//////////////////////////////////////////////////////////////////////
//
// Module: EvtVubAC.cc
// Analytic Coupling Model (based on hep-ph/0608047 by Aglietti, Ferrera and Ricciardi)
// Author: Michael Sigamani           May 2008
//
///////////////////////////////////////////////////////////////

#include "EvtGenBase/EvtPatches.hh"
#include <stdlib.h>
#include "EvtGenBase/EvtParticle.hh"
#include "EvtGenBase/EvtGenKine.hh"
#include "EvtGenBase/EvtPDL.hh"
#include "EvtGenBase/EvtReport.hh"
#include "EvtGenModels/EvtVubAC.hh"
#include <string>
#include "EvtGenBase/EvtVector4R.hh"
#include "EvtGenModels/EvtPFermi.hh"
#include "EvtGenBase/EvtRandom.hh"

using std::cout;
using std::endl;

EvtVubAC::~EvtVubAC() {
}

std::string EvtVubAC::getName(){
  return "VUB_AC";
}

  EvtDecayBase *EvtVubAC::clone() {
  return new EvtVubAC;
}

void EvtVubAC::init() {

  // get parameters (declared in the header file)
  
  // B Meson mass
  mB = 5.2792;
  
  // Perturbative quantities
  CF = 4.0/3.0;
  CA = 3.0;
  double nf = 3.0; 

  //Constants 
  alphaSmZ = getArg(0); 
  c = 0.04;
  q = 0.01;
  k = 0.02;
  
  beta0 = (11.0/3.0*CA - 2.0/3.0*nf)/(4*M_PI);
  alphaSmB = 0.22*alphaSmZ/0.1189;

  gvars.push_back(0.0); // 0
  gvars.push_back(0.0); // 1
  gvars.push_back(0.0); // 2
  gvars.push_back(alphaSmB); // 3
  gvars.push_back(alphaSmZ); // 4
  gvars.push_back(mB); // 5
  gvars.push_back(beta0); // 6
  gvars.push_back(c); // 7
  gvars.push_back(q); // 8
  gvars.push_back(k); // 9

  // check that there are 3 daughters and 1 argument
  checkNDaug(3);
  checkNArg(1);

}

void EvtVubAC::initProbMax() {
  noProbMax();
}

void EvtVubAC::decay(EvtParticle *Bmeson) {

  int j;
  
  EvtParticle *xuhad, *lepton, *neutrino;
  EvtVector4R p4;
  double  u, w, xb, Pp, Pm, pdf, ml, PX(0.0), EX(0.0), sh(0.0), El(0.0) ;

  Bmeson->initializePhaseSpace(getNDaug(), getDaugs());
  
  xuhad = Bmeson->getDaug(0);
  lepton = Bmeson->getDaug(1);
  neutrino = Bmeson ->getDaug(2);

  ml = lepton->mass();

  bool tryit = true;
  while (tryit) {
   
    double mpi = 0.14;
    u = EvtRandom::Flat(0.0,1.0); 
    w = EvtRandom::Flat(0.0,2.0); 
    xb = EvtRandom::Flat(0.0,1.0); 

    EX = w*mB/2.0;
    PX = EX*(1.0-u)/(u+1.0);
    El = (1.0-xb)*mB/2.0; 
    Pp = (EX-PX); 
    Pm = (EX+PX);
    sh = Pm*Pp;  

	if ( ((w*u)/(1.0+u) < xb) && (xb < w/(1.0+u)) && (max(0, w - 1.0) < u) && (sh > 4.0*mpi*mpi) && ( El > ml ) ){ 

     		pdf = rate(u,w,xb);  
     		double testRan = EvtRandom::Flat(0.0,24.2);
			if (pdf >= testRan) tryit = false;
	}
        
 }

  // o.k. we have the three kinemtic variables 
  // now calculate a flat cos Theta_H [-1,1] distribution of the 
  // hadron flight direction w.r.t the B flight direction 
  // because the B is a scalar and should decay isotropic.
  // Then chose a flat Phi_H [0,2Pi] w.r.t the B flight direction 
  // and and a flat Phi_L [0,2Pi] in the W restframe w.r.t the 
  // W flight direction.
  
  double ctH = EvtRandom::Flat(-1,1);
  double phH = EvtRandom::Flat(0,2*M_PI);
  double phL = EvtRandom::Flat(0,2*M_PI);

  // now compute the four vectors in the B Meson restframe
    
  double ptmp,sttmp;
  // calculate the hadron 4 vector in the B Meson restframe
  
  sttmp = sqrt(1-ctH*ctH);
  ptmp = sqrt(EX*EX-sh);
  double pHB[4] = {EX,ptmp*sttmp*cos(phH),ptmp*sttmp*sin(phH),ptmp*ctH};
  p4.set(pHB[0],pHB[1],pHB[2],pHB[3]);
  xuhad->init( getDaug(0), p4);

  // calculate the W 4 vector in the B Meson restrframe

  double apWB = ptmp;
  double pWB[4] = {mB-EX,-pHB[1],-pHB[2],-pHB[3]};

  // first go in the W restframe and calculate the lepton and
  // the neutrino in the W frame

  double mW2   = mB*mB + sh - 2*mB*EX;
  double beta  = ptmp/pWB[0];
  double gamma = pWB[0]/sqrt(mW2);

  double pLW[4];
    
  ptmp = (mW2-ml*ml)/2/sqrt(mW2);
  pLW[0] = sqrt(ml*ml + ptmp*ptmp);

  double ctL = (El - gamma*pLW[0])/beta/gamma/ptmp;
  if ( ctL < -1 ) ctL = -1;
  if ( ctL >  1 ) ctL =  1;
  sttmp = sqrt(1-ctL*ctL);

  // eX' = eZ x eW
  double xW[3] = {-pWB[2],pWB[1],0};
  // eZ' = eW
  double zW[3] = {pWB[1]/apWB,pWB[2]/apWB,pWB[3]/apWB};
  
  double lx = sqrt(xW[0]*xW[0]+xW[1]*xW[1]);
  for (j=0;j<2;j++) 
    xW[j] /= lx;

  // eY' = eZ' x eX'
  double yW[3] = {-pWB[1]*pWB[3],-pWB[2]*pWB[3],pWB[1]*pWB[1]+pWB[2]*pWB[2]};
  double ly = sqrt(yW[0]*yW[0]+yW[1]*yW[1]+yW[2]*yW[2]);
  for (j=0;j<3;j++) 
    yW[j] /= ly;

  // p_lep = |p_lep| * (  sin(Theta) * cos(Phi) * eX'
  //                    + sin(Theta) * sin(Phi) * eY'
  //                    + cos(Theta) *            eZ')
  for (j=0;j<3;j++)
    pLW[j+1] = sttmp*cos(phL)*ptmp*xW[j] 
      +        sttmp*sin(phL)*ptmp*yW[j]
      +          ctL         *ptmp*zW[j];

  double apLW = ptmp;
    
  // boost them back in the B Meson restframe
  
  double appLB = beta*gamma*pLW[0] + gamma*ctL*apLW;
 
  ptmp = sqrt(El*El-ml*ml);
  double ctLL = appLB/ptmp;

  if ( ctLL >  1 ) ctLL =  1;
  if ( ctLL < -1 ) ctLL = -1;
    
  double pLB[4] = {El,0,0,0};
  double pNB[4] = {pWB[0]-El,0,0,0};

  for (j=1;j<4;j++) {
    pLB[j] = pLW[j] + (ctLL*ptmp - ctL*apLW)/apWB*pWB[j];
    pNB[j] = pWB[j] - pLB[j];
  }

  p4.set(pLB[0],pLB[1],pLB[2],pLB[3]);
  lepton->init( getDaug(1), p4);

  p4.set(pNB[0],pNB[1],pNB[2],pNB[3]);
  neutrino->init( getDaug(2), p4);

  return ;

}

double EvtVubAC::rate(double u, double w, double xb) {
std::vector<double> vars(11);
vars[0] = u;
vars[1] = w;
vars[2] = xb;
double dGam = Coeff(u,w,xb)*Sigma(wreg(w/(1+u)),ularge(u)) + d(u,w,xb);

return dGam;
}

double EvtVubAC::PolyLog(double v, double z) {

if (z >= 1) cout << "Error in EvtVubAC: 2nd argument to PolyLog is >= 1." << endl;

double sum = 0.0;
for (int k=1; k<101; k++) { 
sum = sum + pow(z,k)/pow(k,v);
}
return sum;
}

double EvtVubAC::max(double ub, double lb) {
if (ub > lb)
return ub;
else
return lb;
}

double EvtVubAC::wreg(double w) {
std::vector<double> vars(11);
vars[1] = w;
for (int j=3;j<11;j++) {vars[j] = gvars[j];}  
double K=(1+c)/(1+c+pow(c,2));
return K*(c+pow(w,2)/(w+c));
}

double EvtVubAC::ureg(double u) {
std::vector<double> vars(11);  
vars[0] = u;
for (int j=3;j<11;j++) {vars[j] = gvars[j];}
return q + u*u/(u+q);
}

double EvtVubAC::ularge(double u) {
std::vector<double> vars(11);
vars[0] = u;
for (int j=3;j<11;j++) {vars[j] = gvars[j];}
return u - k*u*u;
}

double EvtVubAC::alphaS(double Q) {
std::vector<double> vars(11);
for (int j=3;j<11;j++) {vars[j] = gvars[j];}

double a =1.0/(log(Q*Q/FindRoot(alphaSmZ)));
double b= FindRoot(alphaSmZ)/(FindRoot(alphaSmZ) - Q*Q);
double ans = 1.0/beta0*( a + b );

return ans;
}

double EvtVubAC::Coeff(double u, double w, double xb) {
std::vector<double> vars(11);  
vars[0] = u;
vars[1] = w;
vars[2] = xb;

for (int j=3;j<11;j++) {vars[j] = gvars[j];}

double coeff = Coeff0(w,xb) + alphaS(mB*wreg(w/(1+u)))*Coeff1(w,xb);
return coeff;
}

double EvtVubAC::Coeff0(double w, double xb) {
std::vector<double> vars(11);
vars[1] = w;
vars[2] = xb;
for (int j=3;j<11;j++) {vars[j] = gvars[j];}
return 12.0*(1+xb-w)*(w-xb);
}

double EvtVubAC::Coeff1(double w, double xb) {
std::vector<double> vars(11);
vars[1] = w;
vars[2] = xb;
for (int j=3;j<11;j++) {vars[j] = gvars[j];}
double a = 1+xb-w; 
double b = -PolyLog(2,1-w)-3.0/2.0*log(wreg(w)) - 1.0/2.0*w*f(w) - 35.0/8.0 + (M_PI*M_PI)/6.0;
double c = 1.0/2.0*xb*f(wreg(w));

double ans = 12.0*CF/M_PI*(w-xb)*((a*b)+c);

return ans;
}

double EvtVubAC::d(double u, double w, double xb) {
std::vector<double> vars(11); 
vars[0] = u;
vars[1] = w;
vars[2] = xb;
for (int j=3;j<11;j++) {vars[j] = gvars[j];}

return alphaS(mB*wreg(w/(1.0+u)))*CF/M_PI*d1(u,w,xb);

}

double EvtVubAC::d1(double u, double w, double xb) {
std::vector<double> vars(11);
vars[0] = u;
vars[1] = w;
vars[2] = xb; 
for (int j=3;j<11;j++) {vars[j] = gvars[j];}

double a = 3*pow(w,4)*(24+3*w-8*xb)/(4*pow(1+u,5));
double b = 9*pow(w,4)*(24+3*w-8*xb)/(8*pow(1+u,4));
double c = 9*(-12+w)*pow(-2+w,2)*pow(w-2*xb,2)/(16*pow(1-u,3));
double cc = 9*(-12+w)*pow(-2+w,2)*pow(w-2*xb,2)/(32*pow(1-u,2));
double d = 3*pow(w,2)*(32-47*w-8*w*w+16*xb+20*w*xb+w*w*xb+8*xb*xb-3*w*xb*xb)/(8*pow(1+u,2));
double e = 1/(8*pow(1+u,3))*(3*w*w*(-64+94*w+40*w*w+3*pow(w,3)-32*xb-40*xb*w-10*w*w*xb-16*xb*xb+6*w*xb*xb)); 
double f = 1/(64*(1+u))*(3*(640*w-368*w*w-200*w*w*w-16*pow(w,4)+3*pow(w,5)-384*xb+320*w*xb+528*w*w*xb+112*pow(w,3)*xb-16*pow(w,4)*xb-256*xb*xb-48*w*xb*xb-224*pow(w,2)*pow(xb,2)+24*pow(w,3)*pow(xb,2)));
double g = 1/(64*(1-u))*(3*(-256*w+528*w*w-200*pow(w,3)-16*pow(w,4)+3*pow(w,5)+512*xb-1472*w*xb+528*pow(w,2)*xb+112*pow(w,3)*xb-16*pow(w,4)*xb+640*xb*xb-48*w*xb*xb-224*pow(w,2)*pow(xb,2)+24*pow(w,3)*pow(xb,2)));
double h = 9*pow(w,5)*log(ureg(u))/(4*pow(1+u,6));
double i = 9*pow(w,5)*log(ureg(u))/(2*pow(1+u,5));
double ii = 9*(-12+w)*pow(-2+w,2)*pow(w-2*xb,2)*log(ureg(u))/(16*pow(1-u,4));
double j = 9*(-12+w)*pow(-2+w,2)*pow(w-2*xb,2)*log(ureg(u))/(16*pow(1-u,3));
double k = (3*pow(w,3)*(-10+16*w+pow(w,2)+8*xb-2*w*xb-2*pow(xb,2))*log(ureg(u)))/(8*pow(1+u,3));
double l = (3*pow(w,3)*(-10+16*w+7*pow(w,2)+8*xb-2*w*xb-2*pow(xb,2))*log(ureg(u)))/(8*pow(1+u,4));
double m = 1/(64*pow(1+u,2))*(3*w*(-144*w+208*pow(w,2)+16*pow(w,3)+pow(w,4)-64*xb-80*w*xb-16*pow(w,2)*xb-8*pow(w,3)*xb+48*xb*xb-96*w*xb*xb+16*pow(w,2)*pow(xb,2))*log(ureg(u)));
double n = 1/(64*pow(1-u,2))*(3*(-256*w+624*pow(w,2)-304*pow(w,3)+16*pow(w,4)+pow(w,5)+512*xb-1856*w*xb+944*pow(w,2)*xb-16*pow(w,3)*xb-8*pow(w,4)*xb+1024*xb*xb-464*w*xb*xb-96*pow(w,2)*pow(xb,2)+16*pow(w,3)*pow(xb,2))*log(ureg(u)));

double rem = -a + b - c +cc - d - e + f + g - h +i -ii +j  +k -l -m +n;

return rem;
}

double EvtVubAC::f(double w) {
std::vector<double> vars(11);
vars[1] = w;      
for (int j=3;j<11;j++) {vars[j] = gvars[j];}
  if (w != 1)
        return log(w)/(1-w);
                else
                return -1;
}

double EvtVubAC::Lambda2(double x, const double alphaSmZ) {
std::vector<double> vars(11);
for (int j=3;j<11;j++) {vars[j] = gvars[j];}
double alphaSmB =  0.22*alphaSmZ/0.1189;
double func = (1/beta0)*(1/log(mB*mB/x)+x/(x-mB*mB))-alphaSmB;
return func;
}

double EvtVubAC::FindRoot(const double alphaSmZ){
std::vector<double> vars(11);
for (int j=3;j<11;j++) {vars[j] = gvars[j];}
   double root;
   const double precision=1e-8;
   Bisect(0.0,1.0, precision, root, alphaSmZ);
return root;
}

int EvtVubAC::Bisect(double x1,double x2, double precision,double& root, const double alphaSmZ){
std::vector<double> vars(11);

for (int j=3;j<11;j++) {vars[j] = gvars[j];}

    if( Lambda2(x1,alphaSmZ)*Lambda2(x2,alphaSmZ) > 0 ){
        root = 0;
        return 0;

    } else {

        double x = 0.5*(x1+x2);

        if( fabs(Lambda2(x,alphaSmZ)) < precision){
            root = x;
            return 1;
        } else {

            if( Lambda2(x1,alphaSmZ)*Lambda2(x,alphaSmZ) < 0 ){
                return Bisect(x1,x,precision,root,alphaSmZ);

                } else {
                return Bisect(x,x2,precision,root, alphaSmZ);

            }
        }
    }
}

//Bi-Linear interpolation function for sigma()

double EvtVubAC::Sigma(double x1, double x2){
double ans;
int j = 0;
int k = 0;
int JMAX = 20;
int KMAX = 6282;

 if (x1 < 0.04 | x1 > 1.0 | x2 > 0.9981306360766614) {

        cout<<"Input variables are not in range"<<endl;
        return 0;
        }

        else{

 
double sigma[6283][21] = {{1.4165575231667025e-6,2.367068423885654e-6,3.010516455581869e-6,3.5037825936986625e-6,3.929518324374288e-6,4.306057170491293e-6,4.670305737607004e-6,5.03601978363166e-6,5.38081382734055e-6,5.706111094422232e-6,6.01592741932564e-6,6.312683745642994e-6,6.599149887344445e-6,6.876589598409881e-6,7.146140172115845e-6,7.408228896739411e-6,7.66381903520912e-6,7.914216132923142e-6,8.158375083092094e-6,8.387923687779773e-6,8.609047991600152e-6},
{1.4242950283096505e-6,2.3821813865451333e-6,3.0321094979724177e-6,3.531463105585163e-6,3.963281819193405e-6,4.345928764350666e-6,4.716578534159503e-6,5.0891092458471885e-6,5.440882358124266e-6,5.773300334146699e-6,6.090393611799158e-6,6.394582544259559e-6,6.6886559040585555e-6,6.973876196346317e-6,7.251379536127028e-6,7.521582534359883e-6,7.78545760383978e-6,8.044322886507219e-6,8.297093782815202e-6,8.535252273580483e-6,8.76506526572483e-6},
{1.432085473265309e-6,2.397426211753438e-6,3.053927960769999e-6,3.559478172452427e-6,3.997507657500483e-6,4.386409405362107e-6,4.763630567689123e-6,5.143175144213434e-6,5.5021483329791995e-6,5.841932217571044e-6,6.166572855026258e-6,6.478490721190443e-6,6.780495077370961e-6,7.073848449513044e-6,7.359687275376904e-6,7.638419489154442e-6,7.911031108690893e-6,8.178859267303823e-6,8.440787940213002e-6,8.688163613340468e-6,8.92736042107122e-6},
{1.439929354714352e-6,2.41280463514272e-6,3.0759756040991857e-6,3.5878345116181944e-6,4.0322066625519e-6,4.427515357355928e-6,4.811485212210924e-6,5.198250042510372e-6,5.564655974117598e-6,5.912066071547593e-6,6.244545266975116e-6,6.5645198876533405e-6,6.874832084123841e-6,7.176767831207023e-6,7.471508054632459e-6,7.759532156090581e-6,8.04198240629201e-6,8.32045326864888e-6,8.594180689511984e-6,8.854977185824032e-6,9.110250789357704e-6},
{1.4478271762507601e-6,2.4283184286282795e-6,3.098256291022933e-6,3.6165390675423683e-6,4.067390102434151e-6,4.469263755477156e-6,4.860167832347213e-6,5.254372135627978e-6,5.6284672051347425e-6,5.9838160854326365e-6,6.3245497730126735e-6,6.653205576198729e-6,6.972878946209313e-6,7.285309002010701e-6,7.592510371689441e-6,7.896411617922357e-6,8.20063859130551e-6,8.510772078503667e-6,8.832168193219429e-6,9.165813151304237e-6,9.53285861473224e-6},
{1.4557794485384492e-6,2.4439694016732532e-6,3.1207739929456703e-6,3.6455990425662466e-6,4.103069949395984e-6,4.511674486770287e-6,4.9097162595434805e-6,5.31163173249103e-6,5.693833505594434e-6,6.057899920792941e-6,6.40853743177932e-6,6.749486714584406e-6,7.086268724196642e-6,7.425114172566452e-6,7.775933736046638e-6,8.153858881648055e-6,8.583979262125893e-6,9.104919794810385e-6,9.771190049418475e-6,0.000010655316056335114,0.000011879449548606903},
{1.4637866894434715e-6,2.4597594026488963e-6,3.1435328023270215e-6,3.675022094200968e-6,4.139261015606768e-6,4.554785482753721e-6,4.960261093796092e-6,5.370505023603311e-6,5.762353786846746e-6,6.139117526304596e-6,6.509469970691759e-6,6.885255799616473e-6,7.287458092501649e-6,7.749887299160317e-6,8.32885760857551e-6,9.113946680584014e-6,0.000010246567374771375,0.000011937444274020002,0.000014487810062278417,0.000018317257226721972,0.000024019460747614908},
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{-24.469128158525564,-27.863286081526894,-27.660425552428933,-26.842917884292547,-26.024618843541248,-25.25125552568352,-24.682732226443477,-24.27170086168917,-23.863047272141557,-23.489982247294392,-23.14979713590583,-22.81788499938557,-22.507570082205348,-22.22174504940631,-21.956983122974634,-21.710775965475477,-21.480732797528617,-21.26486784289591,-21.062028371961787,-20.84449250070611,-20.627299039741047},
{-24.538233355648117,-27.941587408538908,-27.738011801498942,-26.917738710384583,-26.096872879366856,-25.32110517070396,-24.751040379574988,-24.33844407624565,-23.92851169826463,-23.554593281063717,-23.21329077251721,-22.880284167651553,-22.569031166029163,-22.28237270034151,-22.016829972621053,-21.76990578189725,-21.53918385715224,-21.322688146319706,-21.11926225561183,-20.9010724737891,-20.683270695561077},
{-24.607535834860755,-28.020108658762183,-27.8158122364257,-26.99276338823256,-26.169321563793346,-25.39114094816614,-24.81953261292074,-24.40536530711688,-23.994148262951057,-23.61937501031207,-23.276948241109494,-22.942844327364583,-22.630651318177115,-22.343156659626402,-22.076831026177388,-21.829187380324584,-21.59778456413187,-21.38065650576027,-21.17664253700059,-20.957796571427025,-20.73938146571163},
{-24.67703616133076,-28.09885040053632,-27.89382740142173,-27.06799241848057,-26.24196536335512,-25.461363291949965,-24.888209325959906,-24.472464979917277,-24.059957419056445,-23.68432784214383,-23.34076991979964,-23.0055658473284,-22.692430885508657,-22.404097239661496,-22.13698659511283,-21.88862109114416,-21.656535258865915,-21.438773249275982,-21.23416953458218,-21.014665090478957,-20.795631511427928},
{-24.746734899963485,-28.177813207905274,-27.97205783420941,-27.143426296272082,-26.3148047447321,-25.53177261276869,-24.957070932316128,-24.539743523462676,-24.125939625315368,-23.74945217021741,-23.404756179312244,-23.068449068523478,-22.754370221111458,-22.46519478096161,-22.197297049569897,-21.948207212786656,-21.715436263300944,-21.49703868769575,-21.291843550396152,-21.071678313310258,-20.85202098474838},
{-24.81663261691574,-28.25699765110039,-28.05050407772069,-27.219065528566716,-26.387840182724176,-25.602369372965768,-25.026117854227778,-24.607201372040436,-24.192095354024787,-23.814748412463814,-23.468907394679263,-23.131494365865365,-22.816469694429543,-22.526449625904206,-22.257762749912217,-22.007946082449052, -21.774487921444234,-21.555453195178416,-21.349664952256717,-21.128836586896796,-20.908550107094925},
{-24.88672988206963,-28.336404305009637,-28.129166676750174,-27.294910618278664,-26.46107214744552,-25.673153977957554,-25.09535050415434,-24.67483894585166,-24.258425071486272,-23.880216964054853,-23.53322395379655,-23.194702105713077,-22.878729653835762,-22.587862102489453,-22.31838402309222,-22.06783805345185,-21.833690583822317,-21.614017086976673,-21.407634040690027,-21.1861402001814,-20.965219124918804},
{-24.95702726318268,-28.41603374108672,-28.208046173589537,-27.370962059532758,-26.53450110432459,-25.74412687594304,-25.16476929106284,-24.74265667324653,-24.324929237249307,-23.945858225924894,-23.597706217726227,-23.258072621247265,-22.94115044485079,-22.649432538542897,-22.379161227901932,-22.12788341025589,-21.893044561729766,-21.672730688005686,-21.465751135896426,-21.24358945764834,-21.022028209641576}};


double wreg[]= {0.04, 0.088, 0.136, 0.18400000000000002, 0.232, 0.27999999999999997,
       0.328, 0.376, 0.424, 0.472, 0.52, 0.5680000000000001, 
       0.6160000000000001, 0.664, 0.7120000000000001, 0.76, 0.808, 
	 0.8560000000000001, 0.904, 0.9520000000000001, 1.0}; 

double ularge[]={0., 0.000999525142261537, 0.0019980512340131984, 0.002995579273830762, 
       0.0039921102592925806, 0.00498764518697925, 0.00598218505247583, 
       0.006975730850371842, 0.007968283574262824, 0.008959844216751223, 
       0.009950413769447386, 0.010939993222970568, 0.011928583566949591, 
       0.012916185790024404, 0.013902800879846744, 0.014888429823081029, 
       0.015873073605405685, 0.016856733211513708, 0.01783940962511399, 
       0.018821103828932206, 0.019801816804711603, 0.020781549533214427, 
       0.02176030299422238, 0.022738078166538056, 0.0237148760279855, 
       0.024690697555411423, 0.025665543724686435, 0.026639415510705367, 
       0.02761231388738883, 0.028584239827683988, 0.029555194303565346, 
       0.03052517828603607, 0.03149419274512877, 0.03246223864990638, 
       0.033429316968463296, 0.03439542866792622, 0.035360574714455306, 
       0.036324756073245035, 0.03728797370852488, 0.03825022858356075, 
       0.03921152166065589, 0.0401718539011513, 0.04113122626542742, 
       0.04208963971290469, 0.043047095202044416, 0.04400359369035023, 
       0.044959136134368416, 0.04591372348968936, 0.046867356710948216, 
       0.04782003675182578, 0.04877176456505006, 0.04972254110239649, 
       0.05067236731468905, 0.05162124415180169, 0.052569172562658695, 
       0.053516153495236085, 0.05446218789656199, 0.05540727671271839, 
       0.056351420888841375, 0.057294621369122334, 0.05823687909680919, 
       0.059178195014206625, 0.060118570062677845, 0.061058005182645037, 
       0.061996501313590135, 0.06293405939405661, 0.06387068036164922, 
       0.06480636515303595, 0.0657411147039485, 0.06667492994918323, 
       0.067607811822602, 0.06853976125713368, 0.06947077918477418, 
       0.07040086653658806, 0.07133002424270929, 0.07225825323234214, 
       0.07318555443376207, 0.07411192877431683, 0.07503737718042691, 
       0.07596190057758734, 0.07688549989036764, 0.07780817604241341, 
       0.07872992995644712, 0.07965076255426873, 0.08057067475675705, 
       0.08148966748387021, 0.08240774165464715, 0.0833248981872079, 
       0.08424113799875499, 0.08515646200557414, 0.08607087112303513, 
       0.0869843662655928, 0.0878969483467883, 0.08880861827924913, 
       0.08971937697469112, 0.09062922534391848, 0.09153816429682515, 
       0.09244619474239557, 0.09335331758870569, 0.09425953374292384, 
       0.09516484411131154, 0.09606924959922447, 0.09697275111111336, 
       0.09787534955052513, 0.09877704582010327, 0.09967784082158937, 
       0.10057773545582349, 0.1014767306227452, 0.10237482722139479, 
       0.10327202614991393, 0.10416832830554645, 0.10506373458463925, 
       0.10595824588264358, 0.10685186309411554, 0.10774458711271706, 
       0.10863641883121689, 0.10952735914149136, 0.11041740893452556, 
       0.1113065691004137, 0.11219484052836048, 0.113082224106682, 
       0.11396872072280606, 0.11485433126327382, 0.11573905661374018, 
       0.1166228976589746, 0.11750585528286273, 0.11838793036840611, 
       0.11926912379772414, 0.12014943645205434, 0.1210288692117536, 
       0.12190742295629853, 0.12278509856428699, 0.12366189691343843, 
       0.12453781888059534, 0.12541286534172336, 0.1262870371719128, 
       0.12716033524537929, 0.12803276043546474, 0.12890431361463794, 
       0.12977499565449568, 0.1306448074257638, 0.13151374979829733, 
       0.13238182364108242, 0.1332490298222363, 0.13411536920900857, 
       0.1349808426677821, 0.13584545106407353, 0.13670919526253478, 
       0.1375720761269531, 0.13843409452025268, 0.13929525130449505, 
       0.1401555473408801, 0.14101498348974706, 0.141873560610575, 
       0.14273127956198417, 0.14358814120173635, 0.1444441463867362, 
       0.1452992959730317, 0.14615359081581536, 0.14700703176942476, 
       0.1478596196873435, 0.14871135542220237, 0.14956223982577965, 
       0.15041227374900246, 0.15126145804194713, 0.1521097935538407, 
       0.15295728113306095, 0.15380392162713807, 0.1546497158827549, 
       0.15549466474574802, 0.15633876906110877, 0.15718202967298356, 
       0.15802444742467525, 0.15886602315864384, 0.15970675771650733, 
       0.16054665193904216, 0.16138570666618468, 0.1622239227370318, 
       0.1630613009898414, 0.16389784226203374, 0.16473354739019208, 
       0.1655684172100632, 0.16640245255655883, 0.1672356542637562, 
       0.16806802316489855, 0.1688995600923966, 0.1697302658778289, 
       0.17056014135194286, 0.17138918734465547, 0.1722174046850543, 
       0.17304479420139818, 0.17387135672111798, 0.1746970930708177, 
       0.17552200407627494, 0.1763460905624421, 0.17716935335344708, 
       0.17799179327259362, 0.17881341114236304, 0.1796342077844143, 
       0.18045418401958513, 0.1812733406678928, 0.18209167854853503, 
       0.18290919847989073, 0.18372590127952082, 0.18454178776416885, 
       0.18535685874976227, 0.18617111505141282, 0.18698455748341758, 
       0.18779718685925983, 0.18860900399160963, 0.18942000969232464, 
       0.19023020477245134, 0.19103959004222526, 0.19184816631107227, 
       0.1926559343876092, 0.19346289507964443, 0.1942690491941792, 
       0.19507439753740796, 0.19587894091471936, 0.19668268013069712, 
       0.19748561598912073, 0.1982877492929661, 0.1990890808444069, 
       0.19988961144481487, 0.2006893418947604, 0.20148827299401428, 
       0.20228640554154742, 0.20308374033553256, 0.2038802781733442, 
       0.20467601985156025, 0.20547096616596217, 0.20626511791153612, 
       0.2070584758824735, 0.2078510408721722, 0.20864281367323678, 
       0.20943379507747983, 0.21022398587592217, 0.21101338685879434, 
       0.21180199881553674, 0.21258982253480097, 0.21337685880445012, 
       0.21416310841155983, 0.21494857214241914, 0.21573325078253125, 
       0.2165171451166138, 0.2173002559286007, 0.2180825840016417, 
       0.21886413011810424, 0.21964489505957363, 0.22042487960685375, 
       0.22120408453996832, 0.2219825106381612, 0.22276015867989762, 
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       0.22586298582436248, 0.2266367552335864, 0.2274097512408314, 
       0.22818197461913237, 0.2289534261407512, 0.22972410657717812, 
       0.23049401669913228, 0.23126315727656221, 0.2320315290786471, 
       0.23279913287379717, 0.23356596942965469, 0.23433203951309467, 
       0.2350973438902254, 0.2358618833263898, 0.23662565858616547, 
       0.23738867043336598, 0.2381509196310414, 0.23891240694147908, 
       0.23967313312620442, 0.24043309894598175, 0.2411923051608149, 
       0.24195075252994824, 0.24270844181186702, 0.24346537376429855, 
       0.24422154914421257, 0.24497696870782248, 0.24573163321058555, 
       0.24648554340720408, 0.24723870005162618, 0.24799110389704615, 
       0.24874275569590532, 0.2494936561998935, 0.25024380615994857, 
       0.250993206326258, 0.2517418574482596, 0.2524897602746421, 
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       0.2687558095823497, 0.26948670653580487, 0.27021687293937857, 
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       0.2731302476479759, 0.27385677224060123, 0.2745825706536297, 
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       0.281800774231195, 0.2825186324145037, 0.2832357730805096, 
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       0.29883277983369727, 0.2995336140991832, 0.30023374786320023, 
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       0.30302729189746225, 0.3037239336426808, 0.30441987907696, 
       0.3051151288962799, 0.3058096837959252, 0.3065035444704858, 
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       0.31134118908994646, 0.3120295208858911, 0.31271716467689936, 
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       0.3154608735348283, 0.3161450876025921, 0.3168286177811924, 
       0.3175114647541937, 0.31819362920447714, 0.31887511181424144, 
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       0.32159423746822724, 0.32227232108453296, 0.32294972693921553, 
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       0.9968335490062404, 0.9968367139536204, 0.996839875737556, 
       0.9968430343612089, 0.9968461898277381, 0.9968493421402992, 
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       0.9977974796348638, 0.9977996811093451, 0.9978018803833973, 
       0.9978040774592198, 0.9978062723390098, 0.9978084650249622, 
       0.99781065551927, 0.9978128438241235, 0.9978150299417113, 
       0.9978172138742196, 0.9978193956238326, 0.9978215751927318, 
       0.9978237525830973, 0.9978259277971062, 0.9978281008369341, 
       0.997830271704754, 0.997832440402737, 0.9978346069330518, 
       0.9978367712978652, 0.9978389334993414, 0.9978410935396429, 
       0.9978432514209298, 0.9978454071453601, 0.9978475607150896, 
       0.9978497121322721, 0.997851861399059, 0.9978540085175998, 
       0.9978561534900414, 0.9978582963185293, 0.9978604370052062, 
       0.997862575552213, 0.9978647119616882, 0.9978668462357685, 
       0.9978689783765882, 0.9978711083862795, 0.9978732362669726, 
       0.9978753620207953, 0.9978774856498738, 0.9978796071563315, 
       0.9978817265422902, 0.9978838438098694, 0.9978859589611864, 
       0.9978880719983565, 0.9978901829234927, 0.9978922917387063, 
       0.997894398446106, 0.9978965030477986, 0.997898605545889, 
       0.9979007059424798, 0.9979028042396713, 0.9979049004395619, 
       0.9979069945442481, 0.9979090865558241, 0.9979111764763818, 
       0.9979132643080114, 0.9979153500528009, 0.9979174337128359, 
       0.9979195152902003, 0.9979215947869758, 0.997923672205242, 
       0.9979257475470765, 0.9979278208145546, 0.9979298920097497, 
       0.9979319611347331, 0.9979340281915742, 0.9979360931823399, 
       0.9979381561090954, 0.9979402169739038, 0.997942275778826, 
       0.997944332525921, 0.9979463872172454, 0.9979484398548543, 
       0.9979504904408002, 0.9979525389771339, 0.997954585465904, 
       0.9979566299091572, 0.997958672308938, 0.9979607126672888, 
       0.9979627509862501, 0.9979647872678604, 0.997966821514156, 
       0.9979688537271714, 0.9979708839089386, 0.9979729120614882, 
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       0.9980465455363937, 0.9980484980632444, 0.9980504486384952, 
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       0.9980582314624865, 0.9980601723089603, 0.9980621112155091, 
       0.9980640481840721, 0.9980659832165863, 0.9980679163149869, 
       0.9980698474812071, 0.998071776717178, 0.9980737040248291, 
       0.9980756294060876, 0.9980775528628794, 0.9980794743971275, 
       0.9980813940107539, 0.9980833117056783, 0.9980852274838183, 
       0.99808714134709, 0.9980890532974072, 0.9980909633366819, 
       0.9980928714668245, 0.9980947776897429, 0.9980966820073436, 
       0.9980985844215309, 0.9981004849342074, 0.9981023835472739, 
       0.9981042802626288, 0.9981061750821689, 0.9981080680077893, 
       0.998109959041383, 0.998111848184841, 0.9981137354400527, 
       0.9981156208089054, 0.9981175042932844, 0.9981193858950734, 
       0.9981212656161542, 0.9981231434584065, 0.9981250194237082, 
       0.9981268935139355, 0.9981287657309624, 0.9981306360766614};


                //Find the correct [j][k] element for a given x1 and x2

                if ( x1==wreg[JMAX] ){j=JMAX;}
                        else{
                for (int y=0; y<=JMAX; y++){
                        if ( (wreg[y] <= x1) && ( x1 < wreg[y+1]) ) { j=y; break;}
                }
                        }
 		if ( x2>ularge[KMAX-1] ){k=KMAX;}
                        else{
                for (int z=0; z<=KMAX; z++){
                        if ( (ularge[z] <= x2) && ( x2 < ularge[z+1]) ) { k=z; break;}
                }
                        }

                //Calculate sigma() using Bi-Linear interpolaion

                double y0, y1, y2, y3;
                double t, u;

                        if ( k==KMAX) {
                        ans =  sigma[k][j];
                        }

                else {
                y0 =  sigma[k][j];
                y1 =  sigma[k][j+1];
                y2 =  sigma[k+1][j+1];
                y3 =  sigma[k+1][j];

                t = (x1-wreg[j])/(wreg[j+1]-wreg[j]);
                u = (x2-ularge[k])/(ularge[k+1]-ularge[k]);

                ans = (1-t)*(1-u)*y0+t*(1-u)*y1 +t*u*y2+(1-t)*u*y3;
                }
        }
return ans;
}