Expansion_nt (expansion Number Type) is used to compute the sign of polynoms exactly. More...

#include <geogram/numerics/expansion_nt.h>

Public Types
enum	Operation { SUM , DIFF , PRODUCT }
	This type is used by the constructor that takes two expansions.

Public Member Functions
	expansion_nt ()
	Constructs an uninitialized expansion_nt.

	expansion_nt (double x)
	Constructs a new expansion_nt from a double. More...

	expansion_nt (const expansion &rhs)
	Constructs a new expansion_nt from an expansion. More...

	expansion_nt (Operation op, const expansion &x, const expansion &y)
	Constructs a new expansion_nt from two expansions. More...

	expansion_nt (Operation op, const expansion &x, const expansion &y, const expansion &z)
	Constructs a new expansion_nt from three expansions. More...

	expansion_nt (Operation op, const expansion &x, const expansion &y, const expansion &z, const expansion &t)
	Constructs a new expansion_nt from four expansions. More...

	expansion_nt (Operation op, double x, double y)
	Constructs a new expansion_nt from two doubles. More...

	expansion_nt (const expansion_nt &rhs)
	Copy-constructor. More...

	expansion_nt (expansion_nt &&rhs)
	Move-constructor. More...

expansion_nt &	operator= (const expansion_nt &rhs)
	Assignment operator. More...

expansion_nt &	operator= (expansion_nt &&rhs)
	Assignment operator with move semantics. More...

	~expansion_nt ()
	Expansion_nt destructor. More...

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

void	negate ()
	Flips the sign of an expansion.

expansion_nt &	operator+= (const expansion_nt &rhs)
	Adds an expansion_nt to this expansion_nt. More...

expansion_nt &	operator-= (const expansion_nt &rhs)
	Subtracts an expansion_nt to this expansion_nt. More...

expansion_nt &	operator*= (const expansion_nt &rhs)
	Multiplies this expansion_nt by an expansion_nt. More...

expansion_nt &	operator+= (double rhs)
	Adds a double to this expansion_nt. More...

expansion_nt &	operator-= (double rhs)
	Subtracts a double from this expansion_nt. More...

expansion_nt &	operator*= (double rhs)
	Multiplies this expansion_nt by a double. More...

expansion_nt	operator+ (const expansion_nt &rhs) const
	Computes the sum of two expansion_nts. More...

expansion_nt	operator- (const expansion_nt &rhs) const
	Computes the difference between two expansion_nts. More...

expansion_nt	operator* (const expansion_nt &rhs) const
	Computes the product between two expansion_nts. More...

expansion_nt	operator+ (double rhs) const
	Computes the sum of an expansion_nt and a double. More...

expansion_nt	operator- (double rhs) const
	Computes the difference between an expansion_nt and a double. More...

expansion_nt	operator* (double rhs) const
	Computes the product between an expansion_nt and a double. More...

expansion_nt	operator- () const
	Computes the opposite of this expansion_nt. More...

Sign	compare (const expansion_nt &rhs) const
	Compares two expansion_nt. More...

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

bool	operator> (const expansion_nt &rhs) const
	Compares this expansion_nt with another one. More...

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

bool	operator< (const expansion_nt &rhs) const
	Compares this expansion_nt with another one. More...

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

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

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

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

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

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

Sign	sign () const
	Gets the sign of this expansion_nt. More...

index_t	length () const
	Gets the length of this expansion. More...

double	component (index_t i) const
	Gets the i-th component of this expansion. More...

	expansion_nt (expansion *rep)
	Constructs a new expansion_nt from an expansion. More...

expansion &	rep ()
	Gets the internal expansion that represents this expansion_nt. More...

const expansion &	rep () const
	Gets the internal expansion that represents this expansion_nt. More...

std::string	to_string () const
	Gets a string representation of this expansion. More...

Protected Member Functions
void	copy (const expansion_nt &rhs)
	Copies an expansion into this one. More...

void	cleanup ()
	Cleanups the memory associated with this expansion_nt.

Friends
expansion_nt	operator- (double a, const expansion_nt &b)

expansion_nt	expansion_nt_sq_dist (const double a, const double b, coord_index_t dim)

expansion_nt	expansion_nt_dot_at (const double a, const double b, const double *c, coord_index_t dim)

Related Functions
(Note that these are not member functions.)
expansion_nt	operator+ (double a, const expansion_nt &b)
	Computes the sum of a double and an expansion_nt. More...

expansion_nt	operator- (double a, const expansion_nt &b)
	Computes the difference between a double and an expansion_nt. More...

expansion_nt	operator* (double a, const expansion_nt &b)
	Computes the product of a double and an expansion_nt. More...

bool	operator== (const expansion_nt &a, const expansion_nt &b)
	Tests equality between two expansion_nts. More...

bool	operator== (const expansion_nt &a, double b)
	Tests equality between an expansion_nt and a double. More...

bool	operator== (double a, const expansion_nt &b)
	Tests equality between a double and an expansion_nt. More...

bool	operator!= (const expansion_nt &a, const expansion_nt &b)
	Tests whether two expansion_nts differ. More...

bool	operator!= (const expansion_nt &a, double b)
	Tests whether an expansion_nt differs from a double. More...

bool	operator!= (double a, const expansion_nt &b)
	Tests whether a double differs from an expansion_nt. More...

expansion_nt	expansion_nt_sq_dist (const double a, const double b, coord_index_t dim)
	Computes an expansion that represents the square distance between two points. More...

expansion_nt	expansion_nt_dot_at (const double a, const double b, const double *c, coord_index_t dim)
	Computes an expansion that represents the dot product of two vectors determined by three points. More...

Detailed Description

Expansion_nt (expansion Number Type) is used to compute the sign of polynoms exactly.

Expansion_nt can be used like float and double. It supports three arithmetic operations (+,-,*), comparisons (>,>=,<,<=,==,!=) and exact sign computation. expansion_nt is a wrapper around an expansion allocated on the heap. When performance is a concern, the lower-level expansion class may be used instead.

Definition at line 70 of file expansion_nt.h.

Constructor & Destructor Documentation

◆ expansion_nt() [1/9]

GEO::expansion_nt::expansion_nt ( double x )

inlineexplicit

Constructs a new expansion_nt from a double.

Parameters

[in] x the value to initialize this expansion.

Definition at line 91 of file expansion_nt.h.

◆ expansion_nt() [2/9]

GEO::expansion_nt::expansion_nt ( const expansion & rhs )

inlineexplicit

Constructs a new expansion_nt from an expansion.

A new expansion is created on the heap and its content is initialized from rhs

Parameters

[in] rhs the expansion to be copied

Definition at line 103 of file expansion_nt.h.

◆ expansion_nt() [3/9]

GEO::expansion_nt::expansion_nt	(	Operation	op,
		const expansion &	x,
		const expansion &	y
	)

inlineexplicit

Constructs a new expansion_nt from two expansions.

A new expansion is created on the heap and its content is initialized from x op y. This function is used by code that combines the low-level API (expansion) with the high-level number type (expansion_nt). When returning the result of operations that combine expansion as an expansion_nt, it makes it possible to avoid copying the result of the last operation by directly assigning it to an expansion_nt.

Parameters

[in]	x,y	the two operands
[in]	op	one of expansion_nt::SUM, expansion_nt::DIFF, expansion_nt::PRODUCT

Definition at line 121 of file expansion_nt.h.

◆ expansion_nt() [4/9]

GEO::expansion_nt::expansion_nt	(	Operation	op,
		const expansion &	x,
		const expansion &	y,
		const expansion &	z
	)

inlineexplicit

Constructs a new expansion_nt from three expansions.

A new expansion is created on the heap and its content is initialized from x op y op z. This function is used by code that combines the low-level API (expansion) with the high-level number type (expansion_nt). When returning the result of operations that combine expansion as an expansion_nt, it makes it possible to avoid copying the result of the last operation by directly assigning it to an expansion_nt.

Parameters

[in]	x,y,z	the three operands
[in]	op	one of expansion_nt::SUM, expansion_nt::PRODUCT

Definition at line 159 of file expansion_nt.h.

◆ expansion_nt() [5/9]

GEO::expansion_nt::expansion_nt	(	Operation	op,
		const expansion &	x,
		const expansion &	y,
		const expansion &	z,
		const expansion &	t
	)

inlineexplicit

Constructs a new expansion_nt from four expansions.

A new expansion is created on the heap and its content is initialized from x op y op z op t. This function is used by code that combines the low-level API (expansion) with the high-level number type (expansion_nt). When returning the result of operations that combine expansion as an expansion_nt, it makes it possible to avoid copying the result of the last operation by directly assigning it to an expansion_nt.

Parameters

[in]	x,y,z,t	the four operands
[in]	op	one of expansion_nt::SUM, expansion_nt::PRODUCT

Definition at line 195 of file expansion_nt.h.

◆ expansion_nt() [6/9]

GEO::expansion_nt::expansion_nt	(	Operation	op,
		double	x,
		double	y
	)

inlineexplicit

Constructs a new expansion_nt from two doubles.

A new expansion is created on the heap and its content is initialized from x op y. This function is used by code that combines the low-level API (expansion) with the high-level number type (expansion_nt). When returning the result of operations that combine expansion as an expansion_nt, it makes it possible to avoid copying the result of the last operation by directly assigning it to an expansion_nt.

Parameters

[in]	x,y	the two operands
[in]	op	one of expansion_nt::SUM, expansion_nt::DIFF, expansion_nt::PRODUCT

Definition at line 235 of file expansion_nt.h.

◆ expansion_nt() [7/9]

GEO::expansion_nt::expansion_nt ( const expansion_nt & rhs )

inline

Copy-constructor.

Parameters

[in] rhs the expansion to be copied

Definition at line 262 of file expansion_nt.h.

◆ expansion_nt() [8/9]

GEO::expansion_nt::expansion_nt ( expansion_nt && rhs )

inline

Move-constructor.

Steals the expansion from rhs

Parameters

[in] rhs the victim expansion_nt

Definition at line 271 of file expansion_nt.h.

◆ ~expansion_nt()

GEO::expansion_nt::~expansion_nt ( )

inline

Expansion_nt destructor.

The stored expansion is deallocated whenever reference counting reaches 0.

Definition at line 307 of file expansion_nt.h.

◆ expansion_nt() [9/9]

GEO::expansion_nt::expansion_nt ( expansion * rep )

inline

Constructs a new expansion_nt from an expansion.

Used internally

Parameters

[in] rep should be a reference-counted expansion, created by new_expansion_on_heap(). Its reference counter is incremented.

Note: most client code will not need to use this (advanced use only).

Definition at line 585 of file expansion_nt.h.

Member Function Documentation

◆ compare() [1/2]

Sign GEO::expansion_nt::compare ( const expansion_nt & rhs ) const

inline

Compares two expansion_nt.

Returns: the sign of this expansion minus rhs

Definition at line 434 of file expansion_nt.h.

◆ compare() [2/2]

Sign GEO::expansion_nt::compare ( double rhs ) const

inline

Compares an expansion_nt with a double.

Returns: the sign of this expansion minus rhs

Definition at line 442 of file expansion_nt.h.

◆ component()

double GEO::expansion_nt::component ( index_t i ) const

inline

Gets the i-th component of this expansion.

Parameters

i	index of the component

Returns: the i-th component of this expansion

Precondition: i < length()

Note: most client code will not need to use this (advanced use only).

Definition at line 572 of file expansion_nt.h.

◆ copy()

void GEO::expansion_nt::copy ( const expansion_nt & rhs )

inlineprotected

Copies an expansion into this one.

current rep_ pointer is supposed to be uninitialized or freed before calling this function.

Parameters

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

Definition at line 632 of file expansion_nt.h.

◆ estimate()

double GEO::expansion_nt::estimate ( ) const

inline

Computes an approximation of the stored value in this expansion.

Returns: an approximation of the stored value.

Definition at line 541 of file expansion_nt.h.

◆ length()

index_t GEO::expansion_nt::length ( ) const

inline

Gets the length of this expansion.

Returns: the number of components used internally to represend this expansion

Note: most client code will not need to use this (advanced use only).

Definition at line 560 of file expansion_nt.h.

◆ operator*() [1/2]

expansion_nt GEO::expansion_nt::operator* ( const expansion_nt & rhs ) const

Computes the product between two expansion_nts.

Parameters

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

Returns: the product between this expansion_nt and rhs

◆ operator*() [2/2]

expansion_nt GEO::expansion_nt::operator* ( double rhs ) const

Computes the product between an expansion_nt and a double.

Parameters

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

Returns: the product between this expansion_nt and rhs

◆ operator*=() [1/2]

expansion_nt& GEO::expansion_nt::operator*= ( const expansion_nt & rhs )

Multiplies this expansion_nt by an expansion_nt.

Parameters

[in] rhs the expansion_nt to multiply this expansion_nt by

Returns: the new value of this expansion_nt

◆ operator*=() [2/2]

expansion_nt& GEO::expansion_nt::operator*= ( double rhs )

Multiplies this expansion_nt 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 scale_fast() instead.

Parameters

[in] rhs the double to multiply this expansion_nt with

Returns: the new value of this expansion_nt

◆ operator+() [1/2]

expansion_nt GEO::expansion_nt::operator+ ( const expansion_nt & rhs ) const

Computes the sum of two expansion_nts.

Parameters

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

Returns: the sum of this expansion_nt and rhs

◆ operator+() [2/2]

expansion_nt GEO::expansion_nt::operator+ ( double rhs ) const

Computes the sum of an expansion_nt and a double.

Parameters

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

Returns: the sum of this expansion_nt and rhs

◆ operator+=() [1/2]

expansion_nt& GEO::expansion_nt::operator+= ( const expansion_nt & rhs )

Adds an expansion_nt to this expansion_nt.

Parameters

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

Returns: the new value of this expansion_nt

◆ operator+=() [2/2]

expansion_nt& GEO::expansion_nt::operator+= ( double rhs )

Adds a double to this expansion_nt.

Parameters

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

Returns: the new value of this expansion_nt

◆ operator-() [1/3]

expansion_nt GEO::expansion_nt::operator- ( ) const

Computes the opposite of this expansion_nt.

Returns: the opposite of this expansion_nt

◆ operator-() [2/3]

expansion_nt GEO::expansion_nt::operator- ( const expansion_nt & rhs ) const

Computes the difference between two expansion_nts.

Parameters

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

Returns: the difference between this expansion_nt and rhs

◆ operator-() [3/3]

expansion_nt GEO::expansion_nt::operator- ( double rhs ) const

Computes the difference between an expansion_nt and a double.

Parameters

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

Returns: the difference between this expansion_nt and rhs

◆ operator-=() [1/2]

expansion_nt& GEO::expansion_nt::operator-= ( const expansion_nt & rhs )

Subtracts an expansion_nt to this expansion_nt.

Parameters

[in] rhs the expansion_nt to be subtracted

Returns: the new value of this expansion_nt

◆ operator-=() [2/2]

expansion_nt& GEO::expansion_nt::operator-= ( double rhs )

Subtracts a double from this expansion_nt.

Parameters

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

Returns: the new value of this expansion_nt

◆ operator<() [1/2]

bool GEO::expansion_nt::operator< ( const expansion_nt & rhs ) const

inline

Compares this expansion_nt with another one.

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

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

Definition at line 475 of file expansion_nt.h.

◆ operator<() [2/2]

bool GEO::expansion_nt::operator< ( double rhs ) const

inline

Compares this expansion_nt with another one.

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

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

Definition at line 519 of file expansion_nt.h.

◆ operator<=() [1/2]

bool GEO::expansion_nt::operator<= ( const expansion_nt & rhs ) const

inline

Compares this expansion_nt with another one.

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

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

Definition at line 486 of file expansion_nt.h.

◆ operator<=() [2/2]

bool GEO::expansion_nt::operator<= ( double rhs ) const

inline

Compares this expansion_nt with another one.

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

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

Definition at line 530 of file expansion_nt.h.

◆ operator=() [1/2]

expansion_nt& GEO::expansion_nt::operator= ( const expansion_nt & rhs )

inline

Assignment operator.

Parameters

[in] rhs the expansion to be copied

Returns: the new value of this expansion (rhs)

Definition at line 281 of file expansion_nt.h.

◆ operator=() [2/2]

expansion_nt& GEO::expansion_nt::operator= ( expansion_nt && rhs )

inline

Assignment operator with move semantics.

Parameters

[in] rhs the expansion to be copied

Returns: the new value of this expansion (rhs)

Definition at line 294 of file expansion_nt.h.

◆ operator>() [1/2]

bool GEO::expansion_nt::operator> ( const expansion_nt & rhs ) const

inline

Compares this expansion_nt with another one.

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

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

Definition at line 453 of file expansion_nt.h.

◆ operator>() [2/2]

bool GEO::expansion_nt::operator> ( double rhs ) const

inline

Compares this expansion_nt with another one.

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

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

Definition at line 497 of file expansion_nt.h.

◆ operator>=() [1/2]

bool GEO::expansion_nt::operator>= ( const expansion_nt & rhs ) const

inline

Compares this expansion_nt with another one.

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

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

Definition at line 464 of file expansion_nt.h.

◆ operator>=() [2/2]

bool GEO::expansion_nt::operator>= ( double rhs ) const

inline

Compares this expansion_nt with another one.

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

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

Definition at line 508 of file expansion_nt.h.

◆ optimize()

void GEO::expansion_nt::optimize ( )

inline

Optimizes the internal representation without changing the represented value.

this function can reduce the length of an expansion

Definition at line 316 of file expansion_nt.h.

◆ rep() [1/2]

expansion& GEO::expansion_nt::rep ( )

inline

Gets the internal expansion that represents this expansion_nt.

Returns: a reference to the expansion that represents this expansion_nt

Note: most client code will not need to use this (advanced use only).

Definition at line 597 of file expansion_nt.h.

◆ rep() [2/2]

const expansion& GEO::expansion_nt::rep ( ) const

inline

Gets the internal expansion that represents this expansion_nt.

Returns: a const reference to the expansion that represents this expansion_nt

Note: most client code will not need to use this (advanced use only).

Definition at line 609 of file expansion_nt.h.

◆ sign()

Sign GEO::expansion_nt::sign ( ) const

inline

Gets the sign of this expansion_nt.

Returns: the sign of this expansion_nt, computed exactly.

Definition at line 549 of file expansion_nt.h.

◆ to_string()

std::string GEO::expansion_nt::to_string ( ) const

inline

Gets a string representation of this expansion.

Returns: a string with the length and components or "null" if this expansion_nt was explicitely set to uninitialized.

Definition at line 618 of file expansion_nt.h.

Friends And Related Function Documentation

◆ expansion_nt_dot_at()

expansion_nt expansion_nt_dot_at	(	const double *	a,
		const double *	b,
		const double *	c,
		coord_index_t	dim
	)

Parameters

[in]	a	an array of `dim` doubles
[in]	b	an array of `dim` doubles
[in]	c	an array of `dim` doubles
[in]	dim	the dimension of the points

Returns: an expansion_nt that represents the exact dot product (a - c).(b - c)

Definition at line 807 of file expansion_nt.h.

◆ expansion_nt_sq_dist()

expansion_nt expansion_nt_sq_dist	(	const double *	a,
		const double *	b,
		coord_index_t	dim
	)

Parameters

[in]	a	an array of `dim` doubles
[in]	b	an array of `dim` doubles
[in]	dim	the dimension of the points

Returns: an expansion_nt that represent the exact squared distance between a and b

Definition at line 786 of file expansion_nt.h.

◆ operator!=() [1/3]

bool operator!=	(	const expansion_nt &	a,
		const expansion_nt &	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 748 of file expansion_nt.h.

◆ operator!=() [2/3]

bool operator!=	(	const expansion_nt &	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 760 of file expansion_nt.h.

◆ operator!=() [3/3]

bool operator!=	(	double	a,
		const expansion_nt &	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 772 of file expansion_nt.h.

◆ operator*()

expansion_nt operator*	(	double	a,
		const expansion_nt &	b
	)

Parameters

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

Returns: an expansion_nt that represents a * b

Definition at line 700 of file expansion_nt.h.

◆ operator+()

expansion_nt operator+	(	double	a,
		const expansion_nt &	b
	)

Parameters

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

Returns: an expansion_nt that represents a + b

Definition at line 676 of file expansion_nt.h.

◆ operator-()

expansion_nt operator-	(	double	a,
		const expansion_nt &	b
	)

Parameters

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

Returns: an expansion_nt that represents a - b

Definition at line 687 of file expansion_nt.h.

◆ operator==() [1/3]

bool operator==	(	const expansion_nt &	a,
		const expansion_nt &	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 712 of file expansion_nt.h.

◆ operator==() [2/3]

bool operator==	(	const expansion_nt &	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 724 of file expansion_nt.h.

◆ operator==() [3/3]

bool operator==	(	double	a,
		const expansion_nt &	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 736 of file expansion_nt.h.

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

geogram/numerics/expansion_nt.h

Public Types

Public Member Functions

Protected Member Functions

Friends

Related Functions

Detailed Description

Constructor & Destructor Documentation

◆ expansion_nt() [1/9]

◆ expansion_nt() [2/9]

◆ expansion_nt() [3/9]

◆ expansion_nt() [4/9]

◆ expansion_nt() [5/9]

◆ expansion_nt() [6/9]

◆ expansion_nt() [7/9]

◆ expansion_nt() [8/9]

◆ ~expansion_nt()

◆ expansion_nt() [9/9]

Member Function Documentation

◆ compare() [1/2]

◆ compare() [2/2]

◆ component()

◆ copy()

◆ estimate()

◆ length()

◆ 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]

◆ optimize()

◆ rep() [1/2]

◆ rep() [2/2]

◆ sign()

◆ to_string()

Friends And Related Function Documentation

◆ expansion_nt_dot_at()

◆ expansion_nt_sq_dist()

◆ operator!=() [1/3]

◆ operator!=() [2/3]

◆ operator!=() [3/3]

◆ operator*()

◆ operator+()

◆ operator-()

◆ operator==() [1/3]

◆ operator==() [2/3]

◆ operator==() [3/3]