feature_histogram.hpp

/*!
 * Copyright (c) 2016 Microsoft Corporation. All rights reserved.
 * Licensed under the MIT License. See LICENSE file in the project root for
 * license information.
 */
#ifndef LIGHTGBM_TREELEARNER_FEATURE_HISTOGRAM_HPP_
#define LIGHTGBM_TREELEARNER_FEATURE_HISTOGRAM_HPP_

#include <LightGBM/bin.h>
#include <LightGBM/dataset.h>
#include <LightGBM/utils/array_args.h>

#include <algorithm>
#include <cmath>
#include <cstring>
#include <memory>
#include <utility>
#include <vector>

#include "monotone_constraints.hpp"
#include "split_info.hpp"

namespace LightGBM {

class FeatureMetainfo {
 public:
  int num_bin;
  MissingType missing_type;
  int8_t offset = 0;
  uint32_t default_bin;
  int8_t monotone_type = 0;
  double penalty = 1.0;
  /*! \brief pointer of tree config */
  const Config* config;
  BinType bin_type;
  /*! \brief random number generator for extremely randomized trees */
  mutable Random rand;
};
/*!
 * \brief FeatureHistogram is used to construct and store a histogram for a
 * feature.
 */
class FeatureHistogram {
 public:
  FeatureHistogram() { data_ = nullptr; }

  ~FeatureHistogram() {}

  /*! \brief Disable copy */
  FeatureHistogram& operator=(const FeatureHistogram&) = delete;
  /*! \brief Disable copy */
  FeatureHistogram(const FeatureHistogram&) = delete;

  /*!
   * \brief Init the feature histogram
   * \param feature the feature data for this histogram
   * \param min_num_data_one_leaf minimal number of data in one leaf
   */
  void Init(hist_t* data, const FeatureMetainfo* meta) {
    meta_ = meta;
    data_ = data;
    ResetFunc();
  }

  void ResetFunc() {
    if (meta_->bin_type == BinType::NumericalBin) {
      FuncForNumrical();
    } else {
      FuncForCategorical();
    }
  }

  hist_t* RawData() { return data_; }

  /*!
   * \brief Subtract current histograms with other
   * \param other The histogram that want to subtract
   */
  void Subtract(const FeatureHistogram& other) {
    for (int i = 0; i < (meta_->num_bin - meta_->offset) * 2; ++i) {
      data_[i] -= other.data_[i];
    }
  }

  void FindBestThreshold(double sum_gradient, double sum_hessian,
                         data_size_t num_data,
                         const ConstraintEntry& constraints,
                         SplitInfo* output) {
    output->default_left = true;
    output->gain = kMinScore;
    find_best_threshold_fun_(sum_gradient, sum_hessian + 2 * kEpsilon, num_data,
                             constraints, output);
    output->gain *= meta_->penalty;
  }

  template <bool USE_RAND, bool USE_L1, bool USE_MAX_OUTPUT>
  double BeforeNumercal(double sum_gradient, double sum_hessian,
                        SplitInfo* output, int* rand_threshold) {
    is_splittable_ = false;
    output->monotone_type = meta_->monotone_type;
    double gain_shift = GetLeafGain<USE_L1, USE_MAX_OUTPUT>(
        sum_gradient, sum_hessian, meta_->config->lambda_l1,
        meta_->config->lambda_l2, meta_->config->max_delta_step);
    *rand_threshold = 0;
    if (USE_RAND) {
      if (meta_->num_bin - 2 > 0) {
        *rand_threshold = meta_->rand.NextInt(0, meta_->num_bin - 2);
      }
    }
    return gain_shift + meta_->config->min_gain_to_split;
  }

  void FuncForNumrical() {
    if (meta_->config->extra_trees) {
      if (meta_->config->monotone_constraints.empty()) {
        FuncForNumricalL1<true, false>();
      } else {
        FuncForNumricalL1<true, true>();
      }
    } else {
      if (meta_->config->monotone_constraints.empty()) {
        FuncForNumricalL1<false, false>();
      } else {
        FuncForNumricalL1<false, true>();
      }
    }
  }
  template <bool USE_RAND, bool USE_MC>
  void FuncForNumricalL1() {
    if (meta_->config->lambda_l1 > 0) {
      if (meta_->config->max_delta_step > 0) {
        FuncForNumricalL2<USE_RAND, USE_MC, true, true>();
      } else {
        FuncForNumricalL2<USE_RAND, USE_MC, true, false>();
      }
    } else {
      if (meta_->config->max_delta_step > 0) {
        FuncForNumricalL2<USE_RAND, USE_MC, false, true>();
      } else {
        FuncForNumricalL2<USE_RAND, USE_MC, false, false>();
      }
    }
  }

  template <bool USE_RAND, bool USE_MC, bool USE_L1, bool USE_MAX_OUTPUT>
  void FuncForNumricalL2() {
    if (meta_->num_bin > 2 && meta_->missing_type != MissingType::None) {
      if (meta_->missing_type == MissingType::Zero) {
        find_best_threshold_fun_ =
            [=](double sum_gradient, double sum_hessian, data_size_t num_data,
                const ConstraintEntry& constraints, SplitInfo* output) {
              int rand_threshold = 0;
              double min_gain_shift =
                  BeforeNumercal<USE_RAND, USE_L1, USE_MAX_OUTPUT>(
                      sum_gradient, sum_hessian, output, &rand_threshold);
              FindBestThresholdSequentially<USE_RAND, USE_MC, USE_L1,
                                            USE_MAX_OUTPUT, true, true, false>(
                  sum_gradient, sum_hessian, num_data, constraints,
                  min_gain_shift, output, rand_threshold);
              FindBestThresholdSequentially<USE_RAND, USE_MC, USE_L1,
                                            USE_MAX_OUTPUT, false, true, false>(
                  sum_gradient, sum_hessian, num_data, constraints,
                  min_gain_shift, output, rand_threshold);
            };
      } else {
        find_best_threshold_fun_ =
            [=](double sum_gradient, double sum_hessian, data_size_t num_data,
                const ConstraintEntry& constraints, SplitInfo* output) {
              int rand_threshold = 0;
              double min_gain_shift =
                  BeforeNumercal<USE_RAND, USE_L1, USE_MAX_OUTPUT>(
                      sum_gradient, sum_hessian, output, &rand_threshold);
              FindBestThresholdSequentially<USE_RAND, USE_MC, USE_L1,
                                            USE_MAX_OUTPUT, true, false, true>(
                  sum_gradient, sum_hessian, num_data, constraints,
                  min_gain_shift, output, rand_threshold);
              FindBestThresholdSequentially<USE_RAND, USE_MC, USE_L1,
                                            USE_MAX_OUTPUT, false, false, true>(
                  sum_gradient, sum_hessian, num_data, constraints,
                  min_gain_shift, output, rand_threshold);
            };
      }
    } else {
      if (meta_->missing_type != MissingType::NaN) {
        find_best_threshold_fun_ =
            [=](double sum_gradient, double sum_hessian, data_size_t num_data,
                const ConstraintEntry& constraints, SplitInfo* output) {
              int rand_threshold = 0;
              double min_gain_shift =
                  BeforeNumercal<USE_RAND, USE_L1, USE_MAX_OUTPUT>(
                      sum_gradient, sum_hessian, output, &rand_threshold);
              FindBestThresholdSequentially<USE_RAND, USE_MC, USE_L1,
                                            USE_MAX_OUTPUT, true, false, false>(
                  sum_gradient, sum_hessian, num_data, constraints,
                  min_gain_shift, output, rand_threshold);
            };
      } else {
        find_best_threshold_fun_ =
            [=](double sum_gradient, double sum_hessian, data_size_t num_data,
                const ConstraintEntry& constraints, SplitInfo* output) {
              int rand_threshold = 0;
              double min_gain_shift =
                  BeforeNumercal<USE_RAND, USE_L1, USE_MAX_OUTPUT>(
                      sum_gradient, sum_hessian, output, &rand_threshold);
              FindBestThresholdSequentially<USE_RAND, USE_MC, USE_L1,
                                            USE_MAX_OUTPUT, true, false, false>(
                  sum_gradient, sum_hessian, num_data, constraints,
                  min_gain_shift, output, rand_threshold);
              output->default_left = false;
            };
      }
    }
  }

  void FuncForCategorical() {
    if (meta_->config->extra_trees) {
      if (meta_->config->monotone_constraints.empty()) {
        FuncForCategoricalL1<true, false>();
      } else {
        FuncForCategoricalL1<true, true>();
      }
    } else {
      if (meta_->config->monotone_constraints.empty()) {
        FuncForCategoricalL1<false, false>();
      } else {
        FuncForCategoricalL1<false, true>();
      }
    }
  }
  template <bool USE_RAND, bool USE_MC>
  void FuncForCategoricalL1() {
    if (meta_->config->lambda_l1 > 0) {
      if (meta_->config->max_delta_step > 0) {
        find_best_threshold_fun_ =
            std::bind(&FeatureHistogram::FindBestThresholdCategoricalInner<
                          USE_RAND, USE_MC, true, true>,
                      this, std::placeholders::_1, std::placeholders::_2,
                      std::placeholders::_3, std::placeholders::_4,
                      std::placeholders::_5);
      } else {
        find_best_threshold_fun_ =
            std::bind(&FeatureHistogram::FindBestThresholdCategoricalInner<
                          USE_RAND, USE_MC, true, false>,
                      this, std::placeholders::_1, std::placeholders::_2,
                      std::placeholders::_3, std::placeholders::_4,
                      std::placeholders::_5);
      }
    } else {
      if (meta_->config->max_delta_step > 0) {
        find_best_threshold_fun_ =
            std::bind(&FeatureHistogram::FindBestThresholdCategoricalInner<
                          USE_RAND, USE_MC, false, true>,
                      this, std::placeholders::_1, std::placeholders::_2,
                      std::placeholders::_3, std::placeholders::_4,
                      std::placeholders::_5);
      } else {
        find_best_threshold_fun_ =
            std::bind(&FeatureHistogram::FindBestThresholdCategoricalInner<
                          USE_RAND, USE_MC, false, false>,
                      this, std::placeholders::_1, std::placeholders::_2,
                      std::placeholders::_3, std::placeholders::_4,
                      std::placeholders::_5);
      }
    }
  }

  template <bool USE_RAND, bool USE_MC, bool USE_L1, bool USE_MAX_OUTPUT>
  void FindBestThresholdCategoricalInner(double sum_gradient,
                                         double sum_hessian,
                                         data_size_t num_data,
                                         const ConstraintEntry& constraints,
                                         SplitInfo* output) {
    is_splittable_ = false;
    output->default_left = false;
    double best_gain = kMinScore;
    data_size_t best_left_count = 0;
    double best_sum_left_gradient = 0;
    double best_sum_left_hessian = 0;
    double gain_shift = GetLeafGain<USE_L1, USE_MAX_OUTPUT>(
        sum_gradient, sum_hessian, meta_->config->lambda_l1,
        meta_->config->lambda_l2, meta_->config->max_delta_step);

    double min_gain_shift = gain_shift + meta_->config->min_gain_to_split;
    bool is_full_categorical = meta_->missing_type == MissingType::None;
    int used_bin = meta_->num_bin - 1 + is_full_categorical;

    std::vector<int> sorted_idx;
    double l2 = meta_->config->lambda_l2;
    bool use_onehot = meta_->num_bin <= meta_->config->max_cat_to_onehot;
    int best_threshold = -1;
    int best_dir = 1;
    const double cnt_factor = num_data / sum_hessian;
    int rand_threshold = 0;
    if (use_onehot) {
      if (USE_RAND) {
        if (used_bin > 0) {
          rand_threshold = meta_->rand.NextInt(0, used_bin);
        }
      }
      for (int t = 0; t < used_bin; ++t) {
        const auto grad = GET_GRAD(data_, t);
        const auto hess = GET_HESS(data_, t);
        data_size_t cnt =
            static_cast<data_size_t>(Common::RoundInt(hess * cnt_factor));
        // if data not enough, or sum hessian too small
        if (cnt < meta_->config->min_data_in_leaf ||
            hess < meta_->config->min_sum_hessian_in_leaf) {
          continue;
        }
        data_size_t other_count = num_data - cnt;
        // if data not enough
        if (other_count < meta_->config->min_data_in_leaf) {
          continue;
        }

        double sum_other_hessian = sum_hessian - hess - kEpsilon;
        // if sum hessian too small
        if (sum_other_hessian < meta_->config->min_sum_hessian_in_leaf) {
          continue;
        }

        double sum_other_gradient = sum_gradient - grad;
        if (USE_RAND) {
          if (t != rand_threshold) {
            continue;
          }
        }
        // current split gain
        double current_gain = GetSplitGains<USE_MC, USE_L1, USE_MAX_OUTPUT>(
            sum_other_gradient, sum_other_hessian, grad, hess + kEpsilon,
            meta_->config->lambda_l1, l2, meta_->config->max_delta_step,
            constraints, 0);
        // gain with split is worse than without split
        if (current_gain <= min_gain_shift) {
          continue;
        }

        // mark to is splittable
        is_splittable_ = true;
        // better split point
        if (current_gain > best_gain) {
          best_threshold = t;
          best_sum_left_gradient = grad;
          best_sum_left_hessian = hess + kEpsilon;
          best_left_count = cnt;
          best_gain = current_gain;
        }
      }
    } else {
      for (int i = 0; i < used_bin; ++i) {
        if (Common::RoundInt(GET_HESS(data_, i) * cnt_factor) >=
            meta_->config->cat_smooth) {
          sorted_idx.push_back(i);
        }
      }
      used_bin = static_cast<int>(sorted_idx.size());

      l2 += meta_->config->cat_l2;

      auto ctr_fun = [this](double sum_grad, double sum_hess) {
        return (sum_grad) / (sum_hess + meta_->config->cat_smooth);
      };
      std::sort(sorted_idx.begin(), sorted_idx.end(),
                [this, &ctr_fun](int i, int j) {
                  return ctr_fun(GET_GRAD(data_, i), GET_HESS(data_, i)) <
                         ctr_fun(GET_GRAD(data_, j), GET_HESS(data_, j));
                });

      std::vector<int> find_direction(1, 1);
      std::vector<int> start_position(1, 0);
      find_direction.push_back(-1);
      start_position.push_back(used_bin - 1);
      const int max_num_cat =
          std::min(meta_->config->max_cat_threshold, (used_bin + 1) / 2);
      int max_threshold = std::max(std::min(max_num_cat, used_bin) - 1, 0);
      if (USE_RAND) {
        if (max_threshold > 0) {
          rand_threshold = meta_->rand.NextInt(0, max_threshold);
        }
      }

      is_splittable_ = false;
      for (size_t out_i = 0; out_i < find_direction.size(); ++out_i) {
        auto dir = find_direction[out_i];
        auto start_pos = start_position[out_i];
        data_size_t min_data_per_group = meta_->config->min_data_per_group;
        data_size_t cnt_cur_group = 0;
        double sum_left_gradient = 0.0f;
        double sum_left_hessian = kEpsilon;
        data_size_t left_count = 0;
        for (int i = 0; i < used_bin && i < max_num_cat; ++i) {
          auto t = sorted_idx[start_pos];
          start_pos += dir;
          const auto grad = GET_GRAD(data_, t);
          const auto hess = GET_HESS(data_, t);
          data_size_t cnt =
              static_cast<data_size_t>(Common::RoundInt(hess * cnt_factor));

          sum_left_gradient += grad;
          sum_left_hessian += hess;
          left_count += cnt;
          cnt_cur_group += cnt;

          if (left_count < meta_->config->min_data_in_leaf ||
              sum_left_hessian < meta_->config->min_sum_hessian_in_leaf) {
            continue;
          }
          data_size_t right_count = num_data - left_count;
          if (right_count < meta_->config->min_data_in_leaf ||
              right_count < min_data_per_group) {
            break;
          }

          double sum_right_hessian = sum_hessian - sum_left_hessian;
          if (sum_right_hessian < meta_->config->min_sum_hessian_in_leaf) {
            break;
          }

          if (cnt_cur_group < min_data_per_group) {
            continue;
          }

          cnt_cur_group = 0;

          double sum_right_gradient = sum_gradient - sum_left_gradient;
          if (USE_RAND) {
            if (i != rand_threshold) {
              continue;
            }
          }
          double current_gain = GetSplitGains<USE_MC, USE_L1, USE_MAX_OUTPUT>(
              sum_left_gradient, sum_left_hessian, sum_right_gradient,
              sum_right_hessian, meta_->config->lambda_l1, l2,
              meta_->config->max_delta_step, constraints, 0);
          if (current_gain <= min_gain_shift) {
            continue;
          }
          is_splittable_ = true;
          if (current_gain > best_gain) {
            best_left_count = left_count;
            best_sum_left_gradient = sum_left_gradient;
            best_sum_left_hessian = sum_left_hessian;
            best_threshold = i;
            best_gain = current_gain;
            best_dir = dir;
          }
        }
      }
    }

    if (is_splittable_) {
      output->left_output =
          CalculateSplittedLeafOutput<USE_MC, USE_L1, USE_MAX_OUTPUT>(
              best_sum_left_gradient, best_sum_left_hessian,
              meta_->config->lambda_l1, l2, meta_->config->max_delta_step,
              constraints);
      output->left_count = best_left_count;
      output->left_sum_gradient = best_sum_left_gradient;
      output->left_sum_hessian = best_sum_left_hessian - kEpsilon;
      output->right_output =
          CalculateSplittedLeafOutput<USE_MC, USE_L1, USE_MAX_OUTPUT>(
              sum_gradient - best_sum_left_gradient,
              sum_hessian - best_sum_left_hessian, meta_->config->lambda_l1, l2,
              meta_->config->max_delta_step, constraints);
      output->right_count = num_data - best_left_count;
      output->right_sum_gradient = sum_gradient - best_sum_left_gradient;
      output->right_sum_hessian =
          sum_hessian - best_sum_left_hessian - kEpsilon;
      output->gain = best_gain - min_gain_shift;
      if (use_onehot) {
        output->num_cat_threshold = 1;
        output->cat_threshold =
            std::vector<uint32_t>(1, static_cast<uint32_t>(best_threshold));
      } else {
        output->num_cat_threshold = best_threshold + 1;
        output->cat_threshold =
            std::vector<uint32_t>(output->num_cat_threshold);
        if (best_dir == 1) {
          for (int i = 0; i < output->num_cat_threshold; ++i) {
            auto t = sorted_idx[i];
            output->cat_threshold[i] = t;
          }
        } else {
          for (int i = 0; i < output->num_cat_threshold; ++i) {
            auto t = sorted_idx[used_bin - 1 - i];
            output->cat_threshold[i] = t;
          }
        }
      }
      output->monotone_type = 0;
    }
  }

  void GatherInfoForThreshold(double sum_gradient, double sum_hessian,
                              uint32_t threshold, data_size_t num_data,
                              SplitInfo* output) {
    if (meta_->bin_type == BinType::NumericalBin) {
      GatherInfoForThresholdNumerical(sum_gradient, sum_hessian, threshold,
                                      num_data, output);
    } else {
      GatherInfoForThresholdCategorical(sum_gradient, sum_hessian, threshold,
                                        num_data, output);
    }
  }

  void GatherInfoForThresholdNumerical(double sum_gradient, double sum_hessian,
                                       uint32_t threshold, data_size_t num_data,
                                       SplitInfo* output) {
    double gain_shift = GetLeafGain<true, true>(
        sum_gradient, sum_hessian, meta_->config->lambda_l1,
        meta_->config->lambda_l2, meta_->config->max_delta_step);
    double min_gain_shift = gain_shift + meta_->config->min_gain_to_split;

    // do stuff here
    const int8_t offset = meta_->offset;

    double sum_right_gradient = 0.0f;
    double sum_right_hessian = kEpsilon;
    data_size_t right_count = 0;

    // set values
    bool use_na_as_missing = false;
    bool skip_default_bin = false;
    if (meta_->missing_type == MissingType::Zero) {
      skip_default_bin = true;
    } else if (meta_->missing_type == MissingType::NaN) {
      use_na_as_missing = true;
    }

    int t = meta_->num_bin - 1 - offset - use_na_as_missing;
    const int t_end = 1 - offset;
    const double cnt_factor = num_data / sum_hessian;
    // from right to left, and we don't need data in bin0
    for (; t >= t_end; --t) {
      if (static_cast<uint32_t>(t + offset) < threshold) {
        break;
      }

      // need to skip default bin
      if (skip_default_bin &&
          (t + offset) == static_cast<int>(meta_->default_bin)) {
        continue;
      }
      const auto grad = GET_GRAD(data_, t);
      const auto hess = GET_HESS(data_, t);
      data_size_t cnt =
          static_cast<data_size_t>(Common::RoundInt(hess * cnt_factor));
      sum_right_gradient += grad;
      sum_right_hessian += hess;
      right_count += cnt;
    }
    double sum_left_gradient = sum_gradient - sum_right_gradient;
    double sum_left_hessian = sum_hessian - sum_right_hessian;
    data_size_t left_count = num_data - right_count;
    double current_gain =
        GetLeafGain<true, true>(
            sum_left_gradient, sum_left_hessian, meta_->config->lambda_l1,
            meta_->config->lambda_l2, meta_->config->max_delta_step) +
        GetLeafGain<true, true>(
            sum_right_gradient, sum_right_hessian, meta_->config->lambda_l1,
            meta_->config->lambda_l2, meta_->config->max_delta_step);

    // gain with split is worse than without split
    if (std::isnan(current_gain) || current_gain <= min_gain_shift) {
      output->gain = kMinScore;
      Log::Warning(
          "'Forced Split' will be ignored since the gain getting worse.");
      return;
    }

    // update split information
    output->threshold = threshold;
    output->left_output = CalculateSplittedLeafOutput<true, true>(
        sum_left_gradient, sum_left_hessian, meta_->config->lambda_l1,
        meta_->config->lambda_l2, meta_->config->max_delta_step);
    output->left_count = left_count;
    output->left_sum_gradient = sum_left_gradient;
    output->left_sum_hessian = sum_left_hessian - kEpsilon;
    output->right_output = CalculateSplittedLeafOutput<true, true>(
        sum_gradient - sum_left_gradient, sum_hessian - sum_left_hessian,
        meta_->config->lambda_l1, meta_->config->lambda_l2,
        meta_->config->max_delta_step);
    output->right_count = num_data - left_count;
    output->right_sum_gradient = sum_gradient - sum_left_gradient;
    output->right_sum_hessian = sum_hessian - sum_left_hessian - kEpsilon;
    output->gain = current_gain - min_gain_shift;
    output->default_left = true;
  }

  void GatherInfoForThresholdCategorical(double sum_gradient,
                                         double sum_hessian, uint32_t threshold,
                                         data_size_t num_data,
                                         SplitInfo* output) {
    // get SplitInfo for a given one-hot categorical split.
    output->default_left = false;
    double gain_shift = GetLeafGain<true, true>(
        sum_gradient, sum_hessian, meta_->config->lambda_l1,
        meta_->config->lambda_l2, meta_->config->max_delta_step);
    double min_gain_shift = gain_shift + meta_->config->min_gain_to_split;
    bool is_full_categorical = meta_->missing_type == MissingType::None;
    int used_bin = meta_->num_bin - 1 + is_full_categorical;
    if (threshold >= static_cast<uint32_t>(used_bin)) {
      output->gain = kMinScore;
      Log::Warning("Invalid categorical threshold split");
      return;
    }
    const double cnt_factor = num_data / sum_hessian;
    const auto grad = GET_GRAD(data_, threshold);
    const auto hess = GET_HESS(data_, threshold);
    data_size_t cnt =
        static_cast<data_size_t>(Common::RoundInt(hess * cnt_factor));

    double l2 = meta_->config->lambda_l2;
    data_size_t left_count = cnt;
    data_size_t right_count = num_data - left_count;
    double sum_left_hessian = hess + kEpsilon;
    double sum_right_hessian = sum_hessian - sum_left_hessian;
    double sum_left_gradient = grad;
    double sum_right_gradient = sum_gradient - sum_left_gradient;
    // current split gain
    double current_gain =
        GetLeafGain<true, true>(sum_right_gradient, sum_right_hessian,
                                meta_->config->lambda_l1, l2,
                                meta_->config->max_delta_step) +
        GetLeafGain<true, true>(sum_left_gradient, sum_left_hessian,
                                meta_->config->lambda_l1, l2,
                                meta_->config->max_delta_step);
    if (std::isnan(current_gain) || current_gain <= min_gain_shift) {
      output->gain = kMinScore;
      Log::Warning(
          "'Forced Split' will be ignored since the gain getting worse.");
      return;
    }

    output->left_output = CalculateSplittedLeafOutput<true, true>(
        sum_left_gradient, sum_left_hessian, meta_->config->lambda_l1, l2,
        meta_->config->max_delta_step);
    output->left_count = left_count;
    output->left_sum_gradient = sum_left_gradient;
    output->left_sum_hessian = sum_left_hessian - kEpsilon;
    output->right_output = CalculateSplittedLeafOutput<true, true>(
        sum_right_gradient, sum_right_hessian, meta_->config->lambda_l1, l2,
        meta_->config->max_delta_step);
    output->right_count = right_count;
    output->right_sum_gradient = sum_gradient - sum_left_gradient;
    output->right_sum_hessian = sum_right_hessian - kEpsilon;
    output->gain = current_gain - min_gain_shift;
    output->num_cat_threshold = 1;
    output->cat_threshold = std::vector<uint32_t>(1, threshold);
  }

  /*!
   * \brief Binary size of this histogram
   */
  int SizeOfHistgram() const {
    return (meta_->num_bin - meta_->offset) * kHistEntrySize;
  }

  /*!
   * \brief Restore histogram from memory
   */
  void FromMemory(char* memory_data) {
    std::memcpy(data_, memory_data,
                (meta_->num_bin - meta_->offset) * kHistEntrySize);
  }

  /*!
   * \brief True if this histogram can be splitted
   */
  bool is_splittable() { return is_splittable_; }

  /*!
   * \brief Set splittable to this histogram
   */
  void set_is_splittable(bool val) { is_splittable_ = val; }

  static double ThresholdL1(double s, double l1) {
    const double reg_s = std::max(0.0, std::fabs(s) - l1);
    return Common::Sign(s) * reg_s;
  }

  template <bool USE_L1, bool USE_MAX_OUTPUT>
  static double CalculateSplittedLeafOutput(double sum_gradients,
                                            double sum_hessians, double l1,
                                            double l2, double max_delta_step) {
    if (USE_L1) {
      double ret = -ThresholdL1(sum_gradients, l1) / (sum_hessians + l2);
      if (USE_MAX_OUTPUT) {
        if (max_delta_step > 0 && std::fabs(ret) > max_delta_step) {
          return Common::Sign(ret) * max_delta_step;
        }
      }
      return ret;
    } else {
      double ret = -sum_gradients / (sum_hessians + l2);
      if (USE_MAX_OUTPUT) {
        if (max_delta_step > 0 && std::fabs(ret) > max_delta_step) {
          return Common::Sign(ret) * max_delta_step;
        }
      }
      return ret;
    }
  }

  template <bool USE_MC, bool USE_L1, bool USE_MAX_OUTPUT>
  static double CalculateSplittedLeafOutput(
      double sum_gradients, double sum_hessians, double l1, double l2,
      double max_delta_step, const ConstraintEntry& constraints) {
    double ret = CalculateSplittedLeafOutput<USE_L1, USE_MAX_OUTPUT>(
        sum_gradients, sum_hessians, l1, l2, max_delta_step);
    if (USE_MC) {
      if (ret < constraints.min) {
        ret = constraints.min;
      } else if (ret > constraints.max) {
        ret = constraints.max;
      }
    }
    return ret;
  }

 private:
  template <bool USE_MC, bool USE_L1, bool USE_MAX_OUTPUT>
  static double GetSplitGains(double sum_left_gradients,
                              double sum_left_hessians,
                              double sum_right_gradients,
                              double sum_right_hessians, double l1, double l2,
                              double max_delta_step,
                              const ConstraintEntry& constraints,
                              int8_t monotone_constraint) {
    if (!USE_MC) {
      return GetLeafGain<USE_L1, USE_MAX_OUTPUT>(sum_left_gradients,
                                                 sum_left_hessians, l1, l2,
                                                 max_delta_step) +
             GetLeafGain<USE_L1, USE_MAX_OUTPUT>(sum_right_gradients,
                                                 sum_right_hessians, l1, l2,
                                                 max_delta_step);
    } else {
      double left_output =
          CalculateSplittedLeafOutput<USE_MC, USE_L1, USE_MAX_OUTPUT>(
              sum_left_gradients, sum_left_hessians, l1, l2, max_delta_step,
              constraints);
      double right_output =
          CalculateSplittedLeafOutput<USE_MC, USE_L1, USE_MAX_OUTPUT>(
              sum_right_gradients, sum_right_hessians, l1, l2, max_delta_step,
              constraints);
      if (((monotone_constraint > 0) && (left_output > right_output)) ||
          ((monotone_constraint < 0) && (left_output < right_output))) {
        return 0;
      }
      return GetLeafGainGivenOutput<USE_L1>(
                 sum_left_gradients, sum_left_hessians, l1, l2, left_output) +
             GetLeafGainGivenOutput<USE_L1>(
                 sum_right_gradients, sum_right_hessians, l1, l2, right_output);
    }
  }

  template <bool USE_L1, bool USE_MAX_OUTPUT>
  static double GetLeafGain(double sum_gradients, double sum_hessians,
                            double l1, double l2, double max_delta_step) {
    if (!USE_MAX_OUTPUT) {
      if (USE_L1) {
        const double sg_l1 = ThresholdL1(sum_gradients, l1);
        return (sg_l1 * sg_l1) / (sum_hessians + l2);
      } else {
        return (sum_gradients * sum_gradients) / (sum_hessians + l2);
      }
    } else {
      double output = CalculateSplittedLeafOutput<USE_L1, USE_MAX_OUTPUT>(
          sum_gradients, sum_hessians, l1, l2, max_delta_step);
      return GetLeafGainGivenOutput<USE_L1>(sum_gradients, sum_hessians, l1, l2,
                                            output);
    }
  }

  template <bool USE_L1>
  static double GetLeafGainGivenOutput(double sum_gradients,
                                       double sum_hessians, double l1,
                                       double l2, double output) {
    if (USE_L1) {
      const double sg_l1 = ThresholdL1(sum_gradients, l1);
      return -(2.0 * sg_l1 * output + (sum_hessians + l2) * output * output);
    } else {
      return -(2.0 * sum_gradients * output +
               (sum_hessians + l2) * output * output);
    }
  }

  template <bool USE_RAND, bool USE_MC, bool USE_L1, bool USE_MAX_OUTPUT,
            bool REVERSE, bool SKIP_DEFAULT_BIN, bool NA_AS_MISSING>
  void FindBestThresholdSequentially(double sum_gradient, double sum_hessian,
                                     data_size_t num_data,
                                     const ConstraintEntry& constraints,
                                     double min_gain_shift, SplitInfo* output,
                                     int rand_threshold) {
    const int8_t offset = meta_->offset;
    double best_sum_left_gradient = NAN;
    double best_sum_left_hessian = NAN;
    double best_gain = kMinScore;
    data_size_t best_left_count = 0;
    uint32_t best_threshold = static_cast<uint32_t>(meta_->num_bin);
    const double cnt_factor = num_data / sum_hessian;
    if (REVERSE) {
      double sum_right_gradient = 0.0f;
      double sum_right_hessian = kEpsilon;
      data_size_t right_count = 0;

      int t = meta_->num_bin - 1 - offset - NA_AS_MISSING;
      const int t_end = 1 - offset;

      // from right to left, and we don't need data in bin0
      for (; t >= t_end; --t) {
        // need to skip default bin
        if (SKIP_DEFAULT_BIN) {
          if ((t + offset) == static_cast<int>(meta_->default_bin)) {
            continue;
          }
        }
        const auto grad = GET_GRAD(data_, t);
        const auto hess = GET_HESS(data_, t);
        data_size_t cnt =
            static_cast<data_size_t>(Common::RoundInt(hess * cnt_factor));
        sum_right_gradient += grad;
        sum_right_hessian += hess;
        right_count += cnt;
        // if data not enough, or sum hessian too small
        if (right_count < meta_->config->min_data_in_leaf ||
            sum_right_hessian < meta_->config->min_sum_hessian_in_leaf) {
          continue;
        }
        data_size_t left_count = num_data - right_count;
        // if data not enough
        if (left_count < meta_->config->min_data_in_leaf) {
          break;
        }

        double sum_left_hessian = sum_hessian - sum_right_hessian;
        // if sum hessian too small
        if (sum_left_hessian < meta_->config->min_sum_hessian_in_leaf) {
          break;
        }

        double sum_left_gradient = sum_gradient - sum_right_gradient;
        if (USE_RAND) {
          if (t - 1 + offset != rand_threshold) {
            continue;
          }
        }
        // current split gain
        double current_gain = GetSplitGains<USE_MC, USE_L1, USE_MAX_OUTPUT>(
            sum_left_gradient, sum_left_hessian, sum_right_gradient,
            sum_right_hessian, meta_->config->lambda_l1,
            meta_->config->lambda_l2, meta_->config->max_delta_step,
            constraints, meta_->monotone_type);
        // gain with split is worse than without split
        if (current_gain <= min_gain_shift) {
          continue;
        }

        // mark to is splittable
        is_splittable_ = true;
        // better split point
        if (current_gain > best_gain) {
          best_left_count = left_count;
          best_sum_left_gradient = sum_left_gradient;
          best_sum_left_hessian = sum_left_hessian;
          // left is <= threshold, right is > threshold.  so this is t-1
          best_threshold = static_cast<uint32_t>(t - 1 + offset);
          best_gain = current_gain;
        }
      }
    } else {
      double sum_left_gradient = 0.0f;
      double sum_left_hessian = kEpsilon;
      data_size_t left_count = 0;

      int t = 0;
      const int t_end = meta_->num_bin - 2 - offset;

      if (NA_AS_MISSING) {
        if (offset == 1) {
          sum_left_gradient = sum_gradient;
          sum_left_hessian = sum_hessian - kEpsilon;
          left_count = num_data;
          for (int i = 0; i < meta_->num_bin - offset; ++i) {
            const auto grad = GET_GRAD(data_, i);
            const auto hess = GET_HESS(data_, i);
            data_size_t cnt =
                static_cast<data_size_t>(Common::RoundInt(hess * cnt_factor));
            sum_left_gradient -= grad;
            sum_left_hessian -= hess;
            left_count -= cnt;
          }
          t = -1;
        }
      }

      for (; t <= t_end; ++t) {
        if (SKIP_DEFAULT_BIN) {
          if ((t + offset) == static_cast<int>(meta_->default_bin)) {
            continue;
          }
        }
        if (t >= 0) {
          sum_left_gradient += GET_GRAD(data_, t);
          sum_left_hessian += GET_HESS(data_, t);
          left_count += static_cast<data_size_t>(
              Common::RoundInt(GET_HESS(data_, t) * cnt_factor));
        }
        // if data not enough, or sum hessian too small
        if (left_count < meta_->config->min_data_in_leaf ||
            sum_left_hessian < meta_->config->min_sum_hessian_in_leaf) {
          continue;
        }
        data_size_t right_count = num_data - left_count;
        // if data not enough
        if (right_count < meta_->config->min_data_in_leaf) {
          break;
        }

        double sum_right_hessian = sum_hessian - sum_left_hessian;
        // if sum hessian too small
        if (sum_right_hessian < meta_->config->min_sum_hessian_in_leaf) {
          break;
        }

        double sum_right_gradient = sum_gradient - sum_left_gradient;
        if (USE_RAND) {
          if (t + offset != rand_threshold) {
            continue;
          }
        }
        // current split gain
        double current_gain = GetSplitGains<USE_MC, USE_L1, USE_MAX_OUTPUT>(
            sum_left_gradient, sum_left_hessian, sum_right_gradient,
            sum_right_hessian, meta_->config->lambda_l1,
            meta_->config->lambda_l2, meta_->config->max_delta_step,
            constraints, meta_->monotone_type);
        // gain with split is worse than without split
        if (current_gain <= min_gain_shift) {
          continue;
        }

        // mark to is splittable
        is_splittable_ = true;
        // better split point
        if (current_gain > best_gain) {
          best_left_count = left_count;
          best_sum_left_gradient = sum_left_gradient;
          best_sum_left_hessian = sum_left_hessian;
          best_threshold = static_cast<uint32_t>(t + offset);
          best_gain = current_gain;
        }
      }
    }

    if (is_splittable_ && best_gain > output->gain + min_gain_shift) {
      // update split information
      output->threshold = best_threshold;
      output->left_output =
          CalculateSplittedLeafOutput<USE_MC, USE_L1, USE_MAX_OUTPUT>(
              best_sum_left_gradient, best_sum_left_hessian,
              meta_->config->lambda_l1, meta_->config->lambda_l2,
              meta_->config->max_delta_step, constraints);
      output->left_count = best_left_count;
      output->left_sum_gradient = best_sum_left_gradient;
      output->left_sum_hessian = best_sum_left_hessian - kEpsilon;
      output->right_output =
          CalculateSplittedLeafOutput<USE_MC, USE_L1, USE_MAX_OUTPUT>(
              sum_gradient - best_sum_left_gradient,
              sum_hessian - best_sum_left_hessian, meta_->config->lambda_l1,
              meta_->config->lambda_l2, meta_->config->max_delta_step,
              constraints);
      output->right_count = num_data - best_left_count;
      output->right_sum_gradient = sum_gradient - best_sum_left_gradient;
      output->right_sum_hessian =
          sum_hessian - best_sum_left_hessian - kEpsilon;
      output->gain = best_gain - min_gain_shift;
      output->default_left = REVERSE;
    }
  }

  const FeatureMetainfo* meta_;
  /*! \brief sum of gradient of each bin */
  hist_t* data_;
  bool is_splittable_ = true;

  std::function<void(double, double, data_size_t, const ConstraintEntry&,
                     SplitInfo*)>
      find_best_threshold_fun_;
};

class HistogramPool {
 public:
  /*!
   * \brief Constructor
   */
  HistogramPool() {
    cache_size_ = 0;
    total_size_ = 0;
  }

  /*!
   * \brief Destructor
   */
  ~HistogramPool() {}

  /*!
   * \brief Reset pool size
   * \param cache_size Max cache size
   * \param total_size Total size will be used
   */
  void Reset(int cache_size, int total_size) {
    cache_size_ = cache_size;
    // at least need 2 bucket to store smaller leaf and larger leaf
    CHECK_GE(cache_size_, 2);
    total_size_ = total_size;
    if (cache_size_ > total_size_) {
      cache_size_ = total_size_;
    }
    is_enough_ = (cache_size_ == total_size_);
    if (!is_enough_) {
      mapper_.resize(total_size_);
      inverse_mapper_.resize(cache_size_);
      last_used_time_.resize(cache_size_);
      ResetMap();
    }
  }

  /*!
   * \brief Reset mapper
   */
  void ResetMap() {
    if (!is_enough_) {
      cur_time_ = 0;
      std::fill(mapper_.begin(), mapper_.end(), -1);
      std::fill(inverse_mapper_.begin(), inverse_mapper_.end(), -1);
      std::fill(last_used_time_.begin(), last_used_time_.end(), 0);
    }
  }
  template <bool USE_DATA, bool USE_CONFIG>
  static void SetFeatureInfo(const Dataset* train_data, const Config* config,
                             std::vector<FeatureMetainfo>* feature_meta) {
    auto& ref_feature_meta = *feature_meta;
    const int num_feature = train_data->num_features();
    ref_feature_meta.resize(num_feature);
#pragma omp parallel for schedule(static, 512) if (num_feature >= 1024)
    for (int i = 0; i < num_feature; ++i) {
      if (USE_DATA) {
        ref_feature_meta[i].num_bin = train_data->FeatureNumBin(i);
        ref_feature_meta[i].default_bin =
            train_data->FeatureBinMapper(i)->GetDefaultBin();
        ref_feature_meta[i].missing_type =
            train_data->FeatureBinMapper(i)->missing_type();
        if (train_data->FeatureBinMapper(i)->GetMostFreqBin() == 0) {
          ref_feature_meta[i].offset = 1;
        } else {
          ref_feature_meta[i].offset = 0;
        }
        ref_feature_meta[i].bin_type =
            train_data->FeatureBinMapper(i)->bin_type();
      }
      if (USE_CONFIG) {
        const int real_fidx = train_data->RealFeatureIndex(i);
        if (!config->monotone_constraints.empty()) {
          ref_feature_meta[i].monotone_type =
              config->monotone_constraints[real_fidx];
        } else {
          ref_feature_meta[i].monotone_type = 0;
        }
        if (!config->feature_contri.empty()) {
          ref_feature_meta[i].penalty = config->feature_contri[real_fidx];
        } else {
          ref_feature_meta[i].penalty = 1.0;
        }
        ref_feature_meta[i].rand = Random(config->extra_seed + i);
      }
      ref_feature_meta[i].config = config;
    }
  }

  void DynamicChangeSize(const Dataset* train_data, bool is_hist_colwise,
                         const Config* config, int cache_size, int total_size) {
    if (feature_metas_.empty()) {
      SetFeatureInfo<true, true>(train_data, config, &feature_metas_);
      uint64_t bin_cnt_over_features = 0;
      for (int i = 0; i < train_data->num_features(); ++i) {
        bin_cnt_over_features +=
            static_cast<uint64_t>(feature_metas_[i].num_bin);
      }
      Log::Info("Total Bins %d", bin_cnt_over_features);
    }
    int old_cache_size = static_cast<int>(pool_.size());
    Reset(cache_size, total_size);

    if (cache_size > old_cache_size) {
      pool_.resize(cache_size);
      data_.resize(cache_size);
    }
    int num_total_bin = static_cast<int>(train_data->NumTotalBin());

    std::vector<int> offsets;
    if (is_hist_colwise) {
      int offset = 0;
      for (int j = 0; j < train_data->num_features(); ++j) {
        offset += train_data->SubFeatureBinOffset(j);
        offsets.push_back(offset);
        auto num_bin = train_data->FeatureNumBin(j);
        if (train_data->FeatureBinMapper(j)->GetMostFreqBin() == 0) {
          num_bin -= 1;
        }
        offset += num_bin;
      }
    } else {
      num_total_bin = 1;
      for (int j = 0; j < train_data->num_features(); ++j) {
        offsets.push_back(num_total_bin);
        num_total_bin += train_data->FeatureBinMapper(j)->num_bin();
        if (train_data->FeatureBinMapper(j)->GetMostFreqBin() == 0) {
          num_total_bin -= 1;
        }
      }
    }
    OMP_INIT_EX();
#pragma omp parallel for schedule(static)
    for (int i = old_cache_size; i < cache_size; ++i) {
      OMP_LOOP_EX_BEGIN();
      pool_[i].reset(new FeatureHistogram[train_data->num_features()]);
      data_[i].resize(num_total_bin * 2);
      for (int j = 0; j < train_data->num_features(); ++j) {
        pool_[i][j].Init(data_[i].data() + offsets[j] * 2, &feature_metas_[j]);
      }
      OMP_LOOP_EX_END();
    }
    OMP_THROW_EX();
  }

  void ResetConfig(const Dataset* train_data, const Config* config) {
    CHECK_GT(train_data->num_features(), 0);
    const Config* old_config = feature_metas_[0].config;
    SetFeatureInfo<false, true>(train_data, config, &feature_metas_);
    // if need to reset the function pointers
    if (old_config->lambda_l1 != config->lambda_l1 ||
        old_config->monotone_constraints != config->monotone_constraints ||
        old_config->extra_trees != config->extra_trees ||
        old_config->max_delta_step != config->max_delta_step) {
#pragma omp parallel for schedule(static)
      for (int i = 0; i < cache_size_; ++i) {
        for (int j = 0; j < train_data->num_features(); ++j) {
          pool_[i][j].ResetFunc();
        }
      }
    }
  }

  /*!
   * \brief Get data for the specific index
   * \param idx which index want to get
   * \param out output data will store into this
   * \return True if this index is in the pool, False if this index is not in
   * the pool
   */
  bool Get(int idx, FeatureHistogram** out) {
    if (is_enough_) {
      *out = pool_[idx].get();
      return true;
    } else if (mapper_[idx] >= 0) {
      int slot = mapper_[idx];
      *out = pool_[slot].get();
      last_used_time_[slot] = ++cur_time_;
      return true;
    } else {
      // choose the least used slot
      int slot = static_cast<int>(ArrayArgs<int>::ArgMin(last_used_time_));
      *out = pool_[slot].get();
      last_used_time_[slot] = ++cur_time_;

      // reset previous mapper
      if (inverse_mapper_[slot] >= 0) mapper_[inverse_mapper_[slot]] = -1;

      // update current mapper
      mapper_[idx] = slot;
      inverse_mapper_[slot] = idx;
      return false;
    }
  }

  /*!
   * \brief Move data from one index to another index
   * \param src_idx
   * \param dst_idx
   */
  void Move(int src_idx, int dst_idx) {
    if (is_enough_) {
      std::swap(pool_[src_idx], pool_[dst_idx]);
      return;
    }
    if (mapper_[src_idx] < 0) {
      return;
    }
    // get slot of src idx
    int slot = mapper_[src_idx];
    // reset src_idx
    mapper_[src_idx] = -1;

    // move to dst idx
    mapper_[dst_idx] = slot;
    last_used_time_[slot] = ++cur_time_;
    inverse_mapper_[slot] = dst_idx;
  }

 private:
  std::vector<std::unique_ptr<FeatureHistogram[]>> pool_;
  std::vector<
      std::vector<hist_t, Common::AlignmentAllocator<hist_t, kAlignedSize>>>
      data_;
  std::vector<FeatureMetainfo> feature_metas_;
  int cache_size_;
  int total_size_;
  bool is_enough_ = false;
  std::vector<int> mapper_;
  std::vector<int> inverse_mapper_;
  std::vector<int> last_used_time_;
  int cur_time_ = 0;
};

}  // namespace LightGBM
#endif  // LightGBM_TREELEARNER_FEATURE_HISTOGRAM_HPP_