text: /*
   * Copyright (c) 2019, Alliance for Open Media. All rights reserved
   *
   * This source code is subject to the terms of the BSD 2 Clause License and
   * the Alliance for Open Media Patent License 1.0. If the BSD 2 Clause License
   * was not distributed with this source code in the LICENSE file, you can
   * obtain it at www.aomedia.org/license/software. If the Alliance for Open
   * Media Patent License 1.0 was not distributed with this source code in the
   * PATENTS file, you can obtain it at www.aomedia.org/license/patent.
   */
  
  /*!\defgroup gf_group_algo Golden Frame Group
   * \ingroup high_level_algo
   * Algorithms regarding determining the length of GF groups and defining GF
   * group structures.
   * @{
   */
  /*! @} - end defgroup gf_group_algo */
  
  #include <stdint.h>
  
  #include "config/aom_config.h"
  #include "config/aom_scale_rtcd.h"
  
  #include "aom/aom_codec.h"
  #include "aom/aom_encoder.h"
  
  #include "av1/common/av1_common_int.h"
  
  #include "av1/encoder/encoder.h"
  #include "av1/encoder/firstpass.h"
  #include "av1/encoder/gop_structure.h"
  #include "av1/encoder/pass2_strategy.h"
  #include "av1/encoder/ratectrl.h"
  #include "av1/encoder/rc_utils.h"
  #include "av1/encoder/temporal_filter.h"
  #include "av1/encoder/thirdpass.h"
  #include "av1/encoder/tpl_model.h"
  #include "av1/encoder/encode_strategy.h"
  
  #define DEFAULT_KF_BOOST 2300
  #define DEFAULT_GF_BOOST 2000
  #define GROUP_ADAPTIVE_MAXQ 1
  
  static void init_gf_stats(GF_GROUP_STATS *gf_stats);
  
  // Calculate an active area of the image that discounts formatting
  // bars and partially discounts other 0 energy areas.
  #define MIN_ACTIVE_AREA 0.5
  #define MAX_ACTIVE_AREA 1.0
  static double calculate_active_area(const FRAME_INFO *frame_info,
                                      const FIRSTPASS_STATS *this_frame) {
    const double active_pct =
        1.0 -
        ((this_frame->intra_skip_pct / 2) +
         ((this_frame->inactive_zone_rows * 2) / (double)frame_info->mb_rows));
    return fclamp(active_pct, MIN_ACTIVE_AREA, MAX_ACTIVE_AREA);
  }
  
  // Calculate a modified Error used in distributing bits between easier and
  // harder frames.
  #define ACT_AREA_CORRECTION 0.5
  static double calculate_modified_err_new(const FRAME_INFO *frame_info,
                                           const FIRSTPASS_STATS *total_stats,
                                           const FIRSTPASS_STATS *this_stats,
                                           int vbrbias, double modified_error_min,
                                           double modified_error_max) {
    if (total_stats == NULL) {
      return 0;
    }
    const double av_weight = total_stats->weight / total_stats->count;
    const double av_err =
        (total_stats->coded_error * av_weight) / total_stats->count;
    double modified_error =
        av_err * pow(this_stats->coded_error * this_stats->weight /
                         DOUBLE_DIVIDE_CHECK(av_err),
                     vbrbias / 100.0);
  
    // Correction for active area. Frames with a reduced active area
    // (eg due to formatting bars) have a higher error per mb for the
    // remaining active MBs. The correction here assumes that coding
    // 0.5N blocks of complexity 2X is a little easier than coding N
    // blocks of complexity X.
    modified_error *=
        pow(calculate_active_area(frame_info, this_stats), ACT_AREA_CORRECTION);
  
    return fclamp(modified_error, modified_error_min, modified_error_max);
  }
  
  static double calculate_modified_err(const FRAME_INFO *frame_info,
                                       const TWO_PASS *twopass,
                                       const AV1EncoderConfig *oxcf,
                                       const FIRSTPASS_STATS *this_frame) {
    const FIRSTPASS_STATS *total_stats = twopass->stats_buf_ctx->total_stats;
    return calculate_modified_err_new(
        frame_info, total_stats, this_frame, oxcf->rc_cfg.vbrbias,
        twopass->modified_error_min, twopass->modified_error_max);
  }
  
  // Resets the first pass file to the given position using a relative seek from
  // the current position.
  static void reset_fpf_position(TWO_PASS_FRAME *p_frame,
                                 const FIRSTPASS_STATS *position) {
    p_frame->stats_in = position;
  }
  
  static int input_stats(TWO_PASS *p, TWO_PASS_FRAME *p_frame,
                         FIRSTPASS_STATS *fps) {
    if (p_frame->stats_in >= p->stats_buf_ctx->stats_in_end) return EOF;
  
    *fps = *p_frame->stats_in;
    ++p_frame->stats_in;
    return 1;
  }
  
  static int input_stats_lap(TWO_PASS *p, TWO_PASS_FRAME *p_frame,
                             FIRSTPASS_STATS *fps) {
    if (p_frame->stats_in >= p->stats_buf_ctx->stats_in_end) return EOF;
  
    *fps = *p_frame->stats_in;
    /* Move old stats[0] out to accommodate for next frame stats  */
    memmove(p->frame_stats_arr[0], p->frame_stats_arr[1],
            (p->stats_buf_ctx->stats_in_end - p_frame->stats_in - 1) *
                sizeof(FIRSTPASS_STATS));
    p->stats_buf_ctx->stats_in_end--;
    return 1;
  }
  
  // Read frame stats at an offset from the current position.
  static const FIRSTPASS_STATS *read_frame_stats(const TWO_PASS *p,
                                                 const TWO_PASS_FRAME *p_frame,
                                                 int offset) {
    if ((offset >= 0 &&
         p_frame->stats_in + offset >= p->stats_buf_ctx->stats_in_end) ||
        (offset < 0 &&
         p_frame->stats_in + offset < p->stats_buf_ctx->stats_in_start)) {
      return NULL;
    }
  
    return &p_frame->stats_in[offset];
  }
  
  // This function returns the maximum target rate per frame.
  static int frame_max_bits(const RATE_CONTROL *rc,
                            const AV1EncoderConfig *oxcf) {
    int64_t max_bits = ((int64_t)rc->avg_frame_bandwidth *
                        (int64_t)oxcf->rc_cfg.vbrmax_section) /
                       100;
    if (max_bits < 0)
      max_bits = 0;
    else if (max_bits > rc->max_frame_bandwidth)
      max_bits = rc->max_frame_bandwidth;
  
    return (int)max_bits;
  }
  
  static const double q_pow_term[(QINDEX_RANGE >> 5) + 1] = { 0.65, 0.70, 0.75,
                                                              0.80, 0.85, 0.90,
                                                              0.95, 0.95, 0.95 };
  #define ERR_DIVISOR 96.0
  static double calc_correction_factor(double err_per_mb, int q) {
    const double error_term = err_per_mb / ERR_DIVISOR;
    const int index = q >> 5;
    // Adjustment to power term based on qindex
    const double power_term =
        q_pow_term[index] +
        (((q_pow_term[index + 1] - q_pow_term[index]) * (q % 32)) / 32.0);
    assert(error_term >= 0.0);
    return fclamp(pow(error_term, power_term), 0.05, 5.0);
  }
  
  // Based on history adjust expectations of bits per macroblock.
  static void twopass_update_bpm_factor(AV1_COMP *cpi, int rate_err_tol) {
    TWO_PASS *twopass = &cpi->ppi->twopass;
    const PRIMARY_RATE_CONTROL *const p_rc = &cpi->ppi->p_rc;
  
    // Based on recent history adjust expectations of bits per macroblock.
    double damp_fac = AOMMAX(5.0, rate_err_tol / 10.0);
    double rate_err_factor = 1.0;
    const double adj_limit = AOMMAX(0.20, (double)(100 - rate_err_tol) / 200.0);
    const double min_fac = 1.0 - adj_limit;
    const double max_fac = 1.0 + adj_limit;
    int err_estimate = p_rc->rate_error_estimate;
  
    if (p_rc->vbr_bits_off_target && p_rc->total_actual_bits > 0) {
      if (cpi->ppi->lap_enabled) {
        rate_err_factor =
            (double)twopass->rolling_arf_group_actual_bits /
            DOUBLE_DIVIDE_CHECK((double)twopass->rolling_arf_group_target_bits);
      } else {
        rate_err_factor =
            1.0 - ((double)(p_rc->vbr_bits_off_target) /
                   AOMMAX(p_rc->total_actual_bits, cpi->ppi->twopass.bits_left));
      }
  
      rate_err_factor = AOMMAX(min_fac, AOMMIN(max_fac, rate_err_factor));
  
      // Adjustment is damped if this is 1 pass with look ahead processing
      // (as there are only ever a few frames of data) and for all but the first
      // GOP in normal two pass.
      if ((twopass->bpm_factor != 1.0) || cpi->ppi->lap_enabled) {
        rate_err_factor = 1.0 + ((rate_err_factor - 1.0) / damp_fac);
      }
    }
  
    // Is the rate control trending in the right direction. Only make
    // an adjustment if things are getting worse.
    if ((rate_err_factor < 1.0 && err_estimate > 0) ||
        (rate_err_factor > 1.0 && err_estimate < 0)) {
      twopass->bpm_factor *= rate_err_factor;
      twopass->bpm_factor = AOMMAX(min_fac, AOMMIN(max_fac, twopass->bpm_factor));
    }
  }
  
  static int qbpm_enumerator(int rate_err_tol) {
    return 1200000 + ((300000 * AOMMIN(75, AOMMAX(rate_err_tol - 25, 0))) / 75);
  }
  
  // Similar to find_qindex_by_rate() function in ratectrl.c, but includes
  // calculation of a correction_factor.
  static int find_qindex_by_rate_with_correction(
      int desired_bits_per_mb, aom_bit_depth_t bit_depth, double error_per_mb,
      double group_weight_factor, int rate_err_tol, int best_qindex,
      int worst_qindex) {
    assert(best_qindex <= worst_qindex);
    int low = best_qindex;
    int high = worst_qindex;
  
    while (low < high) {
      const int mid = (low + high) >> 1;
      const double mid_factor = calc_correction_factor(error_per_mb, mid);
      const double q = av1_convert_qindex_to_q(mid, bit_depth);
      const int enumerator = qbpm_enumerator(rate_err_tol);
      const int mid_bits_per_mb =
          (int)((enumerator * mid_factor * group_weight_factor) / q);
  
      if (mid_bits_per_mb > desired_bits_per_mb) {
        low = mid + 1;
      } else {
        high = mid;
      }
    }
    return low;
  }
  
  /*!\brief Choose a target maximum Q for a group of frames
   *
   * \ingroup rate_control
   *
   * This function is used to estimate a suitable maximum Q for a
   * group of frames. Inititally it is called to get a crude estimate
   * for the whole clip. It is then called for each ARF/GF group to get
   * a revised estimate for that group.
   *
   * \param[in]    cpi                 Top-level encoder structure
   * \param[in]    av_frame_err        The average per frame coded error score
   *                                   for frames making up this section/group.
   * \param[in]    inactive_zone       Used to mask off /ignore part of the
   *                                   frame. The most common use case is where
   *                                   a wide format video (e.g. 16:9) is
   *                                   letter-boxed into a more square format.
   *                                   Here we want to ignore the bands at the
   *                                   top and bottom.
   * \param[in]    av_target_bandwidth The target bits per frame
   *
   * \return The maximum Q for frames in the group.
   */
  static int get_twopass_worst_quality(AV1_COMP *cpi, const double av_frame_err,
                                       double inactive_zone,
                                       int av_target_bandwidth) {
    const RATE_CONTROL *const rc = &cpi->rc;
    const AV1EncoderConfig *const oxcf = &cpi->oxcf;
    const RateControlCfg *const rc_cfg = &oxcf->rc_cfg;
    inactive_zone = fclamp(inactive_zone, 0.0, 0.9999);
  
    if (av_target_bandwidth <= 0) {
      return rc->worst_quality;  // Highest value allowed
    } else {
      const int num_mbs = (oxcf->resize_cfg.resize_mode != RESIZE_NONE)
                              ? cpi->initial_mbs
                              : cpi->common.mi_params.MBs;
      const int active_mbs = AOMMAX(1, num_mbs - (int)(num_mbs * inactive_zone));
      const double av_err_per_mb = av_frame_err / (1.0 - inactive_zone);
      const int target_norm_bits_per_mb =
          (int)((uint64_t)av_target_bandwidth << BPER_MB_NORMBITS) / active_mbs;
      int rate_err_tol = AOMMIN(rc_cfg->under_shoot_pct, rc_cfg->over_shoot_pct);
  
      // Update bpm correction factor based on previous GOP rate error.
      twopass_update_bpm_factor(cpi, rate_err_tol);
  
      // Try and pick a max Q that will be high enough to encode the
      // content at the given rate.
      int q = find_qindex_by_rate_with_correction(
          target_norm_bits_per_mb, cpi->common.seq_params->bit_depth,
          av_err_per_mb, cpi->ppi->twopass.bpm_factor, rate_err_tol,
          rc->best_quality, rc->worst_quality);
  
      // Restriction on active max q for constrained quality mode.
      if (rc_cfg->mode == AOM_CQ) q = AOMMAX(q, rc_cfg->cq_level);
      return q;
    }
  }
  
  #define INTRA_PART 0.005
  #define DEFAULT_DECAY_LIMIT 0.75
  #define LOW_SR_DIFF_TRHESH 0.01
  #define NCOUNT_FRAME_II_THRESH 5.0
  #define LOW_CODED_ERR_PER_MB 0.01
  
  /* This function considers how the quality of prediction may be deteriorating
   * with distance. It comapres the coded error for the last frame and the
   * second reference frame (usually two frames old) and also applies a factor
   * based on the extent of INTRA coding.
   *
   * The decay factor is then used to reduce the contribution of frames further
   * from the alt-ref or golden frame, to the bitframe boost calculation for that
   * alt-ref or golden frame.
   */
  static double get_sr_decay_rate(const FIRSTPASS_STATS *frame) {
    double sr_diff = (frame->sr_coded_error - frame->coded_error);
    double sr_decay = 1.0;
    double modified_pct_inter;
    double modified_pcnt_intra;
  
    modified_pct_inter = frame->pcnt_inter;
    if ((frame->coded_error > LOW_CODED_ERR_PER_MB) &&
        ((frame->intra_error / DOUBLE_DIVIDE_CHECK(frame->coded_error)) <
         (double)NCOUNT_FRAME_II_THRESH)) {
      modified_pct_inter = frame->pcnt_inter - frame->pcnt_neutral;
    }
    modified_pcnt_intra = 100 * (1.0 - modified_pct_inter);
  
    if ((sr_diff > LOW_SR_DIFF_TRHESH)) {
      double sr_diff_part = ((sr_diff * 0.25) / frame->intra_error);
      sr_decay = 1.0 - sr_diff_part - (INTRA_PART * modified_pcnt_intra);
    }
    return AOMMAX(sr_decay, DEFAULT_DECAY_LIMIT);
  }
  
  // This function gives an estimate of how badly we believe the prediction
  // quality is decaying from frame to frame.
  static double get_zero_motion_factor(const FIRSTPASS_STATS *frame) {
    const double zero_motion_pct = frame->pcnt_inter - frame->pcnt_motion;
    double sr_decay = get_sr_decay_rate(frame);
    return AOMMIN(sr_decay, zero_motion_pct);
  }
  
  #define DEFAULT_ZM_FACTOR 0.5
  static double get_prediction_decay_rate(const FIRSTPASS_STATS *frame_stats) {
    const double sr_decay_rate = get_sr_decay_rate(frame_stats);
    double zero_motion_factor =
        DEFAULT_ZM_FACTOR * (frame_stats->pcnt_inter - frame_stats->pcnt_motion);
  
    // Clamp value to range 0.0 to 1.0
    // This should happen anyway if input values are sensibly clamped but checked
    // here just in case.
    if (zero_motion_factor > 1.0)
      zero_motion_factor = 1.0;
    else if (zero_motion_factor < 0.0)
      zero_motion_factor = 0.0;
  
    return AOMMAX(zero_motion_factor,
                  (sr_decay_rate + ((1.0 - sr_decay_rate) * zero_motion_factor)));
  }
  
  // Function to test for a condition where a complex transition is followed
  // by a static section. For example in slide shows where there is a fade
  // between slides. This is to help with more optimal kf and gf positioning.
  static int detect_transition_to_still(const FIRSTPASS_INFO *firstpass_info,
                                        int next_stats_index,
                                        const int min_gf_interval,
                                        const int frame_interval,
                                        const int still_interval,
                                        const double loop_decay_rate,
                                        const double last_decay_rate) {
    // Break clause to detect very still sections after motion
    // For example a static image after a fade or other transition
    // instead of a clean scene cut.
    if (frame_interval > min_gf_interval && loop_decay_rate >= 0.999 &&
        last_decay_rate < 0.9) {
      int stats_left =
          av1_firstpass_info_future_count(firstpass_info, next_stats_index);
      if (stats_left >= still_interval) {
        int j;
        // Look ahead a few frames to see if static condition persists...
        for (j = 0; j < still_interval; ++j) {
          const FIRSTPASS_STATS *stats =
              av1_firstpass_info_peek(firstpass_info, next_stats_index + j);
          if (stats->pcnt_inter - stats->pcnt_motion < 0.999) break;
        }
        // Only if it does do we signal a transition to still.
        return j == still_interval;
      }
    }
    return 0;
  }
  
  // This function detects a flash through the high relative pcnt_second_ref
  // score in the frame following a flash frame. The offset passed in should
  // reflect this.
  static int detect_flash(const TWO_PASS *twopass,
                          const TWO_PASS_FRAME *twopass_frame, const int offset) {
    const FIRSTPASS_STATS *const next_frame =
        read_frame_stats(twopass, twopass_frame, offset);
  
    // What we are looking for here is a situation where there is a
    // brief break in prediction (such as a flash) but subsequent frames
    // are reasonably well predicted by an earlier (pre flash) frame.
    // The recovery after a flash is indicated by a high pcnt_second_ref
    // compared to pcnt_inter.
    return next_frame != NULL &&
           next_frame->pcnt_second_ref > next_frame->pcnt_inter &&
           next_frame->pcnt_second_ref >= 0.5;
  }
  
  // Update the motion related elements to the GF arf boost calculation.
  static void accumulate_frame_motion_stats(const FIRSTPASS_STATS *stats,
                                            GF_GROUP_STATS *gf_stats, double f_w,
                                            double f_h) {
    const double pct = stats->pcnt_motion;
  
    // Accumulate Motion In/Out of frame stats.
    gf_stats->this_frame_mv_in_out = stats->mv_in_out_count * pct;
    gf_stats->mv_in_out_accumulator += gf_stats->this_frame_mv_in_out;
    gf_stats->abs_mv_in_out_accumulator += fabs(gf_stats->this_frame_mv_in_out);
  
    // Accumulate a measure of how uniform (or conversely how random) the motion
    // field is (a ratio of abs(mv) / mv).
    if (pct > 0.05) {
      const double mvr_ratio =
          fabs(stats->mvr_abs) / DOUBLE_DIVIDE_CHECK(fabs(stats->MVr));
      const double mvc_ratio =
          fabs(stats->mvc_abs) / DOUBLE_DIVIDE_CHECK(fabs(stats->MVc));
  
      gf_stats->mv_ratio_accumulator +=
          pct *
          (mvr_ratio < stats->mvr_abs * f_h ? mvr_ratio : stats->mvr_abs * f_h);
      gf_stats->mv_ratio_accumulator +=
          pct *
          (mvc_ratio < stats->mvc_abs * f_w ? mvc_ratio : stats->mvc_abs * f_w);
    }
  }
  
  static void accumulate_this_frame_stats(const FIRSTPASS_STATS *stats,
                                          const double mod_frame_err,
                                          GF_GROUP_STATS *gf_stats) {
    gf_stats->gf_group_err += mod_frame_err;
  #if GROUP_ADAPTIVE_MAXQ
    gf_stats->gf_group_raw_error += stats->coded_error;
  #endif
    gf_stats->gf_group_skip_pct += stats->intra_skip_pct;
    gf_stats->gf_group_inactive_zone_rows += stats->inactive_zone_rows;
  }
  
  static void accumulate_next_frame_stats(const FIRSTPASS_STATS *stats,
                                          const int flash_detected,
                                          const int frames_since_key,
                                          const int cur_idx,
                                          GF_GROUP_STATS *gf_stats, int f_w,
                                          int f_h) {
    accumulate_frame_motion_stats(stats, gf_stats, f_w, f_h);
    // sum up the metric values of current gf group
    gf_stats->avg_sr_coded_error += stats->sr_coded_error;
    gf_stats->avg_pcnt_second_ref += stats->pcnt_second_ref;
    gf_stats->avg_new_mv_count += stats->new_mv_count;
    gf_stats->avg_wavelet_energy += stats->frame_avg_wavelet_energy;
    if (fabs(stats->raw_error_stdev) > 0.000001) {
      gf_stats->non_zero_stdev_count++;
      gf_stats->avg_raw_err_stdev += stats->raw_error_stdev;
    }
  
    // Accumulate the effect of prediction quality decay
    if (!flash_detected) {
      gf_stats->last_loop_decay_rate = gf_stats->loop_decay_rate;
      gf_stats->loop_decay_rate = get_prediction_decay_rate(stats);
  
      gf_stats->decay_accumulator =
          gf_stats->decay_accumulator * gf_stats->loop_decay_rate;
  
      // Monitor for static sections.
      if ((frames_since_key + cur_idx - 1) > 1) {
        gf_stats->zero_motion_accumulator = AOMMIN(
            gf_stats->zero_motion_accumulator, get_zero_motion_factor(stats));
      }
    }
  }
  
  static void average_gf_stats(const int total_frame, GF_GROUP_STATS *gf_stats) {
    if (total_frame) {
      gf_stats->avg_sr_coded_error /= total_frame;
      gf_stats->avg_pcnt_second_ref /= total_frame;
      gf_stats->avg_new_mv_count /= total_frame;
      gf_stats->avg_wavelet_energy /= total_frame;
    }
  
    if (gf_stats->non_zero_stdev_count)
      gf_stats->avg_raw_err_stdev /= gf_stats->non_zero_stdev_count;
  }
  
  #define BOOST_FACTOR 12.5
  static double baseline_err_per_mb(const FRAME_INFO *frame_info) {
    unsigned int screen_area = frame_info->frame_height * frame_info->frame_width;
  
    // Use a different error per mb factor for calculating boost for
    //  different formats.
    if (screen_area <= 640 * 360) {
      return 500.0;
    } else {
      return 1000.0;
    }
  }
  
  static double calc_frame_boost(const PRIMARY_RATE_CONTROL *p_rc,
                                 const FRAME_INFO *frame_info,
                                 const FIRSTPASS_STATS *this_frame,
                                 double this_frame_mv_in_out, double max_boost) {
    double frame_boost;
    const double lq = av1_convert_qindex_to_q(p_rc->avg_frame_qindex[INTER_FRAME],
                                              frame_info->bit_depth);
    const double boost_q_correction = AOMMIN((0.5 + (lq * 0.015)), 1.5);
    const double active_area = calculate_active_area(frame_info, this_frame);
  
    // Underlying boost factor is based on inter error ratio.
    frame_boost = AOMMAX(baseline_err_per_mb(frame_info) * active_area,
                         this_frame->intra_error * active_area) /
                  DOUBLE_DIVIDE_CHECK(this_frame->coded_error);
    frame_boost = frame_boost * BOOST_FACTOR * boost_q_correction;
  
    // Increase boost for frames where new data coming into frame (e.g. zoom out).
    // Slightly reduce boost if there is a net balance of motion out of the frame
    // (zoom in). The range for this_frame_mv_in_out is -1.0 to +1.0.
    if (this_frame_mv_in_out > 0.0)
      frame_boost += frame_boost * (this_frame_mv_in_out * 2.0);
    // In the extreme case the boost is halved.
    else
      frame_boost += frame_boost * (this_frame_mv_in_out / 2.0);
  
    return AOMMIN(frame_boost, max_boost * boost_q_correction);
  }
  
  static double calc_kf_frame_boost(const PRIMARY_RATE_CONTROL *p_rc,
                                    const FRAME_INFO *frame_info,
                                    const FIRSTPASS_STATS *this_frame,
                                    double *sr_accumulator, double max_boost) {
    double frame_boost;
    const double lq = av1_convert_qindex_to_q(p_rc->avg_frame_qindex[INTER_FRAME],
                                              frame_info->bit_depth);
    const double boost_q_correction = AOMMIN((0.50 + (lq * 0.015)), 2.00);
    const double active_area = calculate_active_area(frame_info, this_frame);
  
    // Underlying boost factor is based on inter error ratio.
    frame_boost = AOMMAX(baseline_err_per_mb(frame_info) * active_area,
                         this_frame->intra_error * active_area) /
                  DOUBLE_DIVIDE_CHECK(
                      (this_frame->coded_error + *sr_accumulator) * active_area);
  
    // Update the accumulator for second ref error difference.
    // This is intended to give an indication of how much the coded error is
    // increasing over time.
    *sr_accumulator += (this_frame->sr_coded_error - this_frame->coded_error);
    *sr_accumulator = AOMMAX(0.0, *sr_accumulator);
  
    // Q correction and scaling
    // The 40.0 value here is an experimentally derived baseline minimum.
    // This value is in line with the minimum per frame boost in the alt_ref
    // boost calculation.
    frame_boost = ((frame_boost + 40.0) * boost_q_correction);
  
    return AOMMIN(frame_boost, max_boost * boost_q_correction);
  }
  
  static int get_projected_gfu_boost(const PRIMARY_RATE_CONTROL *p_rc,
                                     int gfu_boost, int frames_to_project,
                                     int num_stats_used_for_gfu_boost) {
    /*
     * If frames_to_project is equal to num_stats_used_for_gfu_boost,
     * it means that gfu_boost was calculated over frames_to_project to
     * begin with(ie; all stats required were available), hence return
     * the original boost.
     */
    if (num_stats_used_for_gfu_boost >= frames_to_project) return gfu_boost;
  
    double min_boost_factor = sqrt(p_rc->baseline_gf_interval);
    // Get the current tpl factor (number of frames = frames_to_project).
    double tpl_factor = av1_get_gfu_boost_projection_factor(
        min_boost_factor, MAX_GFUBOOST_FACTOR, frames_to_project);
    // Get the tpl factor when number of frames = num_stats_used_for_prior_boost.
    double tpl_factor_num_stats = av1_get_gfu_boost_projection_factor(
        min_boost_factor, MAX_GFUBOOST_FACTOR, num_stats_used_for_gfu_boost);
    int projected_gfu_boost =
        (int)rint((tpl_factor * gfu_boost) / tpl_factor_num_stats);
    return projected_gfu_boost;
  }
  
  #define GF_MAX_BOOST 90.0
  #define GF_MIN_BOOST 50
  #define MIN_DECAY_FACTOR 0.01
  int av1_calc_arf_boost(const TWO_PASS *twopass,
                         const TWO_PASS_FRAME *twopass_frame,
                         const PRIMARY_RATE_CONTROL *p_rc, FRAME_INFO *frame_info,
                         int offset, int f_frames, int b_frames,
                         int *num_fpstats_used, int *num_fpstats_required,
                         int project_gfu_boost) {
    int i;
    GF_GROUP_STATS gf_stats;
    init_gf_stats(&gf_stats);
    double boost_score = (double)NORMAL_BOOST;
    int arf_boost;
    int flash_detected = 0;
    if (num_fpstats_used) *num_fpstats_used = 0;
  
    // Search forward from the proposed arf/next gf position.
    for (i = 0; i < f_frames; ++i) {
      const FIRSTPASS_STATS *this_frame =
          read_frame_stats(twopass, twopass_frame, i + offset);
      if (this_frame == NULL) break;
  
      // Update the motion related elements to the boost calculation.
      accumulate_frame_motion_stats(this_frame, &gf_stats,
                                    frame_info->frame_width,
                                    frame_info->frame_height);
  
      // We want to discount the flash frame itself and the recovery
      // frame that follows as both will have poor scores.
      flash_detected = detect_flash(twopass, twopass_frame, i + offset) ||
                       detect_flash(twopass, twopass_frame, i + offset + 1);
  
      // Accumulate the effect of prediction quality decay.
      if (!flash_detected) {
        gf_stats.decay_accumulator *= get_prediction_decay_rate(this_frame);
        gf_stats.decay_accumulator = gf_stats.decay_accumulator < MIN_DECAY_FACTOR
                                         ? MIN_DECAY_FACTOR
                                         : gf_stats.decay_accumulator;
      }
  
      boost_score +=
          gf_stats.decay_accumulator *
          calc_frame_boost(p_rc, frame_info, this_frame,
                           gf_stats.this_frame_mv_in_out, GF_MAX_BOOST);
      if (num_fpstats_used) (*num_fpstats_used)++;
    }
  
    arf_boost = (int)boost_score;
  
    // Reset for backward looking loop.
    boost_score = 0.0;
    init_gf_stats(&gf_stats);
    // Search backward towards last gf position.
    for (i = -1; i >= -b_frames; --i) {
      const FIRSTPASS_STATS *this_frame =
          read_frame_stats(twopass, twopass_frame, i + offset);
      if (this_frame == NULL) break;
  
      // Update the motion related elements to the boost calculation.
      accumulate_frame_motion_stats(this_frame, &gf_stats,
                                    frame_info->frame_width,
                                    frame_info->frame_height);
  
      // We want to discount the the flash frame itself and the recovery
      // frame that follows as both will have poor scores.
      flash_detected = detect_flash(twopass, twopass_frame, i + offset) ||
                       detect_flash(twopass, twopass_frame, i + offset + 1);
  
      // Cumulative effect of prediction quality decay.
      if (!flash_detected) {
        gf_stats.decay_accumulator *= get_prediction_decay_rate(this_frame);
        gf_stats.decay_accumulator = gf_stats.decay_accumulator < MIN_DECAY_FACTOR
                                         ? MIN_DECAY_FACTOR
                                         : gf_stats.decay_accumulator;
      }
  
      boost_score +=
          gf_stats.decay_accumulator *
          calc_frame_boost(p_rc, frame_info, this_frame,
                           gf_stats.this_frame_mv_in_out, GF_MAX_BOOST);
      if (num_fpstats_used) (*num_fpstats_used)++;
    }
    arf_boost += (int)boost_score;
  
    if (project_gfu_boost) {
      assert(num_fpstats_required != NULL);
      assert(num_fpstats_used != NULL);
      *num_fpstats_required = f_frames + b_frames;
      arf_boost = get_projected_gfu_boost(p_rc, arf_boost, *num_fpstats_required,
                                          *num_fpstats_used);
    }
  
    if (arf_boost < ((b_frames + f_frames) * GF_MIN_BOOST))
      arf_boost = ((b_frames + f_frames) * GF_MIN_BOOST);
  
    return arf_boost;
  }
  
  // Calculate a section intra ratio used in setting max loop filter.
  static int calculate_section_intra_ratio(const FIRSTPASS_STATS *begin,
                                           const FIRSTPASS_STATS *end,
                                           int section_length) {
    const FIRSTPASS_STATS *s = begin;
    double intra_error = 0.0;
    double coded_error = 0.0;
    int i = 0;
  
    while (s < end && i < section_length) {
      intra_error += s->intra_error;
      coded_error += s->coded_error;
      ++s;
      ++i;
    }
  
    return (int)(intra_error / DOUBLE_DIVIDE_CHECK(coded_error));
  }
  
  /*!\brief Calculates the bit target for this GF/ARF group
   *
   * \ingroup rate_control
   *
   * Calculates the total bits to allocate in this GF/ARF group.
   *
   * \param[in]    cpi              Top-level encoder structure
   * \param[in]    gf_group_err     Cumulative coded error score for the
   *                                frames making up this group.
   *
   * \return The target total number of bits for this GF/ARF group.
   */
  static int64_t calculate_total_gf_group_bits(AV1_COMP *cpi,
                                               double gf_group_err) {
    const RATE_CONTROL *const rc = &cpi->rc;
    const PRIMARY_RATE_CONTROL *const p_rc = &cpi->ppi->p_rc;
    const TWO_PASS *const twopass = &cpi->ppi->twopass;
    const int max_bits = frame_max_bits(rc, &cpi->oxcf);
    int64_t total_group_bits;
  
    // Calculate the bits to be allocated to the group as a whole.
    if ((twopass->kf_group_bits > 0) && (twopass->kf_group_error_left > 0)) {
      total_group_bits = (int64_t)(twopass->kf_group_bits *
                                   (gf_group_err / twopass->kf_group_error_left));
    } else {
      total_group_bits = 0;
    }
  
    // Clamp odd edge cases.
    total_group_bits = (total_group_bits < 0)
                           ? 0
                           : (total_group_bits > twopass->kf_group_bits)
                                 ? twopass->kf_group_bits
                                 : total_group_bits;
  
    // Clip based on user supplied data rate variability limit.
    if (total_group_bits > (int64_t)max_bits * p_rc->baseline_gf_interval)
      total_group_bits = (int64_t)max_bits * p_rc->baseline_gf_interval;
  
    return total_group_bits;
  }
  
  // Calculate the number of bits to assign to boosted frames in a group.
  static int calculate_boost_bits(int frame_count, int boost,
                                  int64_t total_group_bits) {
    int allocation_chunks;
  
    // return 0 for invalid inputs (could arise e.g. through rounding errors)
    if (!boost || (total_group_bits <= 0)) return 0;
  
    if (frame_count <= 0) return (int)(AOMMIN(total_group_bits, INT_MAX));
  
    allocation_chunks = (frame_count * 100) + boost;
  
    // Prevent overflow.
    if (boost > 1023) {
      int divisor = boost >> 10;
      boost /= divisor;
      allocation_chunks /= divisor;
    }
  
    // Calculate the number of extra bits for use in the boosted frame or frames.
    return AOMMAX((int)(((int64_t)boost * total_group_bits) / allocation_chunks),
                  0);
  }
  
  // Calculate the boost factor based on the number of bits assigned, i.e. the
  // inverse of calculate_boost_bits().
  static int calculate_boost_factor(int frame_count, int bits,
                                    int64_t total_group_bits) {
    return (int)(100.0 * frame_count * bits / (total_group_bits - bits));
  }
  
  // Reduce the number of bits assigned to keyframe or arf if necessary, to
  // prevent bitrate spikes that may break level constraints.
  // frame_type: 0: keyframe; 1: arf.
  static int adjust_boost_bits_for_target_level(const AV1_COMP *const cpi,
                                                RATE_CONTROL *const rc,
                                                int bits_assigned,
                                                int64_t group_bits,
                                                int frame_type) {
    const AV1_COMMON *const cm = &cpi->common;
    const SequenceHeader *const seq_params = cm->seq_params;
    PRIMARY_RATE_CONTROL *const p_rc = &cpi->ppi->p_rc;
    const int temporal_layer_id = cm->temporal_layer_id;
    const int spatial_layer_id = cm->spatial_layer_id;
    for (int index = 0; index < seq_params->operating_points_cnt_minus_1 + 1;
         ++index) {
      if (!is_in_operating_point(seq_params->operating_point_idc[index],
                                 temporal_layer_id, spatial_layer_id)) {
        continue;
      }
  
      const AV1_LEVEL target_level =
          cpi->ppi->level_params.target_seq_level_idx[index];
      if (target_level >= SEQ_LEVELS) continue;
  
      assert(is_valid_seq_level_idx(target_level));
  
      const double level_bitrate_limit = av1_get_max_bitrate_for_level(
          target_level, seq_params->tier[0], seq_params->profile);
      const int target_bits_per_frame =
          (int)(level_bitrate_limit / cpi->framerate);
      if (frame_type == 0) {
        // Maximum bits for keyframe is 8 times the target_bits_per_frame.
        const int level_enforced_max_kf_bits = target_bits_per_frame * 8;
        if (bits_assigned > level_enforced_max_kf_bits) {
          const int frames = rc->frames_to_key - 1;
          p_rc->kf_boost = calculate_boost_factor(
              frames, level_enforced_max_kf_bits, group_bits);
          bits_assigned =
              calculate_boost_bits(frames, p_rc->kf_boost, group_bits);
        }
      } else if (frame_type == 1) {
        // Maximum bits for arf is 4 times the target_bits_per_frame.
        const int level_enforced_max_arf_bits = target_bits_per_frame * 4;
        if (bits_assigned > level_enforced_max_arf_bits) {
          p_rc->gfu_boost =
              calculate_boost_factor(p_rc->baseline_gf_interval,
                                     level_enforced_max_arf_bits, group_bits);
          bits_assigned = calculate_boost_bits(p_rc->baseline_gf_interval,
                                               p_rc->gfu_boost, group_bits);
        }
      } else {
        assert(0);
      }
    }
  
    return bits_assigned;
  }
  
  // Allocate bits to each frame in a GF / ARF group
  double layer_fraction[MAX_ARF_LAYERS + 1] = { 1.0,  0.70, 0.55, 0.60,
                                                0.60, 1.0,  1.0 };
  static void allocate_gf_group_bits(GF_GROUP *gf_group,
                                     PRIMARY_RATE_CONTROL *const p_rc,
                                     RATE_CONTROL *const rc,
                                     int64_t gf_group_bits, int gf_arf_bits,
                                     int key_frame, int use_arf) {
    int64_t total_group_bits = gf_group_bits;
    int base_frame_bits;
    const int gf_group_size = gf_group->size;
    int layer_frames[MAX_ARF_LAYERS + 1] = { 0 };
  
    // For key frames the frame target rate is already set and it
    // is also the golden frame.
    // === [frame_index == 0] ===
    int frame_index = !!key_frame;
  
    // Subtract the extra bits set aside for ARF frames from the Group Total
    if (use_arf) total_group_bits -= gf_arf_bits;
  
    int num_frames =
        AOMMAX(1, p_rc->baseline_gf_interval - (rc->frames_since_key == 0));
    base_frame_bits = (int)(total_group_bits / num_frames);
  
    // Check the number of frames in each layer in case we have a
    // non standard group length.
    int max_arf_layer = gf_group->max_layer_depth - 1;
    for (int idx = frame_index; idx < gf_group_size; ++idx) {
      if ((gf_group->update_type[idx] == ARF_UPDATE) ||
          (gf_group->update_type[idx] == INTNL_ARF_UPDATE)) {
        layer_frames[gf_group->layer_depth[idx]]++;
      }
    }
  
    // Allocate extra bits to each ARF layer
    int i;
    int layer_extra_bits[MAX_ARF_LAYERS + 1] = { 0 };
    for (i = 1; i <= max_arf_layer; ++i) {
      double fraction = (i == max_arf_layer) ? 1.0 : layer_fraction[i];
      layer_extra_bits[i] =
          (int)((gf_arf_bits * fraction) / AOMMAX(1, layer_frames[i]));
      gf_arf_bits -= (int)(gf_arf_bits * fraction);
    }
  
    // Now combine ARF layer and baseline bits to give total bits for each frame.
    int arf_extra_bits;
    for (int idx = frame_index; idx < gf_group_size; ++idx) {
      switch (gf_group->update_type[idx]) {
        case ARF_UPDATE:
        case INTNL_ARF_UPDATE:
          arf_extra_bits = layer_extra_bits[gf_group->layer_depth[idx]];
          gf_group->bit_allocation[idx] = base_frame_bits + arf_extra_bits;
          break;
        case INTNL_OVERLAY_UPDATE:
        case OVERLAY_UPDATE: gf_group->bit_allocation[idx] = 0; break;
        default: gf_group->bit_allocation[idx] = base_frame_bits; break;
      }
    }
  
    // Set the frame following the current GOP to 0 bit allocation. For ARF
    // groups, this next frame will be overlay frame, which is the first frame
    // in the next GOP. For GF group, next GOP will overwrite the rate allocation.
    // Setting this frame to use 0 bit (of out the current GOP budget) will
    // simplify logics in reference frame management.
    if (gf_group_size < MAX_STATIC_GF_GROUP_LENGTH)
      gf_group->bit_allocation[gf_group_size] = 0;
  }
  
  // Returns true if KF group and GF group both are almost completely static.
  static INLINE int is_almost_static(double gf_zero_motion, int kf_zero_motion,
                                     int is_lap_enabled) {
    if (is_lap_enabled) {
      /*
       * when LAP enabled kf_zero_motion is not reliable, so use strict
       * constraint on gf_zero_motion.
       */
      return (gf_zero_motion >= 0.999);
    } else {
      return (gf_zero_motion >= 0.995) &&
             (kf_zero_motion >= STATIC_KF_GROUP_THRESH);
    }
  }
  
  #define ARF_ABS_ZOOM_THRESH 4.4
  static INLINE int detect_gf_cut(AV1_COMP *cpi, int frame_index, int cur_start,
                                  int flash_detected, int active_max_gf_interval,
                                  int active_min_gf_interval,
                                  GF_GROUP_STATS *gf_stats) {
    RATE_CONTROL *const rc = &cpi->rc;
    TWO_PASS *const twopass = &cpi->ppi->twopass;
    InitialDimensions *const initial_dimensions = &cpi->initial_dimensions;
    // Motion breakout threshold for loop below depends on image size.
    const double mv_ratio_accumulator_thresh =
        (initial_dimensions->height + initial_dimensions->width) / 4.0;
  
    if (!flash_detected) {
      // Break clause to detect very still sections after motion. For example,
      // a static image after a fade or other transition.
  
      // TODO(angiebird): This is a temporary change, we will avoid using
      // twopass_frame.stats_in in the follow-up CL
      int index = (int)(cpi->twopass_frame.stats_in -
                        twopass->stats_buf_ctx->stats_in_start);
      if (detect_transition_to_still(&twopass->firstpass_info, index,
                                     rc->min_gf_interval, frame_index - cur_start,
                                     5, gf_stats->loop_decay_rate,
                                     gf_stats->last_loop_decay_rate)) {
        return 1;
      }
    }
  
    // Some conditions to breakout after min interval.
    if (frame_index - cur_start >= active_min_gf_interval &&
        // If possible don't break very close to a kf
        (rc->frames_to_key - frame_index >= rc->min_gf_interval) &&
        ((frame_index - cur_start) & 0x01) && !flash_detected &&
        (gf_stats->mv_ratio_accumulator > mv_ratio_accumulator_thresh ||
         gf_stats->abs_mv_in_out_accumulator > ARF_ABS_ZOOM_THRESH)) {
      return 1;
    }
  
    // If almost totally static, we will not use the the max GF length later,
    // so we can continue for more frames.
    if (((frame_index - cur_start) >= active_max_gf_interval + 1) &&
        !is_almost_static(gf_stats->zero_motion_accumulator,
                          twopass->kf_zeromotion_pct, cpi->ppi->lap_enabled)) {
      return 1;
    }
    return 0;
  }
  
  static int is_shorter_gf_interval_better(AV1_COMP *cpi,
                                           EncodeFrameParams *frame_params,
                                           const EncodeFrameInput *frame_input) {
    RATE_CONTROL *const rc = &cpi->rc;
    PRIMARY_RATE_CONTROL *const p_rc = &cpi->ppi->p_rc;
    int gop_length_decision_method = cpi->sf.tpl_sf.gop_length_decision_method;
    int shorten_gf_interval;
  
    av1_tpl_preload_rc_estimate(cpi, frame_params);
  
    if (gop_length_decision_method == 2) {
      // GF group length is decided based on GF boost and tpl stats of ARFs from
      // base layer, (base+1) layer.
      shorten_gf_interval =
          (p_rc->gfu_boost <
           p_rc->num_stats_used_for_gfu_boost * GF_MIN_BOOST * 1.4) &&
          !av1_tpl_setup_stats(cpi, 3, frame_params, frame_input);
    } else {
      int do_complete_tpl = 1;
      GF_GROUP *const gf_group = &cpi->ppi->gf_group;
      int is_temporal_filter_enabled =
          (rc->frames_since_key > 0 && gf_group->arf_index > -1);
  
      if (is_temporal_filter_enabled) {
        int arf_src_index = gf_group->arf_src_offset[gf_group->arf_index];
        av1_temporal_filter(cpi, arf_src_index, gf_group->arf_index, NULL,
                            &cpi->ppi->alt_ref_buffer);
        aom_extend_frame_borders(&cpi->ppi->alt_ref_buffer,
                                 av1_num_planes(&cpi->common));
      }
  
      if (gop_length_decision_method == 1) {
        // Check if tpl stats of ARFs from base layer, (base+1) layer,
        // (base+2) layer can decide the GF group length.
        int gop_length_eval =
            av1_tpl_setup_stats(cpi, 2, frame_params, frame_input);
  
        if (gop_length_eval != 2) {
          do_complete_tpl = 0;
          shorten_gf_interval = !gop_length_eval;
        }
      }
  
      if (do_complete_tpl) {
        // Decide GF group length based on complete tpl stats.
        shorten_gf_interval =
            !av1_tpl_setup_stats(cpi, 1, frame_params, frame_input);
        // Tpl stats is reused when the ARF is temporally filtered and GF
        // interval is not shortened.
        if (is_temporal_filter_enabled && !shorten_gf_interval) {
          cpi->skip_tpl_setup_stats = 1;
  #if CONFIG_BITRATE_ACCURACY
          av1_vbr_rc_update_q_index_list(&cpi->vbr_rc_info, &cpi->ppi->tpl_data,
                                         gf_group, cpi->gf_frame_index,
                                         cpi->common.seq_params->bit_depth);
  #endif  // CONFIG_BITRATE_ACCURACY
        }
      }
    }
    return shorten_gf_interval;
  }
  
  #define MIN_SHRINK_LEN 6  // the minimum length of gf if we are shrinking
  #define SMOOTH_FILT_LEN 7
  #define HALF_FILT_LEN (SMOOTH_FILT_LEN / 2)
  #define WINDOW_SIZE 7
  #define HALF_WIN (WINDOW_SIZE / 2)
  // A 7-tap gaussian smooth filter
  const double smooth_filt[SMOOTH_FILT_LEN] = { 0.006, 0.061, 0.242, 0.383,
                                                0.242, 0.061, 0.006 };
  
  // Smooth filter intra_error and coded_error in firstpass stats.
  // If stats[i].is_flash==1, the ith element should not be used in the filtering.
  static void smooth_filter_stats(const FIRSTPASS_STATS *stats, int start_idx,
                                  int last_idx, double *filt_intra_err,
                                  double *filt_coded_err) {
    int i, j;
    for (i = start_idx; i <= last_idx; i++) {
      double total_wt = 0;
      for (j = -HALF_FILT_LEN; j <= HALF_FILT_LEN; j++) {
        int idx = AOMMIN(AOMMAX(i + j, start_idx), last_idx);
        if (stats[idx].is_flash) continue;
  
        filt_intra_err[i] +=
            smooth_filt[j + HALF_FILT_LEN] * stats[idx].intra_error;
        total_wt += smooth_filt[j + HALF_FILT_LEN];
      }
      if (total_wt > 0.01) {
        filt_intra_err[i] /= total_wt;
      } else {
        filt_intra_err[i] = stats[i].intra_error;
      }
    }
    for (i = start_idx; i <= last_idx; i++) {
      double total_wt = 0;
      for (j = -HALF_FILT_LEN; j <= HALF_FILT_LEN; j++) {
        int idx = AOMMIN(AOMMAX(i + j, start_idx), last_idx);
        // Coded error involves idx and idx - 1.
        if (stats[idx].is_flash || (idx > 0 && stats[idx - 1].is_flash)) continue;
  
        filt_coded_err[i] +=
            smooth_filt[j + HALF_FILT_LEN] * stats[idx].coded_error;
        total_wt += smooth_filt[j + HALF_FILT_LEN];
      }
      if (total_wt > 0.01) {
        filt_coded_err[i] /= total_wt;
      } else {
        filt_coded_err[i] = stats[i].coded_error;
      }
    }
  }
  
  // Calculate gradient
  static void get_gradient(const double *values, int start, int last,
                           double *grad) {
    if (start == last) {
      grad[start] = 0;
      return;
    }
    for (int i = start; i <= last; i++) {
      int prev = AOMMAX(i - 1, start);
      int next = AOMMIN(i + 1, last);
      grad[i] = (values[next] - values[prev]) / (next - prev);
    }
  }
  
  static int find_next_scenecut(const FIRSTPASS_STATS *const stats_start,
                                int first, int last) {
    // Identify unstable areas caused by scenecuts.
    // Find the max and 2nd max coded error, and the average of the rest frames.
    // If there is only one frame that yields a huge coded error, it is likely a
    // scenecut.
    double this_ratio, max_prev_ratio, max_next_ratio, max_prev_coded,
        max_next_coded;
  
    if (last - first == 0) return -1;
  
    for (int i = first; i <= last; i++) {
      if (stats_start[i].is_flash || (i > 0 && stats_start[i - 1].is_flash))
        continue;
      double temp_intra = AOMMAX(stats_start[i].intra_error, 0.01);
      this_ratio = stats_start[i].coded_error / temp_intra;
      // find the avg ratio in the preceding neighborhood
      max_prev_ratio = 0;
      max_prev_coded = 0;
      for (int j = AOMMAX(first, i - HALF_WIN); j < i; j++) {
        if (stats_start[j].is_flash || (j > 0 && stats_start[j - 1].is_flash))
          continue;
        temp_intra = AOMMAX(stats_start[j].intra_error, 0.01);
        double temp_ratio = stats_start[j].coded_error / temp_intra;
        if (temp_ratio > max_prev_ratio) {
          max_prev_ratio = temp_ratio;
        }
        if (stats_start[j].coded_error > max_prev_coded) {
          max_prev_coded = stats_start[j].coded_error;
        }
      }
      // find the avg ratio in the following neighborhood
      max_next_ratio = 0;
      max_next_coded = 0;
      for (int j = i + 1; j <= AOMMIN(i + HALF_WIN, last); j++) {
        if (stats_start[i].is_flash || (i > 0 && stats_start[i - 1].is_flash))
          continue;
        temp_intra = AOMMAX(stats_start[j].intra_error, 0.01);
        double temp_ratio = stats_start[j].coded_error / temp_intra;
        if (temp_ratio > max_next_ratio) {
          max_next_ratio = temp_ratio;
        }
        if (stats_start[j].coded_error > max_next_coded) {
          max_next_coded = stats_start[j].coded_error;
        }
      }
  
      if (max_prev_ratio < 0.001 && max_next_ratio < 0.001) {
        // the ratios are very small, only check a small fixed threshold
        if (this_ratio < 0.02) continue;
      } else {
        // check if this frame has a larger ratio than the neighborhood
        double max_sr = stats_start[i].sr_coded_error;
        if (i < last) max_sr = AOMMAX(max_sr, stats_start[i + 1].sr_coded_error);
        double max_sr_fr_ratio =
            max_sr / AOMMAX(stats_start[i].coded_error, 0.01);
  
        if (max_sr_fr_ratio > 1.2) continue;
        if (this_ratio < 2 * AOMMAX(max_prev_ratio, max_next_ratio) &&
            stats_start[i].coded_error <
                2 * AOMMAX(max_prev_coded, max_next_coded)) {
          continue;
        }
      }
      return i;
    }
    return -1;
  }
  
  // Remove the region with index next_region.
  // parameter merge: 0: merge with previous; 1: merge with next; 2:
  // merge with both, take type from previous if possible
  // After removing, next_region will be the index of the next region.
  static void remove_region(int merge, REGIONS *regions, int *num_regions,
                            int *next_region) {
    int k = *next_region;
    assert(k < *num_regions);
    if (*num_regions == 1) {
      *num_regions = 0;
      return;
    }
    if (k == 0) {
      merge = 1;
    } else if (k == *num_regions - 1) {
      merge = 0;
    }
    int num_merge = (merge == 2) ? 2 : 1;
    switch (merge) {
      case 0:
        regions[k - 1].last = regions[k].last;
        *next_region = k;
        break;
      case 1:
        regions[k + 1].start = regions[k].start;
        *next_region = k + 1;
        break;
      case 2:
        regions[k - 1].last = regions[k + 1].last;
        *next_region = k;
        break;
      default: assert(0);
    }
    *num_regions -= num_merge;
    for (k = *next_region - (merge == 1); k < *num_regions; k++) {
      regions[k] = regions[k + num_merge];
    }
  }
  
  // Insert a region in the cur_region_idx. The start and last should both be in
  // the current region. After insertion, the cur_region_idx will point to the
  // last region that was splitted from the original region.
  static void insert_region(int start, int last, REGION_TYPES type,
                            REGIONS *regions, int *num_regions,
                            int *cur_region_idx) {
    int k = *cur_region_idx;
    REGION_TYPES this_region_type = regions[k].type;
    int this_region_last = regions[k].last;
    int num_add = (start != regions[k].start) + (last != regions[k].last);
    // move the following regions further to the back
    for (int r = *num_regions - 1; r > k; r--) {
      regions[r + num_add] = regions[r];
    }
    *num_regions += num_add;
    if (start > regions[k].start) {
      regions[k].last = start - 1;
      k++;
      regions[k].start = start;
    }
    regions[k].type = type;
    if (last < this_region_last) {
      regions[k].last = last;
      k++;
      regions[k].start = last + 1;
      regions[k].last = this_region_last;
      regions[k].type = this_region_type;
    } else {
      regions[k].last = this_region_last;
    }
    *cur_region_idx = k;
  }
  
  // Get the average of stats inside a region.
  static void analyze_region(const FIRSTPASS_STATS *stats, int k,
                             REGIONS *regions) {
    int i;
    regions[k].avg_cor_coeff = 0;
    regions[k].avg_sr_fr_ratio = 0;
    regions[k].avg_intra_err = 0;
    regions[k].avg_coded_err = 0;
  
    int check_first_sr = (k != 0);
  
    for (i = regions[k].start; i <= regions[k].last; i++) {
      if (i > regions[k].start || check_first_sr) {
        double num_frames =
            (double)(regions[k].last - regions[k].start + check_first_sr);
        double max_coded_error =
            AOMMAX(stats[i].coded_error, stats[i - 1].coded_error);
        double this_ratio =
            stats[i].sr_coded_error / AOMMAX(max_coded_error, 0.001);
        regions[k].avg_sr_fr_ratio += this_ratio / num_frames;
      }
  
      regions[k].avg_intra_err +=
          stats[i].intra_error / (double)(regions[k].last - regions[k].start + 1);
      regions[k].avg_coded_err +=
          stats[i].coded_error / (double)(regions[k].last - regions[k].start + 1);
  
      regions[k].avg_cor_coeff +=
          AOMMAX(stats[i].cor_coeff, 0.001) /
          (double)(regions[k].last - regions[k].start + 1);
      regions[k].avg_noise_var +=
          AOMMAX(stats[i].noise_var, 0.001) /
          (double)(regions[k].last - regions[k].start + 1);
    }
  }
  
  // Calculate the regions stats of every region.
  static void get_region_stats(const FIRSTPASS_STATS *stats, REGIONS *regions,
                               int num_regions) {
    for (int k = 0; k < num_regions; k++) {
      analyze_region(stats, k, regions);
    }
  }
  
  // Find tentative stable regions
  static int find_stable_regions(const FIRSTPASS_STATS *stats,
                                 const double *grad_coded, int this_start,
                                 int this_last, REGIONS *regions) {
    int i, j, k = 0;
    regions[k].start = this_start;
    for (i = this_start; i <= this_last; i++) {
      // Check mean and variance of stats in a window
      double mean_intra = 0.001, var_intra = 0.001;
      double mean_coded = 0.001, var_coded = 0.001;
      int count = 0;
      for (j = -HALF_WIN; j <= HALF_WIN; j++) {
        int idx = AOMMIN(AOMMAX(i + j, this_start), this_last);
        if (stats[idx].is_flash || (idx > 0 && stats[idx - 1].is_flash)) continue;
        mean_intra += stats[idx].intra_error;
        var_intra += stats[idx].intra_error * stats[idx].intra_error;
        mean_coded += stats[idx].coded_error;
        var_coded += stats[idx].coded_error * stats[idx].coded_error;
        count++;
      }
  
      REGION_TYPES cur_type;
      if (count > 0) {
        mean_intra /= (double)count;
        var_intra /= (double)count;
        mean_coded /= (double)count;
        var_coded /= (double)count;
        int is_intra_stable = (var_intra / (mean_intra * mean_intra) < 1.03);
        int is_coded_stable = (var_coded / (mean_coded * mean_coded) < 1.04 &&
                               fabs(grad_coded[i]) / mean_coded < 0.05) ||
                              mean_coded / mean_intra < 0.05;
        int is_coded_small = mean_coded < 0.5 * mean_intra;
        cur_type = (is_intra_stable && is_coded_stable && is_coded_small)
                       ? STABLE_REGION
                       : HIGH_VAR_REGION;
      } else {
        cur_type = HIGH_VAR_REGION;
      }
  
      // mark a new region if type changes
      if (i == regions[k].start) {
        // first frame in the region
        regions[k].type = cur_type;
      } else if (cur_type != regions[k].type) {
        // Append a new region
        regions[k].last = i - 1;
        regions[k + 1].start = i;
        regions[k + 1].type = cur_type;
        k++;
      }
    }
    regions[k].last = this_last;
    return k + 1;
  }
  
  // Clean up regions that should be removed or merged.
  static void cleanup_regions(REGIONS *regions, int *num_regions) {
    int k = 0;
    while (k < *num_regions) {
      if ((k > 0 && regions[k - 1].type == regions[k].type &&
           regions[k].type != SCENECUT_REGION) ||
          regions[k].last < regions[k].start) {
        remove_region(0, regions, num_regions, &k);
      } else {
        k++;
      }
    }
  }
  
  // Remove regions that are of type and shorter than length.
  // Merge it with its neighboring regions.
  static void remove_short_regions(REGIONS *regions, int *num_regions,
                                   REGION_TYPES type, int length) {
    int k = 0;
    while (k < *num_regions && (*num_regions) > 1) {
      if ((regions[k].last - regions[k].start + 1 < length &&
           regions[k].type == type)) {
        // merge current region with the previous and next regions
        remove_region(2, regions, num_regions, &k);
      } else {
        k++;
      }
    }
    cleanup_regions(regions, num_regions);
  }
  
  static void adjust_unstable_region_bounds(const FIRSTPASS_STATS *stats,
                                            REGIONS *regions, int *num_regions) {
    int i, j, k;
    // Remove regions that are too short. Likely noise.
    remove_short_regions(regions, num_regions, STABLE_REGION, HALF_WIN);
    remove_short_regions(regions, num_regions, HIGH_VAR_REGION, HALF_WIN);
  
    get_region_stats(stats, regions, *num_regions);
  
    // Adjust region boundaries. The thresholds are empirically obtained, but
    // overall the performance is not very sensitive to small changes to them.
    for (k = 0; k < *num_regions; k++) {
      if (regions[k].type == STABLE_REGION) continue;
      if (k > 0) {
        // Adjust previous boundary.
        // First find the average intra/coded error in the previous
        // neighborhood.
        double avg_intra_err = 0;
        const int starti = AOMMAX(regions[k - 1].last - WINDOW_SIZE + 1,
                                  regions[k - 1].start + 1);
        const int lasti = regions[k - 1].last;
        int counti = 0;
        for (i = starti; i <= lasti; i++) {
          avg_intra_err += stats[i].intra_error;
          counti++;
        }
        if (counti > 0) {
          avg_intra_err = AOMMAX(avg_intra_err / (double)counti, 0.001);
          int count_coded = 0, count_grad = 0;
          for (j = lasti + 1; j <= regions[k].last; j++) {
            const int intra_close =
                fabs(stats[j].intra_error - avg_intra_err) / avg_intra_err < 0.1;
            const int coded_small = stats[j].coded_error / avg_intra_err < 0.1;
            const int coeff_close = stats[j].cor_coeff > 0.995;
            if (!coeff_close || !coded_small) count_coded--;
            if (intra_close && count_coded >= 0 && count_grad >= 0) {
              // this frame probably belongs to the previous stable region
              regions[k - 1].last = j;
              regions[k].start = j + 1;
            } else {
              break;
            }
          }
        }
      }  // if k > 0
      if (k < *num_regions - 1) {
        // Adjust next boundary.
        // First find the average intra/coded error in the next neighborhood.
        double avg_intra_err = 0;
        const int starti = regions[k + 1].start;
        const int lasti = AOMMIN(regions[k + 1].last - 1,
                                 regions[k + 1].start + WINDOW_SIZE - 1);
        int counti = 0;
        for (i = starti; i <= lasti; i++) {
          avg_intra_err += stats[i].intra_error;
          counti++;
        }
        if (counti > 0) {
          avg_intra_err = AOMMAX(avg_intra_err / (double)counti, 0.001);
          // At the boundary, coded error is large, but still the frame is stable
          int count_coded = 1, count_grad = 1;
          for (j = starti - 1; j >= regions[k].start; j--) {
            const int intra_close =
                fabs(stats[j].intra_error - avg_intra_err) / avg_intra_err < 0.1;
            const int coded_small =
                stats[j + 1].coded_error / avg_intra_err < 0.1;
            const int coeff_close = stats[j].cor_coeff > 0.995;
            if (!coeff_close || !coded_small) count_coded--;
            if (intra_close && count_coded >= 0 && count_grad >= 0) {
              // this frame probably belongs to the next stable region
              regions[k + 1].start = j;
              regions[k].last = j - 1;
            } else {
              break;
            }
          }
        }
      }  // if k < *num_regions - 1
    }    // end of loop over all regions
  
    cleanup_regions(regions, num_regions);
    remove_short_regions(regions, num_regions, HIGH_VAR_REGION, HALF_WIN);
    get_region_stats(stats, regions, *num_regions);
  
    // If a stable regions has higher error than neighboring high var regions,
    // or if the stable region has a lower average correlation,
    // then it should be merged with them
    k = 0;
    while (k < *num_regions && (*num_regions) > 1) {
      if (regions[k].type == STABLE_REGION &&
          (regions[k].last - regions[k].start + 1) < 2 * WINDOW_SIZE &&
          ((k > 0 &&  // previous regions
            (regions[k].avg_coded_err > regions[k - 1].avg_coded_err * 1.01 ||
             regions[k].avg_cor_coeff < regions[k - 1].avg_cor_coeff * 0.999)) &&
           (k < *num_regions - 1 &&  // next region
            (regions[k].avg_coded_err > regions[k + 1].avg_coded_err * 1.01 ||
             regions[k].avg_cor_coeff < regions[k + 1].avg_cor_coeff * 0.999)))) {
        // merge current region with the previous and next regions
        remove_region(2, regions, num_regions, &k);
        analyze_region(stats, k - 1, regions);
      } else if (regions[k].type == HIGH_VAR_REGION &&
                 (regions[k].last - regions[k].start + 1) < 2 * WINDOW_SIZE &&
                 ((k > 0 &&  // previous regions
                   (regions[k].avg_coded_err <
                        regions[k - 1].avg_coded_err * 0.99 ||
                    regions[k].avg_cor_coeff >
                        regions[k - 1].avg_cor_coeff * 1.001)) &&
                  (k < *num_regions - 1 &&  // next region
                   (regions[k].avg_coded_err <
                        regions[k + 1].avg_coded_err * 0.99 ||
                    regions[k].avg_cor_coeff >
                        regions[k + 1].avg_cor_coeff * 1.001)))) {
        // merge current region with the previous and next regions
        remove_region(2, regions, num_regions, &k);
        analyze_region(stats, k - 1, regions);
      } else {
        k++;
      }
    }
  
    remove_short_regions(regions, num_regions, STABLE_REGION, WINDOW_SIZE);
    remove_short_regions(regions, num_regions, HIGH_VAR_REGION, HALF_WIN);
  }
  
  // Identify blending regions.
  static void find_blending_regions(const FIRSTPASS_STATS *stats,
                                    REGIONS *regions, int *num_regions) {
    int i, k = 0;
    // Blending regions will have large content change, therefore will have a
    // large consistent change in intra error.
    int count_stable = 0;
    while (k < *num_regions) {
      if (regions[k].type == STABLE_REGION) {
        k++;
        count_stable++;
        continue;
      }
      int dir = 0;
      int start = 0, last;
      for (i = regions[k].start; i <= regions[k].last; i++) {
        // First mark the regions that has consistent large change of intra error.
        if (k == 0 && i == regions[k].start) continue;
        if (stats[i].is_flash || (i > 0 && stats[i - 1].is_flash)) continue;
        double grad = stats[i].intra_error - stats[i - 1].intra_error;
        int large_change = fabs(grad) / AOMMAX(stats[i].intra_error, 0.01) > 0.05;
        int this_dir = 0;
        if (large_change) {
          this_dir = (grad > 0) ? 1 : -1;
        }
        // the current trend continues
        if (dir == this_dir) continue;
        if (dir != 0) {
          // Mark the end of a new large change group and add it
          last = i - 1;
          insert_region(start, last, BLENDING_REGION, regions, num_regions, &k);
        }
        dir = this_dir;
        if (k == 0 && i == regions[k].start + 1) {
          start = i - 1;
        } else {
          start = i;
        }
      }
      if (dir != 0) {
        last = regions[k].last;
        insert_region(start, last, BLENDING_REGION, regions, num_regions, &k);
      }
      k++;
    }
  
    // If the blending region has very low correlation, mark it as high variance
    // since we probably cannot benefit from it anyways.
    get_region_stats(stats, regions, *num_regions);
    for (k = 0; k < *num_regions; k++) {
      if (regions[k].type != BLENDING_REGION) continue;
      if (regions[k].last == regions[k].start || regions[k].avg_cor_coeff < 0.6 ||
          count_stable == 0)
        regions[k].type = HIGH_VAR_REGION;
    }
    get_region_stats(stats, regions, *num_regions);
  
    // It is possible for blending to result in a "dip" in intra error (first
    // decrease then increase). Therefore we need to find the dip and combine the
    // two regions.
    k = 1;
    while (k < *num_regions) {
      if (k < *num_regions - 1 && regions[k].type == HIGH_VAR_REGION) {
        // Check if this short high variance regions is actually in the middle of
        // a blending region.
        if (regions[k - 1].type == BLENDING_REGION &&
            regions[k + 1].type == BLENDING_REGION &&
            regions[k].last - regions[k].start < 3) {
          int prev_dir = (stats[regions[k - 1].last].intra_error -
                          stats[regions[k - 1].last - 1].intra_error) > 0
                             ? 1
                             : -1;
          int next_dir = (stats[regions[k + 1].last].intra_error -
                          stats[regions[k + 1].last - 1].intra_error) > 0
                             ? 1
                             : -1;
          if (prev_dir < 0 && next_dir > 0) {
            // This is possibly a mid region of blending. Check the ratios
            double ratio_thres = AOMMIN(regions[k - 1].avg_sr_fr_ratio,
                                        regions[k + 1].avg_sr_fr_ratio) *
                                 0.95;
            if (regions[k].avg_sr_fr_ratio > ratio_thres) {
              regions[k].type = BLENDING_REGION;
              remove_region(2, regions, num_regions, &k);
              analyze_region(stats, k - 1, regions);
              continue;
            }
          }
        }
      }
      // Check if we have a pair of consecutive blending regions.
      if (regions[k - 1].type == BLENDING_REGION &&
          regions[k].type == BLENDING_REGION) {
        int prev_dir = (stats[regions[k - 1].last].intra_error -
                        stats[regions[k - 1].last - 1].intra_error) > 0
                           ? 1
                           : -1;
        int next_dir = (stats[regions[k].last].intra_error -
                        stats[regions[k].last - 1].intra_error) > 0
                           ? 1
                           : -1;
  
        // if both are too short, no need to check
        int total_length = regions[k].last - regions[k - 1].start + 1;
        if (total_length < 4) {
          regions[k - 1].type = HIGH_VAR_REGION;
          k++;
          continue;
        }
  
        int to_merge = 0;
        if (prev_dir < 0 && next_dir > 0) {
          // In this case we check the last frame in the previous region.
          double prev_length =
              (double)(regions[k - 1].last - regions[k - 1].start + 1);
          double last_ratio, ratio_thres;
          if (prev_length < 2.01) {
            // if the previous region is very short
            double max_coded_error =
                AOMMAX(stats[regions[k - 1].last].coded_error,
                       stats[regions[k - 1].last - 1].coded_error);
            last_ratio = stats[regions[k - 1].last].sr_coded_error /
                         AOMMAX(max_coded_error, 0.001);
            ratio_thres = regions[k].avg_sr_fr_ratio * 0.95;
          } else {
            double max_coded_error =
                AOMMAX(stats[regions[k - 1].last].coded_error,
                       stats[regions[k - 1].last - 1].coded_error);
            last_ratio = stats[regions[k - 1].last].sr_coded_error /
                         AOMMAX(max_coded_error, 0.001);
            double prev_ratio =
                (regions[k - 1].avg_sr_fr_ratio * prev_length - last_ratio) /
                (prev_length - 1.0);
            ratio_thres = AOMMIN(prev_ratio, regions[k].avg_sr_fr_ratio) * 0.95;
          }
          if (last_ratio > ratio_thres) {
            to_merge = 1;
          }
        }
  
        if (to_merge) {
          remove_region(0, regions, num_regions, &k);
          analyze_region(stats, k - 1, regions);
          continue;
        } else {
          // These are possibly two separate blending regions. Mark the boundary
          // frame as HIGH_VAR_REGION to separate the two.
          int prev_k = k - 1;
          insert_region(regions[prev_k].last, regions[prev_k].last,
                        HIGH_VAR_REGION, regions, num_regions, &prev_k);
          analyze_region(stats, prev_k, regions);
          k = prev_k + 1;
          analyze_region(stats, k, regions);
        }
      }
      k++;
    }
    cleanup_regions(regions, num_regions);
  }
  
  // Clean up decision for blendings. Remove blending regions that are too short.
  // Also if a very short high var region is between a blending and a stable
  // region, just merge it with one of them.
  static void cleanup_blendings(REGIONS *regions, int *num_regions) {
    int k = 0;
    while (k<*num_regions && * num_regions> 1) {
      int is_short_blending = regions[k].type == BLENDING_REGION &&
                              regions[k].last - regions[k].start + 1 < 5;
      int is_short_hv = regions[k].type == HIGH_VAR_REGION &&
                        regions[k].last - regions[k].start + 1 < 5;
      int has_stable_neighbor =
          ((k > 0 && regions[k - 1].type == STABLE_REGION) ||
           (k < *num_regions - 1 && regions[k + 1].type == STABLE_REGION));
      int has_blend_neighbor =
          ((k > 0 && regions[k - 1].type == BLENDING_REGION) ||
           (k < *num_regions - 1 && regions[k + 1].type == BLENDING_REGION));
      int total_neighbors = (k > 0) + (k < *num_regions - 1);
  
      if (is_short_blending ||
          (is_short_hv &&
           has_stable_neighbor + has_blend_neighbor >= total_neighbors)) {
        // Remove this region.Try to determine whether to combine it with the
        // previous or next region.
        int merge;
        double prev_diff =
            (k > 0)
                ? fabs(regions[k].avg_cor_coeff - regions[k - 1].avg_cor_coeff)
                : 1;
        double next_diff =
            (k < *num_regions - 1)
                ? fabs(regions[k].avg_cor_coeff - regions[k + 1].avg_cor_coeff)
                : 1;
        // merge == 0 means to merge with previous, 1 means to merge with next
        merge = prev_diff > next_diff;
        remove_region(merge, regions, num_regions, &k);
      } else {
        k++;
      }
    }
    cleanup_regions(regions, num_regions);
  }
  
  // Identify stable and unstable regions from first pass stats.
  // Stats_start points to the first frame to analyze.
  // Offset is the offset from the current frame to the frame stats_start is
  // pointing to.
  static void identify_regions(const FIRSTPASS_STATS *const stats_start,
                               int total_frames, int offset, REGIONS *regions,
                               int *total_regions) {
    int k;
    if (total_frames <= 1) return;
  
    // store the initial decisions
    REGIONS temp_regions[MAX_FIRSTPASS_ANALYSIS_FRAMES];
    av1_zero_array(temp_regions, MAX_FIRSTPASS_ANALYSIS_FRAMES);
    // buffers for filtered stats
    double filt_intra_err[MAX_FIRSTPASS_ANALYSIS_FRAMES] = { 0 };
    double filt_coded_err[MAX_FIRSTPASS_ANALYSIS_FRAMES] = { 0 };
    double grad_coded[MAX_FIRSTPASS_ANALYSIS_FRAMES] = { 0 };
  
    int cur_region = 0, this_start = 0, this_last;
  
    int next_scenecut = -1;
    do {
      // first get the obvious scenecuts
      next_scenecut =
          find_next_scenecut(stats_start, this_start, total_frames - 1);
      this_last = (next_scenecut >= 0) ? (next_scenecut - 1) : total_frames - 1;
  
      // low-pass filter the needed stats
      smooth_filter_stats(stats_start, this_start, this_last, filt_intra_err,
                          filt_coded_err);
      get_gradient(filt_coded_err, this_start, this_last, grad_coded);
  
      // find tentative stable regions and unstable regions
      int num_regions = find_stable_regions(stats_start, grad_coded, this_start,
                                            this_last, temp_regions);
  
      adjust_unstable_region_bounds(stats_start, temp_regions, &num_regions);
  
      get_region_stats(stats_start, temp_regions, num_regions);
  
      // Try to identify blending regions in the unstable regions
      find_blending_regions(stats_start, temp_regions, &num_regions);
      cleanup_blendings(temp_regions, &num_regions);
  
      // The flash points should all be considered high variance points
      k = 0;
      while (k < num_regions) {
        if (temp_regions[k].type != STABLE_REGION) {
          k++;
          continue;
        }
        int start = temp_regions[k].start;
        int last = temp_regions[k].last;
        for (int i = start; i <= last; i++) {
          if (stats_start[i].is_flash) {
            insert_region(i, i, HIGH_VAR_REGION, temp_regions, &num_regions, &k);
          }
        }
        k++;
      }
      cleanup_regions(temp_regions, &num_regions);
  
      // copy the regions in the scenecut group
      for (k = 0; k < num_regions; k++) {
        if (temp_regions[k].last < temp_regions[k].start &&
            k == num_regions - 1) {
          num_regions--;
          break;
        }
        regions[k + cur_region] = temp_regions[k];
      }
      cur_region += num_regions;
  
      // add the scenecut region
      if (next_scenecut > -1) {
        // add the scenecut region, and find the next scenecut
        regions[cur_region].type = SCENECUT_REGION;
        regions[cur_region].start = next_scenecut;
        regions[cur_region].last = next_scenecut;
        cur_region++;
        this_start = next_scenecut + 1;
      }
    } while (next_scenecut >= 0);
  
    *total_regions = cur_region;
    get_region_stats(stats_start, regions, *total_regions);
  
    for (k = 0; k < *total_regions; k++) {
      // If scenecuts are very minor, mark them as high variance.
      if (regions[k].type != SCENECUT_REGION ||
          regions[k].avg_cor_coeff *
                  (1 - stats_start[regions[k].start].noise_var /
                           regions[k].avg_intra_err) <
              0.8) {
        continue;
      }
      regions[k].type = HIGH_VAR_REGION;
    }
    cleanup_regions(regions, total_regions);
    get_region_stats(stats_start, regions, *total_regions);
  
    for (k = 0; k < *total_regions; k++) {
      regions[k].start += offset;
      regions[k].last += offset;
    }
  }
  
  static int find_regions_index(const REGIONS *regions, int num_regions,
                                int frame_idx) {
    for (int k = 0; k < num_regions; k++) {
      if (regions[k].start <= frame_idx && regions[k].last >= frame_idx) {
        return k;
      }
    }
    return -1;
  }
  
  /*!\brief Determine the length of future GF groups.
   *
   * \ingroup gf_group_algo
   * This function decides the gf group length of future frames in batch
   *
   * \param[in]    cpi              Top-level encoder structure
   * \param[in]    max_gop_length   Maximum length of the GF group
   * \param[in]    max_intervals    Maximum number of intervals to decide
   *
   * \return Nothing is returned. Instead, cpi->ppi->rc.gf_intervals is
   * changed to store the decided GF group lengths.
   */
  static void calculate_gf_length(AV1_COMP *cpi, int max_gop_length,
                                  int max_intervals) {
    RATE_CONTROL *const rc = &cpi->rc;
    PRIMARY_RATE_CONTROL *const p_rc = &cpi->ppi->p_rc;
    TWO_PASS *const twopass = &cpi->ppi->twopass;
    FIRSTPASS_STATS next_frame;
    const FIRSTPASS_STATS *const start_pos = cpi->twopass_frame.stats_in;
    const FIRSTPASS_STATS *const stats = start_pos - (rc->frames_since_key == 0);
  
    const int f_w = cpi->common.width;
    const int f_h = cpi->common.height;
    int i;
  
    int flash_detected;
  
    av1_zero(next_frame);
  
    if (has_no_stats_stage(cpi)) {
      for (i = 0; i < MAX_NUM_GF_INTERVALS; i++) {
        p_rc->gf_intervals[i] = AOMMIN(rc->max_gf_interval, max_gop_length);
      }
      p_rc->cur_gf_index = 0;
      rc->intervals_till_gf_calculate_due = MAX_NUM_GF_INTERVALS;
      return;
    }
  
    // TODO(urvang): Try logic to vary min and max interval based on q.
    const int active_min_gf_interval = rc->min_gf_interval;
    const int active_max_gf_interval =
        AOMMIN(rc->max_gf_interval, max_gop_length);
    const int min_shrink_int = AOMMAX(MIN_SHRINK_LEN, active_min_gf_interval);
  
    i = (rc->frames_since_key == 0);
    max_intervals = cpi->ppi->lap_enabled ? 1 : max_intervals;
    int count_cuts = 1;
    // If cpi->gf_state.arf_gf_boost_lst is 0, we are starting with a KF or GF.
    int cur_start = -1 + !cpi->ppi->gf_state.arf_gf_boost_lst, cur_last;
    int cut_pos[MAX_NUM_GF_INTERVALS + 1] = { -1 };
    int cut_here;
    GF_GROUP_STATS gf_stats;
    init_gf_stats(&gf_stats);
    while (count_cuts < max_intervals + 1) {
      // reaches next key frame, break here
      if (i >= rc->frames_to_key) {
        cut_here = 2;
      } else if (i - cur_start >= rc->static_scene_max_gf_interval) {
        // reached maximum len, but nothing special yet (almost static)
        // let's look at the next interval
        cut_here = 1;
      } else if (EOF == input_stats(twopass, &cpi->twopass_frame, &next_frame)) {
        // reaches last frame, break
        cut_here = 2;
      } else {
        // Test for the case where there is a brief flash but the prediction
        // quality back to an earlier frame is then restored.
        flash_detected = detect_flash(twopass, &cpi->twopass_frame, 0);
        // TODO(bohanli): remove redundant accumulations here, or unify
        // this and the ones in define_gf_group
        accumulate_next_frame_stats(&next_frame, flash_detected,
                                    rc->frames_since_key, i, &gf_stats, f_w, f_h);
  
        cut_here = detect_gf_cut(cpi, i, cur_start, flash_detected,
                                 active_max_gf_interval, active_min_gf_interval,
                                 &gf_stats);
      }
      if (cut_here) {
        cur_last = i - 1;  // the current last frame in the gf group
        int ori_last = cur_last;
        // The region frame idx does not start from the same frame as cur_start
        // and cur_last. Need to offset them.
        int offset = rc->frames_since_key - p_rc->regions_offset;
        REGIONS *regions = p_rc->regions;
        int num_regions = p_rc->num_regions;
  
        int scenecut_idx = -1;
        // only try shrinking if interval smaller than active_max_gf_interval
        if (cur_last - cur_start <= active_max_gf_interval &&
            cur_last > cur_start) {
          // find the region indices of where the first and last frame belong.
          int k_start =
              find_regions_index(regions, num_regions, cur_start + offset);
          int k_last =
              find_regions_index(regions, num_regions, cur_last + offset);
          if (cur_start + offset == 0) k_start = 0;
  
          // See if we have a scenecut in between
          for (int r = k_start + 1; r <= k_last; r++) {
            if (regions[r].type == SCENECUT_REGION &&
                regions[r].last - offset - cur_start > active_min_gf_interval) {
              scenecut_idx = r;
              break;
            }
          }
  
          // if the found scenecut is very close to the end, ignore it.
          if (regions[num_regions - 1].last - regions[scenecut_idx].last < 4) {
            scenecut_idx = -1;
          }
  
          if (scenecut_idx != -1) {
            // If we have a scenecut, then stop at it.
            // TODO(bohanli): add logic here to stop before the scenecut and for
            // the next gop start from the scenecut with GF
            int is_minor_sc =
                (regions[scenecut_idx].avg_cor_coeff *
                     (1 - stats[regions[scenecut_idx].start - offset].noise_var /
                              regions[scenecut_idx].avg_intra_err) >
                 0.6);
            cur_last = regions[scenecut_idx].last - offset - !is_minor_sc;
          } else {
            int is_last_analysed = (k_last == num_regions - 1) &&
                                   (cur_last + offset == regions[k_last].last);
            int not_enough_regions =
                k_last - k_start <=
                1 + (regions[k_start].type == SCENECUT_REGION);
            // if we are very close to the end, then do not shrink since it may
            // introduce intervals that are too short
            if (!(is_last_analysed && not_enough_regions)) {
              const double arf_length_factor = 0.1;
              double best_score = 0;
              int best_j = -1;
              const int first_frame = regions[0].start - offset;
              const int last_frame = regions[num_regions - 1].last - offset;
              // score of how much the arf helps the whole GOP
              double base_score = 0.0;
              // Accumulate base_score in
              for (int j = cur_start + 1; j < cur_start + min_shrink_int; j++) {
                if (stats + j >= twopass->stats_buf_ctx->stats_in_end) break;
                base_score = (base_score + 1.0) * stats[j].cor_coeff;
              }
              int met_blending = 0;   // Whether we have met blending areas before
              int last_blending = 0;  // Whether the previous frame if blending
              for (int j = cur_start + min_shrink_int; j <= cur_last; j++) {
                if (stats + j >= twopass->stats_buf_ctx->stats_in_end) break;
                base_score = (base_score + 1.0) * stats[j].cor_coeff;
                int this_reg =
                    find_regions_index(regions, num_regions, j + offset);
                if (this_reg < 0) continue;
                // A GOP should include at most 1 blending region.
                if (regions[this_reg].type == BLENDING_REGION) {
                  last_blending = 1;
                  if (met_blending) {
                    break;
                  } else {
                    base_score = 0;
                    continue;
                  }
                } else {
                  if (last_blending) met_blending = 1;
                  last_blending = 0;
                }
  
                // Add the factor of how good the neighborhood is for this
                // candidate arf.
                double this_score = arf_length_factor * base_score;
                double temp_accu_coeff = 1.0;
                // following frames
                int count_f = 0;
                for (int n = j + 1; n <= j + 3 && n <= last_frame; n++) {
                  if (stats + n >= twopass->stats_buf_ctx->stats_in_end) break;
                  temp_accu_coeff *= stats[n].cor_coeff;
                  this_score +=
                      temp_accu_coeff *
                      (1 - stats[n].noise_var /
                               AOMMAX(regions[this_reg].avg_intra_err, 0.001));
                  count_f++;
                }
                // preceding frames
                temp_accu_coeff = 1.0;
                for (int n = j; n > j - 3 * 2 + count_f && n > first_frame; n--) {
                  if (stats + n < twopass->stats_buf_ctx->stats_in_start) break;
                  temp_accu_coeff *= stats[n].cor_coeff;
                  this_score +=
                      temp_accu_coeff *
                      (1 - stats[n].noise_var /
                               AOMMAX(regions[this_reg].avg_intra_err, 0.001));
                }
  
                if (this_score > best_score) {
                  best_score = this_score;
                  best_j = j;
                }
              }
  
              // For blending areas, move one more frame in case we missed the
              // first blending frame.
              int best_reg =
                  find_regions_index(regions, num_regions, best_j + offset);
              if (best_reg < num_regions - 1 && best_reg > 0) {
                if (regions[best_reg - 1].type == BLENDING_REGION &&
                    regions[best_reg + 1].type == BLENDING_REGION) {
                  if (best_j + offset == regions[best_reg].start &&
                      best_j + offset < regions[best_reg].last) {
                    best_j += 1;
                  } else if (best_j + offset == regions[best_reg].last &&
                             best_j + offset > regions[best_reg].start) {
                    best_j -= 1;
                  }
                }
              }
  
              if (cur_last - best_j < 2) best_j = cur_last;
              if (best_j > 0 && best_score > 0.1) cur_last = best_j;
              // if cannot find anything, just cut at the original place.
            }
          }
        }
        cut_pos[count_cuts] = cur_last;
        count_cuts++;
  
        // reset pointers to the shrinked location
        cpi->twopass_frame.stats_in = start_pos + cur_last;
        cur_start = cur_last;
        int cur_region_idx =
            find_regions_index(regions, num_regions, cur_start + 1 + offset);
        if (cur_region_idx >= 0)
          if (regions[cur_region_idx].type == SCENECUT_REGION) cur_start++;
  
        i = cur_last;
  
        if (cut_here > 1 && cur_last == ori_last) break;
  
        // reset accumulators
        init_gf_stats(&gf_stats);
      }
      ++i;
    }
  
    // save intervals
    rc->intervals_till_gf_calculate_due = count_cuts - 1;
    for (int n = 1; n < count_cuts; n++) {
      p_rc->gf_intervals[n - 1] = cut_pos[n] - cut_pos[n - 1];
    }
    p_rc->cur_gf_index = 0;
    cpi->twopass_frame.stats_in = start_pos;
  }
  
  static void correct_frames_to_key(AV1_COMP *cpi) {
    int lookahead_size =
        (int)av1_lookahead_depth(cpi->ppi->lookahead, cpi->compressor_stage);
    if (lookahead_size <
        av1_lookahead_pop_sz(cpi->ppi->lookahead, cpi->compressor_stage)) {
      assert(
          IMPLIES(cpi->oxcf.pass != AOM_RC_ONE_PASS && cpi->ppi->frames_left > 0,
                  lookahead_size == cpi->ppi->frames_left));
      cpi->rc.frames_to_key = AOMMIN(cpi->rc.frames_to_key, lookahead_size);
    } else if (cpi->ppi->frames_left > 0) {
      // Correct frames to key based on limit
      cpi->rc.frames_to_key =
          AOMMIN(cpi->rc.frames_to_key, cpi->ppi->frames_left);
    }
  }
  
  /*!\brief Define a GF group in one pass mode when no look ahead stats are
   * available.
   *
   * \ingroup gf_group_algo
   * This function defines the structure of a GF group, along with various
   * parameters regarding bit-allocation and quality setup in the special
   * case of one pass encoding where no lookahead stats are avialable.
   *
   * \param[in]    cpi             Top-level encoder structure
   *
   * \return Nothing is returned. Instead, cpi->ppi->gf_group is changed.
   */
  static void define_gf_group_pass0(AV1_COMP *cpi) {
    RATE_CONTROL *const rc = &cpi->rc;
    PRIMARY_RATE_CONTROL *const p_rc = &cpi->ppi->p_rc;
    GF_GROUP *const gf_group = &cpi->ppi->gf_group;
    const AV1EncoderConfig *const oxcf = &cpi->oxcf;
    const GFConfig *const gf_cfg = &oxcf->gf_cfg;
    int target;
  
    if (oxcf->q_cfg.aq_mode == CYCLIC_REFRESH_AQ) {
      av1_cyclic_refresh_set_golden_update(cpi);
    } else {
      p_rc->baseline_gf_interval = p_rc->gf_intervals[p_rc->cur_gf_index];
      rc->intervals_till_gf_calculate_due--;
      p_rc->cur_gf_index++;
    }
  
    // correct frames_to_key when lookahead queue is flushing
    correct_frames_to_key(cpi);
  
    if (p_rc->baseline_gf_interval > rc->frames_to_key)
      p_rc->baseline_gf_interval = rc->frames_to_key;
  
    p_rc->gfu_boost = DEFAULT_GF_BOOST;
    p_rc->constrained_gf_group =
        (p_rc->baseline_gf_interval >= rc->frames_to_key) ? 1 : 0;
  
    gf_group->max_layer_depth_allowed = oxcf->gf_cfg.gf_max_pyr_height;
  
    // Rare case when the look-ahead is less than the target GOP length, can't
    // generate ARF frame.
    if (p_rc->baseline_gf_interval > gf_cfg->lag_in_frames ||
        !is_altref_enabled(gf_cfg->lag_in_frames, gf_cfg->enable_auto_arf) ||
        p_rc->baseline_gf_interval < rc->min_gf_interval)
      gf_group->max_layer_depth_allowed = 0;
  
    // Set up the structure of this Group-Of-Pictures (same as GF_GROUP)
    av1_gop_setup_structure(cpi);
  
    // Allocate bits to each of the frames in the GF group.
    // TODO(sarahparker) Extend this to work with pyramid structure.
    for (int cur_index = 0; cur_index < gf_group->size; ++cur_index) {
      const FRAME_UPDATE_TYPE cur_update_type = gf_group->update_type[cur_index];
      if (oxcf->rc_cfg.mode == AOM_CBR) {
        if (cur_update_type == KF_UPDATE) {
          target = av1_calc_iframe_target_size_one_pass_cbr(cpi);
        } else {
          target = av1_calc_pframe_target_size_one_pass_cbr(cpi, cur_update_type);
        }
      } else {
        if (cur_update_type == KF_UPDATE) {
          target = av1_calc_iframe_target_size_one_pass_vbr(cpi);
        } else {
          target = av1_calc_pframe_target_size_one_pass_vbr(cpi, cur_update_type);
        }
      }
      gf_group->bit_allocation[cur_index] = target;
    }
  }
  
  static INLINE void set_baseline_gf_interval(PRIMARY_RATE_CONTROL *p_rc,
                                              int arf_position) {
    p_rc->baseline_gf_interval = arf_position;
  }
  
  // initialize GF_GROUP_STATS
  static void init_gf_stats(GF_GROUP_STATS *gf_stats) {
    gf_stats->gf_group_err = 0.0;
    gf_stats->gf_group_raw_error = 0.0;
    gf_stats->gf_group_skip_pct = 0.0;
    gf_stats->gf_group_inactive_zone_rows = 0.0;
  
    gf_stats->mv_ratio_accumulator = 0.0;
    gf_stats->decay_accumulator = 1.0;
    gf_stats->zero_motion_accumulator = 1.0;
    gf_stats->loop_decay_rate = 1.0;
    gf_stats->last_loop_decay_rate = 1.0;
    gf_stats->this_frame_mv_in_out = 0.0;
    gf_stats->mv_in_out_accumulator = 0.0;
    gf_stats->abs_mv_in_out_accumulator = 0.0;
  
    gf_stats->avg_sr_coded_error = 0.0;
    gf_stats->avg_pcnt_second_ref = 0.0;
    gf_stats->avg_new_mv_count = 0.0;
    gf_stats->avg_wavelet_energy = 0.0;
    gf_stats->avg_raw_err_stdev = 0.0;
    gf_stats->non_zero_stdev_count = 0;
  }
  
  // Analyse and define a gf/arf group.
  #define MAX_GF_BOOST 5400
  /*!\brief Define a GF group.
   *
   * \ingroup gf_group_algo
   * This function defines the structure of a GF group, along with various
   * parameters regarding bit-allocation and quality setup.
   *
   * \param[in]    cpi             Top-level encoder structure
   * \param[in]    frame_params    Structure with frame parameters
   * \param[in]    is_final_pass   Whether this is the final pass for the
   *                               GF group, or a trial (non-zero)
   *
   * \return Nothing is returned. Instead, cpi->ppi->gf_group is changed.
   */
  static void define_gf_group(AV1_COMP *cpi, EncodeFrameParams *frame_params,
                              int is_final_pass) {
    AV1_COMMON *const cm = &cpi->common;
    RATE_CONTROL *const rc = &cpi->rc;
    PRIMARY_RATE_CONTROL *const p_rc = &cpi->ppi->p_rc;
    const AV1EncoderConfig *const oxcf = &cpi->oxcf;
    TWO_PASS *const twopass = &cpi->ppi->twopass;
    FIRSTPASS_STATS next_frame;
    const FIRSTPASS_STATS *const start_pos = cpi->twopass_frame.stats_in;
    GF_GROUP *gf_group = &cpi->ppi->gf_group;
    FRAME_INFO *frame_info = &cpi->frame_info;
    const GFConfig *const gf_cfg = &oxcf->gf_cfg;
    const RateControlCfg *const rc_cfg = &oxcf->rc_cfg;
    const int f_w = cm->width;
    const int f_h = cm->height;
    int i;
    int flash_detected;
    int64_t gf_group_bits;
    const int is_intra_only = rc->frames_since_key == 0;
  
    cpi->ppi->internal_altref_allowed = (gf_cfg->gf_max_pyr_height > 1);
  
    // Reset the GF group data structures unless this is a key
    // frame in which case it will already have been done.
    if (!is_intra_only) {
      av1_zero(cpi->ppi->gf_group);
      cpi->gf_frame_index = 0;
    }
  
    av1_zero(next_frame);
  
    if (has_no_stats_stage(cpi)) {
      define_gf_group_pass0(cpi);
      return;
    }
  
    // correct frames_to_key when lookahead queue is emptying
    if (cpi->ppi->lap_enabled) {
      correct_frames_to_key(cpi);
    }
  
    GF_GROUP_STATS gf_stats;
    init_gf_stats(&gf_stats);
  
    const int can_disable_arf = !gf_cfg->gf_min_pyr_height;
  
    // If this is a key frame or the overlay from a previous arf then
    // the error score / cost of this frame has already been accounted for.
    const int active_min_gf_interval = rc->min_gf_interval;
  
    i = is_intra_only;
    // get the determined gf group length from p_rc->gf_intervals
    while (i < p_rc->gf_intervals[p_rc->cur_gf_index]) {
      // read in the next frame
      if (EOF == input_stats(twopass, &cpi->twopass_frame, &next_frame)) break;
      // Accumulate error score of frames in this gf group.
      double mod_frame_err =
          calculate_modified_err(frame_info, twopass, oxcf, &next_frame);
      // accumulate stats for this frame
      accumulate_this_frame_stats(&next_frame, mod_frame_err, &gf_stats);
      ++i;
    }
  
    reset_fpf_position(&cpi->twopass_frame, start_pos);
  
    i = is_intra_only;
    input_stats(twopass, &cpi->twopass_frame, &next_frame);
    while (i < p_rc->gf_intervals[p_rc->cur_gf_index]) {
      // read in the next frame
      if (EOF == input_stats(twopass, &cpi->twopass_frame, &next_frame)) break;
  
      // Test for the case where there is a brief flash but the prediction
      // quality back to an earlier frame is then restored.
      flash_detected = detect_flash(twopass, &cpi->twopass_frame, 0);
  
      // accumulate stats for next frame
      accumulate_next_frame_stats(&next_frame, flash_detected,
                                  rc->frames_since_key, i, &gf_stats, f_w, f_h);
  
      ++i;
    }
  
    i = p_rc->gf_intervals[p_rc->cur_gf_index];
  
    if (is_final_pass) {
      rc->intervals_till_gf_calculate_due--;
      p_rc->cur_gf_index++;
    }
  
    // Was the group length constrained by the requirement for a new KF?
    p_rc->constrained_gf_group = (i >= rc->frames_to_key) ? 1 : 0;
  
    average_gf_stats(i, &gf_stats);
  
    // Disable internal ARFs for "still" gf groups.
    //   zero_motion_accumulator: minimum percentage of (0,0) motion;
    //   avg_sr_coded_error:      average of the SSE per pixel of each frame;
    //   avg_raw_err_stdev:       average of the standard deviation of (0,0)
    //                            motion error per block of each frame.
    const int can_disable_internal_arfs = gf_cfg->gf_min_pyr_height <= 1;
    if (can_disable_internal_arfs &&
        gf_stats.zero_motion_accumulator > MIN_ZERO_MOTION &&
        gf_stats.avg_sr_coded_error < MAX_SR_CODED_ERROR &&
        gf_stats.avg_raw_err_stdev < MAX_RAW_ERR_VAR) {
      cpi->ppi->internal_altref_allowed = 0;
    }
  
    int use_alt_ref;
    if (can_disable_arf) {
      use_alt_ref =
          !is_almost_static(gf_stats.zero_motion_accumulator,
                            twopass->kf_zeromotion_pct, cpi->ppi->lap_enabled) &&
          p_rc->use_arf_in_this_kf_group && (i < gf_cfg->lag_in_frames) &&
          (i >= MIN_GF_INTERVAL);
    } else {
      use_alt_ref = p_rc->use_arf_in_this_kf_group &&
                    (i < gf_cfg->lag_in_frames) && (i > 2);
    }
  
  #define REDUCE_GF_LENGTH_THRESH 4
  #define REDUCE_GF_LENGTH_TO_KEY_THRESH 9
  #define REDUCE_GF_LENGTH_BY 1
    int alt_offset = 0;
    // The length reduction strategy is tweaked for certain cases, and doesn't
    // work well for certain other cases.
    const int allow_gf_length_reduction =
        ((rc_cfg->mode == AOM_Q && rc_cfg->cq_level <= 128) ||
         !cpi->ppi->internal_altref_allowed) &&
        !is_lossless_requested(rc_cfg);
  
    if (allow_gf_length_reduction && use_alt_ref) {
      // adjust length of this gf group if one of the following condition met
      // 1: only one overlay frame left and this gf is too long
      // 2: next gf group is too short to have arf compared to the current gf
  
      // maximum length of next gf group
      const int next_gf_len = rc->frames_to_key - i;
      const int single_overlay_left =
          next_gf_len == 0 && i > REDUCE_GF_LENGTH_THRESH;
      // the next gf is probably going to have a ARF but it will be shorter than
      // this gf
      const int unbalanced_gf =
          i > REDUCE_GF_LENGTH_TO_KEY_THRESH &&
          next_gf_len + 1 < REDUCE_GF_LENGTH_TO_KEY_THRESH &&
          next_gf_len + 1 >= rc->min_gf_interval;
  
      if (single_overlay_left || unbalanced_gf) {
        const int roll_back = REDUCE_GF_LENGTH_BY;
        // Reduce length only if active_min_gf_interval will be respected later.
        if (i - roll_back >= active_min_gf_interval + 1) {
          alt_offset = -roll_back;
          i -= roll_back;
          if (is_final_pass) rc->intervals_till_gf_calculate_due = 0;
        }
      }
    }
  
    // Should we use the alternate reference frame.
    int ext_len = i - is_intra_only;
    if (use_alt_ref) {
      gf_group->max_layer_depth_allowed = gf_cfg->gf_max_pyr_height;
      set_baseline_gf_interval(&cpi->ppi->p_rc, i);
  
      const int forward_frames = (rc->frames_to_key - i >= ext_len)
                                     ? ext_len
                                     : AOMMAX(0, rc->frames_to_key - i);
  
      // Calculate the boost for alt ref.
      p_rc->gfu_boost = av1_calc_arf_boost(
          twopass, &cpi->twopass_frame, p_rc, frame_info, alt_offset,
          forward_frames, ext_len, &p_rc->num_stats_used_for_gfu_boost,
          &p_rc->num_stats_required_for_gfu_boost, cpi->ppi->lap_enabled);
    } else {
      reset_fpf_position(&cpi->twopass_frame, start_pos);
      gf_group->max_layer_depth_allowed = 0;
      set_baseline_gf_interval(&cpi->ppi->p_rc, i);
  
      p_rc->gfu_boost = AOMMIN(
          MAX_GF_BOOST,
          av1_calc_arf_boost(
              twopass, &cpi->twopass_frame, p_rc, frame_info, alt_offset, ext_len,
              0, &p_rc->num_stats_used_for_gfu_boost,
              &p_rc->num_stats_required_for_gfu_boost, cpi->ppi->lap_enabled));
    }
  
  #define LAST_ALR_BOOST_FACTOR 0.2f
    p_rc->arf_boost_factor = 1.0;
    if (use_alt_ref && !is_lossless_requested(rc_cfg)) {
      // Reduce the boost of altref in the last gf group
      if (rc->frames_to_key - ext_len == REDUCE_GF_LENGTH_BY ||
          rc->frames_to_key - ext_len == 0) {
        p_rc->arf_boost_factor = LAST_ALR_BOOST_FACTOR;
      }
    }
  
    rc->frames_till_gf_update_due = p_rc->baseline_gf_interval;
  
    // Reset the file position.
    reset_fpf_position(&cpi->twopass_frame, start_pos);
  
    if (cpi->ppi->lap_enabled) {
      // Since we don't have enough stats to know the actual error of the
      // gf group, we assume error of each frame to be equal to 1 and set
      // the error of the group as baseline_gf_interval.
      gf_stats.gf_group_err = p_rc->baseline_gf_interval;
    }
    // Calculate the bits to be allocated to the gf/arf group as a whole
    gf_group_bits = calculate_total_gf_group_bits(cpi, gf_stats.gf_group_err);
    p_rc->gf_group_bits = gf_group_bits;
  
  #if GROUP_ADAPTIVE_MAXQ
    // Calculate an estimate of the maxq needed for the group.
    // We are more agressive about correcting for sections
    // where there could be significant overshoot than for easier
    // sections where we do not wish to risk creating an overshoot
    // of the allocated bit budget.
    if ((rc_cfg->mode != AOM_Q) && (p_rc->baseline_gf_interval > 1) &&
        is_final_pass) {
      const int vbr_group_bits_per_frame =
          (int)(gf_group_bits / p_rc->baseline_gf_interval);
      const double group_av_err =
          gf_stats.gf_group_raw_error / p_rc->baseline_gf_interval;
      const double group_av_skip_pct =
          gf_stats.gf_group_skip_pct / p_rc->baseline_gf_interval;
      const double group_av_inactive_zone =
          ((gf_stats.gf_group_inactive_zone_rows * 2) /
           (p_rc->baseline_gf_interval * (double)cm->mi_params.mb_rows));
  
      int tmp_q;
      tmp_q = get_twopass_worst_quality(
          cpi, group_av_err, (group_av_skip_pct + group_av_inactive_zone),
          vbr_group_bits_per_frame);
      rc->active_worst_quality = AOMMAX(tmp_q, rc->active_worst_quality >> 1);
    }
  #endif
  
    // Adjust KF group bits and error remaining.
    if (is_final_pass) twopass->kf_group_error_left -= gf_stats.gf_group_err;
  
    // Set up the structure of this Group-Of-Pictures (same as GF_GROUP)
    av1_gop_setup_structure(cpi);
  
    // Reset the file position.
    reset_fpf_position(&cpi->twopass_frame, start_pos);
  
    // Calculate a section intra ratio used in setting max loop filter.
    if (rc->frames_since_key != 0) {
      twopass->section_intra_rating = calculate_section_intra_ratio(
          start_pos, twopass->stats_buf_ctx->stats_in_end,
          p_rc->baseline_gf_interval);
    }
  
    av1_gop_bit_allocation(cpi, rc, gf_group, rc->frames_since_key == 0,
                           use_alt_ref, gf_group_bits);
  
    frame_params->frame_type =
        rc->frames_since_key == 0 ? KEY_FRAME : INTER_FRAME;
    frame_params->show_frame =
        !(gf_group->update_type[cpi->gf_frame_index] == ARF_UPDATE ||
          gf_group->update_type[cpi->gf_frame_index] == INTNL_ARF_UPDATE);
  
    // TODO(jingning): Generalize this condition.
    if (is_final_pass) {
      cpi->ppi->gf_state.arf_gf_boost_lst = use_alt_ref;
  
      // Reset rolling actual and target bits counters for ARF groups.
      twopass->rolling_arf_group_target_bits = 1;
      twopass->rolling_arf_group_actual_bits = 1;
    }
  #if CONFIG_BITRATE_ACCURACY
    if (is_final_pass) {
      vbr_rc_set_gop_bit_budget(&cpi->vbr_rc_info, p_rc->baseline_gf_interval);
    }
  #endif
  }
  
  // #define FIXED_ARF_BITS
  #ifdef FIXED_ARF_BITS
  #define ARF_BITS_FRACTION 0.75
  #endif
  void av1_gop_bit_allocation(const AV1_COMP *cpi, RATE_CONTROL *const rc,
                              GF_GROUP *gf_group, int is_key_frame, int use_arf,
                              int64_t gf_group_bits) {
    PRIMARY_RATE_CONTROL *const p_rc = &cpi->ppi->p_rc;
    // Calculate the extra bits to be used for boosted frame(s)
  #ifdef FIXED_ARF_BITS
    int gf_arf_bits = (int)(ARF_BITS_FRACTION * gf_group_bits);
  #else
    int gf_arf_bits = calculate_boost_bits(
        p_rc->baseline_gf_interval - (rc->frames_since_key == 0), p_rc->gfu_boost,
        gf_group_bits);
  #endif
  
    gf_arf_bits = adjust_boost_bits_for_target_level(cpi, rc, gf_arf_bits,
                                                     gf_group_bits, 1);
  
    // Allocate bits to each of the frames in the GF group.
    allocate_gf_group_bits(gf_group, p_rc, rc, gf_group_bits, gf_arf_bits,
                           is_key_frame, use_arf);
  }
  
  // Minimum % intra coding observed in first pass (1.0 = 100%)
  #define MIN_INTRA_LEVEL 0.25
  // Minimum ratio between the % of intra coding and inter coding in the first
  // pass after discounting neutral blocks (discounting neutral blocks in this
  // way helps catch scene cuts in clips with very flat areas or letter box
  // format clips with image padding.
  #define INTRA_VS_INTER_THRESH 2.0
  // Hard threshold where the first pass chooses intra for almost all blocks.
  // In such a case even if the frame is not a scene cut coding a key frame
  // may be a good option.
  #define VERY_LOW_INTER_THRESH 0.05
  // Maximum threshold for the relative ratio of intra error score vs best
  // inter error score.
  #define KF_II_ERR_THRESHOLD 1.9
  // In real scene cuts there is almost always a sharp change in the intra
  // or inter error score.
  #define ERR_CHANGE_THRESHOLD 0.4
  // For real scene cuts we expect an improvment in the intra inter error
  // ratio in the next frame.
  #define II_IMPROVEMENT_THRESHOLD 3.5
  #define KF_II_MAX 128.0
  // Intra / Inter threshold very low
  #define VERY_LOW_II 1.5
  // Clean slide transitions we expect a sharp single frame spike in error.
  #define ERROR_SPIKE 5.0
  
  // Slide show transition detection.
  // Tests for case where there is very low error either side of the current frame
  // but much higher just for this frame. This can help detect key frames in
  // slide shows even where the slides are pictures of different sizes.
  // Also requires that intra and inter errors are very similar to help eliminate
  // harmful false positives.
  // It will not help if the transition is a fade or other multi-frame effect.
  static int slide_transition(const FIRSTPASS_STATS *this_frame,
                              const FIRSTPASS_STATS *last_frame,
                              const FIRSTPASS_STATS *next_frame) {
    return (this_frame->intra_error < (this_frame->coded_error * VERY_LOW_II)) &&
           (this_frame->coded_error > (last_frame->coded_error * ERROR_SPIKE)) &&
           (this_frame->coded_error > (next_frame->coded_error * ERROR_SPIKE));
  }
  
  // Threshold for use of the lagging second reference frame. High second ref
  // usage may point to a transient event like a flash or occlusion rather than
  // a real scene cut.
  // We adapt the threshold based on number of frames in this key-frame group so
  // far.
  static double get_second_ref_usage_thresh(int frame_count_so_far) {
    const int adapt_upto = 32;
    const double min_second_ref_usage_thresh = 0.085;
    const double second_ref_usage_thresh_max_delta = 0.035;
    if (frame_count_so_far >= adapt_upto) {
      return min_second_ref_usage_thresh + second_ref_usage_thresh_max_delta;
    }
    return min_second_ref_usage_thresh +
           ((double)frame_count_so_far / (adapt_upto - 1)) *
               second_ref_usage_thresh_max_delta;
  }
  
  static int test_candidate_kf(const FIRSTPASS_INFO *firstpass_info,
                               int this_stats_index, int frame_count_so_far,
                               enum aom_rc_mode rc_mode, int scenecut_mode,
                               int num_mbs) {
    const FIRSTPASS_STATS *last_stats =
        av1_firstpass_info_peek(firstpass_info, this_stats_index - 1);
    const FIRSTPASS_STATS *this_stats =
        av1_firstpass_info_peek(firstpass_info, this_stats_index);
    const FIRSTPASS_STATS *next_stats =
        av1_firstpass_info_peek(firstpass_info, this_stats_index + 1);
    if (last_stats == NULL || this_stats == NULL || next_stats == NULL) {
      return 0;
    }
  
    int is_viable_kf = 0;
    double pcnt_intra = 1.0 - this_stats->pcnt_inter;
    double modified_pcnt_inter =
        this_stats->pcnt_inter - this_stats->pcnt_neutral;
    const double second_ref_usage_thresh =
        get_second_ref_usage_thresh(frame_count_so_far);
    int frames_to_test_after_candidate_key = SCENE_CUT_KEY_TEST_INTERVAL;
    int count_for_tolerable_prediction = 3;
  
    // We do "-1" because the candidate key is not counted.
    int stats_after_this_stats =
        av1_firstpass_info_future_count(firstpass_info, this_stats_index) - 1;
  
    if (scenecut_mode == ENABLE_SCENECUT_MODE_1) {
      if (stats_after_this_stats < 3) {
        return 0;
      } else {
        frames_to_test_after_candidate_key = 3;
        count_for_tolerable_prediction = 1;
      }
    }
    // Make sure we have enough stats after the candidate key.
    frames_to_test_after_candidate_key =
        AOMMIN(frames_to_test_after_candidate_key, stats_after_this_stats);
  
    // Does the frame satisfy the primary criteria of a key frame?
    // See above for an explanation of the test criteria.
    // If so, then examine how well it predicts subsequent frames.
    if (IMPLIES(rc_mode == AOM_Q, frame_count_so_far >= 3) &&
        (this_stats->pcnt_second_ref < second_ref_usage_thresh) &&
        (next_stats->pcnt_second_ref < second_ref_usage_thresh) &&
        ((this_stats->pcnt_inter < VERY_LOW_INTER_THRESH) ||
         slide_transition(this_stats, last_stats, next_stats) ||
         ((pcnt_intra > MIN_INTRA_LEVEL) &&
          (pcnt_intra > (INTRA_VS_INTER_THRESH * modified_pcnt_inter)) &&
          ((this_stats->intra_error /
            DOUBLE_DIVIDE_CHECK(this_stats->coded_error)) <
           KF_II_ERR_THRESHOLD) &&
          ((fabs(last_stats->coded_error - this_stats->coded_error) /
                DOUBLE_DIVIDE_CHECK(this_stats->coded_error) >
            ERR_CHANGE_THRESHOLD) ||
           (fabs(last_stats->intra_error - this_stats->intra_error) /
                DOUBLE_DIVIDE_CHECK(this_stats->intra_error) >
            ERR_CHANGE_THRESHOLD) ||
           ((next_stats->intra_error /
             DOUBLE_DIVIDE_CHECK(next_stats->coded_error)) >
            II_IMPROVEMENT_THRESHOLD))))) {
      int i;
      double boost_score = 0.0;
      double old_boost_score = 0.0;
      double decay_accumulator = 1.0;
  
      // Examine how well the key frame predicts subsequent frames.
      for (i = 1; i <= frames_to_test_after_candidate_key; ++i) {
        // Get the next frame details
        const FIRSTPASS_STATS *local_next_frame =
            av1_firstpass_info_peek(firstpass_info, this_stats_index + i);
        double next_iiratio =
            (BOOST_FACTOR * local_next_frame->intra_error /
             DOUBLE_DIVIDE_CHECK(local_next_frame->coded_error));
  
        if (next_iiratio > KF_II_MAX) next_iiratio = KF_II_MAX;
  
        // Cumulative effect of decay in prediction quality.
        if (local_next_frame->pcnt_inter > 0.85)
          decay_accumulator *= local_next_frame->pcnt_inter;
        else
          decay_accumulator *= (0.85 + local_next_frame->pcnt_inter) / 2.0;
  
        // Keep a running total.
        boost_score += (decay_accumulator * next_iiratio);
  
        // Test various breakout clauses.
        // TODO(any): Test of intra error should be normalized to an MB.
        if ((local_next_frame->pcnt_inter < 0.05) || (next_iiratio < 1.5) ||
            (((local_next_frame->pcnt_inter - local_next_frame->pcnt_neutral) <
              0.20) &&
             (next_iiratio < 3.0)) ||
            ((boost_score - old_boost_score) < 3.0) ||
            (local_next_frame->intra_error < (200.0 / (double)num_mbs))) {
          break;
        }
  
        old_boost_score = boost_score;
      }
  
      // If there is tolerable prediction for at least the next 3 frames then
      // break out else discard this potential key frame and move on
      if (boost_score > 30.0 && (i > count_for_tolerable_prediction)) {
        is_viable_kf = 1;
      } else {
        is_viable_kf = 0;
      }
    }
    return is_viable_kf;
  }
  
  #define FRAMES_TO_CHECK_DECAY 8
  #define KF_MIN_FRAME_BOOST 80.0
  #define KF_MAX_FRAME_BOOST 128.0
  #define MIN_KF_BOOST 600  // Minimum boost for non-static KF interval
  #define MAX_KF_BOOST 3200
  #define MIN_STATIC_KF_BOOST 5400  // Minimum boost for static KF interval
  
  static int detect_app_forced_key(AV1_COMP *cpi) {
    int num_frames_to_app_forced_key = is_forced_keyframe_pending(
        cpi->ppi->lookahead, cpi->ppi->lookahead->max_sz, cpi->compressor_stage);
    return num_frames_to_app_forced_key;
  }
  
  static int get_projected_kf_boost(AV1_COMP *cpi) {
    /*
     * If num_stats_used_for_kf_boost >= frames_to_key, then
     * all stats needed for prior boost calculation are available.
     * Hence projecting the prior boost is not needed in this cases.
     */
    if (cpi->ppi->p_rc.num_stats_used_for_kf_boost >= cpi->rc.frames_to_key)
      return cpi->ppi->p_rc.kf_boost;
  
    // Get the current tpl factor (number of frames = frames_to_key).
    double tpl_factor = av1_get_kf_boost_projection_factor(cpi->rc.frames_to_key);
    // Get the tpl factor when number of frames = num_stats_used_for_kf_boost.
    double tpl_factor_num_stats = av1_get_kf_boost_projection_factor(
        cpi->ppi->p_rc.num_stats_used_for_kf_boost);
    int projected_kf_boost =
        (int)rint((tpl_factor * cpi->ppi->p_rc.kf_boost) / tpl_factor_num_stats);
    return projected_kf_boost;
  }
  
  /*!\brief Determine the location of the next key frame
   *
   * \ingroup gf_group_algo
   * This function decides the placement of the next key frame when a
   * scenecut is detected or the maximum key frame distance is reached.
   *
   * \param[in]    cpi              Top-level encoder structure
   * \param[in]    firstpass_info   struct for firstpass info
   * \param[in]    num_frames_to_detect_scenecut Maximum lookahead frames.
   * \param[in]    search_start_idx   the start index for searching key frame.
   *                                  Set it to one if we already know the
   *                                  current frame is key frame. Otherwise,
   *                                  set it to zero.
   *
   * \return       Number of frames to the next key including the current frame.
   */
  static int define_kf_interval(AV1_COMP *cpi,
                                const FIRSTPASS_INFO *firstpass_info,
                                int num_frames_to_detect_scenecut,
                                int search_start_idx) {
    const TWO_PASS *const twopass = &cpi->ppi->twopass;
    const RATE_CONTROL *const rc = &cpi->rc;
    PRIMARY_RATE_CONTROL *const p_rc = &cpi->ppi->p_rc;
    const AV1EncoderConfig *const oxcf = &cpi->oxcf;
    const KeyFrameCfg *const kf_cfg = &oxcf->kf_cfg;
    double recent_loop_decay[FRAMES_TO_CHECK_DECAY];
    double decay_accumulator = 1.0;
    int i = 0, j;
    int frames_to_key = search_start_idx;
    int frames_since_key = rc->frames_since_key + 1;
    int num_stats_used_for_kf_boost = 1;
    int scenecut_detected = 0;
  
    int num_frames_to_next_key = detect_app_forced_key(cpi);
  
    if (num_frames_to_detect_scenecut == 0) {
      if (num_frames_to_next_key != -1)
        return num_frames_to_next_key;
      else
        return rc->frames_to_key;
    }
  
    if (num_frames_to_next_key != -1)
      num_frames_to_detect_scenecut =
          AOMMIN(num_frames_to_detect_scenecut, num_frames_to_next_key);
  
    // Initialize the decay rates for the recent frames to check
    for (j = 0; j < FRAMES_TO_CHECK_DECAY; ++j) recent_loop_decay[j] = 1.0;
  
    i = 0;
    const int num_mbs = (oxcf->resize_cfg.resize_mode != RESIZE_NONE)
                            ? cpi->initial_mbs
                            : cpi->common.mi_params.MBs;
    const int future_stats_count =
        av1_firstpass_info_future_count(firstpass_info, 0);
    while (frames_to_key < future_stats_count &&
           frames_to_key < num_frames_to_detect_scenecut) {
      // Accumulate total number of stats available till next key frame
      num_stats_used_for_kf_boost++;
  
      // Provided that we are not at the end of the file...
      if ((cpi->ppi->p_rc.enable_scenecut_detection > 0) && kf_cfg->auto_key &&
          frames_to_key + 1 < future_stats_count) {
        double loop_decay_rate;
  
        // Check for a scene cut.
        if (frames_since_key >= kf_cfg->key_freq_min) {
          scenecut_detected = test_candidate_kf(
              &twopass->firstpass_info, frames_to_key, frames_since_key,
              oxcf->rc_cfg.mode, cpi->ppi->p_rc.enable_scenecut_detection,
              num_mbs);
          if (scenecut_detected) {
            break;
          }
        }
  
        // How fast is the prediction quality decaying?
        const FIRSTPASS_STATS *next_stats =
            av1_firstpass_info_peek(firstpass_info, frames_to_key + 1);
        loop_decay_rate = get_prediction_decay_rate(next_stats);
  
        // We want to know something about the recent past... rather than
        // as used elsewhere where we are concerned with decay in prediction
        // quality since the last GF or KF.
        recent_loop_decay[i % FRAMES_TO_CHECK_DECAY] = loop_decay_rate;
        decay_accumulator = 1.0;
        for (j = 0; j < FRAMES_TO_CHECK_DECAY; ++j)
          decay_accumulator *= recent_loop_decay[j];
  
        // Special check for transition or high motion followed by a
        // static scene.
        if (frames_since_key >= kf_cfg->key_freq_min) {
          scenecut_detected = detect_transition_to_still(
              firstpass_info, frames_to_key + 1, rc->min_gf_interval, i,
              kf_cfg->key_freq_max - i, loop_decay_rate, decay_accumulator);
          if (scenecut_detected) {
            // In the case of transition followed by a static scene, the key frame
            // could be a good predictor for the following frames, therefore we
            // do not use an arf.
            p_rc->use_arf_in_this_kf_group = 0;
            break;
          }
        }
  
        // Step on to the next frame.
        ++frames_to_key;
        ++frames_since_key;
  
        // If we don't have a real key frame within the next two
        // key_freq_max intervals then break out of the loop.
        if (frames_to_key >= 2 * kf_cfg->key_freq_max) {
          break;
        }
      } else {
        ++frames_to_key;
        ++frames_since_key;
      }
      ++i;
    }
    if (cpi->ppi->lap_enabled && !scenecut_detected)
      frames_to_key = num_frames_to_next_key;
  
    return frames_to_key;
  }
  
  static double get_kf_group_avg_error(TWO_PASS *twopass,
                                       TWO_PASS_FRAME *twopass_frame,
                                       const FIRSTPASS_STATS *first_frame,
                                       const FIRSTPASS_STATS *start_position,
                                       int frames_to_key) {
    FIRSTPASS_STATS cur_frame = *first_frame;
    int num_frames, i;
    double kf_group_avg_error = 0.0;
  
    reset_fpf_position(twopass_frame, start_position);
  
    for (i = 0; i < frames_to_key; ++i) {
      kf_group_avg_error += cur_frame.coded_error;
      if (EOF == input_stats(twopass, twopass_frame, &cur_frame)) break;
    }
    num_frames = i + 1;
    num_frames = AOMMIN(num_frames, frames_to_key);
    kf_group_avg_error = kf_group_avg_error / num_frames;
  
    return (kf_group_avg_error);
  }
  
  static int64_t get_kf_group_bits(AV1_COMP *cpi, double kf_group_err,
                                   double kf_group_avg_error) {
    RATE_CONTROL *const rc = &cpi->rc;
    TWO_PASS *const twopass = &cpi->ppi->twopass;
    int64_t kf_group_bits;
    if (cpi->ppi->lap_enabled) {
      kf_group_bits = (int64_t)rc->frames_to_key * rc->avg_frame_bandwidth;
      if (cpi->oxcf.rc_cfg.vbr_corpus_complexity_lap) {
        double vbr_corpus_complexity_lap =
            cpi->oxcf.rc_cfg.vbr_corpus_complexity_lap / 10.0;
        /* Get the average corpus complexity of the frame */
        kf_group_bits = (int64_t)(
            kf_group_bits * (kf_group_avg_error / vbr_corpus_complexity_lap));
      }
    } else {
      kf_group_bits = (int64_t)(twopass->bits_left *
                                (kf_group_err / twopass->modified_error_left));
    }
  
    return kf_group_bits;
  }
  
  static int calc_avg_stats(AV1_COMP *cpi, FIRSTPASS_STATS *avg_frame_stat) {
    RATE_CONTROL *const rc = &cpi->rc;
    TWO_PASS *const twopass = &cpi->ppi->twopass;
    FIRSTPASS_STATS cur_frame;
    av1_zero(cur_frame);
    int num_frames = 0;
    // Accumulate total stat using available number of stats.
    for (num_frames = 0; num_frames < (rc->frames_to_key - 1); ++num_frames) {
      if (EOF == input_stats(twopass, &cpi->twopass_frame, &cur_frame)) break;
      av1_accumulate_stats(avg_frame_stat, &cur_frame);
    }
  
    if (num_frames < 2) {
      return num_frames;
    }
    // Average the total stat
    avg_frame_stat->weight = avg_frame_stat->weight / num_frames;
    avg_frame_stat->intra_error = avg_frame_stat->intra_error / num_frames;
    avg_frame_stat->frame_avg_wavelet_energy =
        avg_frame_stat->frame_avg_wavelet_energy / num_frames;
    avg_frame_stat->coded_error = avg_frame_stat->coded_error / num_frames;
    avg_frame_stat->sr_coded_error = avg_frame_stat->sr_coded_error / num_frames;
    avg_frame_stat->pcnt_inter = avg_frame_stat->pcnt_inter / num_frames;
    avg_frame_stat->pcnt_motion = avg_frame_stat->pcnt_motion / num_frames;
    avg_frame_stat->pcnt_second_ref =
        avg_frame_stat->pcnt_second_ref / num_frames;
    avg_frame_stat->pcnt_neutral = avg_frame_stat->pcnt_neutral / num_frames;
    avg_frame_stat->intra_skip_pct = avg_frame_stat->intra_skip_pct / num_frames;
    avg_frame_stat->inactive_zone_rows =
        avg_frame_stat->inactive_zone_rows / num_frames;
    avg_frame_stat->inactive_zone_cols =
        avg_frame_stat->inactive_zone_cols / num_frames;
    avg_frame_stat->MVr = avg_frame_stat->MVr / num_frames;
    avg_frame_stat->mvr_abs = avg_frame_stat->mvr_abs / num_frames;
    avg_frame_stat->MVc = avg_frame_stat->MVc / num_frames;
    avg_frame_stat->mvc_abs = avg_frame_stat->mvc_abs / num_frames;
    avg_frame_stat->MVrv = avg_frame_stat->MVrv / num_frames;
    avg_frame_stat->MVcv = avg_frame_stat->MVcv / num_frames;
    avg_frame_stat->mv_in_out_count =
        avg_frame_stat->mv_in_out_count / num_frames;
    avg_frame_stat->new_mv_count = avg_frame_stat->new_mv_count / num_frames;
    avg_frame_stat->count = avg_frame_stat->count / num_frames;
    avg_frame_stat->duration = avg_frame_stat->duration / num_frames;
  
    return num_frames;
  }
  
  static double get_kf_boost_score(AV1_COMP *cpi, double kf_raw_err,
                                   double *zero_motion_accumulator,
                                   double *sr_accumulator, int use_avg_stat) {
    RATE_CONTROL *const rc = &cpi->rc;
    TWO_PASS *const twopass = &cpi->ppi->twopass;
    FRAME_INFO *const frame_info = &cpi->frame_info;
    FIRSTPASS_STATS frame_stat;
    av1_zero(frame_stat);
    int i = 0, num_stat_used = 0;
    double boost_score = 0.0;
    const double kf_max_boost =
        cpi->oxcf.rc_cfg.mode == AOM_Q
            ? AOMMIN(AOMMAX(rc->frames_to_key * 2.0, KF_MIN_FRAME_BOOST),
                     KF_MAX_FRAME_BOOST)
            : KF_MAX_FRAME_BOOST;
  
    // Calculate the average using available number of stats.
    if (use_avg_stat) num_stat_used = calc_avg_stats(cpi, &frame_stat);
  
    for (i = num_stat_used; i < (rc->frames_to_key - 1); ++i) {
      if (!use_avg_stat &&
          EOF == input_stats(twopass, &cpi->twopass_frame, &frame_stat))
        break;
  
      // Monitor for static sections.
      // For the first frame in kf group, the second ref indicator is invalid.
      if (i > 0) {
        *zero_motion_accumulator =
            AOMMIN(*zero_motion_accumulator, get_zero_motion_factor(&frame_stat));
      } else {
        *zero_motion_accumulator = frame_stat.pcnt_inter - frame_stat.pcnt_motion;
      }
  
      // Not all frames in the group are necessarily used in calculating boost.
      if ((*sr_accumulator < (kf_raw_err * 1.50)) &&
          (i <= rc->max_gf_interval * 2)) {
        double frame_boost;
        double zm_factor;
  
        // Factor 0.75-1.25 based on how much of frame is static.
        zm_factor = (0.75 + (*zero_motion_accumulator / 2.0));
  
        if (i < 2) *sr_accumulator = 0.0;
        frame_boost =
            calc_kf_frame_boost(&cpi->ppi->p_rc, frame_info, &frame_stat,
                                sr_accumulator, kf_max_boost);
        boost_score += frame_boost * zm_factor;
      }
    }
    return boost_score;
  }
  
  /*!\brief Interval(in seconds) to clip key-frame distance to in LAP.
   */
  #define MAX_KF_BITS_INTERVAL_SINGLE_PASS 5
  
  /*!\brief Determine the next key frame group
   *
   * \ingroup gf_group_algo
   * This function decides the placement of the next key frame, and
   * calculates the bit allocation of the KF group and the keyframe itself.
   *
   * \param[in]    cpi              Top-level encoder structure
   * \param[in]    this_frame       Pointer to first pass stats
   *
   * \return Nothing is returned.
   */
  static void find_next_key_frame(AV1_COMP *cpi, FIRSTPASS_STATS *this_frame) {
    RATE_CONTROL *const rc = &cpi->rc;
    PRIMARY_RATE_CONTROL *const p_rc = &cpi->ppi->p_rc;
    TWO_PASS *const twopass = &cpi->ppi->twopass;
    GF_GROUP *const gf_group = &cpi->ppi->gf_group;
    FRAME_INFO *const frame_info = &cpi->frame_info;
    AV1_COMMON *const cm = &cpi->common;
    CurrentFrame *const current_frame = &cm->current_frame;
    const AV1EncoderConfig *const oxcf = &cpi->oxcf;
    const KeyFrameCfg *const kf_cfg = &oxcf->kf_cfg;
    const FIRSTPASS_STATS first_frame = *this_frame;
    FIRSTPASS_STATS next_frame;
    const FIRSTPASS_INFO *firstpass_info = &twopass->firstpass_info;
    av1_zero(next_frame);
  
    rc->frames_since_key = 0;
    // Use arfs if possible.
    p_rc->use_arf_in_this_kf_group = is_altref_enabled(
        oxcf->gf_cfg.lag_in_frames, oxcf->gf_cfg.enable_auto_arf);
  
    // Reset the GF group data structures.
    av1_zero(*gf_group);
    cpi->gf_frame_index = 0;
  
    // KF is always a GF so clear frames till next gf counter.
    rc->frames_till_gf_update_due = 0;
  
    if (has_no_stats_stage(cpi)) {
      int num_frames_to_app_forced_key = detect_app_forced_key(cpi);
      p_rc->this_key_frame_forced =
          current_frame->frame_number != 0 && rc->frames_to_key == 0;
      if (num_frames_to_app_forced_key != -1)
        rc->frames_to_key = num_frames_to_app_forced_key;
      else
        rc->frames_to_key = AOMMAX(1, kf_cfg->key_freq_max);
      correct_frames_to_key(cpi);
      p_rc->kf_boost = DEFAULT_KF_BOOST;
      gf_group->update_type[0] = KF_UPDATE;
      return;
    }
    int i;
    const FIRSTPASS_STATS *const start_position = cpi->twopass_frame.stats_in;
    int kf_bits = 0;
    double zero_motion_accumulator = 1.0;
    double boost_score = 0.0;
    double kf_raw_err = 0.0;
    double kf_mod_err = 0.0;
    double sr_accumulator = 0.0;
    double kf_group_avg_error = 0.0;
    int frames_to_key, frames_to_key_clipped = INT_MAX;
    int64_t kf_group_bits_clipped = INT64_MAX;
  
    // Is this a forced key frame by interval.
    p_rc->this_key_frame_forced = p_rc->next_key_frame_forced;
  
    twopass->kf_group_bits = 0;        // Total bits available to kf group
    twopass->kf_group_error_left = 0;  // Group modified error score.
  
    kf_raw_err = this_frame->intra_error;
    kf_mod_err = calculate_modified_err(frame_info, twopass, oxcf, this_frame);
  
    // We assume the current frame is a key frame and we are looking for the next
    // key frame. Therefore search_start_idx = 1
    frames_to_key = define_kf_interval(cpi, firstpass_info, kf_cfg->key_freq_max,
                                       /*search_start_idx=*/1);
  
    if (frames_to_key != -1) {
      rc->frames_to_key = AOMMIN(kf_cfg->key_freq_max, frames_to_key);
    } else {
      rc->frames_to_key = kf_cfg->key_freq_max;
    }
  
    rc->frames_to_fwd_kf = kf_cfg->fwd_kf_dist;
  
    if (cpi->ppi->lap_enabled) correct_frames_to_key(cpi);
  
    // If there is a max kf interval set by the user we must obey it.
    // We already breakout of the loop above at 2x max.
    // This code centers the extra kf if the actual natural interval
    // is between 1x and 2x.
    if (kf_cfg->auto_key && rc->frames_to_key > kf_cfg->key_freq_max) {
      FIRSTPASS_STATS tmp_frame = first_frame;
  
      rc->frames_to_key /= 2;
  
      // Reset to the start of the group.
      reset_fpf_position(&cpi->twopass_frame, start_position);
      // Rescan to get the correct error data for the forced kf group.
      for (i = 0; i < rc->frames_to_key; ++i) {
        if (EOF == input_stats(twopass, &cpi->twopass_frame, &tmp_frame)) break;
      }
      p_rc->next_key_frame_forced = 1;
    } else if ((cpi->twopass_frame.stats_in ==
                    twopass->stats_buf_ctx->stats_in_end &&
                is_stat_consumption_stage_twopass(cpi)) ||
               rc->frames_to_key >= kf_cfg->key_freq_max) {
      p_rc->next_key_frame_forced = 1;
    } else {
      p_rc->next_key_frame_forced = 0;
    }
  
    double kf_group_err = 0;
    for (i = 0; i < rc->frames_to_key; ++i) {
      const FIRSTPASS_STATS *this_stats =
          av1_firstpass_info_peek(&twopass->firstpass_info, i);
      if (this_stats != NULL) {
        // Accumulate kf group error.
        kf_group_err += calculate_modified_err_new(
            frame_info, &firstpass_info->total_stats, this_stats,
            oxcf->rc_cfg.vbrbias, twopass->modified_error_min,
            twopass->modified_error_max);
        ++p_rc->num_stats_used_for_kf_boost;
      }
    }
  
    // Calculate the number of bits that should be assigned to the kf group.
    if ((twopass->bits_left > 0 && twopass->modified_error_left > 0.0) ||
        (cpi->ppi->lap_enabled && oxcf->rc_cfg.mode != AOM_Q)) {
      // Maximum number of bits for a single normal frame (not key frame).
      const int max_bits = frame_max_bits(rc, oxcf);
  
      // Maximum number of bits allocated to the key frame group.
      int64_t max_grp_bits;
  
      if (oxcf->rc_cfg.vbr_corpus_complexity_lap) {
        kf_group_avg_error =
            get_kf_group_avg_error(twopass, &cpi->twopass_frame, &first_frame,
                                   start_position, rc->frames_to_key);
      }
  
      // Default allocation based on bits left and relative
      // complexity of the section.
      twopass->kf_group_bits =
          get_kf_group_bits(cpi, kf_group_err, kf_group_avg_error);
      // Clip based on maximum per frame rate defined by the user.
      max_grp_bits = (int64_t)max_bits * (int64_t)rc->frames_to_key;
      if (twopass->kf_group_bits > max_grp_bits)
        twopass->kf_group_bits = max_grp_bits;
    } else {
      twopass->kf_group_bits = 0;
    }
    twopass->kf_group_bits = AOMMAX(0, twopass->kf_group_bits);
  
    if (cpi->ppi->lap_enabled) {
      // In the case of single pass based on LAP, frames to  key may have an
      // inaccurate value, and hence should be clipped to an appropriate
      // interval.
      frames_to_key_clipped =
          (int)(MAX_KF_BITS_INTERVAL_SINGLE_PASS * cpi->framerate);
  
      // This variable calculates the bits allocated to kf_group with a clipped
      // frames_to_key.
      if (rc->frames_to_key > frames_to_key_clipped) {
        kf_group_bits_clipped =
            (int64_t)((double)twopass->kf_group_bits * frames_to_key_clipped /
                      rc->frames_to_key);
      }
    }
  
    // Reset the first pass file position.
    reset_fpf_position(&cpi->twopass_frame, start_position);
  
    // Scan through the kf group collating various stats used to determine
    // how many bits to spend on it.
    boost_score = get_kf_boost_score(cpi, kf_raw_err, &zero_motion_accumulator,
                                     &sr_accumulator, 0);
    reset_fpf_position(&cpi->twopass_frame, start_position);
    // Store the zero motion percentage
    twopass->kf_zeromotion_pct = (int)(zero_motion_accumulator * 100.0);
  
    // Calculate a section intra ratio used in setting max loop filter.
    twopass->section_intra_rating = calculate_section_intra_ratio(
        start_position, twopass->stats_buf_ctx->stats_in_end, rc->frames_to_key);
  
    p_rc->kf_boost = (int)boost_score;
  
    if (cpi->ppi->lap_enabled) {
      if (oxcf->rc_cfg.mode == AOM_Q) {
        p_rc->kf_boost = get_projected_kf_boost(cpi);
      } else {
        // TODO(any): Explore using average frame stats for AOM_Q as well.
        boost_score = get_kf_boost_score(
            cpi, kf_raw_err, &zero_motion_accumulator, &sr_accumulator, 1);
        reset_fpf_position(&cpi->twopass_frame, start_position);
        p_rc->kf_boost += (int)boost_score;
      }
    }
  
    // Special case for static / slide show content but don't apply
    // if the kf group is very short.
    if ((zero_motion_accumulator > STATIC_KF_GROUP_FLOAT_THRESH) &&
        (rc->frames_to_key > 8)) {
      p_rc->kf_boost = AOMMAX(p_rc->kf_boost, MIN_STATIC_KF_BOOST);
    } else {
      // Apply various clamps for min and max boost
      p_rc->kf_boost = AOMMAX(p_rc->kf_boost, (rc->frames_to_key * 3));
      p_rc->kf_boost = AOMMAX(p_rc->kf_boost, MIN_KF_BOOST);
  #ifdef STRICT_RC
      p_rc->kf_boost = AOMMIN(p_rc->kf_boost, MAX_KF_BOOST);
  #endif
    }
  
    // Work out how many bits to allocate for the key frame itself.
    // In case of LAP enabled for VBR, if the frames_to_key value is
    // very high, we calculate the bits based on a clipped value of
    // frames_to_key.
    kf_bits = calculate_boost_bits(
        AOMMIN(rc->frames_to_key, frames_to_key_clipped) - 1, p_rc->kf_boost,
        AOMMIN(twopass->kf_group_bits, kf_group_bits_clipped));
    // printf("kf boost = %d kf_bits = %d kf_zeromotion_pct = %d\n",
    // p_rc->kf_boost,
    //        kf_bits, twopass->kf_zeromotion_pct);
    kf_bits = adjust_boost_bits_for_target_level(cpi, rc, kf_bits,
                                                 twopass->kf_group_bits, 0);
  
    twopass->kf_group_bits -= kf_bits;
  
    // Save the bits to spend on the key frame.
    gf_group->bit_allocation[0] = kf_bits;
    gf_group->update_type[0] = KF_UPDATE;
  
    // Note the total error score of the kf group minus the key frame itself.
    if (cpi->ppi->lap_enabled)
      // As we don't have enough stats to know the actual error of the group,
      // we assume the complexity of each frame to be equal to 1, and set the
      // error as the number of frames in the group(minus the keyframe).
      twopass->kf_group_error_left = (double)(rc->frames_to_key - 1);
    else
      twopass->kf_group_error_left = kf_group_err - kf_mod_err;
  
    // Adjust the count of total modified error left.
    // The count of bits left is adjusted elsewhere based on real coded frame
    // sizes.
    twopass->modified_error_left -= kf_group_err;
  }
  
  #define ARF_STATS_OUTPUT 0
  #if ARF_STATS_OUTPUT
  unsigned int arf_count = 0;
  #endif
  
  static int get_section_target_bandwidth(AV1_COMP *cpi) {
    AV1_COMMON *const cm = &cpi->common;
    CurrentFrame *const current_frame = &cm->current_frame;
    RATE_CONTROL *const rc = &cpi->rc;
    TWO_PASS *const twopass = &cpi->ppi->twopass;
    int section_target_bandwidth;
    const int frames_left = (int)(twopass->stats_buf_ctx->total_stats->count -
                                  current_frame->frame_number);
    if (cpi->ppi->lap_enabled)
      section_target_bandwidth = (int)rc->avg_frame_bandwidth;
    else
      section_target_bandwidth = (int)(twopass->bits_left / frames_left);
    return section_target_bandwidth;
  }
  
  static INLINE void set_twopass_params_based_on_fp_stats(
      AV1_COMP *cpi, const FIRSTPASS_STATS *this_frame_ptr) {
    if (this_frame_ptr == NULL) return;
  
    TWO_PASS_FRAME *twopass_frame = &cpi->twopass_frame;
    // The multiplication by 256 reverses a scaling factor of (>> 8)
    // applied when combining MB error values for the frame.
    twopass_frame->mb_av_energy = log((this_frame_ptr->intra_error) + 1.0);
  
    const FIRSTPASS_STATS *const total_stats =
        cpi->ppi->twopass.stats_buf_ctx->total_stats;
    if (is_fp_wavelet_energy_invalid(total_stats) == 0) {
      twopass_frame->frame_avg_haar_energy =
          log((this_frame_ptr->frame_avg_wavelet_energy) + 1.0);
    }
  
    // Set the frame content type flag.
    if (this_frame_ptr->intra_skip_pct >= FC_ANIMATION_THRESH)
      twopass_frame->fr_content_type = FC_GRAPHICS_ANIMATION;
    else
      twopass_frame->fr_content_type = FC_NORMAL;
  }
  
  static void process_first_pass_stats(AV1_COMP *cpi,
                                       FIRSTPASS_STATS *this_frame) {
    AV1_COMMON *const cm = &cpi->common;
    CurrentFrame *const current_frame = &cm->current_frame;
    RATE_CONTROL *const rc = &cpi->rc;
    PRIMARY_RATE_CONTROL *const p_rc = &cpi->ppi->p_rc;
    TWO_PASS *const twopass = &cpi->ppi->twopass;
    FIRSTPASS_STATS *total_stats = twopass->stats_buf_ctx->total_stats;
  
    if (cpi->oxcf.rc_cfg.mode != AOM_Q && current_frame->frame_number == 0 &&
        cpi->gf_frame_index == 0 && total_stats &&
        cpi->ppi->twopass.stats_buf_ctx->total_left_stats) {
      if (cpi->ppi->lap_enabled) {
        /*
         * Accumulate total_stats using available limited number of stats,
         * and assign it to total_left_stats.
         */
        *cpi->ppi->twopass.stats_buf_ctx->total_left_stats = *total_stats;
      }
      // Special case code for first frame.
      const int section_target_bandwidth = get_section_target_bandwidth(cpi);
      const double section_length =
          twopass->stats_buf_ctx->total_left_stats->count;
      const double section_error =
          twopass->stats_buf_ctx->total_left_stats->coded_error / section_length;
      const double section_intra_skip =
          twopass->stats_buf_ctx->total_left_stats->intra_skip_pct /
          section_length;
      const double section_inactive_zone =
          (twopass->stats_buf_ctx->total_left_stats->inactive_zone_rows * 2) /
          ((double)cm->mi_params.mb_rows * section_length);
      const int tmp_q = get_twopass_worst_quality(
          cpi, section_error, section_intra_skip + section_inactive_zone,
          section_target_bandwidth);
  
      rc->active_worst_quality = tmp_q;
      rc->ni_av_qi = tmp_q;
      p_rc->last_q[INTER_FRAME] = tmp_q;
      p_rc->avg_q = av1_convert_qindex_to_q(tmp_q, cm->seq_params->bit_depth);
      p_rc->avg_frame_qindex[INTER_FRAME] = tmp_q;
      p_rc->last_q[KEY_FRAME] = (tmp_q + cpi->oxcf.rc_cfg.best_allowed_q) / 2;
      p_rc->avg_frame_qindex[KEY_FRAME] = p_rc->last_q[KEY_FRAME];
    }
  
    if (cpi->twopass_frame.stats_in <
        cpi->ppi->twopass.stats_buf_ctx->stats_in_end) {
      *this_frame = *cpi->twopass_frame.stats_in;
      ++cpi->twopass_frame.stats_in;
    }
    set_twopass_params_based_on_fp_stats(cpi, this_frame);
  }
  
  static void setup_target_rate(AV1_COMP *cpi) {
    RATE_CONTROL *const rc = &cpi->rc;
    GF_GROUP *const gf_group = &cpi->ppi->gf_group;
  
    int target_rate = gf_group->bit_allocation[cpi->gf_frame_index];
  
    if (has_no_stats_stage(cpi)) {
      av1_rc_set_frame_target(cpi, target_rate, cpi->common.width,
                              cpi->common.height);
    }
  
    rc->base_frame_target = target_rate;
  }
  
  static void mark_flashes(FIRSTPASS_STATS *first_stats,
                           FIRSTPASS_STATS *last_stats) {
    FIRSTPASS_STATS *this_stats = first_stats, *next_stats;
    while (this_stats < last_stats - 1) {
      next_stats = this_stats + 1;
      if (next_stats->pcnt_second_ref > next_stats->pcnt_inter &&
          next_stats->pcnt_second_ref >= 0.5) {
        this_stats->is_flash = 1;
      } else {
        this_stats->is_flash = 0;
      }
      this_stats = next_stats;
    }
    // We always treat the last one as none flash.
    if (last_stats - 1 >= first_stats) {
      (last_stats - 1)->is_flash = 0;
    }
  }
  
  // Estimate the noise variance of each frame from the first pass stats
  static void estimate_noise(FIRSTPASS_STATS *first_stats,
                             FIRSTPASS_STATS *last_stats) {
    FIRSTPASS_STATS *this_stats, *next_stats;
    double C1, C2, C3, noise;
    int count = 0;
    for (this_stats = first_stats + 2; this_stats < last_stats; this_stats++) {
      this_stats->noise_var = 0.0;
      // flashes tend to have high correlation of innovations, so ignore them.
      if (this_stats->is_flash || (this_stats - 1)->is_flash ||
          (this_stats - 2)->is_flash)
        continue;
  
      C1 = (this_stats - 1)->intra_error *
           (this_stats->intra_error - this_stats->coded_error);
      C2 = (this_stats - 2)->intra_error *
           ((this_stats - 1)->intra_error - (this_stats - 1)->coded_error);
      C3 = (this_stats - 2)->intra_error *
           (this_stats->intra_error - this_stats->sr_coded_error);
      if (C1 <= 0 || C2 <= 0 || C3 <= 0) continue;
      C1 = sqrt(C1);
      C2 = sqrt(C2);
      C3 = sqrt(C3);
  
      noise = (this_stats - 1)->intra_error - C1 * C2 / C3;
      noise = AOMMAX(noise, 0.01);
      this_stats->noise_var = noise;
      count++;
    }
  
    // Copy noise from the neighbor if the noise value is not trustworthy
    for (this_stats = first_stats + 2; this_stats < last_stats; this_stats++) {
      if (this_stats->is_flash || (this_stats - 1)->is_flash ||
          (this_stats - 2)->is_flash)
        continue;
      if (this_stats->noise_var < 1.0) {
        int found = 0;
        // TODO(bohanli): consider expanding to two directions at the same time
        for (next_stats = this_stats + 1; next_stats < last_stats; next_stats++) {
          if (next_stats->is_flash || (next_stats - 1)->is_flash ||
              (next_stats - 2)->is_flash || next_stats->noise_var < 1.0)
            continue;
          found = 1;
          this_stats->noise_var = next_stats->noise_var;
          break;
        }
        if (found) continue;
        for (next_stats = this_stats - 1; next_stats >= first_stats + 2;
             next_stats--) {
          if (next_stats->is_flash || (next_stats - 1)->is_flash ||
              (next_stats - 2)->is_flash || next_stats->noise_var < 1.0)
            continue;
          this_stats->noise_var = next_stats->noise_var;
          break;
        }
      }
    }
  
    // copy the noise if this is a flash
    for (this_stats = first_stats + 2; this_stats < last_stats; this_stats++) {
      if (this_stats->is_flash || (this_stats - 1)->is_flash ||
          (this_stats - 2)->is_flash) {
        int found = 0;
        for (next_stats = this_stats + 1; next_stats < last_stats; next_stats++) {
          if (next_stats->is_flash || (next_stats - 1)->is_flash ||
              (next_stats - 2)->is_flash)
            continue;
          found = 1;
          this_stats->noise_var = next_stats->noise_var;
          break;
        }
        if (found) continue;
        for (next_stats = this_stats - 1; next_stats >= first_stats + 2;
             next_stats--) {
          if (next_stats->is_flash || (next_stats - 1)->is_flash ||
              (next_stats - 2)->is_flash)
            continue;
          this_stats->noise_var = next_stats->noise_var;
          break;
        }
      }
    }
  
    // if we are at the first 2 frames, copy the noise
    for (this_stats = first_stats;
         this_stats < first_stats + 2 && (first_stats + 2) < last_stats;
         this_stats++) {
      this_stats->noise_var = (first_stats + 2)->noise_var;
    }
  }
  
  // Estimate correlation coefficient of each frame with its previous frame.
  static void estimate_coeff(FIRSTPASS_STATS *first_stats,
                             FIRSTPASS_STATS *last_stats) {
    FIRSTPASS_STATS *this_stats;
    for (this_stats = first_stats + 1; this_stats < last_stats; this_stats++) {
      const double C =
          sqrt(AOMMAX((this_stats - 1)->intra_error *
                          (this_stats->intra_error - this_stats->coded_error),
                      0.001));
      const double cor_coeff =
          C /
          AOMMAX((this_stats - 1)->intra_error - this_stats->noise_var, 0.001);
  
      this_stats->cor_coeff =
          cor_coeff *
          sqrt(AOMMAX((this_stats - 1)->intra_error - this_stats->noise_var,
                      0.001) /
               AOMMAX(this_stats->intra_error - this_stats->noise_var, 0.001));
      // clip correlation coefficient.
      this_stats->cor_coeff = AOMMIN(AOMMAX(this_stats->cor_coeff, 0), 1);
    }
    first_stats->cor_coeff = 1.0;
  }
  
  void av1_get_second_pass_params(AV1_COMP *cpi,
                                  EncodeFrameParams *const frame_params,
                                  const EncodeFrameInput *const frame_input,
                                  unsigned int frame_flags) {
    RATE_CONTROL *const rc = &cpi->rc;
    PRIMARY_RATE_CONTROL *const p_rc = &cpi->ppi->p_rc;
    TWO_PASS *const twopass = &cpi->ppi->twopass;
    GF_GROUP *const gf_group = &cpi->ppi->gf_group;
    const AV1EncoderConfig *const oxcf = &cpi->oxcf;
  
    const FIRSTPASS_STATS *const start_pos = cpi->twopass_frame.stats_in;
    int update_total_stats = 0;
  
    if (is_stat_consumption_stage(cpi) && !cpi->twopass_frame.stats_in) return;
  
    assert(cpi->twopass_frame.stats_in != NULL);
    const int update_type = gf_group->update_type[cpi->gf_frame_index];
    frame_params->frame_type = gf_group->frame_type[cpi->gf_frame_index];
  
    if (cpi->gf_frame_index < gf_group->size && !(frame_flags & FRAMEFLAGS_KEY)) {
      assert(cpi->gf_frame_index < gf_group->size);
  
      setup_target_rate(cpi);
  
      // If this is an arf frame then we dont want to read the stats file or
      // advance the input pointer as we already have what we need.
      if (update_type == ARF_UPDATE || update_type == INTNL_ARF_UPDATE) {
        const FIRSTPASS_STATS *const this_frame_ptr =
            read_frame_stats(twopass, &cpi->twopass_frame,
                             gf_group->arf_src_offset[cpi->gf_frame_index]);
        set_twopass_params_based_on_fp_stats(cpi, this_frame_ptr);
        return;
      }
    }
  
    if (oxcf->rc_cfg.mode == AOM_Q)
      rc->active_worst_quality = oxcf->rc_cfg.cq_level;
    FIRSTPASS_STATS this_frame;
    av1_zero(this_frame);
    // call above fn
    if (is_stat_consumption_stage(cpi)) {
      if (cpi->gf_frame_index < gf_group->size || rc->frames_to_key == 0) {
        process_first_pass_stats(cpi, &this_frame);
        update_total_stats = 1;
      }
    } else {
      rc->active_worst_quality = oxcf->rc_cfg.cq_level;
    }
  
    if (cpi->gf_frame_index == gf_group->size) {
      if (cpi->ppi->lap_enabled && cpi->ppi->p_rc.enable_scenecut_detection) {
        const int num_frames_to_detect_scenecut = MAX_GF_LENGTH_LAP + 1;
        const int frames_to_key = define_kf_interval(
            cpi, &twopass->firstpass_info, num_frames_to_detect_scenecut,
            /*search_start_idx=*/0);
        if (frames_to_key != -1)
          rc->frames_to_key = AOMMIN(rc->frames_to_key, frames_to_key);
      }
    }
  
    // Keyframe and section processing.
    FIRSTPASS_STATS this_frame_copy;
    this_frame_copy = this_frame;
    if (rc->frames_to_key <= 0) {
      assert(rc->frames_to_key == 0);
      // Define next KF group and assign bits to it.
      frame_params->frame_type = KEY_FRAME;
      find_next_key_frame(cpi, &this_frame);
      this_frame = this_frame_copy;
    }
  
    if (rc->frames_to_fwd_kf <= 0)
      rc->frames_to_fwd_kf = oxcf->kf_cfg.fwd_kf_dist;
  
    // Define a new GF/ARF group. (Should always enter here for key frames).
    if (cpi->gf_frame_index == gf_group->size) {
  #if CONFIG_BITRATE_ACCURACY
      vbr_rc_reset_gop_data(&cpi->vbr_rc_info);
  #endif  // CONFIG_BITRATE_ACCURACY
      int max_gop_length =
          (oxcf->gf_cfg.lag_in_frames >= 32)
              ? AOMMIN(MAX_GF_INTERVAL, oxcf->gf_cfg.lag_in_frames -
                                            oxcf->algo_cfg.arnr_max_frames / 2)
              : MAX_GF_LENGTH_LAP;
  
      // Use the provided gop size in low delay setting
      if (oxcf->gf_cfg.lag_in_frames == 0) max_gop_length = rc->max_gf_interval;
  
      // Identify regions if needed.
      // TODO(bohanli): identify regions for all stats available.
      if (rc->frames_since_key == 0 || rc->frames_since_key == 1 ||
          (p_rc->frames_till_regions_update - rc->frames_since_key <
               rc->frames_to_key &&
           p_rc->frames_till_regions_update - rc->frames_since_key <
               max_gop_length + 1)) {
        // how many frames we can analyze from this frame
        int rest_frames =
            AOMMIN(rc->frames_to_key, MAX_FIRSTPASS_ANALYSIS_FRAMES);
        rest_frames =
            AOMMIN(rest_frames, (int)(twopass->stats_buf_ctx->stats_in_end -
                                      cpi->twopass_frame.stats_in +
                                      (rc->frames_since_key == 0)));
        p_rc->frames_till_regions_update = rest_frames;
  
        if (cpi->ppi->lap_enabled) {
          mark_flashes(twopass->stats_buf_ctx->stats_in_start,
                       twopass->stats_buf_ctx->stats_in_end);
          estimate_noise(twopass->stats_buf_ctx->stats_in_start,
                         twopass->stats_buf_ctx->stats_in_end);
          estimate_coeff(twopass->stats_buf_ctx->stats_in_start,
                         twopass->stats_buf_ctx->stats_in_end);
          identify_regions(cpi->twopass_frame.stats_in, rest_frames,
                           (rc->frames_since_key == 0), p_rc->regions,
                           &p_rc->num_regions);
        } else {
          identify_regions(
              cpi->twopass_frame.stats_in - (rc->frames_since_key == 0),
              rest_frames, 0, p_rc->regions, &p_rc->num_regions);
        }
      }
  
      int cur_region_idx =
          find_regions_index(p_rc->regions, p_rc->num_regions,
                             rc->frames_since_key - p_rc->regions_offset);
      if ((cur_region_idx >= 0 &&
           p_rc->regions[cur_region_idx].type == SCENECUT_REGION) ||
          rc->frames_since_key == 0) {
        // If we start from a scenecut, then the last GOP's arf boost is not
        // needed for this GOP.
        cpi->ppi->gf_state.arf_gf_boost_lst = 0;
      }
  
      int need_gf_len = 1;
      if (cpi->third_pass_ctx && oxcf->pass == AOM_RC_THIRD_PASS) {
        if (!cpi->third_pass_ctx->input_file_name && oxcf->two_pass_output) {
          cpi->third_pass_ctx->input_file_name = oxcf->two_pass_output;
        }
        if (cpi->third_pass_ctx->input_file_name) {
          int gf_len;
          const int order_hint_bits =
              cpi->common.seq_params->order_hint_info.order_hint_bits_minus_1 + 1;
          av1_set_gop_third_pass(cpi->third_pass_ctx, gf_group, order_hint_bits,
                                 &gf_len);
          p_rc->cur_gf_index = 0;
          p_rc->gf_intervals[0] = gf_len;
          need_gf_len = 0;
        }
      }
  
      if (need_gf_len) {
        // TODO(jingning): Resolve the redundant calls here.
        if (rc->intervals_till_gf_calculate_due == 0 || 1) {
          calculate_gf_length(cpi, max_gop_length, MAX_NUM_GF_INTERVALS);
        }
  
        if (max_gop_length > 16 && oxcf->algo_cfg.enable_tpl_model &&
            oxcf->gf_cfg.lag_in_frames >= 32 &&
            cpi->sf.tpl_sf.gop_length_decision_method != 3) {
          int this_idx = rc->frames_since_key +
                         p_rc->gf_intervals[p_rc->cur_gf_index] -
                         p_rc->regions_offset - 1;
          int this_region =
              find_regions_index(p_rc->regions, p_rc->num_regions, this_idx);
          int next_region =
              find_regions_index(p_rc->regions, p_rc->num_regions, this_idx + 1);
          // TODO(angiebird): Figure out why this_region and next_region are -1 in
          // unit test like AltRefFramePresenceTestLarge (aomedia:3134)
          int is_last_scenecut =
              p_rc->gf_intervals[p_rc->cur_gf_index] >= rc->frames_to_key ||
              (this_region != -1 &&
               p_rc->regions[this_region].type == SCENECUT_REGION) ||
              (next_region != -1 &&
               p_rc->regions[next_region].type == SCENECUT_REGION);
  
          int ori_gf_int = p_rc->gf_intervals[p_rc->cur_gf_index];
  
          if (p_rc->gf_intervals[p_rc->cur_gf_index] > 16 &&
              rc->min_gf_interval <= 16) {
            // The calculate_gf_length function is previously used with
            // max_gop_length = 32 with look-ahead gf intervals.
            define_gf_group(cpi, frame_params, 0);
            this_frame = this_frame_copy;
  
            if (is_shorter_gf_interval_better(cpi, frame_params, frame_input)) {
              // A shorter gf interval is better.
              // TODO(jingning): Remove redundant computations here.
              max_gop_length = 16;
              calculate_gf_length(cpi, max_gop_length, 1);
              if (is_last_scenecut &&
                  (ori_gf_int - p_rc->gf_intervals[p_rc->cur_gf_index] < 4)) {
                p_rc->gf_intervals[p_rc->cur_gf_index] = ori_gf_int;
              }
            }
          }
        }
      }
  
      define_gf_group(cpi, frame_params, 0);
  
      if (gf_group->update_type[cpi->gf_frame_index] != ARF_UPDATE &&
          rc->frames_since_key > 0)
        process_first_pass_stats(cpi, &this_frame);
  
      define_gf_group(cpi, frame_params, 1);
  
      av1_write_second_pass_gop_info(cpi);
  
      av1_tf_info_filtering(&cpi->ppi->tf_info, cpi, gf_group);
  
      rc->frames_till_gf_update_due = p_rc->baseline_gf_interval;
      assert(cpi->gf_frame_index == 0);
  #if ARF_STATS_OUTPUT
      {
        FILE *fpfile;
        fpfile = fopen("arf.stt", "a");
        ++arf_count;
        fprintf(fpfile, "%10d %10d %10d %10d %10d\n",
                cpi->common.current_frame.frame_number,
                rc->frames_till_gf_update_due, cpi->ppi->p_rc.kf_boost, arf_count,
                p_rc->gfu_boost);
  
        fclose(fpfile);
      }
  #endif
    }
    assert(cpi->gf_frame_index < gf_group->size);
  
    if (gf_group->update_type[cpi->gf_frame_index] == ARF_UPDATE ||
        gf_group->update_type[cpi->gf_frame_index] == INTNL_ARF_UPDATE) {
      reset_fpf_position(&cpi->twopass_frame, start_pos);
  
      const FIRSTPASS_STATS *const this_frame_ptr =
          read_frame_stats(twopass, &cpi->twopass_frame,
                           gf_group->arf_src_offset[cpi->gf_frame_index]);
      set_twopass_params_based_on_fp_stats(cpi, this_frame_ptr);
    } else {
      // Back up this frame's stats for updating total stats during post encode.
      cpi->twopass_frame.this_frame = update_total_stats ? start_pos : NULL;
    }
  
    frame_params->frame_type = gf_group->frame_type[cpi->gf_frame_index];
    setup_target_rate(cpi);
  }
  
  void av1_init_second_pass(AV1_COMP *cpi) {
    const AV1EncoderConfig *const oxcf = &cpi->oxcf;
    TWO_PASS *const twopass = &cpi->ppi->twopass;
    FRAME_INFO *const frame_info = &cpi->frame_info;
    double frame_rate;
    FIRSTPASS_STATS *stats;
  
    if (!twopass->stats_buf_ctx->stats_in_end) return;
  
    mark_flashes(twopass->stats_buf_ctx->stats_in_start,
                 twopass->stats_buf_ctx->stats_in_end);
    estimate_noise(twopass->stats_buf_ctx->stats_in_start,
                   twopass->stats_buf_ctx->stats_in_end);
    estimate_coeff(twopass->stats_buf_ctx->stats_in_start,
                   twopass->stats_buf_ctx->stats_in_end);
  
    stats = twopass->stats_buf_ctx->total_stats;
  
    *stats = *twopass->stats_buf_ctx->stats_in_end;
    *twopass->stats_buf_ctx->total_left_stats = *stats;
  
    frame_rate = 10000000.0 * stats->count / stats->duration;
    // Each frame can have a different duration, as the frame rate in the source
    // isn't guaranteed to be constant. The frame rate prior to the first frame
    // encoded in the second pass is a guess. However, the sum duration is not.
    // It is calculated based on the actual durations of all frames from the
    // first pass.
    av1_new_framerate(cpi, frame_rate);
    twopass->bits_left =
        (int64_t)(stats->duration * oxcf->rc_cfg.target_bandwidth / 10000000.0);
  
  #if CONFIG_BITRATE_ACCURACY
    vbr_rc_init(&cpi->vbr_rc_info, cpi->ppi->twopass.bits_left,
                (int)round(stats->count));
  #endif
  
    // This variable monitors how far behind the second ref update is lagging.
    twopass->sr_update_lag = 1;
  
    // Scan the first pass file and calculate a modified total error based upon
    // the bias/power function used to allocate bits.
    {
      const double avg_error =
          stats->coded_error / DOUBLE_DIVIDE_CHECK(stats->count);
      const FIRSTPASS_STATS *s = cpi->twopass_frame.stats_in;
      double modified_error_total = 0.0;
      twopass->modified_error_min =
          (avg_error * oxcf->rc_cfg.vbrmin_section) / 100;
      twopass->modified_error_max =
          (avg_error * oxcf->rc_cfg.vbrmax_section) / 100;
      while (s < twopass->stats_buf_ctx->stats_in_end) {
        modified_error_total +=
            calculate_modified_err(frame_info, twopass, oxcf, s);
        ++s;
      }
      twopass->modified_error_left = modified_error_total;
    }
  
    // Reset the vbr bits off target counters
    cpi->ppi->p_rc.vbr_bits_off_target = 0;
    cpi->ppi->p_rc.vbr_bits_off_target_fast = 0;
  
    cpi->ppi->p_rc.rate_error_estimate = 0;
  
    // Static sequence monitor variables.
    twopass->kf_zeromotion_pct = 100;
    twopass->last_kfgroup_zeromotion_pct = 100;
  
    // Initialize bits per macro_block estimate correction factor.
    twopass->bpm_factor = 1.0;
    // Initialize actual and target bits counters for ARF groups so that
    // at the start we have a neutral bpm adjustment.
    twopass->rolling_arf_group_target_bits = 1;
    twopass->rolling_arf_group_actual_bits = 1;
  }
  
  void av1_init_single_pass_lap(AV1_COMP *cpi) {
    TWO_PASS *const twopass = &cpi->ppi->twopass;
  
    if (!twopass->stats_buf_ctx->stats_in_end) return;
  
    // This variable monitors how far behind the second ref update is lagging.
    twopass->sr_update_lag = 1;
  
    twopass->bits_left = 0;
    twopass->modified_error_min = 0.0;
    twopass->modified_error_max = 0.0;
    twopass->modified_error_left = 0.0;
  
    // Reset the vbr bits off target counters
    cpi->ppi->p_rc.vbr_bits_off_target = 0;
    cpi->ppi->p_rc.vbr_bits_off_target_fast = 0;
  
    cpi->ppi->p_rc.rate_error_estimate = 0;
  
    // Static sequence monitor variables.
    twopass->kf_zeromotion_pct = 100;
    twopass->last_kfgroup_zeromotion_pct = 100;
  
    // Initialize bits per macro_block estimate correction factor.
    twopass->bpm_factor = 1.0;
    // Initialize actual and target bits counters for ARF groups so that
    // at the start we have a neutral bpm adjustment.
    twopass->rolling_arf_group_target_bits = 1;
    twopass->rolling_arf_group_actual_bits = 1;
  }
  
  #define MINQ_ADJ_LIMIT 48
  #define MINQ_ADJ_LIMIT_CQ 20
  #define HIGH_UNDERSHOOT_RATIO 2
  void av1_twopass_postencode_update(AV1_COMP *cpi) {
    TWO_PASS *const twopass = &cpi->ppi->twopass;
    RATE_CONTROL *const rc = &cpi->rc;
    PRIMARY_RATE_CONTROL *const p_rc = &cpi->ppi->p_rc;
    const RateControlCfg *const rc_cfg = &cpi->oxcf.rc_cfg;
  
    // Increment the stats_in pointer.
    if (is_stat_consumption_stage(cpi) &&
        (cpi->gf_frame_index < cpi->ppi->gf_group.size ||
         rc->frames_to_key == 0)) {
      const int update_type = cpi->ppi->gf_group.update_type[cpi->gf_frame_index];
      if (update_type != ARF_UPDATE && update_type != INTNL_ARF_UPDATE) {
        FIRSTPASS_STATS this_frame;
        --cpi->twopass_frame.stats_in;
        if (cpi->ppi->lap_enabled) {
          input_stats_lap(twopass, &cpi->twopass_frame, &this_frame);
        } else {
          input_stats(twopass, &cpi->twopass_frame, &this_frame);
        }
      } else if (cpi->ppi->lap_enabled) {
        cpi->twopass_frame.stats_in =
            cpi->ppi->twopass.stats_buf_ctx->stats_in_start;
      }
    }
  
    // VBR correction is done through rc->vbr_bits_off_target. Based on the
    // sign of this value, a limited % adjustment is made to the target rate
    // of subsequent frames, to try and push it back towards 0. This method
    // is designed to prevent extreme behaviour at the end of a clip
    // or group of frames.
    p_rc->vbr_bits_off_target += rc->base_frame_target - rc->projected_frame_size;
    twopass->bits_left = AOMMAX(twopass->bits_left - rc->base_frame_target, 0);
  
  #if CONFIG_FRAME_PARALLEL_ENCODE
    if (cpi->do_update_vbr_bits_off_target_fast) {
      // Subtract current frame's fast_extra_bits.
      p_rc->vbr_bits_off_target_fast -= rc->frame_level_fast_extra_bits;
      rc->frame_level_fast_extra_bits = 0;
    }
  #endif
  
    // Target vs actual bits for this arf group.
    twopass->rolling_arf_group_target_bits += rc->base_frame_target;
    twopass->rolling_arf_group_actual_bits += rc->projected_frame_size;
  
    // Calculate the pct rc error.
    if (p_rc->total_actual_bits) {
      p_rc->rate_error_estimate =
          (int)((p_rc->vbr_bits_off_target * 100) / p_rc->total_actual_bits);
      p_rc->rate_error_estimate = clamp(p_rc->rate_error_estimate, -100, 100);
    } else {
      p_rc->rate_error_estimate = 0;
    }
  
    // Update the active best quality pyramid.
    if (!rc->is_src_frame_alt_ref) {
      const int pyramid_level =
          cpi->ppi->gf_group.layer_depth[cpi->gf_frame_index];
      int i;
      for (i = pyramid_level; i <= MAX_ARF_LAYERS; ++i) {
        p_rc->active_best_quality[i] = cpi->common.quant_params.base_qindex;
  #if CONFIG_TUNE_VMAF
        if (cpi->vmaf_info.original_qindex != -1 &&
            (cpi->oxcf.tune_cfg.tuning >= AOM_TUNE_VMAF_WITH_PREPROCESSING &&
             cpi->oxcf.tune_cfg.tuning <= AOM_TUNE_VMAF_NEG_MAX_GAIN)) {
          p_rc->active_best_quality[i] = cpi->vmaf_info.original_qindex;
        }
  #endif
      }
    }
  
  #if 0
    {
      AV1_COMMON *cm = &cpi->common;
      FILE *fpfile;
      fpfile = fopen("details.stt", "a");
      fprintf(fpfile,
              "%10d %10d %10d %10" PRId64 " %10" PRId64
              " %10d %10d %10d %10.4lf %10.4lf %10.4lf %10.4lf\n",
              cm->current_frame.frame_number, rc->base_frame_target,
              rc->projected_frame_size, rc->total_actual_bits,
              rc->vbr_bits_off_target, p_rc->rate_error_estimate,
              twopass->rolling_arf_group_target_bits,
              twopass->rolling_arf_group_actual_bits,
              (double)twopass->rolling_arf_group_actual_bits /
                  (double)twopass->rolling_arf_group_target_bits,
              twopass->bpm_factor,
              av1_convert_qindex_to_q(cpi->common.quant_params.base_qindex,
                                      cm->seq_params->bit_depth),
              av1_convert_qindex_to_q(rc->active_worst_quality,
                                      cm->seq_params->bit_depth));
      fclose(fpfile);
    }
  #endif
  
    if (cpi->common.current_frame.frame_type != KEY_FRAME) {
      twopass->kf_group_bits -= rc->base_frame_target;
      twopass->last_kfgroup_zeromotion_pct = twopass->kf_zeromotion_pct;
    }
    twopass->kf_group_bits = AOMMAX(twopass->kf_group_bits, 0);
  
    // If the rate control is drifting consider adjustment to min or maxq.
    if ((rc_cfg->mode != AOM_Q) && !cpi->rc.is_src_frame_alt_ref) {
      int maxq_adj_limit;
      int minq_adj_limit;
      maxq_adj_limit = rc->worst_quality - rc->active_worst_quality;
      minq_adj_limit =
          (rc_cfg->mode == AOM_CQ ? MINQ_ADJ_LIMIT_CQ : MINQ_ADJ_LIMIT);
      // Undershoot.
      if (p_rc->rate_error_estimate > rc_cfg->under_shoot_pct) {
        --twopass->extend_maxq;
        if (p_rc->rolling_target_bits >= p_rc->rolling_actual_bits)
          ++twopass->extend_minq;
        // Overshoot.
      } else if (p_rc->rate_error_estimate < -rc_cfg->over_shoot_pct) {
        --twopass->extend_minq;
        if (p_rc->rolling_target_bits < p_rc->rolling_actual_bits)
          ++twopass->extend_maxq;
      } else {
        // Adjustment for extreme local overshoot.
        if (rc->projected_frame_size > (2 * rc->base_frame_target) &&
            rc->projected_frame_size > (2 * rc->avg_frame_bandwidth))
          ++twopass->extend_maxq;
        // Unwind undershoot or overshoot adjustment.
        if (p_rc->rolling_target_bits < p_rc->rolling_actual_bits)
          --twopass->extend_minq;
        else if (p_rc->rolling_target_bits > p_rc->rolling_actual_bits)
          --twopass->extend_maxq;
      }
      twopass->extend_minq = clamp(twopass->extend_minq, 0, minq_adj_limit);
      twopass->extend_maxq = clamp(twopass->extend_maxq, 0, maxq_adj_limit);
  
  #if CONFIG_FRAME_PARALLEL_ENCODE
      if (!frame_is_kf_gf_arf(cpi) && !rc->is_src_frame_alt_ref &&
          p_rc->vbr_bits_off_target_fast) {
        // Subtract current frame's fast_extra_bits.
        p_rc->vbr_bits_off_target_fast -= rc->frame_level_fast_extra_bits;
      }
  #endif
  
      // If there is a big and undexpected undershoot then feed the extra
      // bits back in quickly. One situation where this may happen is if a
      // frame is unexpectedly almost perfectly predicted by the ARF or GF
      // but not very well predcited by the previous frame.
      if (!frame_is_kf_gf_arf(cpi) && !cpi->rc.is_src_frame_alt_ref) {
        int fast_extra_thresh = rc->base_frame_target / HIGH_UNDERSHOOT_RATIO;
        if (rc->projected_frame_size < fast_extra_thresh) {
          p_rc->vbr_bits_off_target_fast +=
              fast_extra_thresh - rc->projected_frame_size;
          p_rc->vbr_bits_off_target_fast = AOMMIN(p_rc->vbr_bits_off_target_fast,
                                                  (4 * rc->avg_frame_bandwidth));
  
          // Fast adaptation of minQ if necessary to use up the extra bits.
          if (rc->avg_frame_bandwidth) {
            twopass->extend_minq_fast = (int)(p_rc->vbr_bits_off_target_fast * 8 /
                                              rc->avg_frame_bandwidth);
          }
          twopass->extend_minq_fast = AOMMIN(
              twopass->extend_minq_fast, minq_adj_limit - twopass->extend_minq);
        } else if (p_rc->vbr_bits_off_target_fast) {
          twopass->extend_minq_fast = AOMMIN(
              twopass->extend_minq_fast, minq_adj_limit - twopass->extend_minq);
        } else {
          twopass->extend_minq_fast = 0;
        }
      }
    }
  
  #if CONFIG_FRAME_PARALLEL_ENCODE
    // Update the frame probabilities obtained from parallel encode frames
    FrameProbInfo *const frame_probs = &cpi->ppi->frame_probs;
    int i, j, loop;
    // Sequentially do average on temp_frame_probs_simulation which holds
    // probabilities of last frame before parallel encode
    for (loop = 0; loop <= cpi->num_frame_recode; loop++) {
      // Sequentially update tx_type_probs
      if (cpi->do_update_frame_probs_txtype[loop] &&
          (cpi->ppi->gf_group.frame_parallel_level[cpi->gf_frame_index] > 0)) {
        const FRAME_UPDATE_TYPE update_type =
            get_frame_update_type(&cpi->ppi->gf_group, cpi->gf_frame_index);
        for (i = 0; i < TX_SIZES_ALL; i++) {
          int left = 1024;
  
          for (j = TX_TYPES - 1; j >= 0; j--) {
            const int new_prob =
                cpi->frame_new_probs[loop].tx_type_probs[update_type][i][j];
            int prob =
                (frame_probs->tx_type_probs[update_type][i][j] + new_prob) >> 1;
            left -= prob;
            if (j == 0) prob += left;
            frame_probs->tx_type_probs[update_type][i][j] = prob;
          }
        }
      }
  
      // Sequentially update obmc_probs
      if (cpi->do_update_frame_probs_obmc[loop] &&
          cpi->ppi->gf_group.frame_parallel_level[cpi->gf_frame_index] > 0) {
        const FRAME_UPDATE_TYPE update_type =
            get_frame_update_type(&cpi->ppi->gf_group, cpi->gf_frame_index);
  
        for (i = 0; i < BLOCK_SIZES_ALL; i++) {
          const int new_prob =
              cpi->frame_new_probs[loop].obmc_probs[update_type][i];
          frame_probs->obmc_probs[update_type][i] =
              (frame_probs->obmc_probs[update_type][i] + new_prob) >> 1;
        }
      }
  
      // Sequentially update warped_probs
      if (cpi->do_update_frame_probs_warp[loop] &&
          cpi->ppi->gf_group.frame_parallel_level[cpi->gf_frame_index] > 0) {
        const FRAME_UPDATE_TYPE update_type =
            get_frame_update_type(&cpi->ppi->gf_group, cpi->gf_frame_index);
        const int new_prob = cpi->frame_new_probs[loop].warped_probs[update_type];
        frame_probs->warped_probs[update_type] =
            (frame_probs->warped_probs[update_type] + new_prob) >> 1;
      }
  
      // Sequentially update switchable_interp_probs
      if (cpi->do_update_frame_probs_interpfilter[loop] &&
          cpi->ppi->gf_group.frame_parallel_level[cpi->gf_frame_index] > 0) {
        const FRAME_UPDATE_TYPE update_type =
            get_frame_update_type(&cpi->ppi->gf_group, cpi->gf_frame_index);
  
        for (i = 0; i < SWITCHABLE_FILTER_CONTEXTS; i++) {
          int left = 1536;
  
          for (j = SWITCHABLE_FILTERS - 1; j >= 0; j--) {
            const int new_prob = cpi->frame_new_probs[loop]
                                     .switchable_interp_probs[update_type][i][j];
            int prob = (frame_probs->switchable_interp_probs[update_type][i][j] +
                        new_prob) >>
                       1;
            left -= prob;
            if (j == 0) prob += left;
            frame_probs->switchable_interp_probs[update_type][i][j] = prob;
          }
        }
      }
    }
  
    // Update framerate obtained from parallel encode frames
    if (cpi->common.show_frame &&
        cpi->ppi->gf_group.frame_parallel_level[cpi->gf_frame_index] > 0)
      cpi->framerate = cpi->new_framerate;
  #endif
  }
  