// # Use symmetrical properties to reduce flop count
// # Changes: flopcount
// FLOPCOUNT = n_iter * ( 69 * n_p ** 2 - 32 * n_p + 63 * n_obstacles * n_p )
// n_iter * [ n_p ** 2 * (12.5 ADD + 23 MULT + 1 DIV + 1 EXP + 2.5 SQRT) + n_p * (- 1.5 ADD + 0.5 SQRT - 2 MULT - 1 EXP + 1 DIV) + n_obstacles * n_p * (12 ADD + 19 MULT + 1 SQRT + 1 DIV + 1 EXP) ]
// # Predecessor: variant_inlining_7_symmetry_1.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]

  // FLOPCOUNT = n_iter * ( {0.5 * (n_p * n_p - n_p) * 6 FLOPS} + {n_p * [ (8 FLOPS) + ((n_p - 1) * 66 FLOPS) + (n_obstacles * 63 FLOPS) ]} + {n_p * 29 FLOPS} )
  // FLOPCOUNT = n_iter * ( {3 * n_p ** 2 - 3 * n_p} + {66 * n_p ** 2 - 58 * n_p + 63 * n_obstacles * n_p} + {29 * n_p} )
  // FLOPCOUNT = n_iter * ( 3 * n_p ** 2 - 3 * n_p + 66 * n_p ** 2 - 58 * n_p + 63 * n_obstacles * n_p + 29 * n_p)
  // FLOPCOUNT = n_iter * ( [3 * n_p ** 2 + 66 * n_p ** 2] +  [- 3 * n_p - 58 * n_p + 29 * n_p] + [63 * n_obstacles * n_p] )
  // FLOPCOUNT = n_iter * ( 69 * n_p ** 2 - 32 * n_p + 63 * n_obstacles * n_p )
  
  // n_iter * {0.5 * (n_p * n_p - n_p) * (3 ADD + 1 SQRT + 2 MULT) + n_p * [(4 MULT + 4 ADD) + ((n_p - 1) * (11 ADD + 22 MULT + 1 DIV + 1 EXP + 2 SQRT)) + (n_obstacles * (12 ADD + 19 MULT + 1 SQRT + 1 DIV + 1 EXP))] + n_p * [ 7 ADD + 17 MULT + 3 SQRT + 2 DIV ]}



  // 0.5 * (n_p * n_p - n_p) * (3 ADD + 1 SQRT + 2 MULT)
  // n_p ** 2 * (1.5 ADD + 0.5 SQRT + 1 MULT) + n_p * (- 1.5 ADD - 0.5 SQRT - 1 MULT)



  // n_p * [(4 MULT + 4 ADD) + ((n_p - 1) * (11 ADD + 22 MULT + 1 DIV + 1 EXP + 2 SQRT)) + (n_obstacles * (12 ADD + 19 MULT + 1 SQRT + 1 DIV + 1 EXP))]
  // n_p * [n_p * (11 ADD + 22 MULT + 1 DIV + 1 EXP + 2 SQRT) - 1 * (7 ADD + 18 MULT + 1 DIV + 1 EXP + 2 SQRT) + n_obstacles * (12 ADD + 19 MULT + 1 SQRT + 1 DIV + 1 EXP)]
  // n_p ** 2 * (11 ADD + 22 MULT + 1 DIV + 1 EXP + 2 SQRT) - n_p * (7 ADD + 18 MULT + 1 DIV + 1 EXP + 2 SQRT) + n_obstacles * n_p * (12 ADD + 19 MULT + 1 SQRT + 1 DIV + 1 EXP)



  // n_p * (7 ADD + 17 MULT + 3 SQRT + 2 DIV)



  // n_p ** 2 * (1.5 ADD + 0.5 SQRT + 1 MULT) + n_p * (- 1.5 ADD - 0.5 SQRT - 1 MULT) + n_p ** 2 * (11 ADD + 22 MULT + 1 DIV + 1 EXP + 2 SQRT) - n_p * (7 ADD + 18 MULT + 1 DIV + 1 EXP + 2 SQRT) + n_obstacles * n_p * (12 ADD + 19 MULT + 1 SQRT + 1 DIV + 1 EXP) + n_p * (7 ADD + 17 MULT + 3 SQRT + 2 DIV)
  // n_p ** 2 * (12.5 ADD + 23 MULT + 1 DIV + 1 EXP + 2.5 SQRT) + n_p * (- 1.5 ADD + 0.5 SQRT - 2 MULT - 1 EXP + 1 DIV) + n_obstacles * n_p * (12 ADD + 19 MULT + 1 SQRT + 1 DIV + 1 EXP)
  // n_p ** 2 * (12.5 A + 23 M + 1 D + 1 E + 2.5 S) + n_p * (- 1.5 A + 0.5 S - 2 M - 1 E + 1 D) + 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
    // total iterations = 0.5 * (n_p * n_p - n_p)
    // flops per iter = 6 FLOPS
    // 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++) {
      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 * [ (8 FLOPS) + ((n_p - 1) * 66 FLOPS) + (n_obstacles * 63 FLOPS) ]
    // n_p * [(4 MULT + 4 ADD) + ((n_p - 1) * (11 ADD + 22 MULT + 1 DIV + 1 EXP + 2 SQRT)) + (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;

      // force between pedestrians
      // FLOPS = ((n_p - 1) * 66 FLOPS)
      for (int j = 0; j < n_p; j++) {
        if (i == j)
          continue;

        // symmetry 
        //double r_ab_x = p.curr_pos_x - pedestrians[j].curr_pos_x;
        //double r_ab_y = p.curr_pos_y - pedestrians[j].curr_pos_y;
        //double r_ab_norm = sqrt(r_ab_x * r_ab_x + r_ab_y * r_ab_y);
        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 {
          // other direction
          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 MULTS + 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 ADD + 1 MULT
        f_alpha_dt_x = f_alpha_dt_x + f_alpha_beta_neg_x * w_val;
        // 2 FLOPS = 1 ADD + 1 MULT
        f_alpha_dt_y = f_alpha_dt_y + f_alpha_beta_neg_y * w_val;
      }

      // force between pedestrian and obstacles
      // FLOPS = n_obstacles * 63 FLOPS
      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 = 2 MULT + 1 DIV + 1 EXP
        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 MULTS + 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.
    // 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);

      // TODO: check correctness of this
      // 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;

      // 2 FLOPS = 1 ADD + 1 MULT
      p.curr_pos_x = p.curr_pos_x + p.curr_vel_x * dt;
      // 2 FLOPS = 1 ADD + 1 MULT
      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 FLOP = 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;
}