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 = delta = alpha = -VALUE_INFINITE;
292 beta = VALUE_INFINITE;
293 optimism[WHITE] = optimism[BLACK] = VALUE_ZERO;
298 if (!rootPos.checkers())
301 Eval::evaluate(rootPos, &rootComplexity);
302 mainThread->complexity = std::min(1.03 + (rootComplexity - 241) / 1552.0, 1.45);
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 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
362 Value prev = rootMoves[pvIdx].averageScore;
363 delta = Value(10) + int(prev) * prev / 16502;
364 alpha = std::max(prev - delta,-VALUE_INFINITE);
365 beta = std::min(prev + delta, VALUE_INFINITE);
367 // Adjust optimism based on root move's previousScore
368 int opt = 120 * prev / (std::abs(prev) + 161);
369 optimism[ us] = Value(opt);
370 optimism[~us] = -optimism[us];
373 // Start with a small aspiration window and, in the case of a fail
374 // high/low, re-search with a bigger window until we don't fail
376 int failedHighCnt = 0;
379 // Adjust the effective depth searched, but ensuring at least one effective increment for every
380 // four searchAgain steps (see issue #2717).
381 Depth adjustedDepth = std::max(1, rootDepth - failedHighCnt - 3 * (searchAgainCounter + 1) / 4);
382 bestValue = Stockfish::search<Root>(rootPos, ss, alpha, beta, adjustedDepth, false);
384 // Bring the best move to the front. It is critical that sorting
385 // is done with a stable algorithm because all the values but the
386 // first and eventually the new best one are set to -VALUE_INFINITE
387 // and we want to keep the same order for all the moves except the
388 // new PV that goes to the front. Note that in case of MultiPV
389 // search the already searched PV lines are preserved.
390 std::stable_sort(rootMoves.begin() + pvIdx, rootMoves.begin() + pvLast);
392 // If search has been stopped, we break immediately. Sorting is
393 // safe because RootMoves is still valid, although it refers to
394 // the previous iteration.
398 // When failing high/low give some update (without cluttering
399 // the UI) before a re-search.
402 && (bestValue <= alpha || bestValue >= beta)
403 && Time.elapsed() > 3000)
404 sync_cout << UCI::pv(rootPos, rootDepth) << sync_endl;
406 // In case of failing low/high increase aspiration window and
407 // re-search, otherwise exit the loop.
408 if (bestValue <= alpha)
410 beta = (alpha + beta) / 2;
411 alpha = std::max(bestValue - delta, -VALUE_INFINITE);
415 mainThread->stopOnPonderhit = false;
417 else if (bestValue >= beta)
419 beta = std::min(bestValue + delta, VALUE_INFINITE);
425 delta += delta / 4 + 2;
427 assert(alpha >= -VALUE_INFINITE && beta <= VALUE_INFINITE);
430 // Sort the PV lines searched so far and update the GUI
431 std::stable_sort(rootMoves.begin() + pvFirst, rootMoves.begin() + pvIdx + 1);
434 && (Threads.stop || pvIdx + 1 == multiPV || Time.elapsed() > 3000))
435 sync_cout << UCI::pv(rootPos, rootDepth) << sync_endl;
439 completedDepth = rootDepth;
441 if (rootMoves[0].pv[0] != lastBestMove)
443 lastBestMove = rootMoves[0].pv[0];
444 lastBestMoveDepth = rootDepth;
447 // Have we found a "mate in x"?
449 && bestValue >= VALUE_MATE_IN_MAX_PLY
450 && VALUE_MATE - bestValue <= 2 * Limits.mate)
456 // If skill level is enabled and time is up, pick a sub-optimal best move
457 if (skill.enabled() && skill.time_to_pick(rootDepth))
458 skill.pick_best(multiPV);
460 // Use part of the gained time from a previous stable move for the current move
461 for (Thread* th : Threads)
463 totBestMoveChanges += th->bestMoveChanges;
464 th->bestMoveChanges = 0;
467 // Do we have time for the next iteration? Can we stop searching now?
468 if ( Limits.use_time_management()
470 && !mainThread->stopOnPonderhit)
472 double fallingEval = (69 + 13 * (mainThread->bestPreviousAverageScore - bestValue)
473 + 6 * (mainThread->iterValue[iterIdx] - bestValue)) / 619.6;
474 fallingEval = std::clamp(fallingEval, 0.5, 1.5);
476 // If the bestMove is stable over several iterations, reduce time accordingly
477 timeReduction = lastBestMoveDepth + 8 < completedDepth ? 1.57 : 0.65;
478 double reduction = (1.4 + mainThread->previousTimeReduction) / (2.08 * timeReduction);
479 double bestMoveInstability = 1 + 1.8 * totBestMoveChanges / Threads.size();
481 double totalTime = Time.optimum() * fallingEval * reduction * bestMoveInstability * mainThread->complexity;
483 // Cap used time in case of a single legal move for a better viewer experience in tournaments
484 // yielding correct scores and sufficiently fast moves.
485 if (rootMoves.size() == 1)
486 totalTime = std::min(500.0, totalTime);
488 // Stop the search if we have exceeded the totalTime
489 if (Time.elapsed() > totalTime)
491 // If we are allowed to ponder do not stop the search now but
492 // keep pondering until the GUI sends "ponderhit" or "stop".
493 if (mainThread->ponder)
494 mainThread->stopOnPonderhit = true;
498 else if ( !mainThread->ponder
499 && Time.elapsed() > totalTime * 0.50)
500 Threads.increaseDepth = false;
502 Threads.increaseDepth = true;
505 mainThread->iterValue[iterIdx] = bestValue;
506 iterIdx = (iterIdx + 1) & 3;
512 mainThread->previousTimeReduction = timeReduction;
514 // If skill level is enabled, swap best PV line with the sub-optimal one
516 std::swap(rootMoves[0], *std::find(rootMoves.begin(), rootMoves.end(),
517 skill.best ? skill.best : skill.pick_best(multiPV)));
523 // search<>() is the main search function for both PV and non-PV nodes
525 template <NodeType nodeType>
526 Value search(Position& pos, Stack* ss, Value alpha, Value beta, Depth depth, bool cutNode) {
528 constexpr bool PvNode = nodeType != NonPV;
529 constexpr bool rootNode = nodeType == Root;
531 // Check if we have an upcoming move which draws by repetition, or
532 // if the opponent had an alternative move earlier to this position.
534 && pos.rule50_count() >= 3
535 && alpha < VALUE_DRAW
536 && pos.has_game_cycle(ss->ply))
538 alpha = value_draw(pos.this_thread());
543 // Dive into quiescence search when the depth reaches zero
545 return qsearch<PvNode ? PV : NonPV>(pos, ss, alpha, beta);
547 assert(-VALUE_INFINITE <= alpha && alpha < beta && beta <= VALUE_INFINITE);
548 assert(PvNode || (alpha == beta - 1));
549 assert(0 < depth && depth < MAX_PLY);
550 assert(!(PvNode && cutNode));
552 Move pv[MAX_PLY+1], capturesSearched[32], quietsSearched[64];
554 ASSERT_ALIGNED(&st, Eval::NNUE::CacheLineSize);
558 Move ttMove, move, excludedMove, bestMove;
559 Depth extension, newDepth;
560 Value bestValue, value, ttValue, eval, maxValue, probCutBeta;
561 bool givesCheck, improving, priorCapture, singularQuietLMR;
562 bool capture, moveCountPruning, ttCapture;
564 int moveCount, captureCount, quietCount, improvement, complexity;
566 // Step 1. Initialize node
567 Thread* thisThread = pos.this_thread();
568 ss->inCheck = pos.checkers();
569 priorCapture = pos.captured_piece();
570 Color us = pos.side_to_move();
571 moveCount = captureCount = quietCount = ss->moveCount = 0;
572 bestValue = -VALUE_INFINITE;
573 maxValue = VALUE_INFINITE;
575 // Check for the available remaining time
576 if (thisThread == Threads.main())
577 static_cast<MainThread*>(thisThread)->check_time();
579 // Used to send selDepth info to GUI (selDepth counts from 1, ply from 0)
580 if (PvNode && thisThread->selDepth < ss->ply + 1)
581 thisThread->selDepth = ss->ply + 1;
585 // Step 2. Check for aborted search and immediate draw
586 if ( Threads.stop.load(std::memory_order_relaxed)
587 || pos.is_draw(ss->ply)
588 || ss->ply >= MAX_PLY)
589 return (ss->ply >= MAX_PLY && !ss->inCheck) ? evaluate(pos)
590 : value_draw(pos.this_thread());
592 // Step 3. Mate distance pruning. Even if we mate at the next move our score
593 // would be at best mate_in(ss->ply+1), but if alpha is already bigger because
594 // a shorter mate was found upward in the tree then there is no need to search
595 // because we will never beat the current alpha. Same logic but with reversed
596 // signs applies also in the opposite condition of being mated instead of giving
597 // mate. In this case return a fail-high score.
598 alpha = std::max(mated_in(ss->ply), alpha);
599 beta = std::min(mate_in(ss->ply+1), beta);
604 thisThread->rootDelta = beta - alpha;
606 assert(0 <= ss->ply && ss->ply < MAX_PLY);
608 (ss+1)->excludedMove = bestMove = MOVE_NONE;
609 (ss+2)->killers[0] = (ss+2)->killers[1] = MOVE_NONE;
610 (ss+2)->cutoffCnt = 0;
611 ss->doubleExtensions = (ss-1)->doubleExtensions;
612 Square prevSq = is_ok((ss-1)->currentMove) ? to_sq((ss-1)->currentMove) : SQ_NONE;
615 // Step 4. Transposition table lookup.
616 excludedMove = ss->excludedMove;
618 tte = TT.probe(posKey, ss->ttHit);
619 ttValue = ss->ttHit ? value_from_tt(tte->value(), ss->ply, pos.rule50_count()) : VALUE_NONE;
620 ttMove = rootNode ? thisThread->rootMoves[thisThread->pvIdx].pv[0]
621 : ss->ttHit ? tte->move() : MOVE_NONE;
622 ttCapture = ttMove && pos.capture_stage(ttMove);
624 // At this point, if excluded, skip straight to step 6, static eval. However,
625 // to save indentation, we list the condition in all code between here and there.
627 ss->ttPv = PvNode || (ss->ttHit && tte->is_pv());
629 // At non-PV nodes we check for an early TT cutoff
633 && tte->depth() > depth - (tte->bound() == BOUND_EXACT)
634 && ttValue != VALUE_NONE // Possible in case of TT access race
635 && (tte->bound() & (ttValue >= beta ? BOUND_LOWER : BOUND_UPPER)))
637 // If ttMove is quiet, update move sorting heuristics on TT hit (~2 Elo)
642 // Bonus for a quiet ttMove that fails high (~2 Elo)
644 update_quiet_stats(pos, ss, ttMove, stat_bonus(depth));
646 // Extra penalty for early quiet moves of the previous ply (~0 Elo on STC, ~2 Elo on LTC)
647 if (prevSq != SQ_NONE && (ss-1)->moveCount <= 2 && !priorCapture)
648 update_continuation_histories(ss-1, pos.piece_on(prevSq), prevSq, -stat_bonus(depth + 1));
650 // Penalty for a quiet ttMove that fails low (~1 Elo)
653 int penalty = -stat_bonus(depth);
654 thisThread->mainHistory[us][from_to(ttMove)] << penalty;
655 update_continuation_histories(ss, pos.moved_piece(ttMove), to_sq(ttMove), penalty);
659 // Partial workaround for the graph history interaction problem
660 // For high rule50 counts don't produce transposition table cutoffs.
661 if (pos.rule50_count() < 90)
665 // Step 5. Tablebases probe
666 if (!rootNode && !excludedMove && TB::Cardinality)
668 int piecesCount = pos.count<ALL_PIECES>();
670 if ( piecesCount <= TB::Cardinality
671 && (piecesCount < TB::Cardinality || depth >= TB::ProbeDepth)
672 && pos.rule50_count() == 0
673 && !pos.can_castle(ANY_CASTLING))
676 TB::WDLScore wdl = Tablebases::probe_wdl(pos, &err);
678 // Force check of time on the next occasion
679 if (thisThread == Threads.main())
680 static_cast<MainThread*>(thisThread)->callsCnt = 0;
682 if (err != TB::ProbeState::FAIL)
684 thisThread->tbHits.fetch_add(1, std::memory_order_relaxed);
686 int drawScore = TB::UseRule50 ? 1 : 0;
688 // use the range VALUE_MATE_IN_MAX_PLY to VALUE_TB_WIN_IN_MAX_PLY to score
689 value = wdl < -drawScore ? VALUE_MATED_IN_MAX_PLY + ss->ply + 1
690 : wdl > drawScore ? VALUE_MATE_IN_MAX_PLY - ss->ply - 1
691 : VALUE_DRAW + 2 * wdl * drawScore;
693 Bound b = wdl < -drawScore ? BOUND_UPPER
694 : wdl > drawScore ? BOUND_LOWER : BOUND_EXACT;
696 if ( b == BOUND_EXACT
697 || (b == BOUND_LOWER ? value >= beta : value <= alpha))
699 tte->save(posKey, value_to_tt(value, ss->ply), ss->ttPv, b,
700 std::min(MAX_PLY - 1, depth + 6),
701 MOVE_NONE, VALUE_NONE);
708 if (b == BOUND_LOWER)
709 bestValue = value, alpha = std::max(alpha, bestValue);
717 CapturePieceToHistory& captureHistory = thisThread->captureHistory;
719 // Step 6. Static evaluation of the position
722 // Skip early pruning when in check
723 ss->staticEval = eval = VALUE_NONE;
729 else if (excludedMove)
731 // Providing the hint that this node's accumulator will be used often brings significant Elo gain (13 Elo)
732 Eval::NNUE::hint_common_parent_position(pos);
733 eval = ss->staticEval;
734 complexity = abs(ss->staticEval - pos.psq_eg_stm());
738 // Never assume anything about values stored in TT
739 ss->staticEval = eval = tte->eval();
740 if (eval == VALUE_NONE)
741 ss->staticEval = eval = evaluate(pos, &complexity);
742 else // Fall back to (semi)classical complexity for TT hits, the NNUE complexity is lost
744 complexity = abs(ss->staticEval - pos.psq_eg_stm());
746 Eval::NNUE::hint_common_parent_position(pos);
749 // ttValue can be used as a better position evaluation (~7 Elo)
750 if ( ttValue != VALUE_NONE
751 && (tte->bound() & (ttValue > eval ? BOUND_LOWER : BOUND_UPPER)))
756 ss->staticEval = eval = evaluate(pos, &complexity);
757 // Save static evaluation into transposition table
758 tte->save(posKey, VALUE_NONE, ss->ttPv, BOUND_NONE, DEPTH_NONE, MOVE_NONE, eval);
761 // Use static evaluation difference to improve quiet move ordering (~4 Elo)
762 if (is_ok((ss-1)->currentMove) && !(ss-1)->inCheck && !priorCapture)
764 int bonus = std::clamp(-19 * int((ss-1)->staticEval + ss->staticEval), -1920, 1920);
765 thisThread->mainHistory[~us][from_to((ss-1)->currentMove)] << bonus;
768 // Set up the improvement variable, which is the difference between the current
769 // static evaluation and the previous static evaluation at our turn (if we were
770 // in check at our previous move we look at the move prior to it). The improvement
771 // margin and the improving flag are used in various pruning heuristics.
772 improvement = (ss-2)->staticEval != VALUE_NONE ? ss->staticEval - (ss-2)->staticEval
773 : (ss-4)->staticEval != VALUE_NONE ? ss->staticEval - (ss-4)->staticEval
775 improving = improvement > 0;
777 // Step 7. Razoring (~1 Elo).
778 // If eval is really low check with qsearch if it can exceed alpha, if it can't,
779 // return a fail low.
780 if (eval < alpha - 426 - 256 * depth * depth)
782 value = qsearch<NonPV>(pos, ss, alpha - 1, alpha);
787 // Step 8. Futility pruning: child node (~40 Elo).
788 // The depth condition is important for mate finding.
791 && eval - futility_margin(depth, improving) - (ss-1)->statScore / 280 >= beta
793 && eval < 25128) // larger than VALUE_KNOWN_WIN, but smaller than TB wins
796 // Step 9. Null move search with verification search (~35 Elo)
798 && (ss-1)->currentMove != MOVE_NULL
799 && (ss-1)->statScore < 18755
801 && eval >= ss->staticEval
802 && ss->staticEval >= beta - 20 * depth - improvement / 13 + 253 + complexity / 25
804 && pos.non_pawn_material(us)
805 && (ss->ply >= thisThread->nmpMinPly))
807 assert(eval - beta >= 0);
809 // Null move dynamic reduction based on depth, eval and complexity of position
810 Depth R = std::min(int(eval - beta) / 172, 6) + depth / 3 + 4 - (complexity > 825);
812 ss->currentMove = MOVE_NULL;
813 ss->continuationHistory = &thisThread->continuationHistory[0][0][NO_PIECE][0];
815 pos.do_null_move(st);
817 Value nullValue = -search<NonPV>(pos, ss+1, -beta, -beta+1, depth-R, !cutNode);
819 pos.undo_null_move();
821 if (nullValue >= beta)
823 // Do not return unproven mate or TB scores
824 if (nullValue >= VALUE_TB_WIN_IN_MAX_PLY)
827 if (thisThread->nmpMinPly || (abs(beta) < VALUE_KNOWN_WIN && depth < 14))
830 assert(!thisThread->nmpMinPly); // Recursive verification is not allowed
832 // Do verification search at high depths, with null move pruning disabled
833 // until ply exceeds nmpMinPly.
834 thisThread->nmpMinPly = ss->ply + 3 * (depth-R) / 4;
836 Value v = search<NonPV>(pos, ss, beta-1, beta, depth-R, false);
838 thisThread->nmpMinPly = 0;
845 probCutBeta = beta + 186 - 54 * improving;
847 // Step 10. ProbCut (~10 Elo)
848 // If we have a good enough capture (or queen promotion) and a reduced search returns a value
849 // much above beta, we can (almost) safely prune the previous move.
852 && abs(beta) < VALUE_TB_WIN_IN_MAX_PLY
853 // if value from transposition table is lower than probCutBeta, don't attempt probCut
854 // there and in further interactions with transposition table cutoff depth is set to depth - 3
855 // because probCut search has depth set to depth - 4 but we also do a move before it
856 // so effective depth is equal to depth - 3
858 && tte->depth() >= depth - 3
859 && ttValue != VALUE_NONE
860 && ttValue < probCutBeta))
862 assert(probCutBeta < VALUE_INFINITE);
864 MovePicker mp(pos, ttMove, probCutBeta - ss->staticEval, &captureHistory);
866 while ((move = mp.next_move()) != MOVE_NONE)
867 if (move != excludedMove && pos.legal(move))
869 assert(pos.capture_stage(move));
871 ss->currentMove = move;
872 ss->continuationHistory = &thisThread->continuationHistory[ss->inCheck]
874 [pos.moved_piece(move)]
877 pos.do_move(move, st);
879 // Perform a preliminary qsearch to verify that the move holds
880 value = -qsearch<NonPV>(pos, ss+1, -probCutBeta, -probCutBeta+1);
882 // If the qsearch held, perform the regular search
883 if (value >= probCutBeta)
884 value = -search<NonPV>(pos, ss+1, -probCutBeta, -probCutBeta+1, depth - 4, !cutNode);
888 if (value >= probCutBeta)
890 // Save ProbCut data into transposition table
891 tte->save(posKey, value_to_tt(value, ss->ply), ss->ttPv, BOUND_LOWER, depth - 3, move, ss->staticEval);
896 Eval::NNUE::hint_common_parent_position(pos);
899 // 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).
900 // Use qsearch if depth is equal or below zero (~9 Elo)
903 depth -= 2 + 2 * (ss->ttHit && tte->depth() >= depth);
906 return qsearch<PV>(pos, ss, alpha, beta);
913 moves_loop: // When in check, search starts here
915 // Step 12. A small Probcut idea, when we are in check (~4 Elo)
916 probCutBeta = beta + 391;
921 && (tte->bound() & BOUND_LOWER)
922 && tte->depth() >= depth - 3
923 && ttValue >= probCutBeta
924 && abs(ttValue) <= VALUE_KNOWN_WIN
925 && abs(beta) <= VALUE_KNOWN_WIN)
928 const PieceToHistory* contHist[] = { (ss-1)->continuationHistory, (ss-2)->continuationHistory,
929 nullptr , (ss-4)->continuationHistory,
930 nullptr , (ss-6)->continuationHistory };
932 Move countermove = prevSq != SQ_NONE ? thisThread->counterMoves[pos.piece_on(prevSq)][prevSq] : MOVE_NONE;
934 MovePicker mp(pos, ttMove, depth, &thisThread->mainHistory,
941 moveCountPruning = singularQuietLMR = false;
943 // Indicate PvNodes that will probably fail low if the node was searched
944 // at a depth equal or greater than the current depth, and the result of this search was a fail low.
945 bool likelyFailLow = PvNode
947 && (tte->bound() & BOUND_UPPER)
948 && tte->depth() >= depth;
950 // Step 13. Loop through all pseudo-legal moves until no moves remain
951 // or a beta cutoff occurs.
952 while ((move = mp.next_move(moveCountPruning)) != MOVE_NONE)
956 if (move == excludedMove)
959 // At root obey the "searchmoves" option and skip moves not listed in Root
960 // Move List. As a consequence any illegal move is also skipped. In MultiPV
961 // mode we also skip PV moves which have been already searched and those
962 // of lower "TB rank" if we are in a TB root position.
963 if (rootNode && !std::count(thisThread->rootMoves.begin() + thisThread->pvIdx,
964 thisThread->rootMoves.begin() + thisThread->pvLast, move))
967 // Check for legality
968 if (!rootNode && !pos.legal(move))
971 ss->moveCount = ++moveCount;
973 if (rootNode && thisThread == Threads.main() && Time.elapsed() > 3000)
974 sync_cout << "info depth " << depth
975 << " currmove " << UCI::move(move, pos.is_chess960())
976 << " currmovenumber " << moveCount + thisThread->pvIdx << sync_endl;
978 (ss+1)->pv = nullptr;
981 capture = pos.capture_stage(move);
982 movedPiece = pos.moved_piece(move);
983 givesCheck = pos.gives_check(move);
985 // Calculate new depth for this move
986 newDepth = depth - 1;
988 Value delta = beta - alpha;
990 Depth r = reduction(improving, depth, moveCount, delta, thisThread->rootDelta);
992 // Step 14. Pruning at shallow depth (~120 Elo). Depth conditions are important for mate finding.
994 && pos.non_pawn_material(us)
995 && bestValue > VALUE_TB_LOSS_IN_MAX_PLY)
997 // Skip quiet moves if movecount exceeds our FutilityMoveCount threshold (~8 Elo)
998 moveCountPruning = moveCount >= futility_move_count(improving, depth);
1000 // Reduced depth of the next LMR search
1001 int lmrDepth = std::max(newDepth - r, 0);
1006 // Futility pruning for captures (~2 Elo)
1010 && ss->staticEval + 182 + 230 * lmrDepth + PieceValue[EG][pos.piece_on(to_sq(move))]
1011 + captureHistory[movedPiece][to_sq(move)][type_of(pos.piece_on(to_sq(move)))] / 7 < alpha)
1015 // SEE based pruning (~11 Elo)
1016 if (!pos.see_ge(move, occupied, Value(-206) * depth))
1018 if (depth < 2 - capture)
1020 // Don't prune the move if opp. King/Queen/Rook is attacked by a slider after the exchanges.
1021 // Since in see_ge we don't update occupied when the king recaptures, we also don't prune the
1022 // move when the opp. King gets a discovered slider attack DURING the exchanges.
1023 Bitboard leftEnemies = pos.pieces(~us, ROOK, QUEEN, KING) & occupied;
1024 Bitboard attacks = 0;
1025 occupied |= to_sq(move);
1026 while (leftEnemies && !attacks)
1028 Square sq = pop_lsb(leftEnemies);
1029 attacks = pos.attackers_to(sq, occupied) & pos.pieces(us) & occupied;
1030 // Exclude Queen/Rook(s) which were already threatened before SEE
1031 if (attacks && sq != pos.square<KING>(~us) && (pos.attackers_to(sq, pos.pieces()) & pos.pieces(us)))
1040 int history = (*contHist[0])[movedPiece][to_sq(move)]
1041 + (*contHist[1])[movedPiece][to_sq(move)]
1042 + (*contHist[3])[movedPiece][to_sq(move)];
1044 // Continuation history based pruning (~2 Elo)
1046 && history < -4405 * (depth - 1))
1049 history += 2 * thisThread->mainHistory[us][from_to(move)];
1051 lmrDepth += history / 7278;
1052 lmrDepth = std::max(lmrDepth, -2);
1054 // Futility pruning: parent node (~13 Elo)
1057 && ss->staticEval + 103 + 138 * lmrDepth <= alpha)
1060 lmrDepth = std::max(lmrDepth, 0);
1062 // Prune moves with negative SEE (~4 Elo)
1063 if (!pos.see_ge(move, Value(-24 * lmrDepth * lmrDepth - 16 * lmrDepth)))
1068 // Step 15. Extensions (~100 Elo)
1069 // We take care to not overdo to avoid search getting stuck.
1070 if (ss->ply < thisThread->rootDepth * 2)
1072 // Singular extension search (~94 Elo). If all moves but one fail low on a
1073 // search of (alpha-s, beta-s), and just one fails high on (alpha, beta),
1074 // then that move is singular and should be extended. To verify this we do
1075 // a reduced search on all the other moves but the ttMove and if the
1076 // result is lower than ttValue minus a margin, then we will extend the ttMove.
1078 && depth >= 4 - (thisThread->completedDepth > 21) + 2 * (PvNode && tte->is_pv())
1080 && !excludedMove // Avoid recursive singular search
1081 /* && ttValue != VALUE_NONE Already implicit in the next condition */
1082 && abs(ttValue) < VALUE_KNOWN_WIN
1083 && (tte->bound() & BOUND_LOWER)
1084 && tte->depth() >= depth - 3)
1086 Value singularBeta = ttValue - (3 + 2 * (ss->ttPv && !PvNode)) * depth / 2;
1087 Depth singularDepth = (depth - 1) / 2;
1089 ss->excludedMove = move;
1090 value = search<NonPV>(pos, ss, singularBeta - 1, singularBeta, singularDepth, cutNode);
1091 ss->excludedMove = MOVE_NONE;
1093 if (value < singularBeta)
1096 singularQuietLMR = !ttCapture;
1098 // Avoid search explosion by limiting the number of double extensions
1100 && value < singularBeta - 25
1101 && ss->doubleExtensions <= 10)
1104 depth += depth < 13;
1108 // Multi-cut pruning
1109 // Our ttMove is assumed to fail high, and now we failed high also on a reduced
1110 // search without the ttMove. So we assume this expected Cut-node is not singular,
1111 // that multiple moves fail high, and we can prune the whole subtree by returning
1113 else if (singularBeta >= beta)
1114 return singularBeta;
1116 // If the eval of ttMove is greater than beta, we reduce it (negative extension) (~7 Elo)
1117 else if (ttValue >= beta)
1118 extension = -2 - !PvNode;
1120 // If the eval of ttMove is less than value, we reduce it (negative extension) (~1 Elo)
1121 else if (ttValue <= value)
1124 // If the eval of ttMove is less than alpha, we reduce it (negative extension) (~1 Elo)
1125 else if (ttValue <= alpha)
1129 // Check extensions (~1 Elo)
1130 else if ( givesCheck
1132 && abs(ss->staticEval) > 88)
1135 // Quiet ttMove extensions (~1 Elo)
1138 && move == ss->killers[0]
1139 && (*contHist[0])[movedPiece][to_sq(move)] >= 5705)
1143 // Add extension to new depth
1144 newDepth += extension;
1145 ss->doubleExtensions = (ss-1)->doubleExtensions + (extension == 2);
1147 // Speculative prefetch as early as possible
1148 prefetch(TT.first_entry(pos.key_after(move)));
1150 // Update the current move (this must be done after singular extension search)
1151 ss->currentMove = move;
1152 ss->continuationHistory = &thisThread->continuationHistory[ss->inCheck]
1157 // Step 16. Make the move
1158 pos.do_move(move, st, givesCheck);
1160 // Decrease reduction if position is or has been on the PV
1161 // and node is not likely to fail low. (~3 Elo)
1166 // Decrease reduction if opponent's move count is high (~1 Elo)
1167 if ((ss-1)->moveCount > 7)
1170 // Increase reduction for cut nodes (~3 Elo)
1174 // Increase reduction if ttMove is a capture (~3 Elo)
1178 // Decrease reduction for PvNodes based on depth (~2 Elo)
1180 r -= 1 + 12 / (3 + depth);
1182 // Decrease reduction if ttMove has been singularly extended (~1 Elo)
1183 if (singularQuietLMR)
1186 // Increase reduction if next ply has a lot of fail high (~5 Elo)
1187 if ((ss+1)->cutoffCnt > 3)
1190 ss->statScore = 2 * thisThread->mainHistory[us][from_to(move)]
1191 + (*contHist[0])[movedPiece][to_sq(move)]
1192 + (*contHist[1])[movedPiece][to_sq(move)]
1193 + (*contHist[3])[movedPiece][to_sq(move)]
1196 // Decrease/increase reduction for moves with a good/bad history (~25 Elo)
1197 r -= ss->statScore / (11079 + 4626 * (depth > 6 && depth < 19));
1199 // Step 17. Late moves reduction / extension (LMR, ~117 Elo)
1200 // We use various heuristics for the sons of a node after the first son has
1201 // been searched. In general we would like to reduce them, but there are many
1202 // cases where we extend a son if it has good chances to be "interesting".
1204 && moveCount > 1 + (PvNode && ss->ply <= 1)
1207 || (cutNode && (ss-1)->moveCount > 1)))
1209 // In general we want to cap the LMR depth search at newDepth, but when
1210 // reduction is negative, we allow this move a limited search extension
1211 // beyond the first move depth. This may lead to hidden double extensions.
1212 Depth d = std::clamp(newDepth - r, 1, newDepth + 1);
1214 value = -search<NonPV>(pos, ss+1, -(alpha+1), -alpha, d, true);
1216 // Do full depth search when reduced LMR search fails high
1217 if (value > alpha && d < newDepth)
1219 // Adjust full depth search based on LMR results - if result
1220 // was good enough search deeper, if it was bad enough search shallower
1221 const bool doDeeperSearch = value > (alpha + 58 + 12 * (newDepth - d));
1222 const bool doEvenDeeperSearch = value > alpha + 588 && ss->doubleExtensions <= 5;
1223 const bool doShallowerSearch = value < bestValue + newDepth;
1225 ss->doubleExtensions = ss->doubleExtensions + doEvenDeeperSearch;
1227 newDepth += doDeeperSearch - doShallowerSearch + doEvenDeeperSearch;
1230 value = -search<NonPV>(pos, ss+1, -(alpha+1), -alpha, newDepth, !cutNode);
1232 int bonus = value <= alpha ? -stat_bonus(newDepth)
1233 : value >= beta ? stat_bonus(newDepth)
1236 update_continuation_histories(ss, movedPiece, to_sq(move), bonus);
1240 // Step 18. Full depth search when LMR is skipped. If expected reduction is high, reduce its depth by 1.
1241 else if (!PvNode || moveCount > 1)
1243 // Increase reduction for cut nodes and not ttMove (~1 Elo)
1244 if (!ttMove && cutNode)
1247 value = -search<NonPV>(pos, ss+1, -(alpha+1), -alpha, newDepth - (r > 4), !cutNode);
1250 // For PV nodes only, do a full PV search on the first move or after a fail
1251 // high (in the latter case search only if value < beta), otherwise let the
1252 // parent node fail low with value <= alpha and try another move.
1253 if (PvNode && (moveCount == 1 || (value > alpha && (rootNode || value < beta))))
1256 (ss+1)->pv[0] = MOVE_NONE;
1258 value = -search<PV>(pos, ss+1, -beta, -alpha, newDepth, false);
1261 // Step 19. Undo move
1262 pos.undo_move(move);
1264 assert(value > -VALUE_INFINITE && value < VALUE_INFINITE);
1266 // Step 20. Check for a new best move
1267 // Finished searching the move. If a stop occurred, the return value of
1268 // the search cannot be trusted, and we return immediately without
1269 // updating best move, PV and TT.
1270 if (Threads.stop.load(std::memory_order_relaxed))
1275 RootMove& rm = *std::find(thisThread->rootMoves.begin(),
1276 thisThread->rootMoves.end(), move);
1278 rm.averageScore = rm.averageScore != -VALUE_INFINITE ? (2 * value + rm.averageScore) / 3 : value;
1280 // PV move or new best move?
1281 if (moveCount == 1 || value > alpha)
1283 rm.score = rm.uciScore = value;
1284 rm.selDepth = thisThread->selDepth;
1285 rm.scoreLowerbound = rm.scoreUpperbound = false;
1289 rm.scoreLowerbound = true;
1292 else if (value <= alpha)
1294 rm.scoreUpperbound = true;
1295 rm.uciScore = alpha;
1302 for (Move* m = (ss+1)->pv; *m != MOVE_NONE; ++m)
1303 rm.pv.push_back(*m);
1305 // We record how often the best move has been changed in each iteration.
1306 // This information is used for time management. In MultiPV mode,
1307 // we must take care to only do this for the first PV line.
1309 && !thisThread->pvIdx)
1310 ++thisThread->bestMoveChanges;
1313 // All other moves but the PV are set to the lowest value: this
1314 // is not a problem when sorting because the sort is stable and the
1315 // move position in the list is preserved - just the PV is pushed up.
1316 rm.score = -VALUE_INFINITE;
1319 if (value > bestValue)
1327 if (PvNode && !rootNode) // Update pv even in fail-high case
1328 update_pv(ss->pv, move, (ss+1)->pv);
1330 if (PvNode && value < beta) // Update alpha! Always alpha < beta
1332 // Reduce other moves if we have found at least one score improvement (~1 Elo)
1334 && ( (improving && complexity > 971)
1335 || value < (5 * alpha + 75 * beta) / 87
1347 assert(value >= beta); // Fail high
1354 // If the move is worse than some previously searched move, remember it to update its stats later
1355 if (move != bestMove)
1357 if (capture && captureCount < 32)
1358 capturesSearched[captureCount++] = move;
1360 else if (!capture && quietCount < 64)
1361 quietsSearched[quietCount++] = move;
1365 // The following condition would detect a stop only after move loop has been
1366 // completed. But in this case bestValue is valid because we have fully
1367 // searched our subtree, and we can anyhow save the result in TT.
1373 // Step 21. Check for mate and stalemate
1374 // All legal moves have been searched and if there are no legal moves, it
1375 // must be a mate or a stalemate. If we are in a singular extension search then
1376 // return a fail low score.
1378 assert(moveCount || !ss->inCheck || excludedMove || !MoveList<LEGAL>(pos).size());
1381 bestValue = excludedMove ? alpha :
1382 ss->inCheck ? mated_in(ss->ply)
1385 // If there is a move which produces search value greater than alpha we update stats of searched moves
1387 update_all_stats(pos, ss, bestMove, bestValue, beta, prevSq,
1388 quietsSearched, quietCount, capturesSearched, captureCount, depth);
1390 // Bonus for prior countermove that caused the fail low
1391 else if (!priorCapture && prevSq != SQ_NONE)
1393 int bonus = (depth > 5) + (PvNode || cutNode) + (bestValue < alpha - 97 * depth) + ((ss-1)->moveCount > 10);
1394 update_continuation_histories(ss-1, pos.piece_on(prevSq), prevSq, stat_bonus(depth) * bonus);
1398 bestValue = std::min(bestValue, maxValue);
1400 // If no good move is found and the previous position was ttPv, then the previous
1401 // opponent move is probably good and the new position is added to the search tree. (~7 Elo)
1402 if (bestValue <= alpha)
1403 ss->ttPv = ss->ttPv || ((ss-1)->ttPv && depth > 3);
1405 // Write gathered information in transposition table
1406 if (!excludedMove && !(rootNode && thisThread->pvIdx))
1407 tte->save(posKey, value_to_tt(bestValue, ss->ply), ss->ttPv,
1408 bestValue >= beta ? BOUND_LOWER :
1409 PvNode && bestMove ? BOUND_EXACT : BOUND_UPPER,
1410 depth, bestMove, ss->staticEval);
1412 assert(bestValue > -VALUE_INFINITE && bestValue < VALUE_INFINITE);
1418 // qsearch() is the quiescence search function, which is called by the main search
1419 // function with zero depth, or recursively with further decreasing depth per call.
1421 template <NodeType nodeType>
1422 Value qsearch(Position& pos, Stack* ss, Value alpha, Value beta, Depth depth) {
1424 static_assert(nodeType != Root);
1425 constexpr bool PvNode = nodeType == PV;
1427 assert(alpha >= -VALUE_INFINITE && alpha < beta && beta <= VALUE_INFINITE);
1428 assert(PvNode || (alpha == beta - 1));
1433 ASSERT_ALIGNED(&st, Eval::NNUE::CacheLineSize);
1437 Move ttMove, move, bestMove;
1439 Value bestValue, value, ttValue, futilityValue, futilityBase;
1440 bool pvHit, givesCheck, capture;
1443 // Step 1. Initialize node
1447 ss->pv[0] = MOVE_NONE;
1450 Thread* thisThread = pos.this_thread();
1451 bestMove = MOVE_NONE;
1452 ss->inCheck = pos.checkers();
1455 // Step 2. Check for an immediate draw or maximum ply reached
1456 if ( pos.is_draw(ss->ply)
1457 || ss->ply >= MAX_PLY)
1458 return (ss->ply >= MAX_PLY && !ss->inCheck) ? evaluate(pos) : VALUE_DRAW;
1460 assert(0 <= ss->ply && ss->ply < MAX_PLY);
1462 // Decide whether or not to include checks: this fixes also the type of
1463 // TT entry depth that we are going to use. Note that in qsearch we use
1464 // only two types of depth in TT: DEPTH_QS_CHECKS or DEPTH_QS_NO_CHECKS.
1465 ttDepth = ss->inCheck || depth >= DEPTH_QS_CHECKS ? DEPTH_QS_CHECKS
1466 : DEPTH_QS_NO_CHECKS;
1468 // Step 3. Transposition table lookup
1470 tte = TT.probe(posKey, ss->ttHit);
1471 ttValue = ss->ttHit ? value_from_tt(tte->value(), ss->ply, pos.rule50_count()) : VALUE_NONE;
1472 ttMove = ss->ttHit ? tte->move() : MOVE_NONE;
1473 pvHit = ss->ttHit && tte->is_pv();
1475 // At non-PV nodes we check for an early TT cutoff
1478 && tte->depth() >= ttDepth
1479 && ttValue != VALUE_NONE // Only in case of TT access race
1480 && (tte->bound() & (ttValue >= beta ? BOUND_LOWER : BOUND_UPPER)))
1483 // Step 4. Static evaluation of the position
1486 ss->staticEval = VALUE_NONE;
1487 bestValue = futilityBase = -VALUE_INFINITE;
1493 // Never assume anything about values stored in TT
1494 if ((ss->staticEval = bestValue = tte->eval()) == VALUE_NONE)
1495 ss->staticEval = bestValue = evaluate(pos);
1497 // ttValue can be used as a better position evaluation (~13 Elo)
1498 if ( ttValue != VALUE_NONE
1499 && (tte->bound() & (ttValue > bestValue ? BOUND_LOWER : BOUND_UPPER)))
1500 bestValue = ttValue;
1503 // In case of null move search use previous static eval with a different sign
1504 ss->staticEval = bestValue =
1505 (ss-1)->currentMove != MOVE_NULL ? evaluate(pos)
1506 : -(ss-1)->staticEval;
1508 // Stand pat. Return immediately if static value is at least beta
1509 if (bestValue >= beta)
1511 // Save gathered info in transposition table
1513 tte->save(posKey, value_to_tt(bestValue, ss->ply), false, BOUND_LOWER,
1514 DEPTH_NONE, MOVE_NONE, ss->staticEval);
1519 if (PvNode && bestValue > alpha)
1522 futilityBase = bestValue + 168;
1525 const PieceToHistory* contHist[] = { (ss-1)->continuationHistory, (ss-2)->continuationHistory,
1526 nullptr , (ss-4)->continuationHistory,
1527 nullptr , (ss-6)->continuationHistory };
1529 // Initialize a MovePicker object for the current position, and prepare
1530 // to search the moves. Because the depth is <= 0 here, only captures,
1531 // queen promotions, and other checks (only if depth >= DEPTH_QS_CHECKS)
1532 // will be generated.
1533 Square prevSq = (ss-1)->currentMove != MOVE_NULL ? to_sq((ss-1)->currentMove) : SQ_NONE;
1534 MovePicker mp(pos, ttMove, depth, &thisThread->mainHistory,
1535 &thisThread->captureHistory,
1539 int quietCheckEvasions = 0;
1541 // Step 5. Loop through all pseudo-legal moves until no moves remain
1542 // or a beta cutoff occurs.
1543 while ((move = mp.next_move()) != MOVE_NONE)
1545 assert(is_ok(move));
1547 // Check for legality
1548 if (!pos.legal(move))
1551 givesCheck = pos.gives_check(move);
1552 capture = pos.capture_stage(move);
1557 if (bestValue > VALUE_TB_LOSS_IN_MAX_PLY)
1559 // Futility pruning and moveCount pruning (~10 Elo)
1561 && to_sq(move) != prevSq
1562 && futilityBase > -VALUE_KNOWN_WIN
1563 && type_of(move) != PROMOTION)
1568 futilityValue = futilityBase + PieceValue[EG][pos.piece_on(to_sq(move))];
1570 if (futilityValue <= alpha)
1572 bestValue = std::max(bestValue, futilityValue);
1576 if (futilityBase <= alpha && !pos.see_ge(move, VALUE_ZERO + 1))
1578 bestValue = std::max(bestValue, futilityBase);
1583 // We prune after 2nd quiet check evasion where being 'in check' is implicitly checked through the counter
1584 // and being a 'quiet' apart from being a tt move is assumed after an increment because captures are pushed ahead.
1585 if (quietCheckEvasions > 1)
1588 // Continuation history based pruning (~3 Elo)
1590 && (*contHist[0])[pos.moved_piece(move)][to_sq(move)] < 0
1591 && (*contHist[1])[pos.moved_piece(move)][to_sq(move)] < 0)
1594 // Do not search moves with bad enough SEE values (~5 Elo)
1595 if (!pos.see_ge(move, Value(-110)))
1599 // Speculative prefetch as early as possible
1600 prefetch(TT.first_entry(pos.key_after(move)));
1602 // Update the current move
1603 ss->currentMove = move;
1604 ss->continuationHistory = &thisThread->continuationHistory[ss->inCheck]
1606 [pos.moved_piece(move)]
1609 quietCheckEvasions += !capture && ss->inCheck;
1611 // Step 7. Make and search the move
1612 pos.do_move(move, st, givesCheck);
1613 value = -qsearch<nodeType>(pos, ss+1, -beta, -alpha, depth - 1);
1614 pos.undo_move(move);
1616 assert(value > -VALUE_INFINITE && value < VALUE_INFINITE);
1618 // Step 8. Check for a new best move
1619 if (value > bestValue)
1627 if (PvNode) // Update pv even in fail-high case
1628 update_pv(ss->pv, move, (ss+1)->pv);
1630 if (PvNode && value < beta) // Update alpha here!
1638 // Step 9. Check for mate
1639 // All legal moves have been searched. A special case: if we're in check
1640 // and no legal moves were found, it is checkmate.
1641 if (ss->inCheck && bestValue == -VALUE_INFINITE)
1643 assert(!MoveList<LEGAL>(pos).size());
1645 return mated_in(ss->ply); // Plies to mate from the root
1648 // Save gathered info in transposition table
1649 tte->save(posKey, value_to_tt(bestValue, ss->ply), pvHit,
1650 bestValue >= beta ? BOUND_LOWER : BOUND_UPPER,
1651 ttDepth, bestMove, ss->staticEval);
1653 assert(bestValue > -VALUE_INFINITE && bestValue < VALUE_INFINITE);
1659 // value_to_tt() adjusts a mate or TB score from "plies to mate from the root" to
1660 // "plies to mate from the current position". Standard scores are unchanged.
1661 // The function is called before storing a value in the transposition table.
1663 Value value_to_tt(Value v, int ply) {
1665 assert(v != VALUE_NONE);
1667 return v >= VALUE_TB_WIN_IN_MAX_PLY ? v + ply
1668 : v <= VALUE_TB_LOSS_IN_MAX_PLY ? v - ply : v;
1672 // value_from_tt() is the inverse of value_to_tt(): it adjusts a mate or TB score
1673 // from the transposition table (which refers to the plies to mate/be mated from
1674 // current position) to "plies to mate/be mated (TB win/loss) from the root". However,
1675 // for mate scores, to avoid potentially false mate scores related to the 50 moves rule
1676 // and the graph history interaction, we return an optimal TB score instead.
1678 Value value_from_tt(Value v, int ply, int r50c) {
1680 if (v == VALUE_NONE)
1683 if (v >= VALUE_TB_WIN_IN_MAX_PLY) // TB win or better
1685 if (v >= VALUE_MATE_IN_MAX_PLY && VALUE_MATE - v > 99 - r50c)
1686 return VALUE_MATE_IN_MAX_PLY - 1; // do not return a potentially false mate score
1691 if (v <= VALUE_TB_LOSS_IN_MAX_PLY) // TB loss or worse
1693 if (v <= VALUE_MATED_IN_MAX_PLY && VALUE_MATE + v > 99 - r50c)
1694 return VALUE_MATED_IN_MAX_PLY + 1; // do not return a potentially false mate score
1703 // update_pv() adds current move and appends child pv[]
1705 void update_pv(Move* pv, Move move, const Move* childPv) {
1707 for (*pv++ = move; childPv && *childPv != MOVE_NONE; )
1713 // update_all_stats() updates stats at the end of search() when a bestMove is found
1715 void update_all_stats(const Position& pos, Stack* ss, Move bestMove, Value bestValue, Value beta, Square prevSq,
1716 Move* quietsSearched, int quietCount, Move* capturesSearched, int captureCount, Depth depth) {
1718 Color us = pos.side_to_move();
1719 Thread* thisThread = pos.this_thread();
1720 CapturePieceToHistory& captureHistory = thisThread->captureHistory;
1721 Piece moved_piece = pos.moved_piece(bestMove);
1724 int bonus1 = stat_bonus(depth + 1);
1726 if (!pos.capture_stage(bestMove))
1728 int bonus2 = bestValue > beta + 153 ? bonus1 // larger bonus
1729 : stat_bonus(depth); // smaller bonus
1731 // Increase stats for the best move in case it was a quiet move
1732 update_quiet_stats(pos, ss, bestMove, bonus2);
1734 // Decrease stats for all non-best quiet moves
1735 for (int i = 0; i < quietCount; ++i)
1737 thisThread->mainHistory[us][from_to(quietsSearched[i])] << -bonus2;
1738 update_continuation_histories(ss, pos.moved_piece(quietsSearched[i]), to_sq(quietsSearched[i]), -bonus2);
1743 // Increase stats for the best move in case it was a capture move
1744 captured = type_of(pos.piece_on(to_sq(bestMove)));
1745 captureHistory[moved_piece][to_sq(bestMove)][captured] << bonus1;
1748 // Extra penalty for a quiet early move that was not a TT move or
1749 // main killer move in previous ply when it gets refuted.
1750 if ( prevSq != SQ_NONE
1751 && ((ss-1)->moveCount == 1 + (ss-1)->ttHit || ((ss-1)->currentMove == (ss-1)->killers[0]))
1752 && !pos.captured_piece())
1753 update_continuation_histories(ss-1, pos.piece_on(prevSq), prevSq, -bonus1);
1755 // Decrease stats for all non-best capture moves
1756 for (int i = 0; i < captureCount; ++i)
1758 moved_piece = pos.moved_piece(capturesSearched[i]);
1759 captured = type_of(pos.piece_on(to_sq(capturesSearched[i])));
1760 captureHistory[moved_piece][to_sq(capturesSearched[i])][captured] << -bonus1;
1765 // update_continuation_histories() updates histories of the move pairs formed
1766 // by moves at ply -1, -2, -4, and -6 with current move.
1768 void update_continuation_histories(Stack* ss, Piece pc, Square to, int bonus) {
1770 for (int i : {1, 2, 4, 6})
1772 // Only update first 2 continuation histories if we are in check
1773 if (ss->inCheck && i > 2)
1775 if (is_ok((ss-i)->currentMove))
1776 (*(ss-i)->continuationHistory)[pc][to] << bonus;
1781 // update_quiet_stats() updates move sorting heuristics
1783 void update_quiet_stats(const Position& pos, Stack* ss, Move move, int bonus) {
1786 if (ss->killers[0] != move)
1788 ss->killers[1] = ss->killers[0];
1789 ss->killers[0] = move;
1792 Color us = pos.side_to_move();
1793 Thread* thisThread = pos.this_thread();
1794 thisThread->mainHistory[us][from_to(move)] << bonus;
1795 update_continuation_histories(ss, pos.moved_piece(move), to_sq(move), bonus);
1797 // Update countermove history
1798 if (is_ok((ss-1)->currentMove))
1800 Square prevSq = to_sq((ss-1)->currentMove);
1801 thisThread->counterMoves[pos.piece_on(prevSq)][prevSq] = move;
1805 // When playing with strength handicap, choose best move among a set of RootMoves
1806 // using a statistical rule dependent on 'level'. Idea by Heinz van Saanen.
1808 Move Skill::pick_best(size_t multiPV) {
1810 const RootMoves& rootMoves = Threads.main()->rootMoves;
1811 static PRNG rng(now()); // PRNG sequence should be non-deterministic
1813 // RootMoves are already sorted by score in descending order
1814 Value topScore = rootMoves[0].score;
1815 int delta = std::min(topScore - rootMoves[multiPV - 1].score, PawnValueMg);
1816 int maxScore = -VALUE_INFINITE;
1817 double weakness = 120 - 2 * level;
1819 // Choose best move. For each move score we add two terms, both dependent on
1820 // weakness. One is deterministic and bigger for weaker levels, and one is
1821 // random. Then we choose the move with the resulting highest score.
1822 for (size_t i = 0; i < multiPV; ++i)
1824 // This is our magic formula
1825 int push = int(( weakness * int(topScore - rootMoves[i].score)
1826 + delta * (rng.rand<unsigned>() % int(weakness))) / 128);
1828 if (rootMoves[i].score + push >= maxScore)
1830 maxScore = rootMoves[i].score + push;
1831 best = rootMoves[i].pv[0];
1841 /// MainThread::check_time() is used to print debug info and, more importantly,
1842 /// to detect when we are out of available time and thus stop the search.
1844 void MainThread::check_time() {
1849 // When using nodes, ensure checking rate is not lower than 0.1% of nodes
1850 callsCnt = Limits.nodes ? std::min(1024, int(Limits.nodes / 1024)) : 1024;
1852 static TimePoint lastInfoTime = now();
1854 TimePoint elapsed = Time.elapsed();
1855 TimePoint tick = Limits.startTime + elapsed;
1857 if (tick - lastInfoTime >= 1000)
1859 lastInfoTime = tick;
1863 // We should not stop pondering until told so by the GUI
1867 if ( (Limits.use_time_management() && (elapsed > Time.maximum() - 10 || stopOnPonderhit))
1868 || (Limits.movetime && elapsed >= Limits.movetime)
1869 || (Limits.nodes && Threads.nodes_searched() >= (uint64_t)Limits.nodes))
1870 Threads.stop = true;
1874 /// UCI::pv() formats PV information according to the UCI protocol. UCI requires
1875 /// that all (if any) unsearched PV lines are sent using a previous search score.
1877 string UCI::pv(const Position& pos, Depth depth) {
1879 std::stringstream ss;
1880 TimePoint elapsed = Time.elapsed() + 1;
1881 const RootMoves& rootMoves = pos.this_thread()->rootMoves;
1882 size_t pvIdx = pos.this_thread()->pvIdx;
1883 size_t multiPV = std::min((size_t)Options["MultiPV"], rootMoves.size());
1884 uint64_t nodesSearched = Threads.nodes_searched();
1885 uint64_t tbHits = Threads.tb_hits() + (TB::RootInTB ? rootMoves.size() : 0);
1887 for (size_t i = 0; i < multiPV; ++i)
1889 bool updated = rootMoves[i].score != -VALUE_INFINITE;
1891 if (depth == 1 && !updated && i > 0)
1894 Depth d = updated ? depth : std::max(1, depth - 1);
1895 Value v = updated ? rootMoves[i].uciScore : rootMoves[i].previousScore;
1897 if (v == -VALUE_INFINITE)
1900 bool tb = TB::RootInTB && abs(v) < VALUE_MATE_IN_MAX_PLY;
1901 v = tb ? rootMoves[i].tbScore : v;
1903 if (ss.rdbuf()->in_avail()) // Not at first line
1908 << " seldepth " << rootMoves[i].selDepth
1909 << " multipv " << i + 1
1910 << " score " << UCI::value(v);
1912 if (Options["UCI_ShowWDL"])
1913 ss << UCI::wdl(v, pos.game_ply());
1915 if (i == pvIdx && !tb && updated) // tablebase- and previous-scores are exact
1916 ss << (rootMoves[i].scoreLowerbound ? " lowerbound" : (rootMoves[i].scoreUpperbound ? " upperbound" : ""));
1918 ss << " nodes " << nodesSearched
1919 << " nps " << nodesSearched * 1000 / elapsed
1920 << " hashfull " << TT.hashfull()
1921 << " tbhits " << tbHits
1922 << " time " << elapsed
1925 for (Move m : rootMoves[i].pv)
1926 ss << " " << UCI::move(m, pos.is_chess960());
1933 /// RootMove::extract_ponder_from_tt() is called in case we have no ponder move
1934 /// before exiting the search, for instance, in case we stop the search during a
1935 /// fail high at root. We try hard to have a ponder move to return to the GUI,
1936 /// otherwise in case of 'ponder on' we have nothing to think on.
1938 bool RootMove::extract_ponder_from_tt(Position& pos) {
1941 ASSERT_ALIGNED(&st, Eval::NNUE::CacheLineSize);
1945 assert(pv.size() == 1);
1947 if (pv[0] == MOVE_NONE)
1950 pos.do_move(pv[0], st);
1951 TTEntry* tte = TT.probe(pos.key(), ttHit);
1955 Move m = tte->move(); // Local copy to be SMP safe
1956 if (MoveList<LEGAL>(pos).contains(m))
1960 pos.undo_move(pv[0]);
1961 return pv.size() > 1;
1964 void Tablebases::rank_root_moves(Position& pos, Search::RootMoves& rootMoves) {
1967 UseRule50 = bool(Options["Syzygy50MoveRule"]);
1968 ProbeDepth = int(Options["SyzygyProbeDepth"]);
1969 Cardinality = int(Options["SyzygyProbeLimit"]);
1970 bool dtz_available = true;
1972 // Tables with fewer pieces than SyzygyProbeLimit are searched with
1973 // ProbeDepth == DEPTH_ZERO
1974 if (Cardinality > MaxCardinality)
1976 Cardinality = MaxCardinality;
1980 if (Cardinality >= popcount(pos.pieces()) && !pos.can_castle(ANY_CASTLING))
1982 // Rank moves using DTZ tables
1983 RootInTB = root_probe(pos, rootMoves);
1987 // DTZ tables are missing; try to rank moves using WDL tables
1988 dtz_available = false;
1989 RootInTB = root_probe_wdl(pos, rootMoves);
1995 // Sort moves according to TB rank
1996 std::stable_sort(rootMoves.begin(), rootMoves.end(),
1997 [](const RootMove &a, const RootMove &b) { return a.tbRank > b.tbRank; } );
1999 // Probe during search only if DTZ is not available and we are winning
2000 if (dtz_available || rootMoves[0].tbScore <= VALUE_DRAW)
2005 // Clean up if root_probe() and root_probe_wdl() have failed
2006 for (auto& m : rootMoves)
2011 } // namespace Stockfish