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Math.cc
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// -*- C++ -*-
#include <iostream>
#include "Math.h"
namespace Herwig {
namespace Math {
using ThePEG::Complex;
using std::cout;
using std::endl;
namespace {
inline Complex Li2Prod(Complex y,Complex y2)
{
static const double a1 =-0.250000000000000e0,a2 =-0.111111111111111e0;
static const double a3 =-0.010000000000000e0,a4 =-0.017006802721088e0;
static const double a5 =-0.019444444444444e0,a6 =-0.020661157024793e0;
static const double a7 =-0.021417300648069e0,a8 =-0.021948866377231e0;
static const double a9 =-0.022349233811171e0,a10 =-0.022663689135191e0;
return y*(1.+a1*y*(1.+a2*y*(1.+a3*y2*(1.+a4*y2*(1.+a5*y2*
(1.+a6*y2*(1.+a7*y2*(1.+a8*y2*(1.+a9*y2*(1.+a10*y2))))))))));
}
inline long double Li2Prod(long double y,long double y2)
{
static const long double a1 =-0.250000000000000e0,a2 =-0.111111111111111e0;
static const long double a3 =-0.010000000000000e0,a4 =-0.017006802721088e0;
static const long double a5 =-0.019444444444444e0,a6 =-0.020661157024793e0;
static const long double a7 =-0.021417300648069e0,a8 =-0.021948866377231e0;
static const long double a9 =-0.022349233811171e0,a10 =-0.022663689135191e0;
return y*(1.+a1*y*(1.+a2*y*(1.+a3*y2*(1.+a4*y2*(1.+a5*y2*
(1.+a6*y2*(1.+a7*y2*(1.+a8*y2*(1.+a9*y2*(1.+a10*y2))))))))));
}
}
Complex Li2(Complex x)
{
Complex z;
static double zeta2= 1.644934066848226e0;
double xr(real(x)),xi(imag(x)),r2(xr*xr+xi*xi);
if(r2>1.&&xr/r2>0.5)
{
z=-log(1./x);
return Li2Prod(z,z*z)+zeta2-log(x)*log(1.-x)+0.5*log(x)*log(x);
}
else if (r2>1.&&(xr/r2)<=0.5)
{
z=-log(1.-1./x);
return -Li2Prod(z,z*z)-zeta2-0.5*pow(log(-x),2);
}
else if(r2==1.&&xi==0.)
{
if(xr>0){return zeta2;}
else{return -0.5*zeta2;}
}
else if(r2<=1.&&xr>0.5)
{
z=-log(x);
return -Li2Prod(z,z*z)+zeta2-log(x)*log(1.-x);
}
else
{
z=-log(1.-x);
return Li2Prod(z,z*z);
}
}
long double ReLi2(long double x)
{
long double z;
static long double zeta2= 1.644934066848226e0;
long double output;
if(x>1.&&x<2.)
{
z=-log(1./x);
output= Li2Prod(z,z*z)+zeta2-log(x)*log(x-1.)+0.5*log(x)*log(x);
}
else if (x>1.||x<-1.)
{
z=-log(1.-1./x);
if(x<-1){output= -Li2Prod(z,z*z)-zeta2-0.5*pow(log(-x),2);}
else{output= -Li2Prod(z,z*z)-0.5*pow(log(x),2)+2.*zeta2;}
}
else if(x== 1.){output= zeta2;}
else if(x==-1.){output= -0.5*zeta2;}
else if(x>0.5)
{
z=-log(x);
output= -Li2Prod(z,z*z)+zeta2-log(x)*log(1.-x);
}
else
{
z=-log(1.-x);
output= Li2Prod(z,z*z);
}
return output;
}
}
}

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