Hypercomplex< mpfr_t, dim > Class Template Reference

#include <Hypercomplex_MPFR.hpp>

Public Member Functions
	Hypercomplex (const mpfr_t *ARR)
	This is the main constructor. More...
	Hypercomplex (const Hypercomplex &H)
	This is the copy constructor. More...
uint64_t	_ () const
	Dimensionality getter. More...
int32_t	norm (mpfr_t norm) const
	Calculate Euclidean norm of a number. More...
Hypercomplex	inv () const
	Calculate inverse of a given number. More...
template<const uint64_t newdim>
Hypercomplex< mpfr_t, newdim >	expand () const
	Cast a number into a higher dimension. More...
Hypercomplex	operator~ () const
	Create a complex conjugate. More...
Hypercomplex	operator- () const
	Create an additive inverse of a given number. More...
Hypercomplex &	operator= (const Hypercomplex &H)
	Assignment operator. More...
mpfr_t const &	operator[] (const uint64_t i) const
	Access operator (const) More...
mpfr_t &	operator[] (const uint64_t i)
	Access operator (non-const) More...
Hypercomplex &	operator+= (const Hypercomplex &H)
	Addition-Assignment operator. More...
Hypercomplex &	operator-= (const Hypercomplex &H)
	Subtraction-Assignment operator. More...
Hypercomplex &	operator*= (const Hypercomplex &H)
	Multiplication-Assignment operator. More...
Hypercomplex &	operator^= (const uint64_t x)
	Power-Assignment operator. More...
Hypercomplex &	operator/= (const Hypercomplex &H)
	Division-Assignment operator. More...

Static Public Member Functions
static void	init ()
	Basis multiplication table initialiser.
static void	clear ()
	Cleanup function: free all memory.
static Hypercomplex	MUL (const Hypercomplex &H1, const Hypercomplex &H2)
	Optimised multiplication function. More...

Detailed Description

template<const uint64_t dim>
class Hypercomplex< mpfr_t, dim >

Partial specialisation of the main class for high precision

Constructor & Destructor Documentation

Hypercomplex() [1/2]

template<const uint64_t dim>

Hypercomplex< mpfr_t, dim >::Hypercomplex ( const mpfr_t *  ARR )

inlineexplicit

This is the main constructor.

Parameters

[in]

ARR

array of MPFR numbers

Template parameters are:

• dimensionality of the algebra

Hypercomplex() [2/2]

template<const uint64_t dim>

Hypercomplex< mpfr_t, dim >::Hypercomplex ( const Hypercomplex< mpfr_t, dim > &  H )

inline

This is the copy constructor.

Parameters

[in]

H

existing class instance

Template parameters are:

• dimensionality of the algebra

Member Function Documentation

_()

template<const uint64_t dim>

uint64_t Hypercomplex< mpfr_t, dim >::_ ( ) const

inline

Dimensionality getter.

Returns

algebraic dimension of the underlying object

expand()

template<const uint64_t dim>

template<const uint64_t newdim>

Hypercomplex< mpfr_t, newdim > Hypercomplex< mpfr_t, dim >::expand ( ) const

inline

Cast a number into a higher dimension.

Returns

new class instance

New dimension is passed as a function template parameter, as the return class is not the same as the caller's class.

inv()

template<const uint64_t dim>

Hypercomplex Hypercomplex< mpfr_t, dim >::inv ( ) const

inline

Calculate inverse of a given number.

Returns

new class instance

MUL()

template<const uint64_t dim>

static Hypercomplex Hypercomplex< mpfr_t, dim >::MUL ( const Hypercomplex< mpfr_t, dim > &  H1, const Hypercomplex< mpfr_t, dim > &  H2  )

inlinestatic

Optimised multiplication function.

Parameters

[in]	H1	LHS operand
[in]	H2	RHS operand

Returns

new class instance

norm()

template<const uint64_t dim>

int32_t Hypercomplex< mpfr_t, dim >::norm ( mpfr_t  norm ) const

inline

Calculate Euclidean norm of a number.

Parameters

[in,out]

norm

MPFR variable for the calculated norm

Returns

exit status

Note that the interface of this method is different than for the fully template class. Following the MPFR logic: function takes as an argument a variable to store the output in.

operator*=()

template<const uint64_t dim>

Hypercomplex & Hypercomplex< mpfr_t, dim >::operator*= ( const Hypercomplex< mpfr_t, dim > &  H )

inline

Multiplication-Assignment operator.

Parameters

[in]

H

existing class instance

Returns

Reference to the caller

operator+=()

template<const uint64_t dim>

Hypercomplex & Hypercomplex< mpfr_t, dim >::operator+= ( const Hypercomplex< mpfr_t, dim > &  H )

inline

Addition-Assignment operator.

Parameters

[in]

H

existing class instance

Returns

Reference to the caller

operator-()

template<const uint64_t dim>

Hypercomplex Hypercomplex< mpfr_t, dim >::operator- ( ) const

inline

Create an additive inverse of a given number.

Returns

new class instance

operator-=()

template<const uint64_t dim>

Hypercomplex & Hypercomplex< mpfr_t, dim >::operator-= ( const Hypercomplex< mpfr_t, dim > &  H )

inline

Subtraction-Assignment operator.

Parameters

[in]

H

existing class instance

Returns

Reference to the caller

operator/=()

template<const uint64_t dim>

Hypercomplex & Hypercomplex< mpfr_t, dim >::operator/= ( const Hypercomplex< mpfr_t, dim > &  H )

inline

Division-Assignment operator.

Parameters

[in]

H

existing class instance

Returns

Reference to the caller

operator=()

template<const uint64_t dim>

Hypercomplex & Hypercomplex< mpfr_t, dim >::operator= ( const Hypercomplex< mpfr_t, dim > &  H )

inline

Assignment operator.

Parameters

[in]

H

existing class instance

Returns

Reference to the caller (for chained assignments)

operator[]() [1/2]

template<const uint64_t dim>

mpfr_t & Hypercomplex< mpfr_t, dim >::operator[] ( const uint64_t  i )

inline

Access operator (non-const)

Parameters

[in]

i

index for the element to access

Returns

i-th element of the number

operator[]() [2/2]

template<const uint64_t dim>

mpfr_t const & Hypercomplex< mpfr_t, dim >::operator[] ( const uint64_t  i ) const

inline

Access operator (const)

Parameters

[in]

i

index for the element to access

Returns

i-th element of the number

operator^=()

template<const uint64_t dim>

Hypercomplex & Hypercomplex< mpfr_t, dim >::operator^= ( const uint64_t  x )

inline

Power-Assignment operator.

Parameters

[in]

x

positive integer

Returns

Reference to the caller

operator~()

template<const uint64_t dim>

Hypercomplex Hypercomplex< mpfr_t, dim >::operator~ ( ) const

inline

Create a complex conjugate.

Returns

new class instance