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((126 - 42 * 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 + 1560 - int(delta) * 945 / int(rootDelta)) / 1024
89 + (!i && reductionScale > 791);
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(334 * d - 531, 1538); }
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 // perft() is our 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 // Search::init() is called at startup to initialize various lookup tables
184 void Search::init() {
186 for (int i = 1; i < MAX_MOVES; ++i)
187 Reductions[i] = int((20.37 + std::log(Threads.size()) / 2) * std::log(i));
191 // Search::clear() resets search state to its initial value
193 void Search::clear() {
195 Threads.main()->wait_for_search_finished();
197 Time.availableNodes = 0;
200 Tablebases::init(Options["SyzygyPath"]); // Free mapped files
204 // MainThread::search() is started when the program receives the UCI 'go'
205 // command. It searches from the root position and outputs the "bestmove".
207 void MainThread::search() {
211 nodes = perft<true>(rootPos, Limits.perft);
212 sync_cout << "\nNodes searched: " << nodes << "\n" << sync_endl;
216 Color us = rootPos.side_to_move();
217 Time.init(Limits, us, rootPos.game_ply());
220 Eval::NNUE::verify();
222 if (rootMoves.empty())
224 rootMoves.emplace_back(MOVE_NONE);
225 sync_cout << "info depth 0 score "
226 << UCI::value(rootPos.checkers() ? -VALUE_MATE : VALUE_DRAW) << sync_endl;
230 Threads.start_searching(); // start non-main threads
231 Thread::search(); // main thread start searching
234 // When we reach the maximum depth, we can arrive here without a raise of
235 // Threads.stop. However, if we are pondering or in an infinite search,
236 // the UCI protocol states that we shouldn't print the best move before the
237 // GUI sends a "stop" or "ponderhit" command. We therefore simply wait here
238 // until the GUI sends one of those commands.
240 while (!Threads.stop && (ponder || Limits.infinite))
241 {} // Busy wait for a stop or a ponder reset
243 // Stop the threads if not already stopped (also raise the stop if
244 // "ponderhit" just reset Threads.ponder).
247 // Wait until all threads have finished
248 Threads.wait_for_search_finished();
250 // When playing in 'nodes as time' mode, subtract the searched nodes from
251 // the available ones before exiting.
253 Time.availableNodes += Limits.inc[us] - Threads.nodes_searched();
255 Thread* bestThread = this;
257 Skill(Options["Skill Level"], Options["UCI_LimitStrength"] ? int(Options["UCI_Elo"]) : 0);
259 if (int(Options["MultiPV"]) == 1 && !Limits.depth && !skill.enabled()
260 && rootMoves[0].pv[0] != MOVE_NONE)
261 bestThread = Threads.get_best_thread();
263 bestPreviousScore = bestThread->rootMoves[0].score;
264 bestPreviousAverageScore = bestThread->rootMoves[0].averageScore;
266 // Send again PV info if we have a new best thread
267 if (bestThread != this)
268 sync_cout << UCI::pv(bestThread->rootPos, bestThread->completedDepth) << sync_endl;
270 sync_cout << "bestmove " << UCI::move(bestThread->rootMoves[0].pv[0], rootPos.is_chess960());
272 if (bestThread->rootMoves[0].pv.size() > 1
273 || bestThread->rootMoves[0].extract_ponder_from_tt(rootPos))
274 std::cout << " ponder " << UCI::move(bestThread->rootMoves[0].pv[1], rootPos.is_chess960());
276 std::cout << sync_endl;
280 // Thread::search() is the main iterative deepening loop. It calls search()
281 // repeatedly with increasing depth until the allocated thinking time has been
282 // consumed, the user stops the search, or the maximum search depth is reached.
284 void Thread::search() {
286 // Allocate stack with extra size to allow access from (ss-7) to (ss+2):
287 // (ss-7) is needed for update_continuation_histories(ss-1) which accesses (ss-6),
288 // (ss+2) is needed for initialization of statScore and killers.
289 Stack stack[MAX_PLY + 10], *ss = stack + 7;
290 Move pv[MAX_PLY + 1];
291 Value alpha, beta, delta;
292 Move lastBestMove = MOVE_NONE;
293 Depth lastBestMoveDepth = 0;
294 MainThread* mainThread = (this == Threads.main() ? Threads.main() : nullptr);
295 double timeReduction = 1, totBestMoveChanges = 0;
296 Color us = rootPos.side_to_move();
299 std::memset(ss - 7, 0, 10 * sizeof(Stack));
300 for (int i = 7; i > 0; --i)
302 (ss - i)->continuationHistory =
303 &this->continuationHistory[0][0][NO_PIECE][0]; // Use as a sentinel
304 (ss - i)->staticEval = VALUE_NONE;
307 for (int i = 0; i <= MAX_PLY + 2; ++i)
312 bestValue = -VALUE_INFINITE;
316 if (mainThread->bestPreviousScore == VALUE_INFINITE)
317 for (int i = 0; i < 4; ++i)
318 mainThread->iterValue[i] = VALUE_ZERO;
320 for (int i = 0; i < 4; ++i)
321 mainThread->iterValue[i] = mainThread->bestPreviousScore;
324 size_t multiPV = size_t(Options["MultiPV"]);
325 Skill skill(Options["Skill Level"], Options["UCI_LimitStrength"] ? int(Options["UCI_Elo"]) : 0);
327 // When playing with strength handicap enable MultiPV search that we will
328 // use behind-the-scenes to retrieve a set of possible moves.
330 multiPV = std::max(multiPV, size_t(4));
332 multiPV = std::min(multiPV, rootMoves.size());
334 int searchAgainCounter = 0;
336 // Iterative deepening loop until requested to stop or the target depth is reached
337 while (++rootDepth < MAX_PLY && !Threads.stop
338 && !(Limits.depth && mainThread && rootDepth > Limits.depth))
340 // Age out PV variability metric
342 totBestMoveChanges /= 2;
344 // Save the last iteration's scores before the first PV line is searched and
345 // all the move scores except the (new) PV are set to -VALUE_INFINITE.
346 for (RootMove& rm : rootMoves)
347 rm.previousScore = rm.score;
352 if (!Threads.increaseDepth)
353 searchAgainCounter++;
355 // MultiPV loop. We perform a full root search for each PV line
356 for (pvIdx = 0; pvIdx < multiPV && !Threads.stop; ++pvIdx)
361 for (pvLast++; pvLast < rootMoves.size(); pvLast++)
362 if (rootMoves[pvLast].tbRank != rootMoves[pvFirst].tbRank)
366 // Reset UCI info selDepth for each depth and each PV line
369 // Reset aspiration window starting size
370 Value prev = rootMoves[pvIdx].averageScore;
371 delta = Value(10) + int(prev) * prev / 17470;
372 alpha = std::max(prev - delta, -VALUE_INFINITE);
373 beta = std::min(prev + delta, VALUE_INFINITE);
375 // Adjust optimism based on root move's previousScore (~4 Elo)
376 int opt = 113 * prev / (std::abs(prev) + 109);
377 optimism[us] = Value(opt);
378 optimism[~us] = -optimism[us];
380 // Start with a small aspiration window and, in the case of a fail
381 // high/low, re-search with a bigger window until we don't fail
383 int failedHighCnt = 0;
386 // Adjust the effective depth searched, but ensure at least one effective increment for every
387 // four searchAgain steps (see issue #2717).
388 Depth adjustedDepth =
389 std::max(1, rootDepth - failedHighCnt - 3 * (searchAgainCounter + 1) / 4);
390 bestValue = Stockfish::search<Root>(rootPos, ss, alpha, beta, adjustedDepth, false);
392 // Bring the best move to the front. It is critical that sorting
393 // is done with a stable algorithm because all the values but the
394 // first and eventually the new best one is set to -VALUE_INFINITE
395 // and we want to keep the same order for all the moves except the
396 // new PV that goes to the front. Note that in the case of MultiPV
397 // search the already searched PV lines are preserved.
398 std::stable_sort(rootMoves.begin() + pvIdx, rootMoves.begin() + pvLast);
400 // If search has been stopped, we break immediately. Sorting is
401 // safe because RootMoves is still valid, although it refers to
402 // the previous iteration.
406 // When failing high/low give some update (without cluttering
407 // the UI) before a re-search.
408 if (mainThread && multiPV == 1 && (bestValue <= alpha || bestValue >= beta)
409 && Time.elapsed() > 3000)
410 sync_cout << UCI::pv(rootPos, rootDepth) << sync_endl;
412 // In case of failing low/high increase aspiration window and
413 // re-search, otherwise exit the loop.
414 if (bestValue <= alpha)
416 beta = (alpha + beta) / 2;
417 alpha = std::max(bestValue - delta, -VALUE_INFINITE);
421 mainThread->stopOnPonderhit = false;
423 else if (bestValue >= beta)
425 beta = std::min(bestValue + delta, VALUE_INFINITE);
433 assert(alpha >= -VALUE_INFINITE && beta <= VALUE_INFINITE);
436 // Sort the PV lines searched so far and update the GUI
437 std::stable_sort(rootMoves.begin() + pvFirst, rootMoves.begin() + pvIdx + 1);
439 if (mainThread && (Threads.stop || pvIdx + 1 == multiPV || Time.elapsed() > 3000))
440 sync_cout << UCI::pv(rootPos, rootDepth) << sync_endl;
444 completedDepth = rootDepth;
446 if (rootMoves[0].pv[0] != lastBestMove)
448 lastBestMove = rootMoves[0].pv[0];
449 lastBestMoveDepth = rootDepth;
452 // Have we found a "mate in x"?
453 if (Limits.mate && bestValue >= VALUE_MATE_IN_MAX_PLY
454 && VALUE_MATE - bestValue <= 2 * Limits.mate)
460 // If the skill level is enabled and time is up, pick a sub-optimal best move
461 if (skill.enabled() && skill.time_to_pick(rootDepth))
462 skill.pick_best(multiPV);
464 // Use part of the gained time from a previous stable move for the current move
465 for (Thread* th : Threads)
467 totBestMoveChanges += th->bestMoveChanges;
468 th->bestMoveChanges = 0;
471 // Do we have time for the next iteration? Can we stop searching now?
472 if (Limits.use_time_management() && !Threads.stop && !mainThread->stopOnPonderhit)
474 double fallingEval = (69 + 13 * (mainThread->bestPreviousAverageScore - bestValue)
475 + 6 * (mainThread->iterValue[iterIdx] - bestValue))
477 fallingEval = std::clamp(fallingEval, 0.5, 1.5);
479 // If the bestMove is stable over several iterations, reduce time accordingly
480 timeReduction = lastBestMoveDepth + 8 < completedDepth ? 1.57 : 0.65;
481 double reduction = (1.4 + mainThread->previousTimeReduction) / (2.08 * timeReduction);
482 double bestMoveInstability = 1 + 1.8 * totBestMoveChanges / Threads.size();
484 double totalTime = Time.optimum() * fallingEval * reduction * bestMoveInstability;
486 // Cap used time in case of a single legal move for a better viewer experience
487 if (rootMoves.size() == 1)
488 totalTime = std::min(500.0, totalTime);
490 // Stop the search if we have exceeded the totalTime
491 if (Time.elapsed() > totalTime)
493 // If we are allowed to ponder do not stop the search now but
494 // keep pondering until the GUI sends "ponderhit" or "stop".
495 if (mainThread->ponder)
496 mainThread->stopOnPonderhit = true;
500 else if (!mainThread->ponder && Time.elapsed() > totalTime * 0.50)
501 Threads.increaseDepth = false;
503 Threads.increaseDepth = true;
506 mainThread->iterValue[iterIdx] = bestValue;
507 iterIdx = (iterIdx + 1) & 3;
513 mainThread->previousTimeReduction = timeReduction;
515 // If the skill level is enabled, swap the best PV line with the sub-optimal one
517 std::swap(rootMoves[0], *std::find(rootMoves.begin(), rootMoves.end(),
518 skill.best ? skill.best : skill.pick_best(multiPV)));
524 // search<>() is the main search function for both PV and non-PV nodes
526 template<NodeType nodeType>
527 Value search(Position& pos, Stack* ss, Value alpha, Value beta, Depth depth, bool cutNode) {
529 constexpr bool PvNode = nodeType != NonPV;
530 constexpr bool rootNode = nodeType == Root;
532 // Dive into quiescence search when the depth reaches zero
534 return qsearch < PvNode ? PV : NonPV > (pos, ss, alpha, beta);
536 // Check if we have an upcoming move that draws by repetition, or
537 // if the opponent had an alternative move earlier to this position.
538 if (!rootNode && alpha < VALUE_DRAW && pos.has_game_cycle(ss->ply))
540 alpha = value_draw(pos.this_thread());
545 assert(-VALUE_INFINITE <= alpha && alpha < beta && beta <= VALUE_INFINITE);
546 assert(PvNode || (alpha == beta - 1));
547 assert(0 < depth && depth < MAX_PLY);
548 assert(!(PvNode && cutNode));
550 Move pv[MAX_PLY + 1], capturesSearched[32], quietsSearched[32];
552 ASSERT_ALIGNED(&st, Eval::NNUE::CacheLineSize);
556 Move ttMove, move, excludedMove, bestMove;
557 Depth extension, newDepth;
558 Value bestValue, value, ttValue, eval, maxValue, probCutBeta;
559 bool givesCheck, improving, priorCapture, singularQuietLMR;
560 bool capture, moveCountPruning, ttCapture;
562 int moveCount, captureCount, quietCount;
564 // Step 1. Initialize node
565 Thread* thisThread = pos.this_thread();
566 ss->inCheck = pos.checkers();
567 priorCapture = pos.captured_piece();
568 Color us = pos.side_to_move();
569 moveCount = captureCount = quietCount = ss->moveCount = 0;
570 bestValue = -VALUE_INFINITE;
571 maxValue = VALUE_INFINITE;
573 // Check for the available remaining time
574 if (thisThread == Threads.main())
575 static_cast<MainThread*>(thisThread)->check_time();
577 // Used to send selDepth info to GUI (selDepth counts from 1, ply from 0)
578 if (PvNode && thisThread->selDepth < ss->ply + 1)
579 thisThread->selDepth = ss->ply + 1;
583 // Step 2. Check for aborted search and immediate draw
584 if (Threads.stop.load(std::memory_order_relaxed) || pos.is_draw(ss->ply)
585 || ss->ply >= MAX_PLY)
586 return (ss->ply >= MAX_PLY && !ss->inCheck) ? evaluate(pos)
587 : value_draw(pos.this_thread());
589 // Step 3. Mate distance pruning. Even if we mate at the next move our score
590 // would be at best mate_in(ss->ply+1), but if alpha is already bigger because
591 // a shorter mate was found upward in the tree then there is no need to search
592 // because we will never beat the current alpha. Same logic but with reversed
593 // signs apply also in the opposite condition of being mated instead of giving
594 // mate. In this case, return a fail-high score.
595 alpha = std::max(mated_in(ss->ply), alpha);
596 beta = std::min(mate_in(ss->ply + 1), beta);
601 thisThread->rootDelta = beta - alpha;
603 assert(0 <= ss->ply && ss->ply < MAX_PLY);
605 (ss + 1)->excludedMove = bestMove = MOVE_NONE;
606 (ss + 2)->killers[0] = (ss + 2)->killers[1] = MOVE_NONE;
607 (ss + 2)->cutoffCnt = 0;
608 ss->doubleExtensions = (ss - 1)->doubleExtensions;
609 Square prevSq = is_ok((ss - 1)->currentMove) ? to_sq((ss - 1)->currentMove) : SQ_NONE;
612 // Step 4. Transposition table lookup.
613 excludedMove = ss->excludedMove;
615 tte = TT.probe(posKey, ss->ttHit);
616 ttValue = ss->ttHit ? value_from_tt(tte->value(), ss->ply, pos.rule50_count()) : VALUE_NONE;
617 ttMove = rootNode ? thisThread->rootMoves[thisThread->pvIdx].pv[0]
618 : ss->ttHit ? tte->move()
620 ttCapture = ttMove && pos.capture_stage(ttMove);
622 // At this point, if excluded, skip straight to step 6, static eval. However,
623 // to save indentation, we list the condition in all code between here and there.
625 ss->ttPv = PvNode || (ss->ttHit && tte->is_pv());
627 // At non-PV nodes we check for an early TT cutoff
628 if (!PvNode && !excludedMove && tte->depth() > depth
629 && ttValue != VALUE_NONE // Possible in case of TT access race or if !ttHit
630 && (tte->bound() & (ttValue >= beta ? BOUND_LOWER : BOUND_UPPER)))
632 // If ttMove is quiet, update move sorting heuristics on TT hit (~2 Elo)
637 // Bonus for a quiet ttMove that fails high (~2 Elo)
639 update_quiet_stats(pos, ss, ttMove, stat_bonus(depth));
641 // Extra penalty for early quiet moves of the previous ply (~0 Elo on STC, ~2 Elo on LTC)
642 if (prevSq != SQ_NONE && (ss - 1)->moveCount <= 2 && !priorCapture)
643 update_continuation_histories(ss - 1, pos.piece_on(prevSq), prevSq,
644 -stat_bonus(depth + 1));
646 // Penalty for a quiet ttMove that fails low (~1 Elo)
649 int penalty = -stat_bonus(depth);
650 thisThread->mainHistory[us][from_to(ttMove)] << penalty;
651 update_continuation_histories(ss, pos.moved_piece(ttMove), to_sq(ttMove), penalty);
655 // Partial workaround for the graph history interaction problem
656 // For high rule50 counts don't produce transposition table cutoffs.
657 if (pos.rule50_count() < 90)
661 // Step 5. Tablebases probe
662 if (!rootNode && !excludedMove && TB::Cardinality)
664 int piecesCount = pos.count<ALL_PIECES>();
666 if (piecesCount <= TB::Cardinality
667 && (piecesCount < TB::Cardinality || depth >= TB::ProbeDepth) && pos.rule50_count() == 0
668 && !pos.can_castle(ANY_CASTLING))
671 TB::WDLScore wdl = Tablebases::probe_wdl(pos, &err);
673 // Force check of time on the next occasion
674 if (thisThread == Threads.main())
675 static_cast<MainThread*>(thisThread)->callsCnt = 0;
677 if (err != TB::ProbeState::FAIL)
679 thisThread->tbHits.fetch_add(1, std::memory_order_relaxed);
681 int drawScore = TB::UseRule50 ? 1 : 0;
683 // use the range VALUE_MATE_IN_MAX_PLY to VALUE_TB_WIN_IN_MAX_PLY to score
684 value = wdl < -drawScore ? VALUE_MATED_IN_MAX_PLY + ss->ply + 1
685 : wdl > drawScore ? VALUE_MATE_IN_MAX_PLY - ss->ply - 1
686 : VALUE_DRAW + 2 * wdl * drawScore;
688 Bound b = wdl < -drawScore ? BOUND_UPPER
689 : wdl > drawScore ? BOUND_LOWER
692 if (b == BOUND_EXACT || (b == BOUND_LOWER ? value >= beta : value <= alpha))
694 tte->save(posKey, value_to_tt(value, ss->ply), ss->ttPv, b,
695 std::min(MAX_PLY - 1, depth + 6), MOVE_NONE, VALUE_NONE);
702 if (b == BOUND_LOWER)
703 bestValue = value, alpha = std::max(alpha, bestValue);
711 CapturePieceToHistory& captureHistory = thisThread->captureHistory;
713 // Step 6. Static evaluation of the position
716 // Skip early pruning when in check
717 ss->staticEval = eval = VALUE_NONE;
721 else if (excludedMove)
723 // Providing the hint that this node's accumulator will be used often brings significant Elo gain (~13 Elo)
724 Eval::NNUE::hint_common_parent_position(pos);
725 eval = ss->staticEval;
729 // Never assume anything about values stored in TT
730 ss->staticEval = eval = tte->eval();
731 if (eval == VALUE_NONE)
732 ss->staticEval = eval = evaluate(pos);
734 Eval::NNUE::hint_common_parent_position(pos);
736 // ttValue can be used as a better position evaluation (~7 Elo)
737 if (ttValue != VALUE_NONE && (tte->bound() & (ttValue > eval ? BOUND_LOWER : BOUND_UPPER)))
742 ss->staticEval = eval = evaluate(pos);
743 // Save static evaluation into the transposition table
744 tte->save(posKey, VALUE_NONE, ss->ttPv, BOUND_NONE, DEPTH_NONE, MOVE_NONE, eval);
747 // Use static evaluation difference to improve quiet move ordering (~4 Elo)
748 if (is_ok((ss - 1)->currentMove) && !(ss - 1)->inCheck && !priorCapture)
750 int bonus = std::clamp(-18 * int((ss - 1)->staticEval + ss->staticEval), -1812, 1812);
751 thisThread->mainHistory[~us][from_to((ss - 1)->currentMove)] << bonus;
754 // Set up the improving flag, which is true if current static evaluation is
755 // bigger than the previous static evaluation at our turn (if we were in
756 // check at our previous move we look at static evaluation at move prior to it
757 // and if we were in check at move prior to it flag is set to true) and is
758 // false otherwise. The improving flag is used in various pruning heuristics.
759 improving = (ss - 2)->staticEval != VALUE_NONE ? ss->staticEval > (ss - 2)->staticEval
760 : (ss - 4)->staticEval != VALUE_NONE ? ss->staticEval > (ss - 4)->staticEval
763 // Step 7. Razoring (~1 Elo)
764 // If eval is really low check with qsearch if it can exceed alpha, if it can't,
765 // return a fail low.
766 // Adjust razor margin according to cutoffCnt. (~1 Elo)
767 if (eval < alpha - 492 - (257 - 200 * ((ss + 1)->cutoffCnt > 3)) * depth * depth)
769 value = qsearch<NonPV>(pos, ss, alpha - 1, alpha);
774 // Step 8. Futility pruning: child node (~40 Elo)
775 // The depth condition is important for mate finding.
776 if (!ss->ttPv && depth < 9
777 && eval - futility_margin(depth, cutNode && !ss->ttHit, improving)
778 - (ss - 1)->statScore / 321
780 && eval >= beta && eval < 29462 // smaller than TB wins
781 && !(!ttCapture && ttMove))
784 // Step 9. Null move search with verification search (~35 Elo)
785 if (!PvNode && (ss - 1)->currentMove != MOVE_NULL && (ss - 1)->statScore < 17257 && eval >= beta
786 && eval >= ss->staticEval && ss->staticEval >= beta - 24 * depth + 281 && !excludedMove
787 && pos.non_pawn_material(us) && ss->ply >= thisThread->nmpMinPly
788 && beta > VALUE_TB_LOSS_IN_MAX_PLY)
790 assert(eval - beta >= 0);
792 // Null move dynamic reduction based on depth and eval
793 Depth R = std::min(int(eval - beta) / 152, 6) + depth / 3 + 4;
795 ss->currentMove = MOVE_NULL;
796 ss->continuationHistory = &thisThread->continuationHistory[0][0][NO_PIECE][0];
798 pos.do_null_move(st);
800 Value nullValue = -search<NonPV>(pos, ss + 1, -beta, -beta + 1, depth - R, !cutNode);
802 pos.undo_null_move();
804 // Do not return unproven mate or TB scores
805 if (nullValue >= beta && nullValue < VALUE_TB_WIN_IN_MAX_PLY)
807 if (thisThread->nmpMinPly || depth < 14)
810 assert(!thisThread->nmpMinPly); // Recursive verification is not allowed
812 // Do verification search at high depths, with null move pruning disabled
813 // until ply exceeds nmpMinPly.
814 thisThread->nmpMinPly = ss->ply + 3 * (depth - R) / 4;
816 Value v = search<NonPV>(pos, ss, beta - 1, beta, depth - R, false);
818 thisThread->nmpMinPly = 0;
825 // Step 10. If the position doesn't have a ttMove, decrease depth by 2
826 // (or by 4 if the TT entry for the current position was hit and the stored depth is greater than or equal to the current depth).
827 // Use qsearch if depth is equal or below zero (~9 Elo)
828 if (PvNode && !ttMove)
829 depth -= 2 + 2 * (ss->ttHit && tte->depth() >= depth);
832 return qsearch<PV>(pos, ss, alpha, beta);
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);
855 while ((move = mp.next_move()) != MOVE_NONE)
856 if (move != excludedMove && pos.legal(move))
858 assert(pos.capture_stage(move));
860 ss->currentMove = move;
861 ss->continuationHistory =
863 ->continuationHistory[ss->inCheck][true][pos.moved_piece(move)][to_sq(move)];
865 pos.do_move(move, st);
867 // Perform a preliminary qsearch to verify that the move holds
868 value = -qsearch<NonPV>(pos, ss + 1, -probCutBeta, -probCutBeta + 1);
870 // If the qsearch held, perform the regular search
871 if (value >= probCutBeta)
872 value = -search<NonPV>(pos, ss + 1, -probCutBeta, -probCutBeta + 1, depth - 4,
877 if (value >= probCutBeta)
879 // Save ProbCut data into transposition table
880 tte->save(posKey, value_to_tt(value, ss->ply), ss->ttPv, BOUND_LOWER, depth - 3,
881 move, ss->staticEval);
882 return value - (probCutBeta - beta);
886 Eval::NNUE::hint_common_parent_position(pos);
889 moves_loop: // When in check, search starts here
891 // Step 12. A small Probcut idea, when we are in check (~4 Elo)
892 probCutBeta = beta + 416;
893 if (ss->inCheck && !PvNode && ttCapture && (tte->bound() & BOUND_LOWER)
894 && tte->depth() >= depth - 4 && ttValue >= probCutBeta
895 && abs(ttValue) < VALUE_TB_WIN_IN_MAX_PLY && abs(beta) < VALUE_TB_WIN_IN_MAX_PLY)
898 const PieceToHistory* contHist[] = {(ss - 1)->continuationHistory,
899 (ss - 2)->continuationHistory,
900 (ss - 3)->continuationHistory,
901 (ss - 4)->continuationHistory,
903 (ss - 6)->continuationHistory};
906 prevSq != SQ_NONE ? thisThread->counterMoves[pos.piece_on(prevSq)][prevSq] : MOVE_NONE;
908 MovePicker mp(pos, ttMove, depth, &thisThread->mainHistory, &captureHistory, contHist,
909 countermove, ss->killers);
912 moveCountPruning = singularQuietLMR = false;
914 // Indicate PvNodes that will probably fail low if the node was searched
915 // at a depth equal to or greater than the current depth, and the result
916 // of this search was a fail low.
917 bool likelyFailLow = PvNode && ttMove && (tte->bound() & BOUND_UPPER) && tte->depth() >= depth;
919 // Step 13. Loop through all pseudo-legal moves until no moves remain
920 // or a beta cutoff occurs.
921 while ((move = mp.next_move(moveCountPruning)) != MOVE_NONE)
925 if (move == excludedMove)
928 // Check for legality
929 if (!pos.legal(move))
932 // At root obey the "searchmoves" option and skip moves not listed in Root
933 // Move List. In MultiPV mode we also skip PV moves that have been already
934 // searched and those of lower "TB rank" if we are in a TB root position.
936 && !std::count(thisThread->rootMoves.begin() + thisThread->pvIdx,
937 thisThread->rootMoves.begin() + thisThread->pvLast, move))
940 ss->moveCount = ++moveCount;
942 if (rootNode && thisThread == Threads.main() && Time.elapsed() > 3000)
943 sync_cout << "info depth " << depth << " currmove "
944 << UCI::move(move, pos.is_chess960()) << " currmovenumber "
945 << moveCount + thisThread->pvIdx << sync_endl;
947 (ss + 1)->pv = nullptr;
950 capture = pos.capture_stage(move);
951 movedPiece = pos.moved_piece(move);
952 givesCheck = pos.gives_check(move);
954 // Calculate new depth for this move
955 newDepth = depth - 1;
957 Value delta = beta - alpha;
959 Depth r = reduction(improving, depth, moveCount, delta, thisThread->rootDelta);
961 // Step 14. Pruning at shallow depth (~120 Elo).
962 // Depth conditions are important for mate finding.
963 if (!rootNode && pos.non_pawn_material(us) && bestValue > VALUE_TB_LOSS_IN_MAX_PLY)
965 // Skip quiet moves if movecount exceeds our FutilityMoveCount threshold (~8 Elo)
966 if (!moveCountPruning)
967 moveCountPruning = moveCount >= futility_move_count(improving, depth);
969 // Reduced depth of the next LMR search
970 int lmrDepth = newDepth - r;
972 if (capture || givesCheck)
974 // Futility pruning for captures (~2 Elo)
975 if (!givesCheck && lmrDepth < 7 && !ss->inCheck
976 && ss->staticEval + 188 + 206 * lmrDepth + PieceValue[pos.piece_on(to_sq(move))]
977 + captureHistory[movedPiece][to_sq(move)]
978 [type_of(pos.piece_on(to_sq(move)))]
983 // SEE based pruning for captures and checks (~11 Elo)
984 if (!pos.see_ge(move, Value(-185) * depth))
989 int history = (*contHist[0])[movedPiece][to_sq(move)]
990 + (*contHist[1])[movedPiece][to_sq(move)]
991 + (*contHist[3])[movedPiece][to_sq(move)];
993 // Continuation history based pruning (~2 Elo)
994 if (lmrDepth < 6 && history < -3232 * depth)
997 history += 2 * thisThread->mainHistory[us][from_to(move)];
999 lmrDepth += history / 5793;
1000 lmrDepth = std::max(lmrDepth, -2);
1002 // Futility pruning: parent node (~13 Elo)
1003 if (!ss->inCheck && lmrDepth < 13 && ss->staticEval + 115 + 122 * lmrDepth <= alpha)
1006 lmrDepth = std::max(lmrDepth, 0);
1008 // Prune moves with negative SEE (~4 Elo)
1009 if (!pos.see_ge(move, Value(-27 * lmrDepth * lmrDepth)))
1014 // Step 15. Extensions (~100 Elo)
1015 // We take care to not overdo to avoid search getting stuck.
1016 if (ss->ply < thisThread->rootDepth * 2)
1018 // Singular extension search (~94 Elo). If all moves but one fail low on a
1019 // search of (alpha-s, beta-s), and just one fails high on (alpha, beta),
1020 // then that move is singular and should be extended. To verify this we do
1021 // a reduced search on all the other moves but the ttMove and if the result
1022 // is lower than ttValue minus a margin, then we will extend the ttMove. Note
1023 // that depth margin and singularBeta margin are known for having non-linear
1024 // scaling. Their values are optimized to time controls of 180+1.8 and longer
1025 // so changing them requires tests at this type of time controls.
1027 && depth >= 4 - (thisThread->completedDepth > 24) + 2 * (PvNode && tte->is_pv())
1028 && move == ttMove && !excludedMove // Avoid recursive singular search
1029 && abs(ttValue) < VALUE_TB_WIN_IN_MAX_PLY && (tte->bound() & BOUND_LOWER)
1030 && tte->depth() >= depth - 3)
1032 Value singularBeta = ttValue - (64 + 57 * (ss->ttPv && !PvNode)) * depth / 64;
1033 Depth singularDepth = (depth - 1) / 2;
1035 ss->excludedMove = move;
1037 search<NonPV>(pos, ss, singularBeta - 1, singularBeta, singularDepth, cutNode);
1038 ss->excludedMove = MOVE_NONE;
1040 if (value < singularBeta)
1043 singularQuietLMR = !ttCapture;
1045 // Avoid search explosion by limiting the number of double extensions
1046 if (!PvNode && value < singularBeta - 18 && ss->doubleExtensions <= 11)
1049 depth += depth < 15;
1053 // Multi-cut pruning
1054 // Our ttMove is assumed to fail high, and now we failed high also on a
1055 // reduced search without the ttMove. So we assume this expected cut-node
1056 // is not singular, that multiple moves fail high, and we can prune the
1057 // whole subtree by returning a softbound.
1058 else if (singularBeta >= beta)
1059 return singularBeta;
1061 // If the eval of ttMove is greater than beta, we reduce it (negative extension) (~7 Elo)
1062 else if (ttValue >= beta)
1063 extension = -2 - !PvNode;
1065 // If we are on a cutNode, reduce it based on depth (negative extension) (~1 Elo)
1067 extension = depth < 19 ? -2 : -1;
1069 // If the eval of ttMove is less than value, we reduce it (negative extension) (~1 Elo)
1070 else if (ttValue <= value)
1074 // Check extensions (~1 Elo)
1075 else if (givesCheck && depth > 9)
1078 // Quiet ttMove extensions (~1 Elo)
1079 else if (PvNode && move == ttMove && move == ss->killers[0]
1080 && (*contHist[0])[movedPiece][to_sq(move)] >= 4194)
1084 // Add extension to new depth
1085 newDepth += extension;
1086 ss->doubleExtensions = (ss - 1)->doubleExtensions + (extension == 2);
1088 // Speculative prefetch as early as possible
1089 prefetch(TT.first_entry(pos.key_after(move)));
1091 // Update the current move (this must be done after singular extension search)
1092 ss->currentMove = move;
1093 ss->continuationHistory =
1094 &thisThread->continuationHistory[ss->inCheck][capture][movedPiece][to_sq(move)];
1096 // Step 16. Make the move
1097 pos.do_move(move, st, givesCheck);
1099 // Decrease reduction if position is or has been on the PV (~4 Elo)
1100 if (ss->ttPv && !likelyFailLow)
1101 r -= cutNode && tte->depth() >= depth ? 3 : 2;
1103 // Decrease reduction if opponent's move count is high (~1 Elo)
1104 if ((ss - 1)->moveCount > 7)
1107 // Increase reduction for cut nodes (~3 Elo)
1111 // Increase reduction if ttMove is a capture (~3 Elo)
1115 // Decrease reduction for PvNodes (~2 Elo)
1119 // Decrease reduction if ttMove has been singularly extended (~1 Elo)
1120 if (singularQuietLMR)
1123 // Increase reduction on repetition (~1 Elo)
1124 if (move == (ss - 4)->currentMove && pos.has_repeated())
1127 // Increase reduction if next ply has a lot of fail high (~5 Elo)
1128 if ((ss + 1)->cutoffCnt > 3)
1131 // Decrease reduction for first generated move (ttMove)
1132 else if (move == ttMove)
1135 ss->statScore = 2 * thisThread->mainHistory[us][from_to(move)]
1136 + (*contHist[0])[movedPiece][to_sq(move)]
1137 + (*contHist[1])[movedPiece][to_sq(move)]
1138 + (*contHist[3])[movedPiece][to_sq(move)] - 3848;
1140 // Decrease/increase reduction for moves with a good/bad history (~25 Elo)
1141 r -= ss->statScore / (10216 + 3855 * (depth > 5 && depth < 23));
1143 // Step 17. Late moves reduction / extension (LMR, ~117 Elo)
1144 // We use various heuristics for the sons of a node after the first son has
1145 // been searched. In general, we would like to reduce them, but there are many
1146 // cases where we extend a son if it has good chances to be "interesting".
1147 if (depth >= 2 && moveCount > 1 + (PvNode && ss->ply <= 1)
1148 && (!ss->ttPv || !capture || (cutNode && (ss - 1)->moveCount > 1)))
1150 // In general we want to cap the LMR depth search at newDepth, but when
1151 // reduction is negative, we allow this move a limited search extension
1152 // beyond the first move depth. This may lead to hidden double extensions.
1153 Depth d = std::clamp(newDepth - r, 1, newDepth + 1);
1155 value = -search<NonPV>(pos, ss + 1, -(alpha + 1), -alpha, d, true);
1157 // Do a full-depth search when reduced LMR search fails high
1158 if (value > alpha && d < newDepth)
1160 // Adjust full-depth search based on LMR results - if the result
1161 // was good enough search deeper, if it was bad enough search shallower.
1162 const bool doDeeperSearch = value > (bestValue + 51 + 10 * (newDepth - d));
1163 const bool doEvenDeeperSearch = value > alpha + 700 && ss->doubleExtensions <= 6;
1164 const bool doShallowerSearch = value < bestValue + newDepth;
1166 ss->doubleExtensions = ss->doubleExtensions + doEvenDeeperSearch;
1168 newDepth += doDeeperSearch - doShallowerSearch + doEvenDeeperSearch;
1171 value = -search<NonPV>(pos, ss + 1, -(alpha + 1), -alpha, newDepth, !cutNode);
1173 int bonus = value <= alpha ? -stat_bonus(newDepth)
1174 : value >= beta ? stat_bonus(newDepth)
1177 update_continuation_histories(ss, movedPiece, to_sq(move), bonus);
1181 // Step 18. Full-depth search when LMR is skipped
1182 else if (!PvNode || moveCount > 1)
1184 // Increase reduction for cut nodes and not ttMove (~1 Elo)
1185 if (!ttMove && cutNode)
1188 // Note that if expected reduction is high, we reduce search depth by 1 here
1189 value = -search<NonPV>(pos, ss + 1, -(alpha + 1), -alpha, newDepth - (r > 3), !cutNode);
1192 // For PV nodes only, do a full PV search on the first move or after a fail high,
1193 // otherwise let the parent node fail low with value <= alpha and try another move.
1194 if (PvNode && (moveCount == 1 || value > alpha))
1197 (ss + 1)->pv[0] = MOVE_NONE;
1199 value = -search<PV>(pos, ss + 1, -beta, -alpha, newDepth, false);
1202 // Step 19. Undo move
1203 pos.undo_move(move);
1205 assert(value > -VALUE_INFINITE && value < VALUE_INFINITE);
1207 // Step 20. Check for a new best move
1208 // Finished searching the move. If a stop occurred, the return value of
1209 // the search cannot be trusted, and we return immediately without
1210 // updating best move, PV and TT.
1211 if (Threads.stop.load(std::memory_order_relaxed))
1217 *std::find(thisThread->rootMoves.begin(), thisThread->rootMoves.end(), move);
1220 rm.averageScore != -VALUE_INFINITE ? (2 * value + rm.averageScore) / 3 : value;
1222 // PV move or new best move?
1223 if (moveCount == 1 || value > alpha)
1225 rm.score = rm.uciScore = value;
1226 rm.selDepth = thisThread->selDepth;
1227 rm.scoreLowerbound = rm.scoreUpperbound = false;
1231 rm.scoreLowerbound = true;
1234 else if (value <= alpha)
1236 rm.scoreUpperbound = true;
1237 rm.uciScore = alpha;
1242 assert((ss + 1)->pv);
1244 for (Move* m = (ss + 1)->pv; *m != MOVE_NONE; ++m)
1245 rm.pv.push_back(*m);
1247 // We record how often the best move has been changed in each iteration.
1248 // This information is used for time management. In MultiPV mode,
1249 // we must take care to only do this for the first PV line.
1250 if (moveCount > 1 && !thisThread->pvIdx)
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);
1273 ss->cutoffCnt += 1 + !ttMove;
1274 assert(value >= beta); // Fail high
1279 // Reduce other moves if we have found at least one score improvement (~2 Elo)
1280 if (depth > 2 && depth < 12 && beta < 13828 && value > -11369)
1284 alpha = value; // Update alpha! Always alpha < beta
1289 // If the move is worse than some previously searched move,
1290 // remember it, to update its stats later.
1291 if (move != bestMove && moveCount <= 32)
1294 capturesSearched[captureCount++] = move;
1297 quietsSearched[quietCount++] = move;
1301 // Step 21. 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 : ss->inCheck ? mated_in(ss->ply) : VALUE_DRAW;
1311 // If there is a move that produces search value greater than alpha we update the stats of searched moves
1313 update_all_stats(pos, ss, bestMove, bestValue, beta, prevSq, quietsSearched, quietCount,
1314 capturesSearched, captureCount, depth);
1316 // Bonus for prior countermove that caused the fail low
1317 else if (!priorCapture && prevSq != SQ_NONE)
1319 int bonus = (depth > 6) + (PvNode || cutNode) + (bestValue < alpha - 653)
1320 + ((ss - 1)->moveCount > 11);
1321 update_continuation_histories(ss - 1, pos.piece_on(prevSq), prevSq,
1322 stat_bonus(depth) * bonus);
1323 thisThread->mainHistory[~us][from_to((ss - 1)->currentMove)]
1324 << stat_bonus(depth) * bonus / 2;
1328 bestValue = std::min(bestValue, maxValue);
1330 // If no good move is found and the previous position was ttPv, then the previous
1331 // opponent move is probably good and the new position is added to the search tree. (~7 Elo)
1332 if (bestValue <= alpha)
1333 ss->ttPv = ss->ttPv || ((ss - 1)->ttPv && depth > 3);
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
1341 depth, bestMove, ss->staticEval);
1343 assert(bestValue > -VALUE_INFINITE && bestValue < VALUE_INFINITE);
1349 // qsearch() is the quiescence search function, which is called by the main search
1350 // function with zero depth, or recursively with further decreasing depth per call.
1352 template<NodeType nodeType>
1353 Value qsearch(Position& pos, Stack* ss, Value alpha, Value beta, Depth depth) {
1355 static_assert(nodeType != Root);
1356 constexpr bool PvNode = nodeType == PV;
1358 assert(alpha >= -VALUE_INFINITE && alpha < beta && beta <= VALUE_INFINITE);
1359 assert(PvNode || (alpha == beta - 1));
1362 // Check if we have an upcoming move that draws by repetition, or
1363 // if the opponent had an alternative move earlier to this position.
1364 if (alpha < VALUE_DRAW && pos.has_game_cycle(ss->ply))
1366 alpha = value_draw(pos.this_thread());
1371 Move pv[MAX_PLY + 1];
1373 ASSERT_ALIGNED(&st, Eval::NNUE::CacheLineSize);
1377 Move ttMove, move, bestMove;
1379 Value bestValue, value, ttValue, futilityValue, futilityBase;
1380 bool pvHit, givesCheck, capture;
1382 Color us = pos.side_to_move();
1384 // Step 1. Initialize node
1388 ss->pv[0] = MOVE_NONE;
1391 Thread* thisThread = pos.this_thread();
1392 bestMove = MOVE_NONE;
1393 ss->inCheck = pos.checkers();
1396 // Step 2. Check for an immediate draw or maximum ply reached
1397 if (pos.is_draw(ss->ply) || ss->ply >= MAX_PLY)
1398 return (ss->ply >= MAX_PLY && !ss->inCheck) ? evaluate(pos) : VALUE_DRAW;
1400 assert(0 <= ss->ply && ss->ply < MAX_PLY);
1402 // Decide whether or not to include checks: this fixes also the type of
1403 // TT entry depth that we are going to use. Note that in qsearch we use
1404 // only two types of depth in TT: DEPTH_QS_CHECKS or DEPTH_QS_NO_CHECKS.
1405 ttDepth = ss->inCheck || depth >= DEPTH_QS_CHECKS ? DEPTH_QS_CHECKS : DEPTH_QS_NO_CHECKS;
1407 // Step 3. Transposition table lookup
1409 tte = TT.probe(posKey, ss->ttHit);
1410 ttValue = ss->ttHit ? value_from_tt(tte->value(), ss->ply, pos.rule50_count()) : VALUE_NONE;
1411 ttMove = ss->ttHit ? tte->move() : MOVE_NONE;
1412 pvHit = ss->ttHit && tte->is_pv();
1414 // At non-PV nodes we check for an early TT cutoff
1415 if (!PvNode && tte->depth() >= ttDepth
1416 && ttValue != VALUE_NONE // Only in case of TT access race or if !ttHit
1417 && (tte->bound() & (ttValue >= beta ? BOUND_LOWER : BOUND_UPPER)))
1420 // Step 4. Static evaluation of the position
1422 bestValue = futilityBase = -VALUE_INFINITE;
1427 // Never assume anything about values stored in TT
1428 if ((ss->staticEval = bestValue = tte->eval()) == VALUE_NONE)
1429 ss->staticEval = bestValue = evaluate(pos);
1431 // ttValue can be used as a better position evaluation (~13 Elo)
1432 if (ttValue != VALUE_NONE
1433 && (tte->bound() & (ttValue > bestValue ? BOUND_LOWER : BOUND_UPPER)))
1434 bestValue = ttValue;
1437 // In case of null move search use previous static eval with a different sign
1438 ss->staticEval = bestValue =
1439 (ss - 1)->currentMove != MOVE_NULL ? evaluate(pos) : -(ss - 1)->staticEval;
1441 // Stand pat. Return immediately if static value is at least beta
1442 if (bestValue >= beta)
1445 tte->save(posKey, value_to_tt(bestValue, ss->ply), false, BOUND_LOWER, DEPTH_NONE,
1446 MOVE_NONE, ss->staticEval);
1451 if (bestValue > alpha)
1454 futilityBase = ss->staticEval + 200;
1457 const PieceToHistory* contHist[] = {(ss - 1)->continuationHistory,
1458 (ss - 2)->continuationHistory};
1460 // Initialize a MovePicker object for the current position, and prepare
1461 // to search the moves. Because the depth is <= 0 here, only captures,
1462 // queen promotions, and other checks (only if depth >= DEPTH_QS_CHECKS)
1463 // will be generated.
1464 Square prevSq = is_ok((ss - 1)->currentMove) ? to_sq((ss - 1)->currentMove) : SQ_NONE;
1465 MovePicker mp(pos, ttMove, depth, &thisThread->mainHistory, &thisThread->captureHistory,
1468 int quietCheckEvasions = 0;
1470 // Step 5. Loop through all pseudo-legal moves until no moves remain
1471 // or a beta cutoff occurs.
1472 while ((move = mp.next_move()) != MOVE_NONE)
1474 assert(is_ok(move));
1476 // Check for legality
1477 if (!pos.legal(move))
1480 givesCheck = pos.gives_check(move);
1481 capture = pos.capture_stage(move);
1486 if (bestValue > VALUE_TB_LOSS_IN_MAX_PLY && pos.non_pawn_material(us))
1488 // Futility pruning and moveCount pruning (~10 Elo)
1489 if (!givesCheck && to_sq(move) != prevSq && futilityBase > VALUE_TB_LOSS_IN_MAX_PLY
1490 && type_of(move) != PROMOTION)
1495 futilityValue = futilityBase + PieceValue[pos.piece_on(to_sq(move))];
1497 // If static eval + value of piece we are going to capture is much lower
1498 // than alpha we can prune this move.
1499 if (futilityValue <= alpha)
1501 bestValue = std::max(bestValue, futilityValue);
1505 // If static eval is much lower than alpha and move is not winning material
1506 // we can prune this move.
1507 if (futilityBase <= alpha && !pos.see_ge(move, VALUE_ZERO + 1))
1509 bestValue = std::max(bestValue, futilityBase);
1513 // If static exchange evaluation is much worse than what is needed to not
1514 // fall below alpha we can prune this move.
1515 if (futilityBase > alpha && !pos.see_ge(move, (alpha - futilityBase) * 4))
1522 // We prune after the second quiet check evasion move, where being 'in check' is
1523 // implicitly checked through the counter, and being a 'quiet move' apart from
1524 // being a tt move is assumed after an increment because captures are pushed ahead.
1525 if (quietCheckEvasions > 1)
1528 // Continuation history based pruning (~3 Elo)
1529 if (!capture && (*contHist[0])[pos.moved_piece(move)][to_sq(move)] < 0
1530 && (*contHist[1])[pos.moved_piece(move)][to_sq(move)] < 0)
1533 // Do not search moves with bad enough SEE values (~5 Elo)
1534 if (!pos.see_ge(move, Value(-90)))
1538 // Speculative prefetch as early as possible
1539 prefetch(TT.first_entry(pos.key_after(move)));
1541 // Update the current move
1542 ss->currentMove = move;
1543 ss->continuationHistory =
1545 ->continuationHistory[ss->inCheck][capture][pos.moved_piece(move)][to_sq(move)];
1547 quietCheckEvasions += !capture && ss->inCheck;
1549 // Step 7. Make and search the move
1550 pos.do_move(move, st, givesCheck);
1551 value = -qsearch<nodeType>(pos, ss + 1, -beta, -alpha, depth - 1);
1552 pos.undo_move(move);
1554 assert(value > -VALUE_INFINITE && value < VALUE_INFINITE);
1556 // Step 8. Check for a new best move
1557 if (value > bestValue)
1565 if (PvNode) // Update pv even in fail-high case
1566 update_pv(ss->pv, move, (ss + 1)->pv);
1568 if (value < beta) // Update alpha here!
1576 // Step 9. Check for mate
1577 // All legal moves have been searched. A special case: if we're in check
1578 // and no legal moves were found, it is checkmate.
1579 if (ss->inCheck && bestValue == -VALUE_INFINITE)
1581 assert(!MoveList<LEGAL>(pos).size());
1583 return mated_in(ss->ply); // Plies to mate from the root
1586 // Save gathered info in transposition table
1587 tte->save(posKey, value_to_tt(bestValue, ss->ply), pvHit,
1588 bestValue >= beta ? BOUND_LOWER : BOUND_UPPER, ttDepth, bestMove, ss->staticEval);
1590 assert(bestValue > -VALUE_INFINITE && bestValue < VALUE_INFINITE);
1596 // value_to_tt() adjusts a mate or TB score from "plies to mate from the root"
1597 // to "plies to mate from the current position". Standard scores are unchanged.
1598 // The function is called before storing a value in the transposition table.
1600 Value value_to_tt(Value v, int ply) {
1602 assert(v != VALUE_NONE);
1604 return v >= VALUE_TB_WIN_IN_MAX_PLY ? v + ply : v <= VALUE_TB_LOSS_IN_MAX_PLY ? v - ply : v;
1608 // value_from_tt() is the inverse of value_to_tt(): it adjusts a mate or TB score
1609 // from the transposition table (which refers to the plies to mate/be mated from
1610 // current position) to "plies to mate/be mated (TB win/loss) from the root".
1611 // However, to avoid potentially false mate scores related to the 50 moves rule
1612 // and the graph history interaction problem, we return an optimal TB score instead.
1614 Value value_from_tt(Value v, int ply, int r50c) {
1616 if (v == VALUE_NONE)
1619 if (v >= VALUE_TB_WIN_IN_MAX_PLY) // TB win or better
1621 if (v >= VALUE_MATE_IN_MAX_PLY && VALUE_MATE - v > 99 - r50c)
1622 return VALUE_MATE_IN_MAX_PLY - 1; // do not return a potentially false mate score
1627 if (v <= VALUE_TB_LOSS_IN_MAX_PLY) // TB loss or worse
1629 if (v <= VALUE_MATED_IN_MAX_PLY && VALUE_MATE + v > 99 - r50c)
1630 return VALUE_MATED_IN_MAX_PLY + 1; // do not return a potentially false mate score
1639 // update_pv() adds current move and appends child pv[]
1641 void update_pv(Move* pv, Move move, const Move* childPv) {
1643 for (*pv++ = move; childPv && *childPv != MOVE_NONE;)
1649 // update_all_stats() updates stats at the end of search() when a bestMove is found
1651 void update_all_stats(const Position& pos,
1657 Move* quietsSearched,
1659 Move* capturesSearched,
1663 Color us = pos.side_to_move();
1664 Thread* thisThread = pos.this_thread();
1665 CapturePieceToHistory& captureHistory = thisThread->captureHistory;
1666 Piece moved_piece = pos.moved_piece(bestMove);
1669 int quietMoveBonus = stat_bonus(depth + 1);
1671 if (!pos.capture_stage(bestMove))
1673 int bestMoveBonus = bestValue > beta + 168 ? quietMoveBonus // larger bonus
1674 : stat_bonus(depth); // smaller bonus
1676 // Increase stats for the best move in case it was a quiet move
1677 update_quiet_stats(pos, ss, bestMove, bestMoveBonus);
1679 // Decrease stats for all non-best quiet moves
1680 for (int i = 0; i < quietCount; ++i)
1682 thisThread->mainHistory[us][from_to(quietsSearched[i])] << -bestMoveBonus;
1683 update_continuation_histories(ss, pos.moved_piece(quietsSearched[i]),
1684 to_sq(quietsSearched[i]), -bestMoveBonus);
1689 // Increase stats for the best move in case it was a capture move
1690 captured = type_of(pos.piece_on(to_sq(bestMove)));
1691 captureHistory[moved_piece][to_sq(bestMove)][captured] << quietMoveBonus;
1694 // Extra penalty for a quiet early move that was not a TT move or
1695 // main killer move in previous ply when it gets refuted.
1696 if (prevSq != SQ_NONE
1697 && ((ss - 1)->moveCount == 1 + (ss - 1)->ttHit
1698 || ((ss - 1)->currentMove == (ss - 1)->killers[0]))
1699 && !pos.captured_piece())
1700 update_continuation_histories(ss - 1, pos.piece_on(prevSq), prevSq, -quietMoveBonus);
1702 // Decrease stats for all non-best capture moves
1703 for (int i = 0; i < captureCount; ++i)
1705 moved_piece = pos.moved_piece(capturesSearched[i]);
1706 captured = type_of(pos.piece_on(to_sq(capturesSearched[i])));
1707 captureHistory[moved_piece][to_sq(capturesSearched[i])][captured] << -quietMoveBonus;
1712 // update_continuation_histories() updates histories of the move pairs formed
1713 // by moves at ply -1, -2, -4, and -6 with current move.
1715 void update_continuation_histories(Stack* ss, Piece pc, Square to, int bonus) {
1717 for (int i : {1, 2, 3, 4, 6})
1719 // Only update the first 2 continuation histories if we are in check
1720 if (ss->inCheck && i > 2)
1722 if (is_ok((ss - i)->currentMove))
1723 (*(ss - i)->continuationHistory)[pc][to] << bonus / (1 + 3 * (i == 3));
1728 // update_quiet_stats() updates move sorting heuristics
1730 void update_quiet_stats(const Position& pos, Stack* ss, Move move, int bonus) {
1733 if (ss->killers[0] != move)
1735 ss->killers[1] = ss->killers[0];
1736 ss->killers[0] = move;
1739 Color us = pos.side_to_move();
1740 Thread* thisThread = pos.this_thread();
1741 thisThread->mainHistory[us][from_to(move)] << bonus;
1742 update_continuation_histories(ss, pos.moved_piece(move), to_sq(move), bonus);
1744 // Update countermove history
1745 if (is_ok((ss - 1)->currentMove))
1747 Square prevSq = to_sq((ss - 1)->currentMove);
1748 thisThread->counterMoves[pos.piece_on(prevSq)][prevSq] = move;
1752 // When playing with strength handicap, choose the best move among a set of RootMoves
1753 // using a statistical rule dependent on 'level'. Idea by Heinz van Saanen.
1755 Move Skill::pick_best(size_t multiPV) {
1757 const RootMoves& rootMoves = Threads.main()->rootMoves;
1758 static PRNG rng(now()); // PRNG sequence should be non-deterministic
1760 // RootMoves are already sorted by score in descending order
1761 Value topScore = rootMoves[0].score;
1762 int delta = std::min(topScore - rootMoves[multiPV - 1].score, PawnValue);
1763 int maxScore = -VALUE_INFINITE;
1764 double weakness = 120 - 2 * level;
1766 // Choose best move. For each move score we add two terms, both dependent on
1767 // weakness. One is deterministic and bigger for weaker levels, and one is
1768 // random. Then we choose the move with the resulting highest score.
1769 for (size_t i = 0; i < multiPV; ++i)
1771 // This is our magic formula
1772 int push = int((weakness * int(topScore - rootMoves[i].score)
1773 + delta * (rng.rand<unsigned>() % int(weakness)))
1776 if (rootMoves[i].score + push >= maxScore)
1778 maxScore = rootMoves[i].score + push;
1779 best = rootMoves[i].pv[0];
1789 // MainThread::check_time() is used to print debug info and, more importantly,
1790 // to detect when we are out of available time and thus stop the search.
1792 void MainThread::check_time() {
1797 // When using nodes, ensure checking rate is not lower than 0.1% of nodes
1798 callsCnt = Limits.nodes ? std::min(512, int(Limits.nodes / 1024)) : 512;
1800 static TimePoint lastInfoTime = now();
1802 TimePoint elapsed = Time.elapsed();
1803 TimePoint tick = Limits.startTime + elapsed;
1805 if (tick - lastInfoTime >= 1000)
1807 lastInfoTime = tick;
1811 // We should not stop pondering until told so by the GUI
1815 if ((Limits.use_time_management() && (elapsed > Time.maximum() || stopOnPonderhit))
1816 || (Limits.movetime && elapsed >= Limits.movetime)
1817 || (Limits.nodes && Threads.nodes_searched() >= uint64_t(Limits.nodes)))
1818 Threads.stop = true;
1822 // UCI::pv() formats PV information according to the UCI protocol. UCI requires
1823 // that all (if any) unsearched PV lines are sent using a previous search score.
1825 string UCI::pv(const Position& pos, Depth depth) {
1827 std::stringstream ss;
1828 TimePoint elapsed = Time.elapsed() + 1;
1829 const RootMoves& rootMoves = pos.this_thread()->rootMoves;
1830 size_t pvIdx = pos.this_thread()->pvIdx;
1831 size_t multiPV = std::min(size_t(Options["MultiPV"]), rootMoves.size());
1832 uint64_t nodesSearched = Threads.nodes_searched();
1833 uint64_t tbHits = Threads.tb_hits() + (TB::RootInTB ? rootMoves.size() : 0);
1835 for (size_t i = 0; i < multiPV; ++i)
1837 bool updated = rootMoves[i].score != -VALUE_INFINITE;
1839 if (depth == 1 && !updated && i > 0)
1842 Depth d = updated ? depth : std::max(1, depth - 1);
1843 Value v = updated ? rootMoves[i].uciScore : rootMoves[i].previousScore;
1845 if (v == -VALUE_INFINITE)
1848 bool tb = TB::RootInTB && abs(v) < VALUE_MATE_IN_MAX_PLY;
1849 v = tb ? rootMoves[i].tbScore : v;
1851 if (ss.rdbuf()->in_avail()) // Not at first line
1855 << " depth " << d << " seldepth " << rootMoves[i].selDepth << " multipv " << i + 1
1856 << " score " << UCI::value(v);
1858 if (Options["UCI_ShowWDL"])
1859 ss << UCI::wdl(v, pos.game_ply());
1861 if (i == pvIdx && !tb && updated) // tablebase- and previous-scores are exact
1862 ss << (rootMoves[i].scoreLowerbound
1864 : (rootMoves[i].scoreUpperbound ? " upperbound" : ""));
1866 ss << " nodes " << nodesSearched << " nps " << nodesSearched * 1000 / elapsed
1867 << " hashfull " << TT.hashfull() << " tbhits " << tbHits << " time " << elapsed << " pv";
1869 for (Move m : rootMoves[i].pv)
1870 ss << " " << UCI::move(m, pos.is_chess960());
1877 // RootMove::extract_ponder_from_tt() is called in case we have no ponder move
1878 // before exiting the search, for instance, in case we stop the search during a
1879 // fail high at root. We try hard to have a ponder move to return to the GUI,
1880 // otherwise in case of 'ponder on' we have nothing to think about.
1882 bool RootMove::extract_ponder_from_tt(Position& pos) {
1885 ASSERT_ALIGNED(&st, Eval::NNUE::CacheLineSize);
1889 assert(pv.size() == 1);
1891 if (pv[0] == MOVE_NONE)
1894 pos.do_move(pv[0], st);
1895 TTEntry* tte = TT.probe(pos.key(), ttHit);
1899 Move m = tte->move(); // Local copy to be SMP safe
1900 if (MoveList<LEGAL>(pos).contains(m))
1904 pos.undo_move(pv[0]);
1905 return pv.size() > 1;
1908 void Tablebases::rank_root_moves(Position& pos, Search::RootMoves& rootMoves) {
1911 UseRule50 = bool(Options["Syzygy50MoveRule"]);
1912 ProbeDepth = int(Options["SyzygyProbeDepth"]);
1913 Cardinality = int(Options["SyzygyProbeLimit"]);
1914 bool dtz_available = true;
1916 // Tables with fewer pieces than SyzygyProbeLimit are searched with
1917 // ProbeDepth == DEPTH_ZERO
1918 if (Cardinality > MaxCardinality)
1920 Cardinality = MaxCardinality;
1924 if (Cardinality >= popcount(pos.pieces()) && !pos.can_castle(ANY_CASTLING))
1926 // Rank moves using DTZ tables
1927 RootInTB = root_probe(pos, rootMoves);
1931 // DTZ tables are missing; try to rank moves using WDL tables
1932 dtz_available = false;
1933 RootInTB = root_probe_wdl(pos, rootMoves);
1939 // Sort moves according to TB rank
1940 std::stable_sort(rootMoves.begin(), rootMoves.end(),
1941 [](const RootMove& a, const RootMove& b) { return a.tbRank > b.tbRank; });
1943 // Probe during search only if DTZ is not available and we are winning
1944 if (dtz_available || rootMoves[0].tbScore <= VALUE_DRAW)
1949 // Clean up if root_probe() and root_probe_wdl() have failed
1950 for (auto& m : rootMoves)
1955 } // namespace Stockfish