/*
  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) 2015-2020 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 <cfloat>
#include <cmath>

#include "search.h"
#include "timeman.h"
#include "uci.h"

TimeManagement Time; // Our global time management object

namespace {

  enum TimeType { OptimumTime, MaxTime };

  constexpr int MoveHorizon   = 50;   // Plan time management at most this many moves ahead
  constexpr double MaxRatio   = 7.3;  // When in trouble, we can step over reserved time with this ratio
  constexpr double StealRatio = 0.34; // However we must not steal time from remaining moves over this ratio


  // move_importance() is a skew-logistic function based on naive statistical
  // analysis of "how many games are still undecided after n half-moves". Game
  // is considered "undecided" as long as neither side has >275cp advantage.
  // Data was extracted from the CCRL game database with some simple filtering criteria.

  double move_importance(int ply) {

    constexpr double XScale = 6.85;
    constexpr double XShift = 64.5;
    constexpr double Skew   = 0.171;

    return pow((1 + exp((ply - XShift) / XScale)), -Skew) + DBL_MIN; // Ensure non-zero
  }

  template<TimeType T>
  TimePoint remaining(TimePoint myTime, int movesToGo, int ply, TimePoint slowMover) {

    constexpr double TMaxRatio   = (T == OptimumTime ? 1.0 : MaxRatio);
    constexpr double TStealRatio = (T == OptimumTime ? 0.0 : StealRatio);

    double moveImportance = (move_importance(ply) * slowMover) / 100.0;
    double otherMovesImportance = 0.0;

    for (int i = 1; i < movesToGo; ++i)
        otherMovesImportance += move_importance(ply + 2 * i);

    double ratio1 = (TMaxRatio * moveImportance) / (TMaxRatio * moveImportance + otherMovesImportance);
    double ratio2 = (moveImportance + TStealRatio * otherMovesImportance) / (moveImportance + otherMovesImportance);

    return TimePoint(myTime * std::min(ratio1, ratio2)); // Intel C++ asks for an explicit cast
  }

} // namespace


/// init() is called at the beginning of the search and calculates the allowed
/// thinking time out of the time control and current game ply. We support four
/// different kinds of time controls, passed in 'limits':
///
///  inc == 0 && movestogo == 0 means: x basetime  [sudden death!]
///  inc == 0 && movestogo != 0 means: x moves in y minutes
///  inc >  0 && movestogo == 0 means: x basetime + z increment
///  inc >  0 && movestogo != 0 means: x moves in y minutes + z increment

void TimeManagement::init(Search::LimitsType& limits, Color us, int ply) {

  TimePoint minThinkingTime = Options["Minimum Thinking Time"];
  TimePoint moveOverhead    = Options["Move Overhead"];
  TimePoint slowMover       = Options["Slow Mover"];
  TimePoint npmsec          = Options["nodestime"];
  TimePoint hypMyTime;

  // If we have to play in 'nodes as time' mode, then convert from time
  // to nodes, and use resulting values in time management formulas.
  // WARNING: to avoid time losses, the given npmsec (nodes per millisecond)
  // must be much lower than the real engine speed.
  if (npmsec)
  {
      if (!availableNodes) // Only once at game start
          availableNodes = npmsec * limits.time[us]; // Time is in msec

      // Convert from milliseconds to nodes
      limits.time[us] = TimePoint(availableNodes);
      limits.inc[us] *= npmsec;
      limits.npmsec = npmsec;
  }

  startTime = limits.startTime;
  optimumTime = maximumTime = std::max(limits.time[us], minThinkingTime);

  const int maxMTG = limits.movestogo ? std::min(limits.movestogo, MoveHorizon) : MoveHorizon;

  // We calculate optimum time usage for different hypothetical "moves to go" values
  // and choose the minimum of calculated search time values. Usually the greatest
  // hypMTG gives the minimum values.
  for (int hypMTG = 1; hypMTG <= maxMTG; ++hypMTG)
  {
      // Calculate thinking time for hypothetical "moves to go"-value
      hypMyTime =  limits.time[us]
                 + limits.inc[us] * (hypMTG - 1)
                 - moveOverhead * (2 + std::min(hypMTG, 40));

      hypMyTime = std::max(hypMyTime, TimePoint(0));

      TimePoint t1 = minThinkingTime + remaining<OptimumTime>(hypMyTime, hypMTG, ply, slowMover);
      TimePoint t2 = minThinkingTime + remaining<MaxTime    >(hypMyTime, hypMTG, ply, slowMover);

      optimumTime = std::min(t1, optimumTime);
      maximumTime = std::min(t2, maximumTime);
  }

  if (Options["Ponder"])
      optimumTime += optimumTime / 4;
}