Subversion Repositories Games.Chess Giants

/*

  Stockfish, a UCI chess playing engine derived from Glaurung 2.1

  Copyright (C) 2004-2008 Tord Romstad (Glaurung author)

  Copyright (C) 2008-2015 Marco Costalba, Joona Kiiski, Tord Romstad

  Copyright (C) 2015-2018 Marco Costalba, Joona Kiiski, Gary Linscott, Tord Romstad

  Stockfish is free software: you can redistribute it and/or modify

  it under the terms of the GNU General Public License as published by

  the Free Software Foundation, either version 3 of the License, or

  (at your option) any later version.

  Stockfish is distributed in the hope that it will be useful,

  but WITHOUT ANY WARRANTY; without even the implied warranty of

  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the

  GNU General Public License for more details.

  You should have received a copy of the GNU General Public License

  along with this program.  If not, see <http://www.gnu.org/licenses/>.

*/

#include <algorithm>

#include <cassert>

#include <cmath>

#include <cstring>   // For std::memset

#include <iostream>

#include <sstream>

#include "evaluate.h"

#include "misc.h"

#include "movegen.h"

#include "movepick.h"

#include "position.h"

#include "search.h"

#include "timeman.h"

#include "thread.h"

#include "tt.h"

#include "uci.h"

#include "syzygy/tbprobe.h"

namespace Search {

  LimitsType Limits;

}

namespace Tablebases {

  int Cardinality;

  bool RootInTB;

  bool UseRule50;

  Depth ProbeDepth;

  Value Score;

}

namespace TB = Tablebases;

using std::string;

using Eval::evaluate;

using namespace Search;

namespace {

  // Different node types, used as a template parameter

  enum NodeType { NonPV, PV };

  // Sizes and phases of the skip-blocks, used for distributing search depths across the threads

  const int skipSize[]  = { 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4 };

  const int skipPhase[] = { 0, 1, 0, 1, 2, 3, 0, 1, 2, 3, 4, 5, 0, 1, 2, 3, 4, 5, 6, 7 };

  // Razoring and futility margin based on depth

  const int razor_margin = 600;

  Value futility_margin(Depth d) { return Value(150 * d / ONE_PLY); }

  // Futility and reductions lookup tables, initialized at startup

  int FutilityMoveCounts[2][16]; // [improving][depth]

  int Reductions[2][2][64][64];  // [pv][improving][depth][moveNumber]

  template <bool PvNode> Depth reduction(bool i, Depth d, int mn) {

    return Reductions[PvNode][i][std::min(d / ONE_PLY, 63)][std::min(mn, 63)] * ONE_PLY;

  }

  // History and stats update bonus, based on depth

  int stat_bonus(Depth depth) {

    int d = depth / ONE_PLY;

    return d > 17 ? 0 : d * d + 2 * d - 2;

  }

  // Skill structure is used to implement strength limit

  struct Skill {

    explicit Skill(int l) : level(l) {}

    bool enabled() const { return level < 20; }

    bool time_to_pick(Depth depth) const { return depth / ONE_PLY == 1 + level; }

    Move pick_best(size_t multiPV);

    int level;

    Move best = MOVE_NONE;

  };

  template <NodeType NT>

  Value search(Position& pos, Stack* ss, Value alpha, Value beta, Depth depth, bool cutNode, bool skipEarlyPruning);

  template <NodeType NT, bool InCheck>

  Value qsearch(Position& pos, Stack* ss, Value alpha, Value beta, Depth depth = DEPTH_ZERO);

  Value value_to_tt(Value v, int ply);

  Value value_from_tt(Value v, int ply);

  void update_pv(Move* pv, Move move, Move* childPv);

  void update_continuation_histories(Stack* ss, Piece pc, Square to, int bonus);

  void update_stats(const Position& pos, Stack* ss, Move move, Move* quiets, int quietsCnt, int bonus);

  void update_capture_stats(const Position& pos, Move move, Move* captures, int captureCnt, int bonus);

  bool pv_is_draw(Position& pos);

  // perft() is our utility to verify move generation. All the leaf nodes up

  // to the given depth are generated and counted, and the sum is returned.

  template<bool Root>

  uint64_t perft(Position& pos, Depth depth) {

    StateInfo st;

    uint64_t cnt, nodes = 0;

    const bool leaf = (depth == 2 * ONE_PLY);

    for (const auto& m : MoveList<LEGAL>(pos))

    {

        if (Root && depth <= ONE_PLY)

            cnt = 1, nodes++;

        else

        {

            pos.do_move(m, st);

            cnt = leaf ? MoveList<LEGAL>(pos).size() : perft<false>(pos, depth - ONE_PLY);

            nodes += cnt;

            pos.undo_move(m);

        }

        if (Root)

            sync_cout << UCI::move(m, pos.is_chess960()) << ": " << cnt << sync_endl;

    }

    return nodes;

  }

} // namespace

/// Search::init() is called during startup to initialize various lookup tables

void Search::init() {

  for (int imp = 0; imp <= 1; ++imp)

      for (int d = 1; d < 64; ++d)

          for (int mc = 1; mc < 64; ++mc)

          {

              double r = log(d) * log(mc) / 1.95;

              Reductions[NonPV][imp][d][mc] = int(std::round(r));

              Reductions[PV][imp][d][mc] = std::max(Reductions[NonPV][imp][d][mc] - 1, 0);

              // Increase reduction for non-PV nodes when eval is not improving

              if (!imp && Reductions[NonPV][imp][d][mc] >= 2)

                Reductions[NonPV][imp][d][mc]++;

          }

  for (int d = 0; d < 16; ++d)

  {

      FutilityMoveCounts[0][d] = int(2.4 + 0.74 * pow(d, 1.78));

      FutilityMoveCounts[1][d] = int(5.0 + 1.00 * pow(d, 2.00));

  }

}

/// Search::clear() resets search state to its initial value

void Search::clear() {

  Threads.main()->wait_for_search_finished();

  Time.availableNodes = 0;

  TT.clear();

  Threads.clear();

}

/// MainThread::search() is called by the main thread when the program receives

/// the UCI 'go' command. It searches from the root position and outputs the "bestmove".

void MainThread::search() {

  if (Limits.perft)

  {

      nodes = perft<true>(rootPos, Limits.perft * ONE_PLY);

      sync_cout << "\nNodes searched: " << nodes << "\n" << sync_endl;

      return;

  }

  Color us = rootPos.side_to_move();

  Time.init(Limits, us, rootPos.game_ply());

  TT.new_search();

  int contempt = Options["Contempt"] * PawnValueEg / 100; // From centipawns

  Eval::Contempt = (us == WHITE ?  make_score(contempt, contempt / 2)

                                : -make_score(contempt, contempt / 2));

  if (rootMoves.empty())

  {

      rootMoves.emplace_back(MOVE_NONE);

      sync_cout << "info depth 0 score "

                << UCI::value(rootPos.checkers() ? -VALUE_MATE : VALUE_DRAW)

                << sync_endl;

  }

  else

  {

      for (Thread* th : Threads)

          if (th != this)

              th->start_searching();

      Thread::search(); // Let's start searching!

  }

  // When we reach the maximum depth, we can arrive here without a raise of

  // Threads.stop. However, if we are pondering or in an infinite search,

  // the UCI protocol states that we shouldn't print the best move before the

  // GUI sends a "stop" or "ponderhit" command. We therefore simply wait here

  // until the GUI sends one of those commands (which also raises Threads.stop).

  Threads.stopOnPonderhit = true;

  while (!Threads.stop && (Threads.ponder || Limits.infinite))

  {} // Busy wait for a stop or a ponder reset

  // Stop the threads if not already stopped (also raise the stop if

  // "ponderhit" just reset Threads.ponder).

  Threads.stop = true;

  // Wait until all threads have finished

  for (Thread* th : Threads)

      if (th != this)

          th->wait_for_search_finished();

  // When playing in 'nodes as time' mode, subtract the searched nodes from

  // the available ones before exiting.

  if (Limits.npmsec)

      Time.availableNodes += Limits.inc[us] - Threads.nodes_searched();

  // Check if there are threads with a better score than main thread

  Thread* bestThread = this;

  if (    Options["MultiPV"] == 1

      && !Limits.depth

      && !Skill(Options["Skill Level"]).enabled()

      &&  rootMoves[0].pv[0] != MOVE_NONE)

  {

      for (Thread* th : Threads)

      {

          Depth depthDiff = th->completedDepth - bestThread->completedDepth;

          Value scoreDiff = th->rootMoves[0].score - bestThread->rootMoves[0].score;

          // Select the thread with the best score, always if it is a mate

          if (    scoreDiff > 0

              && (depthDiff >= 0 || th->rootMoves[0].score >= VALUE_MATE_IN_MAX_PLY))

              bestThread = th;

      }

  }

  previousScore = bestThread->rootMoves[0].score;

  // Send new PV when needed

  if (bestThread != this)

      sync_cout << UCI::pv(bestThread->rootPos, bestThread->completedDepth, -VALUE_INFINITE, VALUE_INFINITE) << sync_endl;

  sync_cout << "bestmove " << UCI::move(bestThread->rootMoves[0].pv[0], rootPos.is_chess960());

  if (bestThread->rootMoves[0].pv.size() > 1 || bestThread->rootMoves[0].extract_ponder_from_tt(rootPos))

      std::cout << " ponder " << UCI::move(bestThread->rootMoves[0].pv[1], rootPos.is_chess960());

  std::cout << sync_endl;

}

/// Thread::search() is the main iterative deepening loop. It calls search()

/// repeatedly with increasing depth until the allocated thinking time has been

/// consumed, the user stops the search, or the maximum search depth is reached.

void Thread::search() {

  Stack stack[MAX_PLY+7], *ss = stack+4; // To reference from (ss-4) to (ss+2)

  Value bestValue, alpha, beta, delta;

  Move  lastBestMove = MOVE_NONE;

  Depth lastBestMoveDepth = DEPTH_ZERO;

  MainThread* mainThread = (this == Threads.main() ? Threads.main() : nullptr);

  double timeReduction = 1.0;

  std::memset(ss-4, 0, 7 * sizeof(Stack));

  for (int i = 4; i > 0; i--)

     (ss-i)->contHistory = &this->contHistory[NO_PIECE][0]; // Use as sentinel

  bestValue = delta = alpha = -VALUE_INFINITE;

  beta = VALUE_INFINITE;

  if (mainThread)

  {

      mainThread->failedLow = false;

      mainThread->bestMoveChanges = 0;

  }

  size_t multiPV = Options["MultiPV"];

  Skill skill(Options["Skill Level"]);

  // When playing with strength handicap enable MultiPV search that we will

  // use behind the scenes to retrieve a set of possible moves.

  if (skill.enabled())

      multiPV = std::max(multiPV, (size_t)4);

  multiPV = std::min(multiPV, rootMoves.size());

  // Iterative deepening loop until requested to stop or the target depth is reached

  while (   (rootDepth += ONE_PLY) < DEPTH_MAX

         && !Threads.stop

         && !(Limits.depth && mainThread && rootDepth / ONE_PLY > Limits.depth))

  {

      // Distribute search depths across the threads

      if (idx)

      {

          int i = (idx - 1) % 20;

          if (((rootDepth / ONE_PLY + rootPos.game_ply() + skipPhase[i]) / skipSize[i]) % 2)

              continue;

      }

      // Age out PV variability metric

      if (mainThread)

          mainThread->bestMoveChanges *= 0.505, mainThread->failedLow = false;

      // Save the last iteration's scores before first PV line is searched and

      // all the move scores except the (new) PV are set to -VALUE_INFINITE.

      for (RootMove& rm : rootMoves)

          rm.previousScore = rm.score;

      // MultiPV loop. We perform a full root search for each PV line

      for (PVIdx = 0; PVIdx < multiPV && !Threads.stop; ++PVIdx)

      {

          // Reset UCI info selDepth for each depth and each PV line

          selDepth = 0;

          // Reset aspiration window starting size

          if (rootDepth >= 5 * ONE_PLY)

          {

              delta = Value(18);

              alpha = std::max(rootMoves[PVIdx].previousScore - delta,-VALUE_INFINITE);

              beta  = std::min(rootMoves[PVIdx].previousScore + delta, VALUE_INFINITE);

          }

          // Start with a small aspiration window and, in the case of a fail

          // high/low, re-search with a bigger window until we're not failing

          // high/low anymore.

          while (true)

          {

              bestValue = ::search<PV>(rootPos, ss, alpha, beta, rootDepth, false, false);

              // Bring the best move to the front. It is critical that sorting

              // is done with a stable algorithm because all the values but the

              // first and eventually the new best one are set to -VALUE_INFINITE

              // and we want to keep the same order for all the moves except the

              // new PV that goes to the front. Note that in case of MultiPV

              // search the already searched PV lines are preserved.

              std::stable_sort(rootMoves.begin() + PVIdx, rootMoves.end());

              // If search has been stopped, we break immediately. Sorting and

              // writing PV back to TT is safe because RootMoves is still

              // valid, although it refers to the previous iteration.

              if (Threads.stop)

                  break;

              // When failing high/low give some update (without cluttering

              // the UI) before a re-search.

              if (   mainThread

                  && multiPV == 1

                  && (bestValue <= alpha || bestValue >= beta)

                  && Time.elapsed() > 3000)

                  sync_cout << UCI::pv(rootPos, rootDepth, alpha, beta) << sync_endl;

              // In case of failing low/high increase aspiration window and

              // re-search, otherwise exit the loop.

              if (bestValue <= alpha)

              {

                  beta = (alpha + beta) / 2;

                  alpha = std::max(bestValue - delta, -VALUE_INFINITE);

                  if (mainThread)

                  {

                      mainThread->failedLow = true;

                      Threads.stopOnPonderhit = false;

                  }

              }

              else if (bestValue >= beta)

                  beta = std::min(bestValue + delta, VALUE_INFINITE);

              else

                  break;

              delta += delta / 4 + 5;

              assert(alpha >= -VALUE_INFINITE && beta <= VALUE_INFINITE);

          }

          // Sort the PV lines searched so far and update the GUI

          std::stable_sort(rootMoves.begin(), rootMoves.begin() + PVIdx + 1);

          if (    mainThread

              && (Threads.stop || PVIdx + 1 == multiPV || Time.elapsed() > 3000))

              sync_cout << UCI::pv(rootPos, rootDepth, alpha, beta) << sync_endl;

      }

      if (!Threads.stop)

          completedDepth = rootDepth;

      if (rootMoves[0].pv[0] != lastBestMove) {

         lastBestMove = rootMoves[0].pv[0];

         lastBestMoveDepth = rootDepth;

      }

      // Have we found a "mate in x"?

      if (   Limits.mate

          && bestValue >= VALUE_MATE_IN_MAX_PLY

          && VALUE_MATE - bestValue <= 2 * Limits.mate)

          Threads.stop = true;

      if (!mainThread)

          continue;

      // If skill level is enabled and time is up, pick a sub-optimal best move

      if (skill.enabled() && skill.time_to_pick(rootDepth))

          skill.pick_best(multiPV);

      // Do we have time for the next iteration? Can we stop searching now?

      if (Limits.use_time_management())

      {

          if (!Threads.stop && !Threads.stopOnPonderhit)

          {

              // Stop the search if only one legal move is available, or if all

              // of the available time has been used

              const int F[] = { mainThread->failedLow,

                                bestValue - mainThread->previousScore };

              int improvingFactor = std::max(229, std::min(715, 357 + 119 * F[0] - 6 * F[1]));

              Color us = rootPos.side_to_move();

              bool thinkHard =    bestValue == VALUE_DRAW

                               && Limits.time[us] - Time.elapsed() > Limits.time[~us]

                               && ::pv_is_draw(rootPos);

              double unstablePvFactor = 1 + mainThread->bestMoveChanges + thinkHard;

              // if the bestMove is stable over several iterations, reduce time for this move,

              // the longer the move has been stable, the more.

              // Use part of the gained time from a previous stable move for the current move.

              timeReduction = 1;

              for (int i : {3, 4, 5})

                  if (lastBestMoveDepth * i < completedDepth && !thinkHard)

                     timeReduction *= 1.3;

              unstablePvFactor *=  std::pow(mainThread->previousTimeReduction, 0.51) / timeReduction;

              if (   rootMoves.size() == 1

                  || Time.elapsed() > Time.optimum() * unstablePvFactor * improvingFactor / 628)

              {

                  // If we are allowed to ponder do not stop the search now but

                  // keep pondering until the GUI sends "ponderhit" or "stop".

                  if (Threads.ponder)

                      Threads.stopOnPonderhit = true;

                  else

                      Threads.stop = true;

              }

          }

      }

  }

  if (!mainThread)

      return;

  mainThread->previousTimeReduction = timeReduction;

  // If skill level is enabled, swap best PV line with the sub-optimal one

  if (skill.enabled())

      std::swap(rootMoves[0], *std::find(rootMoves.begin(), rootMoves.end(),

                skill.best ? skill.best : skill.pick_best(multiPV)));

}

namespace {

  // search<>() is the main search function for both PV and non-PV nodes

  template <NodeType NT>

  Value search(Position& pos, Stack* ss, Value alpha, Value beta, Depth depth, bool cutNode, bool skipEarlyPruning) {

    const bool PvNode = NT == PV;

    const bool rootNode = PvNode && ss->ply == 0;

    assert(-VALUE_INFINITE <= alpha && alpha < beta && beta <= VALUE_INFINITE);

    assert(PvNode || (alpha == beta - 1));

    assert(DEPTH_ZERO < depth && depth < DEPTH_MAX);

    assert(!(PvNode && cutNode));

    assert(depth / ONE_PLY * ONE_PLY == depth);

    Move pv[MAX_PLY+1], capturesSearched[32], quietsSearched[64];

    StateInfo st;

    TTEntry* tte;

    Key posKey;

    Move ttMove, move, excludedMove, bestMove;

    Depth extension, newDepth;

    Value bestValue, value, ttValue, eval, maxValue;

    bool ttHit, inCheck, givesCheck, singularExtensionNode, improving;

    bool captureOrPromotion, doFullDepthSearch, moveCountPruning, skipQuiets, ttCapture, pvExact;

    Piece movedPiece;

    int moveCount, captureCount, quietCount;

    // Step 1. Initialize node

    Thread* thisThread = pos.this_thread();

    inCheck = pos.checkers();

    moveCount = captureCount = quietCount = ss->moveCount = 0;

    ss->statScore = 0;

    bestValue = -VALUE_INFINITE;

    maxValue = VALUE_INFINITE;

    // Check for the available remaining time

    if (thisThread == Threads.main())

        static_cast<MainThread*>(thisThread)->check_time();

    // Used to send selDepth info to GUI (selDepth counts from 1, ply from 0)

    if (PvNode && thisThread->selDepth < ss->ply + 1)

        thisThread->selDepth = ss->ply + 1;

    if (!rootNode)

    {

        // Step 2. Check for aborted search and immediate draw

        if (Threads.stop.load(std::memory_order_relaxed) || pos.is_draw(ss->ply) || ss->ply >= MAX_PLY)

            return ss->ply >= MAX_PLY && !inCheck ? evaluate(pos) : VALUE_DRAW;

        // Step 3. Mate distance pruning. Even if we mate at the next move our score

        // would be at best mate_in(ss->ply+1), but if alpha is already bigger because

        // a shorter mate was found upward in the tree then there is no need to search

        // because we will never beat the current alpha. Same logic but with reversed

        // signs applies also in the opposite condition of being mated instead of giving

        // mate. In this case return a fail-high score.

        alpha = std::max(mated_in(ss->ply), alpha);

        beta = std::min(mate_in(ss->ply+1), beta);

        if (alpha >= beta)

            return alpha;

    }

    assert(0 <= ss->ply && ss->ply < MAX_PLY);

    (ss+1)->ply = ss->ply + 1;

    ss->currentMove = (ss+1)->excludedMove = bestMove = MOVE_NONE;

    ss->contHistory = &thisThread->contHistory[NO_PIECE][0];

    (ss+2)->killers[0] = (ss+2)->killers[1] = MOVE_NONE;

    Square prevSq = to_sq((ss-1)->currentMove);

    // Step 4. Transposition table lookup. We don't want the score of a partial

    // search to overwrite a previous full search TT value, so we use a different

    // position key in case of an excluded move.

    excludedMove = ss->excludedMove;

    posKey = pos.key() ^ Key(excludedMove << 16); // isn't a very good hash

    tte = TT.probe(posKey, ttHit);

    ttValue = ttHit ? value_from_tt(tte->value(), ss->ply) : VALUE_NONE;

    ttMove =  rootNode ? thisThread->rootMoves[thisThread->PVIdx].pv[0]

            : ttHit    ? tte->move() : MOVE_NONE;

    // At non-PV nodes we check for an early TT cutoff

    if (  !PvNode

        && ttHit

        && tte->depth() >= depth

        && ttValue != VALUE_NONE // Possible in case of TT access race

        && (ttValue >= beta ? (tte->bound() & BOUND_LOWER)

                            : (tte->bound() & BOUND_UPPER)))

    {

        // If ttMove is quiet, update move sorting heuristics on TT hit

        if (ttMove)

        {

            if (ttValue >= beta)

            {

                if (!pos.capture_or_promotion(ttMove))

                    update_stats(pos, ss, ttMove, nullptr, 0, stat_bonus(depth));

                // Extra penalty for a quiet TT move in previous ply when it gets refuted

                if ((ss-1)->moveCount == 1 && !pos.captured_piece())

                    update_continuation_histories(ss-1, pos.piece_on(prevSq), prevSq, -stat_bonus(depth + ONE_PLY));

            }

            // Penalty for a quiet ttMove that fails low

            else if (!pos.capture_or_promotion(ttMove))

            {

                int penalty = -stat_bonus(depth);

                thisThread->mainHistory.update(pos.side_to_move(), ttMove, penalty);

                update_continuation_histories(ss, pos.moved_piece(ttMove), to_sq(ttMove), penalty);

            }

        }

        return ttValue;

    }

    // Step 4a. Tablebase probe

    if (!rootNode && TB::Cardinality)

    {

        int piecesCount = pos.count<ALL_PIECES>();

        if (    piecesCount <= TB::Cardinality

            && (piecesCount <  TB::Cardinality || depth >= TB::ProbeDepth)

            &&  pos.rule50_count() == 0

            && !pos.can_castle(ANY_CASTLING))

        {

            TB::ProbeState err;

            TB::WDLScore wdl = Tablebases::probe_wdl(pos, &err);

            if (err != TB::ProbeState::FAIL)

            {

                thisThread->tbHits.fetch_add(1, std::memory_order_relaxed);

                int drawScore = TB::UseRule50 ? 1 : 0;

                value =  wdl < -drawScore ? -VALUE_MATE + MAX_PLY + ss->ply + 1

                       : wdl >  drawScore ?  VALUE_MATE - MAX_PLY - ss->ply - 1

                                          :  VALUE_DRAW + 2 * wdl * drawScore;

                Bound b =  wdl < -drawScore ? BOUND_UPPER

                         : wdl >  drawScore ? BOUND_LOWER : BOUND_EXACT;

                if (    b == BOUND_EXACT

                    || (b == BOUND_LOWER ? value >= beta : value <= alpha))

                {

                    tte->save(posKey, value_to_tt(value, ss->ply), b,

                              std::min(DEPTH_MAX - ONE_PLY, depth + 6 * ONE_PLY),

                              MOVE_NONE, VALUE_NONE, TT.generation());

                    return value;

                }

                if (PvNode)

                {

                    if (b == BOUND_LOWER)

                        bestValue = value, alpha = std::max(alpha, bestValue);

                    else

                        maxValue = value;

                }

            }

        }

    }

    // Step 5. Evaluate the position statically

    if (inCheck)

    {

        ss->staticEval = eval = VALUE_NONE;

        goto moves_loop;

    }

    else if (ttHit)

    {

        // Never assume anything on values stored in TT

        if ((ss->staticEval = eval = tte->eval()) == VALUE_NONE)

            eval = ss->staticEval = evaluate(pos);

        // Can ttValue be used as a better position evaluation?

        if (   ttValue != VALUE_NONE

            && (tte->bound() & (ttValue > eval ? BOUND_LOWER : BOUND_UPPER)))

            eval = ttValue;

    }

    else

    {

        eval = ss->staticEval =

        (ss-1)->currentMove != MOVE_NULL ? evaluate(pos)

                                         : -(ss-1)->staticEval + 2 * Eval::Tempo;

        tte->save(posKey, VALUE_NONE, BOUND_NONE, DEPTH_NONE, MOVE_NONE,

                  ss->staticEval, TT.generation());

    }

    if (skipEarlyPruning || !pos.non_pawn_material(pos.side_to_move()))

        goto moves_loop;

    // Step 6. Razoring (skipped when in check)

    if (   !PvNode

        &&  depth < 4 * ONE_PLY

        &&  eval + razor_margin <= alpha)

    {

        if (depth <= ONE_PLY)

            return qsearch<NonPV, false>(pos, ss, alpha, alpha+1);

        Value ralpha = alpha - razor_margin;

        Value v = qsearch<NonPV, false>(pos, ss, ralpha, ralpha+1);

        if (v <= ralpha)

            return v;

    }

    // Step 7. Futility pruning: child node (skipped when in check)

    if (   !rootNode

        &&  depth < 7 * ONE_PLY

        &&  eval - futility_margin(depth) >= beta

        &&  eval < VALUE_KNOWN_WIN)  // Do not return unproven wins

        return eval;

    // Step 8. Null move search with verification search (is omitted in PV nodes)

    if (   !PvNode

        &&  eval >= beta

        &&  ss->staticEval >= beta - 36 * depth / ONE_PLY + 225

        && (ss->ply >= thisThread->nmp_ply || ss->ply % 2 != thisThread->nmp_odd))

    {

        assert(eval - beta >= 0);

        // Null move dynamic reduction based on depth and value

        Depth R = ((823 + 67 * depth / ONE_PLY) / 256 + std::min((eval - beta) / PawnValueMg, 3)) * ONE_PLY;

        ss->currentMove = MOVE_NULL;

        ss->contHistory = &thisThread->contHistory[NO_PIECE][0];

        pos.do_null_move(st);

        Value nullValue = depth-R < ONE_PLY ? -qsearch<NonPV, false>(pos, ss+1, -beta, -beta+1)

                                            : - search<NonPV>(pos, ss+1, -beta, -beta+1, depth-R, !cutNode, true);

        pos.undo_null_move();

        if (nullValue >= beta)