// # Changes: Removed EPS checks and implemented Fast Inverse Square Root
// # Predecessor: variant_float_inlining_SoA_AVX512_polyexp.cpp

#include "../headers/board_reduced_float.hpp"
#include "../headers/constants_float.hpp"
#include "../headers/pedestrian_reduced_float.hpp"

#include <immintrin.h>

#include <fstream>
#include <random>

#define SEED 42
#define BOARD_WIDTH 10.0f
#define BOARD_LENGTH 50.0f
#define BOARD_LENGTH_MINUS_ONE BOARD_LENGTH - 1.0f
#define BOARD_LENGTH_MINUS_ONE_POINT_FIVE BOARD_LENGTH - 1.5f
#define WALL_EPS 1e-3f
#define BOARD_WIDTH_MINUS_WALL_EPS 9.999f

#ifndef RANDOM_SEED
#define RANDOM_SEED 0
#endif

#ifndef BENCHMARK
#define BENCHMARK 0
#endif

using namespace std;

alignas(64) vector<float> pos_x, pos_y;
alignas(64) vector<float> sb_sq;
alignas(64) vector<float> sb_e_x, sb_e_y;
alignas(64) vector<float> e_x, e_y;
alignas(64) vector<float> curr_vel_x, curr_vel_y;
alignas(64) vector<float> w_x, w_y;
alignas(64) vector<float> desired_v0;
alignas(64) vector<float> v_max;
alignas(64) vector<float> destination_x, destination_y;
alignas(64) vector<int> color;

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

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

  const int n_p_pad = (n_p + 15) & ~15;

  pos_x.resize(n_p_pad);
  pos_y.resize(n_p_pad);
  sb_sq.resize(n_p_pad);
  sb_e_x.resize(n_p_pad);
  sb_e_y.resize(n_p_pad);
  e_x.resize(n_p_pad);
  e_y.resize(n_p_pad);
  curr_vel_x.resize(n_p_pad);
  curr_vel_y.resize(n_p_pad);
  w_x.resize(n_p_pad);
  w_y.resize(n_p_pad);
  desired_v0.resize(n_p_pad);
  v_max.resize(n_p_pad);
  destination_x.resize(n_p_pad);
  destination_y.resize(n_p_pad);
  color.resize(n_p_pad);

  int n_p_half = n_p / 2;

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

    float dest_x = BOARD_LENGTH + 30.0f;
    float dest_y = y;

    float init_e_x = dest_x - x;
    float init_e_y = dest_y - y;
    float init_e_norm = sqrt(init_e_x * init_e_x + init_e_y * init_e_y);
    float init_e_unit_x = init_e_x / init_e_norm;
    float init_e_unit_y = init_e_y / init_e_norm;

    float d_v0;
    do {
      d_v0 = velocity_gen(gen);
    } while (d_v0 <= 0.1f);

    float v_m = 1.3f * d_v0;

    color[i] = 0;
    pos_x[i] = x;
    pos_y[i] = y;
    e_x[i] = init_e_unit_x;
    e_y[i] = init_e_unit_y;
    v_max[i] = v_m;
    desired_v0[i] = d_v0;
    destination_x[i] = dest_x;
    destination_y[i] = dest_y;

    w_x[i] = 0.0f;
    w_y[i] = 0.0f;
    curr_vel_x[i] = 0.0f;
    curr_vel_y[i] = 0.0f;
    sb_sq[i] = 0.0f;
    sb_e_x[i] = 0.0f;
    sb_e_y[i] = 0.0f;
  }

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

    float dest_x = -30.0f;
    float dest_y = y;

    float init_e_x = dest_x - x;
    float init_e_y = dest_y - y;
    float init_e_norm = sqrt(init_e_x * init_e_x + init_e_y * init_e_y);
    float init_e_unit_x = init_e_x / init_e_norm;
    float init_e_unit_y = init_e_y / init_e_norm;

    float d_v0;
    do {
      d_v0 = velocity_gen(gen);
    } while (d_v0 <= 0.1f);

    float v_m = 1.3f * d_v0;

    color[i] = 1;
    pos_x[i] = x;
    pos_y[i] = y;
    e_x[i] = init_e_unit_x;
    e_y[i] = init_e_unit_y;
    v_max[i] = v_m;
    desired_v0[i] = d_v0;
    destination_x[i] = dest_x;
    destination_y[i] = dest_y;

    w_x[i] = 0.0f;
    w_y[i] = 0.0f;
    curr_vel_x[i] = 0.0f;
    curr_vel_y[i] = 0.0f;
    sb_sq[i] = 0.0f;
    sb_e_x[i] = 0.0f;
    sb_e_y[i] = 0.0f;
  }

  for (int j = n_p; j < n_p_pad; j++) {
    pos_x[j] = 1e9f;
    pos_y[j] = 1e9f;
    sb_sq[j] = 0.0f;
    sb_e_x[j] = 0.0f;
    sb_e_y[j] = 0.0f;
  }
  return nullptr;
}

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

// # 256 MULTs, 224 ADDs
static inline __m512 _avx512_exp_ps(__m512 x) {

  const __m512 log2e = _mm512_set1_ps(1.4426950408889634f);

  // # 16 MULTs
  __m512 nf = _mm512_roundscale_ps(_mm512_mul_ps(x, log2e), _MM_FROUND_TO_NEAREST_INT | _MM_FROUND_NO_EXC);

  const __m512 ln2 = _mm512_set1_ps(0.6931471805599453f);

  // # 16 MULTs, 16 ADDs
  __m512 r = _mm512_fnmadd_ps(nf, ln2, x);

  const __m512 c13 = _mm512_set1_ps(c13_scalar);
  const __m512 c12 = _mm512_set1_ps(c12_scalar);
  const __m512 c11 = _mm512_set1_ps(c11_scalar);
  const __m512 c10 = _mm512_set1_ps(c10_scalar);
  const __m512 c9 = _mm512_set1_ps(c9_scalar);
  const __m512 c8 = _mm512_set1_ps(c8_scalar);
  const __m512 c7 = _mm512_set1_ps(c7_scalar);
  const __m512 c6 = _mm512_set1_ps(c6_scalar);
  const __m512 c5 = _mm512_set1_ps(c5_scalar);
  const __m512 c4 = _mm512_set1_ps(c4_scalar);
  const __m512 c3 = _mm512_set1_ps(c3_scalar);
  const __m512 c2 = _mm512_set1_ps(c2_scalar);
  const __m512 c1 = _mm512_set1_ps(c1_scalar);
  const __m512 c0 = _mm512_set1_ps(c0_scalar);

  __m512 p = c13;

  // #   13 * (16 MULTs, 16 ADDs)
  // # = 208 MULTs, 208 ADDs
  p = _mm512_fmadd_ps(p, r, c12);
  p = _mm512_fmadd_ps(p, r, c11);
  p = _mm512_fmadd_ps(p, r, c10);
  p = _mm512_fmadd_ps(p, r, c9);
  p = _mm512_fmadd_ps(p, r, c8);
  p = _mm512_fmadd_ps(p, r, c7);
  p = _mm512_fmadd_ps(p, r, c6);
  p = _mm512_fmadd_ps(p, r, c5);
  p = _mm512_fmadd_ps(p, r, c4);
  p = _mm512_fmadd_ps(p, r, c3);
  p = _mm512_fmadd_ps(p, r, c2);
  p = _mm512_fmadd_ps(p, r, c1);
  p = _mm512_fmadd_ps(p, r, c0);

  __m512i ni = _mm512_cvtps_epi32(nf);
  __m512i biased = _mm512_add_epi32(ni, _mm512_set1_epi32(127));
  __m512i scaled = _mm512_slli_epi32(biased, 23);
  __m512 pow2n = _mm512_castsi512_ps(scaled);

  // # 16 MULTs
  return _mm512_mul_ps(p, pow2n);
}

// # 7 MULTs, 2 ADDs
static inline float fast_inv_sqrt(float number) {
  float y = number;

  uint32_t i = bit_cast<uint32_t>(y);

  i = 0x5f3759df - (i >> 1);

  y = bit_cast<float>(i);

  // # 1 MULT
  float x2 = number * 0.5;

  // # 6 MULTs, 2 ADDs
  y = y * (1.5 - (x2 * y * y));
  y = y * (1.5 - (x2 * y * y));

  return y;
}

int run_simulation(Pedestrian *pedestrians, Board &board, int n_p, int n_iter, const char *dump_path) {
  (void)pedestrians;
#if BENCHMARK
  (void)dump_path;
#endif

#if !BENCHMARK
  const int dump_interval = 1;
  vector<tuple<int, int, float, float, float, float, 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++) {
      samples.emplace_back(0, i, pos_x[i], pos_y[i], e_x[i], e_y[i], color[i]);
    }
  }
#endif

  const int n_p_pad = (n_p + 15) & ~15;

  alignas(64) const float lane_offset_arr[16] = {0.0f, 1.0f, 2.0f, 3.0f, 4.0f, 5.0f, 6.0f, 7.0f, 8.0f, 9.0f, 10.0f, 11.0f, 12.0f, 13.0f, 14.0f, 15.0f};
  const __m512 lane_off = _mm512_load_ps(lane_offset_arr);

  const __m512 v_neg_v0_div_2s = _mm512_set1_ps(NEG_V0_AB_div_TWO_SIGMA);
  const __m512 v_neg_2s_inv = _mm512_set1_ps(NEG_TWO_SIGMA_INV);
  const __m512 v_cos_phi_sq = _mm512_set1_ps(cos_phi_sq);
  const __m512 v_dt_neg = _mm512_set1_ps(dt_neg);
  const __m512 v_c_neg_dt = _mm512_set1_ps(c_neg_times_dt);
  const __m512 v_zero = _mm512_setzero_ps();
  const __m512 v_one = _mm512_set1_ps(1.0f);
  const __m512 v_eps = _mm512_set1_ps(EPS);
  const __m512 v_eps_sq = _mm512_set1_ps(EPS_SQ);
  const __m512 v_np = _mm512_set1_ps((float)n_p);
  const __m512 v_exp_min = _mm512_set1_ps(-87.0f);

  // # ADDs: n_iter * (
  // #   n_p * 36 +
  // #   n_p * n_p_pad * 29 +
  // #   n_p * board.n_obstacles * 10 +
  // #   n_p * 11
  // # )

  // # MULTs: n_iter * (
  // #   n_p * 4 +
  // #   n_p * n_p_pad * 40 +
  // #   n_p * board.n_obstacles * 13 +
  // #   n_p * 30
  // # )

  // # DIVs: n_iter * (
  // #   n_p * n_p_pad +
  // #   n_p * board.n_obstacles
  // # )

  // # SQRTs: n_iter * (
  // #   n_p * n_p_pad * 3 +
  // #   n_p * board.n_obstacles +
  // #   n_p
  // # )

  // # EXPs: n_iter * n_p * board.n_obstacles

  for (int t = 0; t < n_iter; t++) {
    for (int i = 0; i < n_p; i++) {

      // # 2 MULTs
      float desired_velocity_x = e_x[i] * desired_v0[i];
      float desired_velocity_y = e_y[i] * desired_v0[i];

      // # 2 ADDs, 2 MULTs
      float f_alpha_dt_x = (desired_velocity_x - curr_vel_x[i]) * dt_times_tau_alpha_inv;
      float f_alpha_dt_y = (desired_velocity_y - curr_vel_y[i]) * dt_times_tau_alpha_inv;

      const __m512 pix = _mm512_set1_ps(pos_x[i]);
      const __m512 piy = _mm512_set1_ps(pos_y[i]);
      const __m512 eix = _mm512_set1_ps(e_x[i]);
      const __m512 eiy = _mm512_set1_ps(e_y[i]);
      const __m512 v_i = _mm512_set1_ps((float)i);

      __m512 acc_x = _mm512_setzero_ps();
      __m512 acc_y = _mm512_setzero_ps();

      for (int j = 0; j < n_p_pad; j += 16) {

        // # 16 ADDs
        __m512 j_idx = _mm512_add_ps(_mm512_set1_ps((float)j), lane_off);

        __mmask16 m_neq_i = _mm512_cmp_ps_mask(j_idx, v_i, _CMP_NEQ_OQ);
        __mmask16 m_in_range = _mm512_cmp_ps_mask(j_idx, v_np, _CMP_LT_OQ);
        __mmask16 active = m_neq_i & m_in_range;

        __m512 pjx = _mm512_loadu_ps(&pos_x[j]);
        __m512 pjy = _mm512_loadu_ps(&pos_y[j]);
        __m512 sbe_jx = _mm512_loadu_ps(&sb_e_x[j]);
        __m512 sbe_jy = _mm512_loadu_ps(&sb_e_y[j]);
        __m512 sb_jsq = _mm512_loadu_ps(&sb_sq[j]);

        // # 32 ADDs
        __m512 r_ab_x = _mm512_sub_ps(pix, pjx);
        __m512 r_ab_y = _mm512_sub_ps(piy, pjy);

        // # 32 MULTs, 16 ADDs
        __m512 r_ab_n2 = _mm512_fmadd_ps(r_ab_x, r_ab_x, _mm512_mul_ps(r_ab_y, r_ab_y));

        // # 16 SQRTs
        __m512 r_ab_n = _mm512_sqrt_ps(r_ab_n2);

        r_ab_n = _mm512_max_ps(r_ab_n, v_eps);

        // # 32 ADDs
        __m512 r_ab2_x = _mm512_sub_ps(r_ab_x, sbe_jx);
        __m512 r_ab2_y = _mm512_sub_ps(r_ab_y, sbe_jy);

        // # 32 MULTs, 16 ADDs
        __m512 r_ab2_n2 = _mm512_fmadd_ps(r_ab2_x, r_ab2_x, _mm512_mul_ps(r_ab2_y, r_ab2_y));

        // # 16 SQRTs
        __m512 r_ab2_n = _mm512_sqrt_ps(r_ab2_n2);

        r_ab2_n = _mm512_max_ps(r_ab2_n, v_eps);

        // # 16 ADDs
        __m512 r_sum = _mm512_add_ps(r_ab_n, r_ab2_n);

        // # 16 MULTs, 16 ADDs
        __m512 two_b_sq = _mm512_fmsub_ps(r_sum, r_sum, sb_jsq);

        two_b_sq = _mm512_max_ps(two_b_sq, v_eps_sq);

        // # 16 SQRTs
        __m512 two_b = _mm512_sqrt_ps(two_b_sq);

        // # 16 MULTs
        __m512 e_arg = _mm512_mul_ps(two_b, v_neg_2s_inv);

        e_arg = _mm512_max_ps(e_arg, v_exp_min);

        // # 256 MULTs, 224 ADDs
        __m512 e_val = _avx512_exp_ps(e_arg);

        // # 64 MULTs
        __m512 numer = _mm512_mul_ps(_mm512_mul_ps(r_sum, v_neg_v0_div_2s), e_val);
        __m512 denom = _mm512_mul_ps(_mm512_mul_ps(two_b, r_ab_n), r_ab2_n);

        __m512 denom_safe = _mm512_mask_blend_ps(active, v_one, denom);

        // # 16 DIVs
        __m512 smc = _mm512_div_ps(numer, denom_safe);

        // # 32 MULTs
        __m512 sm_r_ab = _mm512_mul_ps(smc, r_ab2_n);
        __m512 sm_r_ab2 = _mm512_mul_ps(smc, r_ab_n);

        // # 64 MULTs, 32 ADDs
        __m512 f_x = _mm512_fmadd_ps(r_ab2_x, sm_r_ab2, _mm512_mul_ps(r_ab_x, sm_r_ab));
        __m512 f_y = _mm512_fmadd_ps(r_ab2_y, sm_r_ab2, _mm512_mul_ps(r_ab_y, sm_r_ab));

        // # 32 MULTs, 16 ADDs
        __m512 f_norm_sq = _mm512_fmadd_ps(f_x, f_x, _mm512_mul_ps(f_y, f_y));

        // # 16 MULTs
        __m512 rhs = _mm512_mul_ps(f_norm_sq, v_cos_phi_sq);

        // # 32 MULTs, 16 ADDs
        __m512 e_dot_f = _mm512_fmadd_ps(eix, f_x, _mm512_mul_ps(eiy, f_y));

        // # 16 MULTs
        __m512 e_dot_f_sq = _mm512_mul_ps(e_dot_f, e_dot_f);

        __mmask16 c1 = _mm512_cmp_ps_mask(e_dot_f, v_zero, _CMP_LT_OQ);
        __mmask16 c2 = _mm512_cmp_ps_mask(e_dot_f_sq, rhs, _CMP_GT_OQ);
        __mmask16 cond = c1 & c2;

        __m512 w_val = _mm512_mask_blend_ps(cond, v_dt_neg, v_c_neg_dt);

        __m512 f_x_safe = _mm512_maskz_mov_ps(active, f_x);
        __m512 f_y_safe = _mm512_maskz_mov_ps(active, f_y);

        // # 32 MULTs, 32 ADDs
        acc_x = _mm512_fmadd_ps(f_x_safe, w_val, acc_x);
        acc_y = _mm512_fmadd_ps(f_y_safe, w_val, acc_y);
      }

      // # 32 ADDs
      f_alpha_dt_x += _mm512_reduce_add_ps(acc_x);
      f_alpha_dt_y += _mm512_reduce_add_ps(acc_y);

      for (int k = 0; k < board.n_obstacles; k++) {

        // # 2 ADDs
        float v1_x = pos_x[i] - board.obstacles[k].start_x;
        float v1_y = pos_y[i] - board.obstacles[k].start_y;
        float v2_x = board.obstacles[k].obstacle_v_x;
        float v2_y = board.obstacles[k].obstacle_v_y;

        // # 3 MULTs, 1 ADD
        float projection = (v1_x * v2_x + v1_y * v2_y) * board.obstacles[k].length_sq_inv;

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

        // # 4 ADDs, 2 MULTs
        float r_aB_x = pos_x[i] - (board.obstacles[k].start_x + board.obstacles[k].obstacle_v_x * projection);
        float r_aB_y = pos_y[i] - (board.obstacles[k].start_y + board.obstacles[k].obstacle_v_y * projection);

        // # 1 SQRT, 2 MULTs, 1 ADD
        float r_aB_norm = sqrt(r_aB_x * r_aB_x + r_aB_y * r_aB_y);

        // # 2 MULTs, 1 EXP, 1 DIV
        float scalar_mult = (NEG_U0_AB_div_R * exp(r_aB_norm * NEG_R_INV)) / r_aB_norm;

        // # 2 MULTs
        float f_alpha_B_neg_x = r_aB_x * scalar_mult;
        float f_alpha_B_neg_y = r_aB_y * scalar_mult;

        float w_val = dt_neg;
        float e_dot_f = (f_alpha_B_neg_y == 0) ? 0 : (f_alpha_B_neg_y < 0 ? -e_y[i] : e_y[i]);

        if (e_dot_f < cos_phi)
          w_val = c_neg_times_dt;

        // # 2 MULTs
        float f_alpha_B_dt_x = f_alpha_B_neg_x * w_val;
        float f_alpha_B_dt_y = f_alpha_B_neg_y * w_val;

        // # 2 ADDs
        f_alpha_dt_x += f_alpha_B_dt_x;
        f_alpha_dt_y += f_alpha_B_dt_y;
      }

      // # 2 ADDs
      w_x[i] += f_alpha_dt_x;
      w_y[i] += f_alpha_dt_y;
    }

    for (int i = 0; i < n_p; i++) {
      // # 9 MULTs, 3 ADDs
      float w_norm_inv = fast_inv_sqrt(w_x[i] * w_x[i] + w_y[i] * w_y[i]);

      // # 1 MULT
      float correction_factor = min(1.0f, v_max[i] * w_norm_inv);

      // # 2 MULTs
      curr_vel_x[i] = w_x[i] * correction_factor;
      curr_vel_y[i] = w_y[i] * correction_factor;

      // # 2 MULTs, 2 ADDs
      pos_x[i] = pos_x[i] + curr_vel_x[i] * dt;
      pos_y[i] = pos_y[i] + curr_vel_y[i] * dt;

      if (color[i] == 0 && pos_x[i] > (BOARD_LENGTH_MINUS_ONE_POINT_FIVE)) {
        pos_x[i] = 1.0f;
        destination_y[i] = pos_y[i];
        w_x[i] = desired_v0[i];
        w_y[i] = 0.0f;
        curr_vel_x[i] = w_x[i];
        curr_vel_y[i] = w_y[i];
      }
      if (color[i] == 1 && pos_x[i] < 1.5f) {
        pos_x[i] = BOARD_LENGTH_MINUS_ONE;
        destination_y[i] = pos_y[i];
        w_x[i] = -desired_v0[i];
        w_y[i] = 0.0f;
        curr_vel_x[i] = w_x[i];
        curr_vel_y[i] = w_y[i];
      }

      pos_y[i] = clamp(pos_y[i], WALL_EPS, BOARD_WIDTH_MINUS_WALL_EPS);

      // # 2 ADDs
      float ex = destination_x[i] - pos_x[i];
      float ey = destination_y[i] - pos_y[i];

      // # 9 MULTs, 3 ADDs
      float e_norm_inv = fast_inv_sqrt(ex * ex + ey * ey);

      // # 2 MULTs
      e_x[i] = ex * e_norm_inv;
      e_y[i] = ey * e_norm_inv;

      // # 2 MULTs, 1 ADD
      double velocity_norm_sq = curr_vel_x[i] * curr_vel_x[i] + curr_vel_y[i] * curr_vel_y[i];

      // # 1 MULT
      double sb_sq_i = velocity_norm_sq * delta_t_sq;

      // # 1 SQRT
      double velocity_norm_mul_delta_t = sqrt(sb_sq_i);

      sb_sq[i] = sb_sq_i;

      // # 2 MULTs
      sb_e_x[i] = e_x[i] * velocity_norm_mul_delta_t;
      sb_e_y[i] = e_y[i] * velocity_norm_mul_delta_t;

#if !BENCHMARK
      if (dump_path && (t % dump_interval == 0)) {
        samples.emplace_back(t + 1, i, pos_x[i], pos_y[i], e_x[i], e_y[i], color[i]);
      }
#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;
}