Aim: This class gathers several types and methods to make computation with integers. More...

#include <DGtal/arithmetic/IntegerComputer.h>

Public Types
typedef IntegerComputer< TInteger >	Self

typedef NumberTraits< TInteger >::SignedVersion	Integer

typedef NumberTraits< Integer >::ParamType	IntegerParamType

typedef NumberTraits< TInteger >::UnsignedVersion	UnsignedInteger

typedef NumberTraits< UnsignedInteger >::ParamType	UnsignedIntegerParamType

typedef SpaceND< 2, Integer >::Point	Point2I

typedef SpaceND< 2, Integer >::Vector	Vector2I

typedef SpaceND< 3, Integer >::Point	Point3I

typedef SpaceND< 3, Integer >::Vector	Vector3I

Public Member Functions
	BOOST_CONCEPT_ASSERT ((concepts::CInteger< Integer >))

	BOOST_CONCEPT_ASSERT ((concepts::CUnsignedNumber< UnsignedInteger >))

	BOOST_CONCEPT_ASSERT ((concepts::CIntegralNumber< UnsignedInteger >))

	~IntegerComputer ()

	IntegerComputer ()

	IntegerComputer (const Self &other)

Self &	operator= (const Self &other)

void	getEuclideanDiv (Integer &q, Integer &r, IntegerParamType a, IntegerParamType b) const

Integer	floorDiv (IntegerParamType na, IntegerParamType nb) const

Integer	ceilDiv (IntegerParamType na, IntegerParamType nb) const

void	getFloorCeilDiv (Integer &fl, Integer &ce, IntegerParamType na, IntegerParamType nb) const

Integer	gcd (IntegerParamType a, IntegerParamType b) const

void	getGcd (Integer &g, IntegerParamType a, IntegerParamType b) const

Integer	getCFrac (std::vector< Integer > &quotients, IntegerParamType a, IntegerParamType b) const

template<typename OutputIterator >
Integer	getCFrac (OutputIterator outIt, IntegerParamType a, IntegerParamType b) const

Point2I	convergent (const std::vector< Integer > &quotients, unsigned int k) const

void	reduce (Vector2I &p) const

Integer	crossProduct (const Vector2I &u, const Vector2I &v) const

void	getCrossProduct (Integer &cp, const Vector2I &u, const Vector2I &v) const

Integer	dotProduct (const Vector2I &u, const Vector2I &v) const

void	getDotProduct (Integer &dp, const Vector2I &u, const Vector2I &v) const

Vector2I	extendedEuclid (IntegerParamType a, IntegerParamType b, IntegerParamType c) const

void	getCoefficientIntersection (Integer &fl, Integer &ce, const Vector2I &p, const Vector2I &u, const Vector2I &N, IntegerParamType c) const

void	getValidBezout (Vector2I &v, const Point2I &A, const Vector2I &u, const Vector2I &N, IntegerParamType c, const Vector2I &N2, IntegerParamType c2, bool compute_v=true) const

void	reduce (Vector3I &p) const

Integer	dotProduct (const Vector3I &u, const Vector3I &v) const

void	getDotProduct (Integer &dp, const Vector3I &u, const Vector3I &v) const

void	selfDisplay (std::ostream &out) const

bool	isValid () const

Static Public Member Functions
static bool	isZero (IntegerParamType a)

static bool	isNotZero (IntegerParamType a)

static bool	isPositive (IntegerParamType a)

static bool	isNegative (IntegerParamType a)

static bool	isPositiveOrZero (IntegerParamType a)

static bool	isNegativeOrZero (IntegerParamType a)

static Integer	abs (IntegerParamType a)

static Integer	max (IntegerParamType a, IntegerParamType b)

static Integer	max (IntegerParamType a, IntegerParamType b, IntegerParamType c)

static Integer	min (IntegerParamType a, IntegerParamType b)

static Integer	min (IntegerParamType a, IntegerParamType b, IntegerParamType c)

static Integer	staticGcd (IntegerParamType a, IntegerParamType b)

Private Attributes
Integer	_m_a
	Used to store parameter a. More...

Integer	_m_b
	Used to store parameter b. More...

Integer	_m_a0
	Used to for successive computation in gcd. More...

Integer	_m_a1
	Used to for successive computation in gcd. More...

Integer	_m_q
	Used to represent a quotient. More...

Integer	_m_r
	Used to represent a remainder. More...

std::vector< Integer >	_m_bezout [4]

Vector2I	_m_v
	Used to represent the Bezout vector. More...

Vector2I	_m_v0
	Used to represent vectors. More...

Vector2I	_m_v1
	Used to represent vectors. More...

Integer	_m_c0
	Used to represent scalar products. More...

Integer	_m_c1
	Used to represent scalar products. More...

Integer	_m_c2
	Used to represent scalar products. More...

Detailed Description

template<typename TInteger>
class DGtal::IntegerComputer< TInteger >

Aim: This class gathers several types and methods to make computation with integers.

Description of template class 'IntegerComputer'

This class is especially useful with using big integers (like GMP), since a substantial part of the execution time cames from the allocation/desallocation of integers. The idea is that the user instantiate once this object and computes gcd, bezout, continued fractions with it.

To be thread-safe, each thread must instantiate an IntegerComputer.

It is a model of boost::CopyConstructible, boost::DefaultConstructible, boost::Assignable. All its member data are mutable.

It is a backport of ImaGene.

Template Parameters

TInteger any model of integer (CInteger), like int, long int, int64_t, BigInteger (when GMP is installed).

Examples: arithmetic/extended-euclid.cpp.

Definition at line 82 of file IntegerComputer.h.

Member Typedef Documentation

◆ Integer

template<typename TInteger >

typedef NumberTraits<TInteger>::SignedVersion DGtal::IntegerComputer< TInteger >::Integer

Definition at line 87 of file IntegerComputer.h.

◆ IntegerParamType

template<typename TInteger >

typedef NumberTraits<Integer>::ParamType DGtal::IntegerComputer< TInteger >::IntegerParamType

Definition at line 88 of file IntegerComputer.h.

◆ Point2I

template<typename TInteger >

typedef SpaceND<2,Integer>::Point DGtal::IntegerComputer< TInteger >::Point2I

Definition at line 93 of file IntegerComputer.h.

◆ Point3I

template<typename TInteger >

typedef SpaceND<3,Integer>::Point DGtal::IntegerComputer< TInteger >::Point3I

Definition at line 95 of file IntegerComputer.h.

◆ Self

template<typename TInteger >

typedef IntegerComputer<TInteger> DGtal::IntegerComputer< TInteger >::Self

Definition at line 86 of file IntegerComputer.h.

◆ UnsignedInteger

template<typename TInteger >

typedef NumberTraits<TInteger>::UnsignedVersion DGtal::IntegerComputer< TInteger >::UnsignedInteger

Definition at line 90 of file IntegerComputer.h.

◆ UnsignedIntegerParamType

template<typename TInteger >

typedef NumberTraits<UnsignedInteger>::ParamType DGtal::IntegerComputer< TInteger >::UnsignedIntegerParamType

Definition at line 91 of file IntegerComputer.h.

◆ Vector2I

template<typename TInteger >

typedef SpaceND<2,Integer>::Vector DGtal::IntegerComputer< TInteger >::Vector2I

Definition at line 94 of file IntegerComputer.h.

◆ Vector3I

template<typename TInteger >

typedef SpaceND<3,Integer>::Vector DGtal::IntegerComputer< TInteger >::Vector3I

Definition at line 96 of file IntegerComputer.h.

Constructor & Destructor Documentation

◆ ~IntegerComputer()

template<typename TInteger >

DGtal::IntegerComputer< TInteger >::~IntegerComputer ( )

Destructor.

◆ IntegerComputer() [1/2]

template<typename TInteger >

DGtal::IntegerComputer< TInteger >::IntegerComputer ( )

Constructor. Each thread must have its own instance for all computations. Such object stores several local variables to limit the number of memory allocations.

Does nothing (member data are allocated, but their values are not used except during the execution of methods).

◆ IntegerComputer() [2/2]

template<typename TInteger >

DGtal::IntegerComputer< TInteger >::IntegerComputer ( const Self & other )

Copy constructor.

Does nothing (member data are allocated, but their values are not used except during the execution of methods).

Parameters

other the object to clone.

Member Function Documentation

◆ abs()

template<typename TInteger >

static Integer DGtal::IntegerComputer< TInteger >::abs ( IntegerParamType a )

static

Parameters

a	any integer.

Returns: its absolute value.

Referenced by checkGenericPlane(), checkPlane(), checkPlaneGroupExtension(), checkWidth(), and testValidBezout().

◆ BOOST_CONCEPT_ASSERT() [1/3]

template<typename TInteger >

DGtal::IntegerComputer< TInteger >::BOOST_CONCEPT_ASSERT ( (concepts::CInteger< Integer >) )

◆ BOOST_CONCEPT_ASSERT() [2/3]

template<typename TInteger >

DGtal::IntegerComputer< TInteger >::BOOST_CONCEPT_ASSERT ( (concepts::CIntegralNumber< UnsignedInteger >) )

◆ BOOST_CONCEPT_ASSERT() [3/3]

template<typename TInteger >

DGtal::IntegerComputer< TInteger >::BOOST_CONCEPT_ASSERT ( (concepts::CUnsignedNumber< UnsignedInteger >) )

◆ ceilDiv()

template<typename TInteger >

Integer DGtal::IntegerComputer< TInteger >::ceilDiv	(	IntegerParamType	na,
		IntegerParamType	nb
	)		const

Computes the ceil value of na/nb.

Parameters

na	any integer.
nb	any integer.

Referenced by checkExtendWithManyPoints(), checkGenericPlane(), checkPlane(), checkPlaneGroupExtension(), checkWidth(), testCeilFloorDiv(), and unionComparisonTest().

◆ convergent()

template<typename TInteger >

Point2I DGtal::IntegerComputer< TInteger >::convergent	(	const std::vector< Integer > &	quotients,
		unsigned int	k
	)		const

Returns the fraction corresponding to the given quotients, more precisely its k-th principal convergent. When k >= quotients.size() - 1, it is the inverse of the function getCFrac.

Parameters

quotients	the sequence of partial quotients.
k	the desired partial convergent.

Returns: the corresponding fraction p_k / q_k as a point (p_k, q_k).

Referenced by testCFrac().

◆ crossProduct()

template<typename TInteger >

Integer DGtal::IntegerComputer< TInteger >::crossProduct	(	const Vector2I &	u,
		const Vector2I &	v
	)		const

Computes and returns the cross product of u and v.

Parameters

u	any vector in Z2.
v	any vector in Z2.

Returns: the cross product of u and v.

Referenced by testValidBezout().

◆ dotProduct() [1/2]

template<typename TInteger >

Integer DGtal::IntegerComputer< TInteger >::dotProduct	(	const Vector2I &	u,
		const Vector2I &	v
	)		const

Computes and returns the dot product of u and v.

Parameters

u	any vector in Z2.
v	any vector in Z2.

Returns: the dot product of u and v.

Referenced by DGtal::FrechetShortcut< TIterator, TInteger >::Tools::angleVectVect(), testCoefficientIntersection(), testValidBezout(), and unionComparisonTest().

◆ dotProduct() [2/2]

template<typename TInteger >

Integer DGtal::IntegerComputer< TInteger >::dotProduct	(	const Vector3I &	u,
		const Vector3I &	v
	)		const

Computes and returns the dot product of u and v.

Parameters

u	any vector in Z2.
v	any vector in Z2.

Returns: the dot product of u and v.

◆ extendedEuclid()

template<typename TInteger >

Vector2I DGtal::IntegerComputer< TInteger >::extendedEuclid	(	IntegerParamType	a,
		IntegerParamType	b,
		IntegerParamType	c
	)		const

Returns a solution of the Diophantine equation: a x + b y = c. The integer c should be a multiple of the gcd of a and b. Uses the extended Euclid algorithm to do it, whose complexity is bounded by max(log(a),log(b)).

The solution is chosen such that:

when c > 0,
- a > 0 implies x >= 0, thus sgn(y)=-sgn(b)
- a < 0 implies x <= 0, thus sgn(y)=-sgn(b)
when c < 0,
- a > 0 implies x <= 0, thus sgn(y)=sgn(b)
- a < 0 implies x >= 0, thus sgn(y)=sgn(b)
abs(x) <= abs(b * c )
abs(y) < abs(a * c )

Parameters

a	any non-null integer.
b	any non-null integer.
c	any integer multiple of gcd(\|a\|,\|b\|).

Returns: a vector (x,y) solution to a x + b y = c.

Referenced by testExtendedEuclid().

◆ floorDiv()

template<typename TInteger >

Integer DGtal::IntegerComputer< TInteger >::floorDiv	(	IntegerParamType	na,
		IntegerParamType	nb
	)		const

Computes the floor value of na/nb.

Parameters

na	any integer.
nb	any integer.

Referenced by testCeilFloorDiv(), testDSLSubsegment(), and unionComparisonTest().

◆ gcd()

template<typename TInteger >

Integer DGtal::IntegerComputer< TInteger >::gcd	(	IntegerParamType	a,
		IntegerParamType	b
	)		const

Returns the greatest common divisor of a and b (a and b may be either positive or negative).

Parameters

a	any integer.
b	any integer.

Returns: the gcd of a and b.

Referenced by testCFrac(), testDSLSubsegment(), testExtendedEuclid(), testGCD(), testInitFraction(), testPatterns(), testReducedFraction(), testSubStandardDSLQ0(), and unionComparisonTest().

◆ getCFrac() [1/2]

template<typename TInteger >

template<typename OutputIterator >

Integer DGtal::IntegerComputer< TInteger >::getCFrac	(	OutputIterator	outIt,
		IntegerParamType	a,
		IntegerParamType	b
	)		const

Computes and outputs the quotients of the simple continued fraction of a / b. (positive) and b (positive). For instance, 5/13=[0;2,1,1,2], which is exactly what is outputed with the OutputIterator outIt.

Template Parameters

OutputIterator a model of boost::OutputIterator

Parameters

outIt	an instance of output iterator that is used to write the successive quotients of the continued fraction of a/b.
a	any positive integer.
b	any positive integer.

Returns: the gcd of a and b.

◆ getCFrac() [2/2]

template<typename TInteger >

Integer DGtal::IntegerComputer< TInteger >::getCFrac	(	std::vector< Integer > &	quotients,
		IntegerParamType	a,
		IntegerParamType	b
	)		const

Computes and push_backs the simple continued fraction of a / b. (positive) and b (positive). For instance, 5/13=[0;2,1,1,2], which is exactly what is pushed at the back of quotients.

Parameters

quotients	(modifies) adds to the back of the vector the quotients of the continued fraction of a/b.
a	any positive integer.
b	any positive integer.

Returns: the gcd of a and b.

Referenced by testCFrac(), and testReducedFraction().

◆ getCoefficientIntersection()

template<typename TInteger >

void DGtal::IntegerComputer< TInteger >::getCoefficientIntersection	(	Integer &	fl,
		Integer &	ce,
		const Vector2I &	p,
		const Vector2I &	u,
		const Vector2I &	N,
		IntegerParamType	c
	)		const

Computes the floor (fl) and the ceiling (ce) value of the real number k such that p + k u lies on the supporting line of the linear constraint N.p <= c.

Otherwise said: (u.N) fl <= c - p.N < (u.N) ce

Parameters

fl	the greatest integer such that (u.N) fl <= c - p.N
ce	the smallest integer such that c - p.N < (u.N) ce
p	any vector in Z2
u	any vector in Z2 in the same quadrant as N.
N	any vector in Z2 in the same quadrant as u.
c	any integer.

Referenced by testCoefficientIntersection().

◆ getCrossProduct()

template<typename TInteger >

void DGtal::IntegerComputer< TInteger >::getCrossProduct	(	Integer &	cp,
		const Vector2I &	u,
		const Vector2I &	v
	)		const

Computes the cross product of u and v.

Parameters

cp	(returns) the cross product of u and v.
u	any vector in Z2.
v	any vector in Z2.

◆ getDotProduct() [1/2]

template<typename TInteger >

void DGtal::IntegerComputer< TInteger >::getDotProduct	(	Integer &	dp,
		const Vector2I &	u,
		const Vector2I &	v
	)		const

Computes and returns the dot product of u and v.

Parameters

dp	(returns) the dot product of u and v.
u	any vector in Z2.
v	any vector in Z2.

◆ getDotProduct() [2/2]

template<typename TInteger >

void DGtal::IntegerComputer< TInteger >::getDotProduct	(	Integer &	dp,
		const Vector3I &	u,
		const Vector3I &	v
	)		const

Computes and returns the dot product of u and v.

Parameters

dp	(returns) the dot product of u and v.
u	any vector in Z3.
v	any vector in Z3.

◆ getEuclideanDiv()

template<typename TInteger >

void DGtal::IntegerComputer< TInteger >::getEuclideanDiv	(	Integer &	q,
		Integer &	r,
		IntegerParamType	a,
		IntegerParamType	b
	)		const

Computes the euclidean division of a/b, returning quotient and remainder. May be faster than computing separately quotient and remainder, depending on the integral type in use.

Todo:: Specialize it for GMP as mpz_fdiv_qr (q.get_mpz_t(), r.get_mpz_t(), a.get_mpz_t(), b.get_mpz_t());

Parameters

q	(returns) the quotient of a/b.
r	(returns) the remainder of a/b.
a	any integer.
b	any integer.

◆ getFloorCeilDiv()

template<typename TInteger >

void DGtal::IntegerComputer< TInteger >::getFloorCeilDiv	(	Integer &	fl,
		Integer &	ce,
		IntegerParamType	na,
		IntegerParamType	nb
	)		const

Computes the floor and ceil value of na/nb.

Parameters

fl	(returns) the floor value of na/nb.
ce	(returns) the ceil value of na/nb.
na	any integer.
nb	any integer.

Referenced by testCeilFloorDiv().

◆ getGcd()

template<typename TInteger >

void DGtal::IntegerComputer< TInteger >::getGcd	(	Integer &	g,
		IntegerParamType	a,
		IntegerParamType	b
	)		const

Returns the greatest common divisor of a and b (a and b may be either positive or negative).

Parameters

g	(returns) the gcd of a and b.
a	any integer.
b	any integer.

Referenced by testGCD().

◆ getValidBezout()

template<typename TInteger >

void DGtal::IntegerComputer< TInteger >::getValidBezout	(	Vector2I &	v,
		const Point2I &	A,
		const Vector2I &	u,
		const Vector2I &	N,
		IntegerParamType	c,
		const Vector2I &	N2,
		IntegerParamType	c2,
		bool	compute_v = `true`
	)		const

Compute the valid bezout vector v of u such that A+v satifies the constraints C2 and such that A+v+u doesn't satify the constraint C2.

(A+v).N2 <= c2, (A+v+u).N2 > c2.

The constraint (N,c) is used like this: if the Bezout is such that (A+v).N > c, then v <- -v. Thus v is oriented toward the constraint.

If ! compute_v, v is used as is. The constraint N.(A+v) <= c should be satisfied.

Parameters

v	(modifies) a Bezout vector for u, with the constraints above.
A	any point in Z2.
u	any vector in Z2.
N	any vector in Z2, defining the first constraint.
c	the integer for the first constraint.
N2	any vector in Z2, defining the second constraint.
c2	the integer for the second constraint.
compute_v	tells if v should be recomputed (true) or is already given (false), default to true.

Referenced by testValidBezout().

◆ isNegative()

template<typename TInteger >

static bool DGtal::IntegerComputer< TInteger >::isNegative ( IntegerParamType a )

static

Parameters

a	any integer.

Returns: true if a < 0.

◆ isNegativeOrZero()

template<typename TInteger >

static bool DGtal::IntegerComputer< TInteger >::isNegativeOrZero ( IntegerParamType a )

static

Parameters

a	any integer.

Returns: true if a <= 0.

◆ isNotZero()

template<typename TInteger >

static bool DGtal::IntegerComputer< TInteger >::isNotZero ( IntegerParamType a )

static

Parameters

a	any integer.

Returns: true if a != 0.

◆ isPositive()

template<typename TInteger >

static bool DGtal::IntegerComputer< TInteger >::isPositive ( IntegerParamType a )

static

Parameters

a	any integer.

Returns: true if a > 0.

◆ isPositiveOrZero()

template<typename TInteger >

static bool DGtal::IntegerComputer< TInteger >::isPositiveOrZero ( IntegerParamType a )

static

Parameters

a	any integer.

Returns: true if a >= 0.

◆ isValid()

template<typename TInteger >

bool DGtal::IntegerComputer< TInteger >::isValid ( ) const

Checks the validity/consistency of the object.

Returns: 'true' if the object is valid, 'false' otherwise.

◆ isZero()

template<typename TInteger >

static bool DGtal::IntegerComputer< TInteger >::isZero ( IntegerParamType a )

static

Parameters

a	any integer.

Returns: true if a == 0.

Referenced by testCeilFloorDiv(), and testGCD().

◆ max() [1/2]

template<typename TInteger >

static Integer DGtal::IntegerComputer< TInteger >::max	(	IntegerParamType	a,
		IntegerParamType	b
	)

static

Parameters

a	any integer.
b	any integer.

Returns: the maximum value of a and b.

◆ max() [2/2]

template<typename TInteger >

static Integer DGtal::IntegerComputer< TInteger >::max	(	IntegerParamType	a,
		IntegerParamType	b,
		IntegerParamType	c
	)

static

Parameters

a	any integer.
b	any integer.
c	any integer.

Returns: the maximum value of a, b and c.

◆ min() [1/2]

template<typename TInteger >

static Integer DGtal::IntegerComputer< TInteger >::min	(	IntegerParamType	a,
		IntegerParamType	b
	)

static

Parameters

a	any integer.
b	any integer.

Returns: the minimum value of a and b.

◆ min() [2/2]

template<typename TInteger >

static Integer DGtal::IntegerComputer< TInteger >::min	(	IntegerParamType	a,
		IntegerParamType	b,
		IntegerParamType	c
	)

static

Parameters

a	any integer.
b	any integer.
c	any integer.

Returns: the minimum value of a, b and c.

◆ operator=()

template<typename TInteger >

Self & DGtal::IntegerComputer< TInteger >::operator= ( const Self & other )

Assignment.

Does nothing (member data are allocated, but their values are not used except during the execution of methods).

Parameters

other the object to copy.

Returns: a reference on 'this'.

◆ reduce() [1/2]

template<typename TInteger >

void DGtal::IntegerComputer< TInteger >::reduce ( Vector2I & p ) const

Makes p irreducible.

Parameters

p	any vector in Z2.

Referenced by testValidBezout().

◆ reduce() [2/2]

template<typename TInteger >

void DGtal::IntegerComputer< TInteger >::reduce ( Vector3I & p ) const

Makes p irreducible.

Parameters

p	any vector in Z3.

◆ selfDisplay()

template<typename TInteger >

void DGtal::IntegerComputer< TInteger >::selfDisplay ( std::ostream & out ) const

Writes/Displays the object on an output stream.

Parameters

out	the output stream where the object is written.

◆ staticGcd()

template<typename TInteger >

static Integer DGtal::IntegerComputer< TInteger >::staticGcd	(	IntegerParamType	a,
		IntegerParamType	b
	)

static

Returns the greatest common divisor of a and b (a and b may be either positive or negative).

Parameters

a	any integer.
b	any integer.

Returns: the gcd of a and b.

Referenced by exhaustiveTestLatticePolytope2D().

Field Documentation

◆ _m_a

template<typename TInteger >

Integer DGtal::IntegerComputer< TInteger >::_m_a

mutableprivate

Used to store parameter a.

Definition at line 508 of file IntegerComputer.h.

◆ _m_a0

template<typename TInteger >

Integer DGtal::IntegerComputer< TInteger >::_m_a0

mutableprivate

Used to for successive computation in gcd.

Definition at line 512 of file IntegerComputer.h.

◆ _m_a1

template<typename TInteger >

Integer DGtal::IntegerComputer< TInteger >::_m_a1

mutableprivate

Used to for successive computation in gcd.

Definition at line 514 of file IntegerComputer.h.

◆ _m_b

template<typename TInteger >

Integer DGtal::IntegerComputer< TInteger >::_m_b

mutableprivate

Used to store parameter b.

Definition at line 510 of file IntegerComputer.h.

◆ _m_bezout

template<typename TInteger >

std::vector<Integer> DGtal::IntegerComputer< TInteger >::_m_bezout[4]

mutableprivate

Used to represent the variables during an extended Euclid computation, [0] are remainders, [1] are quotients, [2] are successive a, [3] are successive b.

Definition at line 522 of file IntegerComputer.h.

◆ _m_c0

template<typename TInteger >

Integer DGtal::IntegerComputer< TInteger >::_m_c0

mutableprivate

Used to represent scalar products.

Definition at line 530 of file IntegerComputer.h.

◆ _m_c1

template<typename TInteger >

Integer DGtal::IntegerComputer< TInteger >::_m_c1

mutableprivate

Used to represent scalar products.

Definition at line 532 of file IntegerComputer.h.

◆ _m_c2

template<typename TInteger >

Integer DGtal::IntegerComputer< TInteger >::_m_c2

mutableprivate

Used to represent scalar products.

Definition at line 534 of file IntegerComputer.h.

◆ _m_q

template<typename TInteger >

Integer DGtal::IntegerComputer< TInteger >::_m_q

mutableprivate

Used to represent a quotient.

Definition at line 516 of file IntegerComputer.h.

◆ _m_r

template<typename TInteger >

Integer DGtal::IntegerComputer< TInteger >::_m_r

mutableprivate

Used to represent a remainder.

Definition at line 518 of file IntegerComputer.h.

◆ _m_v

template<typename TInteger >

Vector2I DGtal::IntegerComputer< TInteger >::_m_v

mutableprivate

Used to represent the Bezout vector.

Definition at line 524 of file IntegerComputer.h.

◆ _m_v0

template<typename TInteger >

Vector2I DGtal::IntegerComputer< TInteger >::_m_v0

mutableprivate

Used to represent vectors.

Definition at line 526 of file IntegerComputer.h.

◆ _m_v1

template<typename TInteger >

Vector2I DGtal::IntegerComputer< TInteger >::_m_v1

mutableprivate

Used to represent vectors.

Definition at line 528 of file IntegerComputer.h.

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

IntegerComputer.h

Public Types

Public Member Functions

Static Public Member Functions

Private Attributes

Detailed Description

Member Typedef Documentation

◆ Integer

◆ IntegerParamType

◆ Point2I

◆ Point3I

◆ Self

◆ UnsignedInteger

◆ UnsignedIntegerParamType

◆ Vector2I

◆ Vector3I

Constructor & Destructor Documentation

◆ ~IntegerComputer()

◆ IntegerComputer() [1/2]

◆ IntegerComputer() [2/2]

Member Function Documentation

◆ abs()

◆ BOOST_CONCEPT_ASSERT() [1/3]

◆ BOOST_CONCEPT_ASSERT() [2/3]

◆ BOOST_CONCEPT_ASSERT() [3/3]

◆ ceilDiv()

◆ convergent()

◆ crossProduct()

◆ dotProduct() [1/2]

◆ dotProduct() [2/2]

◆ extendedEuclid()

◆ floorDiv()

◆ gcd()

◆ getCFrac() [1/2]

◆ getCFrac() [2/2]

◆ getCoefficientIntersection()

◆ getCrossProduct()

◆ getDotProduct() [1/2]

◆ getDotProduct() [2/2]

◆ getEuclideanDiv()

◆ getFloorCeilDiv()

◆ getGcd()

◆ getValidBezout()

◆ isNegative()

◆ isNegativeOrZero()

◆ isNotZero()

◆ isPositive()

◆ isPositiveOrZero()

◆ isValid()

◆ isZero()

◆ max() [1/2]

◆ max() [2/2]

◆ min() [1/2]

◆ min() [2/2]

◆ operator=()

◆ reduce() [1/2]

◆ reduce() [2/2]

◆ selfDisplay()

◆ staticGcd()

Field Documentation

◆ _m_a

◆ _m_a0

◆ _m_a1

◆ _m_b

◆ _m_bezout

◆ _m_c0

◆ _m_c1

◆ _m_c2

◆ _m_q

◆ _m_r

◆ _m_v

◆ _m_v0

◆ _m_v1