dxx::math Namespace Reference

The main namespace of the dxx::math module. More...

Namespaces
namespace	vector_operators
	Operations on vectors. Read the description.
namespace	container_traits
	Advanced type traits for containers.
namespace	norms
	Built-in norms.
namespace	operators
	The namespace that collects all operators defined by dxx.math.* modules.

Classes
struct	Norm
	Defines a norm. Only norm field is required, all other fields can be assigned a nullptr. More...
struct	Sub
	Default difference is subtraction. More...

Concepts
concept	vector
	We can treat any input range as a vector.
concept	mut_vector
	A vector for which the elements can be written to.
concept	vector_like
	Vector for which the element type is convertible to a target vector's type.
concept	mut_vector_like
	Similar to vector_like, but also satisfies mut_vector.

Typedefs
template<typename T>
using	RealOf = detail::RealOf<T>::Type
	(Non-cv-qualified) Real type of the linalg type

Enumerations
enum class	Sign : int { Positive = 1 , Zero = 0 , Negative = -1 }
	Return type of sign. Use std::to_underlying to convert to int.

Functions
template<mut_vector Out, vector_like< Out > U, vector_like< Out > V>
constexpr void	add (U &&u, V &&v, Out &out)
	Element-wise vector addition. Result via output parameter.
template<container_traits::returnable Out, vector_like< Out > U, vector_like< Out > V>
constexpr Out	add (U &&u, V &&v)
	Element-wise vector addition. Result in return value of a user-provided type.
template<vector U, vector_like< U > V>
constexpr std::remove_cvref_t< U >	add (U &&u, V &&v)
	Element-wise vector addition. Result in return value of automatically selected type.
template<mut_vector Out, vector_like< Out > U, std::convertible_to< RealOf< Out > > Scalar>
constexpr void	add (U &&u, const Scalar &scalar, Out &out)
	Element-wise addition of vector elements with a scalar. Result via output parameter.
template<container_traits::returnable Out, vector_like< Out > U, std::convertible_to< RealOf< Out > > Scalar>
constexpr Out	add (U &&u, const Scalar &scalar)
	Element-wise addition of vector elements with a scalar. Result in return value of a user-provided type.
template<vector U, std::convertible_to< RealOf< U > > Scalar>
constexpr std::remove_cvref_t< U >	add (U &&u, const Scalar &scalar)
	Element-wise addition of vector elements with a scalar. Result in return value of automatically selected type.
template<mut_vector Out, std::convertible_to< RealOf< Out > > Scalar, vector_like< Out > U>
constexpr void	add (const Scalar &scalar, U &&u, Out &out)
	Element-wise addition of scalar with vector elements. Result via output parameter.
template<container_traits::returnable Out, std::convertible_to< RealOf< Out > > Scalar, vector_like< Out > U>
constexpr Out	add (const Scalar &scalar, U &&u)
	Element-wise addition of scalar with vector elements. Result in return value of a user-provided type.
template<vector U, std::convertible_to< RealOf< U > > Scalar>
constexpr std::remove_cvref_t< U >	add (const Scalar &scalar, U &&u)
	Element-wise addition of vector elements with a scalar. Result in return value of automatically selected type.
template<mut_vector Out, vector_like< Out > U, vector_like< Out > V>
constexpr void	sub (U &&u, V &&v, Out &out)
	Element-wise vector subtraction. Result via output parameter.
template<container_traits::returnable Out, vector_like< Out > U, vector_like< Out > V>
constexpr Out	sub (U &&u, V &&v)
	Element-wise vector subtraction. Result in return value of a user-provided type.
template<vector U, vector_like< U > V>
constexpr std::remove_cvref_t< U >	sub (U &&u, V &&v)
	Element-wise vector subtraction. Result in return value of automatically selected type.
template<mut_vector Out, vector_like< Out > U, std::convertible_to< RealOf< Out > > Scalar>
constexpr void	sub (U &&u, const Scalar &scalar, Out &out)
	Element-wise subtraction of vector elements with a scalar. Result via output parameter.
template<container_traits::returnable Out, vector_like< Out > U, std::convertible_to< RealOf< Out > > Scalar>
constexpr Out	sub (U &&u, const Scalar &scalar)
	Element-wise subtraction of vector elements with a scalar. Result in return value of a user-provided type.
template<vector U, std::convertible_to< RealOf< U > > Scalar>
constexpr std::remove_cvref_t< U >	sub (U &&u, const Scalar &scalar)
	Element-wise subtraction of vector elements with a scalar. Result in return value of automatically selected type.
template<mut_vector Out, std::convertible_to< RealOf< Out > > Scalar, vector_like< Out > U>
constexpr void	sub (const Scalar &scalar, U &&u, Out &out)
	Element-wise subtraction of scalar with vector elements. Result via output parameter.
template<container_traits::returnable Out, std::convertible_to< RealOf< Out > > Scalar, vector_like< Out > U>
constexpr Out	sub (const Scalar &scalar, U &&u)
	Element-wise subtraction of scalar with vector elements. Result in return value of a user-provided type.
template<vector U, std::convertible_to< RealOf< U > > Scalar>
constexpr std::remove_cvref_t< U >	sub (const Scalar &scalar, U &&u)
	Element-wise subtraction of vector elements with a scalar. Result in return value of automatically selected type.
template<mut_vector Out, vector_like< Out > U, vector_like< Out > V>
constexpr void	mul (U &&u, V &&v, Out &out)
	Element-wise vector multiplication. Result via output parameter.
template<container_traits::returnable Out, vector_like< Out > U, vector_like< Out > V>
constexpr Out	mul (U &&u, V &&v)
	Element-wise vector multiplication. Result in return value of a user-provided type.
template<vector U, vector_like< U > V>
constexpr std::remove_cvref_t< U >	mul (U &&u, V &&v)
	Element-wise vector multiplication. Result in return value of automatically selected type.
template<mut_vector Out, vector_like< Out > U, std::convertible_to< RealOf< Out > > Scalar>
constexpr void	mul (U &&u, const Scalar &scalar, Out &out)
	Element-wise multiplication of vector elements with a scalar. Result via output parameter.
template<container_traits::returnable Out, vector_like< Out > U, std::convertible_to< RealOf< Out > > Scalar>
constexpr Out	mul (U &&u, const Scalar &scalar)
	Element-wise multiplication of vector elements with a scalar. Result in return value of a user-provided type.
template<vector U, std::convertible_to< RealOf< U > > Scalar>
constexpr std::remove_cvref_t< U >	mul (U &&u, const Scalar &scalar)
	Element-wise multiplication of vector elements with a scalar. Result in return value of automatically selected type.
template<mut_vector Out, std::convertible_to< RealOf< Out > > Scalar, vector_like< Out > U>
constexpr void	mul (const Scalar &scalar, U &&u, Out &out)
	Element-wise multiplication of scalar with vector elements. Result via output parameter.
template<container_traits::returnable Out, std::convertible_to< RealOf< Out > > Scalar, vector_like< Out > U>
constexpr Out	mul (const Scalar &scalar, U &&u)
	Element-wise multiplication of scalar with vector elements. Result in return value of a user-provided type.
template<vector U, std::convertible_to< RealOf< U > > Scalar>
constexpr std::remove_cvref_t< U >	mul (const Scalar &scalar, U &&u)
	Element-wise multiplication of vector elements with a scalar. Result in return value of automatically selected type.
template<mut_vector Out, vector_like< Out > U, vector_like< Out > V>
constexpr void	div (U &&u, V &&v, Out &out)
	Element-wise vector division. Result via output parameter.
template<container_traits::returnable Out, vector_like< Out > U, vector_like< Out > V>
constexpr Out	div (U &&u, V &&v)
	Element-wise vector division. Result in return value of a user-provided type.
template<vector U, vector_like< U > V>
constexpr std::remove_cvref_t< U >	div (U &&u, V &&v)
	Element-wise vector division. Result in return value of automatically selected type.
template<mut_vector Out, vector_like< Out > U, std::convertible_to< RealOf< Out > > Scalar>
constexpr void	div (U &&u, const Scalar &scalar, Out &out)
	Element-wise division of vector elements with a scalar. Result via output parameter.
template<container_traits::returnable Out, vector_like< Out > U, std::convertible_to< RealOf< Out > > Scalar>
constexpr Out	div (U &&u, const Scalar &scalar)
	Element-wise division of vector elements with a scalar. Result in return value of a user-provided type.
template<vector U, std::convertible_to< RealOf< U > > Scalar>
constexpr std::remove_cvref_t< U >	div (U &&u, const Scalar &scalar)
	Element-wise division of vector elements with a scalar. Result in return value of automatically selected type.
template<mut_vector Out, std::convertible_to< RealOf< Out > > Scalar, vector_like< Out > U>
constexpr void	div (const Scalar &scalar, U &&u, Out &out)
	Element-wise division of scalar with vector elements. Result via output parameter.
template<container_traits::returnable Out, std::convertible_to< RealOf< Out > > Scalar, vector_like< Out > U>
constexpr Out	div (const Scalar &scalar, U &&u)
	Element-wise division of scalar with vector elements. Result in return value of a user-provided type.
template<vector U, std::convertible_to< RealOf< U > > Scalar>
constexpr std::remove_cvref_t< U >	div (const Scalar &scalar, U &&u)
	Element-wise division of vector elements with a scalar. Result in return value of automatically selected type.
template<mut_vector Out, vector_like< Out > U, vector_like< Out > V>
void	cross (const U &u, const V &v, Out &out)
	Cross product of two 3D vectors (via out parameter).
template<container_traits::returnable Out, vector_like< Out > U, vector_like< Out > V>
constexpr Out	cross (const U &u, const V &v)
	Cross product of two 3D vectors (via return value).
template<container_traits::returnable U, vector_like< U > V>
constexpr U	cross (const U &u, const V &v)
	Cross product of two 3D vectors (via return value of default type).
template<vector U, vector_like< U > V>
constexpr RealOf< U >	dot (const U &u, const V &v)
	Vector dot product.
template<Norm t_norm = norms::euclidean, vector V>
constexpr RealOf< V >	norm (const V &v)
	Calculates norm t_norm for vector v.
template<Norm t_norm = norms::euclidean, vector V>
constexpr RealOf< V >	sq_norm (const V &v)
	Calculates the square of the norm t_norm for vector v.
template<Norm t_norm = norms::euclidean, vector V, vector_like< V > U>
constexpr RealOf< V >	dist (const V &v, const U &u)
	Calculates the distance between vector v and u according to norm t_norm.
template<Norm t_norm = norms::euclidean, vector V, vector_like< V > U>
constexpr RealOf< V >	sq_dist (const V &v, const U &u)
	Calculates the square of the distance between vector v and u according to norm t_norm.
template<typename T, typename Compare = std::less<T>, typename Diff = Sub>
constexpr T	abs_diff (const T &a, const T &b, Compare comp={}, Diff diff={})
	Underflow-safe absolute difference between two numbers.
template<typename T, typename Less = std::less<T>>
constexpr Sign	sign (T t, Less less={}, T zero={})
	Gets the sign of a number.

Detailed Description

The main namespace of the dxx::math module.

Function Documentation

abs_diff()

template<typename T, typename Compare = std::less<T>, typename Diff = Sub>

T dxx::math::abs_diff ( const T & a, const T & b, Compare comp = {}, Diff diff = {} )

inlinenodiscardconstexprexport

Underflow-safe absolute difference between two numbers.

Inspired by ARM's vabdq_u8 instruction and copied from https://www.open-std.org/JTC1/SC22/WG21/docs/papers/2014/n4318.pdf