A rational (fractional) number type. More...

#include <math/m_rational.hpp>

Collaboration diagram for xrt::auxiliary::math::Rational< Scalar >:

Public Types
using	value_type = Scalar

Public Member Functions
constexpr Rational	reciprocal () const noexcept
	Return the reciprocal of this value. More...

constexpr Rational	withNonNegativeDenominator () const noexcept
	Return this value, with the denominator non-negative (0 or positive). More...

constexpr bool	isOverUnity () const noexcept
	Does this rational number represent a value greater than 1, with a positive denominator? More...

constexpr bool	isUnity () const noexcept
	Does this rational number represent 1? More...

constexpr bool	isZero () const noexcept
	Does this rational number represent 0? More...

constexpr bool	isBetweenZeroAndOne () const noexcept
	Does this rational number represent a value between 0 and 1 (exclusive), and has a positive denominator? More...

constexpr Rational	complement () const noexcept
	Get the complementary fraction. More...

constexpr float	as_float () const noexcept
	Get an approximation of this value as a float. More...

constexpr double	as_double () const noexcept
	Get an approximation of this value as a double. More...

Static Public Member Functions
static constexpr Rational< Scalar >	simplestUnity () noexcept
	Return the rational value 1/1, the simplest unity (== 1) value. More...

Data Fields
value_type	numerator

value_type	denominator

Related Functions
(Note that these are not member functions.)
template<typename Scalar >
constexpr Rational< Scalar >	operator* (const Rational< Scalar > &lhs, const Rational< Scalar > &rhs)
	Multiplication operator. More...

template<typename Scalar >
constexpr Rational< Scalar >	operator* (const Rational< Scalar > &lhs, const Scalar &rhs)
	Multiplication operator with a scalar. More...

template<typename Scalar >
constexpr Rational< Scalar >	operator* (const Scalar &lhs, const Rational< Scalar > &rhs)
	Multiplication operator with a scalar. More...

template<typename Scalar >
constexpr bool	operator== (const Rational< Scalar > &lhs, const Rational< Scalar > &rhs)
	Equality comparison operator. More...

template<typename Scalar >
constexpr Rational< Scalar >	operator/ (const Rational< Scalar > &lhs, const Rational< Scalar > &rhs)
	Division operator. More...

template<typename Scalar >
constexpr Rational< Scalar >	operator/ (const Rational< Scalar > &lhs, Scalar rhs)
	Division operator by a scalar. More...

Detailed Description

template<typename Scalar>
struct xrt::auxiliary::math::Rational< Scalar >

A rational (fractional) number type.

Member Function Documentation

◆ as_double()

template<typename Scalar >

constexpr double xrt::auxiliary::math::Rational< Scalar >::as_double ( ) const

inlineconstexprnoexcept

Get an approximation of this value as a double.

◆ as_float()

template<typename Scalar >

constexpr float xrt::auxiliary::math::Rational< Scalar >::as_float ( ) const

inlineconstexprnoexcept

Get an approximation of this value as a float.

◆ complement()

template<typename Scalar >

constexpr Rational xrt::auxiliary::math::Rational< Scalar >::complement ( ) const

inlineconstexprnoexcept

Get the complementary fraction.

Only really makes sense if isBetweenZeroAndOne() is true

Result will have a non-negative denominator.

◆ isBetweenZeroAndOne()

template<typename Scalar >

constexpr bool xrt::auxiliary::math::Rational< Scalar >::isBetweenZeroAndOne ( ) const

inlineconstexprnoexcept

Does this rational number represent a value between 0 and 1 (exclusive), and has a positive denominator?

This is the most common useful range.

◆ isOverUnity()

template<typename Scalar >

constexpr bool xrt::auxiliary::math::Rational< Scalar >::isOverUnity ( ) const

inlineconstexprnoexcept

Does this rational number represent a value greater than 1, with a positive denominator?

◆ isUnity()

template<typename Scalar >

constexpr bool xrt::auxiliary::math::Rational< Scalar >::isUnity ( ) const

inlineconstexprnoexcept

Does this rational number represent 1?

Note: false if denominator is 0, even if numerator is also 0.

◆ isZero()

template<typename Scalar >

constexpr bool xrt::auxiliary::math::Rational< Scalar >::isZero ( ) const

inlineconstexprnoexcept

Does this rational number represent 0?

Note: false if denominator is 0, even if numerator is also 0.

◆ reciprocal()

template<typename Scalar >

constexpr Rational xrt::auxiliary::math::Rational< Scalar >::reciprocal ( ) const

inlineconstexprnoexcept

Return the reciprocal of this value.

Result will have a non-negative denominator.

Referenced by xrt::auxiliary::math::Rational< Scalar >::operator/().

◆ simplestUnity()

template<typename Scalar >

static constexpr Rational< Scalar > xrt::auxiliary::math::Rational< Scalar >::simplestUnity ( )

inlinestaticconstexprnoexcept

Return the rational value 1/1, the simplest unity (== 1) value.

◆ withNonNegativeDenominator()

template<typename Scalar >

constexpr Rational xrt::auxiliary::math::Rational< Scalar >::withNonNegativeDenominator ( ) const

inlineconstexprnoexcept

Return this value, with the denominator non-negative (0 or positive).

Friends And Related Function Documentation

◆ operator*() [1/3]

template<typename Scalar >

constexpr Rational< Scalar > operator*	(	const Rational< Scalar > &	lhs,
		const Rational< Scalar > &	rhs
	)

Warning: does no simplification!

Result will have a non-negative denominator.

◆ operator*() [2/3]

template<typename Scalar >

constexpr Rational< Scalar > operator*	(	const Rational< Scalar > &	lhs,
		const Scalar &	rhs
	)

Warning: does no simplification!

Result will have a non-negative denominator.

◆ operator*() [3/3]

template<typename Scalar >

constexpr Rational< Scalar > operator*	(	const Scalar &	lhs,
		const Rational< Scalar > &	rhs
	)

Warning: does no simplification!

Result will have a non-negative denominator.

◆ operator/() [1/2]

template<typename Scalar >

constexpr Rational< Scalar > operator/	(	const Rational< Scalar > &	lhs,
		const Rational< Scalar > &	rhs
	)

Warning: does no simplification!

Result will have a non-negative denominator.

References xrt::auxiliary::math::Rational< Scalar >::reciprocal().

◆ operator/() [2/2]

template<typename Scalar >

constexpr Rational< Scalar > operator/	(	const Rational< Scalar > &	lhs,
		Scalar	rhs
	)

Warning: does no simplification!

Result will have a non-negative denominator.

◆ operator==()

template<typename Scalar >

constexpr bool operator==	(	const Rational< Scalar > &	lhs,
		const Rational< Scalar > &	rhs
	)

Warning: does no simplification, looks for exact equality!

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

auxiliary/math/m_rational.hpp

Public Types

Public Member Functions

Static Public Member Functions

Data Fields

Related Functions

Detailed Description

Member Function Documentation

◆ as_double()

◆ as_float()

◆ complement()

◆ isBetweenZeroAndOne()

◆ isOverUnity()

◆ isUnity()

◆ isZero()

◆ reciprocal()

◆ simplestUnity()

◆ withNonNegativeDenominator()

Friends And Related Function Documentation

◆ operator*() [1/3]

◆ operator*() [2/3]

◆ operator*() [3/3]

◆ operator/() [1/2]

◆ operator/() [2/2]

◆ operator==()