mpreal.hpp File Reference

#include "detail/function_identity.hpp"
#include "detail/scaled_rational.hpp"
#include "exact_rational.hpp"
#include "math_constants.hpp"
#include "scalar_traits.hpp"
#include <memory>
#include <mpfr.h>
#include <ostream>
#include <uni20/common/initialization.hpp>
#include <variant>
#include "mpreal_functions.hpp"
#include "mpreal_special.hpp"
#include "mpreal_extensions.hpp"

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Classes
class	uni20::mpreal
	Owning exact rational or finite-precision MPFR real, with eager arithmetic. More...
struct	uni20::numeric_limits< mpreal >
	Type properties and explicit runtime limits for exact-or-approximate reals. More...

Namespaces
namespace	uni20

Functions
mpreal	uni20::abs (mpreal const &x)
mpreal	uni20::abs (mpreal const &x, Precision p)
	Evaluate abs(x.at(p)), returning an approximation at finite precision p.
mpreal	uni20::acos (mpreal const &x)
	Inverse cosine in radians; retain input precision or a supported exact result.
mpreal	uni20::acos (mpreal const &x, Precision p)
	Evaluate acos(x.at(p)), returning an approximation at finite precision p.
mpreal	uni20::acosh (mpreal const &x)
	Inverse hyperbolic cosine; retain input precision or a supported exact result.
mpreal	uni20::acosh (mpreal const &x, Precision p)
	Evaluate acosh(x.at(p)), returning an approximation at finite precision p.
mpreal	uni20::asin (mpreal const &x)
	Inverse sine in radians; retain input precision or a supported exact result.
mpreal	uni20::asin (mpreal const &x, Precision p)
	Evaluate asin(x.at(p)), returning an approximation at finite precision p.
mpreal	uni20::asinh (mpreal const &x)
	Inverse hyperbolic sine; retain input precision or a supported exact result.
mpreal	uni20::asinh (mpreal const &x, Precision p)
	Evaluate asinh(x.at(p)), returning an approximation at finite precision p.
mpreal	uni20::atan (mpreal const &x)
mpreal	uni20::atan (mpreal const &x, Precision p)
	Evaluate atan(x.at(p)), returning an approximation at finite precision p.
mpreal	uni20::atan2 (mpreal const &y, mpreal const &x)
mpreal	uni20::atan2 (mpreal const &y, mpreal const &x, Precision p)
	Evaluate atan2(y.at(p), x.at(p)), overriding both operands' precisions.
mpreal	uni20::atanh (mpreal const &x)
	Inverse hyperbolic tangent; retain input precision or a supported exact result.
mpreal	uni20::atanh (mpreal const &x, Precision p)
	Evaluate atanh(x.at(p)), returning an approximation at finite precision p.
mpreal	uni20::cbrt (mpreal const &x)
	Real cube root, including negative arguments; retain input precision or a supported exact result.
mpreal	uni20::cbrt (mpreal const &x, Precision p)
	Evaluate cbrt(x.at(p)), returning an approximation at finite precision p.
mpreal	uni20::conj (mpreal const &x)
mpreal	uni20::cos (mpreal const &x)
mpreal	uni20::cos (mpreal const &x, Precision p)
	Evaluate cos(x.at(p)), returning an approximation at finite precision p.
mpreal	uni20::cosh (mpreal const &x)
	Hyperbolic cosine; retain input precision or a supported exact result.
mpreal	uni20::cosh (mpreal const &x, Precision p)
	Evaluate cosh(x.at(p)), returning an approximation at finite precision p.
mpreal	uni20::epsilon (Precision precision)
	Spacing above one for a specified binary working precision.
mpreal	uni20::exp (mpreal const &x)
mpreal	uni20::exp (mpreal const &x, Precision p)
	Evaluate exp(x.at(p)), returning an approximation at finite precision p.
mpreal	uni20::exp2 (mpreal const &x)
	Base-two exponential; retain input precision or a supported exact result.
mpreal	uni20::exp2 (mpreal const &x, Precision p)
	Evaluate exp2(x.at(p)), returning an approximation at finite precision p.
mpreal	uni20::expm1 (mpreal const &x)
	Exponential minus one without cancellation; retain input precision or exact zero.
mpreal	uni20::expm1 (mpreal const &x, Precision p)
	Evaluate expm1(x.at(p)), returning an approximation at finite precision p.
mpreal	uni20::hypot (mpreal const &x, mpreal const &y)
mpreal	uni20::hypot (mpreal const &x, mpreal const &y, Precision p)
	Evaluate hypot(x.at(p), y.at(p)), overriding both operands' precisions.
bool	uni20::isfinite (mpreal const &x)
bool	uni20::isinf (mpreal const &x)
bool	uni20::isnan (mpreal const &x)
mpreal	uni20::log (mpreal const &x)
mpreal	uni20::log (mpreal const &x, Precision p)
	Evaluate log(x.at(p)), returning an approximation at finite precision p.
mpreal	uni20::log10 (mpreal const &x)
	Base-ten logarithm; retain input precision or a supported exact result.
mpreal	uni20::log10 (mpreal const &x, Precision p)
	Evaluate log10(x.at(p)), returning an approximation at finite precision p.
mpreal	uni20::log1p (mpreal const &x)
	Logarithm of one plus x without cancellation; retain input precision or exact zero.
mpreal	uni20::log1p (mpreal const &x, Precision p)
	Evaluate log1p(x.at(p)), returning an approximation at finite precision p.
mpreal	uni20::log2 (mpreal const &x)
	Base-two logarithm; retain input precision or a supported exact result.
mpreal	uni20::log2 (mpreal const &x, Precision p)
	Evaluate log2(x.at(p)), returning an approximation at finite precision p.
mpreal	uni20::operator* (exact_rational const &a, mpreal const &b)
mpreal	uni20::operator* (mpreal const &a, exact_rational const &b)
mpreal	uni20::operator* (mpreal const &a, mpreal const &b)
mpreal	uni20::operator+ (exact_rational const &a, mpreal const &b)
mpreal	uni20::operator+ (mpreal const &a)
mpreal	uni20::operator+ (mpreal const &a, exact_rational const &b)
mpreal	uni20::operator+ (mpreal const &a, mpreal const &b)
mpreal	uni20::operator- (exact_rational const &a, mpreal const &b)
mpreal	uni20::operator- (mpreal const &a)
mpreal	uni20::operator- (mpreal const &a, exact_rational const &b)
mpreal	uni20::operator- (mpreal const &a, mpreal const &b)
mpreal	uni20::operator/ (exact_rational const &a, mpreal const &b)
mpreal	uni20::operator/ (mpreal const &a, exact_rational const &b)
mpreal	uni20::operator/ (mpreal const &a, mpreal const &b)
std::ostream &	uni20::operator<< (std::ostream &os, exact_rational const &value)
std::ostream &	uni20::operator<< (std::ostream &os, mpreal const &value)
	Stream the round-trip decimal representation, independent of stream precision.
std::partial_ordering	uni20::operator<=> (mpreal const &a, exact_rational const &b)
template<std::integral I> requires (!std::same_as<I, bool>)
std::partial_ordering	uni20::operator<=> (mpreal const &a, I b)
std::partial_ordering	uni20::operator<=> (mpreal const &a, mpreal const &b)
	Compare exact or stored approximate values without rounding either operand.
bool	uni20::operator== (mpreal const &a, exact_rational const &b)
template<std::integral I> requires (!std::same_as<I, bool>)
bool	uni20::operator== (mpreal const &a, I b)
bool	uni20::operator== (mpreal const &a, mpreal const &b)
mpreal	uni20::pow (mpreal const &x, mpreal const &y)
mpreal	uni20::pow (mpreal const &x, mpreal const &y, Precision p)
	Evaluate pow(x.at(p), y.at(p)), overriding both operands' precisions.
bool	uni20::signbit (mpreal const &x)
mpreal	uni20::sin (mpreal const &x)
mpreal	uni20::sin (mpreal const &x, Precision p)
	Evaluate sin(x.at(p)), returning an approximation at finite precision p.
mpreal	uni20::sinh (mpreal const &x)
	Hyperbolic sine; retain input precision or a supported exact result.
mpreal	uni20::sinh (mpreal const &x, Precision p)
	Evaluate sinh(x.at(p)), returning an approximation at finite precision p.
mpreal	uni20::sqrt (mpreal const &x)
mpreal	uni20::sqrt (mpreal const &x, Precision p)
	Evaluate sqrt(x.at(p)), returning an approximation at finite precision p.
mpreal	uni20::tan (mpreal const &x)
mpreal	uni20::tan (mpreal const &x, Precision p)
	Evaluate tan(x.at(p)), returning an approximation at finite precision p.
mpreal	uni20::tanh (mpreal const &x)
	Hyperbolic tangent; retain input precision or a supported exact result.
mpreal	uni20::tanh (mpreal const &x, Precision p)
	Evaluate tanh(x.at(p)), returning an approximation at finite precision p.