numbers Namespace Reference

Classes
struct	NumberTraits
struct	NumberTraits< std::complex< number > >

Functions
bool	is_nan (const double x)
bool	is_finite (const double x)
bool	is_finite (const std::complex< double > &x)
bool	is_finite (const std::complex< float > &x)
bool	is_finite (const std::complex< long double > &x)
template<typename Number1 , typename Number2 >
bool	values_are_equal (const Number1 &value_1, const Number2 &value_2)
template<typename Number1 , typename Number2 >
bool	values_are_not_equal (const Number1 &value_1, const Number2 &value_2)
template<typename Number >
bool	value_is_zero (const Number &value)
template<typename Number1 , typename Number2 >
bool	value_is_less_than (const Number1 &value_1, const Number2 &value_2)
template<typename Number1 , typename Number2 >
bool	value_is_less_than_or_equal_to (const Number1 &value_1, const Number2 &value_2)
template<typename Number1 , typename Number2 >
bool	value_is_greater_than (const Number1 &value_1, const Number2 &value_2)
template<typename Number1 , typename Number2 >
bool	value_is_greater_than_or_equal_to (const Number1 &value_1, const Number2 &value_2)
template<class T >
T	signaling_nan ()

Variables
static const double	E = 2.7182818284590452354
static const double	LOG2E = 1.4426950408889634074
static const double	LOG10E = 0.43429448190325182765
static const double	LN2 = 0.69314718055994530942
static const double	LN10 = 2.30258509299404568402
static const double	PI = 3.14159265358979323846
static const double	PI_2 = 1.57079632679489661923
static const double	PI_4 = 0.78539816339744830962
static const double	SQRT2 = 1.41421356237309504880
static const double	SQRT1_2 = 0.70710678118654752440
static const unsigned int	invalid_unsigned_int
const types::global_dof_index	invalid_size_type
const types::global_dof_index	invalid_dof_index
const types::material_id	invalid_material_id
const types::boundary_id	invalid_boundary_id
const types::boundary_id	internal_face_boundary_id
const types::manifold_id	invalid_manifold_id
const types::manifold_id	flat_manifold_id
const types::subdomain_id	invalid_subdomain_id
const types::subdomain_id	artificial_subdomain_id

Detailed Description

Namespace for the declaration of universal constants. Since the availability in math.h is not always guaranteed, we put them here. Since this file is included by base/config.h, they are available to the whole library.

The constants defined here are a subset of the M_XXX constants sometimes declared in the system include file math.h, but without the prefix M_.

In addition to that, we declare invalid_unsigned_int to be the largest unsigned integer representable; this value is widely used in the library as a marker for an invalid index, an invalid size of an array, and similar purposes.

Function Documentation

bool numbers::is_nan ( const double  x )

inline

Check whether a value is not a number.

This function uses either std::isnan, isnan, or _isnan, whichever is available on the system and returns the result.

If none of the functions detecting NaN is available, this function returns false.

Deprecated:

This function has been deprecated in favor of the C++11 function std::isnan.

Definition at line 422 of file numbers.h.

bool numbers::is_finite ( const double  x )

inline

Return true if the given value is a finite floating point number, i.e. is neither plus or minus infinity nor NaN (not a number).

Note that the argument type of this function is double. In other words, if you give a very large number of type long double, this function may return false even if the number is finite with respect to type long double.

Definition at line 428 of file numbers.h.

bool numbers::is_finite ( const std::complex< double > &  x )

inline

Return true if real and imaginary parts of the given complex number are finite.

Definition at line 436 of file numbers.h.

bool numbers::is_finite ( const std::complex< float > &  x )

inline

Return true if real and imaginary parts of the given complex number are finite.

Definition at line 446 of file numbers.h.

bool numbers::is_finite ( const std::complex< long double > &  x )

inline

Return true if real and imaginary parts of the given complex number are finite.

Again may not work correctly if real or imaginary parts are very large numbers that are infinite in terms of double, but finite with respect to long double.

Definition at line 456 of file numbers.h.

template<typename Number1 , typename Number2 >

bool numbers::values_are_equal ( const Number1 &  value_1, const Number2 &  value_2  )

inline

Return whether two numbers are equal to one another.

For intricate data types (e.g. some automatically differentiable numbers), this function returns the result of the comparison of scalar values stored by the input arguments.

Note

This function expects that value_2 is castable to the type of value_1.

Definition at line 786 of file numbers.h.

template<typename Number1 , typename Number2 >

bool numbers::values_are_not_equal ( const Number1 &  value_1, const Number2 &  value_2  )

inline

Return whether two numbers are not equal to one another.

For intricate data types (e.g. some automatically differentiable numbers), this function returns the result of the comparison of scalar values stored by the input arguments.

Note

This function expects that value_2 is castable to the type of value_1.

Definition at line 794 of file numbers.h.

template<typename Number >

bool numbers::value_is_zero ( const Number &  value )

inline

Return whether or not a value is equal to zero.

For intricate data types (e.g. some automatically differentiable numbers), this function returns the result of the comparison of scalar values stored by the input arguments.

Definition at line 802 of file numbers.h.

template<typename Number1 , typename Number2 >

bool numbers::value_is_less_than ( const Number1 &  value_1, const Number2 &  value_2  )

inline

Return whether value_1 is less than that of value_2.

For intricate data types (e.g. some automatically differentiable numbers), this function returns the result of the comparison of scalar values stored by the input arguments.

Note

This function expects that value_2 is castable to the type of value_1.

Definition at line 810 of file numbers.h.

template<typename Number1 , typename Number2 >

bool numbers::value_is_less_than_or_equal_to ( const Number1 &  value_1, const Number2 &  value_2  )

inline

Return whether value_1 is less than or equal to that of value_2.

For intricate data types (e.g. some automatically differentiable numbers), this function returns the result of the comparison of scalar values stored by the input arguments.

Note

This function expects that value_2 is castable to the type of value_1.

Definition at line 818 of file numbers.h.

template<typename Number1 , typename Number2 >

bool numbers::value_is_greater_than	(	const Number1 &	value_1,
		const Number2 &	value_2
	)

Return whether value_1 is greater than that of value_2.

For intricate data types (e.g. some automatically differentiable numbers), this function returns the result of the comparison of scalar values stored by the input arguments.

Note

This function expects that value_2 is castable to the type of value_1.

Definition at line 827 of file numbers.h.

template<typename Number1 , typename Number2 >

bool numbers::value_is_greater_than_or_equal_to ( const Number1 &  value_1, const Number2 &  value_2  )

inline

Return whether value_1 is greater than or equal to that of value_2.

For intricate data types (e.g. some automatically differentiable numbers), this function returns the result of the comparison of scalar values stored by the input arguments.

Note

This function expects that value_2 is castable to the type of value_1.

Definition at line 835 of file numbers.h.

template<class T >

T numbers::signaling_nan

(

)

Provide an object of type T filled with a signaling NaN that will cause an exception when used in a computation. The content of these objects is a "signaling NaN" ("NaN" stands for "not a number", and "signaling" implies that at least on platforms where this is supported, any arithmetic operation using them terminates the program). The purpose of such objects is to use them as markers for uninitialized objects and arrays that are required to be filled in other places, and to trigger an error when this later initialization does not happen before the first use.

Template Parameters

T	The type of the returned invalid object. This type can either be a scalar, or of type Tensor, SymmetricTensor, or DerivativeForm. Other types may be supported if there is a corresponding specialization of the internal::SignalingNaN::NaNInitializer class for this type.

Note

Because the type T is not used as a function argument, the compiler cannot deduce it from the type of arguments. Consequently, you have to provide it explicitly. For example, the line

Tensor<1,dim> tensor = Utilities::signaling_nan<Tensor<1,dim> >();

initializes a tensor with invalid values.

Definition at line 229 of file signaling_nan.h.

Variable Documentation

const double numbers::E = 2.7182818284590452354

static

e

Definition at line 118 of file numbers.h.

const double numbers::LOG2E = 1.4426950408889634074

static

log_2 e

Definition at line 123 of file numbers.h.

const double numbers::LOG10E = 0.43429448190325182765

static

log_10 e

Definition at line 128 of file numbers.h.

const double numbers::LN2 = 0.69314718055994530942

static

log_e 2

Definition at line 133 of file numbers.h.

const double numbers::LN10 = 2.30258509299404568402

static

log_e 10

Definition at line 138 of file numbers.h.

const double numbers::PI = 3.14159265358979323846

static

pi

Definition at line 143 of file numbers.h.

const double numbers::PI_2 = 1.57079632679489661923

static

pi/2

Definition at line 148 of file numbers.h.

const double numbers::PI_4 = 0.78539816339744830962

static

pi/4

Definition at line 153 of file numbers.h.

const double numbers::SQRT2 = 1.41421356237309504880

static

sqrt(2)

Definition at line 158 of file numbers.h.

const double numbers::SQRT1_2 = 0.70710678118654752440

static

1/sqrt(2)

Definition at line 163 of file numbers.h.

const unsigned int numbers::invalid_unsigned_int

static

Initial value:

=
    static_cast<unsigned int>(-1)

Representation of the largest number that can be put into an unsigned integer. This value is widely used throughout the library as a marker for an invalid unsigned integer value, such as an invalid array index, an invalid array size, and the like.

Definition at line 173 of file types.h.

const types::global_dof_index numbers::invalid_size_type

Initial value:

=
    static_cast<types::global_dof_index>(-1)

Representation of the largest number that can be put into a size_type. This value is used throughout the library as a marker for an invalid size_type value, such as an invalid array index, an invalid array size, and the like. Invalid_size_type is equivalent to invalid_dof_index.

Definition at line 182 of file types.h.

const types::global_dof_index numbers::invalid_dof_index

Initial value:

=
    static_cast<types::global_dof_index>(-1)

An invalid value for indices of degrees of freedom.

Definition at line 188 of file types.h.

const types::material_id numbers::invalid_material_id

Initial value:

=
    static_cast<types::material_id>(-1)

Invalid material_id which we need in several places as a default value. We assume that all material_ids lie in the range [0, invalid_material_id).

Definition at line 196 of file types.h.

const types::boundary_id numbers::invalid_boundary_id

Initial value:

=
    static_cast<types::boundary_id>(-1)

Invalid boundary_id which we need in several places as a default value. We assume that all valid boundary_ids lie in the range [0, invalid_boundary_id).

See also

Glossary entry on boundary indicators

Definition at line 207 of file types.h.

const types::boundary_id numbers::internal_face_boundary_id

Initial value:

=
    static_cast<types::boundary_id>(-1)

A boundary indicator number that we reserve for internal faces. We assume that all valid boundary_ids lie in the range [0, internal_face_boundary_id).

This is an indicator that is used internally (by the library) to differentiate between faces that lie at the boundary of the domain and faces that lie in the interior of the domain. You should never try to assign this boundary indicator to anything in user code.

See also

Glossary entry on boundary indicators

Definition at line 223 of file types.h.

const types::manifold_id numbers::invalid_manifold_id

Initial value:

=
    static_cast<types::manifold_id>(-1)

Invalid manifold_id which we need in several places as a default value. We assume that all valid manifold_ids lie in the range [0, invalid_manifold_id).

See also

Glossary entry on manifold indicators

Definition at line 234 of file types.h.

const types::manifold_id numbers::flat_manifold_id

Initial value:

=
    static_cast<types::manifold_id>(-1)

A manifold_id we reserve for the default flat Cartesian manifold.

See also

Glossary entry on manifold indicators

Definition at line 243 of file types.h.

const types::subdomain_id numbers::invalid_subdomain_id

Initial value:

=
    static_cast<types::subdomain_id>(-1)

A special id for an invalid subdomain id. This value may not be used as a valid id but is used, for example, for default arguments to indicate a subdomain id that is not to be used.

See the glossary for more information.

Definition at line 255 of file types.h.

const types::subdomain_id numbers::artificial_subdomain_id

Initial value:

=
    static_cast<types::subdomain_id>(-2)

The subdomain id assigned to a cell whose true subdomain id we don't know, for example because it resides on a different processor on a mesh that is kept distributed on many processors. Such cells are called "artificial".

See the glossary entries on subdomain ids and artificial cells as well as the Parallel computing with multiple processors using distributed memory module for more information.

Definition at line 272 of file types.h.