gamma.hpp File Reference

#include <concepts>
#include <type_traits>
#include <randlib/math/constants.hpp>
#include <randlib/math/functions.hpp>
#include <randlib/math/beta.hpp>
#include <randlib/math/quadrature.hpp>
#include <randlib/math/roots.hpp>
#include <randlib/math/optimize.hpp>
#include <randlib/math/special_functions.hpp>

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Classes
struct	randlib::math::IncompleteGamma< Real >

Namespaces
namespace	randlib
namespace	randlib::math
	Beta-related functions.

Functions
template<std::floating_point Real>
Real	randlib::math::factorial (Real n)
	Calculate n! using table values for small n <= 255 and built-in gamma function for large n > 255.
template<std::integral Integer>
long double	randlib::math::factorial (Integer n)
template<std::floating_point Real = long double>
Real	randlib::math::doubleFactorial (int n)
	Calculate n!!
template<std::floating_point Real = long double>
Real	randlib::math::lfact (size_t n)
	Calculate log(n!) using table values for small n <= 255 and built-in lgamma function for large n > 255.
template<std::floating_point Real = long double>
Real	randlib::math::ldfact (size_t n)
	ldoublefact
template<std::floating_point Real = long double>
Real	randlib::math::binom (size_t n, size_t k)
	Calculate binomial coefficient.
template<std::floating_point Real = double>
Real	randlib::math::stirlingError (size_t n)
template<std::floating_point Real = double>
Real	randlib::math::logFactorialRatio (size_t x, size_t y)
template<std::floating_point Real>
Real	randlib::math::bd0 (std::type_identity_t< Real > x, Real m)
	Deviance term of the saddle-point expansions of Poisson and binomial probabilities (C.
template<std::floating_point Real>
Real	randlib::math::digamma (Real x)
template<std::floating_point Real>
Real	randlib::math::digammamLog (Real x)
template<std::floating_point Real>
Real	randlib::math::trigamma (Real x)
template<std::floating_point Real>
Real	randlib::math::lpgamma (std::type_identity_t< Real > a, Real x, std::type_identity_t< Real > logA, std::type_identity_t< Real > lgammaA)
	Calculate logarithm of lower incomplete gamma function, accelerated by using precalculated value of log(a) and log(Γ(a))
template<std::floating_point Real>
Real	randlib::math::lpgamma (std::type_identity_t< Real > a, Real x, std::type_identity_t< Real > logX)
	Calculate logarithm of lower incomplete gamma function, accelerated by using precalculated value of log(x)
template<std::floating_point Real>
Real	randlib::math::lpgamma (std::type_identity_t< Real > a, Real x)
	Calculate logarithm of lower incomplete gamma function.
template<std::floating_point Real>
Real	randlib::math::pgamma (std::type_identity_t< Real > a, Real x, std::type_identity_t< Real > logA, std::type_identity_t< Real > lgammaA)
	Calculate lower regularized incomplete gamma function, accelerated by using precalculated value of log(a) and log(Γ(a))
template<std::floating_point Real>
Real	randlib::math::pgamma (std::type_identity_t< Real > a, Real x, std::type_identity_t< Real > logX)
	Calculate lower regularized incomplete gamma function, accelerated by using precalculated value of log(x)
template<std::floating_point Real>
Real	randlib::math::pgamma (std::type_identity_t< Real > a, Real x)
	Calculate lower regularized incomplete gamma function.
template<std::floating_point Real>
Real	randlib::math::lqgamma (std::type_identity_t< Real > a, Real x, std::type_identity_t< Real > logA, std::type_identity_t< Real > lgammaA)
	Calculate logarithm of upper incomplete gamma function, accelerated by using precalculated values of log(a) and log(Γ(a))
template<std::floating_point Real>
Real	randlib::math::lqgamma (std::type_identity_t< Real > a, Real x, std::type_identity_t< Real > logX)
	Calculate logarithm of upper incomplete gamma function, accelerated by using precalculated value of log(x)
template<std::floating_point Real>
Real	randlib::math::lqgamma (std::type_identity_t< Real > a, Real x)
	Calculate logarithm of upper incomplete gamma function.
template<std::floating_point Real>
Real	randlib::math::qgamma (std::type_identity_t< Real > a, Real x, std::type_identity_t< Real > logA, std::type_identity_t< Real > lgammaA)
	Calculate upper regularized incomplete gamma function, accelerated by using precalculated values of log(a) and log(Γ(a))
template<std::floating_point Real>
Real	randlib::math::qgamma (std::type_identity_t< Real > a, Real x, std::type_identity_t< Real > logX)
	Calculate upper regularized incomplete gamma function, accelerated by using precalculated value of log(x)
template<std::floating_point Real>
Real	randlib::math::qgamma (std::type_identity_t< Real > a, Real x)
	Calculate upper regularized incomplete gamma function.
template<std::floating_point Real>
Real	randlib::math::factorialForSmallValue (int n)
	Get n! using product method with table.
template<std::floating_point Real>
Real	randlib::math::digammamLogForLargeX (Real x)
template<std::floating_point Real>
Real	randlib::math::log1pmx (Real t)
template<std::floating_point Real>
Real	randlib::math::logPrefactor (Real a, Real x, Real logX)
template<std::floating_point Real>
Real	randlib::math::lowerSeries (Real a, Real x)
template<std::floating_point Real>
Real	randlib::math::upperContinuedFraction (Real a, Real x)
	Modified Lentz evaluation of the continued fraction for Q(a, x), x ≥ a + 1.
template<std::floating_point Real>
IncompleteGamma< Real >	randlib::math::incompleteGamma (Real a, Real x, Real logX)
	Regularized incomplete gamma ratios P(a, x) and Q(a, x) = 1 - P(a, x) and their logarithms.
template<std::floating_point Real>
void	randlib::math::parametersVerification (Real a, Real x)

Variables
constexpr int	randlib::math::FACTORIAL_TABLESIZE = 175
constexpr long double	randlib::math::FACTORIAL_TABLE []
constexpr long double	randlib::math::LOGFACTORIAL_TABLE []
constexpr size_t	randlib::math::LOGFACTORIAL_TABLESIZE = 255