2 Stockfish, a UCI chess playing engine derived from Glaurung 2.1
3 Copyright (C) 2004-2021 The Stockfish developers (see AUTHORS file)
5 Stockfish is free software: you can redistribute it and/or modify
6 it under the terms of the GNU General Public License as published by
7 the Free Software Foundation, either version 3 of the License, or
8 (at your option) any later version.
10 Stockfish is distributed in the hope that it will be useful,
11 but WITHOUT ANY WARRANTY; without even the implied warranty of
12 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
13 GNU General Public License for more details.
15 You should have received a copy of the GNU General Public License
16 along with this program. If not, see <http://www.gnu.org/licenses/>.
22 #include <cstring> // For std::memset
36 #include "syzygy/tbprobe.h"
45 namespace Tablebases {
53 namespace TB = Tablebases;
57 using namespace Search;
61 // Different node types, used as a template parameter
62 enum NodeType { NonPV, PV };
64 constexpr uint64_t TtHitAverageWindow = 4096;
65 constexpr uint64_t TtHitAverageResolution = 1024;
68 Value futility_margin(Depth d, bool improving) {
69 return Value(214 * (d - improving));
72 // Reductions lookup table, initialized at startup
73 int Reductions[MAX_MOVES]; // [depth or moveNumber]
75 Depth reduction(bool i, Depth d, int mn) {
76 int r = Reductions[d] * Reductions[mn];
77 return (r + 534) / 1024 + (!i && r > 904);
80 constexpr int futility_move_count(bool improving, Depth depth) {
81 return (3 + depth * depth) / (2 - improving);
84 // History and stats update bonus, based on depth
85 int stat_bonus(Depth d) {
86 return d > 14 ? 73 : 6 * d * d + 229 * d - 215;
89 // Add a small random component to draw evaluations to avoid 3-fold blindness
90 Value value_draw(Thread* thisThread) {
91 return VALUE_DRAW + Value(2 * (thisThread->nodes & 1) - 1);
94 // Skill structure is used to implement strength limit
96 explicit Skill(int l) : level(l) {}
97 bool enabled() const { return level < 20; }
98 bool time_to_pick(Depth depth) const { return depth == 1 + level; }
99 Move pick_best(size_t multiPV);
102 Move best = MOVE_NONE;
105 template <NodeType NT>
106 Value search(Position& pos, Stack* ss, Value alpha, Value beta, Depth depth, bool cutNode);
108 template <NodeType NT>
109 Value qsearch(Position& pos, Stack* ss, Value alpha, Value beta, Depth depth = 0);
111 Value value_to_tt(Value v, int ply);
112 Value value_from_tt(Value v, int ply, int r50c);
113 void update_pv(Move* pv, Move move, Move* childPv);
114 void update_continuation_histories(Stack* ss, Piece pc, Square to, int bonus);
115 void update_quiet_stats(const Position& pos, Stack* ss, Move move, int bonus, int depth);
116 void update_all_stats(const Position& pos, Stack* ss, Move bestMove, Value bestValue, Value beta, Square prevSq,
117 Move* quietsSearched, int quietCount, Move* capturesSearched, int captureCount, Depth depth);
119 // perft() is our utility to verify move generation. All the leaf nodes up
120 // to the given depth are generated and counted, and the sum is returned.
122 uint64_t perft(Position& pos, Depth depth) {
125 ASSERT_ALIGNED(&st, Eval::NNUE::CacheLineSize);
127 uint64_t cnt, nodes = 0;
128 const bool leaf = (depth == 2);
130 for (const auto& m : MoveList<LEGAL>(pos))
132 if (Root && depth <= 1)
137 cnt = leaf ? MoveList<LEGAL>(pos).size() : perft<false>(pos, depth - 1);
142 sync_cout << UCI::move(m, pos.is_chess960()) << ": " << cnt << sync_endl;
150 /// Search::init() is called at startup to initialize various lookup tables
152 void Search::init() {
154 for (int i = 1; i < MAX_MOVES; ++i)
155 Reductions[i] = int((21.3 + 2 * std::log(Threads.size())) * std::log(i + 0.25 * std::log(i)));
159 /// Search::clear() resets search state to its initial value
161 void Search::clear() {
163 Threads.main()->wait_for_search_finished();
165 Time.availableNodes = 0;
168 Tablebases::init(Options["SyzygyPath"]); // Free mapped files
172 /// MainThread::search() is started when the program receives the UCI 'go'
173 /// command. It searches from the root position and outputs the "bestmove".
175 void MainThread::search() {
179 nodes = perft<true>(rootPos, Limits.perft);
180 sync_cout << "\nNodes searched: " << nodes << "\n" << sync_endl;
184 Color us = rootPos.side_to_move();
185 Time.init(Limits, us, rootPos.game_ply());
188 Eval::NNUE::verify();
190 if (rootMoves.empty())
192 rootMoves.emplace_back(MOVE_NONE);
193 sync_cout << "info depth 0 score "
194 << UCI::value(rootPos.checkers() ? -VALUE_MATE : VALUE_DRAW)
199 Threads.start_searching(); // start non-main threads
200 Thread::search(); // main thread start searching
203 // When we reach the maximum depth, we can arrive here without a raise of
204 // Threads.stop. However, if we are pondering or in an infinite search,
205 // the UCI protocol states that we shouldn't print the best move before the
206 // GUI sends a "stop" or "ponderhit" command. We therefore simply wait here
207 // until the GUI sends one of those commands.
209 while (!Threads.stop && (ponder || Limits.infinite))
210 {} // Busy wait for a stop or a ponder reset
212 // Stop the threads if not already stopped (also raise the stop if
213 // "ponderhit" just reset Threads.ponder).
216 // Wait until all threads have finished
217 Threads.wait_for_search_finished();
219 // When playing in 'nodes as time' mode, subtract the searched nodes from
220 // the available ones before exiting.
222 Time.availableNodes += Limits.inc[us] - Threads.nodes_searched();
224 Thread* bestThread = this;
226 if ( int(Options["MultiPV"]) == 1
228 && !(Skill(Options["Skill Level"]).enabled() || int(Options["UCI_LimitStrength"]))
229 && rootMoves[0].pv[0] != MOVE_NONE)
230 bestThread = Threads.get_best_thread();
232 bestPreviousScore = bestThread->rootMoves[0].score;
234 // Send again PV info if we have a new best thread
235 if (bestThread != this)
236 sync_cout << UCI::pv(bestThread->rootPos, bestThread->completedDepth, -VALUE_INFINITE, VALUE_INFINITE) << sync_endl;
238 sync_cout << "bestmove " << UCI::move(bestThread->rootMoves[0].pv[0], rootPos.is_chess960());
240 if (bestThread->rootMoves[0].pv.size() > 1 || bestThread->rootMoves[0].extract_ponder_from_tt(rootPos))
241 std::cout << " ponder " << UCI::move(bestThread->rootMoves[0].pv[1], rootPos.is_chess960());
243 std::cout << sync_endl;
247 /// Thread::search() is the main iterative deepening loop. It calls search()
248 /// repeatedly with increasing depth until the allocated thinking time has been
249 /// consumed, the user stops the search, or the maximum search depth is reached.
251 void Thread::search() {
253 // To allow access to (ss-7) up to (ss+2), the stack must be oversized.
254 // The former is needed to allow update_continuation_histories(ss-1, ...),
255 // which accesses its argument at ss-6, also near the root.
256 // The latter is needed for statScores and killer initialization.
257 Stack stack[MAX_PLY+10], *ss = stack+7;
259 Value bestValue, alpha, beta, delta;
260 Move lastBestMove = MOVE_NONE;
261 Depth lastBestMoveDepth = 0;
262 MainThread* mainThread = (this == Threads.main() ? Threads.main() : nullptr);
263 double timeReduction = 1, totBestMoveChanges = 0;
264 Color us = rootPos.side_to_move();
267 std::memset(ss-7, 0, 10 * sizeof(Stack));
268 for (int i = 7; i > 0; i--)
269 (ss-i)->continuationHistory = &this->continuationHistory[0][0][NO_PIECE][0]; // Use as a sentinel
273 bestValue = delta = alpha = -VALUE_INFINITE;
274 beta = VALUE_INFINITE;
278 if (mainThread->bestPreviousScore == VALUE_INFINITE)
279 for (int i = 0; i < 4; ++i)
280 mainThread->iterValue[i] = VALUE_ZERO;
282 for (int i = 0; i < 4; ++i)
283 mainThread->iterValue[i] = mainThread->bestPreviousScore;
286 std::copy(&lowPlyHistory[2][0], &lowPlyHistory.back().back() + 1, &lowPlyHistory[0][0]);
287 std::fill(&lowPlyHistory[MAX_LPH - 2][0], &lowPlyHistory.back().back() + 1, 0);
289 size_t multiPV = size_t(Options["MultiPV"]);
291 // Pick integer skill levels, but non-deterministically round up or down
292 // such that the average integer skill corresponds to the input floating point one.
293 // UCI_Elo is converted to a suitable fractional skill level, using anchoring
294 // to CCRL Elo (goldfish 1.13 = 2000) and a fit through Ordo derived Elo
295 // for match (TC 60+0.6) results spanning a wide range of k values.
297 double floatLevel = Options["UCI_LimitStrength"] ?
298 std::clamp(std::pow((Options["UCI_Elo"] - 1346.6) / 143.4, 1 / 0.806), 0.0, 20.0) :
299 double(Options["Skill Level"]);
300 int intLevel = int(floatLevel) +
301 ((floatLevel - int(floatLevel)) * 1024 > rng.rand<unsigned>() % 1024 ? 1 : 0);
302 Skill skill(intLevel);
304 // When playing with strength handicap enable MultiPV search that we will
305 // use behind the scenes to retrieve a set of possible moves.
307 multiPV = std::max(multiPV, (size_t)4);
309 multiPV = std::min(multiPV, rootMoves.size());
310 ttHitAverage = TtHitAverageWindow * TtHitAverageResolution / 2;
312 int ct = int(Options["Contempt"]) * PawnValueEg / 100; // From centipawns
314 // In analysis mode, adjust contempt in accordance with user preference
315 if (Limits.infinite || Options["UCI_AnalyseMode"])
316 ct = Options["Analysis Contempt"] == "Off" ? 0
317 : Options["Analysis Contempt"] == "Both" ? ct
318 : Options["Analysis Contempt"] == "White" && us == BLACK ? -ct
319 : Options["Analysis Contempt"] == "Black" && us == WHITE ? -ct
322 // Evaluation score is from the white point of view
323 contempt = (us == WHITE ? make_score(ct, ct / 2)
324 : -make_score(ct, ct / 2));
326 int searchAgainCounter = 0;
328 // Iterative deepening loop until requested to stop or the target depth is reached
329 while ( ++rootDepth < MAX_PLY
331 && !(Limits.depth && mainThread && rootDepth > Limits.depth))
333 // Age out PV variability metric
335 totBestMoveChanges /= 2;
337 // Save the last iteration's scores before first PV line is searched and
338 // all the move scores except the (new) PV are set to -VALUE_INFINITE.
339 for (RootMove& rm : rootMoves)
340 rm.previousScore = rm.score;
345 if (!Threads.increaseDepth)
346 searchAgainCounter++;
348 // MultiPV loop. We perform a full root search for each PV line
349 for (pvIdx = 0; pvIdx < multiPV && !Threads.stop; ++pvIdx)
354 for (pvLast++; pvLast < rootMoves.size(); pvLast++)
355 if (rootMoves[pvLast].tbRank != rootMoves[pvFirst].tbRank)
359 // Reset UCI info selDepth for each depth and each PV line
362 // Reset aspiration window starting size
365 Value prev = rootMoves[pvIdx].previousScore;
367 alpha = std::max(prev - delta,-VALUE_INFINITE);
368 beta = std::min(prev + delta, VALUE_INFINITE);
370 // Adjust contempt based on root move's previousScore (dynamic contempt)
371 int dct = ct + (113 - ct / 2) * prev / (abs(prev) + 147);
373 contempt = (us == WHITE ? make_score(dct, dct / 2)
374 : -make_score(dct, dct / 2));
377 // Start with a small aspiration window and, in the case of a fail
378 // high/low, re-search with a bigger window until we don't fail
380 int failedHighCnt = 0;
383 Depth adjustedDepth = std::max(1, rootDepth - failedHighCnt - searchAgainCounter);
384 bestValue = Stockfish::search<PV>(rootPos, ss, alpha, beta, adjustedDepth, false);
386 // Bring the best move to the front. It is critical that sorting
387 // is done with a stable algorithm because all the values but the
388 // first and eventually the new best one are set to -VALUE_INFINITE
389 // and we want to keep the same order for all the moves except the
390 // new PV that goes to the front. Note that in case of MultiPV
391 // search the already searched PV lines are preserved.
392 std::stable_sort(rootMoves.begin() + pvIdx, rootMoves.begin() + pvLast);
394 // If search has been stopped, we break immediately. Sorting is
395 // safe because RootMoves is still valid, although it refers to
396 // the previous iteration.
400 // When failing high/low give some update (without cluttering
401 // the UI) before a re-search.
404 && (bestValue <= alpha || bestValue >= beta)
405 && Time.elapsed() > 3000)
406 sync_cout << UCI::pv(rootPos, rootDepth, alpha, beta) << sync_endl;
408 // In case of failing low/high increase aspiration window and
409 // re-search, otherwise exit the loop.
410 if (bestValue <= alpha)
412 beta = (alpha + beta) / 2;
413 alpha = std::max(bestValue - delta, -VALUE_INFINITE);
417 mainThread->stopOnPonderhit = false;
419 else if (bestValue >= beta)
421 beta = std::min(bestValue + delta, VALUE_INFINITE);
427 delta += delta / 4 + 5;
429 assert(alpha >= -VALUE_INFINITE && beta <= VALUE_INFINITE);
432 // Sort the PV lines searched so far and update the GUI
433 std::stable_sort(rootMoves.begin() + pvFirst, rootMoves.begin() + pvIdx + 1);
436 && (Threads.stop || pvIdx + 1 == multiPV || Time.elapsed() > 3000))
437 sync_cout << UCI::pv(rootPos, rootDepth, alpha, beta) << sync_endl;
441 completedDepth = rootDepth;
443 if (rootMoves[0].pv[0] != lastBestMove) {
444 lastBestMove = rootMoves[0].pv[0];
445 lastBestMoveDepth = rootDepth;
448 // Have we found a "mate in x"?
450 && bestValue >= VALUE_MATE_IN_MAX_PLY
451 && VALUE_MATE - bestValue <= 2 * Limits.mate)
457 // If skill level is enabled and time is up, pick a sub-optimal best move
458 if (skill.enabled() && skill.time_to_pick(rootDepth))
459 skill.pick_best(multiPV);
461 // Do we have time for the next iteration? Can we stop searching now?
462 if ( Limits.use_time_management()
464 && !mainThread->stopOnPonderhit)
466 double fallingEval = (318 + 6 * (mainThread->bestPreviousScore - bestValue)
467 + 6 * (mainThread->iterValue[iterIdx] - bestValue)) / 825.0;
468 fallingEval = std::clamp(fallingEval, 0.5, 1.5);
470 // If the bestMove is stable over several iterations, reduce time accordingly
471 timeReduction = lastBestMoveDepth + 9 < completedDepth ? 1.92 : 0.95;
472 double reduction = (1.47 + mainThread->previousTimeReduction) / (2.32 * timeReduction);
474 // Use part of the gained time from a previous stable move for the current move
475 for (Thread* th : Threads)
477 totBestMoveChanges += th->bestMoveChanges;
478 th->bestMoveChanges = 0;
480 double bestMoveInstability = 1 + 2 * totBestMoveChanges / Threads.size();
482 double totalTime = Time.optimum() * fallingEval * reduction * bestMoveInstability;
484 // Cap used time in case of a single legal move for a better viewer experience in tournaments
485 // yielding correct scores and sufficiently fast moves.
486 if (rootMoves.size() == 1)
487 totalTime = std::min(500.0, totalTime);
489 // Stop the search if we have exceeded the totalTime
490 if (Time.elapsed() > totalTime)
492 // If we are allowed to ponder do not stop the search now but
493 // keep pondering until the GUI sends "ponderhit" or "stop".
494 if (mainThread->ponder)
495 mainThread->stopOnPonderhit = true;
499 else if ( Threads.increaseDepth
500 && !mainThread->ponder
501 && Time.elapsed() > totalTime * 0.58)
502 Threads.increaseDepth = false;
504 Threads.increaseDepth = true;
507 mainThread->iterValue[iterIdx] = bestValue;
508 iterIdx = (iterIdx + 1) & 3;
514 mainThread->previousTimeReduction = timeReduction;
516 // If skill level is enabled, swap best PV line with the sub-optimal one
518 std::swap(rootMoves[0], *std::find(rootMoves.begin(), rootMoves.end(),
519 skill.best ? skill.best : skill.pick_best(multiPV)));
525 // search<>() is the main search function for both PV and non-PV nodes
527 template <NodeType NT>
528 Value search(Position& pos, Stack* ss, Value alpha, Value beta, Depth depth, bool cutNode) {
530 constexpr bool PvNode = NT == PV;
531 const bool rootNode = PvNode && ss->ply == 0;
532 const Depth maxNextDepth = rootNode ? depth : depth + 1;
534 // Check if we have an upcoming move which draws by repetition, or
535 // if the opponent had an alternative move earlier to this position.
536 if ( pos.rule50_count() >= 3
537 && alpha < VALUE_DRAW
539 && pos.has_game_cycle(ss->ply))
541 alpha = value_draw(pos.this_thread());
546 // Dive into quiescence search when the depth reaches zero
548 return qsearch<NT>(pos, ss, alpha, beta);
550 assert(-VALUE_INFINITE <= alpha && alpha < beta && beta <= VALUE_INFINITE);
551 assert(PvNode || (alpha == beta - 1));
552 assert(0 < depth && depth < MAX_PLY);
553 assert(!(PvNode && cutNode));
555 Move pv[MAX_PLY+1], capturesSearched[32], quietsSearched[64];
557 ASSERT_ALIGNED(&st, Eval::NNUE::CacheLineSize);
561 Move ttMove, move, excludedMove, bestMove;
562 Depth extension, newDepth;
563 Value bestValue, value, ttValue, eval, maxValue, probCutBeta;
564 bool formerPv, givesCheck, improving, didLMR, priorCapture;
565 bool captureOrPromotion, doFullDepthSearch, moveCountPruning,
566 ttCapture, singularQuietLMR;
568 int moveCount, captureCount, quietCount;
570 // Step 1. Initialize node
571 Thread* thisThread = pos.this_thread();
572 ss->inCheck = pos.checkers();
573 priorCapture = pos.captured_piece();
574 Color us = pos.side_to_move();
575 moveCount = captureCount = quietCount = ss->moveCount = 0;
576 bestValue = -VALUE_INFINITE;
577 maxValue = VALUE_INFINITE;
579 // Check for the available remaining time
580 if (thisThread == Threads.main())
581 static_cast<MainThread*>(thisThread)->check_time();
583 // Used to send selDepth info to GUI (selDepth counts from 1, ply from 0)
584 if (PvNode && thisThread->selDepth < ss->ply + 1)
585 thisThread->selDepth = ss->ply + 1;
589 // Step 2. Check for aborted search and immediate draw
590 if ( Threads.stop.load(std::memory_order_relaxed)
591 || pos.is_draw(ss->ply)
592 || ss->ply >= MAX_PLY)
593 return (ss->ply >= MAX_PLY && !ss->inCheck) ? evaluate(pos)
594 : value_draw(pos.this_thread());
596 // Step 3. Mate distance pruning. Even if we mate at the next move our score
597 // would be at best mate_in(ss->ply+1), but if alpha is already bigger because
598 // a shorter mate was found upward in the tree then there is no need to search
599 // because we will never beat the current alpha. Same logic but with reversed
600 // signs applies also in the opposite condition of being mated instead of giving
601 // mate. In this case return a fail-high score.
602 alpha = std::max(mated_in(ss->ply), alpha);
603 beta = std::min(mate_in(ss->ply+1), beta);
608 assert(0 <= ss->ply && ss->ply < MAX_PLY);
610 (ss+1)->ply = ss->ply + 1;
611 (ss+1)->ttPv = false;
612 (ss+1)->excludedMove = bestMove = MOVE_NONE;
613 (ss+2)->killers[0] = (ss+2)->killers[1] = MOVE_NONE;
614 Square prevSq = to_sq((ss-1)->currentMove);
616 // Initialize statScore to zero for the grandchildren of the current position.
617 // So statScore is shared between all grandchildren and only the first grandchild
618 // starts with statScore = 0. Later grandchildren start with the last calculated
619 // statScore of the previous grandchild. This influences the reduction rules in
620 // LMR which are based on the statScore of parent position.
622 (ss+2)->statScore = 0;
624 // Step 4. Transposition table lookup. We don't want the score of a partial
625 // search to overwrite a previous full search TT value, so we use a different
626 // position key in case of an excluded move.
627 excludedMove = ss->excludedMove;
628 posKey = excludedMove == MOVE_NONE ? pos.key() : pos.key() ^ make_key(excludedMove);
629 tte = TT.probe(posKey, ss->ttHit);
630 ttValue = ss->ttHit ? value_from_tt(tte->value(), ss->ply, pos.rule50_count()) : VALUE_NONE;
631 ttMove = rootNode ? thisThread->rootMoves[thisThread->pvIdx].pv[0]
632 : ss->ttHit ? tte->move() : MOVE_NONE;
634 ss->ttPv = PvNode || (ss->ttHit && tte->is_pv());
635 formerPv = ss->ttPv && !PvNode;
637 // Update low ply history for previous move if we are near root and position is or has been in PV
640 && ss->ply - 1 < MAX_LPH
642 && is_ok((ss-1)->currentMove))
643 thisThread->lowPlyHistory[ss->ply - 1][from_to((ss-1)->currentMove)] << stat_bonus(depth - 5);
645 // thisThread->ttHitAverage can be used to approximate the running average of ttHit
646 thisThread->ttHitAverage = (TtHitAverageWindow - 1) * thisThread->ttHitAverage / TtHitAverageWindow
647 + TtHitAverageResolution * ss->ttHit;
649 // At non-PV nodes we check for an early TT cutoff
652 && tte->depth() >= depth
653 && ttValue != VALUE_NONE // Possible in case of TT access race
654 && (ttValue >= beta ? (tte->bound() & BOUND_LOWER)
655 : (tte->bound() & BOUND_UPPER)))
657 // If ttMove is quiet, update move sorting heuristics on TT hit
662 // Bonus for a quiet ttMove that fails high
663 if (!pos.capture_or_promotion(ttMove))
664 update_quiet_stats(pos, ss, ttMove, stat_bonus(depth), depth);
666 // Extra penalty for early quiet moves of the previous ply
667 if ((ss-1)->moveCount <= 2 && !priorCapture)
668 update_continuation_histories(ss-1, pos.piece_on(prevSq), prevSq, -stat_bonus(depth + 1));
670 // Penalty for a quiet ttMove that fails low
671 else if (!pos.capture_or_promotion(ttMove))
673 int penalty = -stat_bonus(depth);
674 thisThread->mainHistory[us][from_to(ttMove)] << penalty;
675 update_continuation_histories(ss, pos.moved_piece(ttMove), to_sq(ttMove), penalty);
679 // Partial workaround for the graph history interaction problem
680 // For high rule50 counts don't produce transposition table cutoffs.
681 if (pos.rule50_count() < 90)
685 // Step 5. Tablebases probe
686 if (!rootNode && TB::Cardinality)
688 int piecesCount = pos.count<ALL_PIECES>();
690 if ( piecesCount <= TB::Cardinality
691 && (piecesCount < TB::Cardinality || depth >= TB::ProbeDepth)
692 && pos.rule50_count() == 0
693 && !pos.can_castle(ANY_CASTLING))
696 TB::WDLScore wdl = Tablebases::probe_wdl(pos, &err);
698 // Force check of time on the next occasion
699 if (thisThread == Threads.main())
700 static_cast<MainThread*>(thisThread)->callsCnt = 0;
702 if (err != TB::ProbeState::FAIL)
704 thisThread->tbHits.fetch_add(1, std::memory_order_relaxed);
706 int drawScore = TB::UseRule50 ? 1 : 0;
708 // use the range VALUE_MATE_IN_MAX_PLY to VALUE_TB_WIN_IN_MAX_PLY to score
709 value = wdl < -drawScore ? VALUE_MATED_IN_MAX_PLY + ss->ply + 1
710 : wdl > drawScore ? VALUE_MATE_IN_MAX_PLY - ss->ply - 1
711 : VALUE_DRAW + 2 * wdl * drawScore;
713 Bound b = wdl < -drawScore ? BOUND_UPPER
714 : wdl > drawScore ? BOUND_LOWER : BOUND_EXACT;
716 if ( b == BOUND_EXACT
717 || (b == BOUND_LOWER ? value >= beta : value <= alpha))
719 tte->save(posKey, value_to_tt(value, ss->ply), ss->ttPv, b,
720 std::min(MAX_PLY - 1, depth + 6),
721 MOVE_NONE, VALUE_NONE);
728 if (b == BOUND_LOWER)
729 bestValue = value, alpha = std::max(alpha, bestValue);
737 CapturePieceToHistory& captureHistory = thisThread->captureHistory;
739 // Step 6. Static evaluation of the position
742 // Skip early pruning when in check
743 ss->staticEval = eval = VALUE_NONE;
749 // Never assume anything about values stored in TT
750 ss->staticEval = eval = tte->eval();
751 if (eval == VALUE_NONE)
752 ss->staticEval = eval = evaluate(pos);
754 // Randomize draw evaluation
755 if (eval == VALUE_DRAW)
756 eval = value_draw(thisThread);
758 // Can ttValue be used as a better position evaluation?
759 if ( ttValue != VALUE_NONE
760 && (tte->bound() & (ttValue > eval ? BOUND_LOWER : BOUND_UPPER)))
765 // In case of null move search use previous static eval with a different sign
766 // and addition of two tempos
767 if ((ss-1)->currentMove != MOVE_NULL)
768 ss->staticEval = eval = evaluate(pos);
770 ss->staticEval = eval = -(ss-1)->staticEval;
772 // Save static evaluation into transposition table
773 tte->save(posKey, VALUE_NONE, ss->ttPv, BOUND_NONE, DEPTH_NONE, MOVE_NONE, eval);
776 // Use static evaluation difference to improve quiet move ordering
777 if (is_ok((ss-1)->currentMove) && !(ss-1)->inCheck && !priorCapture)
779 int bonus = std::clamp(-depth * 4 * int((ss-1)->staticEval + ss->staticEval), -1000, 1000);
780 thisThread->mainHistory[~us][from_to((ss-1)->currentMove)] << bonus;
783 // Set up improving flag that is used in various pruning heuristics
784 // We define position as improving if static evaluation of position is better
785 // Than the previous static evaluation at our turn
786 // In case of us being in check at our previous move we look at move prior to it
787 improving = (ss-2)->staticEval == VALUE_NONE
788 ? ss->staticEval > (ss-4)->staticEval || (ss-4)->staticEval == VALUE_NONE
789 : ss->staticEval > (ss-2)->staticEval;
791 // Step 7. Futility pruning: child node (~50 Elo)
794 && eval - futility_margin(depth, improving) >= beta
795 && eval < VALUE_KNOWN_WIN) // Do not return unproven wins
798 // Step 8. Null move search with verification search (~40 Elo)
800 && (ss-1)->currentMove != MOVE_NULL
801 && (ss-1)->statScore < 23767
803 && eval >= ss->staticEval
804 && ss->staticEval >= beta - 20 * depth - 22 * improving + 168 * ss->ttPv + 159
806 && pos.non_pawn_material(us)
807 && (ss->ply >= thisThread->nmpMinPly || us != thisThread->nmpColor))
809 assert(eval - beta >= 0);
811 // Null move dynamic reduction based on depth and value
812 Depth R = (1090 + 81 * depth) / 256 + std::min(int(eval - beta) / 205, 3);
814 ss->currentMove = MOVE_NULL;
815 ss->continuationHistory = &thisThread->continuationHistory[0][0][NO_PIECE][0];
817 pos.do_null_move(st);
819 Value nullValue = -search<NonPV>(pos, ss+1, -beta, -beta+1, depth-R, !cutNode);
821 pos.undo_null_move();
823 if (nullValue >= beta)
825 // Do not return unproven mate or TB scores
826 if (nullValue >= VALUE_TB_WIN_IN_MAX_PLY)
829 if (thisThread->nmpMinPly || (abs(beta) < VALUE_KNOWN_WIN && depth < 14))
832 assert(!thisThread->nmpMinPly); // Recursive verification is not allowed
834 // Do verification search at high depths, with null move pruning disabled
835 // for us, until ply exceeds nmpMinPly.
836 thisThread->nmpMinPly = ss->ply + 3 * (depth-R) / 4;
837 thisThread->nmpColor = us;
839 Value v = search<NonPV>(pos, ss, beta-1, beta, depth-R, false);
841 thisThread->nmpMinPly = 0;
848 probCutBeta = beta + 209 - 44 * improving;
850 // Step 9. ProbCut (~4 Elo)
851 // If we have a good enough capture and a reduced search returns a value
852 // much above beta, we can (almost) safely prune the previous move.
855 && abs(beta) < VALUE_TB_WIN_IN_MAX_PLY
856 // if value from transposition table is lower than probCutBeta, don't attempt probCut
857 // there and in further interactions with transposition table cutoff depth is set to depth - 3
858 // because probCut search has depth set to depth - 4 but we also do a move before it
859 // so effective depth is equal to depth - 3
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);
868 int probCutCount = 0;
869 bool ttPv = ss->ttPv;
872 while ( (move = mp.next_move()) != MOVE_NONE
873 && probCutCount < 2 + 2 * cutNode)
874 if (move != excludedMove && pos.legal(move))
876 assert(pos.capture_or_promotion(move));
879 captureOrPromotion = true;
882 ss->currentMove = move;
883 ss->continuationHistory = &thisThread->continuationHistory[ss->inCheck]
885 [pos.moved_piece(move)]
888 pos.do_move(move, st);
890 // Perform a preliminary qsearch to verify that the move holds
891 value = -qsearch<NonPV>(pos, ss+1, -probCutBeta, -probCutBeta+1);
893 // If the qsearch held, perform the regular search
894 if (value >= probCutBeta)
895 value = -search<NonPV>(pos, ss+1, -probCutBeta, -probCutBeta+1, depth - 4, !cutNode);
899 if (value >= probCutBeta)
901 // if transposition table doesn't have equal or more deep info write probCut data into it
903 && tte->depth() >= depth - 3
904 && ttValue != VALUE_NONE))
905 tte->save(posKey, value_to_tt(value, ss->ply), ttPv,
907 depth - 3, move, ss->staticEval);
914 // Step 10. If the position is not in TT, decrease depth by 2
920 moves_loop: // When in check, search starts from here
922 ttCapture = ttMove && pos.capture_or_promotion(ttMove);
924 // Step 11. A small Probcut idea, when we are in check
925 probCutBeta = beta + 409;
930 && (tte->bound() & BOUND_LOWER)
931 && tte->depth() >= depth - 3
932 && ttValue >= probCutBeta
933 && abs(ttValue) <= VALUE_KNOWN_WIN
934 && abs(beta) <= VALUE_KNOWN_WIN
939 const PieceToHistory* contHist[] = { (ss-1)->continuationHistory, (ss-2)->continuationHistory,
940 nullptr , (ss-4)->continuationHistory,
941 nullptr , (ss-6)->continuationHistory };
943 Move countermove = thisThread->counterMoves[pos.piece_on(prevSq)][prevSq];
945 MovePicker mp(pos, ttMove, depth, &thisThread->mainHistory,
946 &thisThread->lowPlyHistory,
954 singularQuietLMR = moveCountPruning = false;
956 // Indicate PvNodes that will probably fail low if the node was searched
957 // at a depth equal or greater than the current depth, and the result of this search was a fail low.
958 bool likelyFailLow = PvNode
960 && (tte->bound() & BOUND_UPPER)
961 && tte->depth() >= depth;
963 // Step 12. Loop through all pseudo-legal moves until no moves remain
964 // or a beta cutoff occurs.
965 while ((move = mp.next_move(moveCountPruning)) != MOVE_NONE)
969 if (move == excludedMove)
972 // At root obey the "searchmoves" option and skip moves not listed in Root
973 // Move List. As a consequence any illegal move is also skipped. In MultiPV
974 // mode we also skip PV moves which have been already searched and those
975 // of lower "TB rank" if we are in a TB root position.
976 if (rootNode && !std::count(thisThread->rootMoves.begin() + thisThread->pvIdx,
977 thisThread->rootMoves.begin() + thisThread->pvLast, move))
980 // Check for legality
981 if (!rootNode && !pos.legal(move))
984 ss->moveCount = ++moveCount;
986 if (rootNode && thisThread == Threads.main() && Time.elapsed() > 3000)
987 sync_cout << "info depth " << depth
988 << " currmove " << UCI::move(move, pos.is_chess960())
989 << " currmovenumber " << moveCount + thisThread->pvIdx << sync_endl;
991 (ss+1)->pv = nullptr;
994 captureOrPromotion = pos.capture_or_promotion(move);
995 movedPiece = pos.moved_piece(move);
996 givesCheck = pos.gives_check(move);
998 // Calculate new depth for this move
999 newDepth = depth - 1;
1001 // Step 13. Pruning at shallow depth (~200 Elo)
1003 && pos.non_pawn_material(us)
1004 && bestValue > VALUE_TB_LOSS_IN_MAX_PLY)
1006 // Skip quiet moves if movecount exceeds our FutilityMoveCount threshold
1007 moveCountPruning = moveCount >= futility_move_count(improving, depth);
1009 // Reduced depth of the next LMR search
1010 int lmrDepth = std::max(newDepth - reduction(improving, depth, moveCount), 0);
1012 if ( captureOrPromotion
1015 // Capture history based pruning when the move doesn't give check
1018 && captureHistory[movedPiece][to_sq(move)][type_of(pos.piece_on(to_sq(move)))] < 0)
1021 // SEE based pruning
1022 if (!pos.see_ge(move, Value(-218) * depth)) // (~25 Elo)
1027 // Continuation history based pruning (~20 Elo)
1029 && (*contHist[0])[movedPiece][to_sq(move)] < CounterMovePruneThreshold
1030 && (*contHist[1])[movedPiece][to_sq(move)] < CounterMovePruneThreshold)
1033 // Futility pruning: parent node (~5 Elo)
1036 && ss->staticEval + 174 + 157 * lmrDepth <= alpha
1037 && (*contHist[0])[movedPiece][to_sq(move)]
1038 + (*contHist[1])[movedPiece][to_sq(move)]
1039 + (*contHist[3])[movedPiece][to_sq(move)]
1040 + (*contHist[5])[movedPiece][to_sq(move)] / 3 < 28255)
1043 // Prune moves with negative SEE (~20 Elo)
1044 if (!pos.see_ge(move, Value(-(30 - std::min(lmrDepth, 18)) * lmrDepth * lmrDepth)))
1049 // Step 14. Extensions (~75 Elo)
1051 // Singular extension search (~70 Elo). If all moves but one fail low on a
1052 // search of (alpha-s, beta-s), and just one fails high on (alpha, beta),
1053 // then that move is singular and should be extended. To verify this we do
1054 // a reduced search on all the other moves but the ttMove and if the
1055 // result is lower than ttValue minus a margin, then we will extend the ttMove.
1059 && !excludedMove // Avoid recursive singular search
1060 /* && ttValue != VALUE_NONE Already implicit in the next condition */
1061 && abs(ttValue) < VALUE_KNOWN_WIN
1062 && (tte->bound() & BOUND_LOWER)
1063 && tte->depth() >= depth - 3)
1065 Value singularBeta = ttValue - ((formerPv + 4) * depth) / 2;
1066 Depth singularDepth = (depth - 1 + 3 * formerPv) / 2;
1068 ss->excludedMove = move;
1069 value = search<NonPV>(pos, ss, singularBeta - 1, singularBeta, singularDepth, cutNode);
1070 ss->excludedMove = MOVE_NONE;
1072 if (value < singularBeta)
1075 singularQuietLMR = !ttCapture;
1076 if (!PvNode && value < singularBeta - 93)
1080 // Multi-cut pruning
1081 // Our ttMove is assumed to fail high, and now we failed high also on a reduced
1082 // search without the ttMove. So we assume this expected Cut-node is not singular,
1083 // that multiple moves fail high, and we can prune the whole subtree by returning
1085 else if (singularBeta >= beta)
1086 return singularBeta;
1088 // If the eval of ttMove is greater than beta we try also if there is another
1089 // move that pushes it over beta, if so also produce a cutoff.
1090 else if (ttValue >= beta)
1092 ss->excludedMove = move;
1093 value = search<NonPV>(pos, ss, beta - 1, beta, (depth + 3) / 2, cutNode);
1094 ss->excludedMove = MOVE_NONE;
1101 // Add extension to new depth
1102 newDepth += extension;
1104 // Speculative prefetch as early as possible
1105 prefetch(TT.first_entry(pos.key_after(move)));
1107 // Update the current move (this must be done after singular extension search)
1108 ss->currentMove = move;
1109 ss->continuationHistory = &thisThread->continuationHistory[ss->inCheck]
1110 [captureOrPromotion]
1114 // Step 15. Make the move
1115 pos.do_move(move, st, givesCheck);
1117 // Step 16. Late moves reduction / extension (LMR, ~200 Elo)
1118 // We use various heuristics for the sons of a node after the first son has
1119 // been searched. In general we would like to reduce them, but there are many
1120 // cases where we extend a son if it has good chances to be "interesting".
1122 && moveCount > 1 + 2 * rootNode
1123 && ( !captureOrPromotion
1125 || (!PvNode && !formerPv))
1126 && (!PvNode || ss->ply > 1 || thisThread->id() % 4 != 3))
1128 Depth r = reduction(improving, depth, moveCount);
1130 // Decrease reduction if the ttHit running average is large (~0 Elo)
1131 if (thisThread->ttHitAverage > 537 * TtHitAverageResolution * TtHitAverageWindow / 1024)
1134 // Decrease reduction if position is or has been on the PV
1135 // and node is not likely to fail low. (~3 Elo)
1140 // Increase reduction at root and non-PV nodes when the best move does not change frequently
1141 if ( (rootNode || !PvNode)
1142 && thisThread->rootDepth > 10
1143 && thisThread->bestMoveChanges <= 2)
1146 // Decrease reduction if opponent's move count is high (~1 Elo)
1147 if ((ss-1)->moveCount > 13)
1150 // Decrease reduction if ttMove has been singularly extended (~1 Elo)
1151 if (singularQuietLMR)
1154 // Increase reduction for cut nodes (~3 Elo)
1156 r += 1 + !captureOrPromotion;
1158 if (!captureOrPromotion)
1160 // Increase reduction if ttMove is a capture (~3 Elo)
1164 ss->statScore = thisThread->mainHistory[us][from_to(move)]
1165 + (*contHist[0])[movedPiece][to_sq(move)]
1166 + (*contHist[1])[movedPiece][to_sq(move)]
1167 + (*contHist[3])[movedPiece][to_sq(move)]
1170 // Decrease/increase reduction for moves with a good/bad history (~30 Elo)
1172 r -= ss->statScore / 14721;
1175 // In general we want to cap the LMR depth search at newDepth. But if
1176 // reductions are really negative and movecount is low, we allow this move
1177 // to be searched deeper than the first move.
1178 Depth d = std::clamp(newDepth - r, 1, newDepth + (r < -1 && moveCount <= 5));
1180 value = -search<NonPV>(pos, ss+1, -(alpha+1), -alpha, d, true);
1182 // If the son is reduced and fails high it will be re-searched at full depth
1183 doFullDepthSearch = value > alpha && d < newDepth;
1188 doFullDepthSearch = !PvNode || moveCount > 1;
1192 // Step 17. Full depth search when LMR is skipped or fails high
1193 if (doFullDepthSearch)
1195 value = -search<NonPV>(pos, ss+1, -(alpha+1), -alpha, newDepth, !cutNode);
1197 // If the move passed LMR update its stats
1198 if (didLMR && !captureOrPromotion)
1200 int bonus = value > alpha ? stat_bonus(newDepth)
1201 : -stat_bonus(newDepth);
1203 update_continuation_histories(ss, movedPiece, to_sq(move), bonus);
1207 // For PV nodes only, do a full PV search on the first move or after a fail
1208 // high (in the latter case search only if value < beta), otherwise let the
1209 // parent node fail low with value <= alpha and try another move.
1210 if (PvNode && (moveCount == 1 || (value > alpha && (rootNode || value < beta))))
1213 (ss+1)->pv[0] = MOVE_NONE;
1215 value = -search<PV>(pos, ss+1, -beta, -alpha,
1216 std::min(maxNextDepth, newDepth), false);
1219 // Step 18. Undo move
1220 pos.undo_move(move);
1222 assert(value > -VALUE_INFINITE && value < VALUE_INFINITE);
1224 // Step 19. Check for a new best move
1225 // Finished searching the move. If a stop occurred, the return value of
1226 // the search cannot be trusted, and we return immediately without
1227 // updating best move, PV and TT.
1228 if (Threads.stop.load(std::memory_order_relaxed))
1233 RootMove& rm = *std::find(thisThread->rootMoves.begin(),
1234 thisThread->rootMoves.end(), move);
1236 // PV move or new best move?
1237 if (moveCount == 1 || value > alpha)
1240 rm.selDepth = thisThread->selDepth;
1245 for (Move* m = (ss+1)->pv; *m != MOVE_NONE; ++m)
1246 rm.pv.push_back(*m);
1248 // We record how often the best move has been changed in each
1249 // iteration. This information is used for time management and LMR
1251 ++thisThread->bestMoveChanges;
1254 // All other moves but the PV are set to the lowest value: this
1255 // is not a problem when sorting because the sort is stable and the
1256 // move position in the list is preserved - just the PV is pushed up.
1257 rm.score = -VALUE_INFINITE;
1260 if (value > bestValue)
1268 if (PvNode && !rootNode) // Update pv even in fail-high case
1269 update_pv(ss->pv, move, (ss+1)->pv);
1271 if (PvNode && value < beta) // Update alpha! Always alpha < beta
1275 assert(value >= beta); // Fail high
1282 // If the move is worse than some previously searched move, remember it to update its stats later
1283 if (move != bestMove)
1285 if (captureOrPromotion && captureCount < 32)
1286 capturesSearched[captureCount++] = move;
1288 else if (!captureOrPromotion && quietCount < 64)
1289 quietsSearched[quietCount++] = move;
1293 // The following condition would detect a stop only after move loop has been
1294 // completed. But in this case bestValue is valid because we have fully
1295 // searched our subtree, and we can anyhow save the result in TT.
1301 // Step 20. Check for mate and stalemate
1302 // All legal moves have been searched and if there are no legal moves, it
1303 // must be a mate or a stalemate. If we are in a singular extension search then
1304 // return a fail low score.
1306 assert(moveCount || !ss->inCheck || excludedMove || !MoveList<LEGAL>(pos).size());
1309 bestValue = excludedMove ? alpha :
1310 ss->inCheck ? mated_in(ss->ply)
1313 // If there is a move which produces search value greater than alpha we update stats of searched moves
1315 update_all_stats(pos, ss, bestMove, bestValue, beta, prevSq,
1316 quietsSearched, quietCount, capturesSearched, captureCount, depth);
1318 // Bonus for prior countermove that caused the fail low
1319 else if ( (depth >= 3 || PvNode)
1321 update_continuation_histories(ss-1, pos.piece_on(prevSq), prevSq, stat_bonus(depth));
1324 bestValue = std::min(bestValue, maxValue);
1326 // If no good move is found and the previous position was ttPv, then the previous
1327 // opponent move is probably good and the new position is added to the search tree.
1328 if (bestValue <= alpha)
1329 ss->ttPv = ss->ttPv || ((ss-1)->ttPv && depth > 3);
1330 // Otherwise, a counter move has been found and if the position is the last leaf
1331 // in the search tree, remove the position from the search tree.
1333 ss->ttPv = ss->ttPv && (ss+1)->ttPv;
1335 // Write gathered information in transposition table
1336 if (!excludedMove && !(rootNode && thisThread->pvIdx))
1337 tte->save(posKey, value_to_tt(bestValue, ss->ply), ss->ttPv,
1338 bestValue >= beta ? BOUND_LOWER :
1339 PvNode && bestMove ? BOUND_EXACT : BOUND_UPPER,
1340 depth, bestMove, ss->staticEval);
1342 assert(bestValue > -VALUE_INFINITE && bestValue < VALUE_INFINITE);
1348 // qsearch() is the quiescence search function, which is called by the main search
1349 // function with zero depth, or recursively with further decreasing depth per call.
1350 template <NodeType NT>
1351 Value qsearch(Position& pos, Stack* ss, Value alpha, Value beta, Depth depth) {
1353 constexpr bool PvNode = NT == PV;
1355 assert(alpha >= -VALUE_INFINITE && alpha < beta && beta <= VALUE_INFINITE);
1356 assert(PvNode || (alpha == beta - 1));
1361 ASSERT_ALIGNED(&st, Eval::NNUE::CacheLineSize);
1365 Move ttMove, move, bestMove;
1367 Value bestValue, value, ttValue, futilityValue, futilityBase, oldAlpha;
1368 bool pvHit, givesCheck, captureOrPromotion;
1373 oldAlpha = alpha; // To flag BOUND_EXACT when eval above alpha and no available moves
1375 ss->pv[0] = MOVE_NONE;
1378 Thread* thisThread = pos.this_thread();
1379 (ss+1)->ply = ss->ply + 1;
1380 bestMove = MOVE_NONE;
1381 ss->inCheck = pos.checkers();
1384 // Check for an immediate draw or maximum ply reached
1385 if ( pos.is_draw(ss->ply)
1386 || ss->ply >= MAX_PLY)
1387 return (ss->ply >= MAX_PLY && !ss->inCheck) ? evaluate(pos) : VALUE_DRAW;
1389 assert(0 <= ss->ply && ss->ply < MAX_PLY);
1391 // Decide whether or not to include checks: this fixes also the type of
1392 // TT entry depth that we are going to use. Note that in qsearch we use
1393 // only two types of depth in TT: DEPTH_QS_CHECKS or DEPTH_QS_NO_CHECKS.
1394 ttDepth = ss->inCheck || depth >= DEPTH_QS_CHECKS ? DEPTH_QS_CHECKS
1395 : DEPTH_QS_NO_CHECKS;
1396 // Transposition table lookup
1398 tte = TT.probe(posKey, ss->ttHit);
1399 ttValue = ss->ttHit ? value_from_tt(tte->value(), ss->ply, pos.rule50_count()) : VALUE_NONE;
1400 ttMove = ss->ttHit ? tte->move() : MOVE_NONE;
1401 pvHit = ss->ttHit && tte->is_pv();
1405 && tte->depth() >= ttDepth
1406 && ttValue != VALUE_NONE // Only in case of TT access race
1407 && (ttValue >= beta ? (tte->bound() & BOUND_LOWER)
1408 : (tte->bound() & BOUND_UPPER)))
1411 // Evaluate the position statically
1414 ss->staticEval = VALUE_NONE;
1415 bestValue = futilityBase = -VALUE_INFINITE;
1421 // Never assume anything about values stored in TT
1422 if ((ss->staticEval = bestValue = tte->eval()) == VALUE_NONE)
1423 ss->staticEval = bestValue = evaluate(pos);
1425 // Can ttValue be used as a better position evaluation?
1426 if ( ttValue != VALUE_NONE
1427 && (tte->bound() & (ttValue > bestValue ? BOUND_LOWER : BOUND_UPPER)))
1428 bestValue = ttValue;
1431 // In case of null move search use previous static eval with a different sign
1432 // and addition of two tempos
1433 ss->staticEval = bestValue =
1434 (ss-1)->currentMove != MOVE_NULL ? evaluate(pos)
1435 : -(ss-1)->staticEval;
1437 // Stand pat. Return immediately if static value is at least beta
1438 if (bestValue >= beta)
1440 // Save gathered info in transposition table
1442 tte->save(posKey, value_to_tt(bestValue, ss->ply), false, BOUND_LOWER,
1443 DEPTH_NONE, MOVE_NONE, ss->staticEval);
1448 if (PvNode && bestValue > alpha)
1451 futilityBase = bestValue + 155;
1454 const PieceToHistory* contHist[] = { (ss-1)->continuationHistory, (ss-2)->continuationHistory,
1455 nullptr , (ss-4)->continuationHistory,
1456 nullptr , (ss-6)->continuationHistory };
1458 // Initialize a MovePicker object for the current position, and prepare
1459 // to search the moves. Because the depth is <= 0 here, only captures,
1460 // queen and checking knight promotions, and other checks(only if depth >= DEPTH_QS_CHECKS)
1461 // will be generated.
1462 MovePicker mp(pos, ttMove, depth, &thisThread->mainHistory,
1463 &thisThread->captureHistory,
1465 to_sq((ss-1)->currentMove));
1467 // Loop through the moves until no moves remain or a beta cutoff occurs
1468 while ((move = mp.next_move()) != MOVE_NONE)
1470 assert(is_ok(move));
1472 givesCheck = pos.gives_check(move);
1473 captureOrPromotion = pos.capture_or_promotion(move);
1477 // Futility pruning and moveCount pruning
1478 if ( bestValue > VALUE_TB_LOSS_IN_MAX_PLY
1480 && futilityBase > -VALUE_KNOWN_WIN
1481 && type_of(move) != PROMOTION)
1487 futilityValue = futilityBase + PieceValue[EG][pos.piece_on(to_sq(move))];
1489 if (futilityValue <= alpha)
1491 bestValue = std::max(bestValue, futilityValue);
1495 if (futilityBase <= alpha && !pos.see_ge(move, VALUE_ZERO + 1))
1497 bestValue = std::max(bestValue, futilityBase);
1502 // Do not search moves with negative SEE values
1503 if ( bestValue > VALUE_TB_LOSS_IN_MAX_PLY
1504 && !pos.see_ge(move))
1507 // Speculative prefetch as early as possible
1508 prefetch(TT.first_entry(pos.key_after(move)));
1510 // Check for legality just before making the move
1511 if (!pos.legal(move))
1517 ss->currentMove = move;
1518 ss->continuationHistory = &thisThread->continuationHistory[ss->inCheck]
1519 [captureOrPromotion]
1520 [pos.moved_piece(move)]
1523 // Continuation history based pruning
1524 if ( !captureOrPromotion
1525 && bestValue > VALUE_TB_LOSS_IN_MAX_PLY
1526 && (*contHist[0])[pos.moved_piece(move)][to_sq(move)] < CounterMovePruneThreshold
1527 && (*contHist[1])[pos.moved_piece(move)][to_sq(move)] < CounterMovePruneThreshold)
1530 // Make and search the move
1531 pos.do_move(move, st, givesCheck);
1532 value = -qsearch<NT>(pos, ss+1, -beta, -alpha, depth - 1);
1533 pos.undo_move(move);
1535 assert(value > -VALUE_INFINITE && value < VALUE_INFINITE);
1537 // Check for a new best move
1538 if (value > bestValue)
1546 if (PvNode) // Update pv even in fail-high case
1547 update_pv(ss->pv, move, (ss+1)->pv);
1549 if (PvNode && value < beta) // Update alpha here!
1557 // All legal moves have been searched. A special case: if we're in check
1558 // and no legal moves were found, it is checkmate.
1559 if (ss->inCheck && bestValue == -VALUE_INFINITE)
1561 assert(!MoveList<LEGAL>(pos).size());
1563 return mated_in(ss->ply); // Plies to mate from the root
1566 // Save gathered info in transposition table
1567 tte->save(posKey, value_to_tt(bestValue, ss->ply), pvHit,
1568 bestValue >= beta ? BOUND_LOWER :
1569 PvNode && bestValue > oldAlpha ? BOUND_EXACT : BOUND_UPPER,
1570 ttDepth, bestMove, ss->staticEval);
1572 assert(bestValue > -VALUE_INFINITE && bestValue < VALUE_INFINITE);
1578 // value_to_tt() adjusts a mate or TB score from "plies to mate from the root" to
1579 // "plies to mate from the current position". Standard scores are unchanged.
1580 // The function is called before storing a value in the transposition table.
1582 Value value_to_tt(Value v, int ply) {
1584 assert(v != VALUE_NONE);
1586 return v >= VALUE_TB_WIN_IN_MAX_PLY ? v + ply
1587 : v <= VALUE_TB_LOSS_IN_MAX_PLY ? v - ply : v;
1591 // value_from_tt() is the inverse of value_to_tt(): it adjusts a mate or TB score
1592 // from the transposition table (which refers to the plies to mate/be mated from
1593 // current position) to "plies to mate/be mated (TB win/loss) from the root". However,
1594 // for mate scores, to avoid potentially false mate scores related to the 50 moves rule
1595 // and the graph history interaction, we return an optimal TB score instead.
1597 Value value_from_tt(Value v, int ply, int r50c) {
1599 if (v == VALUE_NONE)
1602 if (v >= VALUE_TB_WIN_IN_MAX_PLY) // TB win or better
1604 if (v >= VALUE_MATE_IN_MAX_PLY && VALUE_MATE - v > 99 - r50c)
1605 return VALUE_MATE_IN_MAX_PLY - 1; // do not return a potentially false mate score
1610 if (v <= VALUE_TB_LOSS_IN_MAX_PLY) // TB loss or worse
1612 if (v <= VALUE_MATED_IN_MAX_PLY && VALUE_MATE + v > 99 - r50c)
1613 return VALUE_MATED_IN_MAX_PLY + 1; // do not return a potentially false mate score
1622 // update_pv() adds current move and appends child pv[]
1624 void update_pv(Move* pv, Move move, Move* childPv) {
1626 for (*pv++ = move; childPv && *childPv != MOVE_NONE; )
1632 // update_all_stats() updates stats at the end of search() when a bestMove is found
1634 void update_all_stats(const Position& pos, Stack* ss, Move bestMove, Value bestValue, Value beta, Square prevSq,
1635 Move* quietsSearched, int quietCount, Move* capturesSearched, int captureCount, Depth depth) {
1638 Color us = pos.side_to_move();
1639 Thread* thisThread = pos.this_thread();
1640 CapturePieceToHistory& captureHistory = thisThread->captureHistory;
1641 Piece moved_piece = pos.moved_piece(bestMove);
1642 PieceType captured = type_of(pos.piece_on(to_sq(bestMove)));
1644 bonus1 = stat_bonus(depth + 1);
1645 bonus2 = bestValue > beta + PawnValueMg ? bonus1 // larger bonus
1646 : std::min(bonus1, stat_bonus(depth)); // smaller bonus
1648 if (!pos.capture_or_promotion(bestMove))
1650 // Increase stats for the best move in case it was a quiet move
1651 update_quiet_stats(pos, ss, bestMove, bonus2, depth);
1653 // Decrease stats for all non-best quiet moves
1654 for (int i = 0; i < quietCount; ++i)
1656 thisThread->mainHistory[us][from_to(quietsSearched[i])] << -bonus2;
1657 update_continuation_histories(ss, pos.moved_piece(quietsSearched[i]), to_sq(quietsSearched[i]), -bonus2);
1661 // Increase stats for the best move in case it was a capture move
1662 captureHistory[moved_piece][to_sq(bestMove)][captured] << bonus1;
1664 // Extra penalty for a quiet early move that was not a TT move or
1665 // main killer move in previous ply when it gets refuted.
1666 if ( ((ss-1)->moveCount == 1 + (ss-1)->ttHit || ((ss-1)->currentMove == (ss-1)->killers[0]))
1667 && !pos.captured_piece())
1668 update_continuation_histories(ss-1, pos.piece_on(prevSq), prevSq, -bonus1);
1670 // Decrease stats for all non-best capture moves
1671 for (int i = 0; i < captureCount; ++i)
1673 moved_piece = pos.moved_piece(capturesSearched[i]);
1674 captured = type_of(pos.piece_on(to_sq(capturesSearched[i])));
1675 captureHistory[moved_piece][to_sq(capturesSearched[i])][captured] << -bonus1;
1680 // update_continuation_histories() updates histories of the move pairs formed
1681 // by moves at ply -1, -2, -4, and -6 with current move.
1683 void update_continuation_histories(Stack* ss, Piece pc, Square to, int bonus) {
1685 for (int i : {1, 2, 4, 6})
1687 // Only update first 2 continuation histories if we are in check
1688 if (ss->inCheck && i > 2)
1690 if (is_ok((ss-i)->currentMove))
1691 (*(ss-i)->continuationHistory)[pc][to] << bonus;
1696 // update_quiet_stats() updates move sorting heuristics
1698 void update_quiet_stats(const Position& pos, Stack* ss, Move move, int bonus, int depth) {
1701 if (ss->killers[0] != move)
1703 ss->killers[1] = ss->killers[0];
1704 ss->killers[0] = move;
1707 Color us = pos.side_to_move();
1708 Thread* thisThread = pos.this_thread();
1709 thisThread->mainHistory[us][from_to(move)] << bonus;
1710 update_continuation_histories(ss, pos.moved_piece(move), to_sq(move), bonus);
1712 // Penalty for reversed move in case of moved piece not being a pawn
1713 if (type_of(pos.moved_piece(move)) != PAWN)
1714 thisThread->mainHistory[us][from_to(reverse_move(move))] << -bonus;
1716 // Update countermove history
1717 if (is_ok((ss-1)->currentMove))
1719 Square prevSq = to_sq((ss-1)->currentMove);
1720 thisThread->counterMoves[pos.piece_on(prevSq)][prevSq] = move;
1723 // Update low ply history
1724 if (depth > 11 && ss->ply < MAX_LPH)
1725 thisThread->lowPlyHistory[ss->ply][from_to(move)] << stat_bonus(depth - 7);
1728 // When playing with strength handicap, choose best move among a set of RootMoves
1729 // using a statistical rule dependent on 'level'. Idea by Heinz van Saanen.
1731 Move Skill::pick_best(size_t multiPV) {
1733 const RootMoves& rootMoves = Threads.main()->rootMoves;
1734 static PRNG rng(now()); // PRNG sequence should be non-deterministic
1736 // RootMoves are already sorted by score in descending order
1737 Value topScore = rootMoves[0].score;
1738 int delta = std::min(topScore - rootMoves[multiPV - 1].score, PawnValueMg);
1739 int weakness = 120 - 2 * level;
1740 int maxScore = -VALUE_INFINITE;
1742 // Choose best move. For each move score we add two terms, both dependent on
1743 // weakness. One is deterministic and bigger for weaker levels, and one is
1744 // random. Then we choose the move with the resulting highest score.
1745 for (size_t i = 0; i < multiPV; ++i)
1747 // This is our magic formula
1748 int push = ( weakness * int(topScore - rootMoves[i].score)
1749 + delta * (rng.rand<unsigned>() % weakness)) / 128;
1751 if (rootMoves[i].score + push >= maxScore)
1753 maxScore = rootMoves[i].score + push;
1754 best = rootMoves[i].pv[0];
1764 /// MainThread::check_time() is used to print debug info and, more importantly,
1765 /// to detect when we are out of available time and thus stop the search.
1767 void MainThread::check_time() {
1772 // When using nodes, ensure checking rate is not lower than 0.1% of nodes
1773 callsCnt = Limits.nodes ? std::min(1024, int(Limits.nodes / 1024)) : 1024;
1775 static TimePoint lastInfoTime = now();
1777 TimePoint elapsed = Time.elapsed();
1778 TimePoint tick = Limits.startTime + elapsed;
1780 if (tick - lastInfoTime >= 1000)
1782 lastInfoTime = tick;
1786 // We should not stop pondering until told so by the GUI
1790 if ( (Limits.use_time_management() && (elapsed > Time.maximum() - 10 || stopOnPonderhit))
1791 || (Limits.movetime && elapsed >= Limits.movetime)
1792 || (Limits.nodes && Threads.nodes_searched() >= (uint64_t)Limits.nodes))
1793 Threads.stop = true;
1797 /// UCI::pv() formats PV information according to the UCI protocol. UCI requires
1798 /// that all (if any) unsearched PV lines are sent using a previous search score.
1800 string UCI::pv(const Position& pos, Depth depth, Value alpha, Value beta) {
1802 std::stringstream ss;
1803 TimePoint elapsed = Time.elapsed() + 1;
1804 const RootMoves& rootMoves = pos.this_thread()->rootMoves;
1805 size_t pvIdx = pos.this_thread()->pvIdx;
1806 size_t multiPV = std::min((size_t)Options["MultiPV"], rootMoves.size());
1807 uint64_t nodesSearched = Threads.nodes_searched();
1808 uint64_t tbHits = Threads.tb_hits() + (TB::RootInTB ? rootMoves.size() : 0);
1810 for (size_t i = 0; i < multiPV; ++i)
1812 bool updated = rootMoves[i].score != -VALUE_INFINITE;
1814 if (depth == 1 && !updated && i > 0)
1817 Depth d = updated ? depth : std::max(1, depth - 1);
1818 Value v = updated ? rootMoves[i].score : rootMoves[i].previousScore;
1820 if (v == -VALUE_INFINITE)
1823 bool tb = TB::RootInTB && abs(v) < VALUE_MATE_IN_MAX_PLY;
1824 v = tb ? rootMoves[i].tbScore : v;
1826 if (ss.rdbuf()->in_avail()) // Not at first line
1831 << " seldepth " << rootMoves[i].selDepth
1832 << " multipv " << i + 1
1833 << " score " << UCI::value(v);
1835 if (Options["UCI_ShowWDL"])
1836 ss << UCI::wdl(v, pos.game_ply());
1838 if (!tb && i == pvIdx)
1839 ss << (v >= beta ? " lowerbound" : v <= alpha ? " upperbound" : "");
1841 ss << " nodes " << nodesSearched
1842 << " nps " << nodesSearched * 1000 / elapsed;
1844 if (elapsed > 1000) // Earlier makes little sense
1845 ss << " hashfull " << TT.hashfull();
1847 ss << " tbhits " << tbHits
1848 << " time " << elapsed
1851 for (Move m : rootMoves[i].pv)
1852 ss << " " << UCI::move(m, pos.is_chess960());
1859 /// RootMove::extract_ponder_from_tt() is called in case we have no ponder move
1860 /// before exiting the search, for instance, in case we stop the search during a
1861 /// fail high at root. We try hard to have a ponder move to return to the GUI,
1862 /// otherwise in case of 'ponder on' we have nothing to think on.
1864 bool RootMove::extract_ponder_from_tt(Position& pos) {
1867 ASSERT_ALIGNED(&st, Eval::NNUE::CacheLineSize);
1871 assert(pv.size() == 1);
1873 if (pv[0] == MOVE_NONE)
1876 pos.do_move(pv[0], st);
1877 TTEntry* tte = TT.probe(pos.key(), ttHit);
1881 Move m = tte->move(); // Local copy to be SMP safe
1882 if (MoveList<LEGAL>(pos).contains(m))
1886 pos.undo_move(pv[0]);
1887 return pv.size() > 1;
1890 void Tablebases::rank_root_moves(Position& pos, Search::RootMoves& rootMoves) {
1893 UseRule50 = bool(Options["Syzygy50MoveRule"]);
1894 ProbeDepth = int(Options["SyzygyProbeDepth"]);
1895 Cardinality = int(Options["SyzygyProbeLimit"]);
1896 bool dtz_available = true;
1898 // Tables with fewer pieces than SyzygyProbeLimit are searched with
1899 // ProbeDepth == DEPTH_ZERO
1900 if (Cardinality > MaxCardinality)
1902 Cardinality = MaxCardinality;
1906 if (Cardinality >= popcount(pos.pieces()) && !pos.can_castle(ANY_CASTLING))
1908 // Rank moves using DTZ tables
1909 RootInTB = root_probe(pos, rootMoves);
1913 // DTZ tables are missing; try to rank moves using WDL tables
1914 dtz_available = false;
1915 RootInTB = root_probe_wdl(pos, rootMoves);
1921 // Sort moves according to TB rank
1922 std::stable_sort(rootMoves.begin(), rootMoves.end(),
1923 [](const RootMove &a, const RootMove &b) { return a.tbRank > b.tbRank; } );
1925 // Probe during search only if DTZ is not available and we are winning
1926 if (dtz_available || rootMoves[0].tbScore <= VALUE_DRAW)
1931 // Clean up if root_probe() and root_probe_wdl() have failed
1932 for (auto& m : rootMoves)
1937 } // namespace Stockfish