// This file has to be compiled as c++ due to the use of complex numbers
// Further information on mixing languages: http://www.cae.tntech.edu/help/programming/mixed_languages/view
// And information on how to use the complex library in Visual Studio: http://msdn.microsoft.com/en-us/library/ayweczx2.aspx

// --------------------------------------------------
//  WARNING WARNING WARNING WARNING WARNING WARNING 
// 
// This code must be compiled in Visual Studio due to the use of the complex library
// --------------------------------------------------

#include <complex>
#include <iostream>
#include "Ice.h"

static double T_t=273.16,p_t=0.611657,p_0=101.325;
using namespace std;
// Complex Constants for EOS
double g00=-0.632020233449497e6;
double g01= 0.655022213658955;
double g02=-0.189369929326131e-7;
double g03= 0.339746123271053e-14;
double g04=-0.556464869058991e-21;
double s0= -0.332733756492168e4;
complex <double> t1  ( 0.368017112855051e-1,  0.510878114959572e-1);
complex <double> r1  ( 0.447050716285388e2,   0.656876847463481e2);
complex <double> t2  ( 0.337315741065416,     0.335449415919309);
complex <double> r20 (-0.725974574329220e2,  -0.781008427112870e2);
complex <double> r21 (-0.557107698030123e-4,  0.464578634580806e-4);
complex <double> r22 ( 0.234801409215913e-10,-0.285651142904972e-10);

extern "C" double IsothermCompress_Ice(double T, double p)
{
    // Inputs in K,kPa, Output in 1/Pa
    return -dg2_dp2_Ice(T,p)/dg_dp_Ice(T,p)/1000.0;
}
extern "C" double psub_Ice(double T)
{
    double a[]={0,-0.212144006e2,0.273203819e2,-0.610598130e1};
    double b[]={0,0.333333333e-2,0.120666667e1,0.170333333e1};
    double summer=0,theta;
    theta=T/T_t;
    for (int i=1;i<=3;i++)
    {
        summer+=a[i]*pow(theta,b[i]);
    }
    return p_t*exp(1/theta*summer);
}

extern "C" double g_Ice(double T,double p)
{
    using namespace std;
    complex<double> r2,term1,term2;
    double g0,theta,pi,pi_0;
    theta= T/T_t; pi=p/p_t; pi_0=p_0/p_t;
    g0=g00*pow(pi-pi_0,0.0)+g01*pow(pi-pi_0,1.0)+g02*pow(pi-pi_0,2.0)+g03*pow(pi-pi_0,3.0)+g04*pow(pi-pi_0,4.0);
    r2=r20*pow(pi-pi_0,0.0)+r21*pow(pi-pi_0,1.0)+r22*pow(pi-pi_0,2.0);
    // The two terms of the summation
    term1=r1*((t1-theta)*log(t1-theta)+(t1+theta)*log(t1+theta)-2.0*t1*log(t1)-theta*theta/t1);
    term2=r2*((t2-theta)*log(t2-theta)+(t2+theta)*log(t2+theta)-2.0*t2*log(t2)-theta*theta/t2);
    return g0-s0*T_t*theta+T_t*real(term1+term2);
}

extern "C" double dg_dp_Ice(double T, double p)
{
    using namespace std;
    complex<double> r2_p;
    double g0_p,theta,pi,pi_0;
    theta= T/T_t; pi=p/p_t; pi_0=p_0/p_t;
    g0_p=g01*1.0/p_t*pow(pi-pi_0,1-1.0)+g02*2.0/p_t*pow(pi-pi_0,2-1.0)+g03*3.0/p_t*pow(pi-pi_0,3-1.0)+g04*4.0/p_t*pow(pi-pi_0,4-1.0);
    r2_p=r21*1.0/p_t*pow(pi-pi_0,1-1.0)+r22*2.0/p_t*pow(pi-pi_0,2-1.0);
    return g0_p+T_t*real(r2_p*((t2-theta)*log(t2-theta)+(t2+theta)*log(t2+theta)-2.0*t2*log(t2)-theta*theta/t2));
}

extern "C" double dg2_dp2_Ice(double T, double p)
{
    using namespace std;
    complex<double> r2_pp;
    double g0_pp,theta,pi,pi_0;
    theta= T/T_t; pi=p/p_t; pi_0=p_0/p_t;
    g0_pp=g02*2.0*(2.0-1.0)/p_t/p_t*pow(pi-pi_0,2.0-2.0)+g03*3.0*(3.0-1.0)/p_t/p_t*pow(pi-pi_0,3.0-2.0)+g04*4.0*(4.0-1.0)/p_t/p_t*pow(pi-pi_0,4-2.0);
    r2_pp=r22*2.0/p_t/p_t;
    return g0_pp+T_t*real(r2_pp*((t2-theta)*log(t2-theta)+(t2+theta)*log(t2+theta)-2.0*t2*log(t2)-theta*theta/t2));
}

extern "C" double dg_dT_Ice(double T, double p)
{
    using namespace std;
    complex<double> r2,term1,term2;
    double theta,pi,pi_0;
    theta= T/T_t; pi=p/p_t; pi_0=p_0/p_t;
    r2=r20*pow(pi-pi_0,0.0)+r21*pow(pi-pi_0,1.0)+r22*pow(pi-pi_0,2.0);
    // The two terms of the summation
    term1=r1*(-log(t1-theta)+log(t1+theta)-2.0*theta/t1);
    term2=r2*(-log(t2-theta)+log(t2+theta)-2.0*theta/t2);
    return -s0+real(term1+term2);
}

extern "C" double h_Ice(double T, double p)
{
    // Returned value is in units of J/kg
    return g_Ice(T,p)-T*dg_dT_Ice(T,p);
}