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
79 Value futility_margin(Depth d, bool noTtCutNode, bool improving) {
80 return Value((125 - 43 * noTtCutNode) * (d - improving));
83 // Reductions lookup table initialized at startup
84 int Reductions[MAX_MOVES]; // [depth or moveNumber]
86 Depth reduction(bool i, Depth d, int mn, Value delta, Value rootDelta) {
87 int reductionScale = Reductions[d] * Reductions[mn];
88 return (reductionScale + 1487 - int(delta) * 976 / int(rootDelta)) / 1024
89 + (!i && reductionScale > 808);
92 constexpr int futility_move_count(bool improving, Depth depth) {
93 return improving ? (3 + depth * depth) : (3 + depth * depth) / 2;
96 // History and stats update bonus, based on depth
97 int stat_bonus(Depth d) { return std::min(357 * d - 483, 1511); }
99 // Add a small random component to draw evaluations to avoid 3-fold blindness
100 Value value_draw(const Thread* thisThread) {
101 return VALUE_DRAW - 1 + Value(thisThread->nodes & 0x2);
104 // Skill structure is used to implement strength limit. If we have a UCI_Elo,
105 // we convert it to an appropriate skill level, anchored to the Stash engine.
106 // This method is based on a fit of the Elo results for games played between
107 // Stockfish at various skill levels and various versions of the Stash engine.
108 // Skill 0 .. 19 now covers CCRL Blitz Elo from 1320 to 3190, approximately
109 // Reference: https://github.com/vondele/Stockfish/commit/a08b8d4e9711c2
111 Skill(int skill_level, int uci_elo) {
114 double e = double(uci_elo - 1320) / (3190 - 1320);
115 level = std::clamp((((37.2473 * e - 40.8525) * e + 22.2943) * e - 0.311438), 0.0, 19.0);
118 level = double(skill_level);
120 bool enabled() const { return level < 20.0; }
121 bool time_to_pick(Depth depth) const { return depth == 1 + int(level); }
122 Move pick_best(size_t multiPV);
125 Move best = MOVE_NONE;
128 template<NodeType nodeType>
129 Value search(Position& pos, Stack* ss, Value alpha, Value beta, Depth depth, bool cutNode);
131 template<NodeType nodeType>
132 Value qsearch(Position& pos, Stack* ss, Value alpha, Value beta, Depth depth = 0);
134 Value value_to_tt(Value v, int ply);
135 Value value_from_tt(Value v, int ply, int r50c);
136 void update_pv(Move* pv, Move move, const Move* childPv);
137 void update_continuation_histories(Stack* ss, Piece pc, Square to, int bonus);
138 void update_quiet_stats(const Position& pos, Stack* ss, Move move, int bonus);
139 void update_all_stats(const Position& pos,
145 Move* quietsSearched,
147 Move* capturesSearched,
151 // Utility to verify move generation. All the leaf nodes up
152 // to the given depth are generated and counted, and the sum is returned.
154 uint64_t perft(Position& pos, Depth depth) {
157 ASSERT_ALIGNED(&st, Eval::NNUE::CacheLineSize);
159 uint64_t cnt, nodes = 0;
160 const bool leaf = (depth == 2);
162 for (const auto& m : MoveList<LEGAL>(pos))
164 if (Root && depth <= 1)
169 cnt = leaf ? MoveList<LEGAL>(pos).size() : perft<false>(pos, depth - 1);
174 sync_cout << UCI::move(m, pos.is_chess960()) << ": " << cnt << sync_endl;
182 // Called at startup to initialize various lookup tables
183 void Search::init() {
185 for (int i = 1; i < MAX_MOVES; ++i)
186 Reductions[i] = int((20.37 + std::log(Threads.size()) / 2) * std::log(i));
190 // Resets search state to its initial value
191 void Search::clear() {
193 Threads.main()->wait_for_search_finished();
195 Time.availableNodes = 0;
198 Tablebases::init(Options["SyzygyPath"]); // Free mapped files
202 // Called when the program receives the UCI 'go'
203 // command. It searches from the root position and outputs the "bestmove".
204 void MainThread::search() {
208 nodes = perft<true>(rootPos, Limits.perft);
209 sync_cout << "\nNodes searched: " << nodes << "\n" << sync_endl;
213 Color us = rootPos.side_to_move();
214 Time.init(Limits, us, rootPos.game_ply());
217 Eval::NNUE::verify();
219 if (rootMoves.empty())
221 rootMoves.emplace_back(MOVE_NONE);
222 sync_cout << "info depth 0 score "
223 << UCI::value(rootPos.checkers() ? -VALUE_MATE : VALUE_DRAW) << sync_endl;
227 Threads.start_searching(); // start non-main threads
228 Thread::search(); // main thread start searching
231 // When we reach the maximum depth, we can arrive here without a raise of
232 // Threads.stop. However, if we are pondering or in an infinite search,
233 // the UCI protocol states that we shouldn't print the best move before the
234 // GUI sends a "stop" or "ponderhit" command. We therefore simply wait here
235 // until the GUI sends one of those commands.
237 while (!Threads.stop && (ponder || Limits.infinite))
238 {} // Busy wait for a stop or a ponder reset
240 // Stop the threads if not already stopped (also raise the stop if
241 // "ponderhit" just reset Threads.ponder).
244 // Wait until all threads have finished
245 Threads.wait_for_search_finished();
247 // When playing in 'nodes as time' mode, subtract the searched nodes from
248 // the available ones before exiting.
250 Time.availableNodes += Limits.inc[us] - Threads.nodes_searched();
252 Thread* bestThread = this;
254 Skill(Options["Skill Level"], Options["UCI_LimitStrength"] ? int(Options["UCI_Elo"]) : 0);
256 if (int(Options["MultiPV"]) == 1 && !Limits.depth && !skill.enabled()
257 && rootMoves[0].pv[0] != MOVE_NONE)
258 bestThread = Threads.get_best_thread();
260 bestPreviousScore = bestThread->rootMoves[0].score;
261 bestPreviousAverageScore = bestThread->rootMoves[0].averageScore;
263 // Send again PV info if we have a new best thread
264 if (bestThread != this)
265 sync_cout << UCI::pv(bestThread->rootPos, bestThread->completedDepth) << sync_endl;
267 sync_cout << "bestmove " << UCI::move(bestThread->rootMoves[0].pv[0], rootPos.is_chess960());
269 if (bestThread->rootMoves[0].pv.size() > 1
270 || bestThread->rootMoves[0].extract_ponder_from_tt(rootPos))
271 std::cout << " ponder " << UCI::move(bestThread->rootMoves[0].pv[1], rootPos.is_chess960());
273 std::cout << sync_endl;
277 // Main iterative deepening loop. It calls search()
278 // repeatedly with increasing depth until the allocated thinking time has been
279 // consumed, the user stops the search, or the maximum search depth is reached.
280 void Thread::search() {
282 // Allocate stack with extra size to allow access from (ss - 7) to (ss + 2):
283 // (ss - 7) is needed for update_continuation_histories(ss - 1) which accesses (ss - 6),
284 // (ss + 2) is needed for initialization of cutOffCnt and killers.
285 Stack stack[MAX_PLY + 10], *ss = stack + 7;
286 Move pv[MAX_PLY + 1];
287 Value alpha, beta, delta;
288 Move lastBestMove = MOVE_NONE;
289 Depth lastBestMoveDepth = 0;
290 MainThread* mainThread = (this == Threads.main() ? Threads.main() : nullptr);
291 double timeReduction = 1, totBestMoveChanges = 0;
292 Color us = rootPos.side_to_move();
295 std::memset(ss - 7, 0, 10 * sizeof(Stack));
296 for (int i = 7; i > 0; --i)
298 (ss - i)->continuationHistory =
299 &this->continuationHistory[0][0][NO_PIECE][0]; // Use as a sentinel
300 (ss - i)->staticEval = VALUE_NONE;
303 for (int i = 0; i <= MAX_PLY + 2; ++i)
308 bestValue = -VALUE_INFINITE;
312 if (mainThread->bestPreviousScore == VALUE_INFINITE)
313 for (int i = 0; i < 4; ++i)
314 mainThread->iterValue[i] = VALUE_ZERO;
316 for (int i = 0; i < 4; ++i)
317 mainThread->iterValue[i] = mainThread->bestPreviousScore;
320 size_t multiPV = size_t(Options["MultiPV"]);
321 Skill skill(Options["Skill Level"], Options["UCI_LimitStrength"] ? int(Options["UCI_Elo"]) : 0);
323 // When playing with strength handicap enable MultiPV search that we will
324 // use behind-the-scenes to retrieve a set of possible moves.
326 multiPV = std::max(multiPV, size_t(4));
328 multiPV = std::min(multiPV, rootMoves.size());
330 int searchAgainCounter = 0;
332 // Iterative deepening loop until requested to stop or the target depth is reached
333 while (++rootDepth < MAX_PLY && !Threads.stop
334 && !(Limits.depth && mainThread && rootDepth > Limits.depth))
336 // Age out PV variability metric
338 totBestMoveChanges /= 2;
340 // Save the last iteration's scores before the first PV line is searched and
341 // all the move scores except the (new) PV are set to -VALUE_INFINITE.
342 for (RootMove& rm : rootMoves)
343 rm.previousScore = rm.score;
348 if (!Threads.increaseDepth)
349 searchAgainCounter++;
351 // MultiPV loop. We perform a full root search for each PV line
352 for (pvIdx = 0; pvIdx < multiPV && !Threads.stop; ++pvIdx)
357 for (pvLast++; pvLast < rootMoves.size(); pvLast++)
358 if (rootMoves[pvLast].tbRank != rootMoves[pvFirst].tbRank)
362 // Reset UCI info selDepth for each depth and each PV line
365 // Reset aspiration window starting size
366 Value avg = rootMoves[pvIdx].averageScore;
367 delta = Value(10) + int(avg) * avg / 15335;
368 alpha = std::max(avg - delta, -VALUE_INFINITE);
369 beta = std::min(avg + delta, VALUE_INFINITE);
371 // Adjust optimism based on root move's averageScore (~4 Elo)
372 optimism[us] = 103 * (avg + 33) / (std::abs(avg + 34) + 119);
373 optimism[~us] = -116 * (avg + 40) / (std::abs(avg + 12) + 123);
375 // Start with a small aspiration window and, in the case of a fail
376 // high/low, re-search with a bigger window until we don't fail
378 int failedHighCnt = 0;
381 // Adjust the effective depth searched, but ensure at least one effective increment
382 // for every four searchAgain steps (see issue #2717).
383 Depth adjustedDepth =
384 std::max(1, rootDepth - failedHighCnt - 3 * (searchAgainCounter + 1) / 4);
385 bestValue = Stockfish::search<Root>(rootPos, ss, alpha, beta, adjustedDepth, false);
387 // Bring the best move to the front. It is critical that sorting
388 // is done with a stable algorithm because all the values but the
389 // first and eventually the new best one is set to -VALUE_INFINITE
390 // and we want to keep the same order for all the moves except the
391 // new PV that goes to the front. Note that in the case of MultiPV
392 // search the already searched PV lines are preserved.
393 std::stable_sort(rootMoves.begin() + pvIdx, rootMoves.begin() + pvLast);
395 // If search has been stopped, we break immediately. Sorting is
396 // safe because RootMoves is still valid, although it refers to
397 // the previous iteration.
401 // When failing high/low give some update (without cluttering
402 // the UI) before a re-search.
403 if (mainThread && multiPV == 1 && (bestValue <= alpha || bestValue >= beta)
404 && Time.elapsed() > 3000)
405 sync_cout << UCI::pv(rootPos, rootDepth) << sync_endl;
407 // In case of failing low/high increase aspiration window and
408 // re-search, otherwise exit the loop.
409 if (bestValue <= alpha)
411 beta = (alpha + beta) / 2;
412 alpha = std::max(bestValue - delta, -VALUE_INFINITE);
416 mainThread->stopOnPonderhit = false;
418 else if (bestValue >= beta)
420 beta = std::min(bestValue + delta, VALUE_INFINITE);
428 assert(alpha >= -VALUE_INFINITE && beta <= VALUE_INFINITE);
431 // Sort the PV lines searched so far and update the GUI
432 std::stable_sort(rootMoves.begin() + pvFirst, rootMoves.begin() + pvIdx + 1);
434 if (mainThread && (Threads.stop || pvIdx + 1 == multiPV || Time.elapsed() > 3000))
435 sync_cout << UCI::pv(rootPos, rootDepth) << sync_endl;
439 completedDepth = rootDepth;
441 if (rootMoves[0].pv[0] != lastBestMove)
443 lastBestMove = rootMoves[0].pv[0];
444 lastBestMoveDepth = rootDepth;
447 // Have we found a "mate in x"?
448 if (Limits.mate && bestValue >= VALUE_MATE_IN_MAX_PLY
449 && VALUE_MATE - bestValue <= 2 * Limits.mate)
455 // If the skill level is enabled and time is up, pick a sub-optimal best move
456 if (skill.enabled() && skill.time_to_pick(rootDepth))
457 skill.pick_best(multiPV);
459 // Use part of the gained time from a previous stable move for the current move
460 for (Thread* th : Threads)
462 totBestMoveChanges += th->bestMoveChanges;
463 th->bestMoveChanges = 0;
466 // Do we have time for the next iteration? Can we stop searching now?
467 if (Limits.use_time_management() && !Threads.stop && !mainThread->stopOnPonderhit)
469 double fallingEval = (66 + 14 * (mainThread->bestPreviousAverageScore - bestValue)
470 + 6 * (mainThread->iterValue[iterIdx] - bestValue))
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 ? 1.56 : 0.69;
476 double reduction = (1.4 + mainThread->previousTimeReduction) / (2.03 * timeReduction);
477 double bestMoveInstability = 1 + 1.79 * 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
482 if (rootMoves.size() == 1)
483 totalTime = std::min(500.0, totalTime);
485 // Stop the search if we have exceeded the totalTime
486 if (Time.elapsed() > totalTime)
488 // If we are allowed to ponder do not stop the search now but
489 // keep pondering until the GUI sends "ponderhit" or "stop".
490 if (mainThread->ponder)
491 mainThread->stopOnPonderhit = true;
495 else if (!mainThread->ponder && 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 the skill level is enabled, swap the 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 // Main search function for both PV and non-PV nodes
520 template<NodeType nodeType>
521 Value search(Position& pos, Stack* ss, Value alpha, Value beta, Depth depth, bool cutNode) {
523 constexpr bool PvNode = nodeType != NonPV;
524 constexpr bool rootNode = nodeType == Root;
526 // Dive into quiescence search when the depth reaches zero
528 return qsearch < PvNode ? PV : NonPV > (pos, ss, alpha, beta);
530 // Check if we have an upcoming move that draws by repetition, or
531 // if the opponent had an alternative move earlier to this position.
532 if (!rootNode && alpha < VALUE_DRAW && pos.has_game_cycle(ss->ply))
534 alpha = value_draw(pos.this_thread());
539 assert(-VALUE_INFINITE <= alpha && alpha < beta && beta <= VALUE_INFINITE);
540 assert(PvNode || (alpha == beta - 1));
541 assert(0 < depth && depth < MAX_PLY);
542 assert(!(PvNode && cutNode));
544 Move pv[MAX_PLY + 1], capturesSearched[32], quietsSearched[32];
546 ASSERT_ALIGNED(&st, Eval::NNUE::CacheLineSize);
550 Move ttMove, move, excludedMove, bestMove;
551 Depth extension, newDepth;
552 Value bestValue, value, ttValue, eval, maxValue, probCutBeta;
553 bool givesCheck, improving, priorCapture, singularQuietLMR;
554 bool capture, moveCountPruning, ttCapture;
556 int moveCount, captureCount, quietCount;
558 // Step 1. Initialize node
559 Thread* thisThread = pos.this_thread();
560 ss->inCheck = pos.checkers();
561 priorCapture = pos.captured_piece();
562 Color us = pos.side_to_move();
563 moveCount = captureCount = quietCount = ss->moveCount = 0;
564 bestValue = -VALUE_INFINITE;
565 maxValue = VALUE_INFINITE;
567 // Check for the available remaining time
568 if (thisThread == Threads.main())
569 static_cast<MainThread*>(thisThread)->check_time();
571 // Used to send selDepth info to GUI (selDepth counts from 1, ply from 0)
572 if (PvNode && thisThread->selDepth < ss->ply + 1)
573 thisThread->selDepth = ss->ply + 1;
577 // Step 2. Check for aborted search and immediate draw
578 if (Threads.stop.load(std::memory_order_relaxed) || pos.is_draw(ss->ply)
579 || ss->ply >= MAX_PLY)
580 return (ss->ply >= MAX_PLY && !ss->inCheck) ? evaluate(pos)
581 : value_draw(pos.this_thread());
583 // Step 3. Mate distance pruning. Even if we mate at the next move our score
584 // would be at best mate_in(ss->ply + 1), but if alpha is already bigger because
585 // a shorter mate was found upward in the tree then there is no need to search
586 // because we will never beat the current alpha. Same logic but with reversed
587 // signs apply also in the opposite condition of being mated instead of giving
588 // mate. In this case, return a fail-high score.
589 alpha = std::max(mated_in(ss->ply), alpha);
590 beta = std::min(mate_in(ss->ply + 1), beta);
595 thisThread->rootDelta = beta - alpha;
597 assert(0 <= ss->ply && ss->ply < MAX_PLY);
599 (ss + 1)->excludedMove = bestMove = MOVE_NONE;
600 (ss + 2)->killers[0] = (ss + 2)->killers[1] = MOVE_NONE;
601 (ss + 2)->cutoffCnt = 0;
602 ss->doubleExtensions = (ss - 1)->doubleExtensions;
603 Square prevSq = is_ok((ss - 1)->currentMove) ? to_sq((ss - 1)->currentMove) : SQ_NONE;
606 // Step 4. Transposition table lookup.
607 excludedMove = ss->excludedMove;
609 tte = TT.probe(posKey, ss->ttHit);
610 ttValue = ss->ttHit ? value_from_tt(tte->value(), ss->ply, pos.rule50_count()) : VALUE_NONE;
611 ttMove = rootNode ? thisThread->rootMoves[thisThread->pvIdx].pv[0]
612 : ss->ttHit ? tte->move()
614 ttCapture = ttMove && pos.capture_stage(ttMove);
616 // At this point, if excluded, skip straight to step 6, static eval. However,
617 // to save indentation, we list the condition in all code between here and there.
619 ss->ttPv = PvNode || (ss->ttHit && tte->is_pv());
621 // At non-PV nodes we check for an early TT cutoff
622 if (!PvNode && !excludedMove && tte->depth() > depth
623 && ttValue != VALUE_NONE // Possible in case of TT access race or if !ttHit
624 && (tte->bound() & (ttValue >= beta ? BOUND_LOWER : BOUND_UPPER)))
626 // If ttMove is quiet, update move sorting heuristics on TT hit (~2 Elo)
631 // Bonus for a quiet ttMove that fails high (~2 Elo)
633 update_quiet_stats(pos, ss, ttMove, stat_bonus(depth));
635 // Extra penalty for early quiet moves of
636 // the previous ply (~0 Elo on STC, ~2 Elo on LTC).
637 if (prevSq != SQ_NONE && (ss - 1)->moveCount <= 2 && !priorCapture)
638 update_continuation_histories(ss - 1, pos.piece_on(prevSq), prevSq,
639 -stat_bonus(depth + 1));
641 // Penalty for a quiet ttMove that fails low (~1 Elo)
644 int penalty = -stat_bonus(depth);
645 thisThread->mainHistory[us][from_to(ttMove)] << penalty;
646 update_continuation_histories(ss, pos.moved_piece(ttMove), to_sq(ttMove), penalty);
650 // Partial workaround for the graph history interaction problem
651 // For high rule50 counts don't produce transposition table cutoffs.
652 if (pos.rule50_count() < 90)
656 // Step 5. Tablebases probe
657 if (!rootNode && !excludedMove && TB::Cardinality)
659 int piecesCount = pos.count<ALL_PIECES>();
661 if (piecesCount <= TB::Cardinality
662 && (piecesCount < TB::Cardinality || depth >= TB::ProbeDepth) && pos.rule50_count() == 0
663 && !pos.can_castle(ANY_CASTLING))
666 TB::WDLScore wdl = Tablebases::probe_wdl(pos, &err);
668 // Force check of time on the next occasion
669 if (thisThread == Threads.main())
670 static_cast<MainThread*>(thisThread)->callsCnt = 0;
672 if (err != TB::ProbeState::FAIL)
674 thisThread->tbHits.fetch_add(1, std::memory_order_relaxed);
676 int drawScore = TB::UseRule50 ? 1 : 0;
678 // use the range VALUE_MATE_IN_MAX_PLY to VALUE_TB_WIN_IN_MAX_PLY to score
679 value = wdl < -drawScore ? VALUE_MATED_IN_MAX_PLY + ss->ply + 1
680 : wdl > drawScore ? VALUE_MATE_IN_MAX_PLY - ss->ply - 1
681 : VALUE_DRAW + 2 * wdl * drawScore;
683 Bound b = wdl < -drawScore ? BOUND_UPPER
684 : wdl > drawScore ? BOUND_LOWER
687 if (b == BOUND_EXACT || (b == BOUND_LOWER ? value >= beta : value <= alpha))
689 tte->save(posKey, value_to_tt(value, ss->ply), ss->ttPv, b,
690 std::min(MAX_PLY - 1, depth + 6), MOVE_NONE, VALUE_NONE);
697 if (b == BOUND_LOWER)
698 bestValue = value, alpha = std::max(alpha, bestValue);
706 CapturePieceToHistory& captureHistory = thisThread->captureHistory;
708 // Step 6. Static evaluation of the position
711 // Skip early pruning when in check
712 ss->staticEval = eval = VALUE_NONE;
716 else if (excludedMove)
718 // Providing the hint that this node's accumulator will be used often
719 // brings significant Elo gain (~13 Elo).
720 Eval::NNUE::hint_common_parent_position(pos);
721 eval = ss->staticEval;
725 // Never assume anything about values stored in TT
726 ss->staticEval = eval = tte->eval();
727 if (eval == VALUE_NONE)
728 ss->staticEval = eval = evaluate(pos);
730 Eval::NNUE::hint_common_parent_position(pos);
732 // ttValue can be used as a better position evaluation (~7 Elo)
733 if (ttValue != VALUE_NONE && (tte->bound() & (ttValue > eval ? BOUND_LOWER : BOUND_UPPER)))
738 ss->staticEval = eval = evaluate(pos);
739 // Save static evaluation into the transposition table
740 tte->save(posKey, VALUE_NONE, ss->ttPv, BOUND_NONE, DEPTH_NONE, MOVE_NONE, eval);
743 // Use static evaluation difference to improve quiet move ordering (~4 Elo)
744 if (is_ok((ss - 1)->currentMove) && !(ss - 1)->inCheck && !priorCapture)
746 int bonus = std::clamp(-18 * int((ss - 1)->staticEval + ss->staticEval), -1812, 1812);
747 thisThread->mainHistory[~us][from_to((ss - 1)->currentMove)] << bonus;
750 // Set up the improving flag, which is true if current static evaluation is
751 // bigger than the previous static evaluation at our turn (if we were in
752 // check at our previous move we look at static evaluation at move prior to it
753 // and if we were in check at move prior to it flag is set to true) and is
754 // false otherwise. The improving flag is used in various pruning heuristics.
755 improving = (ss - 2)->staticEval != VALUE_NONE ? ss->staticEval > (ss - 2)->staticEval
756 : (ss - 4)->staticEval != VALUE_NONE ? ss->staticEval > (ss - 4)->staticEval
759 // Step 7. Razoring (~1 Elo)
760 // If eval is really low check with qsearch if it can exceed alpha, if it can't,
761 // return a fail low.
762 // Adjust razor margin according to cutoffCnt. (~1 Elo)
763 if (eval < alpha - 474 - (270 - 174 * ((ss + 1)->cutoffCnt > 3)) * depth * depth)
765 value = qsearch<NonPV>(pos, ss, alpha - 1, alpha);
770 // Step 8. Futility pruning: child node (~40 Elo)
771 // The depth condition is important for mate finding.
772 if (!ss->ttPv && depth < 9
773 && eval - futility_margin(depth, cutNode && !ss->ttHit, improving)
774 - (ss - 1)->statScore / 321
776 && eval >= beta && eval < 29462 // smaller than TB wins
777 && (!ttMove || ttCapture))
780 // Step 9. Null move search with verification search (~35 Elo)
781 if (!PvNode && (ss - 1)->currentMove != MOVE_NULL && (ss - 1)->statScore < 17257 && eval >= beta
782 && eval >= ss->staticEval && ss->staticEval >= beta - 24 * depth + 281 && !excludedMove
783 && pos.non_pawn_material(us) && ss->ply >= thisThread->nmpMinPly
784 && beta > VALUE_TB_LOSS_IN_MAX_PLY)
786 assert(eval - beta >= 0);
788 // Null move dynamic reduction based on depth and eval
789 Depth R = std::min(int(eval - beta) / 152, 6) + depth / 3 + 4;
791 ss->currentMove = MOVE_NULL;
792 ss->continuationHistory = &thisThread->continuationHistory[0][0][NO_PIECE][0];
794 pos.do_null_move(st);
796 Value nullValue = -search<NonPV>(pos, ss + 1, -beta, -beta + 1, depth - R, !cutNode);
798 pos.undo_null_move();
800 // Do not return unproven mate or TB scores
801 if (nullValue >= beta && nullValue < VALUE_TB_WIN_IN_MAX_PLY)
803 if (thisThread->nmpMinPly || depth < 14)
806 assert(!thisThread->nmpMinPly); // Recursive verification is not allowed
808 // Do verification search at high depths, with null move pruning disabled
809 // until ply exceeds nmpMinPly.
810 thisThread->nmpMinPly = ss->ply + 3 * (depth - R) / 4;
812 Value v = search<NonPV>(pos, ss, beta - 1, beta, depth - R, false);
814 thisThread->nmpMinPly = 0;
821 // Step 10. Internal iterative reductions (~9 Elo)
822 // For PV nodes without a ttMove, we decrease depth by 2,
823 // or by 4 if the current position is present in the TT and
824 // the stored depth is greater than or equal to the current depth.
825 // Use qsearch if depth <= 0.
826 if (PvNode && !ttMove)
827 depth -= 2 + 2 * (ss->ttHit && tte->depth() >= depth);
830 return qsearch<PV>(pos, ss, alpha, beta);
832 // For cutNodes without a ttMove, we decrease depth by 2
833 // if current depth >= 8.
834 if (cutNode && depth >= 8 && !ttMove)
837 probCutBeta = beta + 168 - 70 * improving;
839 // Step 11. ProbCut (~10 Elo)
840 // If we have a good enough capture (or queen promotion) and a reduced search returns a value
841 // much above beta, we can (almost) safely prune the previous move.
844 && abs(beta) < VALUE_TB_WIN_IN_MAX_PLY
845 // If value from transposition table is lower than probCutBeta, don't attempt probCut
846 // there and in further interactions with transposition table cutoff depth is set to depth - 3
847 // because probCut search has depth set to depth - 4 but we also do a move before it
848 // So effective depth is equal to depth - 3
849 && !(tte->depth() >= depth - 3 && ttValue != VALUE_NONE && ttValue < probCutBeta))
851 assert(probCutBeta < VALUE_INFINITE);
853 MovePicker mp(pos, ttMove, probCutBeta - ss->staticEval, &captureHistory,
854 thisThread->pawnHistory);
856 while ((move = mp.next_move()) != MOVE_NONE)
857 if (move != excludedMove && pos.legal(move))
859 assert(pos.capture_stage(move));
861 // Prefetch the TT entry for the resulting position
862 prefetch(TT.first_entry(pos.key_after(move)));
864 ss->currentMove = move;
865 ss->continuationHistory =
867 ->continuationHistory[ss->inCheck][true][pos.moved_piece(move)][to_sq(move)];
869 pos.do_move(move, st);
871 // Perform a preliminary qsearch to verify that the move holds
872 value = -qsearch<NonPV>(pos, ss + 1, -probCutBeta, -probCutBeta + 1);
874 // If the qsearch held, perform the regular search
875 if (value >= probCutBeta)
876 value = -search<NonPV>(pos, ss + 1, -probCutBeta, -probCutBeta + 1, depth - 4,
881 if (value >= probCutBeta)
883 // Save ProbCut data into transposition table
884 tte->save(posKey, value_to_tt(value, ss->ply), ss->ttPv, BOUND_LOWER, depth - 3,
885 move, ss->staticEval);
886 return value - (probCutBeta - beta);
890 Eval::NNUE::hint_common_parent_position(pos);
893 moves_loop: // When in check, search starts here
895 // Step 12. A small Probcut idea, when we are in check (~4 Elo)
896 probCutBeta = beta + 416;
897 if (ss->inCheck && !PvNode && ttCapture && (tte->bound() & BOUND_LOWER)
898 && tte->depth() >= depth - 4 && ttValue >= probCutBeta
899 && abs(ttValue) < VALUE_TB_WIN_IN_MAX_PLY && abs(beta) < VALUE_TB_WIN_IN_MAX_PLY)
902 const PieceToHistory* contHist[] = {(ss - 1)->continuationHistory,
903 (ss - 2)->continuationHistory,
904 (ss - 3)->continuationHistory,
905 (ss - 4)->continuationHistory,
907 (ss - 6)->continuationHistory};
910 prevSq != SQ_NONE ? thisThread->counterMoves[pos.piece_on(prevSq)][prevSq] : MOVE_NONE;
912 MovePicker mp(pos, ttMove, depth, &thisThread->mainHistory, &captureHistory, contHist,
913 thisThread->pawnHistory, countermove, ss->killers);
916 moveCountPruning = singularQuietLMR = false;
918 // Indicate PvNodes that will probably fail low if the node was searched
919 // at a depth equal to or greater than the current depth, and the result
920 // of this search was a fail low.
921 bool likelyFailLow = PvNode && ttMove && (tte->bound() & BOUND_UPPER) && tte->depth() >= depth;
923 // Step 13. Loop through all pseudo-legal moves until no moves remain
924 // or a beta cutoff occurs.
925 while ((move = mp.next_move(moveCountPruning)) != MOVE_NONE)
929 if (move == excludedMove)
932 // Check for legality
933 if (!pos.legal(move))
936 // At root obey the "searchmoves" option and skip moves not listed in Root
937 // Move List. In MultiPV mode we also skip PV moves that have been already
938 // searched and those of lower "TB rank" if we are in a TB root position.
940 && !std::count(thisThread->rootMoves.begin() + thisThread->pvIdx,
941 thisThread->rootMoves.begin() + thisThread->pvLast, move))
944 ss->moveCount = ++moveCount;
946 if (rootNode && thisThread == Threads.main() && Time.elapsed() > 3000)
947 sync_cout << "info depth " << depth << " currmove "
948 << UCI::move(move, pos.is_chess960()) << " currmovenumber "
949 << moveCount + thisThread->pvIdx << sync_endl;
951 (ss + 1)->pv = nullptr;
954 capture = pos.capture_stage(move);
955 movedPiece = pos.moved_piece(move);
956 givesCheck = pos.gives_check(move);
958 // Calculate new depth for this move
959 newDepth = depth - 1;
961 Value delta = beta - alpha;
963 Depth r = reduction(improving, depth, moveCount, delta, thisThread->rootDelta);
965 // Step 14. Pruning at shallow depth (~120 Elo).
966 // Depth conditions are important for mate finding.
967 if (!rootNode && pos.non_pawn_material(us) && bestValue > VALUE_TB_LOSS_IN_MAX_PLY)
969 // Skip quiet moves if movecount exceeds our FutilityMoveCount threshold (~8 Elo)
970 if (!moveCountPruning)
971 moveCountPruning = moveCount >= futility_move_count(improving, depth);
973 // Reduced depth of the next LMR search
974 int lmrDepth = newDepth - r;
976 if (capture || givesCheck)
978 // Futility pruning for captures (~2 Elo)
979 if (!givesCheck && lmrDepth < 7 && !ss->inCheck)
981 Piece capturedPiece = pos.piece_on(to_sq(move));
983 ss->staticEval + 239 + 291 * lmrDepth + PieceValue[capturedPiece]
984 + captureHistory[movedPiece][to_sq(move)][type_of(capturedPiece)] / 7;
985 if (futilityEval < alpha)
989 // SEE based pruning for captures and checks (~11 Elo)
990 if (!pos.see_ge(move, Value(-185) * depth))
995 int history = (*contHist[0])[movedPiece][to_sq(move)]
996 + (*contHist[1])[movedPiece][to_sq(move)]
997 + (*contHist[3])[movedPiece][to_sq(move)]
998 + thisThread->pawnHistory[pawn_structure(pos)][movedPiece][to_sq(move)];
1000 // Continuation history based pruning (~2 Elo)
1001 if (lmrDepth < 6 && history < -3645 * depth)
1004 history += 2 * thisThread->mainHistory[us][from_to(move)];
1006 lmrDepth += history / 7836;
1007 lmrDepth = std::max(lmrDepth, -1);
1009 // Futility pruning: parent node (~13 Elo)
1010 if (!ss->inCheck && lmrDepth < 13 && ss->staticEval + 77 + 124 * lmrDepth <= alpha)
1013 lmrDepth = std::max(lmrDepth, 0);
1015 // Prune moves with negative SEE (~4 Elo)
1016 if (!pos.see_ge(move, Value(-26 * lmrDepth * lmrDepth)))
1021 // Step 15. Extensions (~100 Elo)
1022 // We take care to not overdo to avoid search getting stuck.
1023 if (ss->ply < thisThread->rootDepth * 2)
1025 // Singular extension search (~94 Elo). If all moves but one fail low on a
1026 // search of (alpha-s, beta-s), and just one fails high on (alpha, beta),
1027 // then that move is singular and should be extended. To verify this we do
1028 // a reduced search on all the other moves but the ttMove and if the result
1029 // is lower than ttValue minus a margin, then we will extend the ttMove. Note
1030 // that depth margin and singularBeta margin are known for having non-linear
1031 // scaling. Their values are optimized to time controls of 180+1.8 and longer
1032 // so changing them requires tests at this type of time controls.
1033 // Recursive singular search is avoided.
1034 if (!rootNode && move == ttMove && !excludedMove
1035 && depth >= 4 - (thisThread->completedDepth > 24) + 2 * (PvNode && tte->is_pv())
1036 && abs(ttValue) < VALUE_TB_WIN_IN_MAX_PLY && (tte->bound() & BOUND_LOWER)
1037 && tte->depth() >= depth - 3)
1039 Value singularBeta = ttValue - (64 + 57 * (ss->ttPv && !PvNode)) * depth / 64;
1040 Depth singularDepth = (depth - 1) / 2;
1042 ss->excludedMove = move;
1044 search<NonPV>(pos, ss, singularBeta - 1, singularBeta, singularDepth, cutNode);
1045 ss->excludedMove = MOVE_NONE;
1047 if (value < singularBeta)
1050 singularQuietLMR = !ttCapture;
1052 // Avoid search explosion by limiting the number of double extensions
1053 if (!PvNode && value < singularBeta - 18 && ss->doubleExtensions <= 11)
1056 depth += depth < 15;
1060 // Multi-cut pruning
1061 // Our ttMove is assumed to fail high, and now we failed high also on a
1062 // reduced search without the ttMove. So we assume this expected cut-node
1063 // is not singular, that multiple moves fail high, and we can prune the
1064 // whole subtree by returning a softbound.
1065 else if (singularBeta >= beta)
1066 return singularBeta;
1068 // If the eval of ttMove is greater than beta, reduce it (negative extension) (~7 Elo)
1069 else if (ttValue >= beta)
1070 extension = -2 - !PvNode;
1072 // If we are on a cutNode, reduce it based on depth (negative extension) (~1 Elo)
1074 extension = depth < 19 ? -2 : -1;
1076 // If the eval of ttMove is less than value, reduce it (negative extension) (~1 Elo)
1077 else if (ttValue <= value)
1081 // Check extensions (~1 Elo)
1082 else if (givesCheck && depth > 9)
1085 // Quiet ttMove extensions (~1 Elo)
1086 else if (PvNode && move == ttMove && move == ss->killers[0]
1087 && (*contHist[0])[movedPiece][to_sq(move)] >= 4194)
1091 // Add extension to new depth
1092 newDepth += extension;
1093 ss->doubleExtensions = (ss - 1)->doubleExtensions + (extension == 2);
1095 // Speculative prefetch as early as possible
1096 prefetch(TT.first_entry(pos.key_after(move)));
1098 // Update the current move (this must be done after singular extension search)
1099 ss->currentMove = move;
1100 ss->continuationHistory =
1101 &thisThread->continuationHistory[ss->inCheck][capture][movedPiece][to_sq(move)];
1103 // Step 16. Make the move
1104 pos.do_move(move, st, givesCheck);
1106 // Decrease reduction if position is or has been on the PV (~4 Elo)
1107 if (ss->ttPv && !likelyFailLow)
1108 r -= cutNode && tte->depth() >= depth ? 3 : 2;
1110 // Decrease reduction if opponent's move count is high (~1 Elo)
1111 if ((ss - 1)->moveCount > 7)
1114 // Increase reduction for cut nodes (~3 Elo)
1118 // Increase reduction if ttMove is a capture (~3 Elo)
1122 // Decrease reduction for PvNodes (~2 Elo)
1126 // Decrease reduction if a quiet ttMove has been singularly extended (~1 Elo)
1127 if (singularQuietLMR)
1130 // Increase reduction on repetition (~1 Elo)
1131 if (move == (ss - 4)->currentMove && pos.has_repeated())
1134 // Increase reduction if next ply has a lot of fail high (~5 Elo)
1135 if ((ss + 1)->cutoffCnt > 3)
1138 // Decrease reduction for first generated move (ttMove)
1139 else if (move == ttMove)
1142 ss->statScore = 2 * thisThread->mainHistory[us][from_to(move)]
1143 + (*contHist[0])[movedPiece][to_sq(move)]
1144 + (*contHist[1])[movedPiece][to_sq(move)]
1145 + (*contHist[3])[movedPiece][to_sq(move)] - 3848;
1147 // Decrease/increase reduction for moves with a good/bad history (~25 Elo)
1148 r -= ss->statScore / (10216 + 3855 * (depth > 5 && depth < 23));
1150 // Step 17. Late moves reduction / extension (LMR, ~117 Elo)
1151 // We use various heuristics for the sons of a node after the first son has
1152 // been searched. In general, we would like to reduce them, but there are many
1153 // cases where we extend a son if it has good chances to be "interesting".
1154 if (depth >= 2 && moveCount > 1 + (PvNode && ss->ply <= 1)
1155 && (!ss->ttPv || !capture || (cutNode && (ss - 1)->moveCount > 1)))
1157 // In general we want to cap the LMR depth search at newDepth, but when
1158 // reduction is negative, we allow this move a limited search extension
1159 // beyond the first move depth. This may lead to hidden double extensions.
1160 Depth d = std::clamp(newDepth - r, 1, newDepth + 1);
1162 value = -search<NonPV>(pos, ss + 1, -(alpha + 1), -alpha, d, true);
1164 // Do a full-depth search when reduced LMR search fails high
1165 if (value > alpha && d < newDepth)
1167 // Adjust full-depth search based on LMR results - if the result
1168 // was good enough search deeper, if it was bad enough search shallower.
1169 const bool doDeeperSearch = value > (bestValue + 51 + 10 * (newDepth - d));
1170 const bool doEvenDeeperSearch = value > alpha + 700 && ss->doubleExtensions <= 6;
1171 const bool doShallowerSearch = value < bestValue + newDepth;
1173 ss->doubleExtensions = ss->doubleExtensions + doEvenDeeperSearch;
1175 newDepth += doDeeperSearch - doShallowerSearch + doEvenDeeperSearch;
1178 value = -search<NonPV>(pos, ss + 1, -(alpha + 1), -alpha, newDepth, !cutNode);
1180 int bonus = value <= alpha ? -stat_bonus(newDepth)
1181 : value >= beta ? stat_bonus(newDepth)
1184 update_continuation_histories(ss, movedPiece, to_sq(move), bonus);
1188 // Step 18. Full-depth search when LMR is skipped
1189 else if (!PvNode || moveCount > 1)
1191 // Increase reduction for cut nodes without ttMove (~1 Elo)
1192 if (!ttMove && cutNode)
1195 // Note that if expected reduction is high, we reduce search depth by 1 here
1196 value = -search<NonPV>(pos, ss + 1, -(alpha + 1), -alpha, newDepth - (r > 3), !cutNode);
1199 // For PV nodes only, do a full PV search on the first move or after a fail high,
1200 // otherwise let the parent node fail low with value <= alpha and try another move.
1201 if (PvNode && (moveCount == 1 || value > alpha))
1204 (ss + 1)->pv[0] = MOVE_NONE;
1206 value = -search<PV>(pos, ss + 1, -beta, -alpha, newDepth, false);
1209 // Step 19. Undo move
1210 pos.undo_move(move);
1212 assert(value > -VALUE_INFINITE && value < VALUE_INFINITE);
1214 // Step 20. Check for a new best move
1215 // Finished searching the move. If a stop occurred, the return value of
1216 // the search cannot be trusted, and we return immediately without
1217 // updating best move, PV and TT.
1218 if (Threads.stop.load(std::memory_order_relaxed))
1224 *std::find(thisThread->rootMoves.begin(), thisThread->rootMoves.end(), move);
1227 rm.averageScore != -VALUE_INFINITE ? (2 * value + rm.averageScore) / 3 : value;
1229 // PV move or new best move?
1230 if (moveCount == 1 || value > alpha)
1232 rm.score = rm.uciScore = value;
1233 rm.selDepth = thisThread->selDepth;
1234 rm.scoreLowerbound = rm.scoreUpperbound = false;
1238 rm.scoreLowerbound = true;
1241 else if (value <= alpha)
1243 rm.scoreUpperbound = true;
1244 rm.uciScore = alpha;
1249 assert((ss + 1)->pv);
1251 for (Move* m = (ss + 1)->pv; *m != MOVE_NONE; ++m)
1252 rm.pv.push_back(*m);
1254 // We record how often the best move has been changed in each iteration.
1255 // This information is used for time management. In MultiPV mode,
1256 // we must take care to only do this for the first PV line.
1257 if (moveCount > 1 && !thisThread->pvIdx)
1258 ++thisThread->bestMoveChanges;
1261 // All other moves but the PV, are set to the lowest value: this
1262 // is not a problem when sorting because the sort is stable and the
1263 // move position in the list is preserved - just the PV is pushed up.
1264 rm.score = -VALUE_INFINITE;
1267 if (value > bestValue)
1275 if (PvNode && !rootNode) // Update pv even in fail-high case
1276 update_pv(ss->pv, move, (ss + 1)->pv);
1280 ss->cutoffCnt += 1 + !ttMove;
1281 assert(value >= beta); // Fail high
1286 // Reduce other moves if we have found at least one score improvement (~2 Elo)
1287 if (depth > 2 && depth < 12 && beta < 13828 && value > -11369)
1291 alpha = value; // Update alpha! Always alpha < beta
1296 // If the move is worse than some previously searched move,
1297 // remember it, to update its stats later.
1298 if (move != bestMove && moveCount <= 32)
1301 capturesSearched[captureCount++] = move;
1304 quietsSearched[quietCount++] = move;
1308 // Step 21. Check for mate and stalemate
1309 // All legal moves have been searched and if there are no legal moves, it
1310 // must be a mate or a stalemate. If we are in a singular extension search then
1311 // return a fail low score.
1313 assert(moveCount || !ss->inCheck || excludedMove || !MoveList<LEGAL>(pos).size());
1316 bestValue = excludedMove ? alpha : ss->inCheck ? mated_in(ss->ply) : VALUE_DRAW;
1318 // If there is a move that produces search value greater than alpha we update the stats of searched moves
1320 update_all_stats(pos, ss, bestMove, bestValue, beta, prevSq, quietsSearched, quietCount,
1321 capturesSearched, captureCount, depth);
1323 // Bonus for prior countermove that caused the fail low
1324 else if (!priorCapture && prevSq != SQ_NONE)
1326 int bonus = (depth > 6) + (PvNode || cutNode) + (bestValue < alpha - 657)
1327 + ((ss - 1)->moveCount > 10);
1328 update_continuation_histories(ss - 1, pos.piece_on(prevSq), prevSq,
1329 stat_bonus(depth) * bonus);
1330 thisThread->mainHistory[~us][from_to((ss - 1)->currentMove)]
1331 << stat_bonus(depth) * bonus / 2;
1335 bestValue = std::min(bestValue, maxValue);
1337 // If no good move is found and the previous position was ttPv, then the previous
1338 // opponent move is probably good and the new position is added to the search tree. (~7 Elo)
1339 if (bestValue <= alpha)
1340 ss->ttPv = ss->ttPv || ((ss - 1)->ttPv && depth > 3);
1342 // Write gathered information in transposition table
1343 if (!excludedMove && !(rootNode && thisThread->pvIdx))
1344 tte->save(posKey, value_to_tt(bestValue, ss->ply), ss->ttPv,
1345 bestValue >= beta ? BOUND_LOWER
1346 : PvNode && bestMove ? BOUND_EXACT
1348 depth, bestMove, ss->staticEval);
1350 assert(bestValue > -VALUE_INFINITE && bestValue < VALUE_INFINITE);
1356 // Quiescence search function, which is called by the main search
1357 // function with zero depth, or recursively with further decreasing depth per call.
1359 template<NodeType nodeType>
1360 Value qsearch(Position& pos, Stack* ss, Value alpha, Value beta, Depth depth) {
1362 static_assert(nodeType != Root);
1363 constexpr bool PvNode = nodeType == PV;
1365 assert(alpha >= -VALUE_INFINITE && alpha < beta && beta <= VALUE_INFINITE);
1366 assert(PvNode || (alpha == beta - 1));
1369 // Check if we have an upcoming move that draws by repetition, or
1370 // if the opponent had an alternative move earlier to this position.
1371 if (alpha < VALUE_DRAW && pos.has_game_cycle(ss->ply))
1373 alpha = value_draw(pos.this_thread());
1378 Move pv[MAX_PLY + 1];
1380 ASSERT_ALIGNED(&st, Eval::NNUE::CacheLineSize);
1384 Move ttMove, move, bestMove;
1386 Value bestValue, value, ttValue, futilityValue, futilityBase;
1387 bool pvHit, givesCheck, capture;
1389 Color us = pos.side_to_move();
1391 // Step 1. Initialize node
1395 ss->pv[0] = MOVE_NONE;
1398 Thread* thisThread = pos.this_thread();
1399 bestMove = MOVE_NONE;
1400 ss->inCheck = pos.checkers();
1403 // Step 2. Check for an immediate draw or maximum ply reached
1404 if (pos.is_draw(ss->ply) || ss->ply >= MAX_PLY)
1405 return (ss->ply >= MAX_PLY && !ss->inCheck) ? evaluate(pos) : VALUE_DRAW;
1407 assert(0 <= ss->ply && ss->ply < MAX_PLY);
1409 // Decide whether or not to include checks: this fixes also the type of
1410 // TT entry depth that we are going to use. Note that in qsearch we use
1411 // only two types of depth in TT: DEPTH_QS_CHECKS or DEPTH_QS_NO_CHECKS.
1412 ttDepth = ss->inCheck || depth >= DEPTH_QS_CHECKS ? DEPTH_QS_CHECKS : DEPTH_QS_NO_CHECKS;
1414 // Step 3. Transposition table lookup
1416 tte = TT.probe(posKey, ss->ttHit);
1417 ttValue = ss->ttHit ? value_from_tt(tte->value(), ss->ply, pos.rule50_count()) : VALUE_NONE;
1418 ttMove = ss->ttHit ? tte->move() : MOVE_NONE;
1419 pvHit = ss->ttHit && tte->is_pv();
1421 // At non-PV nodes we check for an early TT cutoff
1422 if (!PvNode && tte->depth() >= ttDepth
1423 && ttValue != VALUE_NONE // Only in case of TT access race or if !ttHit
1424 && (tte->bound() & (ttValue >= beta ? BOUND_LOWER : BOUND_UPPER)))
1427 // Step 4. Static evaluation of the position
1429 bestValue = futilityBase = -VALUE_INFINITE;
1434 // Never assume anything about values stored in TT
1435 if ((ss->staticEval = bestValue = tte->eval()) == VALUE_NONE)
1436 ss->staticEval = bestValue = evaluate(pos);
1438 // ttValue can be used as a better position evaluation (~13 Elo)
1439 if (ttValue != VALUE_NONE
1440 && (tte->bound() & (ttValue > bestValue ? BOUND_LOWER : BOUND_UPPER)))
1441 bestValue = ttValue;
1444 // In case of null move search use previous static eval with a different sign
1445 ss->staticEval = bestValue =
1446 (ss - 1)->currentMove != MOVE_NULL ? evaluate(pos) : -(ss - 1)->staticEval;
1448 // Stand pat. Return immediately if static value is at least beta
1449 if (bestValue >= beta)
1452 tte->save(posKey, value_to_tt(bestValue, ss->ply), false, BOUND_LOWER, DEPTH_NONE,
1453 MOVE_NONE, ss->staticEval);
1458 if (bestValue > alpha)
1461 futilityBase = ss->staticEval + 200;
1464 const PieceToHistory* contHist[] = {(ss - 1)->continuationHistory,
1465 (ss - 2)->continuationHistory};
1467 // Initialize a MovePicker object for the current position, and prepare
1468 // to search the moves. Because the depth is <= 0 here, only captures,
1469 // queen promotions, and other checks (only if depth >= DEPTH_QS_CHECKS)
1470 // will be generated.
1471 Square prevSq = is_ok((ss - 1)->currentMove) ? to_sq((ss - 1)->currentMove) : SQ_NONE;
1472 MovePicker mp(pos, ttMove, depth, &thisThread->mainHistory, &thisThread->captureHistory,
1473 contHist, thisThread->pawnHistory, prevSq);
1475 int quietCheckEvasions = 0;
1477 // Step 5. Loop through all pseudo-legal moves until no moves remain
1478 // or a beta cutoff occurs.
1479 while ((move = mp.next_move()) != MOVE_NONE)
1481 assert(is_ok(move));
1483 // Check for legality
1484 if (!pos.legal(move))
1487 givesCheck = pos.gives_check(move);
1488 capture = pos.capture_stage(move);
1493 if (bestValue > VALUE_TB_LOSS_IN_MAX_PLY && pos.non_pawn_material(us))
1495 // Futility pruning and moveCount pruning (~10 Elo)
1496 if (!givesCheck && to_sq(move) != prevSq && futilityBase > VALUE_TB_LOSS_IN_MAX_PLY
1497 && type_of(move) != PROMOTION)
1502 futilityValue = futilityBase + PieceValue[pos.piece_on(to_sq(move))];
1504 // If static eval + value of piece we are going to capture is much lower
1505 // than alpha we can prune this move.
1506 if (futilityValue <= alpha)
1508 bestValue = std::max(bestValue, futilityValue);
1512 // If static eval is much lower than alpha and move is not winning material
1513 // we can prune this move.
1514 if (futilityBase <= alpha && !pos.see_ge(move, VALUE_ZERO + 1))
1516 bestValue = std::max(bestValue, futilityBase);
1520 // If static exchange evaluation is much worse than what is needed to not
1521 // fall below alpha we can prune this move.
1522 if (futilityBase > alpha && !pos.see_ge(move, (alpha - futilityBase) * 4))
1529 // We prune after the second quiet check evasion move, where being 'in check' is
1530 // implicitly checked through the counter, and being a 'quiet move' apart from
1531 // being a tt move is assumed after an increment because captures are pushed ahead.
1532 if (quietCheckEvasions > 1)
1535 // Continuation history based pruning (~3 Elo)
1536 if (!capture && (*contHist[0])[pos.moved_piece(move)][to_sq(move)] < 0
1537 && (*contHist[1])[pos.moved_piece(move)][to_sq(move)] < 0)
1540 // Do not search moves with bad enough SEE values (~5 Elo)
1541 if (!pos.see_ge(move, Value(-90)))
1545 // Speculative prefetch as early as possible
1546 prefetch(TT.first_entry(pos.key_after(move)));
1548 // Update the current move
1549 ss->currentMove = move;
1550 ss->continuationHistory =
1552 ->continuationHistory[ss->inCheck][capture][pos.moved_piece(move)][to_sq(move)];
1554 quietCheckEvasions += !capture && ss->inCheck;
1556 // Step 7. Make and search the move
1557 pos.do_move(move, st, givesCheck);
1558 value = -qsearch<nodeType>(pos, ss + 1, -beta, -alpha, depth - 1);
1559 pos.undo_move(move);
1561 assert(value > -VALUE_INFINITE && value < VALUE_INFINITE);
1563 // Step 8. Check for a new best move
1564 if (value > bestValue)
1572 if (PvNode) // Update pv even in fail-high case
1573 update_pv(ss->pv, move, (ss + 1)->pv);
1575 if (value < beta) // Update alpha here!
1583 // Step 9. Check for mate
1584 // All legal moves have been searched. A special case: if we're in check
1585 // and no legal moves were found, it is checkmate.
1586 if (ss->inCheck && bestValue == -VALUE_INFINITE)
1588 assert(!MoveList<LEGAL>(pos).size());
1590 return mated_in(ss->ply); // Plies to mate from the root
1593 // Save gathered info in transposition table
1594 tte->save(posKey, value_to_tt(bestValue, ss->ply), pvHit,
1595 bestValue >= beta ? BOUND_LOWER : BOUND_UPPER, ttDepth, bestMove, ss->staticEval);
1597 assert(bestValue > -VALUE_INFINITE && bestValue < VALUE_INFINITE);
1603 // Adjusts a mate or TB score from "plies to mate from the root"
1604 // to "plies to mate from the current position". Standard scores are unchanged.
1605 // The function is called before storing a value in the transposition table.
1606 Value value_to_tt(Value v, int ply) {
1608 assert(v != VALUE_NONE);
1610 return v >= VALUE_TB_WIN_IN_MAX_PLY ? v + ply : v <= VALUE_TB_LOSS_IN_MAX_PLY ? v - ply : v;
1614 // Inverse of value_to_tt(): it adjusts a mate or TB score
1615 // from the transposition table (which refers to the plies to mate/be mated from
1616 // current position) to "plies to mate/be mated (TB win/loss) from the root".
1617 // However, to avoid potentially false mate scores related to the 50 moves rule
1618 // and the graph history interaction problem, we return an optimal TB score instead.
1619 Value value_from_tt(Value v, int ply, int r50c) {
1621 if (v == VALUE_NONE)
1624 if (v >= VALUE_TB_WIN_IN_MAX_PLY) // TB win or better
1626 if (v >= VALUE_MATE_IN_MAX_PLY && VALUE_MATE - v > 99 - r50c)
1627 return VALUE_MATE_IN_MAX_PLY - 1; // do not return a potentially false mate score
1632 if (v <= VALUE_TB_LOSS_IN_MAX_PLY) // TB loss or worse
1634 if (v <= VALUE_MATED_IN_MAX_PLY && VALUE_MATE + v > 99 - r50c)
1635 return VALUE_MATED_IN_MAX_PLY + 1; // do not return a potentially false mate score
1644 // Adds current move and appends child pv[]
1645 void update_pv(Move* pv, Move move, const Move* childPv) {
1647 for (*pv++ = move; childPv && *childPv != MOVE_NONE;)
1653 // Updates stats at the end of search() when a bestMove is found
1654 void update_all_stats(const Position& pos,
1660 Move* quietsSearched,
1662 Move* capturesSearched,
1666 Color us = pos.side_to_move();
1667 Thread* thisThread = pos.this_thread();
1668 CapturePieceToHistory& captureHistory = thisThread->captureHistory;
1669 Piece moved_piece = pos.moved_piece(bestMove);
1672 int quietMoveBonus = stat_bonus(depth + 1);
1674 if (!pos.capture_stage(bestMove))
1676 int bestMoveBonus = bestValue > beta + 168 ? quietMoveBonus // larger bonus
1677 : stat_bonus(depth); // smaller bonus
1679 // Increase stats for the best move in case it was a quiet move
1680 update_quiet_stats(pos, ss, bestMove, bestMoveBonus);
1681 thisThread->pawnHistory[pawn_structure(pos)][moved_piece][to_sq(bestMove)]
1684 // Decrease stats for all non-best quiet moves
1685 for (int i = 0; i < quietCount; ++i)
1687 thisThread->pawnHistory[pawn_structure(pos)][pos.moved_piece(quietsSearched[i])]
1688 [to_sq(quietsSearched[i])]
1690 thisThread->mainHistory[us][from_to(quietsSearched[i])] << -bestMoveBonus;
1691 update_continuation_histories(ss, pos.moved_piece(quietsSearched[i]),
1692 to_sq(quietsSearched[i]), -bestMoveBonus);
1697 // Increase stats for the best move in case it was a capture move
1698 captured = type_of(pos.piece_on(to_sq(bestMove)));
1699 captureHistory[moved_piece][to_sq(bestMove)][captured] << quietMoveBonus;
1702 // Extra penalty for a quiet early move that was not a TT move or
1703 // main killer move in previous ply when it gets refuted.
1704 if (prevSq != SQ_NONE
1705 && ((ss - 1)->moveCount == 1 + (ss - 1)->ttHit
1706 || ((ss - 1)->currentMove == (ss - 1)->killers[0]))
1707 && !pos.captured_piece())
1708 update_continuation_histories(ss - 1, pos.piece_on(prevSq), prevSq, -quietMoveBonus);
1710 // Decrease stats for all non-best capture moves
1711 for (int i = 0; i < captureCount; ++i)
1713 moved_piece = pos.moved_piece(capturesSearched[i]);
1714 captured = type_of(pos.piece_on(to_sq(capturesSearched[i])));
1715 captureHistory[moved_piece][to_sq(capturesSearched[i])][captured] << -quietMoveBonus;
1720 // Updates histories of the move pairs formed
1721 // by moves at ply -1, -2, -3, -4, and -6 with current move.
1722 void update_continuation_histories(Stack* ss, Piece pc, Square to, int bonus) {
1724 for (int i : {1, 2, 3, 4, 6})
1726 // Only update the first 2 continuation histories if we are in check
1727 if (ss->inCheck && i > 2)
1729 if (is_ok((ss - i)->currentMove))
1730 (*(ss - i)->continuationHistory)[pc][to] << bonus / (1 + 3 * (i == 3));
1735 // Updates move sorting heuristics
1736 void update_quiet_stats(const Position& pos, Stack* ss, Move move, int bonus) {
1739 if (ss->killers[0] != move)
1741 ss->killers[1] = ss->killers[0];
1742 ss->killers[0] = move;
1745 Color us = pos.side_to_move();
1746 Thread* thisThread = pos.this_thread();
1747 thisThread->mainHistory[us][from_to(move)] << bonus;
1748 update_continuation_histories(ss, pos.moved_piece(move), to_sq(move), bonus);
1750 // Update countermove history
1751 if (is_ok((ss - 1)->currentMove))
1753 Square prevSq = to_sq((ss - 1)->currentMove);
1754 thisThread->counterMoves[pos.piece_on(prevSq)][prevSq] = move;
1758 // When playing with strength handicap, choose the best move among a set of RootMoves
1759 // using a statistical rule dependent on 'level'. Idea by Heinz van Saanen.
1760 Move Skill::pick_best(size_t multiPV) {
1762 const RootMoves& rootMoves = Threads.main()->rootMoves;
1763 static PRNG rng(now()); // PRNG sequence should be non-deterministic
1765 // RootMoves are already sorted by score in descending order
1766 Value topScore = rootMoves[0].score;
1767 int delta = std::min(topScore - rootMoves[multiPV - 1].score, PawnValue);
1768 int maxScore = -VALUE_INFINITE;
1769 double weakness = 120 - 2 * level;
1771 // Choose best move. For each move score we add two terms, both dependent on
1772 // weakness. One is deterministic and bigger for weaker levels, and one is
1773 // random. Then we choose the move with the resulting highest score.
1774 for (size_t i = 0; i < multiPV; ++i)
1776 // This is our magic formula
1777 int push = int((weakness * int(topScore - rootMoves[i].score)
1778 + delta * (rng.rand<unsigned>() % int(weakness)))
1781 if (rootMoves[i].score + push >= maxScore)
1783 maxScore = rootMoves[i].score + push;
1784 best = rootMoves[i].pv[0];
1794 // Used to print debug info and, more importantly,
1795 // to detect when we are out of available time and thus stop the search.
1796 void MainThread::check_time() {
1801 // When using nodes, ensure checking rate is not lower than 0.1% of nodes
1802 callsCnt = Limits.nodes ? std::min(512, int(Limits.nodes / 1024)) : 512;
1804 static TimePoint lastInfoTime = now();
1806 TimePoint elapsed = Time.elapsed();
1807 TimePoint tick = Limits.startTime + elapsed;
1809 if (tick - lastInfoTime >= 1000)
1811 lastInfoTime = tick;
1815 // We should not stop pondering until told so by the GUI
1819 if ((Limits.use_time_management() && (elapsed > Time.maximum() || stopOnPonderhit))
1820 || (Limits.movetime && elapsed >= Limits.movetime)
1821 || (Limits.nodes && Threads.nodes_searched() >= uint64_t(Limits.nodes)))
1822 Threads.stop = true;
1826 // Formats PV information according to the UCI protocol. UCI requires
1827 // that all (if any) unsearched PV lines are sent using a previous search score.
1828 string UCI::pv(const Position& pos, Depth depth) {
1830 std::stringstream ss;
1831 TimePoint elapsed = Time.elapsed() + 1;
1832 const RootMoves& rootMoves = pos.this_thread()->rootMoves;
1833 size_t pvIdx = pos.this_thread()->pvIdx;
1834 size_t multiPV = std::min(size_t(Options["MultiPV"]), rootMoves.size());
1835 uint64_t nodesSearched = Threads.nodes_searched();
1836 uint64_t tbHits = Threads.tb_hits() + (TB::RootInTB ? rootMoves.size() : 0);
1838 for (size_t i = 0; i < multiPV; ++i)
1840 bool updated = rootMoves[i].score != -VALUE_INFINITE;
1842 if (depth == 1 && !updated && i > 0)
1845 Depth d = updated ? depth : std::max(1, depth - 1);
1846 Value v = updated ? rootMoves[i].uciScore : rootMoves[i].previousScore;
1848 if (v == -VALUE_INFINITE)
1851 bool tb = TB::RootInTB && abs(v) < VALUE_MATE_IN_MAX_PLY;
1852 v = tb ? rootMoves[i].tbScore : v;
1854 if (ss.rdbuf()->in_avail()) // Not at first line
1858 << " depth " << d << " seldepth " << rootMoves[i].selDepth << " multipv " << i + 1
1859 << " score " << UCI::value(v);
1861 if (Options["UCI_ShowWDL"])
1862 ss << UCI::wdl(v, pos.game_ply());
1864 if (i == pvIdx && !tb && updated) // tablebase- and previous-scores are exact
1865 ss << (rootMoves[i].scoreLowerbound
1867 : (rootMoves[i].scoreUpperbound ? " upperbound" : ""));
1869 ss << " nodes " << nodesSearched << " nps " << nodesSearched * 1000 / elapsed
1870 << " hashfull " << TT.hashfull() << " tbhits " << tbHits << " time " << elapsed << " pv";
1872 for (Move m : rootMoves[i].pv)
1873 ss << " " << UCI::move(m, pos.is_chess960());
1880 // Called in case we have no ponder move
1881 // before exiting the search, for instance, in case we stop the search during a
1882 // fail high at root. We try hard to have a ponder move to return to the GUI,
1883 // otherwise in case of 'ponder on' we have nothing to think about.
1884 bool RootMove::extract_ponder_from_tt(Position& pos) {
1887 ASSERT_ALIGNED(&st, Eval::NNUE::CacheLineSize);
1891 assert(pv.size() == 1);
1893 if (pv[0] == MOVE_NONE)
1896 pos.do_move(pv[0], st);
1897 TTEntry* tte = TT.probe(pos.key(), ttHit);
1901 Move m = tte->move(); // Local copy to be SMP safe
1902 if (MoveList<LEGAL>(pos).contains(m))
1906 pos.undo_move(pv[0]);
1907 return pv.size() > 1;
1910 void Tablebases::rank_root_moves(Position& pos, Search::RootMoves& rootMoves) {
1913 UseRule50 = bool(Options["Syzygy50MoveRule"]);
1914 ProbeDepth = int(Options["SyzygyProbeDepth"]);
1915 Cardinality = int(Options["SyzygyProbeLimit"]);
1916 bool dtz_available = true;
1918 // Tables with fewer pieces than SyzygyProbeLimit are searched with
1919 // ProbeDepth == DEPTH_ZERO
1920 if (Cardinality > MaxCardinality)
1922 Cardinality = MaxCardinality;
1926 if (Cardinality >= popcount(pos.pieces()) && !pos.can_castle(ANY_CASTLING))
1928 // Rank moves using DTZ tables
1929 RootInTB = root_probe(pos, rootMoves);
1933 // DTZ tables are missing; try to rank moves using WDL tables
1934 dtz_available = false;
1935 RootInTB = root_probe_wdl(pos, rootMoves);
1941 // Sort moves according to TB rank
1942 std::stable_sort(rootMoves.begin(), rootMoves.end(),
1943 [](const RootMove& a, const RootMove& b) { return a.tbRank > b.tbRank; });
1945 // Probe during search only if DTZ is not available and we are winning
1946 if (dtz_available || rootMoves[0].tbScore <= VALUE_DRAW)
1951 // Clean up if root_probe() and root_probe_wdl() have failed
1952 for (auto& m : rootMoves)
1957 } // namespace Stockfish