num_collect::functions::impl::gamma_lanczos< Real > Class Template Reference

Class to calculate gamma function using approximation derived by Lanczos [20]. More...

#include <num_collect/functions/impl/gamma_lanczos.h>

Collaboration diagram for num_collect::functions::impl::gamma_lanczos< Real >:

Static Public Member Functions
template<typename T > requires ( std::is_same_v<T, Real> || std::is_same_v<T, std::complex<Real>>)
static constexpr auto	gamma (T x) -> T
	Calculate a value of gamma function.
static constexpr auto	log_gamma (Real x) -> Real
	Calculate a natural logarithm of a value of gamma function.

Static Public Attributes
static constexpr std::array< Real, num_coeffs >	coeffs
	Coefficients.
static constexpr auto	constant = static_cast<Real>(0.999999999999997092)
	Constant term.
static constexpr std::size_t	num_coeffs = 14
	Number of coefficients.
static constexpr auto	rational
	Rational for parameter.
static constexpr auto	series_coeff = static_cast<Real>(2.5066282746310005)
	Coefficient for the series.

Detailed Description

template<base::concepts::real_scalar Real>
class num_collect::functions::impl::gamma_lanczos< Real >

Class to calculate gamma function using approximation derived by Lanczos [20].

Definition at line 38 of file gamma_lanczos.h.

Member Function Documentation

gamma()

template<base::concepts::real_scalar Real>

template<typename T >
requires ( std::is_same_v<T, Real> || std::is_same_v<T, std::complex<Real>>)

static constexpr auto num_collect::functions::impl::gamma_lanczos< Real >::gamma ( T x ) -> T

inlinestaticnodiscardconstexpr

Calculate a value of gamma function.

Template Parameters

T	Type of the argument.

Parameters

[in]

x

Argument.

Returns

Value of gamma function.

Definition at line 80 of file gamma_lanczos.h.

log_gamma()

template<base::concepts::real_scalar Real>

static constexpr auto num_collect::functions::impl::gamma_lanczos< Real >::log_gamma ( Real x ) -> Real

inlinestaticnodiscardconstexpr

Calculate a natural logarithm of a value of gamma function.

Parameters

[in]

x

Argument.

Returns

Natural logarithm of the value of gamma function.

Definition at line 99 of file gamma_lanczos.h.

Member Data Documentation

coeffs

template<base::concepts::real_scalar Real>

std::array<Real, num_coeffs> num_collect::functions::impl::gamma_lanczos< Real >::coeffs

staticconstexpr

Initial value:

{
        static_cast<Real>(57.1562356658629235),
        static_cast<Real>(-59.5979603554754912),
        static_cast<Real>(14.1360979747417471),
        static_cast<Real>(-0.491913816097620199),
        static_cast<Real>(0.339946499848118887e-4),
        static_cast<Real>(0.465236289270485756e-4),
        static_cast<Real>(-0.983744753048795646e-4),
        static_cast<Real>(0.158088703224912494e-3),
        static_cast<Real>(-0.210264441724104883e-3),
        static_cast<Real>(0.217439618115212643e-3),
        static_cast<Real>(-0.164318106536762890e-3),
        static_cast<Real>(0.844182239838527433e-4),
        static_cast<Real>(-0.261908384015814087e-4),
        static_cast<Real>(0.368991826295316234e-5)}

Coefficients.

Definition at line 44 of file gamma_lanczos.h.

constant

template<base::concepts::real_scalar Real>

auto num_collect::functions::impl::gamma_lanczos< Real >::constant = static_cast<Real>(0.999999999999997092)

staticconstexpr

Constant term.

Definition at line 61 of file gamma_lanczos.h.

num_coeffs

template<base::concepts::real_scalar Real>

std::size_t num_collect::functions::impl::gamma_lanczos< Real >::num_coeffs = 14

staticconstexpr

Number of coefficients.

Definition at line 41 of file gamma_lanczos.h.

rational

template<base::concepts::real_scalar Real>

auto num_collect::functions::impl::gamma_lanczos< Real >::rational

staticconstexpr

Initial value:

=
        static_cast<Real>(671) / static_cast<Real>(128)

Rational for parameter.

Definition at line 67 of file gamma_lanczos.h.

series_coeff

template<base::concepts::real_scalar Real>

auto num_collect::functions::impl::gamma_lanczos< Real >::series_coeff = static_cast<Real>(2.5066282746310005)

staticconstexpr

Coefficient for the series.

Definition at line 64 of file gamma_lanczos.h.

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The documentation for this class was generated from the following file:

• include/num_collect/functions/impl/gamma_lanczos.h