2 Stockfish, a UCI chess playing engine derived from Glaurung 2.1
3 Copyright (C) 2004-2023 The Stockfish developers (see AUTHORS file)
5 Stockfish is free software: you can redistribute it and/or modify
6 it under the terms of the GNU General Public License as published by
7 the Free Software Foundation, either version 3 of the License, or
8 (at your option) any later version.
10 Stockfish is distributed in the hope that it will be useful,
11 but WITHOUT ANY WARRANTY; without even the implied warranty of
12 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
13 GNU General Public License for more details.
15 You should have received a copy of the GNU General Public License
16 along with this program. If not, see <http://www.gnu.org/licenses/>.
28 #include <initializer_list>
39 #include "nnue/evaluate_nnue.h"
40 #include "nnue/nnue_common.h"
42 #include "syzygy/tbprobe.h"
55 namespace Tablebases {
63 namespace TB = Tablebases;
67 using namespace Search;
71 // Different node types, used as a template parameter
72 enum NodeType { NonPV, PV, Root };
75 Value futility_margin(Depth d, bool noTtCutNode, bool improving) {
76 return Value((140 - 40 * noTtCutNode) * (d - improving));
79 // Reductions lookup table initialized at startup
80 int Reductions[MAX_MOVES]; // [depth or moveNumber]
82 Depth reduction(bool i, Depth d, int mn, Value delta, Value rootDelta) {
83 int reductionScale = Reductions[d] * Reductions[mn];
84 return (reductionScale + 1372 - int(delta) * 1073 / int(rootDelta)) / 1024
85 + (!i && reductionScale > 936);
88 constexpr int futility_move_count(bool improving, Depth depth) {
89 return improving ? (3 + depth * depth)
90 : (3 + depth * depth) / 2;
93 // History and stats update bonus, based on depth
94 int stat_bonus(Depth d) {
95 return std::min(336 * d - 547, 1561);
98 // Add a small random component to draw evaluations to avoid 3-fold blindness
99 Value value_draw(const Thread* thisThread) {
100 return VALUE_DRAW - 1 + Value(thisThread->nodes & 0x2);
103 // Skill structure is used to implement strength limit.
104 // If we have a UCI_Elo, we convert it to an appropriate skill level, anchored to the Stash engine.
105 // This method is based on a fit of the Elo results for games played between the master at various
106 // skill levels and various versions of the Stash engine, all ranked at CCRL.
107 // Skill 0 .. 19 now covers CCRL Blitz Elo from 1320 to 3190, approximately
108 // Reference: https://github.com/vondele/Stockfish/commit/a08b8d4e9711c20acedbfe17d618c3c384b339ec
110 Skill(int skill_level, int uci_elo) {
113 double e = double(uci_elo - 1320) / (3190 - 1320);
114 level = std::clamp((((37.2473 * e - 40.8525) * e + 22.2943) * e - 0.311438), 0.0, 19.0);
117 level = double(skill_level);
119 bool enabled() const { return level < 20.0; }
120 bool time_to_pick(Depth depth) const { return depth == 1 + int(level); }
121 Move pick_best(size_t multiPV);
124 Move best = MOVE_NONE;
127 template <NodeType nodeType>
128 Value search(Position& pos, Stack* ss, Value alpha, Value beta, Depth depth, bool cutNode);
130 template <NodeType nodeType>
131 Value qsearch(Position& pos, Stack* ss, Value alpha, Value beta, Depth depth = 0);
133 Value value_to_tt(Value v, int ply);
134 Value value_from_tt(Value v, int ply, int r50c);
135 void update_pv(Move* pv, Move move, const Move* childPv);
136 void update_continuation_histories(Stack* ss, Piece pc, Square to, int bonus);
137 void update_quiet_stats(const Position& pos, Stack* ss, Move move, int bonus);
138 void update_all_stats(const Position& pos, Stack* ss, Move bestMove, Value bestValue, Value beta, Square prevSq,
139 Move* quietsSearched, int quietCount, Move* capturesSearched, int captureCount, Depth depth);
141 // perft() is our utility to verify move generation. All the leaf nodes up
142 // to the given depth are generated and counted, and the sum is returned.
144 uint64_t perft(Position& pos, Depth depth) {
147 ASSERT_ALIGNED(&st, Eval::NNUE::CacheLineSize);
149 uint64_t cnt, nodes = 0;
150 const bool leaf = (depth == 2);
152 for (const auto& m : MoveList<LEGAL>(pos))
154 if (Root && depth <= 1)
159 cnt = leaf ? MoveList<LEGAL>(pos).size() : perft<false>(pos, depth - 1);
164 sync_cout << UCI::move(m, pos.is_chess960()) << ": " << cnt << sync_endl;
172 /// Search::init() is called at startup to initialize various lookup tables
174 void Search::init() {
176 for (int i = 1; i < MAX_MOVES; ++i)
177 Reductions[i] = int((20.57 + std::log(Threads.size()) / 2) * std::log(i));
181 /// Search::clear() resets search state to its initial value
183 void Search::clear() {
185 Threads.main()->wait_for_search_finished();
187 Time.availableNodes = 0;
190 Tablebases::init(Options["SyzygyPath"]); // Free mapped files
194 /// MainThread::search() is started when the program receives the UCI 'go'
195 /// command. It searches from the root position and outputs the "bestmove".
197 void MainThread::search() {
201 nodes = perft<true>(rootPos, Limits.perft);
202 sync_cout << "\nNodes searched: " << nodes << "\n" << sync_endl;
206 Color us = rootPos.side_to_move();
207 Time.init(Limits, us, rootPos.game_ply());
210 Eval::NNUE::verify();
212 if (rootMoves.empty())
214 rootMoves.emplace_back(MOVE_NONE);
215 sync_cout << "info depth 0 score "
216 << UCI::value(rootPos.checkers() ? -VALUE_MATE : VALUE_DRAW)
221 Threads.start_searching(); // start non-main threads
222 Thread::search(); // main thread start searching
225 // When we reach the maximum depth, we can arrive here without a raise of
226 // Threads.stop. However, if we are pondering or in an infinite search,
227 // the UCI protocol states that we shouldn't print the best move before the
228 // GUI sends a "stop" or "ponderhit" command. We therefore simply wait here
229 // until the GUI sends one of those commands.
231 while (!Threads.stop && (ponder || Limits.infinite))
232 {} // Busy wait for a stop or a ponder reset
234 // Stop the threads if not already stopped (also raise the stop if
235 // "ponderhit" just reset Threads.ponder).
238 // Wait until all threads have finished
239 Threads.wait_for_search_finished();
241 // When playing in 'nodes as time' mode, subtract the searched nodes from
242 // the available ones before exiting.
244 Time.availableNodes += Limits.inc[us] - Threads.nodes_searched();
246 Thread* bestThread = this;
247 Skill skill = Skill(Options["Skill Level"], Options["UCI_LimitStrength"] ? int(Options["UCI_Elo"]) : 0);
249 if ( int(Options["MultiPV"]) == 1
252 && rootMoves[0].pv[0] != MOVE_NONE)
253 bestThread = Threads.get_best_thread();
255 bestPreviousScore = bestThread->rootMoves[0].score;
256 bestPreviousAverageScore = bestThread->rootMoves[0].averageScore;
258 // Send again PV info if we have a new best thread
259 if (bestThread != this)
260 sync_cout << UCI::pv(bestThread->rootPos, bestThread->completedDepth) << sync_endl;
262 sync_cout << "bestmove " << UCI::move(bestThread->rootMoves[0].pv[0], rootPos.is_chess960());
264 if (bestThread->rootMoves[0].pv.size() > 1 || bestThread->rootMoves[0].extract_ponder_from_tt(rootPos))
265 std::cout << " ponder " << UCI::move(bestThread->rootMoves[0].pv[1], rootPos.is_chess960());
267 std::cout << sync_endl;
271 /// Thread::search() is the main iterative deepening loop. It calls search()
272 /// repeatedly with increasing depth until the allocated thinking time has been
273 /// consumed, the user stops the search, or the maximum search depth is reached.
275 void Thread::search() {
277 // Allocate stack with extra size to allow access from (ss-7) to (ss+2)
278 // (ss-7) is needed for update_continuation_histories(ss-1, ...) which accesses (ss-6)
279 // (ss+2) is needed for initialization of statScore and killers
280 Stack stack[MAX_PLY+10], *ss = stack+7;
282 Value alpha, beta, delta;
283 Move lastBestMove = MOVE_NONE;
284 Depth lastBestMoveDepth = 0;
285 MainThread* mainThread = (this == Threads.main() ? Threads.main() : nullptr);
286 double timeReduction = 1, totBestMoveChanges = 0;
287 Color us = rootPos.side_to_move();
290 std::memset(ss-7, 0, 10 * sizeof(Stack));
291 for (int i = 7; i > 0; --i)
293 (ss-i)->continuationHistory = &this->continuationHistory[0][0][NO_PIECE][0]; // Use as a sentinel
294 (ss-i)->staticEval = VALUE_NONE;
297 for (int i = 0; i <= MAX_PLY + 2; ++i)
302 bestValue = -VALUE_INFINITE;
306 if (mainThread->bestPreviousScore == VALUE_INFINITE)
307 for (int i = 0; i < 4; ++i)
308 mainThread->iterValue[i] = VALUE_ZERO;
310 for (int i = 0; i < 4; ++i)
311 mainThread->iterValue[i] = mainThread->bestPreviousScore;
314 size_t multiPV = size_t(Options["MultiPV"]);
315 Skill skill(Options["Skill Level"], Options["UCI_LimitStrength"] ? int(Options["UCI_Elo"]) : 0);
317 // When playing with strength handicap enable MultiPV search that we will
318 // use behind-the-scenes to retrieve a set of possible moves.
320 multiPV = std::max(multiPV, size_t(4));
322 multiPV = std::min(multiPV, rootMoves.size());
324 int searchAgainCounter = 0;
326 // Iterative deepening loop until requested to stop or the target depth is reached
327 while ( ++rootDepth < MAX_PLY
329 && !(Limits.depth && mainThread && rootDepth > Limits.depth))
331 // Age out PV variability metric
333 totBestMoveChanges /= 2;
335 // Save the last iteration's scores before the first PV line is searched and
336 // all the move scores except the (new) PV are set to -VALUE_INFINITE.
337 for (RootMove& rm : rootMoves)
338 rm.previousScore = rm.score;
343 if (!Threads.increaseDepth)
344 searchAgainCounter++;
346 // MultiPV loop. We perform a full root search for each PV line
347 for (pvIdx = 0; pvIdx < multiPV && !Threads.stop; ++pvIdx)
352 for (pvLast++; pvLast < rootMoves.size(); pvLast++)
353 if (rootMoves[pvLast].tbRank != rootMoves[pvFirst].tbRank)
357 // Reset UCI info selDepth for each depth and each PV line
360 // Reset aspiration window starting size
361 Value prev = rootMoves[pvIdx].averageScore;
362 delta = Value(10) + int(prev) * prev / 15799;
363 alpha = std::max(prev - delta,-VALUE_INFINITE);
364 beta = std::min(prev + delta, VALUE_INFINITE);
366 // Adjust optimism based on root move's previousScore (~4 Elo)
367 int opt = 109 * prev / (std::abs(prev) + 141);
368 optimism[ us] = Value(opt);
369 optimism[~us] = -optimism[us];
371 // Start with a small aspiration window and, in the case of a fail
372 // high/low, re-search with a bigger window until we don't fail
374 int failedHighCnt = 0;
377 // Adjust the effective depth searched, but ensure at least one effective increment for every
378 // four searchAgain steps (see issue #2717).
379 Depth adjustedDepth = std::max(1, rootDepth - failedHighCnt - 3 * (searchAgainCounter + 1) / 4);
380 bestValue = Stockfish::search<Root>(rootPos, ss, alpha, beta, adjustedDepth, false);
382 // Bring the best move to the front. It is critical that sorting
383 // is done with a stable algorithm because all the values but the
384 // first and eventually the new best one is set to -VALUE_INFINITE
385 // and we want to keep the same order for all the moves except the
386 // new PV that goes to the front. Note that in the case of MultiPV
387 // search the already searched PV lines are preserved.
388 std::stable_sort(rootMoves.begin() + pvIdx, rootMoves.begin() + pvLast);
390 // If search has been stopped, we break immediately. Sorting is
391 // safe because RootMoves is still valid, although it refers to
392 // the previous iteration.
396 // When failing high/low give some update (without cluttering
397 // the UI) before a re-search.
400 && (bestValue <= alpha || bestValue >= beta)
401 && Time.elapsed() > 3000)
402 sync_cout << UCI::pv(rootPos, rootDepth) << sync_endl;
404 // In case of failing low/high increase aspiration window and
405 // re-search, otherwise exit the loop.
406 if (bestValue <= alpha)
408 beta = (alpha + beta) / 2;
409 alpha = std::max(bestValue - delta, -VALUE_INFINITE);
413 mainThread->stopOnPonderhit = false;
415 else if (bestValue >= beta)
417 beta = std::min(bestValue + delta, VALUE_INFINITE);
425 assert(alpha >= -VALUE_INFINITE && beta <= VALUE_INFINITE);
428 // Sort the PV lines searched so far and update the GUI
429 std::stable_sort(rootMoves.begin() + pvFirst, rootMoves.begin() + pvIdx + 1);
432 && (Threads.stop || pvIdx + 1 == multiPV || Time.elapsed() > 3000))
433 sync_cout << UCI::pv(rootPos, rootDepth) << sync_endl;
437 completedDepth = rootDepth;
439 if (rootMoves[0].pv[0] != lastBestMove)
441 lastBestMove = rootMoves[0].pv[0];
442 lastBestMoveDepth = rootDepth;
445 // Have we found a "mate in x"?
447 && bestValue >= VALUE_MATE_IN_MAX_PLY
448 && VALUE_MATE - bestValue <= 2 * Limits.mate)
454 // If the skill level is enabled and time is up, pick a sub-optimal best move
455 if (skill.enabled() && skill.time_to_pick(rootDepth))
456 skill.pick_best(multiPV);
458 // Use part of the gained time from a previous stable move for the current move
459 for (Thread* th : Threads)
461 totBestMoveChanges += th->bestMoveChanges;
462 th->bestMoveChanges = 0;
465 // Do we have time for the next iteration? Can we stop searching now?
466 if ( Limits.use_time_management()
468 && !mainThread->stopOnPonderhit)
470 double fallingEval = (69 + 13 * (mainThread->bestPreviousAverageScore - bestValue)
471 + 6 * (mainThread->iterValue[iterIdx] - bestValue)) / 619.6;
472 fallingEval = std::clamp(fallingEval, 0.5, 1.5);
474 // If the bestMove is stable over several iterations, reduce time accordingly
475 timeReduction = lastBestMoveDepth + 8 < completedDepth ? 1.57 : 0.65;
476 double reduction = (1.4 + mainThread->previousTimeReduction) / (2.08 * timeReduction);
477 double bestMoveInstability = 1 + 1.8 * totBestMoveChanges / Threads.size();
479 double totalTime = Time.optimum() * fallingEval * reduction * bestMoveInstability;
481 // Cap used time in case of a single legal move for a better viewer experience in tournaments
482 // yielding correct scores and sufficiently fast moves.
483 if (rootMoves.size() == 1)
484 totalTime = std::min(500.0, totalTime);
486 // Stop the search if we have exceeded the totalTime
487 if (Time.elapsed() > totalTime)
489 // If we are allowed to ponder do not stop the search now but
490 // keep pondering until the GUI sends "ponderhit" or "stop".
491 if (mainThread->ponder)
492 mainThread->stopOnPonderhit = true;
496 else if ( !mainThread->ponder
497 && Time.elapsed() > totalTime * 0.50)
498 Threads.increaseDepth = false;
500 Threads.increaseDepth = true;
503 mainThread->iterValue[iterIdx] = bestValue;
504 iterIdx = (iterIdx + 1) & 3;
510 mainThread->previousTimeReduction = timeReduction;
512 // If the skill level is enabled, swap the best PV line with the sub-optimal one
514 std::swap(rootMoves[0], *std::find(rootMoves.begin(), rootMoves.end(),
515 skill.best ? skill.best : skill.pick_best(multiPV)));
521 // search<>() is the main search function for both PV and non-PV nodes
523 template <NodeType nodeType>
524 Value search(Position& pos, Stack* ss, Value alpha, Value beta, Depth depth, bool cutNode) {
526 constexpr bool PvNode = nodeType != NonPV;
527 constexpr bool rootNode = nodeType == Root;
529 // Dive into quiescence search when the depth reaches zero
531 return qsearch<PvNode ? PV : NonPV>(pos, ss, alpha, beta);
533 // Check if we have an upcoming move that draws by repetition, or
534 // if the opponent had an alternative move earlier to this position.
536 && alpha < VALUE_DRAW
537 && pos.has_game_cycle(ss->ply))
539 alpha = value_draw(pos.this_thread());
544 assert(-VALUE_INFINITE <= alpha && alpha < beta && beta <= VALUE_INFINITE);
545 assert(PvNode || (alpha == beta - 1));
546 assert(0 < depth && depth < MAX_PLY);
547 assert(!(PvNode && cutNode));
549 Move pv[MAX_PLY+1], capturesSearched[32], quietsSearched[64];
551 ASSERT_ALIGNED(&st, Eval::NNUE::CacheLineSize);
555 Move ttMove, move, excludedMove, bestMove;
556 Depth extension, newDepth;
557 Value bestValue, value, ttValue, eval, maxValue, probCutBeta;
558 bool givesCheck, improving, priorCapture, singularQuietLMR;
559 bool capture, moveCountPruning, ttCapture;
561 int moveCount, captureCount, quietCount;
563 // Step 1. Initialize node
564 Thread* thisThread = pos.this_thread();
565 ss->inCheck = pos.checkers();
566 priorCapture = pos.captured_piece();
567 Color us = pos.side_to_move();
568 moveCount = captureCount = quietCount = ss->moveCount = 0;
569 bestValue = -VALUE_INFINITE;
570 maxValue = VALUE_INFINITE;
572 // Check for the available remaining time
573 if (thisThread == Threads.main())
574 static_cast<MainThread*>(thisThread)->check_time();
576 // Used to send selDepth info to GUI (selDepth counts from 1, ply from 0)
577 if (PvNode && thisThread->selDepth < ss->ply + 1)
578 thisThread->selDepth = ss->ply + 1;
582 // Step 2. Check for aborted search and immediate draw
583 if ( Threads.stop.load(std::memory_order_relaxed)
584 || pos.is_draw(ss->ply)
585 || ss->ply >= MAX_PLY)
586 return (ss->ply >= MAX_PLY && !ss->inCheck) ? evaluate(pos)
587 : value_draw(pos.this_thread());
589 // Step 3. Mate distance pruning. Even if we mate at the next move our score
590 // would be at best mate_in(ss->ply+1), but if alpha is already bigger because
591 // a shorter mate was found upward in the tree then there is no need to search
592 // because we will never beat the current alpha. Same logic but with reversed
593 // signs apply also in the opposite condition of being mated instead of giving
594 // mate. In this case, return a fail-high score.
595 alpha = std::max(mated_in(ss->ply), alpha);
596 beta = std::min(mate_in(ss->ply+1), beta);
601 thisThread->rootDelta = beta - alpha;
603 assert(0 <= ss->ply && ss->ply < MAX_PLY);
605 (ss+1)->excludedMove = bestMove = MOVE_NONE;
606 (ss+2)->killers[0] = (ss+2)->killers[1] = MOVE_NONE;
607 (ss+2)->cutoffCnt = 0;
608 ss->doubleExtensions = (ss-1)->doubleExtensions;
609 Square prevSq = is_ok((ss-1)->currentMove) ? to_sq((ss-1)->currentMove) : SQ_NONE;
612 // Step 4. Transposition table lookup.
613 excludedMove = ss->excludedMove;
615 tte = TT.probe(posKey, ss->ttHit);
616 ttValue = ss->ttHit ? value_from_tt(tte->value(), ss->ply, pos.rule50_count()) : VALUE_NONE;
617 ttMove = rootNode ? thisThread->rootMoves[thisThread->pvIdx].pv[0]
618 : ss->ttHit ? tte->move() : MOVE_NONE;
619 ttCapture = ttMove && pos.capture_stage(ttMove);
621 // At this point, if excluded, skip straight to step 6, static eval. However,
622 // to save indentation, we list the condition in all code between here and there.
624 ss->ttPv = PvNode || (ss->ttHit && tte->is_pv());
626 // At non-PV nodes we check for an early TT cutoff
629 && tte->depth() > depth
630 && ttValue != VALUE_NONE // Possible in case of TT access race or if !ttHit
631 && (tte->bound() & (ttValue >= beta ? BOUND_LOWER : BOUND_UPPER)))
633 // If ttMove is quiet, update move sorting heuristics on TT hit (~2 Elo)
638 // Bonus for a quiet ttMove that fails high (~2 Elo)
640 update_quiet_stats(pos, ss, ttMove, stat_bonus(depth));
642 // Extra penalty for early quiet moves of the previous ply (~0 Elo on STC, ~2 Elo on LTC)
643 if (prevSq != SQ_NONE && (ss-1)->moveCount <= 2 && !priorCapture)
644 update_continuation_histories(ss-1, pos.piece_on(prevSq), prevSq, -stat_bonus(depth + 1));
646 // Penalty for a quiet ttMove that fails low (~1 Elo)
649 int penalty = -stat_bonus(depth);
650 thisThread->mainHistory[us][from_to(ttMove)] << penalty;
651 update_continuation_histories(ss, pos.moved_piece(ttMove), to_sq(ttMove), penalty);
655 // Partial workaround for the graph history interaction problem
656 // For high rule50 counts don't produce transposition table cutoffs.
657 if (pos.rule50_count() < 90)
661 // Step 5. Tablebases probe
662 if (!rootNode && !excludedMove && TB::Cardinality)
664 int piecesCount = pos.count<ALL_PIECES>();
666 if ( piecesCount <= TB::Cardinality
667 && (piecesCount < TB::Cardinality || depth >= TB::ProbeDepth)
668 && pos.rule50_count() == 0
669 && !pos.can_castle(ANY_CASTLING))
672 TB::WDLScore wdl = Tablebases::probe_wdl(pos, &err);
674 // Force check of time on the next occasion
675 if (thisThread == Threads.main())
676 static_cast<MainThread*>(thisThread)->callsCnt = 0;
678 if (err != TB::ProbeState::FAIL)
680 thisThread->tbHits.fetch_add(1, std::memory_order_relaxed);
682 int drawScore = TB::UseRule50 ? 1 : 0;
684 // use the range VALUE_MATE_IN_MAX_PLY to VALUE_TB_WIN_IN_MAX_PLY to score
685 value = wdl < -drawScore ? VALUE_MATED_IN_MAX_PLY + ss->ply + 1
686 : wdl > drawScore ? VALUE_MATE_IN_MAX_PLY - ss->ply - 1
687 : VALUE_DRAW + 2 * wdl * drawScore;
689 Bound b = wdl < -drawScore ? BOUND_UPPER
690 : wdl > drawScore ? BOUND_LOWER : BOUND_EXACT;
692 if ( b == BOUND_EXACT
693 || (b == BOUND_LOWER ? value >= beta : value <= alpha))
695 tte->save(posKey, value_to_tt(value, ss->ply), ss->ttPv, b,
696 std::min(MAX_PLY - 1, depth + 6),
697 MOVE_NONE, VALUE_NONE);
704 if (b == BOUND_LOWER)
705 bestValue = value, alpha = std::max(alpha, bestValue);
713 CapturePieceToHistory& captureHistory = thisThread->captureHistory;
715 // Step 6. Static evaluation of the position
718 // Skip early pruning when in check
719 ss->staticEval = eval = VALUE_NONE;
723 else if (excludedMove)
725 // Providing the hint that this node's accumulator will be used often brings significant Elo gain (~13 Elo)
726 Eval::NNUE::hint_common_parent_position(pos);
727 eval = ss->staticEval;
731 // Never assume anything about values stored in TT
732 ss->staticEval = eval = tte->eval();
733 if (eval == VALUE_NONE)
734 ss->staticEval = eval = evaluate(pos);
736 Eval::NNUE::hint_common_parent_position(pos);
738 // ttValue can be used as a better position evaluation (~7 Elo)
739 if ( ttValue != VALUE_NONE
740 && (tte->bound() & (ttValue > eval ? BOUND_LOWER : BOUND_UPPER)))
745 ss->staticEval = eval = evaluate(pos);
746 // Save static evaluation into the transposition table
747 tte->save(posKey, VALUE_NONE, ss->ttPv, BOUND_NONE, DEPTH_NONE, MOVE_NONE, eval);
750 // Use static evaluation difference to improve quiet move ordering (~4 Elo)
751 if (is_ok((ss-1)->currentMove) && !(ss-1)->inCheck && !priorCapture)
753 int bonus = std::clamp(-18 * int((ss-1)->staticEval + ss->staticEval), -1817, 1817);
754 thisThread->mainHistory[~us][from_to((ss-1)->currentMove)] << bonus;
757 // Set up the improving flag, which is true if current static evaluation is
758 // bigger than the previous static evaluation at our turn (if we were in
759 // check at our previous move we look at static evaluation at move prior to it
760 // and if we were in check at move prior to it flag is set to true) and is
761 // false otherwise. The improving flag is used in various pruning heuristics.
762 improving = (ss-2)->staticEval != VALUE_NONE ? ss->staticEval > (ss-2)->staticEval
763 : (ss-4)->staticEval != VALUE_NONE ? ss->staticEval > (ss-4)->staticEval
766 // Step 7. Razoring (~1 Elo)
767 // If eval is really low check with qsearch if it can exceed alpha, if it can't,
768 // return a fail low.
769 if (eval < alpha - 456 - 252 * depth * depth)
771 value = qsearch<NonPV>(pos, ss, alpha - 1, alpha);
776 // Step 8. Futility pruning: child node (~40 Elo)
777 // The depth condition is important for mate finding.
780 && eval - futility_margin(depth, cutNode && !ss->ttHit, improving) - (ss-1)->statScore / 306 >= beta
782 && eval < 24923) // smaller than TB wins
785 // Step 9. Null move search with verification search (~35 Elo)
787 && (ss-1)->currentMove != MOVE_NULL
788 && (ss-1)->statScore < 17329
790 && eval >= ss->staticEval
791 && ss->staticEval >= beta - 21 * depth + 258
793 && pos.non_pawn_material(us)
794 && ss->ply >= thisThread->nmpMinPly
795 && beta > VALUE_TB_LOSS_IN_MAX_PLY)
797 assert(eval - beta >= 0);
799 // Null move dynamic reduction based on depth and eval
800 Depth R = std::min(int(eval - beta) / 173, 6) + depth / 3 + 4;
802 ss->currentMove = MOVE_NULL;
803 ss->continuationHistory = &thisThread->continuationHistory[0][0][NO_PIECE][0];
805 pos.do_null_move(st);
807 Value nullValue = -search<NonPV>(pos, ss+1, -beta, -beta+1, depth-R, !cutNode);
809 pos.undo_null_move();
811 if (nullValue >= beta)
813 // Do not return unproven mate or TB scores
814 nullValue = std::min(nullValue, VALUE_TB_WIN_IN_MAX_PLY-1);
816 if (thisThread->nmpMinPly || depth < 14)
819 assert(!thisThread->nmpMinPly); // Recursive verification is not allowed
821 // Do verification search at high depths, with null move pruning disabled
822 // until ply exceeds nmpMinPly.
823 thisThread->nmpMinPly = ss->ply + 3 * (depth-R) / 4;
825 Value v = search<NonPV>(pos, ss, beta-1, beta, depth-R, false);
827 thisThread->nmpMinPly = 0;
834 // Step 10. If the position doesn't have a ttMove, decrease depth by 2
835 // (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).
836 // Use qsearch if depth is equal or below zero (~9 Elo)
839 depth -= 2 + 2 * (ss->ttHit && tte->depth() >= depth);
842 return qsearch<PV>(pos, ss, alpha, beta);
849 probCutBeta = beta + 168 - 61 * improving;
851 // Step 11. ProbCut (~10 Elo)
852 // If we have a good enough capture (or queen promotion) and a reduced search returns a value
853 // much above beta, we can (almost) safely prune the previous move.
856 && abs(beta) < VALUE_TB_WIN_IN_MAX_PLY
857 // If value from transposition table is lower than probCutBeta, don't attempt probCut
858 // there and in further interactions with transposition table cutoff depth is set to depth - 3
859 // because probCut search has depth set to depth - 4 but we also do a move before it
860 // So effective depth is equal to depth - 3
861 && !( tte->depth() >= depth - 3
862 && ttValue != VALUE_NONE
863 && ttValue < probCutBeta))
865 assert(probCutBeta < VALUE_INFINITE);
867 MovePicker mp(pos, ttMove, probCutBeta - ss->staticEval, &captureHistory);
869 while ((move = mp.next_move()) != MOVE_NONE)
870 if (move != excludedMove && pos.legal(move))
872 assert(pos.capture_stage(move));
874 ss->currentMove = move;
875 ss->continuationHistory = &thisThread->continuationHistory[ss->inCheck]
877 [pos.moved_piece(move)]
880 pos.do_move(move, st);
882 // Perform a preliminary qsearch to verify that the move holds
883 value = -qsearch<NonPV>(pos, ss+1, -probCutBeta, -probCutBeta+1);
885 // If the qsearch held, perform the regular search
886 if (value >= probCutBeta)
887 value = -search<NonPV>(pos, ss+1, -probCutBeta, -probCutBeta+1, depth - 4, !cutNode);
891 if (value >= probCutBeta)
893 // Save ProbCut data into transposition table
894 tte->save(posKey, value_to_tt(value, ss->ply), ss->ttPv, BOUND_LOWER, depth - 3, move, ss->staticEval);
899 Eval::NNUE::hint_common_parent_position(pos);
902 moves_loop: // When in check, search starts here
904 // Step 12. A small Probcut idea, when we are in check (~4 Elo)
905 probCutBeta = beta + 413;
909 && (tte->bound() & BOUND_LOWER)
910 && tte->depth() >= depth - 4
911 && ttValue >= probCutBeta
912 && abs(ttValue) < VALUE_TB_WIN_IN_MAX_PLY
913 && abs(beta) < VALUE_TB_WIN_IN_MAX_PLY)
916 const PieceToHistory* contHist[] = { (ss-1)->continuationHistory, (ss-2)->continuationHistory,
917 nullptr , (ss-4)->continuationHistory,
918 nullptr , (ss-6)->continuationHistory };
920 Move countermove = prevSq != SQ_NONE ? thisThread->counterMoves[pos.piece_on(prevSq)][prevSq] : MOVE_NONE;
922 MovePicker mp(pos, ttMove, depth, &thisThread->mainHistory,
929 moveCountPruning = singularQuietLMR = false;
931 // Indicate PvNodes that will probably fail low if the node was searched
932 // at a depth equal to or greater than the current depth, and the result
933 // of this search was a fail low.
934 bool likelyFailLow = PvNode
936 && (tte->bound() & BOUND_UPPER)
937 && tte->depth() >= depth;
939 // Step 13. Loop through all pseudo-legal moves until no moves remain
940 // or a beta cutoff occurs.
941 while ((move = mp.next_move(moveCountPruning)) != MOVE_NONE)
945 if (move == excludedMove)
948 // At root obey the "searchmoves" option and skip moves not listed in Root
949 // Move List. As a consequence, any illegal move is also skipped. In MultiPV
950 // mode we also skip PV moves that have been already searched and those
951 // of lower "TB rank" if we are in a TB root position.
952 if (rootNode && !std::count(thisThread->rootMoves.begin() + thisThread->pvIdx,
953 thisThread->rootMoves.begin() + thisThread->pvLast, move))
956 // Check for legality
957 if (!rootNode && !pos.legal(move))
960 ss->moveCount = ++moveCount;
962 if (rootNode && thisThread == Threads.main() && Time.elapsed() > 3000)
963 sync_cout << "info depth " << depth
964 << " currmove " << UCI::move(move, pos.is_chess960())
965 << " currmovenumber " << moveCount + thisThread->pvIdx << sync_endl;
967 (ss+1)->pv = nullptr;
970 capture = pos.capture_stage(move);
971 movedPiece = pos.moved_piece(move);
972 givesCheck = pos.gives_check(move);
974 // Calculate new depth for this move
975 newDepth = depth - 1;
977 Value delta = beta - alpha;
979 Depth r = reduction(improving, depth, moveCount, delta, thisThread->rootDelta);
981 // Step 14. Pruning at shallow depth (~120 Elo). Depth conditions are important for mate finding.
983 && pos.non_pawn_material(us)
984 && bestValue > VALUE_TB_LOSS_IN_MAX_PLY)
986 // Skip quiet moves if movecount exceeds our FutilityMoveCount threshold (~8 Elo)
987 moveCountPruning = moveCount >= futility_move_count(improving, depth);
989 // Reduced depth of the next LMR search
990 int lmrDepth = newDepth - r;
995 // Futility pruning for captures (~2 Elo)
999 && ss->staticEval + 197 + 248 * lmrDepth + PieceValue[pos.piece_on(to_sq(move))]
1000 + captureHistory[movedPiece][to_sq(move)][type_of(pos.piece_on(to_sq(move)))] / 7 < alpha)
1003 // SEE based pruning for captures and checks (~11 Elo)
1004 if (!pos.see_ge(move, Value(-205) * depth))
1009 int history = (*contHist[0])[movedPiece][to_sq(move)]
1010 + (*contHist[1])[movedPiece][to_sq(move)]
1011 + (*contHist[3])[movedPiece][to_sq(move)];
1013 // Continuation history based pruning (~2 Elo)
1015 && history < -3832 * depth)
1018 history += 2 * thisThread->mainHistory[us][from_to(move)];
1020 lmrDepth += history / 7011;
1021 lmrDepth = std::max(lmrDepth, -2);
1023 // Futility pruning: parent node (~13 Elo)
1026 && ss->staticEval + 112 + 138 * lmrDepth <= alpha)
1029 lmrDepth = std::max(lmrDepth, 0);
1031 // Prune moves with negative SEE (~4 Elo)
1032 if (!pos.see_ge(move, Value(-31 * lmrDepth * lmrDepth)))
1037 // Step 15. Extensions (~100 Elo)
1038 // We take care to not overdo to avoid search getting stuck.
1039 if (ss->ply < thisThread->rootDepth * 2)
1041 // Singular extension search (~94 Elo). If all moves but one fail low on a
1042 // search of (alpha-s, beta-s), and just one fails high on (alpha, beta),
1043 // then that move is singular and should be extended. To verify this we do
1044 // a reduced search on all the other moves but the ttMove and if the result
1045 // is lower than ttValue minus a margin, then we will extend the ttMove. Note
1046 // that depth margin and singularBeta margin are known for having non-linear
1047 // scaling. Their values are optimized to time controls of 180+1.8 and longer
1048 // so changing them requires tests at this type of time controls.
1050 && depth >= 4 - (thisThread->completedDepth > 22) + 2 * (PvNode && tte->is_pv())
1052 && !excludedMove // Avoid recursive singular search
1053 /* && ttValue != VALUE_NONE Already implicit in the next condition */
1054 && abs(ttValue) < VALUE_TB_WIN_IN_MAX_PLY
1055 && (tte->bound() & BOUND_LOWER)
1056 && tte->depth() >= depth - 3)
1058 Value singularBeta = ttValue - (82 + 65 * (ss->ttPv && !PvNode)) * depth / 64;
1059 Depth singularDepth = (depth - 1) / 2;
1061 ss->excludedMove = move;
1062 value = search<NonPV>(pos, ss, singularBeta - 1, singularBeta, singularDepth, cutNode);
1063 ss->excludedMove = MOVE_NONE;
1065 if (value < singularBeta)
1068 singularQuietLMR = !ttCapture;
1070 // Avoid search explosion by limiting the number of double extensions
1072 && value < singularBeta - 21
1073 && ss->doubleExtensions <= 11)
1076 depth += depth < 13;
1080 // Multi-cut pruning
1081 // Our ttMove is assumed to fail high, and now we failed high also on a
1082 // reduced search without the ttMove. So we assume this expected cut-node
1083 // is not singular, that multiple moves fail high, and we can prune the
1084 // whole subtree by returning a softbound.
1085 else if (singularBeta >= beta)
1086 return singularBeta;
1088 // If the eval of ttMove is greater than beta, we reduce it (negative extension) (~7 Elo)
1089 else if (ttValue >= beta)
1090 extension = -2 - !PvNode;
1092 // If we are on a cutNode, reduce it based on depth (negative extension) (~1 Elo)
1094 extension = depth < 17 ? -3 : -1;
1096 // If the eval of ttMove is less than value, we reduce it (negative extension) (~1 Elo)
1097 else if (ttValue <= value)
1101 // Check extensions (~1 Elo)
1102 else if ( givesCheck
1106 // Quiet ttMove extensions (~1 Elo)
1109 && move == ss->killers[0]
1110 && (*contHist[0])[movedPiece][to_sq(move)] >= 5168)
1114 // Add extension to new depth
1115 newDepth += extension;
1116 ss->doubleExtensions = (ss-1)->doubleExtensions + (extension == 2);
1118 // Speculative prefetch as early as possible
1119 prefetch(TT.first_entry(pos.key_after(move)));
1121 // Update the current move (this must be done after singular extension search)
1122 ss->currentMove = move;
1123 ss->continuationHistory = &thisThread->continuationHistory[ss->inCheck]
1128 // Step 16. Make the move
1129 pos.do_move(move, st, givesCheck);
1131 // Decrease reduction if position is or has been on the PV and not likely to fail low. (~3 Elo)
1132 // Decrease further on cutNodes. (~1 Elo)
1135 r -= cutNode && tte->depth() >= depth ? 3 : 2;
1137 // Decrease reduction if opponent's move count is high (~1 Elo)
1138 if ((ss-1)->moveCount > 8)
1141 // Increase reduction for cut nodes (~3 Elo)
1145 // Increase reduction if ttMove is a capture (~3 Elo)
1149 // Decrease reduction for PvNodes (~2 Elo)
1153 // Decrease reduction if ttMove has been singularly extended (~1 Elo)
1154 if (singularQuietLMR)
1157 // Increase reduction on repetition (~1 Elo)
1158 if ( move == (ss-4)->currentMove
1159 && pos.has_repeated())
1162 // Increase reduction if next ply has a lot of fail high (~5 Elo)
1163 if ((ss+1)->cutoffCnt > 3)
1166 // Decrease reduction for first generated move (ttMove)
1167 else if (move == ttMove)
1170 ss->statScore = 2 * thisThread->mainHistory[us][from_to(move)]
1171 + (*contHist[0])[movedPiece][to_sq(move)]
1172 + (*contHist[1])[movedPiece][to_sq(move)]
1173 + (*contHist[3])[movedPiece][to_sq(move)]
1176 // Decrease/increase reduction for moves with a good/bad history (~25 Elo)
1177 r -= ss->statScore / (11124 + 4740 * (depth > 5 && depth < 22));
1179 // Step 17. Late moves reduction / extension (LMR, ~117 Elo)
1180 // We use various heuristics for the sons of a node after the first son has
1181 // been searched. In general, we would like to reduce them, but there are many
1182 // cases where we extend a son if it has good chances to be "interesting".
1184 && moveCount > 1 + (PvNode && ss->ply <= 1)
1187 || (cutNode && (ss-1)->moveCount > 1)))
1189 // In general we want to cap the LMR depth search at newDepth, but when
1190 // reduction is negative, we allow this move a limited search extension
1191 // beyond the first move depth. This may lead to hidden double extensions.
1192 Depth d = std::clamp(newDepth - r, 1, newDepth + 1);
1194 value = -search<NonPV>(pos, ss+1, -(alpha+1), -alpha, d, true);
1196 // Do a full-depth search when reduced LMR search fails high
1197 if (value > alpha && d < newDepth)
1199 // Adjust full-depth search based on LMR results - if the result
1200 // was good enough search deeper, if it was bad enough search shallower
1201 const bool doDeeperSearch = value > (bestValue + 64 + 11 * (newDepth - d));
1202 const bool doEvenDeeperSearch = value > alpha + 711 && ss->doubleExtensions <= 6;
1203 const bool doShallowerSearch = value < bestValue + newDepth;
1205 ss->doubleExtensions = ss->doubleExtensions + doEvenDeeperSearch;
1207 newDepth += doDeeperSearch - doShallowerSearch + doEvenDeeperSearch;
1210 value = -search<NonPV>(pos, ss+1, -(alpha+1), -alpha, newDepth, !cutNode);
1212 int bonus = value <= alpha ? -stat_bonus(newDepth)
1213 : value >= beta ? stat_bonus(newDepth)
1216 update_continuation_histories(ss, movedPiece, to_sq(move), bonus);
1220 // Step 18. Full-depth search when LMR is skipped. If expected reduction is high, reduce its depth by 1.
1221 else if (!PvNode || moveCount > 1)
1223 // Increase reduction for cut nodes and not ttMove (~1 Elo)
1224 if (!ttMove && cutNode)
1227 value = -search<NonPV>(pos, ss+1, -(alpha+1), -alpha, newDepth - (r > 3), !cutNode);
1230 // For PV nodes only, do a full PV search on the first move or after a fail high,
1231 // otherwise let the parent node fail low with value <= alpha and try another move.
1232 if (PvNode && (moveCount == 1 || value > alpha))
1235 (ss+1)->pv[0] = MOVE_NONE;
1237 value = -search<PV>(pos, ss+1, -beta, -alpha, newDepth, false);
1240 // Step 19. Undo move
1241 pos.undo_move(move);
1243 assert(value > -VALUE_INFINITE && value < VALUE_INFINITE);
1245 // Step 20. Check for a new best move
1246 // Finished searching the move. If a stop occurred, the return value of
1247 // the search cannot be trusted, and we return immediately without
1248 // updating best move, PV and TT.
1249 if (Threads.stop.load(std::memory_order_relaxed))
1254 RootMove& rm = *std::find(thisThread->rootMoves.begin(),
1255 thisThread->rootMoves.end(), move);
1257 rm.averageScore = rm.averageScore != -VALUE_INFINITE ? (2 * value + rm.averageScore) / 3 : value;
1259 // PV move or new best move?
1260 if (moveCount == 1 || value > alpha)
1262 rm.score = rm.uciScore = value;
1263 rm.selDepth = thisThread->selDepth;
1264 rm.scoreLowerbound = rm.scoreUpperbound = false;
1268 rm.scoreLowerbound = true;
1271 else if (value <= alpha)
1273 rm.scoreUpperbound = true;
1274 rm.uciScore = alpha;
1281 for (Move* m = (ss+1)->pv; *m != MOVE_NONE; ++m)
1282 rm.pv.push_back(*m);
1284 // We record how often the best move has been changed in each iteration.
1285 // This information is used for time management. In MultiPV mode,
1286 // we must take care to only do this for the first PV line.
1288 && !thisThread->pvIdx)
1289 ++thisThread->bestMoveChanges;
1292 // All other moves but the PV, are set to the lowest value: this
1293 // is not a problem when sorting because the sort is stable and the
1294 // move position in the list is preserved - just the PV is pushed up.
1295 rm.score = -VALUE_INFINITE;
1298 if (value > bestValue)
1306 if (PvNode && !rootNode) // Update pv even in fail-high case
1307 update_pv(ss->pv, move, (ss+1)->pv);
1311 ss->cutoffCnt += 1 + !ttMove;
1312 assert(value >= beta); // Fail high
1317 // Reduce other moves if we have found at least one score improvement (~2 Elo)
1325 alpha = value; // Update alpha! Always alpha < beta
1331 // If the move is worse than some previously searched move, remember it, to update its stats later
1332 if (move != bestMove)
1334 if (capture && captureCount < 32)
1335 capturesSearched[captureCount++] = move;
1337 else if (!capture && quietCount < 64)
1338 quietsSearched[quietCount++] = move;
1342 // The following condition would detect a stop only after move loop has been
1343 // completed. But in this case, bestValue is valid because we have fully
1344 // searched our subtree, and we can anyhow save the result in TT.
1350 // Step 21. Check for mate and stalemate
1351 // All legal moves have been searched and if there are no legal moves, it
1352 // must be a mate or a stalemate. If we are in a singular extension search then
1353 // return a fail low score.
1355 assert(moveCount || !ss->inCheck || excludedMove || !MoveList<LEGAL>(pos).size());
1358 bestValue = excludedMove ? alpha :
1359 ss->inCheck ? mated_in(ss->ply)
1362 // If there is a move that produces search value greater than alpha we update the stats of searched moves
1364 update_all_stats(pos, ss, bestMove, bestValue, beta, prevSq,
1365 quietsSearched, quietCount, capturesSearched, captureCount, depth);
1367 // Bonus for prior countermove that caused the fail low
1368 else if (!priorCapture && prevSq != SQ_NONE)
1370 int bonus = (depth > 5) + (PvNode || cutNode) + (bestValue < alpha - 800) + ((ss-1)->moveCount > 12);
1371 update_continuation_histories(ss-1, pos.piece_on(prevSq), prevSq, stat_bonus(depth) * bonus);
1372 thisThread->mainHistory[~us][from_to((ss-1)->currentMove)] << stat_bonus(depth) * bonus / 2;
1376 bestValue = std::min(bestValue, maxValue);
1378 // If no good move is found and the previous position was ttPv, then the previous
1379 // opponent move is probably good and the new position is added to the search tree. (~7 Elo)
1380 if (bestValue <= alpha)
1381 ss->ttPv = ss->ttPv || ((ss-1)->ttPv && depth > 3);
1383 // Write gathered information in transposition table
1384 if (!excludedMove && !(rootNode && thisThread->pvIdx))
1385 tte->save(posKey, value_to_tt(bestValue, ss->ply), ss->ttPv,
1386 bestValue >= beta ? BOUND_LOWER :
1387 PvNode && bestMove ? BOUND_EXACT : BOUND_UPPER,
1388 depth, bestMove, ss->staticEval);
1390 assert(bestValue > -VALUE_INFINITE && bestValue < VALUE_INFINITE);
1396 // qsearch() is the quiescence search function, which is called by the main search
1397 // function with zero depth, or recursively with further decreasing depth per call.
1399 template <NodeType nodeType>
1400 Value qsearch(Position& pos, Stack* ss, Value alpha, Value beta, Depth depth) {
1402 static_assert(nodeType != Root);
1403 constexpr bool PvNode = nodeType == PV;
1405 assert(alpha >= -VALUE_INFINITE && alpha < beta && beta <= VALUE_INFINITE);
1406 assert(PvNode || (alpha == beta - 1));
1409 // Check if we have an upcoming move that draws by repetition, or
1410 // if the opponent had an alternative move earlier to this position.
1411 if ( alpha < VALUE_DRAW
1412 && pos.has_game_cycle(ss->ply))
1414 alpha = value_draw(pos.this_thread());
1421 ASSERT_ALIGNED(&st, Eval::NNUE::CacheLineSize);
1425 Move ttMove, move, bestMove;
1427 Value bestValue, value, ttValue, futilityValue, futilityBase;
1428 bool pvHit, givesCheck, capture;
1430 Color us = pos.side_to_move();
1432 // Step 1. Initialize node
1436 ss->pv[0] = MOVE_NONE;
1439 Thread* thisThread = pos.this_thread();
1440 bestMove = MOVE_NONE;
1441 ss->inCheck = pos.checkers();
1444 // Step 2. Check for an immediate draw or maximum ply reached
1445 if ( pos.is_draw(ss->ply)
1446 || ss->ply >= MAX_PLY)
1447 return (ss->ply >= MAX_PLY && !ss->inCheck) ? evaluate(pos) : VALUE_DRAW;
1449 assert(0 <= ss->ply && ss->ply < MAX_PLY);
1451 // Decide whether or not to include checks: this fixes also the type of
1452 // TT entry depth that we are going to use. Note that in qsearch we use
1453 // only two types of depth in TT: DEPTH_QS_CHECKS or DEPTH_QS_NO_CHECKS.
1454 ttDepth = ss->inCheck || depth >= DEPTH_QS_CHECKS ? DEPTH_QS_CHECKS
1455 : DEPTH_QS_NO_CHECKS;
1457 // Step 3. Transposition table lookup
1459 tte = TT.probe(posKey, ss->ttHit);
1460 ttValue = ss->ttHit ? value_from_tt(tte->value(), ss->ply, pos.rule50_count()) : VALUE_NONE;
1461 ttMove = ss->ttHit ? tte->move() : MOVE_NONE;
1462 pvHit = ss->ttHit && tte->is_pv();
1464 // At non-PV nodes we check for an early TT cutoff
1466 && tte->depth() >= ttDepth
1467 && ttValue != VALUE_NONE // Only in case of TT access race or if !ttHit
1468 && (tte->bound() & (ttValue >= beta ? BOUND_LOWER : BOUND_UPPER)))
1471 // Step 4. Static evaluation of the position
1473 bestValue = futilityBase = -VALUE_INFINITE;
1478 // Never assume anything about values stored in TT
1479 if ((ss->staticEval = bestValue = tte->eval()) == VALUE_NONE)
1480 ss->staticEval = bestValue = evaluate(pos);
1482 // ttValue can be used as a better position evaluation (~13 Elo)
1483 if ( ttValue != VALUE_NONE
1484 && (tte->bound() & (ttValue > bestValue ? BOUND_LOWER : BOUND_UPPER)))
1485 bestValue = ttValue;
1488 // In case of null move search use previous static eval with a different sign
1489 ss->staticEval = bestValue = (ss-1)->currentMove != MOVE_NULL ? evaluate(pos)
1490 : -(ss-1)->staticEval;
1492 // Stand pat. Return immediately if static value is at least beta
1493 if (bestValue >= beta)
1495 // Save gathered info in transposition table
1497 tte->save(posKey, value_to_tt(bestValue, ss->ply), false, BOUND_LOWER,
1498 DEPTH_NONE, MOVE_NONE, ss->staticEval);
1503 if (bestValue > alpha)
1506 futilityBase = std::min(ss->staticEval, bestValue) + 200;
1509 const PieceToHistory* contHist[] = { (ss-1)->continuationHistory, (ss-2)->continuationHistory,
1510 nullptr , (ss-4)->continuationHistory,
1511 nullptr , (ss-6)->continuationHistory };
1513 // Initialize a MovePicker object for the current position, and prepare
1514 // to search the moves. Because the depth is <= 0 here, only captures,
1515 // queen promotions, and other checks (only if depth >= DEPTH_QS_CHECKS)
1516 // will be generated.
1517 Square prevSq = is_ok((ss-1)->currentMove) ? to_sq((ss-1)->currentMove) : SQ_NONE;
1518 MovePicker mp(pos, ttMove, depth, &thisThread->mainHistory,
1519 &thisThread->captureHistory,
1523 int quietCheckEvasions = 0;
1525 // Step 5. Loop through all pseudo-legal moves until no moves remain
1526 // or a beta cutoff occurs.
1527 while ((move = mp.next_move()) != MOVE_NONE)
1529 assert(is_ok(move));
1531 // Check for legality
1532 if (!pos.legal(move))
1535 givesCheck = pos.gives_check(move);
1536 capture = pos.capture_stage(move);
1541 if (bestValue > VALUE_TB_LOSS_IN_MAX_PLY && pos.non_pawn_material(us))
1543 // Futility pruning and moveCount pruning (~10 Elo)
1545 && to_sq(move) != prevSq
1546 && futilityBase > VALUE_TB_LOSS_IN_MAX_PLY
1547 && type_of(move) != PROMOTION)
1552 futilityValue = futilityBase + PieceValue[pos.piece_on(to_sq(move))];
1554 // If static eval + value of piece we are going to capture is much lower
1555 // than alpha we can prune this move
1556 if (futilityValue <= alpha)
1558 bestValue = std::max(bestValue, futilityValue);
1562 // If static eval is much lower than alpha and move is not winning material
1563 // we can prune this move
1564 if (futilityBase <= alpha && !pos.see_ge(move, VALUE_ZERO + 1))
1566 bestValue = std::max(bestValue, futilityBase);
1570 // If static exchange evaluation is much worse than what is needed to not
1571 // fall below alpha we can prune this move
1572 if (futilityBase > alpha && !pos.see_ge(move, (alpha - futilityBase) * 4))
1579 // We prune after the second quiet check evasion move, where being 'in check' is
1580 // implicitly checked through the counter, and being a 'quiet move' apart from
1581 // 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(-95)))
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 (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);
1721 int quietMoveBonus = stat_bonus(depth + 1);
1723 if (!pos.capture_stage(bestMove))
1725 int bestMoveBonus = bestValue > beta + 145 ? quietMoveBonus // larger bonus
1726 : stat_bonus(depth); // smaller bonus
1728 // Increase stats for the best move in case it was a quiet move
1729 update_quiet_stats(pos, ss, bestMove, bestMoveBonus);
1731 // Decrease stats for all non-best quiet moves
1732 for (int i = 0; i < quietCount; ++i)
1734 thisThread->mainHistory[us][from_to(quietsSearched[i])] << -bestMoveBonus;
1735 update_continuation_histories(ss, pos.moved_piece(quietsSearched[i]), to_sq(quietsSearched[i]), -bestMoveBonus);
1740 // Increase stats for the best move in case it was a capture move
1741 captured = type_of(pos.piece_on(to_sq(bestMove)));
1742 captureHistory[moved_piece][to_sq(bestMove)][captured] << quietMoveBonus;
1745 // Extra penalty for a quiet early move that was not a TT move or
1746 // main killer move in previous ply when it gets refuted.
1747 if ( prevSq != SQ_NONE
1748 && ((ss-1)->moveCount == 1 + (ss-1)->ttHit || ((ss-1)->currentMove == (ss-1)->killers[0]))
1749 && !pos.captured_piece())
1750 update_continuation_histories(ss-1, pos.piece_on(prevSq), prevSq, -quietMoveBonus);
1752 // Decrease stats for all non-best capture moves
1753 for (int i = 0; i < captureCount; ++i)
1755 moved_piece = pos.moved_piece(capturesSearched[i]);
1756 captured = type_of(pos.piece_on(to_sq(capturesSearched[i])));
1757 captureHistory[moved_piece][to_sq(capturesSearched[i])][captured] << -quietMoveBonus;
1762 // update_continuation_histories() updates histories of the move pairs formed
1763 // by moves at ply -1, -2, -4, and -6 with current move.
1765 void update_continuation_histories(Stack* ss, Piece pc, Square to, int bonus) {
1767 for (int i : {1, 2, 4, 6})
1769 // Only update the first 2 continuation histories if we are in check
1770 if (ss->inCheck && i > 2)
1772 if (is_ok((ss-i)->currentMove))
1773 (*(ss-i)->continuationHistory)[pc][to] << bonus;
1778 // update_quiet_stats() updates move sorting heuristics
1780 void update_quiet_stats(const Position& pos, Stack* ss, Move move, int bonus) {
1783 if (ss->killers[0] != move)
1785 ss->killers[1] = ss->killers[0];
1786 ss->killers[0] = move;
1789 Color us = pos.side_to_move();
1790 Thread* thisThread = pos.this_thread();
1791 thisThread->mainHistory[us][from_to(move)] << bonus;
1792 update_continuation_histories(ss, pos.moved_piece(move), to_sq(move), bonus);
1794 // Update countermove history
1795 if (is_ok((ss-1)->currentMove))
1797 Square prevSq = to_sq((ss-1)->currentMove);
1798 thisThread->counterMoves[pos.piece_on(prevSq)][prevSq] = move;
1802 // When playing with strength handicap, choose the best move among a set of RootMoves
1803 // using a statistical rule dependent on 'level'. Idea by Heinz van Saanen.
1805 Move Skill::pick_best(size_t multiPV) {
1807 const RootMoves& rootMoves = Threads.main()->rootMoves;
1808 static PRNG rng(now()); // PRNG sequence should be non-deterministic
1810 // RootMoves are already sorted by score in descending order
1811 Value topScore = rootMoves[0].score;
1812 int delta = std::min(topScore - rootMoves[multiPV - 1].score, PawnValue);
1813 int maxScore = -VALUE_INFINITE;
1814 double weakness = 120 - 2 * level;
1816 // Choose best move. For each move score we add two terms, both dependent on
1817 // weakness. One is deterministic and bigger for weaker levels, and one is
1818 // random. Then we choose the move with the resulting highest score.
1819 for (size_t i = 0; i < multiPV; ++i)
1821 // This is our magic formula
1822 int push = int(( weakness * int(topScore - rootMoves[i].score)
1823 + delta * (rng.rand<unsigned>() % int(weakness))) / 128);
1825 if (rootMoves[i].score + push >= maxScore)
1827 maxScore = rootMoves[i].score + push;
1828 best = rootMoves[i].pv[0];
1838 /// MainThread::check_time() is used to print debug info and, more importantly,
1839 /// to detect when we are out of available time and thus stop the search.
1841 void MainThread::check_time() {
1846 // When using nodes, ensure checking rate is not lower than 0.1% of nodes
1847 callsCnt = Limits.nodes ? std::min(512, int(Limits.nodes / 1024)) : 512;
1849 static TimePoint lastInfoTime = now();
1851 TimePoint elapsed = Time.elapsed();
1852 TimePoint tick = Limits.startTime + elapsed;
1854 if (tick - lastInfoTime >= 1000)
1856 lastInfoTime = tick;
1860 // We should not stop pondering until told so by the GUI
1864 if ( (Limits.use_time_management() && (elapsed > Time.maximum() || stopOnPonderhit))
1865 || (Limits.movetime && elapsed >= Limits.movetime)
1866 || (Limits.nodes && Threads.nodes_searched() >= uint64_t(Limits.nodes)))
1867 Threads.stop = true;
1871 /// UCI::pv() formats PV information according to the UCI protocol. UCI requires
1872 /// that all (if any) unsearched PV lines are sent using a previous search score.
1874 string UCI::pv(const Position& pos, Depth depth) {
1876 std::stringstream ss;
1877 TimePoint elapsed = Time.elapsed() + 1;
1878 const RootMoves& rootMoves = pos.this_thread()->rootMoves;
1879 size_t pvIdx = pos.this_thread()->pvIdx;
1880 size_t multiPV = std::min(size_t(Options["MultiPV"]), rootMoves.size());
1881 uint64_t nodesSearched = Threads.nodes_searched();
1882 uint64_t tbHits = Threads.tb_hits() + (TB::RootInTB ? rootMoves.size() : 0);
1884 for (size_t i = 0; i < multiPV; ++i)
1886 bool updated = rootMoves[i].score != -VALUE_INFINITE;
1888 if (depth == 1 && !updated && i > 0)
1891 Depth d = updated ? depth : std::max(1, depth - 1);
1892 Value v = updated ? rootMoves[i].uciScore : rootMoves[i].previousScore;
1894 if (v == -VALUE_INFINITE)
1897 bool tb = TB::RootInTB && abs(v) < VALUE_MATE_IN_MAX_PLY;
1898 v = tb ? rootMoves[i].tbScore : v;
1900 if (ss.rdbuf()->in_avail()) // Not at first line
1905 << " seldepth " << rootMoves[i].selDepth
1906 << " multipv " << i + 1
1907 << " score " << UCI::value(v);
1909 if (Options["UCI_ShowWDL"])
1910 ss << UCI::wdl(v, pos.game_ply());
1912 if (i == pvIdx && !tb && updated) // tablebase- and previous-scores are exact
1913 ss << (rootMoves[i].scoreLowerbound ? " lowerbound" : (rootMoves[i].scoreUpperbound ? " upperbound" : ""));
1915 ss << " nodes " << nodesSearched
1916 << " nps " << nodesSearched * 1000 / elapsed
1917 << " hashfull " << TT.hashfull()
1918 << " tbhits " << tbHits
1919 << " time " << elapsed
1922 for (Move m : rootMoves[i].pv)
1923 ss << " " << UCI::move(m, pos.is_chess960());
1930 /// RootMove::extract_ponder_from_tt() is called in case we have no ponder move
1931 /// before exiting the search, for instance, in case we stop the search during a
1932 /// fail high at root. We try hard to have a ponder move to return to the GUI,
1933 /// otherwise in case of 'ponder on' we have nothing to think about.
1935 bool RootMove::extract_ponder_from_tt(Position& pos) {
1938 ASSERT_ALIGNED(&st, Eval::NNUE::CacheLineSize);
1942 assert(pv.size() == 1);
1944 if (pv[0] == MOVE_NONE)
1947 pos.do_move(pv[0], st);
1948 TTEntry* tte = TT.probe(pos.key(), ttHit);
1952 Move m = tte->move(); // Local copy to be SMP safe
1953 if (MoveList<LEGAL>(pos).contains(m))
1957 pos.undo_move(pv[0]);
1958 return pv.size() > 1;
1961 void Tablebases::rank_root_moves(Position& pos, Search::RootMoves& rootMoves) {
1964 UseRule50 = bool(Options["Syzygy50MoveRule"]);
1965 ProbeDepth = int(Options["SyzygyProbeDepth"]);
1966 Cardinality = int(Options["SyzygyProbeLimit"]);
1967 bool dtz_available = true;
1969 // Tables with fewer pieces than SyzygyProbeLimit are searched with
1970 // ProbeDepth == DEPTH_ZERO
1971 if (Cardinality > MaxCardinality)
1973 Cardinality = MaxCardinality;
1977 if (Cardinality >= popcount(pos.pieces()) && !pos.can_castle(ANY_CASTLING))
1979 // Rank moves using DTZ tables
1980 RootInTB = root_probe(pos, rootMoves);
1984 // DTZ tables are missing; try to rank moves using WDL tables
1985 dtz_available = false;
1986 RootInTB = root_probe_wdl(pos, rootMoves);
1992 // Sort moves according to TB rank
1993 std::stable_sort(rootMoves.begin(), rootMoves.end(),
1994 [](const RootMove &a, const RootMove &b) { return a.tbRank > b.tbRank; } );
1996 // Probe during search only if DTZ is not available and we are winning
1997 if (dtz_available || rootMoves[0].tbScore <= VALUE_DRAW)
2002 // Clean up if root_probe() and root_probe_wdl() have failed
2003 for (auto& m : rootMoves)
2008 } // namespace Stockfish