kyosu::cayley_dickson< Type, N > Class Template Reference

Cayley-Dickson algebra main abstraction It is built so that all operation over C, Q and other such algebra can be done in a streamlined fashion based on the Cayley–Dickson construction. More...

#include <kyosu/types/cayley_dickson.hpp>

Detailed Description

template<eve::floating_scalar_value Type, unsigned int N>
requires (N> 1 && std::has_single_bit(N))
class kyosu::cayley_dickson< Type, N >

Cayley-Dickson algebra main abstraction It is built so that all operation over C, Q and other such algebra can be done in a streamlined fashion based on the Cayley–Dickson construction.

Public Member Functions
constexpr	cayley_dickson () noexcept
	Default Cayley-Dickson constructor.
template<unsigned int M> requires (M > 1 && M == N/2) (N>1)
constexpr	cayley_dickson (cayley_dickson< Type, M > const &a) noexcept
	Constructs a Cayley-Dickson instance from an Cayley-Dickson of smaller dimension.
template<unsigned int M> requires (M > 1 && M == N/2)
constexpr	cayley_dickson (cayley_dickson< Type, M > const &a, cayley_dickson< Type, M > const &b) noexcept
	Constructs a Cayley-Dickson instance by aggregating two Cayley-Dickson of smaller dimension.
constexpr	cayley_dickson (kumi::sized_product_type< N > auto const &vs)
	Construct a Cayley-Dickson instance from a properly sized product_type.
template<std::convertible_to< Type > T>
constexpr	cayley_dickson (T v) noexcept
	Construct a Cayley-Dickson from a real value.
template<std::convertible_to< Type > T0, std::convertible_to< Type >... Ts> requires ( (1+sizeof...(Ts)) <= static_dimension )
constexpr	cayley_dickson (T0 v0, Ts... vs) noexcept
	Construct a Cayley-Dickson instance from a sequences of real values.
KYOSU_FORCEINLINE auto &	operator++ () noexcept
	Pre-incrementation operator.
KYOSU_FORCEINLINE auto	operator++ (int) noexcept
	Post-incrementation operator.
KYOSU_FORCEINLINE auto &	operator-- () noexcept
	Pre-decrementation operator.
KYOSU_FORCEINLINE auto	operator-- (int) noexcept
	Post-decrementation operator.
template<concepts::cayley_dickson T> requires (T::static_dimension<N)
constexpr cayley_dickson &	operator= (T const &a) noexcept
	Assign a smaller Cayley-Dickson to another.

Related Functions
(Note that these are not member functions.)
Deduction Guides
template<kumi::product_type Tuple>
	cayley_dickson (Tuple const &) -> cayley_dickson< kumi::element_t< 0, Tuple >, kumi::size_v< Tuple > >
	Deduction guide for constructing from product type.
template<typename T0 , std::convertible_to< T0 >... Ts>
	cayley_dickson (T0, Ts...) -> cayley_dickson< T0, 1+sizeof...(Ts)>
	Deduction guide for constructing from sequence of values.
Compound Assignment Operators
constexpr auto &	operator+= (concepts::cayley_dickson auto &self, concepts::real auto other) noexcept
	Adds the real value other to self and returns the new value of self.
template<concepts::cayley_dickson Self, concepts::cayley_dickson Other>
constexpr auto &	operator+= (Self &self, Other const &other) noexcept
	Adds the Cayley-dickson value other to self and returns the new value of self.
constexpr auto &	operator-= (concepts::cayley_dickson auto &self, concepts::real auto other) noexcept
	Substracts the real value other from self and returns the new value of self.
template<concepts::cayley_dickson Self, concepts::cayley_dickson Other>
constexpr auto &	operator-= (Self &self, Other const &other) noexcept
	Substracts the Cayley-dickson value other from self and returns the new value of self.
constexpr auto &	operator*= (concepts::cayley_dickson auto &self, concepts::real auto other) noexcept
	Multiplies self by the real value other and returns the new value of self.
template<concepts::cayley_dickson Self, concepts::cayley_dickson Other>
constexpr Self &	operator*= (Self &self, Other const &other) noexcept
	Multiplies self by the Cayley-dickson value other and returns the new value of self.
constexpr auto &	operator/= (concepts::cayley_dickson auto &self, concepts::real auto other) noexcept
	Divides self by the real value other and returns the new value of self.
template<concepts::cayley_dickson Self, concepts::cayley_dickson Other>
constexpr Self &	operator/= (Self &self, Other const &other) noexcept
	Divides self by the Cayley-dickson value other and returns the new value of self.
Streaming Operators
template<concepts::cayley_dickson CD>
std::ostream &	operator<< (std::ostream &os, CD const &z)
	Stream insertion for Cayley-dickson based types.
User-defined Literals
constexpr kyosu::complex_t< double >	operator""_i (long double d) noexcept
	Forms a kyosu::complex_t<double> with real part zero and imaginary part d
constexpr kyosu::complex_t< float >	operator""_if (long double d) noexcept
	Forms a kyosu::complex_t<float> with real part zero and imaginary part d
constexpr kyosu::quaternion_t< double >	operator""_j (long double d) noexcept
	Forms a kyosu::quaternion_t<double> with all parts zero and \(j\) part equals to d
constexpr kyosu::quaternion_t< float >	operator""_jf (long double d) noexcept
	Forms a kyosu::quaternion_t<float> with all parts zero and \(j\) part equals to d
constexpr kyosu::quaternion_t< double >	operator""_k (long double d) noexcept
	Forms a kyosu::quaternion_t<double> with all parts zero and \(k\) part equals to d
constexpr kyosu::quaternion_t< float >	operator""_kf (long double d) noexcept
	Forms a kyosu::quaternion_t<float> with all parts zero and \(k\) part equals to d
Unary Operators
template<concepts::cayley_dickson Z>
constexpr auto	operator+ (Z const &z) noexcept
	Identity for Cayley-Dickson value.
template<concepts::cayley_dickson Z>
constexpr auto	operator- (Z const &z) noexcept
	Compute the negation of a given Cayley-Dickson value.
Binary Operators
template<eve::value T1, eve::value T2>
as_cayley_dickson_t< T1, T2 >	operator+ (T1 const &a, T2 const &b) noexcept
	Returns the sum of a Cayley-Dickson value and a real value in any order.
template<eve::value T1, eve::value T2>
as_cayley_dickson_t< T1, T2 >	operator- (T1 const &a, T2 const &b) noexcept
	Returns the difference of two Cayley-Dickson values.
template<eve::value T1, eve::value T2>
as_cayley_dickson_t< T1, T2 >	operator* (T1 const &a, T2 const &b) noexcept
	Returns the product of two Cayley-Dickson values.
template<eve::value T1, eve::value T2>
as_cayley_dickson_t< T1, T2 >	operator/ (T1 const &a, T2 const &b) noexcept
	Returns the ration of two Cayley-Dickson values.
template<concepts::cayley_dickson T1, concepts::real T2>
constexpr auto	operator== (T1 const &a, T2 b)
	Compares a Cayley-Dickson value and a real for equality.
template<concepts::real T1, concepts::cayley_dickson T2>
constexpr auto	operator== (T1 const &a, T2 b)
	Compares a real and a Cayley-Dickson value for equality.
template<concepts::cayley_dickson T1, concepts::real T2>
constexpr auto	operator!= (T1 const &a, T2 b)
	Compares a Cayley-Dickson value and a real for inequality.
template<concepts::real T1, concepts::cayley_dickson T2>
constexpr auto	operator!= (T1 const &a, T2 b)
	Compares a real and a Cayley-Dickson value for inequality.