#include <cmath>
#include <iostream>
#include "../includeCXX/sfx_compute_sheba.h"
#include "../includeCXX/sfx_surface.h"

template<typename T>
void get_psi_mh(T &psi_m, T &psi_h,
    const T zeta_m, const T zeta_h,
    const T alpha_m, const T alpha_h,
    const T a_m, const T a_h, 
    const T b_m, const T b_h,
    const T c_h)
{
    T x_m, x_h;
    T q_m, q_h;

    if (zeta_m >= 0.0) 
    {
        q_m = pow((1.0 - b_m) / b_m, 1.0 / 3.0);
        x_m = pow(1.0 + zeta_m, 1.0 / 3.0);

        psi_m = -3.0 * (a_m / b_m) * (x_m - 1.0) + 0.5 * (a_m / b_m) * q_m * (2.0 * log((x_m + q_m) / (1.0 + q_m)) - log((x_m * x_m - x_m * q_m + q_m * q_m) / (1.0 - q_m + q_m * q_m)) + 2.0 * sqrt(3.0) * (atan((2.0 * x_m - q_m) / (sqrt(3.0) * q_m)) - atan((2.0 - q_m) / (sqrt(3.0) * q_m))));
    }                                
    else
    {    x_m = pow(1.0 - alpha_m * zeta_m, 0.25);
        psi_m = (4.0 * atan(1.0) / 2.0) + 2.0 * log(0.5 * (1.0 + x_m)) + log(0.5 * (1.0 + x_m * x_m)) - 2.0 * atan(x_m);
    }

    if (zeta_h >= 0.0)
    {    
        q_h = sqrt(c_h * c_h - 4.0);
        x_h = zeta_h;

        psi_h = -0.5 * b_h * log(1.0 + c_h * x_h + x_h * x_h) + ((-a_h / q_h) + ((b_h * c_h) / (2.0 * q_h))) * (log((2.0 * x_h + c_h - q_h) / (2.0 * x_h + c_h + q_h)) - log((c_h - q_h) / (c_h + q_h)));
    }
    else
    {
        x_h = pow(1.0 - alpha_h * zeta_h, 0.25);
        psi_h = 2.0 * log(0.5 * (1.0 + x_h * x_h));
    }
}

template void get_psi_mh(float &psi_m, float &psi_h,
    const float zeta_m, const float zeta_h,
    const float alpha_m, const float alpha_h,
    const float a_m, const float a_h, 
    const float b_m, const float b_h,
    const float c_h);
template void get_psi_mh(double &psi_m, double &psi_h,
    const double zeta_m, const double zeta_h,
    const double alpha_m, const double alpha_h,
    const double a_m, const double a_h, 
    const double b_m, const double b_h,
    const double c_h);

template<typename T>
void get_psi(T &psi_m, T &psi_h,
    const T zeta,
    const T alpha_m, const T alpha_h,
    const T a_m, const T a_h, 
    const T b_m, const T b_h,
    const T c_h)
{
    T x_m, x_h;
    T q_m, q_h;

    if (zeta >= 0.0) 
    {
        q_m = pow((1.0 - b_m) / b_m, 1.0 / 3.0);
        q_h = sqrt(c_h * c_h - 4.0);

        x_m = pow(1.0 + zeta, 1.0 / 3.0);
        x_h = zeta;

        psi_m = -3.0 * (a_m / b_m) * (x_m - 1.0) + 0.5 * (a_m / b_m) * q_m * (2.0 * log((x_m + q_m) / (1.0 + q_m)) - log((x_m * x_m - x_m * q_m + q_m * q_m) / (1.0 - q_m + q_m * q_m)) + 2.0 * sqrt(3.0) * (atan((2.0 * x_m - q_m) / (sqrt(3.0) * q_m)) - atan((2.0 - q_m) / (sqrt(3.0) * q_m))));

        psi_h = -0.5 * b_h * log(1.0 + c_h * x_h + x_h * x_h) + ((-a_h / q_h) + ((b_h * c_h) / (2.0 * q_h))) * (log((2.0 * x_h + c_h - q_h) / (2.0 * x_h + c_h + q_h)) - log((c_h - q_h) / (c_h + q_h)));
    }
    else
    {
        x_m = pow(1.0 - alpha_m * zeta, 0.25);
        x_h = pow(1.0 - alpha_h * zeta, 0.25); 

        psi_m = (4.0 * atan(1.0) / 2.0) + 2.0 * log(0.5 * (1.0 + x_m)) + log(0.5 * (1.0 + x_m * x_m)) - 2.0 * atan(x_m);
        psi_h = 2.0 * log(0.5 * (1.0 + x_h * x_h));
    }
}

template void get_psi(float &psi_m, float &psi_h,
    const float zeta,
    const float alpha_m, const float alpha_h,
    const float a_m, const float a_h, 
    const float b_m, const float b_h,
    const float c_h);
template void get_psi(double &psi_m, double &psi_h,
    const double zeta,
    const double alpha_m, const double alpha_h,
    const double a_m, const double a_h, 
    const double b_m, const double b_h,
    const double c_h);

template<typename T>
void get_dynamic_scales(T &Udyn, T &Tdyn, T &Qdyn, T &zeta,
    const T U, const T Tsemi, const T dT, const T dQ, const T z, const T z0_m, const T z0_t, const T beta,
    const T kappa, const T Pr_t_0_inv,
    const T alpha_m, const T alpha_h,
    const T a_m, const T a_h, 
    const T b_m, const T b_h,
    const T c_h,
    const int maxiters)
{
    T psi_m, psi_h, psi0_m, psi0_h, Linv;
    const T gamma = 0.61;

    Udyn = kappa * U / log(z / z0_m);
    Tdyn = kappa * dT * Pr_t_0_inv / log(z / z0_t);
    Qdyn = kappa * dQ * Pr_t_0_inv / log(z / z0_t);
    zeta = 0.0;

    // --- no wind
    if (Udyn < 1e-5) 
        return;

    Linv = kappa * beta * (Tdyn + gamma * Qdyn * Tsemi) / (Udyn * Udyn);
    zeta = z * Linv;

    // --- near neutral case
    if (Linv < 1e-5) 
        return;

    for (int i = 0; i < maxiters; i++)
    {
        get_psi(psi_m, psi_h, zeta, alpha_m, alpha_h,
        a_m, a_h, 
        b_m, b_h,
        c_h);
        
        get_psi_mh(psi0_m, psi0_h, z0_m * Linv, z0_t * Linv, 
        alpha_m, alpha_h,
        a_m, a_h, 
        b_m, b_h,
        c_h);

        Udyn = kappa * U / (log(z / z0_m) - (psi_m - psi0_m));
        Tdyn = kappa * dT * Pr_t_0_inv / (log(z / z0_t) - (psi_h - psi0_h));
        Qdyn = kappa * dQ * Pr_t_0_inv / (log(z / z0_t) - (psi_h - psi0_h));

        if (Udyn < 1e-5) 
            break;

        Linv = kappa * beta * (Tdyn + gamma * Qdyn * Tsemi) / (Udyn * Udyn);
        zeta = z * Linv;
    }
}

template void get_dynamic_scales(float &Udyn, float &Tdyn, float &Qdyn, float & zeta,
    const float U, const float Tsemi, const float dT, const float dQ, const float z, const float z0_m, const float z0_t, const float beta,
    const float kappa, const float Pr_t_0_inv,
    const float alpha_m, const float alpha_h,
    const float a_m, const float a_h, 
    const float b_m, const float b_h,
    const float c_h,
    const int maxiters);
template void get_dynamic_scales(double &Udyn, double &Tdyn, double &Qdyn, double & zeta,
    const double U, const double Tsemi, const double dT, const double dQ, const double z, const double z0_m, const double z0_t, const double beta,
    const double kappa, const double Pr_t_0_inv,
    const double alpha_m, const double alpha_h,
    const double a_m, const double a_h, 
    const double b_m, const double b_h,
    const double c_h,
    const int maxiters);

template<typename T>
void get_phi(T &phi_m, T &phi_h,
    const T zeta, 
    const T alpha_m, const T alpha_h,
    const T a_m, const T a_h, 
    const T b_m, const T b_h,
    const T c_h)
{
    if (zeta >= 0.0) 
    {
        phi_m = 1.0 + (a_m * zeta * pow(1.0 + zeta, 1.0 / 3.0) ) / (1.0 + b_m * zeta);
        phi_h = 1.0 + (a_h * zeta + b_h * zeta * zeta) / (1.0 + c_h * zeta + zeta * zeta);
    }
    else
    {
        phi_m = pow(1.0 - alpha_m * zeta, -0.25);
        phi_h = pow(1.0 - alpha_h * zeta, -0.5);
    }
}

template void get_phi(float &phi_m, float &phi_h,
    const float zeta, 
    const float alpha_m, const float alpha_h,
    const float a_m, const float a_h, 
    const float b_m, const float b_h,
    const float c_h);
template void get_phi(double &phi_m, double &phi_h,
    const double zeta, 
    const double alpha_m, const double alpha_h,
    const double a_m, const double a_h, 
    const double b_m, const double b_h,
    const double c_h);

template<typename T>
void compute_flux_sheba_cpu(T *zeta_, T *Rib_, T *Re_, T *B_, T *z0_m_, T *z0_t_, T *Rib_conv_lim_, T *Cm_, T *Ct_, T *Km_, T *Pr_t_inv_,
    const T *U_, const T *dT_, const T *Tsemi_, const T *dQ_, const T *h_, const T *in_z0_m_,
    const T kappa, const T Pr_t_0_inv,
    const T alpha_m, const T alpha_h, 
    const T a_m, const T a_h, 
    const T b_m, const T b_h,
    const T c_h,
    const T Re_rough_min, 
    const T B1_rough, const T B2_rough,
    const T B_max_land, const T B_max_ocean, const T B_max_lake,
    const T gamma_c, const T Re_visc_min,
    const T Pr_m, const T nu_air, const T g, 
    const int maxiters_charnock,
    const int grid_size)
{
    T h, U, dT, Tsemi, dQ, z0_m;
    T z0_t, B, h0_m, h0_t, u_dyn0, Re, 
    zeta, Rib, Udyn, Tdyn, Qdyn, phi_m, phi_h,
    Km, Pr_t_inv, Cm, Ct;

    const T B3_rough = kappa * Pr_m, B4_rough =(0.14 * (pow(30.0, B2_rough))) * (pow(Pr_m, 0.8));
    const T h_charnock = 10.0, c1_charnock = log(h_charnock * (g / gamma_c)), c2_charnock = Re_visc_min * nu_air * c1_charnock;

    int surface_type;

    for (int step = 0; step < grid_size; step++)
    {
        U = U_[step];
        Tsemi = Tsemi_[step];
        dT = dT_[step];
        dQ = dQ_[step];
        h = h_[step];
        z0_m = in_z0_m_[step];

        if (z0_m < 0.0) surface_type = 0;
        else            surface_type = 1;

        if (surface_type == 0) 
        {
            get_charnock_roughness(z0_m, u_dyn0, h, U, kappa, h_charnock, c1_charnock, c2_charnock, maxiters_charnock);
            h0_m = h / z0_m;
        }
        if (surface_type == 1) 
        {
            h0_m = h / z0_m;
            u_dyn0 = U * kappa / log(h0_m);
        }

        Re = u_dyn0 * z0_m / nu_air;
        get_thermal_roughness(z0_t, B, z0_m, Re, Re_rough_min, B1_rough, B2_rough, B3_rough, B4_rough, B_max_ocean, B_max_lake, B_max_land, surface_type);

        // --- define relative height [thermal]
        h0_t = h / z0_t;

        // --- define Ri-bulk
        Rib = (g / Tsemi) * h * (dT + 0.61e0 * Tsemi * dQ) / (U*U);

        // --- get the fluxes
        // ----------------------------------------------------------------------------
        get_dynamic_scales(Udyn, Tdyn, Qdyn, zeta, U, Tsemi, dT, dQ, h, z0_m, z0_t, (g / Tsemi), kappa, Pr_t_0_inv, alpha_m, alpha_h, a_m, a_h, b_m, b_h, c_h, 10);
        // ----------------------------------------------------------------------------

        get_phi(phi_m, phi_h, zeta, alpha_m, alpha_h, a_m, a_h, b_m, b_h, c_h);
        // ----------------------------------------------------------------------------

        // --- define transfer coeff. (momentum) & (heat)
        Cm = 0.0;
        if (U > 0.0)
            Cm = Udyn / U;
        Ct = 0.0;
        if (fabs(dT) > 0.0) 
            Ct = Tdyn / dT;

        // --- define eddy viscosity & inverse Prandtl number
        Km = kappa * Cm * U * h / phi_m;
        Pr_t_inv = phi_m / phi_h;

        zeta_[step]         = zeta;
        Rib_[step]          = Rib;
        Re_[step]           = Re;
        B_[step]            = B;
        z0_m_[step]         = z0_m;
        z0_t_[step]         = z0_t;
        Rib_conv_lim_[step] = 0.0;
        Cm_[step]           = Cm;
        Ct_[step]           = Ct;
        Km_[step]           = Km;
        Pr_t_inv_[step]     = Pr_t_inv;
    }
}

template void compute_flux_sheba_cpu(float *zeta_, float *Rib_, float *Re_, float *B_, float *z0_m_, float *z0_t_, float *Rib_conv_lim_, float *Cm_, float *Ct_, float *Km_, float *Pr_t_inv_,
    const float *U, const float *dt, const float *T_semi, const float *dq, const float *H, const float *in_z0_m,
    const float kappa, const float Pr_t_0_inv, 
    const float alpha_m, const float alpha_h,
    const float a_m, const float a_h, 
    const float b_m, const float b_h,
    const float c_h,
    const float Re_rough_min, 
    const float B1_rough, const float B2_rough,
    const float B_max_land, const float B_max_ocean, const float B_max_lake,
    const float gamma_c, const float Re_visc_min,
    const float Pr_m, const float nu_air, const float g, 
    const int maxiters_charnock, 
    const int grid_size);
template void compute_flux_sheba_cpu(double *zeta_, double *Rib_, double *Re_, double *B_, double *z0_m_, double *z0_t_, double *Rib_conv_lim_, double *Cm_, double *Ct_, double *Km_, double *Pr_t_inv_,
    const double *U, const double *dt, const double *T_semi, const double *dq, const double *H, const double *in_z0_m, 
    const double kappa, const double Pr_t_0_inv, 
    const double alpha_m, const double alpha_h, 
    const double a_m, const double a_h, 
    const double b_m, const double b_h,
    const double c_h,
    const double Re_rough_min, 
    const double B1_rough, const double B2_rough,
    const double B_max_land, const double B_max_ocean, const double B_max_lake,
    const double gamma_c, const double Re_visc_min,
    const double Pr_m, const double nu_air, const double g, 
    const int maxiters_charnock,
    const int grid_size);