rationalg (generic rational) is used to compute the sign of rational fractions exactly. More...

#include <geogram/basic/rationalg.h>

Public Types
typedef T	value_type

Public Member Functions
	rationalg (double x)
	Constructs a new rationalg from a double. More...

	rationalg (const T &x)
	Constructs a new rationalg from an T. More...

	rationalg (T &&x)
	Constructs a new rationalg from an T with move semantics. More...

	rationalg (double num, double denom)
	Constructs a new rationalg from two doubles. More...

	rationalg (const T &num, const T &denom)
	Constructs a new rationalg from two T. More...

	rationalg (T &&num, T &&denom)
	Constructs a new rationalg from two T with move semantics. More...

	rationalg (const rationalg< T > &rhs)=default
	Copy-constructor. More...

	rationalg (rationalg< T > &&rhs)=default
	Move-constructor. More...

rationalg< T > &	operator= (const rationalg< T > &rhs)=default
	Assignment operator. More...

rationalg< T > &	operator= (rationalg< T > &&rhs)=default
	Assignment operator with move semantics. More...

const T &	num () const
	gets the numerator. More...

const T &	denom () const
	gets the denominator. More...

T &	num ()
	gets the numerator. More...

T &	denom ()
	gets the denominator. More...

void	optimize ()
	Optimizes the internal representation without changing the represented value.

rationalg< T > &	operator+= (const rationalg< T > &rhs)
	Adds a rationalg to this rationalg. More...

rationalg< T > &	operator-= (const rationalg< T > &rhs)
	Subtracts a rationalg to this rationalg. More...

rationalg< T > &	operator*= (const rationalg< T > &rhs)
	Multiplies this rationalg by a rationalg. More...

rationalg< T > &	operator/= (const rationalg< T > &rhs)
	Divides this rationalg by a rationalg. More...

rationalg< T > &	operator+= (double rhs)
	Adds a double to this rationalg. More...

rationalg< T > &	operator-= (double rhs)
	Subtracts a double from this rationalg. More...

rationalg< T > &	operator*= (double rhs)
	Multiplies this rationalg by a double. More...

rationalg< T > &	operator/= (double rhs)
	Divides this rationalg by a double. More...

rationalg< T >	operator+ (const rationalg< T > &rhs) const
	Computes the sum of two rationalgs. More...

rationalg< T >	operator- (const rationalg< T > &rhs) const
	Computes the difference between two rationalgs. More...

rationalg< T >	operator* (const rationalg< T > &rhs) const
	Computes the product between two rationalgs. More...

rationalg< T >	operator/ (const rationalg< T > &rhs) const
	Computes the ratio between two rationalgs. More...

rationalg< T >	operator+ (double rhs) const
	Computes the sum of a rationalg and a double. More...

rationalg< T >	operator- (double rhs) const
	Computes the difference between a rationalg and a double. More...

rationalg< T >	operator* (double rhs) const
	Computes the product between a rationalg and a double. More...

rationalg< T >	operator/ (double rhs) const
	Computes the ratio between a rationalg and a double. More...

rationalg< T >	operator- () const
	Computes the opposite of this rationalg. More...

Sign	sign () const
	Gets the sign of a rationalg. More...

Sign	compare (const rationalg< T > &rhs) const
	Compares two rationalg. More...

Sign	compare (double rhs) const
	Compares a rationalg with a double. More...

bool	operator> (const rationalg< T > &rhs) const
	Compares this rationalg with another one. More...

bool	operator>= (const rationalg< T > &rhs) const
	Compares this rationalg with another one. More...

bool	operator< (const rationalg< T > &rhs) const
	Compares this rationalg with another one. More...

bool	operator<= (const rationalg< T > &rhs) const
	Compares this rationalg with another one. More...

bool	operator> (double rhs) const
	Compares this rationalg with another one. More...

bool	operator>= (double rhs) const
	Compares this rationalg with another one. More...

bool	operator< (double rhs) const
	Compares this rationalg with another one. More...

bool	operator<= (double rhs) const
	Compares this rationalg with another one. More...

double	estimate () const
	Computes an approximation of the stored value in this rational. More...

Protected Member Functions
void	copy (const rationalg< T > &rhs)
	Copies a rational into this one. More...

bool	has_same_denom (const rationalg< T > &rhs) const
	Tests whether a rationalg has trivially the same denominator this rationalg. More...

Related Functions
(Note that these are not member functions.)
template<class T >
rationalg< T >	operator+ (double a, const rationalg< T > &b)
	Computes the sum of a double and a rationalg. More...

template<class T >
rationalg< T >	operator- (double a, const rationalg< T > &b)
	Computes the difference between a double and a rationalg. More...

template<class T >
rationalg< T >	operator* (double a, const rationalg< T > &b)
	Computes the product of a double and a rationalg. More...

template<class T >
rationalg< T >	operator/ (double a, const rationalg< T > &b)
	Computes the ratio between a double and a rationalg. More...

template<class T >
bool	operator== (const rationalg< T > &a, const rationalg< T > &b)
	Tests equality between two rationalgs. More...

template<class T >
bool	operator== (const rationalg< T > &a, double b)
	Tests equality between a rationalg and a double. More...

template<class T >
bool	operator== (double a, const rationalg< T > &b)
	Tests equality between a double and a rationalg. More...

template<class T >
bool	operator!= (const rationalg< T > &a, const rationalg< T > &b)
	Tests whether two rationalgs differ. More...

template<class T >
bool	operator!= (const rationalg< T > &a, double b)
	Tests whether a rationalg differs from a double. More...

template<class T >
bool	operator!= (double a, const rationalg< T > &b)
	Tests whether a double differs from a rationalg. More...

Detailed Description

template<class T>
class GEO::rationalg< T >

rationalg (generic rational) is used to compute the sign of rational fractions exactly.

rationalg can be used like float and double. It supports four arithmetic operations (+,-,*,/), comparisons (>,>=,<,<=,==,!=) and exact sign computation.

Definition at line 59 of file rationalg.h.

Constructor & Destructor Documentation

◆ rationalg() [1/8]

template<class T >

GEO::rationalg< T >::rationalg ( double x )

inlineexplicit

Constructs a new rationalg from a double.

Parameters

[in] x the value to initialize this rationalg.

Definition at line 69 of file rationalg.h.

◆ rationalg() [2/8]

template<class T >

GEO::rationalg< T >::rationalg ( const T & x )

inlineexplicit

Constructs a new rationalg from an T.

Parameters

[in] x the value to initialize this rationalg.

Definition at line 76 of file rationalg.h.

◆ rationalg() [3/8]

template<class T >

GEO::rationalg< T >::rationalg ( T && x )

inlineexplicit

Constructs a new rationalg from an T with move semantics.

Parameters

[in] x the victim T

Definition at line 84 of file rationalg.h.

◆ rationalg() [4/8]

template<class T >

GEO::rationalg< T >::rationalg	(	double	num,
		double	denom
	)

inlineexplicit

Constructs a new rationalg from two doubles.

Parameters

[in]	num	the numerator
[in]	denom	the denominator

Definition at line 92 of file rationalg.h.

◆ rationalg() [5/8]

template<class T >

GEO::rationalg< T >::rationalg	(	const T &	num,
		const T &	denom
	)

inlineexplicit

Constructs a new rationalg from two T.

Parameters

[in]	num	the numerator
[in]	denom	the denominator

Definition at line 101 of file rationalg.h.

◆ rationalg() [6/8]

template<class T >

GEO::rationalg< T >::rationalg	(	T &&	num,
		T &&	denom
	)

inlineexplicit

Constructs a new rationalg from two T with move semantics.

Parameters

[in]	num	the numerator
[in]	denom	the denominator

Definition at line 111 of file rationalg.h.

◆ rationalg() [7/8]

template<class T >

GEO::rationalg< T >::rationalg ( const rationalg< T > & rhs )

default

Copy-constructor.

Parameters

[in] rhs the rational to be copied

◆ rationalg() [8/8]

template<class T >

GEO::rationalg< T >::rationalg ( rationalg< T > && rhs )

default

Move-constructor.

Parameters

[in] rhs the rational to be copied

Member Function Documentation

◆ compare() [1/2]

template<class T >

Sign GEO::rationalg< T >::compare ( const rationalg< T > & rhs ) const

inline

Compares two rationalg.

Returns: the sign of this rationalg minus rhs

Definition at line 427 of file rationalg.h.

◆ compare() [2/2]

template<class T >

Sign GEO::rationalg< T >::compare ( double rhs ) const

inline

Compares a rationalg with a double.

Returns: the sign of this expansion minus rhs

Definition at line 444 of file rationalg.h.

◆ copy()

template<class T >

void GEO::rationalg< T >::copy ( const rationalg< T > & rhs )

inlineprotected

Copies a rational into this one.

Parameters

[in] rhs a const reference to the rational to be copied

Definition at line 554 of file rationalg.h.

◆ denom() [1/2]

template<class T >

T& GEO::rationalg< T >::denom ( )

inline

gets the denominator.

Returns: a reference to the denominator.

Definition at line 170 of file rationalg.h.

◆ denom() [2/2]

template<class T >

const T& GEO::rationalg< T >::denom ( ) const

inline

gets the denominator.

Returns: a const reference to the denominator.

Definition at line 154 of file rationalg.h.

◆ estimate()

template<class T >

double GEO::rationalg< T >::estimate ( ) const

inline

Computes an approximation of the stored value in this rational.

Returns: an approximation of the stored value.

Definition at line 545 of file rationalg.h.

◆ has_same_denom()

template<class T >

bool GEO::rationalg< T >::has_same_denom ( const rationalg< T > & rhs ) const

inlineprotected

Tests whether a rationalg has trivially the same denominator this rationalg.

This function is used to implement faster addition, subtraction and tests when it can be quickly determined that both operands have the same denominator.

Return values

true	if it is trivial that `rhs` has the same denominator as this rationalg.
false	otherwise.

Definition at line 569 of file rationalg.h.

◆ num() [1/2]

template<class T >

T& GEO::rationalg< T >::num ( )

inline

gets the numerator.

Returns: a reference to the numerator.

Definition at line 162 of file rationalg.h.

◆ num() [2/2]

template<class T >

const T& GEO::rationalg< T >::num ( ) const

inline

gets the numerator.

Returns: a const reference to the numerator.

Definition at line 146 of file rationalg.h.

◆ operator*() [1/2]

template<class T >

rationalg<T> GEO::rationalg< T >::operator* ( const rationalg< T > & rhs ) const

inline

Computes the product between two rationalgs.

Parameters

[in] rhs the rationalg to be multiplied by this rationalg

Returns: the product between this rationalg and rhs

Definition at line 328 of file rationalg.h.

◆ operator*() [2/2]

template<class T >

rationalg<T> GEO::rationalg< T >::operator* ( double rhs ) const

inline

Computes the product between a rationalg and a double.

Parameters

[in] rhs the double to be multiplied by this rationalg

Returns: the product between this rationalg and rhs

Definition at line 378 of file rationalg.h.

◆ operator*=() [1/2]

template<class T >

rationalg<T>& GEO::rationalg< T >::operator*= ( const rationalg< T > & rhs )

inline

Multiplies this rationalg by a rationalg.

Parameters

[in] rhs the rationalg to multiply this rationalg by

Returns: the new value of this rationalg

Definition at line 220 of file rationalg.h.

◆ operator*=() [2/2]

template<class T >

rationalg<T>& GEO::rationalg< T >::operator*= ( double rhs )

inline

Multiplies this rationalg by a double.

If the double is a constant (possibly negative) power of two (e.g. 0.125, 0.5, 2.0, 4.0 ...), one may use num().scale_fast() / denom().scale_fast() instead.

Parameters

[in] rhs the double to multiply this rationalg with

Returns: the new value of this rationalg

Definition at line 265 of file rationalg.h.

◆ operator+() [1/2]

template<class T >

rationalg<T> GEO::rationalg< T >::operator+ ( const rationalg< T > & rhs ) const

inline

Computes the sum of two rationalgs.

Parameters

[in] rhs the rationalg to be added to this rationalg

Returns: the sum of this rationalg and rhs

Definition at line 290 of file rationalg.h.

◆ operator+() [2/2]

template<class T >

rationalg<T> GEO::rationalg< T >::operator+ ( double rhs ) const

inline

Computes the sum of a rationalg and a double.

Parameters

[in] rhs the double to be added to this rationalg

Returns: the sum of this rationalg and rhs

Definition at line 354 of file rationalg.h.

◆ operator+=() [1/2]

template<class T >

rationalg<T>& GEO::rationalg< T >::operator+= ( const rationalg< T > & rhs )

inline

Adds a rationalg to this rationalg.

Parameters

[in] rhs the rationalg to be added to this rationalg

Returns: the new value of this rationalg

Definition at line 190 of file rationalg.h.

◆ operator+=() [2/2]

template<class T >

rationalg<T>& GEO::rationalg< T >::operator+= ( double rhs )

inline

Adds a double to this rationalg.

Parameters

[in] rhs the double to be added to this rationalg

Returns: the new value of this rationalg

Definition at line 242 of file rationalg.h.

◆ operator-() [1/3]

template<class T >

rationalg<T> GEO::rationalg< T >::operator- ( ) const

inline

Computes the opposite of this rationalg.

Returns: the opposite of this rationalg

Definition at line 403 of file rationalg.h.

◆ operator-() [2/3]

template<class T >

rationalg<T> GEO::rationalg< T >::operator- ( const rationalg< T > & rhs ) const

inline

Computes the difference between two rationalgs.

Parameters

[in] rhs the rationalg to be subtracted from this rationalg

Returns: the difference between this rationalg and rhs

Definition at line 309 of file rationalg.h.

◆ operator-() [3/3]

template<class T >

rationalg<T> GEO::rationalg< T >::operator- ( double rhs ) const

inline

Computes the difference between a rationalg and a double.

Parameters

[in] rhs the double to be subtracted from this rationalg

Returns: the difference between this rationalg and rhs

Definition at line 366 of file rationalg.h.

◆ operator-=() [1/2]

template<class T >

rationalg<T>& GEO::rationalg< T >::operator-= ( const rationalg< T > & rhs )

inline

Subtracts a rationalg to this rationalg.

Parameters

[in] rhs the rationalg to be subtracted

Returns: the new value of this rationalg

Definition at line 205 of file rationalg.h.

◆ operator-=() [2/2]

template<class T >

rationalg<T>& GEO::rationalg< T >::operator-= ( double rhs )

inline

Subtracts a double from this rationalg.

Parameters

[in] rhs the double to be subtracted from this rationalg

Returns: the new value of this rationalg

Definition at line 252 of file rationalg.h.

◆ operator/() [1/2]

template<class T >

rationalg<T> GEO::rationalg< T >::operator/ ( const rationalg< T > & rhs ) const

inline

Computes the ratio between two rationalgs.

Parameters

[in] rhs the rationalg to be multiplied by this rationalg

Returns: the ratio between this rationalg and rhs

Definition at line 341 of file rationalg.h.

◆ operator/() [2/2]

template<class T >

rationalg<T> GEO::rationalg< T >::operator/ ( double rhs ) const

inline

Computes the ratio between a rationalg and a double.

Parameters

[in] rhs the double to be multiplied by this rationalg

Returns: the ratio between this rationalg and rhs

Definition at line 390 of file rationalg.h.

◆ operator/=() [1/2]

template<class T >

rationalg<T>& GEO::rationalg< T >::operator/= ( const rationalg< T > & rhs )

inline

Divides this rationalg by a rationalg.

Parameters

[in] rhs the rationalg to divide this rationalg by

Returns: the new value of this rationalg

Definition at line 231 of file rationalg.h.

◆ operator/=() [2/2]

template<class T >

rationalg<T>& GEO::rationalg< T >::operator/= ( double rhs )

inline

Divides this rationalg by a double.

If the double is a constant (possibly negative) power of two (e.g. 0.125, 0.5, 2.0, 4.0 ...), one may use num().scale_fast() / denom().scale_fast() instead.

Parameters

[in] rhs the double to multiply this rationalg with

Returns: the new value of this rationalg

Definition at line 278 of file rationalg.h.

◆ operator<() [1/2]

template<class T >

bool GEO::rationalg< T >::operator< ( const rationalg< T > & rhs ) const

inline

Compares this rationalg with another one.

Internally computes the sign of the difference between this rationalg and rhs.

Returns: true if this rationalg is smaller than rhs, false otherwise

Definition at line 479 of file rationalg.h.

◆ operator<() [2/2]

template<class T >

bool GEO::rationalg< T >::operator< ( double rhs ) const

inline

Compares this rationalg with another one.

Internally computes the sign of the difference between this rationalg and rhs.

Returns: true if this rationalg is smaller than rhs, false otherwise

Definition at line 523 of file rationalg.h.

◆ operator<=() [1/2]

template<class T >

bool GEO::rationalg< T >::operator<= ( const rationalg< T > & rhs ) const

inline

Compares this rationalg with another one.

Internally computes the sign of the difference between this rationalg and rhs.

Returns: true if this rationalg is smaller or equal than rhs, false otherwise

Definition at line 490 of file rationalg.h.

◆ operator<=() [2/2]

template<class T >

bool GEO::rationalg< T >::operator<= ( double rhs ) const

inline

Compares this rationalg with another one.

Internally computes the sign of the difference between this rationalg and rhs.

Returns: true if this rationalg is smaller or equal than rhs, false otherwise

Definition at line 534 of file rationalg.h.

◆ operator=() [1/2]

template<class T >

rationalg<T>& GEO::rationalg< T >::operator= ( const rationalg< T > & rhs )

default

Assignment operator.

Parameters

[in] rhs the rational to be copied

Returns: the new value of this rational (rhs)

◆ operator=() [2/2]

template<class T >

rationalg<T>& GEO::rationalg< T >::operator= ( rationalg< T > && rhs )

default

Assignment operator with move semantics.

Parameters

[in] rhs the victim rationalg

Returns: the new value of this rational (rhs)

◆ operator>() [1/2]

template<class T >

bool GEO::rationalg< T >::operator> ( const rationalg< T > & rhs ) const

inline

Compares this rationalg with another one.

Internally computes the sign of the difference between this rationalg and rhs.

Returns: true if this rationalg is greater than rhs, false otherwise

Definition at line 457 of file rationalg.h.

◆ operator>() [2/2]

template<class T >

bool GEO::rationalg< T >::operator> ( double rhs ) const

inline

Compares this rationalg with another one.

Internally computes the sign of the difference between this rationalg and rhs.

Returns: true if this rationalg is greater than rhs, false otherwise

Definition at line 501 of file rationalg.h.

◆ operator>=() [1/2]

template<class T >

bool GEO::rationalg< T >::operator>= ( const rationalg< T > & rhs ) const

inline

Compares this rationalg with another one.

Internally computes the sign of the difference between this rationalg and rhs.

Returns: true if this rationalg is greater or equal than rhs, false otherwise

Definition at line 468 of file rationalg.h.

◆ operator>=() [2/2]

template<class T >

bool GEO::rationalg< T >::operator>= ( double rhs ) const

inline

Compares this rationalg with another one.

Internally computes the sign of the difference between this rationalg and rhs.

Returns: true if this rationalg is greater or equal than rhs, false otherwise

Definition at line 512 of file rationalg.h.

◆ sign()

template<class T >

Sign GEO::rationalg< T >::sign ( ) const

inline

Gets the sign of a rationalg.

Returns: one of POSITIVE,ZERO,NEGATIVE

Definition at line 416 of file rationalg.h.

Friends And Related Function Documentation

◆ operator!=() [1/3]

template<class T >

bool operator!=	(	const rationalg< T > &	a,
		const rationalg< T > &	b
	)

Implemented by testing whether the difference between a and b is different from 0.

Returns: true if a and b do not represent the same exact value, false otherwise

Definition at line 681 of file rationalg.h.

◆ operator!=() [2/3]

template<class T >

bool operator!=	(	const rationalg< T > &	a,
		double	b
	)

Implemented by testing whether the difference between a and b is different from 0.

Returns: true if a and b do not represent the same exact value, false otherwise

Definition at line 694 of file rationalg.h.

◆ operator!=() [3/3]

template<class T >

bool operator!=	(	double	a,
		const rationalg< T > &	b
	)

Implemented by testing whether the difference between a and b is different from 0.

Returns: true if a and b do not represent the same exact value, false otherwise

Definition at line 707 of file rationalg.h.

◆ operator*()

template<class T >

rationalg< T > operator*	(	double	a,
		const rationalg< T > &	b
	)

Parameters

[in]	a	the double
[in]	b	the rationalg to be multiplied

Returns: a rationalg that represents a * b

Definition at line 614 of file rationalg.h.

◆ operator+()

template<class T >

rationalg< T > operator+	(	double	a,
		const rationalg< T > &	b
	)

Parameters

[in]	a	the double to be added
[in]	b	the rationalg to be added

Returns: a rationalg that represents a + b

Definition at line 588 of file rationalg.h.

◆ operator-()

template<class T >

rationalg< T > operator-	(	double	a,
		const rationalg< T > &	b
	)

Parameters

[in]	a	the double
[in]	b	the rationalg to be subtracted

Returns: a rationalg that represents a - b

Definition at line 600 of file rationalg.h.

◆ operator/()

template<class T >

rationalg< T > operator/	(	double	a,
		const rationalg< T > &	b
	)

Parameters

[in]	a	the double
[in]	b	the rationalg to be divided

Returns: a rationalg that represents a / b

Definition at line 626 of file rationalg.h.

◆ operator==() [1/3]

template<class T >

bool operator==	(	const rationalg< T > &	a,
		const rationalg< T > &	b
	)

Implemented by testing whether the difference between a and b is 0.

Returns: true if a and b represent exactly the same value, false otherwise

Definition at line 642 of file rationalg.h.

◆ operator==() [2/3]

template<class T >

bool operator==	(	const rationalg< T > &	a,
		double	b
	)

Implemented by testing whether the difference between a and b is 0.

Returns: true if a and b represent exactly the same value, false otherwise

Definition at line 655 of file rationalg.h.

◆ operator==() [3/3]

template<class T >

bool operator==	(	double	a,
		const rationalg< T > &	b
	)

Implemented by testing whether the difference between a and b is 0.

Returns: true if a and b represent exactly the same value, false otherwise

Definition at line 668 of file rationalg.h.

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

geogram/basic/rationalg.h

Public Types

Public Member Functions

Protected Member Functions

Related Functions

Detailed Description

template<class T> class GEO::rationalg< T >

Constructor & Destructor Documentation

◆ rationalg() [1/8]

◆ rationalg() [2/8]

◆ rationalg() [3/8]

◆ rationalg() [4/8]

◆ rationalg() [5/8]

◆ rationalg() [6/8]

◆ rationalg() [7/8]

◆ rationalg() [8/8]

Member Function Documentation

◆ compare() [1/2]

◆ compare() [2/2]

◆ copy()

◆ denom() [1/2]

◆ denom() [2/2]

◆ estimate()

◆ has_same_denom()

◆ num() [1/2]

◆ num() [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-() [1/3]

◆ operator-() [2/3]

◆ operator-() [3/3]

◆ 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]

◆ sign()

Friends And Related Function Documentation

◆ operator!=() [1/3]

◆ operator!=() [2/3]

◆ operator!=() [3/3]

◆ operator*()

◆ operator+()

◆ operator-()

◆ operator/()

◆ operator==() [1/3]

◆ operator==() [2/3]

◆ operator==() [3/3]

template<class T>
class GEO::rationalg< T >