TLi2 Class Reference

#include <TLi2.h>

List of all members.

Public Member Functions
	TLi2 ()
	~TLi2 ()
Static Public Member Functions
static double	Eval (const double &x)
static double	Li2Cern (const double &x)
static double	Li2My (const double &x)

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Detailed Description

Definition at line 4 of file TLi2.h.

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Constructor & Destructor Documentation

TLi2::TLi2

(

)

[inline]

Definition at line 6 of file TLi2.h.

{};

TLi2::~TLi2

(

)

[inline]

Definition at line 7 of file TLi2.h.

{};

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Member Function Documentation

static double TLi2::Eval

(

const double &

x

)

[inline, static]

Definition at line 8 of file TLi2.h.

References Li2My().

Referenced by TPiKFun::Eval_even(), TMuKFun::Eval_even(), TPiKFun::Eval_even_odd(), TMuKFun::Eval_even_odd(), TPiKFun::Eval_odd(), TMuKFun::Eval_odd(), TPiKFun::Eval_odd_ultra(), TMuKFun::Eval_odd_ultra(), TKFun::kfun(), and TEKFun::kfun().

                                     {
    return Li2My(x);
  };

double TLi2::Li2Cern

(

const double &

x

)

[static]

Definition at line 46 of file TLi2.C.

References genRecEmupikp::i, M_PI, one, s, t(), and zero.

                                   {
  static long double pi3  = M_PI*M_PI/3; 
  static long double pi6  = M_PI*M_PI/6;
  static long double pi12 = M_PI*M_PI/12;
  static long double c[20]={0.42996693560813697L, 0.40975987533077105L,
                            -0.01858843665014592L, 0.00145751084062268L,
                            -0.00014304184442340L, 0.00001588415541880L,
                            -0.00000190784959387L, 0.00000024195180854L,
                            -0.00000003193341274L, 0.00000000434545063L,
                            -0.00000000060578480L, 0.00000000008612098L,
                            -0.00000000001244332L, 0.00000000000182256L,
                            -0.00000000000027007L, 0.00000000000004042L,
                            -0.00000000000000610L, 0.00000000000000093L,
                            -0.00000000000000014L, 0.00000000000000002L};
  long double h,t,y,s,l,ll,a,alfa,b0,b1,b2,*cp;
  static long double two = 2L, one=1L, half=0.5L, zero = 0L;
  if(x == one){
    h = pi6;
  }else if(x == -one){
    h = -pi12;
  }else{
    t = -x;
    if(t <= -two){
      y =-one/(one + t);
      s = one;
      l = log(-t);
      ll = log(one + one/t);
      a =-pi3 + half*(l*l - ll*ll);
    }else if(t < -one){
      y =-one-t;
      s =-one;
      a = log(-t);
      a =-pi6 + a*(a + log(one + one/t));
    }else if(t <= -half){
      y =-(one+t)/t;
      s = one;
      a = log(-t);
      a =-pi6 + a*(-half*a+log(one + t));
    }else if(t < zero){
      y =-t/(one + t);
      s =-one;
      a = half*log(one + t)*log(one + t);
    }else if(t <= one){
      y = t;
      s = one;
      a = zero;
    }else{
      y = one/t;
      s =-one;
      a = pi6 + half*log(t)*log(t);
    }
    h    = y + y - one;
    alfa = h + h;
    b1   = zero;
    b2   = zero;
    cp   = &c[19];
    for(int i = 20; i; i--,cp--){
      b0 = *cp + alfa*b1 - b2;
      b2 = b1;
      b1 = b0;
    }
    h    = -(s*(b0-h*b2)+a);
  }
  //  std::cout<<"TLI2 "<<x<<" "<<h<<std::endl;
  return h;
}

double TLi2::Li2My

(

const double &

x

)

[static]

Definition at line 113 of file TLi2.C.

References H00, H01, H02, H03, H04, H05, H06, H07, H08, H09, H10, H11, H12, H13, H14, H15, H16, H17, H18, H19, K00, K01, K02, K03, K04, K05, K06, K07, K08, K09, K10, K11, K12, K13, K14, K15, K16, K17, K18, K19, M_PI, one, s, t(), and zero.

Referenced by Eval().

                                 {
  const double  pi3  =  M_PI*M_PI/3; 
  const double  pi6  =  M_PI*M_PI/6;
  const double mpi12 = -M_PI*M_PI/12;
  const double two = 2, one=1, half=0.5, zero = 0;
  static double t,h,y,s,a,l,ll;
  if ( x ==  one) return  pi6;
  if ( x == -one) return mpi12;
  t = -x;
  if(t <= -two){
    // 2 < x < +inf
    y =-one/(one + t);
    s = one;
    l = log(-t);
    ll= log(one + one/t);
    a =-pi3 + half*(l*l - ll*ll);
  }else if(t < -one){
    // 1 < x < 2
    y =-one-t;
    s =-one;
    a = log(-t);
    a =-pi6 + a*(a + log(one + one/t));
  }else if(t <= -half){
    // 0.5 < x < 1
    y =-(one+t)/t;
    s = one;
    a = log(-t);
    a =-pi6 + a*(-half*a+log(one + t));
  }else if(t < zero){
    // 0 < x < 0.5
    h = 4*x - one;
    // minimax approximation
    return 
      H00+(H01+(H02+(H03+(H04+(H05+(H06+(H07+(H08+(H09+(H10+(H11+(H12+(H13+(H14+(H15+(H16+(H17+(H18+H19*h)*h)*h)*h)*h)*h)*h)*h)*h)*h)*h)*h)*h)*h)*h)*h)*h)*h)*h;
  }else if(t <= one){
    // -1 < x < 0
    y = t;
    s = one;
    a = zero;
  }else{
    // -inf < x < -1
    y = one/t;
    s =-one;
    a = log(t);
    a = pi6 + half*a*a;
  }
  h = -two*y + one;
  // minimax approximation in  -1 < x < 0 range
  return
    (K00+(K01+(K02+(K03+(K04+(K05+(K06+(K07+(K08+(K09+(K10+(K11+(K12+(K13+(K14+(K15+(K16+(K17+(K18+K19*h)*h)*h)*h)*h)*h)*h)*h)*h)*h)*h)*h)*h)*h)*h)*h)*h)*h)*h)*s-a;
}

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