mpreal_special.hpp File Reference

#include "detail/exact_bernoulli.hpp"
#include "detail/math_integer.hpp"
#include "math_results.hpp"
#include "mpreal.hpp"
#include <vector>

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Namespaces
namespace	uni20

Functions
mpreal	uni20::agm (mpreal const &a, mpreal const &x)
	Nonnegative real arithmetic-geometric mean.
mpreal	uni20::agm (mpreal const &a, mpreal const &x, Precision p)
	Convert both inputs to finite precision p, then evaluate agm at p.
mpreal	uni20::airy_ai (mpreal const &x)
	Real Airy Ai; MPFR recommends arguments with magnitude below about 500.
mpreal	uni20::airy_ai (mpreal const &x, Precision p)
	Convert the input to finite precision p, then evaluate airy_ai at p.
template<detail::MathInteger I>
mpreal	uni20::bessel_j (I n, mpreal const &x)
	Bessel function of the first kind, with a checked signed integer order.
template<detail::MathInteger I>
mpreal	uni20::bessel_j (I n, mpreal const &x, Precision p)
	Convert x to p, then evaluate bessel_j(n,x) at p.
template<detail::MathInteger I>
mpreal	uni20::bessel_y (I n, mpreal const &x)
	Bessel function of the second kind, with a checked signed integer order.
template<detail::MathInteger I>
mpreal	uni20::bessel_y (I n, mpreal const &x, Precision p)
	Convert x to p, then evaluate bessel_y(n,x) at p.
mpreal	uni20::beta (mpreal const &a, mpreal const &x)
	Real Beta function; positive rational/integer pairs retain exact values.
mpreal	uni20::beta (mpreal const &a, mpreal const &x, Precision p)
	Convert both inputs to finite precision p, then evaluate beta at p.
mpreal	uni20::digamma (mpreal const &x)
	Logarithmic derivative of Gamma; finite working precision is required.
mpreal	uni20::digamma (mpreal const &x, Precision p)
	Convert the input to finite precision p, then evaluate digamma at p.
mpreal	uni20::dilog_real (mpreal const &x)
	Real part of the dilogarithm; this is not a complex branch-valued API.
mpreal	uni20::dilog_real (mpreal const &x, Precision p)
	Convert the input to finite precision p, then evaluate dilog_real at p.
mpreal	uni20::erf (mpreal const &x)
	Error function, retaining exact zero or the input precision.
mpreal	uni20::erf (mpreal const &x, Precision p)
	Convert the input to finite precision p, then evaluate erf at p.
mpreal	uni20::erfc (mpreal const &x)
	Complementary error function, evaluated without subtracting erf from one.
mpreal	uni20::erfc (mpreal const &x, Precision p)
	Convert the input to finite precision p, then evaluate erfc at p.
mpreal	uni20::expint (mpreal const &x)
	Real exponential integral Ei, with its real principal-value meaning.
mpreal	uni20::expint (mpreal const &x, Precision p)
	Convert the input to finite precision p, then evaluate expint at p.
template<detail::MathInteger I>
mpreal	uni20::factorial (I n, Precision p)
	Factorial of a nonnegative integer, at an explicitly chosen arithmetic state.
mpreal	uni20::lgamma (mpreal const &x)
	Natural logarithm of abs(Gamma(x)), including negative Gamma values.
mpreal	uni20::lgamma (mpreal const &x, Precision p)
	Convert x to p, then evaluate log(abs(Gamma(x))) at p.
lgamma_result< mpreal >	uni20::lgamma_sign (mpreal const &x)
	Log(abs(Gamma(x))) and the sign of Gamma, as owning values.
lgamma_result< mpreal >	uni20::lgamma_sign (mpreal const &x, Precision p)
	Convert x to p, then evaluate log-absolute-Gamma and its sign.
mpreal	uni20::tgamma (mpreal const &x)
	Real Gamma function; exact positive integers produce exact factorials.
mpreal	uni20::tgamma (mpreal const &x, Precision p)
	Convert the input to finite precision p, then evaluate tgamma at p.
mpreal	uni20::upper_gamma (mpreal const &a, mpreal const &x)
	Upper incomplete Gamma, with shape a and lower integration endpoint x.
mpreal	uni20::upper_gamma (mpreal const &a, mpreal const &x, Precision p)
	Convert both inputs to finite precision p, then evaluate upper_gamma at p.
mpreal	uni20::zeta (mpreal const &x)
	Riemann zeta; nonpositive integer arguments retain exact rational results.
mpreal	uni20::zeta (mpreal const &x, Precision p)
	Convert the input to finite precision p, then evaluate zeta at p.