special_generic.h File Reference

#include <cmath>
#include "scalar.h"

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Functions
double	Ei (double x)
	Computes the exponential integral function Ei(x).
double	Li2 (double x)
	Computes the dilogarithm function Li2(x).
scalar_t	CLi2 (scalar_t x)
	Computes the complex dilogarithm function.
scalar_t	CLi3 (scalar_t x)
	Computes the complex trilogarithm function.
scalar_t	CLi4 (scalar_t x)
	Computes the complex quadrilogarithm function.
double	Li3 (double x)
	Computes the trilogarithm function Li3(x).
double	Cl2 (double x)
	Computes the Clausen function Cl2(x).
double	Cl3 (double x)
	Computes the Clausen function Cl3(x).
double	I0 (double x)
double	I1 (double x)
double	K0 (double x)
double	K1 (double x)
double	K2 (double x)
double	K3 (double x)
double	K4 (double x)
double	Lbessel (double x)
double	Mbessel (double x)
double	Nbessel (double x)
double	K0exp (double x, double z)
double	K1exp (double x, double z)
double	K2exp (double x, double z)
double	kron (int x, int y)
	Kronecker delta function.
template<typename T >
int	sgn (T val)
	Returns the sign of a value.
template<class T >
std::enable_if_t< not std::numeric_limits< T >::is_integer, bool >	fpeq (T x, T y, std::size_t n)
	Compares two floating point numbers with a given precision.

Function Documentation

Cl2()

double Cl2

(

double

x

)

Computes the Clausen function Cl2(x).

Parameters

x	Input value.

Returns

Result of the Clausen function.

Definition at line 1333 of file polylog.cpp.

Cl3()

double Cl3

(

double

x

)

Computes the Clausen function Cl3(x).

Parameters

x	Input value.

Returns

Result of the Clausen function.

Definition at line 1337 of file polylog.cpp.

CLi2()

scalar_t CLi2

(

scalar_t

x

)

Computes the complex dilogarithm function.

Parameters

x	Complex input value.

Returns

Complex dilogarithm result.

Definition at line 1312 of file polylog.cpp.

CLi3()

scalar_t CLi3

(

scalar_t

x

)

Computes the complex trilogarithm function.

Parameters

x	Complex input value.

Returns

Complex trilogarithm result.

Definition at line 1320 of file polylog.cpp.

CLi4()

scalar_t CLi4

(

scalar_t

x

)

Computes the complex quadrilogarithm function.

Parameters

x	Complex input value.

Returns

Complex quadrilogarithm result.

Definition at line 1326 of file polylog.cpp.

Ei()

double Ei

(

double

x

)

Computes the exponential integral function Ei(x).

Parameters

x	Input value.

Returns

Result of the exponential integral.

Definition at line 106 of file exponential_integral.cpp.

fpeq()

template<class T >

std::enable_if_t< not std::numeric_limits< T >::is_integer, bool > fpeq	(	T	x,
		T	y,
		std::size_t	n
	)

Compares two floating point numbers with a given precision.

Template Parameters

T	Floating point type.

Parameters

x	First number.
y	Second number.
n	Number of machine epsilons allowed.

Returns

True if numbers are approximately equal.

Definition at line 107 of file special_generic.h.

I0()

double I0

(

double

x

)

Definition at line 7 of file special_generic.cpp.

I1()

double I1

(

double

x

)

Definition at line 28 of file special_generic.cpp.

K0()

double K0

(

double

x

)

Definition at line 51 of file special_generic.cpp.

K0exp()

double K0exp	(	double	x,
		double	z
	)

Definition at line 124 of file special_generic.cpp.

K1()

double K1

(

double

x

)

Definition at line 66 of file special_generic.cpp.

K1exp()

double K1exp	(	double	x,
		double	z
	)

Definition at line 140 of file special_generic.cpp.

K2()

double K2

(

double

x

)

Definition at line 81 of file special_generic.cpp.

K2exp()

double K2exp	(	double	x,
		double	z
	)

Definition at line 154 of file special_generic.cpp.

K3()

double K3

(

double

x

)

Definition at line 88 of file special_generic.cpp.

K4()

double K4

(

double

x

)

Definition at line 95 of file special_generic.cpp.

kron()

double kron	(	int	x,
		int	y
	)

Kronecker delta function.

Parameters

x	First integer.
y	Second integer.

Returns

1 if x == y, else 0.

Definition at line 3 of file special_generic.cpp.

Lbessel()

double Lbessel

(

double

x

)

Definition at line 102 of file special_generic.cpp.

Li2()

double Li2

(

double

x

)

Computes the dilogarithm function Li2(x).

Parameters

x	Input value.

Returns

Result of the dilogarithm.

Definition at line 1257 of file polylog.cpp.

Li3()

double Li3

(

double

x

)

Computes the trilogarithm function Li3(x).

Parameters

x	Input value.

Returns

Result of the trilogarithm.

Definition at line 1267 of file polylog.cpp.

Mbessel()

double Mbessel

(

double

x

)

Definition at line 109 of file special_generic.cpp.

Nbessel()

double Nbessel

(

double

x

)

Definition at line 116 of file special_generic.cpp.

sgn()

template<typename T >

int sgn

(

T

val

)

Returns the sign of a value.

Template Parameters

T	Type (must be comparable).

Parameters

val	Value to check.

Returns

-1, 0, or 1 depending on sign of val.

Definition at line 93 of file special_generic.h.