#include "forces.hpp"
#include "constants.hpp"
#include <math.h>

// Flop count: 2 ADDs, 5 MULTs, 1 SQRT
double w(Vector2d e, Vector2d f) {
  if (e.dot(f) >= f.norm() * cos_phi)
    return dt_neg;
  else
    return c_neg_times_dt;
}

// Flop count: 2 ADDs, 4 MULTs
Vector2d acceleration_term_dt(const Pedestrian &alpha) {

  // # 2 MULTs
  Vector2d desired_velocity = alpha.e * alpha.desired_v0;

  Vector2d actual_velocity = alpha.curr_vel;

  // # 2 ADDs, 2 MULTs
  Vector2d f_alpha_0_dt = (desired_velocity - actual_velocity) * dt_times_tau_alpha_inv;

  return f_alpha_0_dt;
}


// Flop count: 12 ADDs, 23 MULTs, 1 DIV, 4 SQRTs, 1 EXP
Vector2d pedestrian_repulsion_dt(const Pedestrian &alpha, const Pedestrian &beta) {

    // # 2 ADDs
    // $\vec{r}_{\alpha\beta}$
    Vector2d r_ab = alpha.curr_pos - beta.curr_pos;

    // # 1 ADD, 2 MULTs, 1 SQRT
    // $\Arrowvert \vec{r}_{\alpha \beta} \Arrowvert$
    double r_ab_norm = r_ab.norm();
    r_ab_norm = r_ab_norm > EPS ? r_ab_norm : EPS; // Avoid division by zero

    // $v_\beta \Delta t \vec{e}_\beta$
    Vector2d s_b_e = beta.s_b_e;

    // # 2 ADDs
    // $\vec{r}_{\alpha\beta} - \vec{v}_{\beta}\varDelta_{t}\vec{e}_{\beta}$
    Vector2d r_ab2 = r_ab - s_b_e;

    // # 1 ADD, 2 MULTs, 1 SQRT
    // $\Arrowvert \vec{r}_{\alpha \beta} - v_\beta \Delta t \vec{e}_\beta \Arrowvert$
    double r_ab2_norm = r_ab2.norm();
    r_ab2_norm = r_ab2_norm > EPS ? r_ab2_norm : EPS; // Avoid division by zero

    // # 1 ADD
    // $\Arrowvert \vec{r}_{\alpha \beta} \Arrowvert + \Arrowvert \vec{r}_{\alpha \beta} - v_\beta \Delta t \vec{e}_\beta \Arrowvert$
    double r_ab_norm_sum = r_ab_norm + r_ab2_norm;

    // # 1 ADD, 1 MULTs, 1 SQRT
    //
    // $2b = \sqrt{(\Arrowvert \vec{r}_{\alpha \beta} \Arrowvert + \Arrowvert \vec{r}_{\alpha \beta} - v_\beta \Delta t \vec{e}_\beta \Arrowvert)^2 - (v_\beta \Delta t)^2}$
    //
    double two_b_sq = r_ab_norm_sum * r_ab_norm_sum - beta.s_b_sq;
    two_b_sq = two_b_sq > EPS_SQ ? two_b_sq : EPS_SQ; // Avoid sqrt of negative and avoid division by zero
    double two_b = sqrt(two_b_sq);

    // # 5 MULTs, 1 DIV, 1 EXP
    //
    // $\frac{-V^0_{\alpha\beta}}{2\sigma}\,e^{-b/\sigma}\,\frac{\Arrowvert \vec{r}_{\alpha \beta} \Arrowvert + \Arrowvert \vec{r}_{\alpha \beta} - v_\beta \Delta t \vec{e}_\beta \Arrowvert}{2b\,\Arrowvert \vec{r}_{\alpha \beta} \Arrowvert\,\Arrowvert \vec{r}_{\alpha \beta} - v_\beta \Delta t \vec{e}_\beta \Arrowvert}$
    //
    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 MULT
    //
    // $\frac{-V^0_{\alpha\beta}}{2\sigma}\,e^{-b/\sigma}\,\frac{\Arrowvert \vec{r}_{\alpha \beta} \Arrowvert + \Arrowvert \vec{r}_{\alpha \beta} - v_\beta \Delta t \vec{e}_\beta \Arrowvert}{2b\,\Arrowvert \vec{r}_{\alpha \beta} \Arrowvert}$
    //
    double scalar_mult_r_ab = scalar_mult_common * r_ab2_norm;

    // # 1 MULT
    //
    // $\frac{-V^0_{\alpha\beta}}{2\sigma}\,e^{-b/\sigma}\,\frac{\Arrowvert \vec{r}_{\alpha \beta} \Arrowvert + \Arrowvert \vec{r}_{\alpha \beta} - v_\beta \Delta t \vec{e}_\beta \Arrowvert}{2b\,\Arrowvert \vec{r}_{\alpha \beta} - v_\beta \Delta t \vec{e}_\beta \Arrowvert}$
    //
    double scalar_mult_r_ab2 = scalar_mult_common * r_ab_norm;

    // # 2 ADDs, 4 MULTs
    //
    // $\vec{-f}_{\alpha \beta}(\vec{r}_{\alpha \beta}) = \frac{-V^0_{\alpha \beta}}{2\sigma}e^{-b / \sigma} 2\grad_{\vec{r}_{\alpha \beta}}b $
    //
    //
    //          $= \frac{-V^0_{\alpha\beta}}{2\sigma}\,e^{-b/\sigma}\,\frac{\Arrowvert \vec{r}_{\alpha \beta} \Arrowvert + \Arrowvert \vec{r}_{\alpha \beta} - v_\beta \Delta t \vec{e}_\beta \Arrowvert}{2b\,\Arrowvert \vec{r}_{\alpha \beta} \Arrowvert}\,\vec{r}_{\alpha \beta} + \frac{-V^0_{\alpha\beta}}{2\sigma}\,e^{-b/\sigma}\,\frac{\Arrowvert \vec{r}_{\alpha \beta} \Arrowvert + \Arrowvert \vec{r}_{\alpha \beta} - v_\beta \Delta t \vec{e}_\beta \Arrowvert}{2b\,\Arrowvert \vec{r}_{\alpha \beta} - v_\beta \Delta t \vec{e}_\beta \Arrowvert}\,(\vec{r}_{\alpha \beta} - v_\beta \Delta t \vec{e}_\beta)$
    //
    //
    //
    // $2\grad_{\vec{r}_{\alpha \beta}}b = \frac{(\Arrowvert \vec{r}_{\alpha \beta} \Arrowvert + \Arrowvert \vec{r}_{\alpha \beta} - v_\beta \Delta t \vec{e}_\beta \Arrowvert)(\frac{\vec{r}_{\alpha \beta}}{\Arrowvert \vec{r}_{\alpha \beta} \Arrowvert} + \frac{\vec{r}_{\alpha \beta} - v_\beta \Delta t \vec{e}_\beta}{\Arrowvert \vec{r}_{\alpha \beta} - v_\beta \Delta t \vec{e}_\beta \Arrowvert})}{2b}$
    //
    //
    //       $= \frac{\Arrowvert \vec{r}_{\alpha \beta} \Arrowvert + \Arrowvert \vec{r}_{\alpha \beta} - v_\beta Delta t \vec{e}_\beta \Arrowvert}{2b\,\Arrowvert \vec{r}_{\alpha \beta} \Arrowvert}\,\vec{r}_{\alpha \beta} + \frac{\Arrowvert \vec{r}_{\alpha \beta} \Arrowvert + \Arrowvert \vec{r}_{\alpha \beta} - v_\beta \Delta t \vec{e}_\beta \Arrowvert}{2b\,\Arrowvert \vec{r}_{\alpha \beta} - v_\beta \Delta t \vec{e}_\beta \Arrowvert}\,(\vec{r}_{\alpha \beta} - v_\beta \Delta t \vec{e}_\beta)$
    //
    //
    Vector2d f_alpha_beta_neg = r_ab * scalar_mult_r_ab + r_ab2 * scalar_mult_r_ab2;

    // # 2 ADDs, 7 MULTs, 1 SQRT
    //
    // $\vec{F}_{\alpha\beta}(\vec{e}_{\alpha}, \vec{r}_{\alpha \beta}).dt = w(\vec{e}_{\alpha}, -\vec{f}_{\alpha\beta}(\vec{r}_{\alpha \beta})).\vec{f}_{\alpha\beta}(\vec{r}_{\alpha \beta}).dt$
    //
    Vector2d f_alpha_beta_dt = f_alpha_beta_neg * w(alpha.e, f_alpha_beta_neg);

    return f_alpha_beta_dt;
}


// Flop count: 10 ADDs, 18 MULTs, 1 DIVs, 2 SQRTs, 1 EXP
Vector2d obstacle_repulsion_dt(const Pedestrian &alpha, const Obstacle &B) {

    // # 7 ADDs, 5 MULTs
    // $\vec{r}_{\alpha B}$
    Vector2d r_aB = alpha.curr_pos - B.find_nearest_obstacle_point(alpha.curr_pos);

    // # 1 ADD, 2 MULTs, 1 SQRT
    // $\Arrowvert \vec{r}_{\alpha B} \Arrowvert$
    double r_aB_norm = r_aB.norm();
    r_aB_norm = r_aB_norm > EPS ? r_aB_norm : EPS; // Avoid division by zero

    // # 2 MULTs, 1 DIV, 1 EXP
    //
    // $\frac{-U^0_{\alpha B}}{R} e^{- \Arrowvert \vec{r}_{\alpha B} \Arrowvert / R}$
    //
    double scalar_mult = (NEG_U0_AB_div_R * exp(r_aB_norm * NEG_R_INV)) / r_aB_norm;

    // # 2 MULTs
    //
    // $-\vec{F}_{\alpha B}(\vec{r}_{\alpha B}) = \frac{-U^0_{\alpha B}}{R} e^{- \Arrowvert \vec{r}_{\alpha B} \Arrowvert / R} \frac{\vec{r}_{\alpha B}}{\Arrowvert \vec{r}_{\alpha B} \Arrowvert}$
    //
    Vector2d f_alpha_B_neg = r_aB * scalar_mult;

    // # 2 ADDs, 7 MULTs, 1 SQRT
    //
    // $\vec{F}_{\alpha B}(\vec{e}_{\alpha}, \vec{r}_{\alpha B}).dt = w(\vec{e}_{\alpha}, -\vec{F}_{\alpha B}(\vec{r}_{\alpha B})).\vec{F}_{\alpha B}(\vec{r}_{\alpha B}).dt$
    //
    Vector2d f_alpha_B_dt = f_alpha_B_neg * w(alpha.e, f_alpha_B_neg);

    return f_alpha_B_dt;
  }