// # ILP
// # Changes: FLOPCOUNT
// n_iter * [ n_p ** 2 * (12.5 A + 2.5 S + 23 M + 1 D + 1 E) + n_p * (6.5 A + 0.5 S - 2 M + 1 D - 1 E) + n_obstacles * n_p * (12 A + 19 M + 1 S + 1 D + 1 E)]
// # Predecessor: variant_inlining_7_symmetry_2_ilp.cpp

#include "../headers/board.hpp"
#include "../headers/constants.hpp"
#include "../headers/pedestrian_reduced.hpp"

#include <algorithm>
#include <cmath>
#include <fstream>
#include <iostream>
#include <math.h>
#include <random>
#include <tuple>
#include <vector>

#define SEED 42
#define BOARD_WIDTH 10.0
#define BOARD_LENGTH 50.0
#define WALL_EPS 1e-3
#define BOARD_WIDTH_MINUS_WALL_EPS 9.999

#ifndef RANDOM_SEED
#define RANDOM_SEED 0
#endif

#ifndef BENCHMARK
#define BENCHMARK 0
#endif

using namespace std;

Pedestrian *init_pedestrians(int n_p) {
#if RANDOM_SEED
  random_device rd;
  mt19937 gen(rd());
#else
  mt19937 gen(SEED);
#endif

  normal_distribution<double> velocity_gen(v0_mean, v0_std_dev);
  uniform_real_distribution<double> y_gen(0.3, BOARD_WIDTH - 0.3);
  uniform_real_distribution<double> x_gen_left(2.0, BOARD_LENGTH / 2.0);
  uniform_real_distribution<double> x_gen_right(BOARD_LENGTH / 2.0, BOARD_LENGTH - 2.0);

  Pedestrian *P = new Pedestrian[n_p];

  int n_p_half = n_p / 2;

  for (int i = 0; i < n_p_half; i++) {
    double x = x_gen_left(gen);
    double y = y_gen(gen);

    double start_pos_x = x;
    double start_pos_y = y;

    double destination_x = BOARD_LENGTH + 30.0;
    double destination_y = y;

    double init_e_x = destination_x - start_pos_x;
    double init_e_y = destination_y - start_pos_y;
    double init_e_norm = sqrt(init_e_x * init_e_x + init_e_y * init_e_y);
    double init_e_unit_x = init_e_x / init_e_norm;
    double init_e_unit_y = init_e_y / init_e_norm;

    double desired_v0;
    do {
      desired_v0 = velocity_gen(gen);
    } while (desired_v0 <= 0.1);

    double v_max = 1.3 * desired_v0;

    P[i] = Pedestrian(0, 0, 0, start_pos_x, start_pos_y, init_e_unit_x, init_e_unit_y, v_max, desired_v0, destination_x, destination_y);
  }

  for (int i = n_p_half; i < n_p; i++) {
    double x = x_gen_right(gen);
    double y = y_gen(gen);

    double start_pos_x = x;
    double start_pos_y = y;
    double destination_x = -30;
    double destination_y = y;

    double init_e_x = destination_x - start_pos_x;
    double init_e_y = destination_y - start_pos_y;
    double init_e_norm = sqrt(init_e_x * init_e_x + init_e_y * init_e_y);
    double init_e_unit_x = init_e_x / init_e_norm;
    double init_e_unit_y = init_e_y / init_e_norm;

    double desired_v0;
    do {
      desired_v0 = velocity_gen(gen);
    } while (desired_v0 <= 0.1);

    double v_max = 1.3 * desired_v0;

    P[i] = Pedestrian(1, 0, 0, start_pos_x, start_pos_y, init_e_unit_x, init_e_unit_y, v_max, desired_v0, destination_x, destination_y);
  }

  return P;
}

Board init_board_without_obstacles() { return Board(BOARD_LENGTH, BOARD_WIDTH, 0, nullptr); }

int run_simulation(Pedestrian *pedestrians, Board &board, int n_p, int n_iter, const char *dump_path) {

#if BENCHMARK
  (void)dump_path;
#endif

#if !BENCHMARK
  const int dump_interval = 1;

  vector<tuple<int, int, double, double, double, double, int>> samples;

  if (dump_path) {
    samples.reserve(static_cast<size_t>(n_iter / dump_interval + 1) * n_p);

    for (int i = 0; i < n_p; i++) {
      Pedestrian &p = pedestrians[i];
      samples.emplace_back(0, i, p.curr_pos_x, p.curr_pos_y, p.e_x, p.e_y, p.color);
    }
  }
#endif

  // here we have real (simple) symmetry
  std::vector<double> r_ab_x_lut(n_p * n_p, 0.0);
  std::vector<double> r_ab_y_lut(n_p * n_p, 0.0);
  std::vector<double> r_ab_norm_lut(n_p * n_p, 0.0);
  // use NAME[i * n_p + j]



  // n_iter * [ 0.5 * (n_p * n_p - n_p) * (3 ADD + 1 SQRT + 2 MULT) + n_p * [ (12 ADD + 4 MULT) + ((n_p - 1) * (11 ADD + 22 MULT + 2 SQRT + 1 DIV + 1 EXP)) ] + n_p * (7 ADD + 17 MULT + 3 SQRT + 2 DIV) + n_obstacles * n_p * (12 ADD + 19 MULT + 1 SQRT + 1 DIV + 1 EXP)]
  // n_iter * [ 0.5 * n_p ** 2 * (3 A + 1 S + 2 M) - 0.5 * n_p * (3 A + 1 S + 2 M) + n_p ** 2 * (11 A + 22 M + 2 S + 1 D + 1 E) + n_p * (1 A - 18 M - 2 S - 1 D - 1 E) + n_p * (7 A + 17 M + 3 S + 2 D) + n_obstacles * n_p * (12 A + 19 M + 1 S + 1 D + 1 E)]
  // n_iter * [ n_p ** 2 * (1.5 A + 0.5 S + 1 M + 11 A + 22 M + 2 S + 1 D + 1 E) + n_p * (- 1.5 A - 0.5 S - 1 M + 1 A - 18 M - 2 S - 1 D - 1 E + 7 A + 17 M + 3 S + 2 D) + n_obstacles * n_p * (12 A + 19 M + 1 S + 1 D + 1 E)]
  // n_iter * [ n_p ** 2 * (12.5 A + 2.5 S + 23 M + 1 D + 1 E) + n_p * (6.5 A + 0.5 S - 2 M + 1 D - 1 E) + n_obstacles * n_p * (12 A + 19 M + 1 S + 1 D + 1 E)]
  for (int t = 0; t < n_iter; t++) {

    // get all distances first
    // No ILP because no accumulators
    // FLOPCOUNT = 0.5 * (n_p * n_p - n_p) * 6 FLOPS
    // 0.5 * (n_p * n_p - n_p) * (3 ADD + 1 SQRT + 2 MULT)
    for (int i = 0; i < n_p; i++) {
      // only upper triangle
      for (int j = i + 1; j < n_p; j++) {
        // 1 FLOP = 1 ADD
        double dx = pedestrians[i].curr_pos_x - pedestrians[j].curr_pos_x;
        // 1 FLOP = 1 ADD
        double dy = pedestrians[i].curr_pos_y - pedestrians[j].curr_pos_y;
        // 4 FLOPS = 1 SQRT + 2 MULT + 1 ADD
        double norm = sqrt(dx * dx + dy * dy);
        r_ab_x_lut[i * n_p + j] = dx;
        r_ab_y_lut[i * n_p + j] = dy;
        r_ab_norm_lut[i * n_p + j] = norm;
      }
    }


    // FLOPCOUNT = n_p * [ 16 FLOPS + ((n_p - 1) * 66 FLOPS) + (n_obstacles * 63 FLOPS)]
    // n_p * [ (12 ADD + 4 MULT) + ((n_p - 1) * (11 ADD + 22 MULT + 2 SQRT + 1 DIV + 1 EXP)) + n_obstacles * (12 ADD + 19 MULT + 1 SQRT + 1 DIV + 1 EXP) ]
    for (int i = 0; i < n_p; i++) {
      Pedestrian &p = pedestrians[i];

      // 1 FLOP = 1 MULT
      double desired_velocity_x = p.e_x * p.desired_v0;
      // 1 FLOP = 1 MULT
      double desired_velocity_y = p.e_y * p.desired_v0;

      // 2 FLOPS = 1 ADD + 1 MULT
      double f_alpha_dt_x = (desired_velocity_x - p.curr_vel_x) * dt_times_tau_alpha_inv;
      // 2 FLOPS = 1 ADD + 1 MULT
      double f_alpha_dt_y = (desired_velocity_y - p.curr_vel_y) * dt_times_tau_alpha_inv;

      // accumulators for ILP
      // f_alpha_dt_x = f_alpha_dt_x + f_alpha_beta_neg_x * w_val;
      // f_alpha_dt_y = f_alpha_dt_y + f_alpha_beta_neg_y * w_val;
      double acc_0_x = 0.0, acc_1_x = 0.0, acc_2_x = 0.0, acc_3_x = 0.0;
      double acc_0_y = 0.0, acc_1_y = 0.0, acc_2_y = 0.0, acc_3_y = 0.0;

      const double p_e_x = p.e_x;
      const double p_e_y = p.e_y;


      // force between pedestrians --> no symmetry because of different accelerations
      // ILP
      int j = 0;
      // FLOPCOUNT = ((n_p - 1) * 66 FLOPS)
      // ((n_p - 1) * (11 ADD + 22 MULT + 2 SQRT + 1 DIV + 1 EXP))
      for (; j <= n_p - 4; j+=4) {
        // distance symmetry
        double r_ab_x_0, r_ab_y_0, r_ab_norm_0;
        double r_ab_x_1, r_ab_y_1, r_ab_norm_1;
        double r_ab_x_2, r_ab_y_2, r_ab_norm_2;
        double r_ab_x_3, r_ab_y_3, r_ab_norm_3;

        int j0 = j, j1 = j+1, j2 = j+2, j3 = j+3;

        // skip i == j
        // FLOPCOUNT = 66 FLOPS
        // 11 ADD + 22 MULT + 2 SQRT + 1 DIV + 1 EXP
        if (i != j0) {
          if (i < j0) {
            r_ab_x_0 = r_ab_x_lut[i * n_p + j0];
            r_ab_y_0 = r_ab_y_lut[i * n_p + j0];
            r_ab_norm_0 = r_ab_norm_lut[i * n_p + j0];
          } else {
            // other direction
            // I think here we can optimize for sure, currently not using LUT good
            r_ab_x_0 = -1 * r_ab_x_lut[j0 * n_p + i];
            r_ab_y_0 = -1 * r_ab_y_lut[j0 * n_p + i];
            r_ab_norm_0 = r_ab_norm_lut[j0 * n_p + i];
          }
          // the math, see paper
          // 1 FLOP = 1 ADD
          double r_ab2_x_0 = r_ab_x_0 - pedestrians[j0].s_b_e_x;
          // 1 FLOP = 1 ADD
          double r_ab2_y_0 = r_ab_y_0 - pedestrians[j0].s_b_e_y;

          // 4 FLOPS = 1 SQRT + 2 MULT + 1 ADD
          double r_ab2_norm_0 = sqrt(r_ab2_x_0 * r_ab2_x_0 + r_ab2_y_0 * r_ab2_y_0);
          
          // 1 FLOP = 1 ADD
          double r_ab_norm_sum_0 = r_ab_norm_0 + r_ab2_norm_0;
          
          // 2 FLOPS = 1 MULT + 1 ADD
          double two_b_sq_0 = r_ab_norm_sum_0 * r_ab_norm_sum_0 - pedestrians[j0].s_b_sq;
          
          // 1 FLOP = 1 SQRT
          double two_b_0 = sqrt(two_b_sq_0);
          
          // 36 FLOPS = 1 DIV + 5 MULT + 1 EXP
          double scalar_mult_common_0 = (r_ab_norm_sum_0 / (two_b_0 * r_ab_norm_0 * r_ab2_norm_0)) * (NEG_V0_AB_div_TWO_SIGMA * exp(two_b_0 * NEG_TWO_SIGMA_INV));
          
          // 1 FLOP = 1 MULT
          double scalar_mult_r_ab_0 = scalar_mult_common_0 * r_ab2_norm_0;
          
          // 1 FLOP = 1 MULT
          double scalar_mult_r_ab2_0 = scalar_mult_common_0 * r_ab_norm_0;

          // 3 FLOPS = 2 MULT + 1 ADD
          double f_alpha_beta_neg_x_0 = r_ab_x_0 * scalar_mult_r_ab_0 + r_ab2_x_0 * scalar_mult_r_ab2_0;
          
          // 3 FLOPS = 2 MULT + 1 ADD
          double f_alpha_beta_neg_y_0 = r_ab_y_0 * scalar_mult_r_ab_0 + r_ab2_y_0 * scalar_mult_r_ab2_0;

          double w_val_0;
          // 4 FLOPS = 3 MULT + 1 ADD
          double a_0 = (p_e_x * f_alpha_beta_neg_x_0 + p_e_y * f_alpha_beta_neg_y_0) * cos_phi_inv;
          // 3 FLOPS = 2 MULT + 1 ADD
          double b_sq_0 = f_alpha_beta_neg_x_0 * f_alpha_beta_neg_x_0 + f_alpha_beta_neg_y_0 * f_alpha_beta_neg_y_0;
          
          w_val_0 = dt_neg;
          // 1 FLOP = 1 MULT
          if (a_0 >= 0 && (a_0 * a_0 > b_sq_0)) {
            w_val_0 = c_neg_times_dt;
          }

          // 2 FLOPS = 1 ADD + 1 MULT
          acc_0_x += f_alpha_beta_neg_x_0 * w_val_0;
          // 2 FLOPS = 1 ADD + 1 MULT
          acc_0_y += f_alpha_beta_neg_y_0 * w_val_0;
        }

        // skip i == j
        // FLOPCOUNT= 66 FLOPS
        if (i != j1) {
          if (i < j1) {
            r_ab_x_1 = r_ab_x_lut[i * n_p + j1];
            r_ab_y_1 = r_ab_y_lut[i * n_p + j1];
            r_ab_norm_1 = r_ab_norm_lut[i * n_p + j1];
          } else {
            // other direction
            // I think here we can optimize for sure, currently not using LUT good
            r_ab_x_1 = -1 * r_ab_x_lut[j1 * n_p + i];
            r_ab_y_1 = -1 * r_ab_y_lut[j1 * n_p + i];
            r_ab_norm_1 = r_ab_norm_lut[j1 * n_p + i];
          }
          // the math, see paper
          // 1 FLOP = 1 ADD
          double r_ab2_x_1 = r_ab_x_1 - pedestrians[j1].s_b_e_x;
          // 1 FLOP = 1 ADD
          double r_ab2_y_1 = r_ab_y_1 - pedestrians[j1].s_b_e_y;

          // 4 FLOPS = 1 SQRT + 2 MULT + 1 ADD
          double r_ab2_norm_1 = sqrt(r_ab2_x_1 * r_ab2_x_1 + r_ab2_y_1 * r_ab2_y_1);
          
          // 1 FLOP = 1 ADD
          double r_ab_norm_sum_1 = r_ab_norm_1 + r_ab2_norm_1;
          
          // 2 FLOPS = 1 MULT + 1 ADD
          double two_b_sq_1 = r_ab_norm_sum_1 * r_ab_norm_sum_1 - pedestrians[j1].s_b_sq;
          
          // 1 FLOP = 1 SQRT
          double two_b_1 = sqrt(two_b_sq_1);
          
          // 36 FLOPS = 1 DIV + 5 MULT + 1 EXP
          double scalar_mult_common_1 = (r_ab_norm_sum_1 / (two_b_1 * r_ab_norm_1 * r_ab2_norm_1)) * (NEG_V0_AB_div_TWO_SIGMA * exp(two_b_1 * NEG_TWO_SIGMA_INV));
          double scalar_mult_r_ab_1 = scalar_mult_common_1 * r_ab2_norm_1;
          double scalar_mult_r_ab2_1 = scalar_mult_common_1 * r_ab_norm_1;

          // 3 FLOPS = 2 MULT + 1 ADD
          double f_alpha_beta_neg_x_1 = r_ab_x_1 * scalar_mult_r_ab_1 + r_ab2_x_1 * scalar_mult_r_ab2_1;
          // 3 FLOPS = 2 MULT + 1 ADD
          double f_alpha_beta_neg_y_1 = r_ab_y_1 * scalar_mult_r_ab_1 + r_ab2_y_1 * scalar_mult_r_ab2_1;

          double w_val_1;
          // 4 FLOPS = 3 MULT + 1 ADD
          double a_1 = (p_e_x * f_alpha_beta_neg_x_1 + p_e_y * f_alpha_beta_neg_y_1) * cos_phi_inv;
          // 3 FLOPS = 2 MULT + 1 ADD
          double b_sq_1 = f_alpha_beta_neg_x_1 * f_alpha_beta_neg_x_1 + f_alpha_beta_neg_y_1 * f_alpha_beta_neg_y_1;
          
          w_val_1 = dt_neg;
          // 1 FLOP = 1 MULT
          if (a_1 >= 0 && (a_1 * a_1 > b_sq_1)) {
            w_val_1 = c_neg_times_dt;
          }

          // 2 FLOPS = 1 MULT + 1 ADD
          acc_1_x += f_alpha_beta_neg_x_1 * w_val_1;
          // 2 FLOPS = 1 MULT + 1 ADD
          acc_1_y += f_alpha_beta_neg_y_1 * w_val_1;
        }

        // skip i == j
        // FLOPCOUNT = 66 FLOPS
        if (i != j2) {
          if (i < j2) {
            r_ab_x_2 = r_ab_x_lut[i * n_p + j2];
            r_ab_y_2 = r_ab_y_lut[i * n_p + j2];
            r_ab_norm_2 = r_ab_norm_lut[i * n_p + j2];
          } else {
            // other direction
            // I think here we can optimize for sure, currently not using LUT good
            r_ab_x_2 = -1 * r_ab_x_lut[j2 * n_p + i];
            r_ab_y_2 = -1 * r_ab_y_lut[j2 * n_p + i];
            r_ab_norm_2 = r_ab_norm_lut[j2 * n_p + i];
          }
          // the math, see paper
          double r_ab2_x_2 = r_ab_x_2 - pedestrians[j2].s_b_e_x;
          double r_ab2_y_2 = r_ab_y_2 - pedestrians[j2].s_b_e_y;

          double r_ab2_norm_2 = sqrt(r_ab2_x_2 * r_ab2_x_2 + r_ab2_y_2 * r_ab2_y_2);
          double r_ab_norm_sum_2 = r_ab_norm_2 + r_ab2_norm_2;
          double two_b_sq_2 = r_ab_norm_sum_2 * r_ab_norm_sum_2 - pedestrians[j2].s_b_sq;
          double two_b_2 = sqrt(two_b_sq_2);
          double scalar_mult_common_2 = (r_ab_norm_sum_2 / (two_b_2 * r_ab_norm_2 * r_ab2_norm_2)) * (NEG_V0_AB_div_TWO_SIGMA * exp(two_b_2 * NEG_TWO_SIGMA_INV));
          double scalar_mult_r_ab_2 = scalar_mult_common_2 * r_ab2_norm_2;
          double scalar_mult_r_ab2_2 = scalar_mult_common_2 * r_ab_norm_2;

          double f_alpha_beta_neg_x_2 = r_ab_x_2 * scalar_mult_r_ab_2 + r_ab2_x_2 * scalar_mult_r_ab2_2;
          double f_alpha_beta_neg_y_2 = r_ab_y_2 * scalar_mult_r_ab_2 + r_ab2_y_2 * scalar_mult_r_ab2_2;

          double w_val_2;
          double a_2 = (p_e_x * f_alpha_beta_neg_x_2 + p_e_y * f_alpha_beta_neg_y_2) * cos_phi_inv;
          double b_sq_2 = f_alpha_beta_neg_x_2 * f_alpha_beta_neg_x_2 + f_alpha_beta_neg_y_2 * f_alpha_beta_neg_y_2;
          
          w_val_2 = dt_neg;
          if (a_2 >= 0 && (a_2 * a_2 > b_sq_2)) {
            w_val_2 = c_neg_times_dt;
          }

          acc_2_x += f_alpha_beta_neg_x_2 * w_val_2;
          acc_2_y += f_alpha_beta_neg_y_2 * w_val_2;
        }

        // skip i == j
        // FLOPCOUNT = 66 FLOPS
        if (i != j3) {
          if (i < j3) {
            r_ab_x_3 = r_ab_x_lut[i * n_p + j3];
            r_ab_y_3 = r_ab_y_lut[i * n_p + j3];
            r_ab_norm_3 = r_ab_norm_lut[i * n_p + j3];
          } else {
            // other direction
            // I think here we can optimize for sure, currently not using LUT good
            r_ab_x_3 = -1 * r_ab_x_lut[j3 * n_p + i];
            r_ab_y_3 = -1 * r_ab_y_lut[j3 * n_p + i];
            r_ab_norm_3 = r_ab_norm_lut[j3 * n_p + i];
          }
          // the math, see paper
          double r_ab2_x_3 = r_ab_x_3 - pedestrians[j3].s_b_e_x;
          double r_ab2_y_3 = r_ab_y_3 - pedestrians[j3].s_b_e_y;

          double r_ab2_norm_3 = sqrt(r_ab2_x_3 * r_ab2_x_3 + r_ab2_y_3 * r_ab2_y_3);
          double r_ab_norm_sum_3 = r_ab_norm_3 + r_ab2_norm_3;
          double two_b_sq_3 = r_ab_norm_sum_3 * r_ab_norm_sum_3 - pedestrians[j3].s_b_sq;
          double two_b_3 = sqrt(two_b_sq_3);
          double scalar_mult_common_3 = (r_ab_norm_sum_3 / (two_b_3 * r_ab_norm_3 * r_ab2_norm_3)) * (NEG_V0_AB_div_TWO_SIGMA * exp(two_b_3 * NEG_TWO_SIGMA_INV));
          double scalar_mult_r_ab_3 = scalar_mult_common_3 * r_ab2_norm_3;
          double scalar_mult_r_ab2_3 = scalar_mult_common_3 * r_ab_norm_3;

          double f_alpha_beta_neg_x_3 = r_ab_x_3 * scalar_mult_r_ab_3 + r_ab2_x_3 * scalar_mult_r_ab2_3;
          double f_alpha_beta_neg_y_3 = r_ab_y_3 * scalar_mult_r_ab_3 + r_ab2_y_3 * scalar_mult_r_ab2_3;

          double w_val_3;
          double a_3 = (p_e_x * f_alpha_beta_neg_x_3 + p_e_y * f_alpha_beta_neg_y_3) * cos_phi_inv;
          double b_sq_3 = f_alpha_beta_neg_x_3 * f_alpha_beta_neg_x_3 + f_alpha_beta_neg_y_3 * f_alpha_beta_neg_y_3;
          
          w_val_3 = dt_neg;
          if (a_3 >= 0 && (a_3 * a_3 > b_sq_3)) {
            w_val_3 = c_neg_times_dt;
          }

          acc_3_x += f_alpha_beta_neg_x_3 * w_val_3;
          acc_3_y += f_alpha_beta_neg_y_3 * w_val_3;
        }
      }

      // add the result
      // 4 FLOPS = 4 ADD
      f_alpha_dt_x += acc_0_x + acc_1_x + acc_2_x + acc_3_x;
      // 4 FLOPS = 4 ADD
      f_alpha_dt_y += acc_0_y + acc_1_y + acc_2_y + acc_3_y;

      // remaining
      // 66 FLOPS --> see ILP loop
      // 11 ADD + 22 MULT + 2 SQRT + 1 DIV + 1 EXP
      for (; j < n_p; j++) {
        if (i == j) continue;

        double r_ab_x, r_ab_y, r_ab_norm;
        if (i < j) {
          r_ab_x = r_ab_x_lut[i * n_p + j];
          r_ab_y = r_ab_y_lut[i * n_p + j];
          r_ab_norm = r_ab_norm_lut[i * n_p + j];
        } else {
          r_ab_x = -1 * r_ab_x_lut[j * n_p + i];
          r_ab_y = -1 * r_ab_y_lut[j * n_p + i];
          r_ab_norm = r_ab_norm_lut[j * n_p + i];
        }

        // 1 FLOP = 1 ADD
        double r_ab2_x = r_ab_x - pedestrians[j].s_b_e_x;
        // 1 FLOP = 1 ADD
        double r_ab2_y = r_ab_y - pedestrians[j].s_b_e_y;

        // 4 FLOPS = 1 SQRT + 2 MULT + 1 ADD
        double r_ab2_norm = sqrt(r_ab2_x * r_ab2_x + r_ab2_y * r_ab2_y);
        // 1 FLOP = 1 ADD
        double r_ab_norm_sum = r_ab_norm + r_ab2_norm;
        // 2 FLOPS = 1 MULT + 1 ADD
        double two_b_sq = r_ab_norm_sum * r_ab_norm_sum - pedestrians[j].s_b_sq;
        // 1 FLOP = 1 SQRT
        double two_b = sqrt(two_b_sq);
        // 36 FLOPS = 1 DIV + 5 MULT + 1 EXP
        double scalar_mult_common = (r_ab_norm_sum / (two_b * r_ab_norm * r_ab2_norm)) * (NEG_V0_AB_div_TWO_SIGMA * exp(two_b * NEG_TWO_SIGMA_INV));
        // 1 FLOP = 1 MULT
        double scalar_mult_r_ab = scalar_mult_common * r_ab2_norm;
        // 1 FLOP = 1 MULT
        double scalar_mult_r_ab2 = scalar_mult_common * r_ab_norm;

        // 3 FLOPS = 2 MULT + 1 ADD
        double f_alpha_beta_neg_x = r_ab_x * scalar_mult_r_ab + r_ab2_x * scalar_mult_r_ab2;
        // 3 FLOPS = 2 MULT + 1 ADD
        double f_alpha_beta_neg_y = r_ab_y * scalar_mult_r_ab + r_ab2_y * scalar_mult_r_ab2;

        double w_val;
        // 4 FLOPS = 3 MULT + 1 ADD
        double a = (p_e_x * f_alpha_beta_neg_x + p_e_y * f_alpha_beta_neg_y) * cos_phi_inv;
        // 3 FLOPS = 2 MULT + 1 ADD
        double b_sq = f_alpha_beta_neg_x * f_alpha_beta_neg_x + f_alpha_beta_neg_y * f_alpha_beta_neg_y;
        
        w_val = dt_neg;
        // 1 FLOP = 1 MULT
        if (a >= 0 && (a * a > b_sq)) {
          w_val = c_neg_times_dt;
        }

        // 2 FLOPS = 1 MULT + 1 ADD
        f_alpha_dt_x = f_alpha_dt_x + f_alpha_beta_neg_x * w_val;
        // 2 FLOPS = 1 MULT + 1 ADD
        f_alpha_dt_y = f_alpha_dt_y + f_alpha_beta_neg_y * w_val;
      }


      // force between pedestrian and obstacles
      // initialized with 0 obstacles, might consider deleting this?
      // to sparse to use ILP
      // FLOPCOUNT = n_obstacles * 63 FLOPS
      // n_obstacles * (12 ADD + 19 MULT + 1 SQRT + 1 DIV + 1 EXP)
      for (int k = 0; k < board.n_obstacles; k++) {

        // 1 FLOP = 1 ADD
        double v1_x = p.curr_pos_x - board.obstacles[k].start.x;
        // 1 FLOP = 1 ADD
        double v1_y = p.curr_pos_y - board.obstacles[k].start.y;

        // 4 FLOPS = 3 MULT + 1 ADD
        double projection = (v1_x * board.obstacles[k].obstacle_v.x + v1_y * board.obstacles[k].obstacle_v.y) * board.obstacles[k].length_sq_inv;

        if (projection < 0.0)
          projection = 0.0;
        else if (projection > 1.0)
          projection = 1.0;

        // 3 FLOPS = 1 MULT + 2 ADD
        double r_aB_x = p.curr_pos_x - (board.obstacles[k].start.x + board.obstacles[k].obstacle_v.x * projection);
        // 3 FLOPS = 1 MULT + 2 ADD
        double r_aB_y = p.curr_pos_y - (board.obstacles[k].start.y + board.obstacles[k].obstacle_v.y * projection);

        // 4 FLOPS = 1 SQRT + 2 MULT + 1 ADD
        double r_aB_norm = sqrt(r_aB_x * r_aB_x + r_aB_y * r_aB_y);
        // 33 FLOPS = 1 DIV + 2 MULT + 1 EXPT
        double scalar_mult = (NEG_U0_AB_div_R * exp(r_aB_norm * NEG_R_INV)) / r_aB_norm;
        // 1 FLOP = 1 MULT
        double f_alpha_B_neg_x = r_aB_x * scalar_mult;
        // 1 FLOP = 1 MULT
        double f_alpha_B_neg_y = r_aB_y * scalar_mult;

        double w_val;
        // 4 FLOPS = 3 MULT + 1 ADD
        double a = (p.e_x * f_alpha_B_neg_x + p.e_y * f_alpha_B_neg_y) * cos_phi_inv;
        // 3 FLOPS = 2 MULT + 1 ADD
        double b_sq = f_alpha_B_neg_x * f_alpha_B_neg_x + f_alpha_B_neg_y * f_alpha_B_neg_y;

        w_val = dt_neg;
        // 1 FLOP = 1 MULT
        if (a >= 0 && (a * a > b_sq)) {
          w_val = c_neg_times_dt;
        }

        // 1 FLOP = 1 MULT
        double f_alpha_B_dt_x = f_alpha_B_neg_x * w_val;
        // 1 FLOP = 1 MULT
        double f_alpha_B_dt_y = f_alpha_B_neg_y * w_val;

        // 1 FLOP = 1 ADD
        f_alpha_dt_x += f_alpha_B_dt_x;
        // 1 FLOP = 1 ADD
        f_alpha_dt_y += f_alpha_B_dt_y;
      }

      // 1 FLOP = 1 ADD
      p.w_x += f_alpha_dt_x;
      // 1 FLOP = 1 ADD
      p.w_y += f_alpha_dt_y;
    }

    // update the positions etc.
    // ILP is not possible I think
    // FLOPCOUNT = n_p * 29 FLOPS
    // n_p * (7 ADD + 17 MULT + 3 SQRT + 2 DIV)
    for (int i = 0; i < n_p; i++) {
      Pedestrian &p = pedestrians[i];

      // 4 FLOPS = 1 SQRT + 2 MULT + 1 ADD
      double w_norm = sqrt(p.w_x * p.w_x + p.w_y * p.w_y);

      // 1 FLOP = 1 DIV
      double correction_factor = min(1.0, p.v_max / w_norm);

      // 1 FLOP = 1 MULT
      p.curr_vel_x = p.w_x * correction_factor;
      // 1 FLOP = 1 MULT
      p.curr_vel_y = p.w_y * correction_factor;

      // maybe move this calculation to a separate loop to enable ILP
      // 2 FLOPS = 1 MULT + 1 ADD
      p.curr_pos_x = p.curr_pos_x + p.curr_vel_x * dt;
      // 2 FLOPS = 1 MULT + 1 ADD
      p.curr_pos_y = p.curr_pos_y + p.curr_vel_y * dt;

      if (p.color == 0 && p.curr_pos_x > (BOARD_LENGTH - 1.5)) {
        p.curr_pos_x = 1.0;
        p.destination_y = p.curr_pos_y;
        p.w_x = p.desired_v0;
        p.w_y = 0.0;
        p.curr_vel_x = p.w_x;
        p.curr_vel_y = p.w_y;
      }
      if (p.color == 1 && p.curr_pos_x < 1.5) {
        p.curr_pos_x = BOARD_LENGTH - 1.0;
        p.destination_y = p.curr_pos_y;
        p.w_x = -p.desired_v0;
        p.w_y = 0.0;
        p.curr_vel_x = p.w_x;
        p.curr_vel_y = p.w_y;
      }

      p.curr_pos_y = clamp(p.curr_pos_y, WALL_EPS, BOARD_WIDTH_MINUS_WALL_EPS);

      // 1 FLOP = 1 ADD
      double e_x = p.destination_x - p.curr_pos_x;
      // 1 FLOP = 1 ADD
      double e_y = p.destination_y - p.curr_pos_y;

      // 5 FLOPS = 1 DIV + 1 SQRT + 2 MULT + 1 ADD
      double e_norm_inv = 1.0 / sqrt(e_x * e_x + e_y * e_y);

      // 1 FLOP = 1 MULT
      p.e_x = e_x * e_norm_inv;
      // 1 FLOP = 1 MULT
      p.e_y = e_y * e_norm_inv;

      // 3 FLOPS = 2 MULT + 1 ADD
      double velocity_norm_sq = p.curr_vel_x * p.curr_vel_x + p.curr_vel_y * p.curr_vel_y;

      // 1 FLOP = 1 SQRT
      double velocity_norm = sqrt(velocity_norm_sq);

      // 1 FLOP = 1 MULT
      p.s_b_sq = velocity_norm_sq * delta_t_sq;

      // 2 FLOPS = 2 MULT
      p.s_b_e_x = p.e_x * (velocity_norm * delta_t);
      // 2 FLOPS = 2 MULT
      p.s_b_e_y = p.e_y * (velocity_norm * delta_t);

#if !BENCHMARK
      if (dump_path && (t % dump_interval == 0)) {
        samples.emplace_back(t + 1, i, p.curr_pos_x, p.curr_pos_y, p.e_x, p.e_y, p.color);
      }
#endif
    }
  }

#if !BENCHMARK
  if (dump_path) {
    ofstream out(dump_path);
    out << "time,id,x,y,p.e.x,p.e.y,color\n";

    for (auto &[t, id, x, y, e_x, e_y, c] : samples) {
      out << t << ',' << id << ',' << x << ',' << y << ',' << e_x << ',' << e_y << ',' << c << '\n';
    }
  }
#endif

  return 0;
}