This class can be used to express rationals. More...

#include <Rational.hpp>

Public Member Functions
constexpr	Rational ()
	Instantiate an object without parameters. More...

constexpr	Rational (IntType numerator, IntType denominator, bool willBeReduce=true, bool willDenominatorBeVerified=true)
	Create a rational from a numerator and a denominator. More...

template<typename FloatingType >
constexpr	Rational (const FloatingType &nonRational)
	Create a rational from a floating number. More...

constexpr	Rational (const Rational< IntType > &reference)=default
	Default copy constructor. More...

template<typename AnotherIntType >
constexpr	Rational (Rational< AnotherIntType > &copiedRational)
	Copy constructor with another int type. More...

	~Rational ()=default
	Default Destructor. More...

constexpr IntType	getNumerator () const noexcept

constexpr IntType	getDenominator () const noexcept

const IntType &	operator[] (const size_t &id) const
	Getter with [] operator. More...

constexpr IntType	getLargerOperand () const noexcept

constexpr IntType	getLowerOperand () const noexcept

constexpr void	setNumerator (IntType numerator)

constexpr void	setDenominator (IntType denominator)

IntType &	operator[] (const size_t &id)
	Setter with [] operator. Example: rational[0] = 1 and rational[1] = 2 //// total => (1/2) More...

bool	isNegative () const noexcept

bool	isInteger () const noexcept

bool	isZero () const noexcept

constexpr Rational< IntType >	operator+ (const Rational< IntType > &anotherRational) const
	Addition operation between 2 rationals. More...

template<typename NonRationalType >
constexpr Rational< IntType >	operator+ (const NonRationalType &nonRational) const
	Addition operation between a rational and another type. Example: Rational + int. More...

constexpr Rational< IntType >	operator- (const Rational< IntType > &anotherRational) const
	Subtraction operation between 2 rationals. More...

template<typename NonRationalType >
constexpr Rational< IntType >	operator- (const NonRationalType &nonRational) const
	Subtraction operation between a rational and another type. Example: Rational - int. More...

constexpr Rational< IntType >	operator* (const Rational< IntType > &anotherRational) const
	Multiplication operation between 2 rationals. More...

template<typename NonRationalType >
constexpr Rational< IntType >	operator* (const NonRationalType &nonRational) const
	Multiplication operation between a rational and another type. Example: Rational * int. More...

constexpr Rational< IntType >	operator/ (const Rational< IntType > &anotherRational) const
	Division operation between 2 rationals. More...

template<typename NonRationalType >
constexpr Rational< IntType >	operator/ (const NonRationalType &nonRational) const
	Division operation between a rational and another type. Example: Rational / int. More...

constexpr bool	operator== (const Rational< IntType > &anotherRational) const
	Comparison between 2 rationals. More...

template<typename NonRationalType >
constexpr bool	operator== (const NonRationalType &nonRational) const
	Comparison between a rational and a non-rational. Example: Rational == int. More...

constexpr bool	operator!= (const Rational< IntType > &anotherRational) const
	Different comparison between 2 rationals. More...

template<typename NonRationalType >
constexpr bool	operator!= (const NonRationalType &nonRational) const
	Different comparison between a rational and a non-rational. Example: Rational != int. More...

constexpr bool	operator< (const Rational< IntType > &anotherRational) const
	< Comparison between 2 rationals More...

template<typename NonRationalType >
constexpr bool	operator< (const NonRationalType &nonRational) const
	< Comparison between a rational and a non-rational. Example: Rational < int More...

constexpr bool	operator<= (const Rational< IntType > &anotherRational) const
	<= Comparison between 2 rationals More...

template<typename NonRationalType >
constexpr bool	operator<= (const NonRationalType &nonRational) const
	<= Comparison between a rational and a non-rational. Example: Rational <= int More...

constexpr bool	operator> (const Rational< IntType > &anotherRational) const
	> Comparison between 2 rationals More...

template<typename NonRationalType >
constexpr bool	operator> (const NonRationalType &nonRational) const
	> Comparison between a rational and a non-rational. Example: Rational > int More...

constexpr bool	operator>= (const Rational< IntType > &anotherRational) const
	>= Comparison between 2 rationals More...

template<typename NonRationalType >
constexpr bool	operator>= (const NonRationalType &nonRational) const
	>= Comparison between a rational and a non-rational. Example: Rational >= int More...

constexpr Rational< IntType >	operator+= (const Rational< IntType > &anotherRational)
	Addition assignment operation between 2 rationals. More...

template<typename NonRationalType >
constexpr Rational< IntType >	operator+= (const NonRationalType &nonRational)
	Addition assignment operation between a rational and another type. Example: Rational += int. More...

constexpr void	operator++ ()
	Increment operator. More...

constexpr Rational< IntType >	operator-= (const Rational< IntType > &anotherRational)

template<typename NonRationalType >
constexpr Rational< IntType >	operator-= (const NonRationalType &nonRational)
	Subtraction assignment operation between a rational and another type. Example: Rational - int. More...

constexpr void	operator-- ()
	Decrement operator. More...

constexpr Rational< IntType >	operator*= (const Rational< IntType > &anotherRational)
	Multiplication assignment operation between 2 rationals. More...

template<typename NonRationalType >
constexpr Rational< IntType >	operator*= (const NonRationalType &nonRational)
	Multiplication assignment operation between a rational and another type. Example: Rational * int. More...

constexpr Rational< IntType >	operator/= (const Rational< IntType > &anotherRational)
	Division assignment operation between 2 rationals. More...

template<typename NonRationalType >
constexpr Rational< IntType >	operator/= (const NonRationalType &nonRational)
	Multiplication assignment operation between a rational and another type. Example: Rational * int. More...

constexpr Rational< IntType >	inverse () const
	Inverse a rational : a / b into b / a. More...

constexpr Rational< IntType >	sqrt () const
	Give the square root of a rational. More...

constexpr Rational< IntType >	cos () const
	Give the cosine of a rational. More...

constexpr Rational< IntType >	exp () const
	Give the exponential of a rational. More...

template<typename FloatingType >
constexpr Rational< IntType >	pow (const FloatingType &k) const
	Give the power of a rational. More...

constexpr Rational< IntType >	abs () const
	Give the abs of a rational. More...

constexpr Rational< IntType >	simplify () const noexcept
	Simplify the Rational with GCD (called in constructor) More...

constexpr Rational< IntType >	toApproximation (unsigned int digitsKept=Constant::DEFAULT_KEPT_DIGITS_APPROXIMATE) const
	Get an approximation of a given Rational. We assume that you don't ask a bigger precision that you don't have. More...

constexpr IntType	toInteger () const noexcept
	Get the integer part of the ratio. More...

template<typename FloatingType = float>
constexpr FloatingType	toRealNumber () const noexcept
	Get an approximation floating point number of the ratio. More...

std::string	toString () const noexcept
	Return ( numerator / denominator ) as a string. More...

template<typename FloatingType >
Rational< IntType > constexpr	fromFloatingPoint (const FloatingType floatingRatio, size_t iter)

Static Public Member Functions
static constexpr Rational< IntType >	min (Rational< IntType > rational1, Rational< IntType > rational2) noexcept
	Return the minimum between two rationals. More...

template<typename ... Args>
static constexpr Rational< IntType >	min (Rational< IntType > rational, Args... args) noexcept
	Variadic: Return the minimum between various rationals. More...

static constexpr Rational< IntType >	max (Rational< IntType > rational1, Rational< IntType > rational2) noexcept
	Return the maximum between two rationals. More...

template<typename ... Args>
static constexpr Rational< IntType >	max (Rational< IntType > rational, Args... args) noexcept
	Variadic: Return the maximum between various rationals. More...

static constexpr Rational< IntType >	Zero () noexcept
	Return zero in Rational Type. More...

static constexpr Rational< IntType >	One () noexcept
	Return one in Rational Type. More...

static constexpr Rational< IntType >	Pi () noexcept
	Return Pi in Rational Type. More...

static constexpr Rational< IntType >	Infinite () noexcept
	Return an approximation of +infinite in Rational Type. More...

template<typename FloatingType = double>
static constexpr Rational< IntType >	fromFloatingPoint (FloatingType floatingRatio, size_t iter=Constant::DEFAULT_ITERATIONS_FROM_FP)
	A method who automatically set numerator and denominator to approach the float parameter. More...

constexpr static void	print (const Rational< IntType > rational) noexcept
	Print the value of a rational. More...

template<typename... Args>
constexpr static void	print (const Rational< IntType > rational, Args... args) noexcept
	Variadic: Print the values of various rationals. More...

Protected Member Functions
constexpr void	verifyTemplateType () const
	Verify if the template is correct. Throw an exception if the template is a floating point. More...

constexpr void	verifyDenominator (IntType denominator, bool checkIfDenominatorIsNull=true)
	Verify if the denominator is null or negative. More...

template<typename AnotherIntType >
constexpr void	verifyNumberLargeness (Rational< AnotherIntType > &anotherRational) const
	Verify if the operands are superior to the limit of IntType. More...

Static Protected Member Functions
static constexpr Rational< IntType >	checkForOverflowThenReturn (const long long int numerator, const long long int denominator)
	Check for overflow before returning a value. More...

Protected Attributes
IntType	m_numerator
	Rational's numerator. More...

IntType	m_denominator
	Rational's denominator. More...

Friends
template<typename NonRationalType >
constexpr friend Rational< IntType >	operator+ (const NonRationalType nonRational, const Rational< IntType > &rational)
	Addition operation between a non-rational and a rational. Example: int + Rational. More...

template<typename NonRationalType >
constexpr friend Rational< IntType >	operator- (const NonRationalType nonRational, const Rational< IntType > &rational)
	Subtraction operation between a non-rational and a rational. Example: int - Rational. More...

constexpr friend Rational	operator- (const Rational &rational)
	Unary operator, allow to do -Rational. More...

template<typename NonRationalType >
constexpr friend Rational< IntType >	operator* (const NonRationalType nonRational, const Rational< IntType > &rational)
	Multiplication operation between a non-rational and a rational. Example: int * Rational. More...

template<typename NonRationalType >
constexpr friend Rational< IntType >	operator/ (const NonRationalType nonRational, const Rational< IntType > &rational)
	Division operation between a non-rational and a rational. Example: int / Rational. More...

template<typename NonRationalType >
constexpr friend bool	operator== (const NonRationalType nonRational, const Rational< IntType > &rational)
	Comparison between a non-rational and a rational. Example: int == Rational. More...

template<typename NonRationalType >
constexpr friend bool	operator!= (const NonRationalType nonRational, const Rational< IntType > &rational)
	Different comparison between a non-rational and a rational. Example: int != Rational. More...

template<typename NonRationalType >
constexpr friend bool	operator< (const NonRationalType nonRational, const Rational< IntType > &rational)
	< Comparison between a non-rational and a rational. Example: int < Rational More...

template<typename NonRationalType >
constexpr friend bool	operator<= (const NonRationalType nonRational, const Rational< IntType > &rational)
	<= Comparison between a non-rational and a rational. Example: int <= Rational More...

template<typename NonRationalType >
constexpr friend bool	operator> (const NonRationalType nonRational, const Rational< IntType > &rational)
	< Comparison between a non-rational and a rational. Example: int > Rational More...

template<typename NonRationalType >
constexpr friend bool	operator>= (const NonRationalType nonRational, const Rational< IntType > &rational)
	>= Comparison between a non-rational and a rational. Example: int >= Rational More...

Detailed Description

template<typename IntType = int>
class Arkulib::Rational< IntType >

This class can be used to express rationals.

Template Parameters

IntType

Definition at line 27 of file Rational.hpp.

Constructor & Destructor Documentation

◆ Rational() [1/5]

template<typename IntType = int>

constexpr Arkulib::Rational< IntType >::Rational ( )

inlineconstexpr

Instantiate an object without parameters.

Definition at line 38 of file Rational.hpp.

◆ Rational() [2/5]

template<typename IntType >

constexpr Arkulib::Rational< IntType >::Rational	(	IntType	numerator,
		IntType	denominator,
		bool	willBeReduce = `true`,
		bool	willDenominatorBeVerified = `true`
	)

constexpr

Create a rational from a numerator and a denominator.

Parameters

numerator
denominator
willBeReduce
willDenominatorBeVerified

Definition at line 942 of file Rational.hpp.

◆ Rational() [3/5]

template<typename IntType >

template<typename FloatingType >

constexpr Arkulib::Rational< IntType >::Rational ( const FloatingType & nonRational )

explicitconstexpr

Create a rational from a floating number.

Template Parameters

FloatingType

Parameters

nonRational

Definition at line 958 of file Rational.hpp.

◆ Rational() [4/5]

template<typename IntType = int>

constexpr Arkulib::Rational< IntType >::Rational ( const Rational< IntType > & reference )

inlineconstexprdefault

Default copy constructor.

Parameters

reference

◆ Rational() [5/5]

template<typename IntType >

template<typename AnotherIntType >

constexpr Arkulib::Rational< IntType >::Rational ( Rational< AnotherIntType > & copiedRational )

explicitconstexpr

Copy constructor with another int type.

Template Parameters

AnotherIntType

Parameters

copiedRational

Definition at line 981 of file Rational.hpp.

◆ ~Rational()

template<typename IntType = int>

Arkulib::Rational< IntType >::~Rational ( )

inlinedefault

Default Destructor.

Member Function Documentation

◆ getNumerator()

template<typename IntType = int>

constexpr IntType Arkulib::Rational< IntType >::getNumerator ( ) const

inlineconstexprnoexcept

Definition at line 85 of file Rational.hpp.

◆ getDenominator()

template<typename IntType = int>

constexpr IntType Arkulib::Rational< IntType >::getDenominator ( ) const

inlineconstexprnoexcept

Definition at line 87 of file Rational.hpp.

◆ operator[]() [1/2]

template<typename IntType >

const IntType & Arkulib::Rational< IntType >::operator[] ( const size_t & id ) const

inline

Getter with [] operator.

Parameters

id

Returns: If id == 0 => return numerator; if id == 1 => return denominator

Definition at line 991 of file Rational.hpp.

◆ getLargerOperand()

template<typename IntType = int>

constexpr IntType Arkulib::Rational< IntType >::getLargerOperand ( ) const

inlineconstexprnoexcept

Returns: The numerator if numerator > denominator. Return denominator else.

Definition at line 99 of file Rational.hpp.

◆ getLowerOperand()

template<typename IntType = int>

constexpr IntType Arkulib::Rational< IntType >::getLowerOperand ( ) const

inlineconstexprnoexcept

Returns: The denominator if numerator > denominator. Return numerator else.

Definition at line 106 of file Rational.hpp.

◆ setNumerator()

template<typename IntType = int>

constexpr void Arkulib::Rational< IntType >::setNumerator ( IntType numerator )

inlineconstexpr

Definition at line 114 of file Rational.hpp.

◆ setDenominator()

template<typename IntType = int>

constexpr void Arkulib::Rational< IntType >::setDenominator ( IntType denominator )

inlineconstexpr

Definition at line 116 of file Rational.hpp.

◆ operator[]() [2/2]

template<typename IntType >

IntType & Arkulib::Rational< IntType >::operator[] ( const size_t & id )

inline

Setter with [] operator. Example: rational[0] = 1 and rational[1] = 2 //// total => (1/2)

Parameters

id

Definition at line 998 of file Rational.hpp.

◆ isNegative()

template<typename IntType = int>

bool Arkulib::Rational< IntType >::isNegative ( ) const

inlinenoexcept

Returns: True if the rational is negative

Definition at line 134 of file Rational.hpp.

◆ isInteger()

template<typename IntType = int>

bool Arkulib::Rational< IntType >::isInteger ( ) const

inlinenoexcept

Returns: True if the rational is an integer

Definition at line 139 of file Rational.hpp.

◆ isZero()

template<typename IntType = int>

bool Arkulib::Rational< IntType >::isZero ( ) const

inlinenoexcept

Returns: True if the rational is equal to zero

Definition at line 144 of file Rational.hpp.

◆ operator+() [1/2]

template<typename IntType >

constexpr Rational< IntType > Arkulib::Rational< IntType >::operator+ ( const Rational< IntType > & anotherRational ) const

constexpr

Addition operation between 2 rationals.

Parameters

anotherRational

Returns: The sum in Rational

Definition at line 1009 of file Rational.hpp.

◆ operator+() [2/2]

template<typename IntType = int>

template<typename NonRationalType >

constexpr Rational< IntType > Arkulib::Rational< IntType >::operator+ ( const NonRationalType & nonRational ) const

inlineconstexpr

Addition operation between a rational and another type. Example: Rational + int.

Template Parameters

NonRationalType

Parameters

nonRational

Returns: The sum in Rational

Definition at line 164 of file Rational.hpp.

◆ operator-() [1/2]

template<typename IntType >

constexpr Rational< IntType > Arkulib::Rational< IntType >::operator- ( const Rational< IntType > & anotherRational ) const

constexpr

Subtraction operation between 2 rationals.

Parameters

anotherRational

Returns: The subtraction in Rational

Definition at line 1021 of file Rational.hpp.

◆ operator-() [2/2]

template<typename IntType = int>

template<typename NonRationalType >

constexpr Rational< IntType > Arkulib::Rational< IntType >::operator- ( const NonRationalType & nonRational ) const

inlineconstexpr

Subtraction operation between a rational and another type. Example: Rational - int.

Template Parameters

NonRationalType

Parameters

nonRational

Returns: The subtraction in Rational

Definition at line 201 of file Rational.hpp.

◆ operator*() [1/2]

template<typename IntType >

constexpr Rational< IntType > Arkulib::Rational< IntType >::operator* ( const Rational< IntType > & anotherRational ) const

constexpr

Multiplication operation between 2 rationals.

Parameters

anotherRational

Returns: The multiplication in Rational

Definition at line 1033 of file Rational.hpp.

◆ operator*() [2/2]

template<typename IntType = int>

template<typename NonRationalType >

constexpr Rational< IntType > Arkulib::Rational< IntType >::operator* ( const NonRationalType & nonRational ) const

inlineconstexpr

Multiplication operation between a rational and another type. Example: Rational * int.

Template Parameters

NonRationalType

Parameters

nonRational

Returns: The multiplication in Rational

Definition at line 247 of file Rational.hpp.

◆ operator/() [1/2]

template<typename IntType >

constexpr Rational< IntType > Arkulib::Rational< IntType >::operator/ ( const Rational< IntType > & anotherRational ) const

constexpr

Division operation between 2 rationals.

Parameters

anotherRational

Returns: The division in Rational

Definition at line 1045 of file Rational.hpp.

◆ operator/() [2/2]

template<typename IntType = int>

template<typename NonRationalType >

constexpr Rational< IntType > Arkulib::Rational< IntType >::operator/ ( const NonRationalType & nonRational ) const

inlineconstexpr

Division operation between a rational and another type. Example: Rational / int.

Template Parameters

NonRationalType

Parameters

nonRational

Returns: The division in Rational

Definition at line 284 of file Rational.hpp.

◆ operator==() [1/2]

template<typename IntType = int>

constexpr bool Arkulib::Rational< IntType >::operator== ( const Rational< IntType > & anotherRational ) const

inlineconstexpr

Comparison between 2 rationals.

Parameters

anotherRational

Returns: True if the first rational is equal to the second

Definition at line 312 of file Rational.hpp.

◆ operator==() [2/2]

template<typename IntType = int>

template<typename NonRationalType >

constexpr bool Arkulib::Rational< IntType >::operator== ( const NonRationalType & nonRational ) const

inlineconstexpr

Comparison between a rational and a non-rational. Example: Rational == int.

Template Parameters

NonRationalType

Parameters

nonRational

Returns: True if the rational is equal to the second operand

Definition at line 327 of file Rational.hpp.

◆ operator!=() [1/2]

template<typename IntType = int>

constexpr bool Arkulib::Rational< IntType >::operator!= ( const Rational< IntType > & anotherRational ) const

inlineconstexpr

Different comparison between 2 rationals.

Parameters

anotherRational

Returns: True if the first rational is different to the second

Definition at line 355 of file Rational.hpp.

◆ operator!=() [2/2]

template<typename IntType = int>

template<typename NonRationalType >

constexpr bool Arkulib::Rational< IntType >::operator!= ( const NonRationalType & nonRational ) const

inlineconstexpr

Different comparison between a rational and a non-rational. Example: Rational != int.

Template Parameters

NonRationalType

Parameters

nonRational

Returns: True if the rational is different to the second operand

Definition at line 370 of file Rational.hpp.

◆ operator<() [1/2]

template<typename IntType = int>

constexpr bool Arkulib::Rational< IntType >::operator< ( const Rational< IntType > & anotherRational ) const

inlineconstexpr

< Comparison between 2 rationals

Parameters

anotherRational

Returns: True if the first rational is inferior to the second

Definition at line 398 of file Rational.hpp.

◆ operator<() [2/2]

template<typename IntType = int>

template<typename NonRationalType >

constexpr bool Arkulib::Rational< IntType >::operator< ( const NonRationalType & nonRational ) const

inlineconstexpr

< Comparison between a rational and a non-rational. Example: Rational < int

Template Parameters

NonRationalType

Parameters

nonRational

Returns: True if the rational is inferior to the second operand

Definition at line 409 of file Rational.hpp.

◆ operator<=() [1/2]

template<typename IntType = int>

constexpr bool Arkulib::Rational< IntType >::operator<= ( const Rational< IntType > & anotherRational ) const

inlineconstexpr

<= Comparison between 2 rationals

Parameters

anotherRational

Returns: True if the first rational is inferior to the second

Definition at line 435 of file Rational.hpp.

◆ operator<=() [2/2]

template<typename IntType = int>

template<typename NonRationalType >

constexpr bool Arkulib::Rational< IntType >::operator<= ( const NonRationalType & nonRational ) const

inlineconstexpr

<= Comparison between a rational and a non-rational. Example: Rational <= int

Template Parameters

NonRationalType

Parameters

nonRational

Returns: True if the rational is inferior to the second operand

Definition at line 446 of file Rational.hpp.

◆ operator>() [1/2]

template<typename IntType = int>

constexpr bool Arkulib::Rational< IntType >::operator> ( const Rational< IntType > & anotherRational ) const

inlineconstexpr

> Comparison between 2 rationals

Parameters

anotherRational

Returns: True if the first rational is inferior to the second

Definition at line 474 of file Rational.hpp.

◆ operator>() [2/2]

template<typename IntType = int>

template<typename NonRationalType >

constexpr bool Arkulib::Rational< IntType >::operator> ( const NonRationalType & nonRational ) const

inlineconstexpr

> Comparison between a rational and a non-rational. Example: Rational > int

Template Parameters

NonRationalType

Parameters

nonRational

Returns: True if the rational is inferior to the second operand

Definition at line 485 of file Rational.hpp.

◆ operator>=() [1/2]

template<typename IntType = int>

constexpr bool Arkulib::Rational< IntType >::operator>= ( const Rational< IntType > & anotherRational ) const

inlineconstexpr

>= Comparison between 2 rationals

Parameters

anotherRational

Returns: True if the first rational is inferior to the second

Definition at line 513 of file Rational.hpp.

◆ operator>=() [2/2]

template<typename IntType = int>

template<typename NonRationalType >

constexpr bool Arkulib::Rational< IntType >::operator>= ( const NonRationalType & nonRational ) const

inlineconstexpr

>= Comparison between a rational and a non-rational. Example: Rational >= int

Template Parameters

NonRationalType

Parameters

nonRational

Returns: True if the rational is inferior to the second operand

Definition at line 524 of file Rational.hpp.

◆ operator+=() [1/2]

template<typename IntType = int>

constexpr Rational< IntType > Arkulib::Rational< IntType >::operator+= ( const Rational< IntType > & anotherRational )

inlineconstexpr

Addition assignment operation between 2 rationals.

Parameters

anotherRational

Returns: The sum assignment in Rational

Definition at line 552 of file Rational.hpp.

◆ operator+=() [2/2]

template<typename IntType = int>

template<typename NonRationalType >

constexpr Rational< IntType > Arkulib::Rational< IntType >::operator+= ( const NonRationalType & nonRational )

inlineconstexpr

Addition assignment operation between a rational and another type. Example: Rational += int.

Template Parameters

NonRationalType

Parameters

nonRational

Returns: The sum assigment in Rational

Definition at line 564 of file Rational.hpp.

◆ operator++()

template<typename IntType = int>

constexpr void Arkulib::Rational< IntType >::operator++ ( )

inlineconstexpr

Increment operator.

Definition at line 576 of file Rational.hpp.

◆ operator-=() [1/2]

template<typename IntType = int>

constexpr Rational< IntType > Arkulib::Rational< IntType >::operator-= ( const Rational< IntType > & anotherRational )

inlineconstexpr

Parameters

anotherRational

Returns: The subtraction in Rational

Definition at line 587 of file Rational.hpp.

◆ operator-=() [2/2]

template<typename IntType = int>

template<typename NonRationalType >

constexpr Rational< IntType > Arkulib::Rational< IntType >::operator-= ( const NonRationalType & nonRational )

inlineconstexpr

Subtraction assignment operation between a rational and another type. Example: Rational - int.

Template Parameters

NonRationalType

Parameters

nonRational

Returns: The subtraction assigment in Rational

Definition at line 599 of file Rational.hpp.

◆ operator--()

template<typename IntType = int>

constexpr void Arkulib::Rational< IntType >::operator-- ( )

inlineconstexpr

Decrement operator.

Definition at line 611 of file Rational.hpp.

◆ operator*=() [1/2]

template<typename IntType = int>

constexpr Rational< IntType > Arkulib::Rational< IntType >::operator*= ( const Rational< IntType > & anotherRational )

inlineconstexpr

Multiplication assignment operation between 2 rationals.

Parameters

anotherRational

Returns: The multiplication in Rational

Definition at line 622 of file Rational.hpp.

◆ operator*=() [2/2]

template<typename IntType = int>

template<typename NonRationalType >

constexpr Rational< IntType > Arkulib::Rational< IntType >::operator*= ( const NonRationalType & nonRational )

inlineconstexpr

Multiplication assignment operation between a rational and another type. Example: Rational * int.

Template Parameters

NonRationalType

Parameters

nonRational

Returns: The multiplication assigment in Rational

Definition at line 634 of file Rational.hpp.

◆ operator/=() [1/2]

template<typename IntType = int>

constexpr Rational< IntType > Arkulib::Rational< IntType >::operator/= ( const Rational< IntType > & anotherRational )

inlineconstexpr

Division assignment operation between 2 rationals.

Parameters

anotherRational

Returns: The division in Rational

Definition at line 648 of file Rational.hpp.

◆ operator/=() [2/2]

template<typename IntType = int>

template<typename NonRationalType >

constexpr Rational< IntType > Arkulib::Rational< IntType >::operator/= ( const NonRationalType & nonRational )

inlineconstexpr

Multiplication assignment operation between a rational and another type. Example: Rational * int.

Template Parameters

NonRationalType

Parameters

nonRational

Returns: The multiplication assigment in Rational

Definition at line 660 of file Rational.hpp.

◆ inverse()

template<typename IntType = int>

constexpr Rational< IntType > Arkulib::Rational< IntType >::inverse ( ) const

inlineconstexpr

Inverse a rational : a / b into b / a.

Returns: The inverted Rational

Definition at line 674 of file Rational.hpp.

◆ sqrt()

template<typename IntType >

constexpr Rational< IntType > Arkulib::Rational< IntType >::sqrt

constexpr

Give the square root of a rational.

Returns: The square root as a Rational

Definition at line 1057 of file Rational.hpp.

◆ cos()

template<typename IntType >

Rational< IntType > constexpr Arkulib::Rational< IntType >::cos

constexpr

Give the cosine of a rational.

Returns: The cosine as a Rational

Definition at line 1065 of file Rational.hpp.

◆ exp()

template<typename IntType >

Rational< IntType > constexpr Arkulib::Rational< IntType >::exp

constexpr

Give the exponential of a rational.

Returns: The exponential as a Rational

Definition at line 1072 of file Rational.hpp.

◆ pow()

template<typename IntType >

template<typename FloatingType >

constexpr Rational< IntType > Arkulib::Rational< IntType >::pow ( const FloatingType & k ) const

constexpr

Give the power of a rational.

Returns: The power as a Rational

Definition at line 1080 of file Rational.hpp.

◆ abs()

template<typename IntType = int>

constexpr Rational< IntType > Arkulib::Rational< IntType >::abs ( ) const

inlineconstexpr

Give the abs of a rational.

Returns: The Rational in absolute value

Definition at line 708 of file Rational.hpp.

◆ simplify()

template<typename IntType >

Rational< IntType > constexpr Arkulib::Rational< IntType >::simplify

constexprnoexcept

Simplify the Rational with GCD (called in constructor)

Definition at line 1087 of file Rational.hpp.

◆ min() [1/2]

template<typename IntType >

constexpr Rational< IntType > Arkulib::Rational< IntType >::min	(	Rational< IntType >	rational1,
		Rational< IntType >	rational2
	)

staticconstexprnoexcept

Return the minimum between two rationals.

Parameters

rational1
rational2

Returns

Definition at line 1103 of file Rational.hpp.

◆ min() [2/2]

template<typename IntType >

template<typename... Args>

constexpr Rational< IntType > Arkulib::Rational< IntType >::min	(	Rational< IntType >	rational,
		Args...	args
	)

staticconstexprnoexcept

Variadic: Return the minimum between various rationals.

Template Parameters

Args

Parameters

rational
args

Returns

Definition at line 1112 of file Rational.hpp.

◆ max() [1/2]

template<typename IntType >

constexpr Rational< IntType > Arkulib::Rational< IntType >::max	(	Rational< IntType >	rational1,
		Rational< IntType >	rational2
	)

staticconstexprnoexcept

Return the maximum between two rationals.

Parameters

rational1
rational2

Returns

Definition at line 1124 of file Rational.hpp.

◆ max() [2/2]

template<typename IntType >

template<typename... Args>

constexpr Rational< IntType > Arkulib::Rational< IntType >::max	(	Rational< IntType >	rational,
		Args...	args
	)

staticconstexprnoexcept

Variadic: Return the maximum between various rationals.

Template Parameters

Args

Parameters

rational
args

Returns

Definition at line 1133 of file Rational.hpp.

◆ Zero()

template<typename IntType = int>

static constexpr Rational< IntType > Arkulib::Rational< IntType >::Zero ( )

inlinestaticconstexprnoexcept

Return zero in Rational Type.

Returns: Rational with 0 as numerator and 1 as denominator

Definition at line 781 of file Rational.hpp.

◆ One()

template<typename IntType = int>

static constexpr Rational< IntType > Arkulib::Rational< IntType >::One ( )

inlinestaticconstexprnoexcept

Return one in Rational Type.

Returns: Rational with 1 as numerator and 1 as denominator

Definition at line 787 of file Rational.hpp.

◆ Pi()

template<typename IntType = int>

static constexpr Rational< IntType > Arkulib::Rational< IntType >::Pi ( )

inlinestaticconstexprnoexcept

Return Pi in Rational Type.

Returns: An approximation of Pi

Definition at line 793 of file Rational.hpp.

◆ Infinite()

template<typename IntType = int>

static constexpr Rational< IntType > Arkulib::Rational< IntType >::Infinite ( )

inlinestaticconstexprnoexcept

Return an approximation of +infinite in Rational Type.

Returns: 1 as numerator and 0 as denominator

Definition at line 799 of file Rational.hpp.

◆ toApproximation()

template<typename IntType >

constexpr Rational< IntType > Arkulib::Rational< IntType >::toApproximation ( unsigned int digitsKept = Constant::DEFAULT_KEPT_DIGITS_APPROXIMATE ) const

inlineconstexpr

Get an approximation of a given Rational. We assume that you don't ask a bigger precision that you don't have.

Parameters

digitsKept

Returns: The approximated Ratio

Definition at line 1145 of file Rational.hpp.

◆ toInteger()

template<typename IntType = int>

constexpr IntType Arkulib::Rational< IntType >::toInteger ( ) const

inlineconstexprnoexcept

Get the integer part of the ratio.

Returns: An int (type IntType)

Definition at line 818 of file Rational.hpp.

◆ toRealNumber()

template<typename IntType = int>

template<typename FloatingType = float>

constexpr FloatingType Arkulib::Rational< IntType >::toRealNumber ( ) const

inlineconstexprnoexcept

Get an approximation floating point number of the ratio.

Template Parameters

FloatingType

Returns: A floating point number (type FloatingType)

Definition at line 829 of file Rational.hpp.

◆ toString()

template<typename IntType = int>

std::string Arkulib::Rational< IntType >::toString ( ) const

inlinenoexcept

Return ( numerator / denominator ) as a string.

Returns: std::string

Definition at line 838 of file Rational.hpp.

◆ fromFloatingPoint() [1/2]

template<typename IntType = int>

template<typename FloatingType = double>

static constexpr Rational< IntType > Arkulib::Rational< IntType >::fromFloatingPoint	(	FloatingType	floatingRatio,
		size_t	iter = `Constant::DEFAULT_ITERATIONS_FROM_FP`
	)

staticconstexpr

A method who automatically set numerator and denominator to approach the float parameter.

Template Parameters

FloatingType

Parameters

floatingRatio
iter

Returns: The rational wanted

◆ print() [1/2]

template<typename IntType = int>

constexpr static void Arkulib::Rational< IntType >::print ( const Rational< IntType > rational )

inlinestaticconstexprnoexcept

Print the value of a rational.

Template Parameters

IntType

Parameters

rational

Definition at line 860 of file Rational.hpp.

◆ print() [2/2]

template<typename IntType = int>

template<typename... Args>

constexpr static void Arkulib::Rational< IntType >::print	(	const Rational< IntType >	rational,
		Args...	args
	)

inlinestaticconstexprnoexcept

Variadic: Print the values of various rationals.

Template Parameters

IntType
Args

Parameters

rational
args

Definition at line 872 of file Rational.hpp.

◆ verifyTemplateType()

template<typename IntType = int>

constexpr void Arkulib::Rational< IntType >::verifyTemplateType ( ) const

inlineconstexprprotected

Verify if the template is correct. Throw an exception if the template is a floating point.

Definition at line 894 of file Rational.hpp.

◆ verifyDenominator()

template<typename IntType >

constexpr void Arkulib::Rational< IntType >::verifyDenominator	(	IntType	denominator,
		bool	checkIfDenominatorIsNull = `true`
	)

constexprprotected

Verify if the denominator is null or negative.

Parameters

denominator
checkIfDenominatorIsNull

Definition at line 1195 of file Rational.hpp.

◆ verifyNumberLargeness()

template<typename IntType >

template<typename AnotherIntType >

constexpr void Arkulib::Rational< IntType >::verifyNumberLargeness ( Rational< AnotherIntType > & anotherRational ) const

constexprprotected

Verify if the operands are superior to the limit of IntType.

Template Parameters

AnotherIntType

Parameters

anotherRational

Definition at line 1183 of file Rational.hpp.

◆ checkForOverflowThenReturn()

template<typename IntType = int>

static constexpr Rational< IntType > Arkulib::Rational< IntType >::checkForOverflowThenReturn	(	const long long int	numerator,
		const long long int	denominator
	)

inlinestaticconstexprprotected

Check for overflow before returning a value.

Parameters

numerator
denominator

Returns: The rational if there is no error. If these is an overflow error, it'll throw an exception

Definition at line 919 of file Rational.hpp.

◆ fromFloatingPoint() [2/2]

template<typename IntType = int>

template<typename FloatingType >

Rational< IntType > constexpr Arkulib::Rational< IntType >::fromFloatingPoint	(	const FloatingType	floatingRatio,
		size_t	iter
	)

constexpr

Definition at line 1152 of file Rational.hpp.

Friends And Related Function Documentation

◆ operator+

template<typename IntType = int>

template<typename NonRationalType >

constexpr friend Rational< IntType > operator+	(	const NonRationalType	nonRational,
		const Rational< IntType > &	rational
	)

friend

Addition operation between a non-rational and a rational. Example: int + Rational.

Template Parameters

NonRationalType

Parameters

nonRational
rational

Returns: The sum in Rational

Definition at line 176 of file Rational.hpp.

◆ operator- [1/2]

template<typename IntType = int>

template<typename NonRationalType >

constexpr friend Rational< IntType > operator-	(	const NonRationalType	nonRational,
		const Rational< IntType > &	rational
	)

friend

Subtraction operation between a non-rational and a rational. Example: int - Rational.

Template Parameters

NonRationalType

Parameters

nonRational
rational

Returns: The subtraction in Rational

Definition at line 213 of file Rational.hpp.

◆ operator- [2/2]

template<typename IntType = int>

constexpr friend Rational operator- ( const Rational< IntType > & rational )

friend

Unary operator, allow to do -Rational.

Parameters

rational

Returns: The rational in negative

Definition at line 225 of file Rational.hpp.

◆ operator*

template<typename IntType = int>

template<typename NonRationalType >

constexpr friend Rational< IntType > operator*	(	const NonRationalType	nonRational,
		const Rational< IntType > &	rational
	)

friend

Multiplication operation between a non-rational and a rational. Example: int * Rational.

Template Parameters

NonRationalType

Parameters

nonRational
rational

Returns: The multiplication in Rational

Definition at line 259 of file Rational.hpp.

◆ operator/

template<typename IntType = int>

template<typename NonRationalType >

constexpr friend Rational< IntType > operator/	(	const NonRationalType	nonRational,
		const Rational< IntType > &	rational
	)

friend

Division operation between a non-rational and a rational. Example: int / Rational.

Template Parameters

NonRationalType

Parameters

nonRational
rational

Returns: The division in Rational

Definition at line 296 of file Rational.hpp.

◆ operator==

template<typename IntType = int>

template<typename NonRationalType >

constexpr friend bool operator==	(	const NonRationalType	nonRational,
		const Rational< IntType > &	rational
	)

friend

Comparison between a non-rational and a rational. Example: int == Rational.

Template Parameters

NonRationalType

Parameters

nonRational
rational

Returns: True if the non-rational is equal to the rational

Definition at line 339 of file Rational.hpp.

◆ operator!=

template<typename IntType = int>

template<typename NonRationalType >

constexpr friend bool operator!=	(	const NonRationalType	nonRational,
		const Rational< IntType > &	rational
	)

friend

Different comparison between a non-rational and a rational. Example: int != Rational.

Template Parameters

NonRationalType

Parameters

nonRational
rational

Returns: True if the non-rational is different to the rational

Definition at line 382 of file Rational.hpp.

◆ operator<

template<typename IntType = int>

template<typename NonRationalType >

constexpr friend bool operator<	(	const NonRationalType	nonRational,
		const Rational< IntType > &	rational
	)

friend

< Comparison between a non-rational and a rational. Example: int < Rational

Template Parameters

NonRationalType

Parameters

nonRational
rational

Returns: True if the non-rational is inferior to the rational

Definition at line 419 of file Rational.hpp.

◆ operator<=

template<typename IntType = int>

template<typename NonRationalType >

constexpr friend bool operator<=	(	const NonRationalType	nonRational,
		const Rational< IntType > &	rational
	)

friend

<= Comparison between a non-rational and a rational. Example: int <= Rational

Template Parameters

NonRationalType

Parameters

nonRational
rational

Returns: True if the non-rational is inferior to the rational

Definition at line 458 of file Rational.hpp.

◆ operator>

template<typename IntType = int>

template<typename NonRationalType >

constexpr friend bool operator>	(	const NonRationalType	nonRational,
		const Rational< IntType > &	rational
	)

friend

< Comparison between a non-rational and a rational. Example: int > Rational

Template Parameters

NonRationalType

Parameters

nonRational
rational

Returns: True if the non-rational is superior to the rational

Definition at line 497 of file Rational.hpp.

◆ operator>=

template<typename IntType = int>

template<typename NonRationalType >

constexpr friend bool operator>=	(	const NonRationalType	nonRational,
		const Rational< IntType > &	rational
	)

friend

>= Comparison between a non-rational and a rational. Example: int >= Rational

Template Parameters

NonRationalType

Parameters

nonRational
rational

Returns: True if the non-rational is superior to the rational

Definition at line 536 of file Rational.hpp.

Member Data Documentation

◆ m_numerator

template<typename IntType = int>

IntType Arkulib::Rational< IntType >::m_numerator

protected

Rational's numerator.

Definition at line 883 of file Rational.hpp.

◆ m_denominator

template<typename IntType = int>

IntType Arkulib::Rational< IntType >::m_denominator

protected

Rational's denominator.

Definition at line 885 of file Rational.hpp.

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

include/Rational.hpp

Public Member Functions

Static Public Member Functions

Protected Member Functions

Static Protected Member Functions

Protected Attributes

Friends

Detailed Description

Constructor & Destructor Documentation

◆ Rational() [1/5]

◆ Rational() [2/5]

◆ Rational() [3/5]

◆ Rational() [4/5]

◆ Rational() [5/5]

◆ ~Rational()

Member Function Documentation

◆ getNumerator()

◆ getDenominator()

◆ operator[]() [1/2]

◆ getLargerOperand()

◆ getLowerOperand()

◆ setNumerator()

◆ setDenominator()

◆ operator[]() [2/2]

◆ isNegative()

◆ isInteger()

◆ isZero()

◆ operator+() [1/2]

◆ operator+() [2/2]

◆ operator-() [1/2]

◆ operator-() [2/2]

◆ operator*() [1/2]

◆ operator*() [2/2]

◆ operator/() [1/2]

◆ operator/() [2/2]

◆ operator==() [1/2]

◆ operator==() [2/2]

◆ operator!=() [1/2]

◆ operator!=() [2/2]

◆ operator<() [1/2]

◆ operator<() [2/2]

◆ operator<=() [1/2]

◆ operator<=() [2/2]

◆ operator>() [1/2]

◆ operator>() [2/2]

◆ operator>=() [1/2]

◆ operator>=() [2/2]

◆ operator+=() [1/2]

◆ operator+=() [2/2]

◆ operator++()

◆ operator-=() [1/2]

◆ operator-=() [2/2]

◆ operator--()

◆ operator*=() [1/2]

◆ operator*=() [2/2]

◆ operator/=() [1/2]

◆ operator/=() [2/2]

◆ inverse()

◆ sqrt()

◆ cos()

◆ exp()

◆ pow()

◆ abs()

◆ simplify()

◆ min() [1/2]

◆ min() [2/2]

◆ max() [1/2]

◆ max() [2/2]

◆ Zero()

◆ One()

◆ Pi()

◆ Infinite()

◆ toApproximation()

◆ toInteger()

◆ toRealNumber()

◆ toString()

◆ fromFloatingPoint() [1/2]

◆ print() [1/2]

◆ print() [2/2]

◆ verifyTemplateType()

◆ verifyDenominator()