Exact rational number. More...

#include <rational.hpp>

Public Member Functions
	rational () noexcept
	Empty constructor.

template<typename T , std::enable_if_t< std::is_integral_v< T >, bool > = true>
	rational (T n, uint64_t d=1) noexcept
	Constructor with numerator and denominator. More...

	rational (const integer &n, const integer &d=1) noexcept
	Constructor with numerator and denominator. More...

	rational (const std::string &s) noexcept
	Constructor with string. More...

	rational (const rational &r) noexcept
	Copy constructor. More...

	rational (integer &&i) noexcept
	Move constructor. More...

	rational (integer &&n, integer &&d) noexcept
	Move constructor with numerator and denominator. More...

	rational (rational &&r) noexcept
	Move constructor. More...

	~rational () noexcept
	Destructor.

template<typename T , std::enable_if_t< std::is_integral_v< T >, bool > = true>
void	set_number (T n, uint64_t d=1) noexcept
	Overwrites the value of this rational with \(n/d\). More...

void	set_str (const std::string &s) noexcept
	Overwrites the value in the string s. More...

void	set_integer (const integer &n, const integer &d) noexcept
	Overwrites the value of this rational with the value \(n/d\). More...

void	set_rational (const rational &r) noexcept
	Overwrites the value of this rational with the value \(n/d\). More...

void	invert () noexcept
	Changes numerator and denominator. More...

template<typename T , std::enable_if_t< std::is_integral_v< T >, bool > = true>
rational &	operator= (T i) noexcept
	Assignment operator. More...

rational &	operator= (const std::string &s) noexcept
	Assignment operator. More...

rational &	operator= (const integer &i) noexcept
	Assignment operator. More...

rational &	operator= (const rational &r) noexcept
	Assignment operator. More...

rational &	operator= (integer &&i) noexcept
	Move assignment operator. More...

rational &	operator= (rational &&r) noexcept
	Move assignment operator. More...

template<typename T , std::enable_if_t< std::is_integral_v< T >, bool > = true>
bool	operator== (T i) const noexcept
	Equality operator. More...

bool	operator== (const integer &i) const noexcept
	Equality operator. More...

bool	operator== (const rational &r) const noexcept
	Equality operator. More...

template<typename T , std::enable_if_t< std::is_integral_v< T >, bool > = true>
bool	operator!= (T i) const noexcept
	Non-equality operator. More...

bool	operator!= (const integer &i) const noexcept
	Non-equality operator. More...

bool	operator!= (const rational &r) const noexcept
	Non-equality operator. More...

template<typename T , std::enable_if_t< std::is_integral_v< T >, bool > = true>
bool	operator< (T i) const noexcept
	Less than operator. More...

bool	operator< (const integer &i) const noexcept
	Less than operator. More...

bool	operator< (const rational &r) const noexcept
	Less than operator. More...

template<typename T , std::enable_if_t< std::is_integral_v< T >, bool > = true>
bool	operator<= (T i) const noexcept
	Less than or equal to operator. More...

bool	operator<= (const integer &i) const noexcept
	Less than or equal to operator. More...

bool	operator<= (const rational &r) const noexcept
	Less than or equal to operator. More...

template<typename T , std::enable_if_t< std::is_integral_v< T >, bool > = true>
bool	operator> (T i) const noexcept
	Greater than operator. More...

bool	operator> (const integer &i) const noexcept
	Greater than operator. More...

bool	operator> (const rational &r) const noexcept
	Greater than operator. More...

template<typename T , std::enable_if_t< std::is_integral_v< T >, bool > = true>
bool	operator>= (T i) const noexcept
	Greater than or equal to operator. More...

bool	operator>= (const integer &i) const noexcept
	Greater than or equal to operator. More...

bool	operator>= (const rational &r) const noexcept
	Greater than or equal to operator. More...

template<typename T , std::enable_if_t< std::is_integral_v< T >, bool > = true>
rational	operator+ (T i) const noexcept
	Addition operator. More...

rational	operator+ (const integer &i) const noexcept
	Addition operator. More...

rational	operator+ (const rational &r) const noexcept
	Addition operator. More...

template<typename T , std::enable_if_t< std::is_integral_v< T >, bool > = true>
rational &	operator+= (T i) noexcept
	Addition operator. More...

rational &	operator+= (const integer &i) noexcept
	Addition operator. More...

rational &	operator+= (const rational &r) noexcept
	Addition operator. More...

rational	operator- () const noexcept
	Substraction unary operator.

template<typename T , std::enable_if_t< std::is_integral_v< T >, bool > = true>
rational	operator- (T i) const noexcept
	Substraction operator. More...

rational	operator- (const integer &i) const noexcept
	Substraction operator. More...

rational	operator- (const rational &r) const noexcept
	Substraction operator. More...

template<typename T , std::enable_if_t< std::is_integral_v< T >, bool > = true>
rational &	operator-= (T i) noexcept
	Substraction operator. More...

rational &	operator-= (const integer &i) noexcept
	Substraction operator. More...

rational &	operator-= (const rational &r) noexcept
	Substraction operator. More...

template<typename T , std::enable_if_t< std::is_integral_v< T >, bool > = true>
rational	operator* (T i) const noexcept
	Multiplication operator. More...

rational	operator* (const integer &i) const noexcept
	Multiplication operator. More...

rational	operator* (const rational &r) const noexcept
	Multiplication operator. More...

template<typename T , std::enable_if_t< std::is_integral_v< T >, bool > = true>
rational &	operator*= (T i) noexcept
	Multiplication operator. More...

rational &	operator*= (const integer &i) noexcept
	Multiplication operator. More...

rational &	operator*= (const rational &r) noexcept
	Multiplication operator. More...

template<typename T , std::enable_if_t< std::is_integral_v< T >, bool > = true>
rational	operator/ (T i) const noexcept
	Division operator. More...

rational	operator/ (const integer &i) const noexcept
	Division operator. More...

rational	operator/ (const rational &r) const noexcept
	Division operator. More...

template<typename T , std::enable_if_t< std::is_integral_v< T >, bool > = true>
rational &	operator/= (T i) noexcept
	Division operator. More...

rational &	operator/= (const integer &i) noexcept
	Division operator. More...

rational &	operator/= (const rational &r) noexcept
	Division operator. More...

rational	power (uint64_t i) const noexcept
	Exponentiation operator. More...

rational	power (const integer &i) const noexcept
	Exponentiation operator. More...

rational &	powt (uint64_t i) noexcept
	Exponentiation operator. More...

rational &	powt (const integer &i) noexcept
	Exponentiation operator. More...

bool	is_initialized () const noexcept
	Returns whether this object is initialised or not.

int64_t	get_sign () const noexcept
	Returns the sign of this rational.

std::size_t	bytes () const noexcept
	Returns the amount of bytes this integer occupies.

integer	to_integer () const noexcept
	Converts this rational to an integer value. More...

void	as_integer (integer &i) const noexcept
	Converts this rational to an integer value. More...

double	to_double () const noexcept
	Converts this rational to a double-precision floating-point value.

void	as_double (double &d) const noexcept
	Converts this rational to a double-precision floating-point value.

std::string	to_string () const noexcept
	Converts this integer to a string.

void	as_string (std::string &s) const noexcept
	Converts this integer to a string.

integer	get_numerator () const noexcept
	Returns the numerator of this rational number.

integer	get_denominator () const noexcept
	Returns the denominator of this rational number.

void	swap (rational &r) noexcept
	Swaps the value of this rational with rational r's value. More...

Private Attributes
mpq_t	m_val
	Structure from GMP storing the rational's value.

bool	m_initialized = true
	Is this rational initialised?

Friends
template<typename T , std::enable_if_t< std::is_integral_v< T >, bool > = true>
bool	operator== (T i, const rational &r) noexcept
	Equality operator. More...

bool	operator== (const integer &i, const rational &r) noexcept
	Equality operator. More...

bool	operator!= (int64_t i, const rational &r) noexcept
	Non-equality operator. More...

bool	operator!= (const integer &i, const rational &r) noexcept
	Non-equality operator. More...

template<typename T , std::enable_if_t< std::is_integral_v< T >, bool > = true>
bool	operator< (T i, const rational &r) noexcept
	Less than operator. More...

bool	operator< (const integer &i, const rational &r) noexcept
	Less than operator. More...

template<typename T , std::enable_if_t< std::is_integral_v< T >, bool > = true>
bool	operator<= (T i, const rational &r) noexcept
	Less than or equal to operator. More...

bool	operator<= (const integer &i, const rational &r) noexcept
	Less than or equal to operator. More...

template<typename T , std::enable_if_t< std::is_integral_v< T >, bool > = true>
bool	operator> (T i, const rational &r) noexcept
	Greater than operator. More...

bool	operator> (const integer &i, const rational &r) noexcept
	Greater than operator. More...

template<typename T , std::enable_if_t< std::is_integral_v< T >, bool > = true>
bool	operator>= (T i, const rational &r) noexcept
	Greater than or equal to operator. More...

bool	operator>= (const integer &i, const rational &r) noexcept
	Greater than or equal to operator. More...

template<typename T , std::enable_if_t< std::is_integral_v< T >, bool > = true>
rational	operator+ (T i, const rational &r) noexcept
	Addition operator. More...

rational	operator+ (const integer &i, const rational &r) noexcept
	Addition operator. More...

template<typename T , std::enable_if_t< std::is_integral_v< T >, bool > = true>
rational	operator- (T i, const rational &r) noexcept
	Substraction operator. More...

rational	operator- (const integer &i, const rational &r) noexcept
	Substraction operator. More...

template<typename T , std::enable_if_t< std::is_integral_v< T >, bool > = true>
rational	operator* (T i, const rational &r) noexcept
	Multiplication operator. More...

rational	operator* (const integer &i, const rational &r) noexcept
	Multiplication operator. More...

template<typename T , std::enable_if_t< std::is_integral_v< T >, bool > = true>
rational	operator/ (T i, const rational &r) noexcept
	Division operator. More...

void	swap (rational &r1, rational &r2) noexcept
	Swaps two rationals. More...

Detailed Description

Exact rational number.

This class wraps the mpq_t data structure from GMP with operators for an easy usage.

Constructor & Destructor Documentation

◆ rational() [1/7]

template<typename T , std::enable_if_t< std::is_integral_v< T >, bool > = true>

lal::numeric::rational::rational	(	T	n,
		uint64_t	d = `1`
	)

inlinenoexcept

Constructor with numerator and denominator.

Parameters

n	Numerator, signed integer (basic type).
d	Denominator, unsigned integer (basic type).

◆ rational() [2/7]

lal::numeric::rational::rational	(	const integer &	n,
		const integer &	d = `1`
	)

inlinenoexcept

Constructor with numerator and denominator.

Parameters

n	Numerator, a lal::numeric::integer.
d	Denominator, a lal::numeric::integer.

◆ rational() [3/7]

lal::numeric::rational::rational ( const std::string & s )

inlinenoexcept

Constructor with string.

Parameters

s A string.

◆ rational() [4/7]

lal::numeric::rational::rational ( const rational & r )

inlinenoexcept

Copy constructor.

Parameters

r	A lal::numeric::rational.

◆ rational() [5/7]

lal::numeric::rational::rational ( integer && i )

inlinenoexcept

Move constructor.

Parameters

i	A lal::numeric::integer

◆ rational() [6/7]

lal::numeric::rational::rational	(	integer &&	n,
		integer &&	d
	)

inlinenoexcept

Move constructor with numerator and denominator.

Parameters

n	Numerator, a lal::numeric::integer.
d	Denominator, a lal::numeric::integer.

Postcondition: Objects n and d are not initialized.

◆ rational() [7/7]

lal::numeric::rational::rational ( rational && r )

inlinenoexcept

Move constructor.

Parameters

r	A lal::numeric::rational.

Postcondition: Object r is not initialized.

Member Function Documentation

◆ as_integer()

void lal::numeric::rational::as_integer ( integer & i ) const

noexcept

Converts this rational to an integer value.

This function returns \(\left\lfloor n/d \right\rfloor\) where \(n,d\) are, respectively, the numerator and denominator.

Parameters

[out] i Integer representation of this rational.

◆ invert()

void lal::numeric::rational::invert ( )

inlinenoexcept

Changes numerator and denominator.

If this rational value was \(n/d\) then after calling this method it will be \(d/n\).

◆ operator!=() [1/3]

bool lal::numeric::rational::operator!= ( const integer & i ) const

inlinenoexcept

Non-equality operator.

Parameters

i	A lal::numeric::integer.

◆ operator!=() [2/3]

bool lal::numeric::rational::operator!= ( const rational & r ) const

inlinenoexcept

Non-equality operator.

Parameters

r	A lal::numeric::rational.

◆ operator!=() [3/3]

template<typename T , std::enable_if_t< std::is_integral_v< T >, bool > = true>

bool lal::numeric::rational::operator!= ( T i ) const

inlinenoexcept

Non-equality operator.

Parameters

i	An integer (basic type) number.

◆ operator*() [1/3]

rational lal::numeric::rational::operator* ( const integer & i ) const

inlinenoexcept

Multiplication operator.

Parameters

i	A lal::numeric::integer.

◆ operator*() [2/3]

rational lal::numeric::rational::operator* ( const rational & r ) const

inlinenoexcept

Multiplication operator.

Parameters

r	A lal::numeric::rational.

◆ operator*() [3/3]

template<typename T , std::enable_if_t< std::is_integral_v< T >, bool > = true>

rational lal::numeric::rational::operator* ( T i ) const

inlinenoexcept

Multiplication operator.

Parameters

i	An integer (basic type) number.

◆ operator*=() [1/3]

rational & lal::numeric::rational::operator*= ( const integer & i )

inlinenoexcept

Multiplication operator.

Parameters

i	A lal::numeric::integer.

◆ operator*=() [2/3]

rational & lal::numeric::rational::operator*= ( const rational & r )

inlinenoexcept

Multiplication operator.

Parameters

r	A lal::numeric::rational.

◆ operator*=() [3/3]

template<typename T , std::enable_if_t< std::is_integral_v< T >, bool > = true>

rational & lal::numeric::rational::operator*= ( T i )

inlinenoexcept

Multiplication operator.

Parameters

i	An integer (basic type) number.

◆ operator+() [1/3]

rational lal::numeric::rational::operator+ ( const integer & i ) const

inlinenoexcept

Addition operator.

Parameters

i	A lal::numeric::integer.

◆ operator+() [2/3]

rational lal::numeric::rational::operator+ ( const rational & r ) const

inlinenoexcept

Addition operator.

Parameters

r	A lal::numeric::rational.

◆ operator+() [3/3]

template<typename T , std::enable_if_t< std::is_integral_v< T >, bool > = true>

rational lal::numeric::rational::operator+ ( T i ) const

inlinenoexcept

Addition operator.

Parameters

i	An integer (basic type) number.

◆ operator+=() [1/3]

rational & lal::numeric::rational::operator+= ( const integer & i )

inlinenoexcept

Addition operator.

Parameters

i	A lal::numeric::integer.

◆ operator+=() [2/3]

rational & lal::numeric::rational::operator+= ( const rational & r )

inlinenoexcept

Addition operator.

Parameters

r	A lal::numeric::rational.

◆ operator+=() [3/3]

template<typename T , std::enable_if_t< std::is_integral_v< T >, bool > = true>

rational & lal::numeric::rational::operator+= ( T i )

inlinenoexcept

Addition operator.

Parameters

i	An integer (basic type) number.

◆ operator-() [1/3]

rational lal::numeric::rational::operator- ( const integer & i ) const

inlinenoexcept

Substraction operator.

Parameters

i	A lal::numeric::integer.

◆ operator-() [2/3]

rational lal::numeric::rational::operator- ( const rational & r ) const

inlinenoexcept

Substraction operator.

Parameters

r	A lal::numeric::rational.

◆ operator-() [3/3]

template<typename T , std::enable_if_t< std::is_integral_v< T >, bool > = true>

rational lal::numeric::rational::operator- ( T i ) const

inlinenoexcept

Substraction operator.

Parameters

i	An integer (basic type) number.

◆ operator-=() [1/3]

rational & lal::numeric::rational::operator-= ( const integer & i )

inlinenoexcept

Substraction operator.

Parameters

i	A lal::numeric::integer.

◆ operator-=() [2/3]

rational & lal::numeric::rational::operator-= ( const rational & r )

inlinenoexcept

Substraction operator.

Parameters

r	A lal::numeric::rational.

◆ operator-=() [3/3]

template<typename T , std::enable_if_t< std::is_integral_v< T >, bool > = true>

rational & lal::numeric::rational::operator-= ( T i )

inlinenoexcept

Substraction operator.

Parameters

i	An integer (basic type) number.

◆ operator/() [1/3]

rational lal::numeric::rational::operator/ ( const integer & i ) const

inlinenoexcept

Division operator.

Parameters

i	A lal::numeric::integer.

◆ operator/() [2/3]

rational lal::numeric::rational::operator/ ( const rational & r ) const

inlinenoexcept

Division operator.

Parameters

r	A lal::numeric::rational.

◆ operator/() [3/3]

template<typename T , std::enable_if_t< std::is_integral_v< T >, bool > = true>

rational lal::numeric::rational::operator/ ( T i ) const

inlinenoexcept

Division operator.

Parameters

i	An integer (basic type) number.

◆ operator/=() [1/3]

rational & lal::numeric::rational::operator/= ( const integer & i )

noexcept

Division operator.

Parameters

i	A lal::numeric::integer.

◆ operator/=() [2/3]

rational & lal::numeric::rational::operator/= ( const rational & r )

noexcept

Division operator.

Parameters

r	A lal::numeric::rational.

◆ operator/=() [3/3]

template<typename T , std::enable_if_t< std::is_integral_v< T >, bool > = true>

rational & lal::numeric::rational::operator/= ( T i )

inlinenoexcept

Division operator.

Parameters

i	An integer (basic type) number.

◆ operator<() [1/3]

bool lal::numeric::rational::operator< ( const integer & i ) const

inlinenoexcept

Less than operator.

Parameters

i	A lal::numeric::integer.

◆ operator<() [2/3]

bool lal::numeric::rational::operator< ( const rational & r ) const

inlinenoexcept

Less than operator.

Parameters

r	A lal::numeric::rational.

◆ operator<() [3/3]

template<typename T , std::enable_if_t< std::is_integral_v< T >, bool > = true>

bool lal::numeric::rational::operator< ( T i ) const

inlinenoexcept

Less than operator.

Parameters

i	An integer (basic type) number.

◆ operator<=() [1/3]

bool lal::numeric::rational::operator<= ( const integer & i ) const

inlinenoexcept

Less than or equal to operator.

Parameters

i	A lal::numeric::integer.

◆ operator<=() [2/3]

bool lal::numeric::rational::operator<= ( const rational & r ) const

inlinenoexcept

Less than or equal to operator.

Parameters

r	A lal::numeric::rational.

◆ operator<=() [3/3]

template<typename T , std::enable_if_t< std::is_integral_v< T >, bool > = true>

bool lal::numeric::rational::operator<= ( T i ) const

inlinenoexcept

Less than or equal to operator.

Parameters

i	An integer (basic type) number.

◆ operator=() [1/6]

rational & lal::numeric::rational::operator= ( const integer & i )

inlinenoexcept

Assignment operator.

Parameters

i	A lal::numeric::integer.

◆ operator=() [2/6]

rational & lal::numeric::rational::operator= ( const rational & r )

inlinenoexcept

Assignment operator.

Parameters

r	A lal::numeric::rational.

◆ operator=() [3/6]

rational & lal::numeric::rational::operator= ( const std::string & s )

inlinenoexcept

Assignment operator.

Parameters

s A string.

◆ operator=() [4/6]

rational & lal::numeric::rational::operator= ( integer && i )

inlinenoexcept

Move assignment operator.

Parameters

i	A lal::numeric::integer.

Postcondition: Object i is not initialized.

◆ operator=() [5/6]

rational & lal::numeric::rational::operator= ( rational && r )

inlinenoexcept

Move assignment operator.

Parameters

r	A lal::numeric::rational.

Postcondition: Object i is not initialized.

◆ operator=() [6/6]

template<typename T , std::enable_if_t< std::is_integral_v< T >, bool > = true>

rational & lal::numeric::rational::operator= ( T i )

inlinenoexcept

Assignment operator.

Parameters

i	An integer (basic type) number.

◆ operator==() [1/3]

bool lal::numeric::rational::operator== ( const integer & i ) const

inlinenoexcept

Equality operator.

Parameters

i	A lal::numeric::integer.

◆ operator==() [2/3]

bool lal::numeric::rational::operator== ( const rational & r ) const

inlinenoexcept

Equality operator.

Parameters

r	A lal::numeric::rational.

◆ operator==() [3/3]

template<typename T , std::enable_if_t< std::is_integral_v< T >, bool > = true>

bool lal::numeric::rational::operator== ( T i ) const

inlinenoexcept

Equality operator.

Parameters

i	An integer (basic type) number.

◆ operator>() [1/3]

bool lal::numeric::rational::operator> ( const integer & i ) const

inlinenoexcept

Greater than operator.

Parameters

i	A lal::numeric::integer.

◆ operator>() [2/3]

bool lal::numeric::rational::operator> ( const rational & r ) const

inlinenoexcept

Greater than operator.

Parameters

r	A lal::numeric::rational.

◆ operator>() [3/3]

template<typename T , std::enable_if_t< std::is_integral_v< T >, bool > = true>

bool lal::numeric::rational::operator> ( T i ) const

inlinenoexcept

Greater than operator.

Parameters

i	An integer (basic type) number.

◆ operator>=() [1/3]

bool lal::numeric::rational::operator>= ( const integer & i ) const

inlinenoexcept

Greater than or equal to operator.

Parameters

i	A lal::numeric::integer.

◆ operator>=() [2/3]

bool lal::numeric::rational::operator>= ( const rational & r ) const

inlinenoexcept

Greater than or equal to operator.

Parameters

r	A lal::numeric::rational.

◆ operator>=() [3/3]

template<typename T , std::enable_if_t< std::is_integral_v< T >, bool > = true>

bool lal::numeric::rational::operator>= ( T i ) const

inlinenoexcept

Greater than or equal to operator.

Parameters

i	An integer (basic type) number.

◆ power() [1/2]

rational lal::numeric::rational::power ( const integer & i ) const

noexcept

Exponentiation operator.

Parameters

i	A lal::numeric::integer.

◆ power() [2/2]

rational lal::numeric::rational::power ( uint64_t i ) const

noexcept

Exponentiation operator.

Parameters

i	An unsigned integer (basic type).

◆ powt() [1/2]

rational & lal::numeric::rational::powt ( const integer & i )

noexcept

Exponentiation operator.

Parameters

i	A lal::numeric::integer.

◆ powt() [2/2]

rational & lal::numeric::rational::powt ( uint64_t i )

noexcept

Exponentiation operator.

Parameters

i	An unsigned integer (basic type).

◆ set_integer()

void lal::numeric::rational::set_integer	(	const integer &	n,
		const integer &	d
	)

inlinenoexcept

Overwrites the value of this rational with the value \(n/d\).

Parameters

n	Numerator, a lal::numeric::integer.
d	Denominator, a lal::numeric::integer.

◆ set_number()

template<typename T , std::enable_if_t< std::is_integral_v< T >, bool > = true>

void lal::numeric::rational::set_number	(	T	n,
		uint64_t	d = `1`
	)

inlinenoexcept

Overwrites the value of this rational with \(n/d\).

Parameters

n	Numerator, signed integer (basic type).
d	Denominator, unsigned integer (basic type).

◆ set_rational()

void lal::numeric::rational::set_rational ( const rational & r )

inlinenoexcept

Overwrites the value of this rational with the value \(n/d\).

Parameters

r	A lal::numeric::rational.

◆ set_str()

void lal::numeric::rational::set_str ( const std::string & s )

inlinenoexcept

Overwrites the value in the string s.

Parameters

s A string.

◆ swap()

void lal::numeric::rational::swap ( rational & r )

inlinenoexcept

Swaps the value of this rational with rational r's value.

If none of the rationals is initialised, it does nothing.
If only one of the rationals is initialised, moves the contents of the initialised rational to the other. At the end, one of the two rationals is left uninitiliased.
If both rationals are initialised, swaps the values they contain.

◆ to_integer()

integer lal::numeric::rational::to_integer ( ) const

inlinenoexcept

Converts this rational to an integer value.

This function returns \(\left\lfloor n/d \right\rfloor\) where \(n,d\) are, respectively, the numerator and denominator.

Returns: The floor of this rational.

Friends And Related Function Documentation

◆ operator!= [1/2]

bool operator!=	(	const integer &	i,
		const rational &	r
	)

friend

Non-equality operator.

Parameters

i	A lal::numeric::integer.
r	A lal::numeric::rational.

◆ operator!= [2/2]

bool operator!=	(	int64_t	i,
		const rational &	r
	)

friend

Non-equality operator.

Parameters

i	An integer (basic type) number.
r	A lal::numeric::rational.

◆ operator* [1/2]

rational operator*	(	const integer &	i,
		const rational &	r
	)

friend

Multiplication operator.

Parameters

i	A lal::numeric::integer.
r	A lal::numeric::rational.

◆ operator* [2/2]

template<typename T , std::enable_if_t< std::is_integral_v< T >, bool > = true>

rational operator*	(	T	i,
		const rational &	r
	)

friend

Multiplication operator.

Parameters

i	An integer (basic type) number.
r	A lal::numeric::rational.

◆ operator+ [1/2]

rational operator+	(	const integer &	i,
		const rational &	r
	)

friend

Addition operator.

Parameters

i	A lal::numeric::integer.
r	A lal::numeric::rational.

◆ operator+ [2/2]

template<typename T , std::enable_if_t< std::is_integral_v< T >, bool > = true>

rational operator+	(	T	i,
		const rational &	r
	)

friend

Addition operator.

Parameters

i	An integer (basic type) number.
r	A lal::numeric::rational.

◆ operator- [1/2]

rational operator-	(	const integer &	i,
		const rational &	r
	)

friend

Substraction operator.

Parameters

i	A lal::numeric::integer.
r	A lal::numeric::rational.

◆ operator- [2/2]

template<typename T , std::enable_if_t< std::is_integral_v< T >, bool > = true>

rational operator-	(	T	i,
		const rational &	r
	)

friend

Substraction operator.

Parameters

i	An integer (basic type) number.
r	A lal::numeric::rational.

◆ operator/

template<typename T , std::enable_if_t< std::is_integral_v< T >, bool > = true>

rational operator/	(	T	i,
		const rational &	r
	)

friend

Division operator.

Parameters

i	An integer (basic type) number.
r	Rational value.

◆ operator< [1/2]

bool operator<	(	const integer &	i,
		const rational &	r
	)

friend

Less than operator.

Parameters

i	A lal::numeric::integer.
r	A lal::numeric::rational.

◆ operator< [2/2]

template<typename T , std::enable_if_t< std::is_integral_v< T >, bool > = true>

bool operator<	(	T	i,
		const rational &	r
	)

friend

Less than operator.

Parameters

i	An integer (basic type) number.
r	A lal::numeric::rational.

◆ operator<= [1/2]

bool operator<=	(	const integer &	i,
		const rational &	r
	)

friend

Less than or equal to operator.

Parameters

i	A lal::numeric::integer.
r	A lal::numeric::rational.

◆ operator<= [2/2]

template<typename T , std::enable_if_t< std::is_integral_v< T >, bool > = true>

bool operator<=	(	T	i,
		const rational &	r
	)

friend

Less than or equal to operator.

Parameters

i	An integer (basic type) number.
r	A lal::numeric::rational.

◆ operator== [1/2]

bool operator==	(	const integer &	i,
		const rational &	r
	)

friend

Equality operator.

Parameters

i	A lal::numeric::integer.
r	A lal::numeric::rational.

◆ operator== [2/2]

template<typename T , std::enable_if_t< std::is_integral_v< T >, bool > = true>

bool operator==	(	T	i,
		const rational &	r
	)

friend

Equality operator.

Parameters

i	An integer (basic type) number.
r	A lal::numeric::rational.

◆ operator> [1/2]

bool operator>	(	const integer &	i,
		const rational &	r
	)

friend

Greater than operator.

Parameters

i	A lal::numeric::integer.
r	A lal::numeric::rational.

◆ operator> [2/2]

template<typename T , std::enable_if_t< std::is_integral_v< T >, bool > = true>

bool operator>	(	T	i,
		const rational &	r
	)

friend

Greater than operator.

Parameters

i	An integer (basic type) number.
r	A lal::numeric::rational.

◆ operator>= [1/2]

bool operator>=	(	const integer &	i,
		const rational &	r
	)

friend

Greater than or equal to operator.

Parameters

i	A lal::numeric::integer.
r	A lal::numeric::rational.

◆ operator>= [2/2]

template<typename T , std::enable_if_t< std::is_integral_v< T >, bool > = true>

bool operator>=	(	T	i,
		const rational &	r
	)

friend

Greater than or equal to operator.

Parameters

i	An integer (basic type) number.
r	A lal::numeric::rational.

◆ swap

void swap	(	rational &	r1,
		rational &	r2
	)

friend

Swaps two rationals.

Parameters

r1	Input rational.
r2	Input rational.

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

lal/numeric/rational.hpp

Public Member Functions

Private Attributes

Friends

Detailed Description

Constructor & Destructor Documentation

◆ rational() [1/7]

◆ rational() [2/7]

◆ rational() [3/7]

◆ rational() [4/7]

◆ rational() [5/7]

◆ rational() [6/7]

◆ rational() [7/7]

Member Function Documentation

◆ as_integer()

◆ invert()

◆ operator!=() [1/3]

◆ operator!=() [2/3]

◆ operator!=() [3/3]

◆ operator*() [1/3]

◆ operator*() [2/3]

◆ operator*() [3/3]

◆ operator*=() [1/3]

◆ operator*=() [2/3]

◆ operator*=() [3/3]

◆ operator+() [1/3]

◆ operator+() [2/3]

◆ operator+() [3/3]

◆ operator+=() [1/3]

◆ operator+=() [2/3]

◆ operator+=() [3/3]

◆ operator-() [1/3]

◆ operator-() [2/3]

◆ operator-() [3/3]

◆ operator-=() [1/3]

◆ operator-=() [2/3]

◆ operator-=() [3/3]

◆ operator/() [1/3]

◆ operator/() [2/3]

◆ operator/() [3/3]

◆ operator/=() [1/3]

◆ operator/=() [2/3]

◆ operator/=() [3/3]

◆ operator<() [1/3]

◆ operator<() [2/3]

◆ operator<() [3/3]

◆ operator<=() [1/3]

◆ operator<=() [2/3]

◆ operator<=() [3/3]

◆ operator=() [1/6]

◆ operator=() [2/6]

◆ operator=() [3/6]

◆ operator=() [4/6]

◆ operator=() [5/6]

◆ operator=() [6/6]

◆ operator==() [1/3]

◆ operator==() [2/3]

◆ operator==() [3/3]

◆ operator>() [1/3]

◆ operator>() [2/3]

◆ operator>() [3/3]

◆ operator>=() [1/3]

◆ operator>=() [2/3]

◆ operator>=() [3/3]

◆ power() [1/2]

◆ power() [2/2]

◆ powt() [1/2]

◆ powt() [2/2]

◆ set_integer()

◆ set_number()

◆ set_rational()

◆ set_str()

◆ swap()

◆ to_integer()

Friends And Related Function Documentation

◆ operator!= [1/2]

◆ operator!= [2/2]

◆ operator* [1/2]

◆ operator* [2/2]

◆ operator+ [1/2]

◆ operator+ [2/2]