GEO::expansion Class Reference

Represents numbers in arbitrary precision with a low-level API. More...

#include <geogram/numerics/multi_precision.h>

Public Member Functions
index_t	length () const
	Gets the length of this expansion. More...
index_t	capacity () const
	Gets the capacity of this expansion. More...
void	set_length (index_t new_length)
	Changes the length of an expansion. More...
const double &	operator[] (index_t i) const
	Low level access to a component. More...
double &	operator[] (index_t i)
	Low level access to a component. More...
double *	data ()
	Low level access to the array of components. More...
const double *	data () const
	Low level access to the array of components. More...
	expansion (index_t capa)
	Client code should not use this constructor. More...
expansion &	assign (double a)
	Assigns a number to this expansion. More...
expansion &	assign (const expansion &rhs)
	Copies an expansion to this expansion. More...
expansion &	assign_abs (const expansion &rhs)
	Copies the absolute value of an expansion to this expansion. More...
expansion &	assign_sum (double a, double b)
	Assigns the sum of two doubles to this expansion (should not be used by client code). More...
expansion &	assign_diff (double a, double b)
	Assigns the difference of two doubles to this expansion (should not be used by client code). More...
expansion &	assign_product (double a, double b)
	Assigns the product of two doubles to this expansion (should not be used by client code). More...
expansion &	assign_square (double a)
	Assigns the square of a double to this expansion (should not be used by client code). More...
expansion &	assign_sum (const expansion &a, double b)
	Assigns the sum of an expansion and a double to this expansion (should not be used by client code). More...
expansion &	assign_diff (const expansion &a, double b)
	Assigns the difference between an expansion and a double to this expansion (should not be used by client code). More...
expansion &	assign_product (const expansion &a, double b)
	Assigns the product between an expansion and a double to this expansion (should not be used by client code). More...
expansion &	assign_sum (const expansion &a, const expansion &b)
	Assigns the sum of two expansions to this expansion (should not be used by client code). More...
expansion &	assign_sum (const expansion &a, const expansion &b, const expansion &c)
	Assigns the sum of three expansions to this expansion (should not be used by client code). More...
expansion &	assign_sum (const expansion &a, const expansion &b, const expansion &c, const expansion &d)
	Assigns the sum of four expansions to this expansion (should not be used by client code). More...
expansion &	assign_diff (const expansion &a, const expansion &b)
	Assigns the difference between two expansions to this expansion (should not be used by client code). More...
expansion &	assign_product (const expansion &a, const expansion &b)
	Assigns the product of two expansions to this expansion (should not be used by client code). More...
expansion &	assign_product (const expansion &a, const expansion &b, const expansion &c)
	Assigns the product of three expansions to this expansion (should not be used by client code). More...
expansion &	assign_square (const expansion &a)
	Assigns the product of an expansions to this expansion (should not be used by client code). More...
expansion &	assign_det2x2 (const expansion &a11, const expansion &a12, const expansion &a21, const expansion &a22)
	Assigns a 2x2 determinant to this expansion (should not be used by client code). More...
expansion &	assign_det3x3 (const expansion &a11, const expansion &a12, const expansion &a13, const expansion &a21, const expansion &a22, const expansion &a23, const expansion &a31, const expansion &a32, const expansion &a33)
	Assigns a 3x3 determinant to this expansion (should not be used by client code). More...
expansion &	assign_det_111_2x3 (const expansion &a21, const expansion &a22, const expansion &a23, const expansion &a31, const expansion &a32, const expansion &a33)
	Assigns a 3x3 determinant to this expansion where the first row is 1 1 1(should not be used by client code). More...
expansion &	assign_sq_dist (const double *p1, const double *p2, coord_index_t dim)
	Assigns the squared distance between two points to this expansion (should not be used by client code). More...
expansion &	assign_dot_at (const double *p1, const double *p2, const double *p0, coord_index_t dim)
	Assigns the dot product of two vectors to this expansion (should not be used by client code). More...
expansion &	assign_length2 (const expansion &x, const expansion &y, const expansion &z)
	Assigns the length of a vector to this expansion (should not be used by client code). Do not call this function directly, use expansion_length2() macro instead. More...
expansion &	negate ()
	Changes the sign of an expansion. More...
expansion &	scale_fast (double s)
	Multiplies this expansion by a power of two. More...
double	estimate () const
	Computes an approximation of the stored value in this expansion. More...
Sign	sign () const
	Gets the sign of the expansion. More...
bool	is_same_as (const expansion &rhs) const
	Compares two expansions bit-by-bit. More...
bool	is_same_as (double rhs) const
	Compares an expansion and a double bit-by-bit. More...
Sign	compare (const expansion &rhs) const
	Compares two expansions. More...
Sign	compare (double rhs) const
	Compares two expansions. More...
bool	equals (const expansion &rhs) const
	Compares two expansions. More...
bool	equals (double rhs) const
	Compares an expansion and a double. More...
std::ostream &	show (std::ostream &out) const
	Displays all the components of this expansion (for debugging purposes). More...
std::string	to_string () const
	Gets a string representation of this expansion. More...
void	optimize ()
	Optimizes the internal representation without changing the represented value. More...

Static Public Member Functions
static size_t	bytes (index_t capa)
	Computes the amount of memory required to store an expansion. More...
static size_t	bytes_on_stack (index_t capa)
	Computes the amount of memory required to store an expansion on the stack. More...
static expansion *	new_expansion_on_heap (index_t capa)
	Allocates an expansion on the heap. More...
static void	delete_expansion_on_heap (expansion *e)
	Deallocates an expansion on the heap. More...
static index_t	sum_capacity (double a, double b)
	Computes the required capacity to store the sum of two doubles. More...
static index_t	diff_capacity (double a, double b)
	Computes the required capacity of an expansion to store the exact difference of two doubles. More...
static index_t	product_capacity (double a, double b)
	Computes the required capacity of an expansion to store the exact product of two doubles. More...
static index_t	square_capacity (double a)
	Computes the required capacity of an expansion to store the exact square of a double. More...
static index_t	sum_capacity (const expansion &a, double b)
	Computes the required capacity of an expansion to store the exact sum of an expansion and a double. More...
static index_t	diff_capacity (const expansion &a, double b)
	Computes the required capacity of an expansion to store the exact difference between an expansion and a double. More...
static index_t	product_capacity (const expansion &a, double b)
	Computes the required capacity of an expansion to store the exact product between an expansion and a double. More...
static index_t	sum_capacity (const expansion &a, const expansion &b)
	Computes the required capacity of an expansion to store the exact sum of two expansions. More...
static index_t	sum_capacity (const expansion &a, const expansion &b, const expansion &c)
	Computes the required capacity of an expansion to store the exact sum of three expansions. More...
static index_t	sum_capacity (const expansion &a, const expansion &b, const expansion &c, const expansion &d)
	Computes the required capacity of an expansion to store the exact sum of four expansions. More...
static index_t	diff_capacity (const expansion &a, const expansion &b)
	Computes the required capacity of an expansion to store the exact difference of two expansions. More...
static index_t	product_capacity (const expansion &a, const expansion &b)
	Computes the required capacity of an expansion to store the exact product of two expansions. More...
static index_t	product_capacity (const expansion &a, const expansion &b, const expansion &c)
	Computes the required capacity of an expansion to store the exact product of three expansions. More...
static index_t	square_capacity (const expansion &a)
	Computes the required capacity of an expansion to store the exact square of an expansion. More...
static index_t	det2x2_capacity (const expansion &a11, const expansion &a12, const expansion &a21, const expansion &a22)
	Computes the required capacity of an expansion to store an exact 2x2 determinant. More...
static index_t	det3x3_capacity (const expansion &a11, const expansion &a12, const expansion &a13, const expansion &a21, const expansion &a22, const expansion &a23, const expansion &a31, const expansion &a32, const expansion &a33)
	Computes the required capacity of an expansion to store an exact 3x3 determinant. More...
static index_t	det_111_2x3_capacity (const expansion &a21, const expansion &a22, const expansion &a23, const expansion &a31, const expansion &a32, const expansion &a33)
	Computes the required capacity of an expansion to store an exact 3x3 determinant where the first row is 1 1 1. More...
static index_t	sq_dist_capacity (coord_index_t dim)
	Computes the required capacity of an expansion to store the exact squared distance between two points of specified dimension. More...
static index_t	dot_at_capacity (coord_index_t dim)
	Computes the required capacity of an expansion to store the exact dot product between two vectors. More...
static index_t	length2_capacity (const expansion &x, const expansion &y, const expansion &z)
	Computes the required capacity to store the length of a 3d vector. More...
static void	initialize ()
	Initializes the expansion class. More...
static void	show_all_stats ()
	Show global statistics.

Protected Member Functions
expansion &	assign_sub_product (const double *a, index_t a_length, const expansion &b)
	Assigns a sub-product to this expansion. More...
	expansion (const expansion &rhs)=delete
	Expansions cannot be copied.
expansion &	operator= (const expansion &rhs)=delete
	Expansions cannot be copied.

Static Protected Member Functions
static index_t	sub_product_capacity (index_t a_length, index_t b_length)
	Computes the required capacity of an expansion to store an exact sub-product. More...

Friends
class	expansion_nt

Related Functions
(Note that these are not member functions.)
void	two_sum (double a, double b, double &x, double &y)
	Sums two doubles into a length 2 expansion. More...
void	two_diff (double a, double b, double &x, double &y)
	Subtracts two doubles into a length 2 expansion. More...
void	split (double a, double &ahi, double &alo)
	Splits a number into two components, ready for computing a product. More...
void	two_product (double a, double b, double &x, double &y)
	Multiplies two doubles into a length 2 expansion. More...
void	square (double a, double &x, double &y)
	Squares a number into a length 2 expansion. More...
#define	new_expansion_on_stack(capa)    (new (alloca(expansion::bytes_on_stack(capa)))expansion(capa))
	Allocates an expansion on the stack. More...
#define	expansion_create(a)    new_expansion_on_stack(1)->assign(a)
	Creates an expansion from a double. More...
#define	expansion_abs(e)    new_expansion_on_stack(e.length())->assign_abs(e)
	Creates an expansion from the absolute value of another expansion. More...
#define	expansion_sum(a, b)
	Computes an expansion that represents the exact sum of its arguments. More...
#define	expansion_sum3(a, b, c)
	Computes an expansion that represents the exact sum of its arguments. More...
#define	expansion_sum4(a, b, c, d)
	Computes an expansion that represents the exact sum of its arguments. More...
#define	expansion_diff(a, b)
	Computes an expansion that represents the exact difference of its arguments. More...
#define	expansion_product(a, b)
	Computes an expansion that represents the exact product of its arguments. More...
#define	expansion_product3(a, b, c)
	Computes an expansion that represents the exact product of its arguments. More...
#define	expansion_square(a)
	Computes an expansion that represents the exact square of its argument. More...
#define	expansion_det2x2(a11, a12, a21, a22)
	Computes an expansion that represents the exact 2x2 determinant of its arguments. More...
#define	expansion_det3x3(a11, a12, a13, a21, a22, a23, a31, a32, a33)
	Computes an expansion that represents the exact 3x3 determinant of its arguments. More...
#define	expansion_det_111_2x3(a21, a22, a23, a31, a32, a33)
	Computes an expansion that represents the exact 3x3 determinant of its arguments where the first row is 1 1 1. More...
#define	expansion_sq_dist(a, b, dim)
	Computes an expansion that represents the exact squared distance between its argument. More...
#define	expansion_dot_at(a, b, c, dim)
	Computes an expansion that represents the exact dot product dot(a-c,b-c) More...
#define	expansion_length2(x, y, z)
	Computes an expansion that represents the exact squared length of a 3d vector. More...

Detailed Description

Represents numbers in arbitrary precision with a low-level API.

The three basic operations sum, difference and product are implemented, as well as some geometric functions (squared distance and dot product). The sign of an expansion can be exactly computed. expansion is useful to implement exact geometric predicates. Some of Jonathan Shewchuk's expansion manipulation functions are used. A higher-level (but less efficient) interface is available through the expansion_nt class (expansion number type, that overloads operators).

Definition at line 197 of file multi_precision.h.

Constructor & Destructor Documentation

expansion()

GEO::expansion::expansion ( index_t  capa )

inline

Client code should not use this constructor.

This constructor should not be used by client code, use new_expansion_on_stack() and new_expansion_on_heap() instead. This constructor initializes this expansion's length and capacity. Note that it should be created with enough space, using placement syntax of operator new.

Parameters

[in]

capa

the capacity

Definition at line 323 of file multi_precision.h.

Member Function Documentation

assign() [1/2]

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

inline

Copies an expansion to this expansion.

Parameters

[in]

rhs

the expansion to be copied

Returns

the new value of this expansion (rhs)

Definition at line 379 of file multi_precision.h.

assign() [2/2]

expansion& GEO::expansion::assign ( double  a )

inline

Assigns a number to this expansion.

Parameters

[in]

a

the number

Returns

the new value of this expansion (a)

Definition at line 368 of file multi_precision.h.

assign_abs()

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

inline

Copies the absolute value of an expansion to this expansion.

Parameters

[in]

rhs

the expansion to be copied

Returns

the new value of this expansion that is, abs(rhs)

Definition at line 393 of file multi_precision.h.

assign_det2x2()

expansion& GEO::expansion::assign_det2x2	(	const expansion &	a11,
		const expansion &	a12,
		const expansion &	a21,
		const expansion &	a22
	)

Assigns a 2x2 determinant to this expansion (should not be used by client code).

Do not use directly, use expansion_det2x2() macro instead.

Parameters

[in]

a11,a12,a21,a22

coefficients of the determinant

Returns

the new value of this expansion, with the exact determinant a11 * a22 - a21 * a12

Precondition

capacity() >= det_2x2_capacity(a11,a12,,a21,a22)

assign_det3x3()

expansion& GEO::expansion::assign_det3x3	(	const expansion &	a11,
		const expansion &	a12,
		const expansion &	a13,
		const expansion &	a21,
		const expansion &	a22,
		const expansion &	a23,
		const expansion &	a31,
		const expansion &	a32,
		const expansion &	a33
	)

Assigns a 3x3 determinant to this expansion (should not be used by client code).

Do not use directly, use expansion_det3x3() macro instead.

Parameters

[in]

a11,a12,a13,a21,a22,a23,a31,a32,a33

coefficients of the determinant

Returns

the new value of this expansion, with the exact 3x3 determinant

Precondition

capacity() >= det_3x3_capacity(a11,a12,a13,a21,a22,a23,a31,a32,a33)

assign_det_111_2x3()

expansion& GEO::expansion::assign_det_111_2x3	(	const expansion &	a21,
		const expansion &	a22,
		const expansion &	a23,
		const expansion &	a31,
		const expansion &	a32,
		const expansion &	a33
	)

Assigns a 3x3 determinant to this expansion where the first row is 1 1 1(should not be used by client code).

Do not use directly, use expansion_det_111_3x3() macro instead.

Parameters

[in]

a21,a22,a23,a31,a32,a33

coefficients of the determinant

Returns

the new value of this expansion, with the exact 3x3 determinant

Precondition

capacity() >= det__111_2x3capacity(a21,a22,a23,a31,a32,a33)

assign_diff() [1/3]

expansion& GEO::expansion::assign_diff	(	const expansion &	a,
		const expansion &	b
	)

Assigns the difference between two expansions to this expansion (should not be used by client code).

Do not use directly, use expansion_diff() macro instead.

Parameters

[in]	a	first expansion
[in]	b	second expansion

Returns

the new value of this expansion (a - b)

Precondition

capacity() >= diff_capacity(a,b)

assign_diff() [2/3]

expansion& GEO::expansion::assign_diff	(	const expansion &	a,
		double	b
	)

Assigns the difference between an expansion and a double to this expansion (should not be used by client code).

Do not use directly, use expansion_diff() macro instead.

Parameters

[in]	a	the expansion
[in]	b	the double

Returns

the new value of this expansion (a - b)

Precondition

capacity() >= diff_capacity(a,b)

assign_diff() [3/3]

expansion& GEO::expansion::assign_diff ( double  a, double  b  )

inline

Assigns the difference of two doubles to this expansion (should not be used by client code).

Do not use directly, use expansion_diff() macro instead.

Parameters

[in]	a	first number
[in]	b	second number

Returns

the new value of this expansion (a - b)

Precondition

capacity() >= diff_capacity(a,b)

Definition at line 459 of file multi_precision.h.

assign_dot_at()

expansion& GEO::expansion::assign_dot_at	(	const double *	p1,
		const double *	p2,
		const double *	p0,
		coord_index_t	dim
	)

Assigns the dot product of two vectors to this expansion (should not be used by client code).

Do not use directly, use expansion_dot_at() macro instead.

Parameters

[in]	p1	pointer to the coordinates of a point
[in]	p2	pointer to the coordinates of a point
[in]	p0	pointer to the coordinates of a point
[in]	dim	dimension of the points

Returns

the new value of this expansion, with the dot product (p1-p0).(p2-p0)

assign_length2()

expansion& GEO::expansion::assign_length2	(	const expansion &	x,
		const expansion &	y,
		const expansion &	z
	)

Assigns the length of a vector to this expansion (should not be used by client code). Do not call this function directly, use expansion_length2() macro instead.

Parameters

[in]

x,y,z

coordinates of the vector

Returns

the new value of this expansion, with the squared length of [x,y,z]

assign_product() [1/4]

expansion& GEO::expansion::assign_product	(	const expansion &	a,
		const expansion &	b
	)

Assigns the product of two expansions to this expansion (should not be used by client code).

Do not use directly, use expansion_product() macro instead.

Parameters

[in]	a	first expansion
[in]	b	second expansion

Returns

the new value of this expansion (a * b)

Precondition

capacity() >= product_capacity(a,b)

assign_product() [2/4]

expansion& GEO::expansion::assign_product	(	const expansion &	a,
		const expansion &	b,
		const expansion &	c
	)

Assigns the product of three expansions to this expansion (should not be used by client code).

Do not use directly, use expansion_product3() macro instead.

Parameters

[in]	a	first expansion
[in]	b	second expansion
[in]	c	third expansion

Returns

the new value of this expansion (a * b * c)

Precondition

capacity() >= product_capacity(a,b,c)

assign_product() [3/4]

expansion& GEO::expansion::assign_product	(	const expansion &	a,
		double	b
	)

Assigns the product between an expansion and a double to this expansion (should not be used by client code).

Do not use directly, use expansion_product() macro instead.

Parameters

[in]	a	the expansion
[in]	b	the double

Returns

the new value of this expansion (a * b)

Precondition

capacity() >= product_capacity(a,b)

assign_product() [4/4]

expansion& GEO::expansion::assign_product ( double  a, double  b  )

inline

Assigns the product of two doubles to this expansion (should not be used by client code).

Do not use directly, use expansion_product() macro instead.

Parameters

[in]	a	first number
[in]	b	second number

Returns

the new value of this expansion (a * b)

Precondition

capacity() >= product_capacity(a,b)

Definition at line 491 of file multi_precision.h.

assign_sq_dist()

expansion& GEO::expansion::assign_sq_dist	(	const double *	p1,
		const double *	p2,
		coord_index_t	dim
	)

Assigns the squared distance between two points to this expansion (should not be used by client code).

Do not use directly, use expansion_sq_dist() macro instead.

Parameters

[in]	p1	pointer to the coordinates of the first point
[in]	p2	pointer to the coordinates of the second point
[in]	dim	dimension of the points

Returns

the new value of this expansion, with the squared distance between p1 and p2

Precondition

capacity() >= sq_dist_capacity(dim)

assign_square() [1/2]

expansion& GEO::expansion::assign_square

(

const expansion &

a

)

Assigns the product of an expansions to this expansion (should not be used by client code).

Do not use directly, use expansion_square() macro instead.

Parameters

[in]

a

the expansion to be squared

Returns

the new value of this expansion (a * a )

Precondition

capacity() >= square_capacity(a)

assign_square() [2/2]

expansion& GEO::expansion::assign_square ( double  a )

inline

Assigns the square of a double to this expansion (should not be used by client code).

Do not use directly, use expansion_square() macro instead.

Parameters

[in]

a

the number to be squared

Returns

the new value of this expansion (a * a)

Precondition

capacity() >= square_capacity(a)

Definition at line 520 of file multi_precision.h.

assign_sub_product()

expansion& GEO::expansion::assign_sub_product ( const double *  a, index_t  a_length, const expansion &  b  )

protected

Assigns a sub-product to this expansion.

Used by assign_product() when operating in balanced distillation mode. Recursively assembles sub-sums.

Parameters

[in]	a	a pointer to the first component of the first term
[in]	a_length	number of components in first term
[in]	b	second term

Returns

the new value of this expansion, with [a1...a_length]*b.

assign_sum() [1/5]

expansion& GEO::expansion::assign_sum	(	const expansion &	a,
		const expansion &	b
	)

Assigns the sum of two expansions to this expansion (should not be used by client code).

Do not use directly, use expansion_sum() macro instead.

Parameters

[in]	a	first expansion
[in]	b	second expansion

Returns

the new value of this expansion (a + b)

Precondition

capacity() >= sum_capacity(a,b)

assign_sum() [2/5]

expansion& GEO::expansion::assign_sum	(	const expansion &	a,
		const expansion &	b,
		const expansion &	c
	)

Assigns the sum of three expansions to this expansion (should not be used by client code).

Do not use directly, use expansion_sum3() macro instead.

Parameters

[in]	a	first expansion
[in]	b	second expansion
[in]	c	third expansion

Returns

the new value of this expansion (a + b + c)

Precondition

capacity() >= sum_capacity(a,b,c)

assign_sum() [3/5]

expansion& GEO::expansion::assign_sum	(	const expansion &	a,
		const expansion &	b,
		const expansion &	c,
		const expansion &	d
	)

Assigns the sum of four expansions to this expansion (should not be used by client code).

Do not use directly, use expansion_sum4() macro instead.

Parameters

[in]	a	first expansion
[in]	b	second expansion
[in]	c	third expansion
[in]	d	fourth expansion

Returns

the new value of this expansion (a + b + c + d)

Precondition

capacity() >= sum_capacity(a,b,c,d)

assign_sum() [4/5]

expansion& GEO::expansion::assign_sum	(	const expansion &	a,
		double	b
	)

Assigns the sum of an expansion and a double to this expansion (should not be used by client code).

Do not use directly, use expansion_sum() macro instead.

Parameters

[in]	a	the expansion
[in]	b	the double

Returns

the new value of this expansion (a + b)

Precondition

capacity() >= sum_capacity(a,b)

assign_sum() [5/5]

expansion& GEO::expansion::assign_sum ( double  a, double  b  )

inline

Assigns the sum of two doubles to this expansion (should not be used by client code).

Do not use directly, use expansion_sum() macro instead.

Parameters

[in]	a	first number to sum
[in]	b	second number to sum

Returns

the new value of this expansion (a + b)

Precondition

capacity() >= sum_capacity(a,b)

Definition at line 427 of file multi_precision.h.

bytes()

static size_t GEO::expansion::bytes ( index_t  capa )

inlinestatic

Computes the amount of memory required to store an expansion.

Parameters

[in]

capa

the required capacity

Returns

the total number of bytes required to store an expansion of capacity capa.

Definition at line 279 of file multi_precision.h.

bytes_on_stack()

static size_t GEO::expansion::bytes_on_stack ( index_t  capa )

inlinestatic

Computes the amount of memory required to store an expansion on the stack.

Behaves like bytes() but in debug mode checks that this will fit on the stack.

Parameters

[in]

capa

the required capacity

Returns

the total number of bytes required to store an expansion of capacity capa.

Definition at line 299 of file multi_precision.h.

capacity()

index_t GEO::expansion::capacity ( ) const

inline

Gets the capacity of this expansion.

Returns

the maximum number of components that can be stored in this expansion

Definition at line 212 of file multi_precision.h.

compare() [1/2]

Sign GEO::expansion::compare

(

const expansion &

rhs

)

const

Compares two expansions.

Returns

the sign of this expansion minus rhs.

compare() [2/2]

Sign GEO::expansion::compare

(

double

rhs

)

const

Compares two expansions.

Returns

the sign of this expansion minus rhs.

data() [1/2]

double* GEO::expansion::data ( )

inline

Low level access to the array of components.

Returns

a pointer to the array that stores the components

Definition at line 259 of file multi_precision.h.

data() [2/2]

const double* GEO::expansion::data ( ) const

inline

Low level access to the array of components.

Returns

a const pointer to the array that stores the components

Definition at line 268 of file multi_precision.h.

delete_expansion_on_heap()

static void GEO::expansion::delete_expansion_on_heap ( expansion *  e )

static

Deallocates an expansion on the heap.

Parameters

[in]

e

the expansion

Precondition

e should have been previously allocated by new_expansion_on_heap()

det2x2_capacity()

static index_t GEO::expansion::det2x2_capacity ( const expansion &  a11, const expansion &  a12, const expansion &  a21, const expansion &  a22  )

inlinestatic

Computes the required capacity of an expansion to store an exact 2x2 determinant.

Parameters

[in]

a11,a12,a21,a22

coefficients of the determinant

Returns

the required capacity of an expansion to store the exact determinant a11 * a22 - a21 * a12

Definition at line 815 of file multi_precision.h.

det3x3_capacity()

static index_t GEO::expansion::det3x3_capacity ( const expansion &  a11, const expansion &  a12, const expansion &  a13, const expansion &  a21, const expansion &  a22, const expansion &  a23, const expansion &  a31, const expansion &  a32, const expansion &  a33  )

inlinestatic

Computes the required capacity of an expansion to store an exact 3x3 determinant.

Parameters

[in]

a11,a12,a13,a21,a22,a23,a31,a32,a33

coefficients of the determinant

Returns

the required capacity of an expansion to store the exact value of the determinant

Definition at line 847 of file multi_precision.h.

det_111_2x3_capacity()

static index_t GEO::expansion::det_111_2x3_capacity ( const expansion &  a21, const expansion &  a22, const expansion &  a23, const expansion &  a31, const expansion &  a32, const expansion &  a33  )

inlinestatic

Computes the required capacity of an expansion to store an exact 3x3 determinant where the first row is 1 1 1.

Parameters

[in]

a21,a22,a23,a31,a32,a33

coefficients of the determinant

Returns

the required capacity of an expansion to store the exact value of the determinant

Definition at line 890 of file multi_precision.h.

diff_capacity() [1/3]

static index_t GEO::expansion::diff_capacity ( const expansion &  a, const expansion &  b  )

inlinestatic

Computes the required capacity of an expansion to store the exact difference of two expansions.

Parameters

[in]	a	first expansion
[in]	b	second expansion

Returns

the required capacity of an expansion to store the exact difference between a and b

Definition at line 709 of file multi_precision.h.

diff_capacity() [2/3]

static index_t GEO::expansion::diff_capacity ( const expansion &  a, double  b  )

inlinestatic

Computes the required capacity of an expansion to store the exact difference between an expansion and a double.

Parameters

[in]	a	first number as an expansion
[in]	b	second number as a double

Returns

the required capacity of an expansion to store the exact difference of a and b

Note

The result does not depend on the value of the double argument b.

Definition at line 565 of file multi_precision.h.

diff_capacity() [3/3]

static index_t GEO::expansion::diff_capacity ( double  a, double  b  )

inlinestatic

Computes the required capacity of an expansion to store the exact difference of two doubles.

Parameters

[in]	a	first number
[in]	b	second number

Returns

the required capacity of an expansion to store the exact difference of two doubles

Note

The result does not depend on the values of the two numbers.

Definition at line 443 of file multi_precision.h.

dot_at_capacity()

static index_t GEO::expansion::dot_at_capacity ( coord_index_t  dim )

inlinestatic

Computes the required capacity of an expansion to store the exact dot product between two vectors.

Parameters

[in]

dim

dimension of the vectors

Returns

the required capacity of an expansion to store the dot product between two dim%-dimensional vectors specified by differences of doubles.

Definition at line 954 of file multi_precision.h.

equals() [1/2]

bool GEO::expansion::equals ( const expansion &  rhs ) const

inline

Compares two expansions.

Return values

true	if the two expansions represent the same number
false	otherwise

Definition at line 1099 of file multi_precision.h.

equals() [2/2]

bool GEO::expansion::equals ( double  rhs ) const

inline

Compares an expansion and a double.

Return values

true	if the expansion and rhs represent the same number
false	otherwise

Definition at line 1109 of file multi_precision.h.

estimate()

double GEO::expansion::estimate ( ) const

inline

Computes an approximation of the stored value in this expansion.

Returns

an approximation of the stored value.

Definition at line 1042 of file multi_precision.h.

initialize()

static void GEO::expansion::initialize ( )

static

Initializes the expansion class.

This function needs to be called once in the program, before using any expansion object and operation (it computes some internally-used constants).

is_same_as() [1/2]

bool GEO::expansion::is_same_as

(

const expansion &

rhs

)

const

Compares two expansions bit-by-bit.

This function may return false even if the expansion and rhs represent the same number

Return values

true	if the two expansions are the same
false	otherwise

is_same_as() [2/2]

bool GEO::expansion::is_same_as

(

double

rhs

)

const

Compares an expansion and a double bit-by-bit.

This function may return false even if the expansion and rhs represent the same number

Return values

true	if the expansion has a single component with value rhs
false	otherwise

length()

index_t GEO::expansion::length ( ) const

inline

Gets the length of this expansion.

Returns

the number of components of this expansion

Definition at line 203 of file multi_precision.h.

length2_capacity()

static index_t GEO::expansion::length2_capacity ( const expansion &  x, const expansion &  y, const expansion &  z  )

inlinestatic

Computes the required capacity to store the length of a 3d vector.

Parameters

[in]

x,y,z

coordinates of the vector

Returns

the capacity required to store the squared norm of [x,y,z]

Definition at line 983 of file multi_precision.h.

negate()

expansion& GEO::expansion::negate ( )

inline

Changes the sign of an expansion.

Returns

the new value of this expansion

Definition at line 1015 of file multi_precision.h.

new_expansion_on_heap()

static expansion* GEO::expansion::new_expansion_on_heap ( index_t  capa )

static

Allocates an expansion on the heap.

Allocates also some space for the reference counter.

Parameters

[in]

capa

capacity (i.e. maximum length) of the expansion.

Returns

a pointer to the newly allocated expansion

operator[]() [1/2]

double& GEO::expansion::operator[] ( index_t  i )

inline

Low level access to a component.

Returns

a reference to the ith component of this expansion

Definition at line 245 of file multi_precision.h.

operator[]() [2/2]

const double& GEO::expansion::operator[] ( index_t  i ) const

inline

Low level access to a component.

Returns

a const reference to the ith component of this expansion

Definition at line 231 of file multi_precision.h.

optimize()

void GEO::expansion::optimize

(

)

Optimizes the internal representation without changing the represented value.

this function can reduce the length of an expansion

product_capacity() [1/4]

static index_t GEO::expansion::product_capacity ( const expansion &  a, const expansion &  b  )

inlinestatic

Computes the required capacity of an expansion to store the exact product of two expansions.

Parameters

[in]	a	first expansion
[in]	b	second expansion

Returns

the required capacity of an expansion to store the exact product of a and b

Definition at line 733 of file multi_precision.h.

product_capacity() [2/4]

static index_t GEO::expansion::product_capacity ( const expansion &  a, const expansion &  b, const expansion &  c  )

inlinestatic

Computes the required capacity of an expansion to store the exact product of three expansions.

Parameters

[in]	a	first expansion
[in]	b	second expansion
[in]	c	third expansion

Returns

the required capacity of an expansion to store the exact product of a, b and c

Definition at line 760 of file multi_precision.h.

product_capacity() [3/4]

static index_t GEO::expansion::product_capacity ( const expansion &  a, double  b  )

inlinestatic

Computes the required capacity of an expansion to store the exact product between an expansion and a double.

Parameters

[in]	a	the expansion
[in]	b	the double

Returns

the required capacity of an expansion to store the exact product between a and b

Note

The result does not depend on the value of the double argument b.

Definition at line 592 of file multi_precision.h.

product_capacity() [4/4]

static index_t GEO::expansion::product_capacity ( double  a, double  b  )

inlinestatic

Computes the required capacity of an expansion to store the exact product of two doubles.

Parameters

[in]	a	first number
[in]	b	second number

Returns

the required capacity of an expansion to store the exact product of two doubles

Note

The result does not depend on the values of the two numbers.

Definition at line 475 of file multi_precision.h.

scale_fast()

expansion& GEO::expansion::scale_fast ( double  s )

inline

Multiplies this expansion by a power of two.

Parameters

[in]

s

the factor to be used to scale this expansion.

Returns

the new value of this expansion

Note

Does not check for overflows/underflows

Precondition

s should be a (possibly negative) power of two.

Definition at line 1029 of file multi_precision.h.

set_length()

void GEO::expansion::set_length ( index_t  new_length )

inline

Changes the length of an expansion.

Parameters

[in]

new_length

new length of the expansion

Precondition

new_length <= capacity()

Definition at line 221 of file multi_precision.h.

show()

std::ostream& GEO::expansion::show ( std::ostream &  out ) const

inline

Displays all the components of this expansion (for debugging purposes).

Parameters

[out]

out

an output stream used to print the components

Definition at line 1118 of file multi_precision.h.

sign()

Sign GEO::expansion::sign ( ) const

inline

Gets the sign of the expansion.

Returns

the sign of this expansion, computed exactly.

Definition at line 1054 of file multi_precision.h.

sq_dist_capacity()

static index_t GEO::expansion::sq_dist_capacity ( coord_index_t  dim )

inlinestatic

Computes the required capacity of an expansion to store the exact squared distance between two points of specified dimension.

Parameters

[in]

dim

dimension of the points

Returns

the required capacity of an expansion to store the exact squared distance between points of dimension dim

Definition at line 926 of file multi_precision.h.

square_capacity() [1/2]

static index_t GEO::expansion::square_capacity ( const expansion &  a )

inlinestatic

Computes the required capacity of an expansion to store the exact square of an expansion.

Parameters

[in]

a

the expansion to be squared

Returns

the required capacity of an expansion to store the exact square a * a

Definition at line 788 of file multi_precision.h.

square_capacity() [2/2]

static index_t GEO::expansion::square_capacity ( double  a )

inlinestatic

Computes the required capacity of an expansion to store the exact square of a double.

Parameters

[in]

a

the number to be squared

Returns

the required capacity of an expansion to store the exact square of a double.

Note

The result does not depend on the value of the number a.

Definition at line 506 of file multi_precision.h.

sub_product_capacity()

static index_t GEO::expansion::sub_product_capacity ( index_t  a_length, index_t  b_length  )

inlinestaticprotected

Computes the required capacity of an expansion to store an exact sub-product.

Parameters

[in]	a_length	number of components in first sub-expansion
[in]	b_length	number of components in second sub-expansion

Returns

the required capacity of an expansion to store the exact product of two expansions of lengths a_length and b_length

Definition at line 1159 of file multi_precision.h.

sum_capacity() [1/5]

static index_t GEO::expansion::sum_capacity ( const expansion &  a, const expansion &  b  )

inlinestatic

Computes the required capacity of an expansion to store the exact sum of two expansions.

Parameters

[in]	a	first expansion
[in]	b	second expansion

Returns

the required capacity of an expansion to store the exact sum of a and b

Definition at line 621 of file multi_precision.h.

sum_capacity() [2/5]

static index_t GEO::expansion::sum_capacity ( const expansion &  a, const expansion &  b, const expansion &  c  )

inlinestatic

Computes the required capacity of an expansion to store the exact sum of three expansions.

Parameters

[in]	a	first expansion
[in]	b	second expansion
[in]	c	third expansion

Returns

the required capacity of an expansion to store the exact sum of a, b and c

Definition at line 646 of file multi_precision.h.

sum_capacity() [3/5]

static index_t GEO::expansion::sum_capacity ( const expansion &  a, const expansion &  b, const expansion &  c, const expansion &  d  )

inlinestatic

Computes the required capacity of an expansion to store the exact sum of four expansions.

Parameters

[in]	a	first expansion
[in]	b	second expansion
[in]	c	third expansion
[in]	d	fourth expansion

Returns

the required capacity of an expansion to store the exact sum of a, b, c and d

Definition at line 677 of file multi_precision.h.

sum_capacity() [4/5]

static index_t GEO::expansion::sum_capacity ( const expansion &  a, double  b  )

inlinestatic

Computes the required capacity of an expansion to store the exact sum of an expansion and a double.

Parameters

[in]	a	first number as an expansion
[in]	b	second number as a double

Returns

the required capacity of an expansion to store the exact sum of a and b

Note

The result does not depend on the value of the double argument b.

Definition at line 538 of file multi_precision.h.

sum_capacity() [5/5]

static index_t GEO::expansion::sum_capacity ( double  a, double  b  )

inlinestatic

Computes the required capacity to store the sum of two doubles.

Parameters

[in]	a	first number
[in]	b	second number

Returns

the required capacity of an expansion to store the exact sum of two doubles

Note

The result does not depend on the values of the two numbers.

Definition at line 411 of file multi_precision.h.

to_string()

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

inline

Gets a string representation of this expansion.

Returns

a string with the length and components

Definition at line 1131 of file multi_precision.h.

Friends And Related Function Documentation

expansion_abs

#define expansion_abs (   e )     new_expansion_on_stack(e.length())->assign_abs(e)

related

Creates an expansion from the absolute value of another expansion.

Parameters

[in]

e

the expansion

Returns

a reference to an expansion, allocated on the stack.

const expansion& e1 = expansion_abs(e);

Warning

Do not return or use the returned reference outside the calling function.

Definition at line 1238 of file multi_precision.h.

expansion_create

#define expansion_create (   a )     new_expansion_on_stack(1)->assign(a)

related

Creates an expansion from a double.

Parameters

[in]

a

the double

Returns

a reference to an expansion, allocated on the stack.

const expansion& e1 = expansion_create(a);

Warning

Do not return or use the returned reference outside the calling function.

Definition at line 1221 of file multi_precision.h.

expansion_det2x2

#define expansion_det2x2 (   a11,   a12,   a21,   a22  )

related

Value:

    new_expansion_on_stack(                        \
        expansion::det2x2_capacity(a11, a12, a21, a22) \
    )->assign_det2x2(a11, a12, a21, a22)

Computes an expansion that represents the exact 2x2 determinant of its arguments.

Returns

a reference to an expansion, allocated on the stack.

const expansion& a11 = ...;
const expansion& a12 = ...;
const expansion& a21 = ...;
const expansion& a22 = ...;
expansion& d12 = expansion_set2x2(a11,a12,a21,a22);

Definition at line 1411 of file multi_precision.h.

expansion_det3x3

#define expansion_det3x3 (   a11,   a12,   a13,   a21,   a22,   a23,   a31,   a32,   a33  )

related

Value:

    new_expansion_on_stack(                                             \
        expansion::det3x3_capacity(a11,a12,a13,a21,a22,a23,a31,a32,a33) \
    )->assign_det3x3(a11, a12, a13, a21, a22, a23, a31, a32, a33)

Computes an expansion that represents the exact 3x3 determinant of its arguments.

Returns

a reference to an expansion, allocated on the stack.

const expansion& a11 = ...;
...
const expansion& a33 = ...;
expansion& d = expansion_det3x3(
    a11,a12,a13,a21,a22,a23,a31,a32,a33
);

Warning

Do not return or use the returned reference outside the calling function.

Definition at line 1432 of file multi_precision.h.

expansion_det_111_2x3

#define expansion_det_111_2x3 (   a21,   a22,   a23,   a31,   a32,   a33  )

related

Value:

    new_expansion_on_stack(                                      \
        expansion::det_111_2x3_capacity(a21, a22, a23, a31, a32, a33) \
    )->assign_det_111_2x3(a21, a22, a23, a31, a32, a33)

Computes an expansion that represents the exact 3x3 determinant of its arguments where the first row is 1 1 1.

Returns

a reference to an expansion, allocated on the stack.

const expansion& a21 = ...;
...
const expansion& a33 = ...;
expansion& d = expansion_det_111_2x3(
    a21,a22,a23,a31,a32,a33
);

Warning

Do not return or use the returned reference outside the calling function.

Definition at line 1454 of file multi_precision.h.

expansion_diff

#define expansion_diff (   a,   b  )

related

Value:

    new_expansion_on_stack(             \
        expansion::diff_capacity(a, b)   \
    )->assign_diff(a, b)

Computes an expansion that represents the exact difference of its arguments.

Parameters

[in]	a	a double or an expansion
[in]	b	a double or an expansion

Returns

a reference to an expansion, allocated on the stack.

expansion& e1 = ...;
expansion& e2 = ...;
expansion& e3 = expansion_diff(e1,e2);
double x = ...;
expansion& e4 = expansion_diff(e1,x);

Warning

Do not return or use the returned reference outside the calling function.

Definition at line 1327 of file multi_precision.h.

expansion_dot_at

#define expansion_dot_at (   a,   b,   c,   dim  )

related

Value:

    new_expansion_on_stack(                   \
        expansion::dot_at_capacity(dim)       \
    )->assign_dot_at(a, b, c, dim)

Computes an expansion that represents the exact dot product dot(a-c,b-c)

Parameters

[in]	a	first point (specified as a const double*)
[in]	b	second point (specified as a const double*)
[in]	c	third point (specified as a const double*)
[in]	dim	dimension of the points

Returns

a reference to an expansion, allocated on the stack.

const double* p1 = ...;
const double* p2 = ...;
const double* p0 = ...;
expansion& dot12 = expansion_dot_at(p1,p2,p0,3);

Warning

Do not return or use the returned reference outside the calling function.

Definition at line 1500 of file multi_precision.h.

expansion_length2

#define expansion_length2 (   x,   y,   z  )

related

Value:

    new_expansion_on_stack(                   \
       expansion::length2_capacity(x,y,z)     \
    )->assign_length2(x,y,z)

Computes an expansion that represents the exact squared length of a 3d vector.

Parameters

[in]

x,y,z

coordinates of the vector (specified as expansion)

Returns

a reference to an expansion, allocated on the stack.

const expansion& x = ...;
const expansion& y = ...;
const expansion& z = ...;
expansion& l = expansion_length2(x,y,z);

Warning

Do not return or use the returned reference outside the calling function.

Definition at line 1521 of file multi_precision.h.

expansion_product

#define expansion_product (   a,   b  )

related

Value:

    new_expansion_on_stack(               \
        expansion::product_capacity(a, b)  \
    )->assign_product(a, b)

Computes an expansion that represents the exact product of its arguments.

Parameters

[in]	a	a double or an expansion
[in]	b	a double or an expansion

Returns

a reference to an expansion, allocated on the stack.

expansion& e1 = ...;
expansion& e2 = ...;
expansion& e3 = expansion_product(e1,e2);
double x = ...;
expansion& e4 = expansion_product(e1,x);

Warning

Do not return or use the returned reference outside the calling function.

Definition at line 1349 of file multi_precision.h.

expansion_product3

#define expansion_product3 (   a,   b,   c  )

related

Value:

    new_expansion_on_stack(                 \
        expansion::product_capacity(a, b, c)  \
    )->assign_product(a, b, c)

Computes an expansion that represents the exact product of its arguments.

Parameters

[in]	a	an expansion
[in]	b	an expansion
[in]	c	an expansion

Returns

a reference to an expansion, allocated on the stack.

expansion& e1 = ...;
expansion& e2 = ...;
expansion& e3 = ...;
expansion& e4 = expansion_product3(e1,e2,e3);

Warning

Do not return or use the returned reference outside the calling function.

Definition at line 1371 of file multi_precision.h.

expansion_sq_dist

#define expansion_sq_dist (   a,   b,   dim  )

related

Value:

    new_expansion_on_stack(                  \
        expansion::sq_dist_capacity(dim)     \
    )->assign_sq_dist(a, b, dim)

Computes an expansion that represents the exact squared distance between its argument.

Parameters

[in]	a	first point (specified as a const double*)
[in]	b	second point (specified as a const double*)
[in]	dim	dimension of the points

Returns

a reference to an expansion, allocated on the stack.

const double* p1 = ...;
const double* p2 = ...;
expansion& d12 = expansion_sq_dist(p1,p2,3);

Warning

Do not return or use the returned reference outside the calling function.

Definition at line 1477 of file multi_precision.h.

expansion_square

#define expansion_square (   a )

related

Value:

    new_expansion_on_stack(             \
        expansion::square_capacity(a)   \
    )->assign_square(a)

Computes an expansion that represents the exact square of its argument.

Parameters

[in]

a

a double or an expansion

Returns

a reference to an expansion, allocated on the stack.

expansion& e1 = ...;
expansion& e2 = expansion_square(e1);
double x = ...;
expansion& e3 = expansion_square(x);

Warning

Do not return or use the returned reference outside the calling function.

Definition at line 1391 of file multi_precision.h.

expansion_sum

#define expansion_sum (   a,   b  )

related

Value:

    new_expansion_on_stack(           \
        expansion::sum_capacity(a, b)   \
    )->assign_sum(a, b)

Computes an expansion that represents the exact sum of its arguments.

Parameters

[in]	a	a double or an expansion
[in]	b	a double or an expansion

Returns

a reference to an expansion, allocated on the stack.

expansion& e1 = ...;
expansion& e2 = ...;
expansion& e3 = expansion_sum(e1,e2);
double x = ...;
expansion& e4 = expansion_sum(e1,x);

Warning

Do not return or use the returned reference outside the calling function.

Definition at line 1258 of file multi_precision.h.

expansion_sum3

#define expansion_sum3 (   a,   b,   c  )

related

Value:

    new_expansion_on_stack(            \
        expansion::sum_capacity(a, b, c) \
    )->assign_sum(a, b, c)

Computes an expansion that represents the exact sum of its arguments.

Parameters

[in]	a	an expansion
[in]	b	an expansion
[in]	c	an expansion

Returns

a reference to an expansion, allocated on the stack.

expansion& e1 = ...;
expansion& e2 = ...;
expansion& e3 = ...;
expansion& e4 = expansion_sum3(e1,e2,e3);

Warning

Do not return or use the returned reference outside the calling function.

Definition at line 1280 of file multi_precision.h.

expansion_sum4

#define expansion_sum4 (   a,   b,   c,   d  )

related

Value:

    new_expansion_on_stack(              \
        expansion::sum_capacity(a, b, c, d) \
    )->assign_sum(a, b, c, d)

Computes an expansion that represents the exact sum of its arguments.

Parameters

[in]	a	an expansion
[in]	b	an expansion
[in]	c	an expansion
[in]	d	an expansion

Returns

a reference to an expansion, allocated on the stack.

expansion& e1 = ...;
expansion& e2 = ...;
expansion& e3 = ...;
expansion& e4 = ...;
expansion& e5 = expansion_sum4(e1,e2,e3,e4);

Warning

Do not return or use the returned reference outside the calling function.

Definition at line 1305 of file multi_precision.h.

new_expansion_on_stack

#define new_expansion_on_stack (   capa )     (new (alloca(expansion::bytes_on_stack(capa)))expansion(capa))

related

Allocates an expansion on the stack.

It can only be a macro (and not an inline function) since alloca() cannot be called from inline functions.

• capa required capacity of the expansion.

Definition at line 341 of file multi_precision.h.

split()

void split ( double  a, double &  ahi, double &  alo  )

related

Splits a number into two components, ready for computing a product.

By Jonathan Shewchuk.

Parameters

[in]	a	input number.
[out]	ahi	split number, high-magnitude part.
[out]	alo	split number, low-magnitude part.

Definition at line 113 of file multi_precision.h.

square()

void square ( double  a, double &  x, double &  y  )

related

Squares a number into a length 2 expansion.

By Jonathan Shewchuk.

Parameters

[in]	a	number to square.
[out]	x	high-magnitude component of the result.
[out]	y	low-magnitude component of the result.

Definition at line 161 of file multi_precision.h.

two_diff()

void two_diff ( double  a, double  b, double &  x, double &  y  )

related

Subtracts two doubles into a length 2 expansion.

By Jonathan Shewchuk.

Parameters

[in]	a	first number.
[in]	b	the number to subtract from a.
[out]	x	high-magnitude component of the result.
[out]	y	low-magnitude component of the result.

Definition at line 95 of file multi_precision.h.

two_product()

void two_product ( double  a, double  b, double &  x, double &  y  )

related

Multiplies two doubles into a length 2 expansion.

By Jonathan Shewchuk.

Parameters

[in]	a	first number to multiply.
[in]	b	second number to multiply.
[out]	x	high-magnitude component of the result.
[out]	y	low-magnitude component of the result.

Definition at line 129 of file multi_precision.h.

two_sum()

void two_sum ( double  a, double  b, double &  x, double &  y  )

related

Sums two doubles into a length 2 expansion.

By Jonathan Shewchuk.

Parameters

[in]	a	one of the numbers to sum.
[in]	b	the other numbers to sum.
[out]	x	high-magnitude component of the result.
[out]	y	low-magnitude component of the result.

Definition at line 77 of file multi_precision.h.

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

• geogram/numerics/multi_precision.h