fun::Fraction< Z > Struct Template Reference

Fraction. More...

#include <fractions.hpp>

Collaboration diagram for fun::Fraction< Z >:

Public Member Functions
constexpr	Fraction (Z num, Z den)
	Construct a new Fraction object from two values.
constexpr auto	normalize () -> Z
	normalize to a canonical form
constexpr void	normalize1 ()
	normalize to a canonical form
constexpr auto	normalize2 () -> Z
	normalize to a canonical form
constexpr	Fraction (Z &&num)
	Construct a new Fraction object from a single value (rvalue).
constexpr	Fraction (const Z &num)
	Construct a new Fraction object from a single value (const ref).
constexpr	Fraction ()
	Default construct a new Fraction object (0/1).
constexpr auto	num () const noexcept -> const Z &
constexpr auto	den () const noexcept -> const Z &
constexpr auto	cross (const Fraction &rhs) const -> Z
	Cross product of two fractions.
constexpr void	reciprocal () noexcept(std::is_nothrow_swappable_v< Z >)
	reciprocal
constexpr auto	operator*= (Fraction rhs) -> Fraction &
	multiply and assign
constexpr auto	operator*= (Z rhs) -> Fraction &
	multiply and assign
constexpr auto	operator/= (Fraction rhs) -> Fraction &
	divide and assign
constexpr auto	operator/= (const Z &rhs) -> Fraction &
	divide and assign
constexpr auto	operator- () const -> Fraction
	Negate.
constexpr auto	operator+ (const Fraction &rhs) const -> Fraction
	Add.
constexpr auto	operator- (const Fraction &frac) const -> Fraction
	Subtract.
constexpr auto	operator- (const Z &i) const -> Fraction
constexpr auto	operator+= (const Fraction &rhs) -> Fraction &
constexpr auto	operator-= (const Fraction &rhs) -> Fraction &
constexpr auto	operator+= (const Z &i) -> Fraction &
constexpr auto	operator-= (const Z &rhs) -> Fraction &

Public Attributes
Z	_num
Z	_den

Friends
constexpr auto	operator* (Fraction lhs, const Fraction &rhs) -> Fraction
	multiply
constexpr auto	operator* (Fraction lhs, const Z &rhs) -> Fraction
	multiply
constexpr auto	operator* (const Z &lhs, Fraction rhs) -> Fraction
	multiply
constexpr auto	operator/ (Fraction lhs, const Fraction &rhs) -> Fraction
	divide
constexpr auto	operator/ (Fraction lhs, const Z &rhs) -> Fraction
	divide
constexpr auto	operator/ (const Z &lhs, Fraction rhs) -> Fraction
	divide
constexpr auto	operator+ (Fraction frac, const Z &i) -> Fraction
	Add.
constexpr auto	operator+ (const Z &i, Fraction frac) -> Fraction
	Add.
constexpr auto	operator- (const Z &c, const Fraction &frac) -> Fraction
constexpr auto	operator+ (int &&c, const Fraction &frac) -> Fraction
constexpr auto	operator- (int &&c, const Fraction &frac) -> Fraction
constexpr auto	operator* (int &&c, const Fraction &frac) -> Fraction
template<typename Stream >
auto	operator<< (Stream &os, const Fraction &frac) -> Stream &

Comparison operators
==, !=, <, >, <=, >= etc.
constexpr auto	operator!= (const Fraction &rhs) const -> bool
constexpr auto	operator> (const Fraction &rhs) const -> bool
	Greater than.
constexpr auto	operator>= (const Fraction &rhs) const -> bool
	Greater than or euqal to.
constexpr auto	operator<= (const Fraction &rhs) const -> bool
	Less than or equal to.
constexpr auto	operator> (const Z &rhs) const -> bool
	Greater than.
constexpr auto	operator<= (const Z &rhs) const -> bool
	Less than or equal to.
constexpr auto	operator>= (const Z &rhs) const -> bool
	Greater than or equal to.
constexpr auto	operator== (Fraction lhs, Z rhs) -> bool
	Equal to.
constexpr auto	operator< (Fraction lhs, Z rhs) -> bool
	Less than.
constexpr auto	operator< (Z lhs, Fraction rhs) -> bool
	Less than.
constexpr auto	operator== (const Z &lhs, const Fraction &rhs) -> bool
	Equal to.
constexpr friend auto	operator== (Fraction lhs, Fraction rhs) -> bool
	Equal to.
constexpr friend auto	operator< (Fraction lhs, Fraction rhs) -> bool
	Less than.
constexpr auto	operator> (const Z &lhs, const Fraction &rhs) -> bool
	Greater than.
constexpr auto	operator<= (const Z &lhs, const Fraction &rhs) -> bool
	Less than or equal to.
constexpr auto	operator>= (const Z &lhs, const Fraction &rhs) -> bool
	Greater than or euqal to.

Detailed Description

template<Integral Z>
struct fun::Fraction< Z >

Fraction.

Template Parameters

Z

Constructor & Destructor Documentation

Fraction() [1/4]

template<Integral Z>

constexpr fun::Fraction< Z >::Fraction ( Z  num, Z  den  )

inlineconstexpr

Construct a new Fraction object from two values.

Parameters

[in]	num	numerator
[in]	den	denominator

Fraction() [2/4]

template<Integral Z>

constexpr fun::Fraction< Z >::Fraction ( Z &&  num )

inlineexplicitconstexpr

Construct a new Fraction object from a single value (rvalue).

Fraction() [3/4]

template<Integral Z>

constexpr fun::Fraction< Z >::Fraction ( const Z &  num )

inlineexplicitconstexpr

Construct a new Fraction object from a single value (const ref).

Fraction() [4/4]

template<Integral Z>

constexpr fun::Fraction< Z >::Fraction ( )

inlineconstexpr

Default construct a new Fraction object (0/1).

Member Function Documentation

cross()

template<Integral Z>

constexpr auto fun::Fraction< Z >::cross ( const Fraction< Z > &  rhs ) const -> Z

inlineconstexpr

Cross product of two fractions.

\[ a/b \times c/d = ad - bc \]

Parameters

[in]

rhs

Returns

Z

den()

template<Integral Z>

constexpr auto fun::Fraction< Z >::den ( ) const -> const Z&

inlineconstexprnoexcept

Returns

const Z&

normalize()

template<Integral Z>

constexpr auto fun::Fraction< Z >::normalize ( ) -> Z

inlineconstexpr

normalize to a canonical form

denominator is always non-negative and co-prime with numerator

normalize1()

template<Integral Z>

constexpr void fun::Fraction< Z >::normalize1 ( )

inlineconstexpr

normalize to a canonical form

denominator is always non-negative

normalize2()

template<Integral Z>

constexpr auto fun::Fraction< Z >::normalize2 ( ) -> Z

inlineconstexpr

normalize to a canonical form

denominator is always co-prime with numerator

num()

template<Integral Z>

constexpr auto fun::Fraction< Z >::num ( ) const -> const Z&

inlineconstexprnoexcept

Returns

const Z&

operator!=()

template<Integral Z>

constexpr auto fun::Fraction< Z >::operator!= ( const Fraction< Z > &  rhs ) const -> bool

inlineconstexpr

Parameters

[in]

rhs

Returns

true

false

operator*=() [1/2]

template<Integral Z>

constexpr auto fun::Fraction< Z >::operator*= ( Fraction< Z >  rhs ) -> Fraction&

inlineconstexpr

multiply and assign

Parameters

[in]

rhs

Returns

Fraction&

operator*=() [2/2]

template<Integral Z>

constexpr auto fun::Fraction< Z >::operator*= ( Z  rhs ) -> Fraction&

inlineconstexpr

multiply and assign

Parameters

[in]

rhs

Returns

Fraction&

operator+()

template<Integral Z>

constexpr auto fun::Fraction< Z >::operator+ ( const Fraction< Z > &  rhs ) const -> Fraction

inlineconstexpr

Add.

Parameters

[in]

rhs

Returns

Fraction

operator+=() [1/2]

template<Integral Z>

constexpr auto fun::Fraction< Z >::operator+= ( const Fraction< Z > &  rhs ) -> Fraction&

inlineconstexpr

Parameters

[in]

rhs

Returns

Fraction

operator+=() [2/2]

template<Integral Z>

constexpr auto fun::Fraction< Z >::operator+= ( const Z &  i ) -> Fraction&

inlineconstexpr

Parameters

[in]

i

Returns

Fraction

operator-() [1/3]

template<Integral Z>

constexpr auto fun::Fraction< Z >::operator- ( ) const -> Fraction

inlineconstexpr

Negate.

Returns

Fraction

operator-() [2/3]

template<Integral Z>

constexpr auto fun::Fraction< Z >::operator- ( const Fraction< Z > &  frac ) const -> Fraction

inlineconstexpr

Subtract.

Parameters

[in]

frac

Returns

Fraction

operator-() [3/3]

template<Integral Z>

constexpr auto fun::Fraction< Z >::operator- ( const Z &  i ) const -> Fraction

inlineconstexpr

Parameters

[in]

i

Returns

Fraction

operator-=() [1/2]

template<Integral Z>

constexpr auto fun::Fraction< Z >::operator-= ( const Fraction< Z > &  rhs ) -> Fraction&

inlineconstexpr

Parameters

[in]

rhs

Returns

Fraction

operator-=() [2/2]

template<Integral Z>

constexpr auto fun::Fraction< Z >::operator-= ( const Z &  rhs ) -> Fraction&

inlineconstexpr

Parameters

[in]

rhs

Returns

Fraction

operator/=() [1/2]

template<Integral Z>

constexpr auto fun::Fraction< Z >::operator/= ( const Z &  rhs ) -> Fraction&

inlineconstexpr

divide and assign

Parameters

[in]

rhs

Returns

Fraction&

operator/=() [2/2]

template<Integral Z>

constexpr auto fun::Fraction< Z >::operator/= ( Fraction< Z >  rhs ) -> Fraction&

inlineconstexpr

divide and assign

Parameters

[in]

rhs

Returns

Fraction&

operator<=() [1/2]

template<Integral Z>

constexpr auto fun::Fraction< Z >::operator<= ( const Fraction< Z > &  rhs ) const -> bool

inlineconstexpr

Less than or equal to.

Parameters

[in]

rhs

Returns

true

false

operator<=() [2/2]

template<Integral Z>

constexpr auto fun::Fraction< Z >::operator<= ( const Z &  rhs ) const -> bool

inlineconstexpr

Less than or equal to.

Parameters

[in]

rhs

Returns

true

false

operator>() [1/2]

template<Integral Z>

constexpr auto fun::Fraction< Z >::operator> ( const Fraction< Z > &  rhs ) const -> bool

inlineconstexpr

Greater than.

Parameters

[in]

rhs

Returns

true

false

operator>() [2/2]

template<Integral Z>

constexpr auto fun::Fraction< Z >::operator> ( const Z &  rhs ) const -> bool

inlineconstexpr

Greater than.

Parameters

[in]

rhs

Returns

true

false

operator>=() [1/2]

template<Integral Z>

constexpr auto fun::Fraction< Z >::operator>= ( const Fraction< Z > &  rhs ) const -> bool

inlineconstexpr

Greater than or euqal to.

Parameters

[in]

rhs

Returns

true

false

operator>=() [2/2]

template<Integral Z>

constexpr auto fun::Fraction< Z >::operator>= ( const Z &  rhs ) const -> bool

inlineconstexpr

Greater than or equal to.

Parameters

[in]

rhs

Returns

true

false

reciprocal()

template<Integral Z>

constexpr void fun::Fraction< Z >::reciprocal ( )

inlineconstexprnoexcept

reciprocal

Friends And Related Symbol Documentation

operator* [1/4]

template<Integral Z>

constexpr auto operator* ( const Z &  lhs, Fraction< Z >  rhs  ) -> Fraction

friend

multiply

Parameters

[in]	lhs
[in]	rhs

Returns

Fraction

operator* [2/4]

template<Integral Z>

constexpr auto operator* ( Fraction< Z >  lhs, const Fraction< Z > &  rhs  ) -> Fraction

friend

multiply

Parameters

[in]	lhs
[in]	rhs

Returns

Fraction

operator* [3/4]

template<Integral Z>

constexpr auto operator* ( Fraction< Z >  lhs, const Z &  rhs  ) -> Fraction

friend

multiply

Parameters

[in]	lhs
[in]	rhs

Returns

Fraction

operator* [4/4]

template<Integral Z>

constexpr auto operator* ( int &&  c, const Fraction< Z > &  frac  ) -> Fraction

friend

Parameters

[in]	c
[in]	frac

Returns

Fraction<Z>

operator+ [1/3]

template<Integral Z>

constexpr auto operator+ ( const Z &  i, Fraction< Z >  frac  ) -> Fraction

friend

Add.

Parameters

[in]	i
[in]	frac

Returns

Fraction

operator+ [2/3]

template<Integral Z>

constexpr auto operator+ ( Fraction< Z >  frac, const Z &  i  ) -> Fraction

friend

Add.

Parameters

[in]	frac
[in]	i

Returns

Fraction

operator+ [3/3]

template<Integral Z>

constexpr auto operator+ ( int &&  c, const Fraction< Z > &  frac  ) -> Fraction

friend

Parameters

[in]	c
[in]	frac

Returns

Fraction

operator- [1/2]

template<Integral Z>

constexpr auto operator- ( const Z &  c, const Fraction< Z > &  frac  ) -> Fraction

friend

Parameters

[in]	c
[in]	frac

Returns

Fraction

operator- [2/2]

template<Integral Z>

constexpr auto operator- ( int &&  c, const Fraction< Z > &  frac  ) -> Fraction

friend

Parameters

[in]	c
[in]	frac

Returns

Fraction

operator/ [1/3]

template<Integral Z>

constexpr auto operator/ ( const Z &  lhs, Fraction< Z >  rhs  ) -> Fraction

friend

divide

Parameters

[in]	lhs
[in]	rhs

Returns

Fraction

operator/ [2/3]

template<Integral Z>

constexpr auto operator/ ( Fraction< Z >  lhs, const Fraction< Z > &  rhs  ) -> Fraction

friend

divide

Parameters

[in]	lhs
[in]	rhs

Returns

Fraction

operator/ [3/3]

template<Integral Z>

constexpr auto operator/ ( Fraction< Z >  lhs, const Z &  rhs  ) -> Fraction

friend

divide

Parameters

[in]	lhs
[in]	rhs

Returns

Fraction

operator< [1/3]

template<Integral Z>

constexpr friend auto operator< ( Fraction< Z >  lhs, Fraction< Z >  rhs  ) -> bool

friend

Less than.

Parameters

[in]	lhs
[in]	rhs

Returns

true

false

operator< [2/3]

template<Integral Z>

constexpr auto operator< ( Fraction< Z >  lhs, Z  rhs  ) -> bool

friend

Less than.

Parameters

[in]	lhs
[in]	rhs

Returns

true

false

operator< [3/3]

template<Integral Z>

constexpr auto operator< ( Z  lhs, Fraction< Z >  rhs  ) -> bool

friend

Less than.

Parameters

[in]	lhs
[in]	rhs

Returns

true

false

operator<<

template<Integral Z>

template<typename Stream >

auto operator<< ( Stream &  os, const Fraction< Z > &  frac  ) -> Stream&

friend

Template Parameters

Stream
Z

Parameters

[in]	os
[in]	frac

Returns

Stream&

operator<=

template<Integral Z>

constexpr auto operator<= ( const Z &  lhs, const Fraction< Z > &  rhs  ) -> bool

friend

Less than or equal to.

Parameters

[in]	lhs
[in]	rhs

Returns

true

false

operator== [1/3]

template<Integral Z>

constexpr auto operator== ( const Z &  lhs, const Fraction< Z > &  rhs  ) -> bool

friend

Equal to.

Parameters

[in]	lhs
[in]	rhs

Returns

true

false

operator== [2/3]

template<Integral Z>

constexpr friend auto operator== ( Fraction< Z >  lhs, Fraction< Z >  rhs  ) -> bool

friend

Equal to.

Parameters

[in]

rhs

Returns

true

false

Equal to

Parameters

[in]	lhs
[in]	rhs

Returns

true

false

operator== [3/3]

template<Integral Z>

constexpr auto operator== ( Fraction< Z >  lhs, Z  rhs  ) -> bool

friend

Equal to.

Parameters

[in]	lhs
[in]	rhs

Returns

true

false

operator>

template<Integral Z>

constexpr auto operator> ( const Z &  lhs, const Fraction< Z > &  rhs  ) -> bool

friend

Greater than.

Parameters

[in]	lhs
[in]	rhs

Returns

true

false

operator>=

template<Integral Z>

constexpr auto operator>= ( const Z &  lhs, const Fraction< Z > &  rhs  ) -> bool

friend

Greater than or euqal to.

Parameters

[in]	lhs
[in]	rhs

Returns

true

false

Member Data Documentation

_den

template<Integral Z>

Z fun::Fraction< Z >::_den

_num

template<Integral Z>

Z fun::Fraction< Z >::_num

---

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

• projgeom/fractions.hpp