreUpperbound ? " upperbound" : ""));
1913 ss << " nodes " << nodesSearched
1914 << " nps " << nodesSearched * 1000 / elapsed
1915 << " hashfull " << TT.hashfull()
1916 << " tbhits " << tbHits
1917 << " time " << elapsed
1920 for (Move m : rootMoves[i].pv)
1921 ss << " " << UCI::move(m, pos.is_chess960());
1928 /// RootMove::extract_ponder_from_tt() is called in case we have no ponder move
1929 /// before exiting the search, for instance, in case we stop the search during a
1930 /// fail high at root. We try hard to have a ponder move to return to the GUI,
1931 /// otherwise in case of 'ponder on' we have nothing to think about.
1933 bool RootMove::extract_ponder_from_tt(Position& pos) {
1936 ASSERT_ALIGNED(&st, Eval::NNUE::CacheLineSize);
1940 assert(pv.size() == 1);
1942 if (pv[0] == MOVE_NONE)
1945 pos.do_move(pv[0], st);
1946 TTEntry* tte = TT.probe(pos.key(), ttHit);
1950 Move m = tte->move(); // Local copy to be SMP safe
1951 if (MoveList<LEGAL>(pos).contains(m))
1955 pos.undo_move(pv[0]);
1956 return pv.size() > 1;
1959 void Tablebases::rank_root_moves(Position& pos, Search::RootMoves& rootMoves) {
1962 UseRule50 = bool(Options["Syzygy50MoveRule"]);
1963 ProbeDepth = int(Options["SyzygyProbeDepth"]);
1964 Cardinality = int(Options["SyzygyProbeLimit"]);
1965 bool dtz_available = true;
1967 // Tables with fewer pieces than SyzygyProbeLimit are searched with
1968 // ProbeDepth == DEPTH_ZERO
1969 if (Cardinality > MaxCardinality)
1971 Cardinality = MaxCardinality;
1975 if (Cardinality >= popcount(pos.pieces()) && !pos.can_castle(ANY_CASTLING))
1977 // Rank moves using DTZ tables
1978 RootInTB = root_probe(pos, rootMoves);
1982 // DTZ tables are missing; try to rank moves using WDL tables
1983 dtz_available = false;
1984 RootInTB = root_probe_wdl(pos, rootMoves);
1990 // Sort moves according to TB rank
1991 std::stable_sort(rootMoves.begin(), rootMoves.end(),
1992 [](const RootMove &a, const RootMove &b) { return a.tbRank > b.tbRank; } );
1994 // Probe during search only if DTZ is not available and we are winning
1995 if (dtz_available || rootMoves[0].tbScore <= VALUE_DRAW)
2000 // Clean up if root_probe() and root_probe_wdl() have failed
2001 for (auto& m : rootMoves)
2006 } // namespace Stockfish