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"
45 namespace Tablebases {
53 namespace TB = Tablebases;
57 using namespace Search;
61 // Different node types, used as a template parameter
62 enum NodeType { NonPV, PV, Root };
65 Value futility_margin(Depth d, bool improving) {
66 return Value(154 * (d - improving));
69 // Reductions lookup table, initialized at startup
70 int Reductions[MAX_MOVES]; // [depth or moveNumber]
72 Depth reduction(bool i, Depth d, int mn, Value delta, Value rootDelta) {
73 int r = Reductions[d] * Reductions[mn];
74 return (r + 1449 - int(delta) * 1032 / int(rootDelta)) / 1024 + (!i && r > 941);
77 constexpr int futility_move_count(bool improving, Depth depth) {
78 return improving ? (3 + depth * depth)
79 : (3 + depth * depth) / 2;
82 // History and stats update bonus, based on depth
83 int stat_bonus(Depth d) {
84 return std::min(340 * d - 470, 1855);
87 // Add a small random component to draw evaluations to avoid 3-fold blindness
88 Value value_draw(const Thread* thisThread) {
89 return VALUE_DRAW - 1 + Value(thisThread->nodes & 0x2);
92 // Skill structure is used to implement strength limit. If we have an uci_elo then
93 // we convert it to a suitable fractional skill level using anchoring to CCRL Elo
94 // (goldfish 1.13 = 2000) and a fit through Ordo derived Elo for match (TC 60+0.6)
95 // results spanning a wide range of k values.
97 Skill(int skill_level, int uci_elo) {
100 double e = double(uci_elo - 1320) / (3190 - 1320);
101 level = std::clamp((((37.2473 * e - 40.8525) * e + 22.2943) * e - 0.311438), 0.0, 19.0);
104 level = double(skill_level);
106 bool enabled() const { return level < 20.0; }
107 bool time_to_pick(Depth depth) const { return depth == 1 + int(level); }
108 Move pick_best(size_t multiPV);
111 Move best = MOVE_NONE;
114 template <NodeType nodeType>
115 Value search(Position& pos, Stack* ss, Value alpha, Value beta, Depth depth, bool cutNode);
117 template <NodeType nodeType>
118 Value qsearch(Position& pos, Stack* ss, Value alpha, Value beta, Depth depth = 0);
120 Value value_to_tt(Value v, int ply);
121 Value value_from_tt(Value v, int ply, int r50c);
122 void update_pv(Move* pv, Move move, const Move* childPv);
123 void update_continuation_histories(Stack* ss, Piece pc, Square to, int bonus);
124 void update_quiet_stats(const Position& pos, Stack* ss, Move move, int bonus);
125 void update_all_stats(const Position& pos, Stack* ss, Move bestMove, Value bestValue, Value beta, Square prevSq,
126 Move* quietsSearched, int quietCount, Move* capturesSearched, int captureCount, Depth depth);
128 // perft() is our utility to verify move generation. All the leaf nodes up
129 // to the given depth are generated and counted, and the sum is returned.
131 uint64_t perft(Position& pos, Depth depth) {
134 ASSERT_ALIGNED(&st, Eval::NNUE::CacheLineSize);
136 uint64_t cnt, nodes = 0;
137 const bool leaf = (depth == 2);
139 for (const auto& m : MoveList<LEGAL>(pos))
141 if (Root && depth <= 1)
146 cnt = leaf ? MoveList<LEGAL>(pos).size() : perft<false>(pos, depth - 1);
151 sync_cout << UCI::move(m, pos.is_chess960()) << ": " << cnt << sync_endl;
159 /// Search::init() is called at startup to initialize various lookup tables
161 void Search::init() {
163 for (int i = 1; i < MAX_MOVES; ++i)
164 Reductions[i] = int((19.47 + std::log(Threads.size()) / 2) * std::log(i));
168 /// Search::clear() resets search state to its initial value
170 void Search::clear() {
172 Threads.main()->wait_for_search_finished();
174 Time.availableNodes = 0;
177 Tablebases::init(Options["SyzygyPath"]); // Free mapped files
181 /// MainThread::search() is started when the program receives the UCI 'go'
182 /// command. It searches from the root position and outputs the "bestmove".
184 void MainThread::search() {
188 nodes = perft<true>(rootPos, Limits.perft);
189 sync_cout << "\nNodes searched: " << nodes << "\n" << sync_endl;
193 Color us = rootPos.side_to_move();
194 Time.init(Limits, us, rootPos.game_ply());
197 Eval::NNUE::verify();
199 if (rootMoves.empty())
201 rootMoves.emplace_back(MOVE_NONE);
202 sync_cout << "info depth 0 score "
203 << UCI::value(rootPos.checkers() ? -VALUE_MATE : VALUE_DRAW)
208 Threads.start_searching(); // start non-main threads
209 Thread::search(); // main thread start searching
212 // When we reach the maximum depth, we can arrive here without a raise of
213 // Threads.stop. However, if we are pondering or in an infinite search,
214 // the UCI protocol states that we shouldn't print the best move before the
215 // GUI sends a "stop" or "ponderhit" command. We therefore simply wait here
216 // until the GUI sends one of those commands.
218 while (!Threads.stop && (ponder || Limits.infinite))
219 {} // Busy wait for a stop or a ponder reset
221 // Stop the threads if not already stopped (also raise the stop if
222 // "ponderhit" just reset Threads.ponder).
225 // Wait until all threads have finished
226 Threads.wait_for_search_finished();
228 // When playing in 'nodes as time' mode, subtract the searched nodes from
229 // the available ones before exiting.
231 Time.availableNodes += Limits.inc[us] - Threads.nodes_searched();
233 Thread* bestThread = this;
234 Skill skill = Skill(Options["Skill Level"], Options["UCI_LimitStrength"] ? int(Options["UCI_Elo"]) : 0);
236 if ( int(Options["MultiPV"]) == 1
239 && rootMoves[0].pv[0] != MOVE_NONE)
240 bestThread = Threads.get_best_thread();
242 bestPreviousScore = bestThread->rootMoves[0].score;
243 bestPreviousAverageScore = bestThread->rootMoves[0].averageScore;
245 // Send again PV info if we have a new best thread
246 if (bestThread != this)
247 sync_cout << UCI::pv(bestThread->rootPos, bestThread->completedDepth) << sync_endl;
249 sync_cout << "bestmove " << UCI::move(bestThread->rootMoves[0].pv[0], rootPos.is_chess960());
251 if (bestThread->rootMoves[0].pv.size() > 1 || bestThread->rootMoves[0].extract_ponder_from_tt(rootPos))
252 std::cout << " ponder " << UCI::move(bestThread->rootMoves[0].pv[1], rootPos.is_chess960());
254 std::cout << sync_endl;
258 /// Thread::search() is the main iterative deepening loop. It calls search()
259 /// repeatedly with increasing depth until the allocated thinking time has been
260 /// consumed, the user stops the search, or the maximum search depth is reached.
262 void Thread::search() {
264 // To allow access to (ss-7) up to (ss+2), the stack must be oversized.
265 // The former is needed to allow update_continuation_histories(ss-1, ...),
266 // which accesses its argument at ss-6, also near the root.
267 // The latter is needed for statScore and killer initialization.
268 Stack stack[MAX_PLY+10], *ss = stack+7;
270 Value alpha, beta, delta;
271 Move lastBestMove = MOVE_NONE;
272 Depth lastBestMoveDepth = 0;
273 MainThread* mainThread = (this == Threads.main() ? Threads.main() : nullptr);
274 double timeReduction = 1, totBestMoveChanges = 0;
275 Color us = rootPos.side_to_move();
278 std::memset(ss-7, 0, 10 * sizeof(Stack));
279 for (int i = 7; i > 0; --i)
281 (ss-i)->continuationHistory = &this->continuationHistory[0][0][NO_PIECE][0]; // Use as a sentinel
282 (ss-i)->staticEval = VALUE_NONE;
285 for (int i = 0; i <= MAX_PLY + 2; ++i)
290 bestValue = delta = alpha = -VALUE_INFINITE;
291 beta = VALUE_INFINITE;
295 if (mainThread->bestPreviousScore == VALUE_INFINITE)
296 for (int i = 0; i < 4; ++i)
297 mainThread->iterValue[i] = VALUE_ZERO;
299 for (int i = 0; i < 4; ++i)
300 mainThread->iterValue[i] = mainThread->bestPreviousScore;
303 size_t multiPV = size_t(Options["MultiPV"]);
304 Skill skill(Options["Skill Level"], Options["UCI_LimitStrength"] ? int(Options["UCI_Elo"]) : 0);
306 // When playing with strength handicap enable MultiPV search that we will
307 // use behind the scenes to retrieve a set of possible moves.
309 multiPV = std::max(multiPV, (size_t)4);
311 multiPV = std::min(multiPV, rootMoves.size());
313 complexityAverage.set(153, 1);
315 optimism[us] = optimism[~us] = VALUE_ZERO;
317 int searchAgainCounter = 0;
319 // Iterative deepening loop until requested to stop or the target depth is reached
320 while ( ++rootDepth < MAX_PLY
322 && !(Limits.depth && mainThread && rootDepth > Limits.depth))
324 // Age out PV variability metric
326 totBestMoveChanges /= 2;
328 // Save the last iteration's scores before first PV line is searched and
329 // all the move scores except the (new) PV are set to -VALUE_INFINITE.
330 for (RootMove& rm : rootMoves)
331 rm.previousScore = rm.score;
336 if (!Threads.increaseDepth)
337 searchAgainCounter++;
339 // MultiPV loop. We perform a full root search for each PV line
340 for (pvIdx = 0; pvIdx < multiPV && !Threads.stop; ++pvIdx)
345 for (pvLast++; pvLast < rootMoves.size(); pvLast++)
346 if (rootMoves[pvLast].tbRank != rootMoves[pvFirst].tbRank)
350 // Reset UCI info selDepth for each depth and each PV line
353 // Reset aspiration window starting size
356 Value prev = rootMoves[pvIdx].averageScore;
357 delta = Value(10) + int(prev) * prev / 16502;
358 alpha = std::max(prev - delta,-VALUE_INFINITE);
359 beta = std::min(prev + delta, VALUE_INFINITE);
361 // Adjust optimism based on root move's previousScore
362 int opt = 120 * prev / (std::abs(prev) + 161);
363 optimism[ us] = Value(opt);
364 optimism[~us] = -optimism[us];
367 // Start with a small aspiration window and, in the case of a fail
368 // high/low, re-search with a bigger window until we don't fail
370 int failedHighCnt = 0;
373 // Adjust the effective depth searched, but ensuring at least one effective increment for every
374 // four searchAgain steps (see issue #2717).
375 Depth adjustedDepth = std::max(1, rootDepth - failedHighCnt - 3 * (searchAgainCounter + 1) / 4);
376 bestValue = Stockfish::search<Root>(rootPos, ss, alpha, beta, adjustedDepth, false);
378 // Bring the best move to the front. It is critical that sorting
379 // is done with a stable algorithm because all the values but the
380 // first and eventually the new best one are set to -VALUE_INFINITE
381 // and we want to keep the same order for all the moves except the
382 // new PV that goes to the front. Note that in case of MultiPV
383 // search the already searched PV lines are preserved.
384 std::stable_sort(rootMoves.begin() + pvIdx, rootMoves.begin() + pvLast);
386 // If search has been stopped, we break immediately. Sorting is
387 // safe because RootMoves is still valid, although it refers to
388 // the previous iteration.
392 // When failing high/low give some update (without cluttering
393 // the UI) before a re-search.
396 && (bestValue <= alpha || bestValue >= beta)
397 && Time.elapsed() > 3000)
398 sync_cout << UCI::pv(rootPos, rootDepth) << sync_endl;
400 // In case of failing low/high increase aspiration window and
401 // re-search, otherwise exit the loop.
402 if (bestValue <= alpha)
404 beta = (alpha + beta) / 2;
405 alpha = std::max(bestValue - delta, -VALUE_INFINITE);
409 mainThread->stopOnPonderhit = false;
411 else if (bestValue >= beta)
413 beta = std::min(bestValue + delta, VALUE_INFINITE);
419 delta += delta / 4 + 2;
421 assert(alpha >= -VALUE_INFINITE && beta <= VALUE_INFINITE);
424 // Sort the PV lines searched so far and update the GUI
425 std::stable_sort(rootMoves.begin() + pvFirst, rootMoves.begin() + pvIdx + 1);
428 && (Threads.stop || pvIdx + 1 == multiPV || Time.elapsed() > 3000))
429 sync_cout << UCI::pv(rootPos, rootDepth) << sync_endl;
433 completedDepth = rootDepth;
435 if (rootMoves[0].pv[0] != lastBestMove)
437 lastBestMove = rootMoves[0].pv[0];
438 lastBestMoveDepth = rootDepth;
441 // Have we found a "mate in x"?
443 && bestValue >= VALUE_MATE_IN_MAX_PLY
444 && VALUE_MATE - bestValue <= 2 * Limits.mate)
450 // If skill level is enabled and time is up, pick a sub-optimal best move
451 if (skill.enabled() && skill.time_to_pick(rootDepth))
452 skill.pick_best(multiPV);
454 // Use part of the gained time from a previous stable move for the current move
455 for (Thread* th : Threads)
457 totBestMoveChanges += th->bestMoveChanges;
458 th->bestMoveChanges = 0;
461 // Do we have time for the next iteration? Can we stop searching now?
462 if ( Limits.use_time_management()
464 && !mainThread->stopOnPonderhit)
466 double fallingEval = (69 + 13 * (mainThread->bestPreviousAverageScore - bestValue)
467 + 6 * (mainThread->iterValue[iterIdx] - bestValue)) / 619.6;
468 fallingEval = std::clamp(fallingEval, 0.5, 1.5);
470 // If the bestMove is stable over several iterations, reduce time accordingly
471 timeReduction = lastBestMoveDepth + 8 < completedDepth ? 1.57 : 0.65;
472 double reduction = (1.4 + mainThread->previousTimeReduction) / (2.08 * timeReduction);
473 double bestMoveInstability = 1 + 1.8 * totBestMoveChanges / Threads.size();
474 int complexity = mainThread->complexityAverage.value();
475 double complexPosition = std::min(1.03 + (complexity - 241) / 1552.0, 1.45);
477 double totalTime = Time.optimum() * fallingEval * reduction * bestMoveInstability * complexPosition;
479 // Cap used time in case of a single legal move for a better viewer experience in tournaments
480 // yielding correct scores and sufficiently fast moves.
481 if (rootMoves.size() == 1)
482 totalTime = std::min(500.0, totalTime);
484 // Stop the search if we have exceeded the totalTime
485 if (Time.elapsed() > totalTime)
487 // If we are allowed to ponder do not stop the search now but
488 // keep pondering until the GUI sends "ponderhit" or "stop".
489 if (mainThread->ponder)
490 mainThread->stopOnPonderhit = true;
494 else if ( !mainThread->ponder
495 && Time.elapsed() > totalTime * 0.50)
496 Threads.increaseDepth = false;
498 Threads.increaseDepth = true;
501 mainThread->iterValue[iterIdx] = bestValue;
502 iterIdx = (iterIdx + 1) & 3;
508 mainThread->previousTimeReduction = timeReduction;
510 // If skill level is enabled, swap best PV line with the sub-optimal one
512 std::swap(rootMoves[0], *std::find(rootMoves.begin(), rootMoves.end(),
513 skill.best ? skill.best : skill.pick_best(multiPV)));
519 // search<>() is the main search function for both PV and non-PV nodes
521 template <NodeType nodeType>
522 Value search(Position& pos, Stack* ss, Value alpha, Value beta, Depth depth, bool cutNode) {
524 constexpr bool PvNode = nodeType != NonPV;
525 constexpr bool rootNode = nodeType == Root;
527 // Check if we have an upcoming move which draws by repetition, or
528 // if the opponent had an alternative move earlier to this position.
530 && pos.rule50_count() >= 3
531 && alpha < VALUE_DRAW
532 && pos.has_game_cycle(ss->ply))
534 alpha = value_draw(pos.this_thread());
539 // Dive into quiescence search when the depth reaches zero
541 return qsearch<PvNode ? PV : NonPV>(pos, ss, alpha, beta);
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, improvement, complexity;
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 applies 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)->ttPv = false;
605 (ss+1)->excludedMove = bestMove = MOVE_NONE;
606 (ss+2)->killers[0] = (ss+2)->killers[1] = MOVE_NONE;
607 (ss+2)->cutoffCnt = 0;
608 ss->doubleExtensions = (ss-1)->doubleExtensions;
609 Square prevSq = to_sq((ss-1)->currentMove);
611 // Initialize statScore to zero for the grandchildren of the current position.
612 // So statScore is shared between all grandchildren and only the first grandchild
613 // starts with statScore = 0. Later grandchildren start with the last calculated
614 // statScore of the previous grandchild. This influences the reduction rules in
615 // LMR which are based on the statScore of parent position.
617 (ss+2)->statScore = 0;
619 // Step 4. Transposition table lookup.
620 excludedMove = ss->excludedMove;
622 tte = TT.probe(posKey, ss->ttHit);
623 ttValue = ss->ttHit ? value_from_tt(tte->value(), ss->ply, pos.rule50_count()) : VALUE_NONE;
624 ttMove = rootNode ? thisThread->rootMoves[thisThread->pvIdx].pv[0]
625 : ss->ttHit ? tte->move() : MOVE_NONE;
626 ttCapture = ttMove && pos.capture_stage(ttMove);
628 // At this point, if excluded, skip straight to step 6, static eval. However,
629 // to save indentation, we list the condition in all code between here and there.
631 ss->ttPv = PvNode || (ss->ttHit && tte->is_pv());
633 // At non-PV nodes we check for an early TT cutoff
637 && tte->depth() > depth - (tte->bound() == BOUND_EXACT)
638 && ttValue != VALUE_NONE // Possible in case of TT access race
639 && (tte->bound() & (ttValue >= beta ? BOUND_LOWER : BOUND_UPPER)))
641 // If ttMove is quiet, update move sorting heuristics on TT hit (~2 Elo)
646 // Bonus for a quiet ttMove that fails high (~2 Elo)
648 update_quiet_stats(pos, ss, ttMove, stat_bonus(depth));
650 // Extra penalty for early quiet moves of the previous ply (~0 Elo on STC, ~2 Elo on LTC)
651 if ((ss-1)->moveCount <= 2 && !priorCapture)
652 update_continuation_histories(ss-1, pos.piece_on(prevSq), prevSq, -stat_bonus(depth + 1));
654 // Penalty for a quiet ttMove that fails low (~1 Elo)
657 int penalty = -stat_bonus(depth);
658 thisThread->mainHistory[us][from_to(ttMove)] << penalty;
659 update_continuation_histories(ss, pos.moved_piece(ttMove), to_sq(ttMove), penalty);
663 // Partial workaround for the graph history interaction problem
664 // For high rule50 counts don't produce transposition table cutoffs.
665 if (pos.rule50_count() < 90)
669 // Step 5. Tablebases probe
670 if (!rootNode && !excludedMove && TB::Cardinality)
672 int piecesCount = pos.count<ALL_PIECES>();
674 if ( piecesCount <= TB::Cardinality
675 && (piecesCount < TB::Cardinality || depth >= TB::ProbeDepth)
676 && pos.rule50_count() == 0
677 && !pos.can_castle(ANY_CASTLING))
680 TB::WDLScore wdl = Tablebases::probe_wdl(pos, &err);
682 // Force check of time on the next occasion
683 if (thisThread == Threads.main())
684 static_cast<MainThread*>(thisThread)->callsCnt = 0;
686 if (err != TB::ProbeState::FAIL)
688 thisThread->tbHits.fetch_add(1, std::memory_order_relaxed);
690 int drawScore = TB::UseRule50 ? 1 : 0;
692 // use the range VALUE_MATE_IN_MAX_PLY to VALUE_TB_WIN_IN_MAX_PLY to score
693 value = wdl < -drawScore ? VALUE_MATED_IN_MAX_PLY + ss->ply + 1
694 : wdl > drawScore ? VALUE_MATE_IN_MAX_PLY - ss->ply - 1
695 : VALUE_DRAW + 2 * wdl * drawScore;
697 Bound b = wdl < -drawScore ? BOUND_UPPER
698 : wdl > drawScore ? BOUND_LOWER : BOUND_EXACT;
700 if ( b == BOUND_EXACT
701 || (b == BOUND_LOWER ? value >= beta : value <= alpha))
703 tte->save(posKey, value_to_tt(value, ss->ply), ss->ttPv, b,
704 std::min(MAX_PLY - 1, depth + 6),
705 MOVE_NONE, VALUE_NONE);
712 if (b == BOUND_LOWER)
713 bestValue = value, alpha = std::max(alpha, bestValue);
721 CapturePieceToHistory& captureHistory = thisThread->captureHistory;
723 // Step 6. Static evaluation of the position
726 // Skip early pruning when in check
727 ss->staticEval = eval = VALUE_NONE;
733 else if (excludedMove)
735 // Providing the hint that this node's accumulator will be used often brings significant Elo gain (13 elo)
736 Eval::NNUE::hint_common_parent_position(pos);
737 eval = ss->staticEval;
738 complexity = abs(ss->staticEval - pos.psq_eg_stm());
742 // Never assume anything about values stored in TT
743 ss->staticEval = eval = tte->eval();
744 if (eval == VALUE_NONE)
745 ss->staticEval = eval = evaluate(pos, &complexity);
746 else // Fall back to (semi)classical complexity for TT hits, the NNUE complexity is lost
748 complexity = abs(ss->staticEval - pos.psq_eg_stm());
750 Eval::NNUE::hint_common_parent_position(pos);
753 // ttValue can be used as a better position evaluation (~7 Elo)
754 if ( ttValue != VALUE_NONE
755 && (tte->bound() & (ttValue > eval ? BOUND_LOWER : BOUND_UPPER)))
760 ss->staticEval = eval = evaluate(pos, &complexity);
761 // Save static evaluation into transposition table
762 tte->save(posKey, VALUE_NONE, ss->ttPv, BOUND_NONE, DEPTH_NONE, MOVE_NONE, eval);
765 thisThread->complexityAverage.update(complexity);
767 // Use static evaluation difference to improve quiet move ordering (~4 Elo)
768 if (is_ok((ss-1)->currentMove) && !(ss-1)->inCheck && !priorCapture)
770 int bonus = std::clamp(-19 * int((ss-1)->staticEval + ss->staticEval), -1920, 1920);
771 thisThread->mainHistory[~us][from_to((ss-1)->currentMove)] << bonus;
774 // Set up the improvement variable, which is the difference between the current
775 // static evaluation and the previous static evaluation at our turn (if we were
776 // in check at our previous move we look at the move prior to it). The improvement
777 // margin and the improving flag are used in various pruning heuristics.
778 improvement = (ss-2)->staticEval != VALUE_NONE ? ss->staticEval - (ss-2)->staticEval
779 : (ss-4)->staticEval != VALUE_NONE ? ss->staticEval - (ss-4)->staticEval
781 improving = improvement > 0;
783 // Step 7. Razoring (~1 Elo).
784 // If eval is really low check with qsearch if it can exceed alpha, if it can't,
785 // return a fail low.
786 if (eval < alpha - 426 - 252 * depth * depth)
788 value = qsearch<NonPV>(pos, ss, alpha - 1, alpha);
793 // Step 8. Futility pruning: child node (~40 Elo).
794 // The depth condition is important for mate finding.
797 && eval - futility_margin(depth, improving) - (ss-1)->statScore / 280 >= beta
799 && eval < 25128) // larger than VALUE_KNOWN_WIN, but smaller than TB wins
802 // Step 9. Null move search with verification search (~35 Elo)
804 && (ss-1)->currentMove != MOVE_NULL
805 && (ss-1)->statScore < 18755
807 && eval >= ss->staticEval
808 && ss->staticEval >= beta - 19 * depth - improvement / 13 + 253 + complexity / 25
810 && pos.non_pawn_material(us)
811 && (ss->ply >= thisThread->nmpMinPly || us != thisThread->nmpColor))
813 assert(eval - beta >= 0);
815 // Null move dynamic reduction based on depth, eval and complexity of position
816 Depth R = std::min(int(eval - beta) / 168, 6) + depth / 3 + 4 - (complexity > 825);
818 ss->currentMove = MOVE_NULL;
819 ss->continuationHistory = &thisThread->continuationHistory[0][0][NO_PIECE][0];
821 pos.do_null_move(st);
823 Value nullValue = -search<NonPV>(pos, ss+1, -beta, -beta+1, depth-R, !cutNode);
825 pos.undo_null_move();
827 if (nullValue >= beta)
829 // Do not return unproven mate or TB scores
830 if (nullValue >= VALUE_TB_WIN_IN_MAX_PLY)
833 if (thisThread->nmpMinPly || (abs(beta) < VALUE_KNOWN_WIN && depth < 14))
836 assert(!thisThread->nmpMinPly); // Recursive verification is not allowed
838 // Do verification search at high depths, with null move pruning disabled
839 // for us, until ply exceeds nmpMinPly.
840 thisThread->nmpMinPly = ss->ply + 3 * (depth-R) / 4;
841 thisThread->nmpColor = us;
843 Value v = search<NonPV>(pos, ss, beta-1, beta, depth-R, false);
845 thisThread->nmpMinPly = 0;
852 probCutBeta = beta + 186 - 54 * improving;
854 // Step 10. ProbCut (~10 Elo)
855 // If we have a good enough capture (or queen promotion) and a reduced search returns a value
856 // much above beta, we can (almost) safely prune the previous move.
859 && abs(beta) < VALUE_TB_WIN_IN_MAX_PLY
860 // if value from transposition table is lower than probCutBeta, don't attempt probCut
861 // there and in further interactions with transposition table cutoff depth is set to depth - 3
862 // because probCut search has depth set to depth - 4 but we also do a move before it
863 // so effective depth is equal to depth - 3
865 && tte->depth() >= depth - 3
866 && ttValue != VALUE_NONE
867 && ttValue < probCutBeta))
869 assert(probCutBeta < VALUE_INFINITE);
871 MovePicker mp(pos, ttMove, probCutBeta - ss->staticEval, &captureHistory);
873 while ((move = mp.next_move()) != MOVE_NONE)
874 if (move != excludedMove && pos.legal(move))
876 assert(pos.capture_stage(move));
878 ss->currentMove = move;
879 ss->continuationHistory = &thisThread->continuationHistory[ss->inCheck]
881 [pos.moved_piece(move)]
884 pos.do_move(move, st);
886 // Perform a preliminary qsearch to verify that the move holds
887 value = -qsearch<NonPV>(pos, ss+1, -probCutBeta, -probCutBeta+1);
889 // If the qsearch held, perform the regular search
890 if (value >= probCutBeta)
891 value = -search<NonPV>(pos, ss+1, -probCutBeta, -probCutBeta+1, depth - 4, !cutNode);
895 if (value >= probCutBeta)
897 // Save ProbCut data into transposition table
898 tte->save(posKey, value_to_tt(value, ss->ply), ss->ttPv, BOUND_LOWER, depth - 3, move, ss->staticEval);
903 Eval::NNUE::hint_common_parent_position(pos);
906 // Step 11. If the position is not in TT, decrease depth by 3.
907 // Use qsearch if depth is equal or below zero (~9 Elo)
913 return qsearch<PV>(pos, ss, alpha, beta);
920 moves_loop: // When in check, search starts here
922 // Step 12. A small Probcut idea, when we are in check (~4 Elo)
923 probCutBeta = beta + 391;
928 && (tte->bound() & BOUND_LOWER)
929 && tte->depth() >= depth - 3
930 && ttValue >= probCutBeta
931 && abs(ttValue) <= VALUE_KNOWN_WIN
932 && abs(beta) <= VALUE_KNOWN_WIN)
935 const PieceToHistory* contHist[] = { (ss-1)->continuationHistory, (ss-2)->continuationHistory,
936 nullptr , (ss-4)->continuationHistory,
937 nullptr , (ss-6)->continuationHistory };
939 Move countermove = thisThread->counterMoves[pos.piece_on(prevSq)][prevSq];
941 MovePicker mp(pos, ttMove, depth, &thisThread->mainHistory,
948 moveCountPruning = singularQuietLMR = false;
950 // Indicate PvNodes that will probably fail low if the node was searched
951 // at a depth equal or greater than the current depth, and the result of this search was a fail low.
952 bool likelyFailLow = PvNode
954 && (tte->bound() & BOUND_UPPER)
955 && tte->depth() >= depth;
957 // Step 13. Loop through all pseudo-legal moves until no moves remain
958 // or a beta cutoff occurs.
959 while ((move = mp.next_move(moveCountPruning)) != MOVE_NONE)
963 if (move == excludedMove)
966 // At root obey the "searchmoves" option and skip moves not listed in Root
967 // Move List. As a consequence any illegal move is also skipped. In MultiPV
968 // mode we also skip PV moves which have been already searched and those
969 // of lower "TB rank" if we are in a TB root position.
970 if (rootNode && !std::count(thisThread->rootMoves.begin() + thisThread->pvIdx,
971 thisThread->rootMoves.begin() + thisThread->pvLast, move))
974 // Check for legality
975 if (!rootNode && !pos.legal(move))
978 ss->moveCount = ++moveCount;
980 if (rootNode && thisThread == Threads.main() && Time.elapsed() > 3000)
981 sync_cout << "info depth " << depth
982 << " currmove " << UCI::move(move, pos.is_chess960())
983 << " currmovenumber " << moveCount + thisThread->pvIdx << sync_endl;
985 (ss+1)->pv = nullptr;
988 capture = pos.capture_stage(move);
989 movedPiece = pos.moved_piece(move);
990 givesCheck = pos.gives_check(move);
992 // Calculate new depth for this move
993 newDepth = depth - 1;
995 Value delta = beta - alpha;
997 Depth r = reduction(improving, depth, moveCount, delta, thisThread->rootDelta);
999 // Step 14. Pruning at shallow depth (~120 Elo). Depth conditions are important for mate finding.
1001 && pos.non_pawn_material(us)
1002 && bestValue > VALUE_TB_LOSS_IN_MAX_PLY)
1004 // Skip quiet moves if movecount exceeds our FutilityMoveCount threshold (~8 Elo)
1005 moveCountPruning = moveCount >= futility_move_count(improving, depth);
1007 // Reduced depth of the next LMR search
1008 int lmrDepth = std::max(newDepth - r, 0);
1013 // Futility pruning for captures (~2 Elo)
1018 && ss->staticEval + 182 + 230 * lmrDepth + PieceValue[EG][pos.piece_on(to_sq(move))]
1019 + captureHistory[movedPiece][to_sq(move)][type_of(pos.piece_on(to_sq(move)))] / 7 < alpha)
1022 // SEE based pruning (~11 Elo)
1023 if (!pos.see_ge(move, Value(-206) * depth))
1028 int history = (*contHist[0])[movedPiece][to_sq(move)]
1029 + (*contHist[1])[movedPiece][to_sq(move)]
1030 + (*contHist[3])[movedPiece][to_sq(move)];
1032 // Continuation history based pruning (~2 Elo)
1034 && history < -4405 * (depth - 1))
1037 history += 2 * thisThread->mainHistory[us][from_to(move)];
1039 lmrDepth += history / 7278;
1040 lmrDepth = std::max(lmrDepth, -2);
1042 // Futility pruning: parent node (~13 Elo)
1045 && ss->staticEval + 103 + 138 * lmrDepth <= alpha)
1048 lmrDepth = std::max(lmrDepth, 0);
1050 // Prune moves with negative SEE (~4 Elo)
1051 if (!pos.see_ge(move, Value(-24 * lmrDepth * lmrDepth - 15 * lmrDepth)))
1056 // Step 15. Extensions (~100 Elo)
1057 // We take care to not overdo to avoid search getting stuck.
1058 if (ss->ply < thisThread->rootDepth * 2)
1060 // Singular extension search (~94 Elo). If all moves but one fail low on a
1061 // search of (alpha-s, beta-s), and just one fails high on (alpha, beta),
1062 // then that move is singular and should be extended. To verify this we do
1063 // a reduced search on all the other moves but the ttMove and if the
1064 // result is lower than ttValue minus a margin, then we will extend the ttMove.
1066 && depth >= 4 - (thisThread->completedDepth > 21) + 2 * (PvNode && tte->is_pv())
1068 && !excludedMove // Avoid recursive singular search
1069 /* && ttValue != VALUE_NONE Already implicit in the next condition */
1070 && abs(ttValue) < VALUE_KNOWN_WIN
1071 && (tte->bound() & BOUND_LOWER)
1072 && tte->depth() >= depth - 3)
1074 Value singularBeta = ttValue - (2 + (ss->ttPv && !PvNode)) * depth;
1075 Depth singularDepth = (depth - 1) / 2;
1077 ss->excludedMove = move;
1078 // the search with excludedMove will update ss->staticEval
1079 value = search<NonPV>(pos, ss, singularBeta - 1, singularBeta, singularDepth, cutNode);
1080 ss->excludedMove = MOVE_NONE;
1082 if (value < singularBeta)
1085 singularQuietLMR = !ttCapture;
1087 // Avoid search explosion by limiting the number of double extensions
1089 && value < singularBeta - 25
1090 && ss->doubleExtensions <= 10)
1093 depth += depth < 13;
1097 // Multi-cut pruning
1098 // Our ttMove is assumed to fail high, and now we failed high also on a reduced
1099 // search without the ttMove. So we assume this expected Cut-node is not singular,
1100 // that multiple moves fail high, and we can prune the whole subtree by returning
1102 else if (singularBeta >= beta)
1103 return singularBeta;
1105 // If the eval of ttMove is greater than beta, we reduce it (negative extension)
1106 else if (ttValue >= beta)
1109 // If the eval of ttMove is less than value, we reduce it (negative extension)
1110 else if (ttValue <= value)
1113 // If the eval of ttMove is less than alpha, we reduce it (negative extension)
1114 else if (ttValue <= alpha)
1118 // Check extensions (~1 Elo)
1119 else if ( givesCheck
1121 && abs(ss->staticEval) > 88)
1124 // Quiet ttMove extensions (~1 Elo)
1127 && move == ss->killers[0]
1128 && (*contHist[0])[movedPiece][to_sq(move)] >= 5705)
1132 // Add extension to new depth
1133 newDepth += extension;
1134 ss->doubleExtensions = (ss-1)->doubleExtensions + (extension == 2);
1136 // Speculative prefetch as early as possible
1137 prefetch(TT.first_entry(pos.key_after(move)));
1139 // Update the current move (this must be done after singular extension search)
1140 ss->currentMove = move;
1141 ss->continuationHistory = &thisThread->continuationHistory[ss->inCheck]
1146 // Step 16. Make the move
1147 pos.do_move(move, st, givesCheck);
1149 // Decrease reduction if position is or has been on the PV
1150 // and node is not likely to fail low. (~3 Elo)
1155 // Decrease reduction if opponent's move count is high (~1 Elo)
1156 if ((ss-1)->moveCount > 7)
1159 // Increase reduction for cut nodes (~3 Elo)
1163 // Increase reduction if ttMove is a capture (~3 Elo)
1167 // Decrease reduction for PvNodes based on depth
1169 r -= 1 + 12 / (3 + depth);
1171 // Decrease reduction if ttMove has been singularly extended (~1 Elo)
1172 if (singularQuietLMR)
1175 // Decrease reduction if we move a threatened piece (~1 Elo)
1177 && (mp.threatenedPieces & from_sq(move)))
1180 // Increase reduction if next ply has a lot of fail high
1181 if ((ss+1)->cutoffCnt > 3)
1184 // Decrease reduction if move is a killer and we have a good history
1185 if (move == ss->killers[0]
1186 && (*contHist[0])[movedPiece][to_sq(move)] >= 3722)
1189 ss->statScore = 2 * thisThread->mainHistory[us][from_to(move)]
1190 + (*contHist[0])[movedPiece][to_sq(move)]
1191 + (*contHist[1])[movedPiece][to_sq(move)]
1192 + (*contHist[3])[movedPiece][to_sq(move)]
1195 // Decrease/increase reduction for moves with a good/bad history (~30 Elo)
1196 r -= ss->statScore / (11791 + 3992 * (depth > 6 && depth < 19));
1198 // Step 17. Late moves reduction / extension (LMR, ~117 Elo)
1199 // We use various heuristics for the sons of a node after the first son has
1200 // been searched. In general we would like to reduce them, but there are many
1201 // cases where we extend a son if it has good chances to be "interesting".
1203 && moveCount > 1 + (PvNode && ss->ply <= 1)
1206 || (cutNode && (ss-1)->moveCount > 1)))
1208 // In general we want to cap the LMR depth search at newDepth, but when
1209 // reduction is negative, we allow this move a limited search extension
1210 // beyond the first move depth. This may lead to hidden double extensions.
1211 Depth d = std::clamp(newDepth - r, 1, newDepth + 1);
1213 value = -search<NonPV>(pos, ss+1, -(alpha+1), -alpha, d, true);
1215 // Do full depth search when reduced LMR search fails high
1216 if (value > alpha && d < newDepth)
1218 // Adjust full depth search based on LMR results - if result
1219 // was good enough search deeper, if it was bad enough search shallower
1220 const bool doDeeperSearch = value > (alpha + 58 + 12 * (newDepth - d));
1221 const bool doEvenDeeperSearch = value > alpha + 588 && ss->doubleExtensions <= 5;
1222 const bool doShallowerSearch = value < bestValue + newDepth;
1224 ss->doubleExtensions = ss->doubleExtensions + doEvenDeeperSearch;
1226 newDepth += doDeeperSearch - doShallowerSearch + doEvenDeeperSearch;
1229 value = -search<NonPV>(pos, ss+1, -(alpha+1), -alpha, newDepth, !cutNode);
1231 int bonus = value > alpha ? stat_bonus(newDepth)
1232 : -stat_bonus(newDepth);
1234 update_continuation_histories(ss, movedPiece, to_sq(move), bonus);
1238 // Step 18. Full depth search when LMR is skipped. If expected reduction is high, reduce its depth by 1.
1239 else if (!PvNode || moveCount > 1)
1241 // Increase reduction for cut nodes and not ttMove (~1 Elo)
1242 if (!ttMove && cutNode)
1245 value = -search<NonPV>(pos, ss+1, -(alpha+1), -alpha, newDepth - (r > 4), !cutNode);
1248 // For PV nodes only, do a full PV search on the first move or after a fail
1249 // high (in the latter case search only if value < beta), otherwise let the
1250 // parent node fail low with value <= alpha and try another move.
1251 if (PvNode && (moveCount == 1 || (value > alpha && (rootNode || value < beta))))
1254 (ss+1)->pv[0] = MOVE_NONE;
1256 value = -search<PV>(pos, ss+1, -beta, -alpha, newDepth, false);
1259 // Step 19. Undo move
1260 pos.undo_move(move);
1262 assert(value > -VALUE_INFINITE && value < VALUE_INFINITE);
1264 // Step 20. Check for a new best move
1265 // Finished searching the move. If a stop occurred, the return value of
1266 // the search cannot be trusted, and we return immediately without
1267 // updating best move, PV and TT.
1268 if (Threads.stop.load(std::memory_order_relaxed))
1273 RootMove& rm = *std::find(thisThread->rootMoves.begin(),
1274 thisThread->rootMoves.end(), move);
1276 rm.averageScore = rm.averageScore != -VALUE_INFINITE ? (2 * value + rm.averageScore) / 3 : value;
1278 // PV move or new best move?
1279 if (moveCount == 1 || value > alpha)
1281 rm.score = rm.uciScore = value;
1282 rm.selDepth = thisThread->selDepth;
1283 rm.scoreLowerbound = rm.scoreUpperbound = false;
1287 rm.scoreLowerbound = true;
1290 else if (value <= alpha)
1292 rm.scoreUpperbound = true;
1293 rm.uciScore = alpha;
1300 for (Move* m = (ss+1)->pv; *m != MOVE_NONE; ++m)
1301 rm.pv.push_back(*m);
1303 // We record how often the best move has been changed in each iteration.
1304 // This information is used for time management. In MultiPV mode,
1305 // we must take care to only do this for the first PV line.
1307 && !thisThread->pvIdx)
1308 ++thisThread->bestMoveChanges;
1311 // All other moves but the PV are set to the lowest value: this
1312 // is not a problem when sorting because the sort is stable and the
1313 // move position in the list is preserved - just the PV is pushed up.
1314 rm.score = -VALUE_INFINITE;
1317 if (value > bestValue)
1325 if (PvNode && !rootNode) // Update pv even in fail-high case
1326 update_pv(ss->pv, move, (ss+1)->pv);
1328 if (PvNode && value < beta) // Update alpha! Always alpha < beta
1332 // Reduce other moves if we have found at least one score improvement
1344 assert(value >= beta); // Fail high
1351 // If the move is worse than some previously searched move, remember it to update its stats later
1352 if (move != bestMove)
1354 if (capture && captureCount < 32)
1355 capturesSearched[captureCount++] = move;
1357 else if (!capture && quietCount < 64)
1358 quietsSearched[quietCount++] = move;
1362 // The following condition would detect a stop only after move loop has been
1363 // completed. But in this case bestValue is valid because we have fully
1364 // searched our subtree, and we can anyhow save the result in TT.
1370 // Step 21. Check for mate and stalemate
1371 // All legal moves have been searched and if there are no legal moves, it
1372 // must be a mate or a stalemate. If we are in a singular extension search then
1373 // return a fail low score.
1375 assert(moveCount || !ss->inCheck || excludedMove || !MoveList<LEGAL>(pos).size());
1378 bestValue = excludedMove ? alpha :
1379 ss->inCheck ? mated_in(ss->ply)
1382 // If there is a move which produces search value greater than alpha we update stats of searched moves
1384 update_all_stats(pos, ss, bestMove, bestValue, beta, prevSq,
1385 quietsSearched, quietCount, capturesSearched, captureCount, depth);
1387 // Bonus for prior countermove that caused the fail low
1388 else if (!priorCapture)
1390 int bonus = (depth > 5) + (PvNode || cutNode) + (bestValue < alpha - 97 * depth) + ((ss-1)->moveCount > 10);
1391 update_continuation_histories(ss-1, pos.piece_on(prevSq), prevSq, stat_bonus(depth) * bonus);
1395 bestValue = std::min(bestValue, maxValue);
1397 // If no good move is found and the previous position was ttPv, then the previous
1398 // opponent move is probably good and the new position is added to the search tree.
1399 if (bestValue <= alpha)
1400 ss->ttPv = ss->ttPv || ((ss-1)->ttPv && depth > 3);
1402 // Write gathered information in transposition table
1403 if (!excludedMove && !(rootNode && thisThread->pvIdx))
1404 tte->save(posKey, value_to_tt(bestValue, ss->ply), ss->ttPv,
1405 bestValue >= beta ? BOUND_LOWER :
1406 PvNode && bestMove ? BOUND_EXACT : BOUND_UPPER,
1407 depth, bestMove, ss->staticEval);
1409 assert(bestValue > -VALUE_INFINITE && bestValue < VALUE_INFINITE);
1415 // qsearch() is the quiescence search function, which is called by the main search
1416 // function with zero depth, or recursively with further decreasing depth per call.
1418 template <NodeType nodeType>
1419 Value qsearch(Position& pos, Stack* ss, Value alpha, Value beta, Depth depth) {
1421 static_assert(nodeType != Root);
1422 constexpr bool PvNode = nodeType == PV;
1424 assert(alpha >= -VALUE_INFINITE && alpha < beta && beta <= VALUE_INFINITE);
1425 assert(PvNode || (alpha == beta - 1));
1430 ASSERT_ALIGNED(&st, Eval::NNUE::CacheLineSize);
1434 Move ttMove, move, bestMove;
1436 Value bestValue, value, ttValue, futilityValue, futilityBase;
1437 bool pvHit, givesCheck, capture;
1440 // Step 1. Initialize node
1444 ss->pv[0] = MOVE_NONE;
1447 Thread* thisThread = pos.this_thread();
1448 bestMove = MOVE_NONE;
1449 ss->inCheck = pos.checkers();
1452 // Step 2. Check for an immediate draw or maximum ply reached
1453 if ( pos.is_draw(ss->ply)
1454 || ss->ply >= MAX_PLY)
1455 return (ss->ply >= MAX_PLY && !ss->inCheck) ? evaluate(pos) : VALUE_DRAW;
1457 assert(0 <= ss->ply && ss->ply < MAX_PLY);
1459 // Decide whether or not to include checks: this fixes also the type of
1460 // TT entry depth that we are going to use. Note that in qsearch we use
1461 // only two types of depth in TT: DEPTH_QS_CHECKS or DEPTH_QS_NO_CHECKS.
1462 ttDepth = ss->inCheck || depth >= DEPTH_QS_CHECKS ? DEPTH_QS_CHECKS
1463 : DEPTH_QS_NO_CHECKS;
1465 // Step 3. Transposition table lookup
1467 tte = TT.probe(posKey, ss->ttHit);
1468 ttValue = ss->ttHit ? value_from_tt(tte->value(), ss->ply, pos.rule50_count()) : VALUE_NONE;
1469 ttMove = ss->ttHit ? tte->move() : MOVE_NONE;
1470 pvHit = ss->ttHit && tte->is_pv();
1472 // At non-PV nodes we check for an early TT cutoff
1475 && tte->depth() >= ttDepth
1476 && ttValue != VALUE_NONE // Only in case of TT access race
1477 && (tte->bound() & (ttValue >= beta ? BOUND_LOWER : BOUND_UPPER)))
1480 // Step 4. Static evaluation of the position
1483 ss->staticEval = VALUE_NONE;
1484 bestValue = futilityBase = -VALUE_INFINITE;
1490 // Never assume anything about values stored in TT
1491 if ((ss->staticEval = bestValue = tte->eval()) == VALUE_NONE)
1492 ss->staticEval = bestValue = evaluate(pos);
1494 // ttValue can be used as a better position evaluation (~13 Elo)
1495 if ( ttValue != VALUE_NONE
1496 && (tte->bound() & (ttValue > bestValue ? BOUND_LOWER : BOUND_UPPER)))
1497 bestValue = ttValue;
1500 // In case of null move search use previous static eval with a different sign
1501 ss->staticEval = bestValue =
1502 (ss-1)->currentMove != MOVE_NULL ? evaluate(pos)
1503 : -(ss-1)->staticEval;
1505 // Stand pat. Return immediately if static value is at least beta
1506 if (bestValue >= beta)
1508 // Save gathered info in transposition table
1510 tte->save(posKey, value_to_tt(bestValue, ss->ply), false, BOUND_LOWER,
1511 DEPTH_NONE, MOVE_NONE, ss->staticEval);
1516 if (PvNode && bestValue > alpha)
1519 futilityBase = bestValue + 168;
1522 const PieceToHistory* contHist[] = { (ss-1)->continuationHistory, (ss-2)->continuationHistory,
1523 nullptr , (ss-4)->continuationHistory,
1524 nullptr , (ss-6)->continuationHistory };
1526 // Initialize a MovePicker object for the current position, and prepare
1527 // to search the moves. Because the depth is <= 0 here, only captures,
1528 // queen promotions, and other checks (only if depth >= DEPTH_QS_CHECKS)
1529 // will be generated.
1530 Square prevSq = to_sq((ss-1)->currentMove);
1531 MovePicker mp(pos, ttMove, depth, &thisThread->mainHistory,
1532 &thisThread->captureHistory,
1536 int quietCheckEvasions = 0;
1538 // Step 5. Loop through all pseudo-legal moves until no moves remain
1539 // or a beta cutoff occurs.
1540 while ((move = mp.next_move()) != MOVE_NONE)
1542 assert(is_ok(move));
1544 // Check for legality
1545 if (!pos.legal(move))
1548 givesCheck = pos.gives_check(move);
1549 capture = pos.capture_stage(move);
1554 if (bestValue > VALUE_TB_LOSS_IN_MAX_PLY)
1556 // Futility pruning and moveCount pruning (~10 Elo)
1558 && to_sq(move) != prevSq
1559 && futilityBase > -VALUE_KNOWN_WIN
1560 && type_of(move) != PROMOTION)
1565 futilityValue = futilityBase + PieceValue[EG][pos.piece_on(to_sq(move))];
1567 if (futilityValue <= alpha)
1569 bestValue = std::max(bestValue, futilityValue);
1573 if (futilityBase <= alpha && !pos.see_ge(move, VALUE_ZERO + 1))
1575 bestValue = std::max(bestValue, futilityBase);
1580 // We prune after 2nd quiet check evasion where being 'in check' is implicitly checked through the counter
1581 // and being a 'quiet' apart from being a tt move is assumed after an increment because captures are pushed ahead.
1582 if (quietCheckEvasions > 1)
1585 // Continuation history based pruning (~3 Elo)
1587 && (*contHist[0])[pos.moved_piece(move)][to_sq(move)] < 0
1588 && (*contHist[1])[pos.moved_piece(move)][to_sq(move)] < 0)
1591 // Do not search moves with bad enough SEE values (~5 Elo)
1592 if (!pos.see_ge(move, Value(-110)))
1596 // Speculative prefetch as early as possible
1597 prefetch(TT.first_entry(pos.key_after(move)));
1599 // Update the current move
1600 ss->currentMove = move;
1601 ss->continuationHistory = &thisThread->continuationHistory[ss->inCheck]
1603 [pos.moved_piece(move)]
1606 quietCheckEvasions += !capture && ss->inCheck;
1608 // Step 7. Make and search the move
1609 pos.do_move(move, st, givesCheck);
1610 value = -qsearch<nodeType>(pos, ss+1, -beta, -alpha, depth - 1);
1611 pos.undo_move(move);
1613 assert(value > -VALUE_INFINITE && value < VALUE_INFINITE);
1615 // Step 8. Check for a new best move
1616 if (value > bestValue)
1624 if (PvNode) // Update pv even in fail-high case
1625 update_pv(ss->pv, move, (ss+1)->pv);
1627 if (PvNode && value < beta) // Update alpha here!
1635 // Step 9. Check for mate
1636 // All legal moves have been searched. A special case: if we're in check
1637 // and no legal moves were found, it is checkmate.
1638 if (ss->inCheck && bestValue == -VALUE_INFINITE)
1640 assert(!MoveList<LEGAL>(pos).size());
1642 return mated_in(ss->ply); // Plies to mate from the root
1645 // Save gathered info in transposition table
1646 tte->save(posKey, value_to_tt(bestValue, ss->ply), pvHit,
1647 bestValue >= beta ? BOUND_LOWER : BOUND_UPPER,
1648 ttDepth, bestMove, ss->staticEval);
1650 assert(bestValue > -VALUE_INFINITE && bestValue < VALUE_INFINITE);
1656 // value_to_tt() adjusts a mate or TB score from "plies to mate from the root" to
1657 // "plies to mate from the current position". Standard scores are unchanged.
1658 // The function is called before storing a value in the transposition table.
1660 Value value_to_tt(Value v, int ply) {
1662 assert(v != VALUE_NONE);
1664 return v >= VALUE_TB_WIN_IN_MAX_PLY ? v + ply
1665 : v <= VALUE_TB_LOSS_IN_MAX_PLY ? v - ply : v;
1669 // value_from_tt() is the inverse of value_to_tt(): it adjusts a mate or TB score
1670 // from the transposition table (which refers to the plies to mate/be mated from
1671 // current position) to "plies to mate/be mated (TB win/loss) from the root". However,
1672 // for mate scores, to avoid potentially false mate scores related to the 50 moves rule
1673 // and the graph history interaction, we return an optimal TB score instead.
1675 Value value_from_tt(Value v, int ply, int r50c) {
1677 if (v == VALUE_NONE)
1680 if (v >= VALUE_TB_WIN_IN_MAX_PLY) // TB win or better
1682 if (v >= VALUE_MATE_IN_MAX_PLY && VALUE_MATE - v > 99 - r50c)
1683 return VALUE_MATE_IN_MAX_PLY - 1; // do not return a potentially false mate score
1688 if (v <= VALUE_TB_LOSS_IN_MAX_PLY) // TB loss or worse
1690 if (v <= VALUE_MATED_IN_MAX_PLY && VALUE_MATE + v > 99 - r50c)
1691 return VALUE_MATED_IN_MAX_PLY + 1; // do not return a potentially false mate score
1700 // update_pv() adds current move and appends child pv[]
1702 void update_pv(Move* pv, Move move, const Move* childPv) {
1704 for (*pv++ = move; childPv && *childPv != MOVE_NONE; )
1710 // update_all_stats() updates stats at the end of search() when a bestMove is found
1712 void update_all_stats(const Position& pos, Stack* ss, Move bestMove, Value bestValue, Value beta, Square prevSq,
1713 Move* quietsSearched, int quietCount, Move* capturesSearched, int captureCount, Depth depth) {
1715 Color us = pos.side_to_move();
1716 Thread* thisThread = pos.this_thread();
1717 CapturePieceToHistory& captureHistory = thisThread->captureHistory;
1718 Piece moved_piece = pos.moved_piece(bestMove);
1719 PieceType captured = type_of(pos.piece_on(to_sq(bestMove)));
1720 int bonus1 = stat_bonus(depth + 1);
1722 if (!pos.capture_stage(bestMove))
1724 int bonus2 = bestValue > beta + 153 ? bonus1 // larger bonus
1725 : stat_bonus(depth); // smaller bonus
1727 // Increase stats for the best move in case it was a quiet move
1728 update_quiet_stats(pos, ss, bestMove, bonus2);
1730 // Decrease stats for all non-best quiet moves
1731 for (int i = 0; i < quietCount; ++i)
1733 thisThread->mainHistory[us][from_to(quietsSearched[i])] << -bonus2;
1734 update_continuation_histories(ss, pos.moved_piece(quietsSearched[i]), to_sq(quietsSearched[i]), -bonus2);
1738 // Increase stats for the best move in case it was a capture move
1739 captureHistory[moved_piece][to_sq(bestMove)][captured] << bonus1;
1741 // Extra penalty for a quiet early move that was not a TT move or
1742 // main killer move in previous ply when it gets refuted.
1743 if ( ((ss-1)->moveCount == 1 + (ss-1)->ttHit || ((ss-1)->currentMove == (ss-1)->killers[0]))
1744 && !pos.captured_piece())
1745 update_continuation_histories(ss-1, pos.piece_on(prevSq), prevSq, -bonus1);
1747 // Decrease stats for all non-best capture moves
1748 for (int i = 0; i < captureCount; ++i)
1750 moved_piece = pos.moved_piece(capturesSearched[i]);
1751 captured = type_of(pos.piece_on(to_sq(capturesSearched[i])));
1752 captureHistory[moved_piece][to_sq(capturesSearched[i])][captured] << -bonus1;
1757 // update_continuation_histories() updates histories of the move pairs formed
1758 // by moves at ply -1, -2, -4, and -6 with current move.
1760 void update_continuation_histories(Stack* ss, Piece pc, Square to, int bonus) {
1762 for (int i : {1, 2, 4, 6})
1764 // Only update first 2 continuation histories if we are in check
1765 if (ss->inCheck && i > 2)
1767 if (is_ok((ss-i)->currentMove))
1768 (*(ss-i)->continuationHistory)[pc][to] << bonus;
1773 // update_quiet_stats() updates move sorting heuristics
1775 void update_quiet_stats(const Position& pos, Stack* ss, Move move, int bonus) {
1778 if (ss->killers[0] != move)
1780 ss->killers[1] = ss->killers[0];
1781 ss->killers[0] = move;
1784 Color us = pos.side_to_move();
1785 Thread* thisThread = pos.this_thread();
1786 thisThread->mainHistory[us][from_to(move)] << bonus;
1787 update_continuation_histories(ss, pos.moved_piece(move), to_sq(move), bonus);
1789 // Update countermove history
1790 if (is_ok((ss-1)->currentMove))
1792 Square prevSq = to_sq((ss-1)->currentMove);
1793 thisThread->counterMoves[pos.piece_on(prevSq)][prevSq] = move;
1797 // When playing with strength handicap, choose best move among a set of RootMoves
1798 // using a statistical rule dependent on 'level'. Idea by Heinz van Saanen.
1800 Move Skill::pick_best(size_t multiPV) {
1802 const RootMoves& rootMoves = Threads.main()->rootMoves;
1803 static PRNG rng(now()); // PRNG sequence should be non-deterministic
1805 // RootMoves are already sorted by score in descending order
1806 Value topScore = rootMoves[0].score;
1807 int delta = std::min(topScore - rootMoves[multiPV - 1].score, PawnValueMg);
1808 int maxScore = -VALUE_INFINITE;
1809 double weakness = 120 - 2 * level;
1811 // Choose best move. For each move score we add two terms, both dependent on
1812 // weakness. One is deterministic and bigger for weaker levels, and one is
1813 // random. Then we choose the move with the resulting highest score.
1814 for (size_t i = 0; i < multiPV; ++i)
1816 // This is our magic formula
1817 int push = int(( weakness * int(topScore - rootMoves[i].score)
1818 + delta * (rng.rand<unsigned>() % int(weakness))) / 128);
1820 if (rootMoves[i].score + push >= maxScore)
1822 maxScore = rootMoves[i].score + push;
1823 best = rootMoves[i].pv[0];
1833 /// MainThread::check_time() is used to print debug info and, more importantly,
1834 /// to detect when we are out of available time and thus stop the search.
1836 void MainThread::check_time() {
1841 // When using nodes, ensure checking rate is not lower than 0.1% of nodes
1842 callsCnt = Limits.nodes ? std::min(1024, int(Limits.nodes / 1024)) : 1024;
1844 static TimePoint lastInfoTime = now();
1846 TimePoint elapsed = Time.elapsed();
1847 TimePoint tick = Limits.startTime + elapsed;
1849 if (tick - lastInfoTime >= 1000)
1851 lastInfoTime = tick;
1855 // We should not stop pondering until told so by the GUI
1859 if ( (Limits.use_time_management() && (elapsed > Time.maximum() - 10 || stopOnPonderhit))
1860 || (Limits.movetime && elapsed >= Limits.movetime)
1861 || (Limits.nodes && Threads.nodes_searched() >= (uint64_t)Limits.nodes))
1862 Threads.stop = true;
1866 /// UCI::pv() formats PV information according to the UCI protocol. UCI requires
1867 /// that all (if any) unsearched PV lines are sent using a previous search score.
1869 string UCI::pv(const Position& pos, Depth depth) {
1871 std::stringstream ss;
1872 TimePoint elapsed = Time.elapsed() + 1;
1873 const RootMoves& rootMoves = pos.this_thread()->rootMoves;
1874 size_t pvIdx = pos.this_thread()->pvIdx;
1875 size_t multiPV = std::min((size_t)Options["MultiPV"], rootMoves.size());
1876 uint64_t nodesSearched = Threads.nodes_searched();
1877 uint64_t tbHits = Threads.tb_hits() + (TB::RootInTB ? rootMoves.size() : 0);
1879 for (size_t i = 0; i < multiPV; ++i)
1881 bool updated = rootMoves[i].score != -VALUE_INFINITE;
1883 if (depth == 1 && !updated && i > 0)
1886 Depth d = updated ? depth : std::max(1, depth - 1);
1887 Value v = updated ? rootMoves[i].uciScore : rootMoves[i].previousScore;
1889 if (v == -VALUE_INFINITE)
1892 bool tb = TB::RootInTB && abs(v) < VALUE_MATE_IN_MAX_PLY;
1893 v = tb ? rootMoves[i].tbScore : v;
1895 if (ss.rdbuf()->in_avail()) // Not at first line
1900 << " seldepth " << rootMoves[i].selDepth
1901 << " multipv " << i + 1
1902 << " score " << UCI::value(v);
1904 if (Options["UCI_ShowWDL"])
1905 ss << UCI::wdl(v, pos.game_ply());
1907 if (i == pvIdx && !tb && updated) // tablebase- and previous-scores are exact
1908 ss << (rootMoves[i].scoreLowerbound ? " lowerbound" : (rootMoves[i].scoreUpperbound ? " upperbound" : ""));
1910 ss << " nodes " << nodesSearched
1911 << " nps " << nodesSearched * 1000 / elapsed
1912 << " hashfull " << TT.hashfull()
1913 << " tbhits " << tbHits
1914 << " time " << elapsed
1917 for (Move m : rootMoves[i].pv)
1918 ss << " " << UCI::move(m, pos.is_chess960());
1925 /// RootMove::extract_ponder_from_tt() is called in case we have no ponder move
1926 /// before exiting the search, for instance, in case we stop the search during a
1927 /// fail high at root. We try hard to have a ponder move to return to the GUI,
1928 /// otherwise in case of 'ponder on' we have nothing to think on.
1930 bool RootMove::extract_ponder_from_tt(Position& pos) {
1933 ASSERT_ALIGNED(&st, Eval::NNUE::CacheLineSize);
1937 assert(pv.size() == 1);
1939 if (pv[0] == MOVE_NONE)
1942 pos.do_move(pv[0], st);
1943 TTEntry* tte = TT.probe(pos.key(), ttHit);
1947 Move m = tte->move(); // Local copy to be SMP safe
1948 if (MoveList<LEGAL>(pos).contains(m))
1952 pos.undo_move(pv[0]);
1953 return pv.size() > 1;
1956 void Tablebases::rank_root_moves(Position& pos, Search::RootMoves& rootMoves) {
1959 UseRule50 = bool(Options["Syzygy50MoveRule"]);
1960 ProbeDepth = int(Options["SyzygyProbeDepth"]);
1961 Cardinality = int(Options["SyzygyProbeLimit"]);
1962 bool dtz_available = true;
1964 // Tables with fewer pieces than SyzygyProbeLimit are searched with
1965 // ProbeDepth == DEPTH_ZERO
1966 if (Cardinality > MaxCardinality)
1968 Cardinality = MaxCardinality;
1972 if (Cardinality >= popcount(pos.pieces()) && !pos.can_castle(ANY_CASTLING))
1974 // Rank moves using DTZ tables
1975 RootInTB = root_probe(pos, rootMoves);
1979 // DTZ tables are missing; try to rank moves using WDL tables
1980 dtz_available = false;
1981 RootInTB = root_probe_wdl(pos, rootMoves);
1987 // Sort moves according to TB rank
1988 std::stable_sort(rootMoves.begin(), rootMoves.end(),
1989 [](const RootMove &a, const RootMove &b) { return a.tbRank > b.tbRank; } );
1991 // Probe during search only if DTZ is not available and we are winning
1992 if (dtz_available || rootMoves[0].tbScore <= VALUE_DRAW)
1997 // Clean up if root_probe() and root_probe_wdl() have failed
1998 for (auto& m : rootMoves)
2003 } // namespace Stockfish