Partial permutation of \(\{0\dots 15\}\); see also HPCombi::Perm16; partial means it might not be defined everywhere (but where it's defined, it's injective). More...

#include <perm16.hpp>

Inheritance diagram for HPCombi::PPerm16:

Public Member Functions
	PPerm16 ()=default

constexpr	PPerm16 (const PPerm16 &vv)=default

constexpr	PPerm16 (const vect vv)

constexpr	PPerm16 (const epu8 x)

	PPerm16 (std::vector< uint8_t > dom, std::vector< uint8_t > rng, size_t=0)

	PPerm16 (std::initializer_list< uint8_t > il)

PPerm16 &	operator= (const PPerm16 &)=default

bool	validate (size_t k=16) const
	Return whether `*this` is a well constructed object.

PPerm16	operator* (const PPerm16 &p) const
	The product of two partial perrmutations.

PPerm16	inverse_ref () const
	The inverse of a partial permutation.

PPerm16	right_one () const

PPerm16	left_one () const

Public Member Functions inherited from HPCombi::PTransf16
	PTransf16 ()=default

constexpr	PTransf16 (const vect vv)

constexpr	PTransf16 (const epu8 x)

	PTransf16 (std::vector< uint8_t > dom, std::vector< uint8_t > rng, size_t=0)

	PTransf16 (std::initializer_list< uint8_t > il)

bool	validate (size_t k=16) const
	Return whether `*this` is a well constructed object.

PTransf16	operator* (const PTransf16 &p) const
	The product of two partial transformations.

epu8	image_mask_cmpestrm (bool complement=false) const
	Returns a mask for the image of `*this`.

epu8	image_mask_ref (bool complement=false) const
	Returns a mask for the image of `*this`.

epu8	image_mask (bool complement=false) const

uint32_t	image_bitset (bool complement=false) const
	Returns a bit mask for the image of `*this`.

epu8	domain_mask (bool complement=false) const
	Returns a mask for the domain of `*this`.

uint32_t	domain_bitset (bool complement=false) const
	Returns a bit mask for the domain of `*this`.

PTransf16	right_one () const
	Returns the partial right identity for `*this`.

PTransf16	left_one () const
	Returns the partial left identity for `*this`.

uint32_t	rank_ref () const
	Returns the size of the image of `*this`.

uint32_t	rank () const
	Returns the size of the image of `*this`.

uint32_t	rank_cmpestrm () const
	Returns the size of the image of `*this`.

epu8	fix_points_mask (bool complement=false) const
	Returns a mask for the fix point of `*this`.

uint32_t	fix_points_bitset (bool complement=false) const
	Returns a bit mask for the fix point of `*this`.

uint8_t	smallest_fix_point () const
	Returns the smallest fix point of `*this`.

uint8_t	smallest_moved_point () const
	Returns the smallest non fix point of `*this`.

uint8_t	largest_fix_point () const
	Returns the largest fix point of `*this`.

uint8_t	largest_moved_point () const
	Returns the largest non fix point of `*this`.

uint8_t	nb_fix_points () const
	Returns the number of fix points of `*this`.

Public Member Functions inherited from HPCombi::Vect16
	Vect16 ()=default

constexpr	Vect16 (epu8 x)

	Vect16 (std::initializer_list< uint8_t > il, uint8_t def=0)

constexpr	operator epu8 () const

array &	as_array ()

const array &	as_array () const

const uint8_t &	operator[] (uint64_t i) const

uint8_t &	operator[] (uint64_t i)

size_t	first_diff (const Vect16 &u, size_t bound=size()) const

size_t	last_diff (const Vect16 &u, size_t bound=size()) const

size_t	first_zero (size_t bound=size()) const

size_t	last_zero (size_t bound=size()) const

size_t	first_non_zero (size_t bound=size()) const

size_t	last_non_zero (size_t bound=size()) const

const_iterator	cbegin () const

const_iterator	cend () const

iterator	begin ()

iterator	end ()

const_iterator	begin () const

const_iterator	end () const

bool	operator== (const Vect16 &b) const

bool	operator!= (const Vect16 &b) const

bool	operator< (const Vect16 &b) const

int8_t	less_partial (const Vect16 &b, int k) const

Vect16	permuted (const Vect16 &b) const

uint8_t	sum () const

Vect16	partial_sums () const

Vect16	eval16 () const

bool	is_permutation () const

bool	is_permutation (size_t k) const

Static Public Member Functions
static constexpr PPerm16	one ()
	The identity partial permutations.

Static Public Member Functions inherited from HPCombi::PTransf16
static constexpr size_t	size ()

static constexpr PTransf16	one ()
	The identity partial transformation.

Static Public Member Functions inherited from HPCombi::Vect16
static constexpr size_t	size ()

Additional Inherited Members
Public Types inherited from HPCombi::PTransf16
using	vect = HPCombi::Vect16

using	array = typename decltype(Epu8)::array

Public Types inherited from HPCombi::Vect16
using	array = typename decltype(Epu8)::array

using	value_type = uint8_t

using	iterator = typename array::iterator

using	const_iterator = typename array::const_iterator

Public Attributes inherited from HPCombi::Vect16
epu8	v

Detailed Description

Partial permutation of \(\{0\dots 15\}\); see also HPCombi::Perm16; partial means it might not be defined everywhere (but where it's defined, it's injective).

Undefined images are encoded as 0xFF.

Constructor & Destructor Documentation

◆ PPerm16() [1/6]

HPCombi::PPerm16::PPerm16 ( )

default

◆ PPerm16() [2/6]

HPCombi::PPerm16::PPerm16 ( const PPerm16 & vv )

constexprdefault

◆ PPerm16() [3/6]

HPCombi::PPerm16::PPerm16 ( const vect vv )

inlineconstexpr

◆ PPerm16() [4/6]

HPCombi::PPerm16::PPerm16 ( const epu8 x )

inlineconstexpr

◆ PPerm16() [5/6]

HPCombi::PPerm16::PPerm16	(	std::vector< uint8_t >	dom,
		std::vector< uint8_t >	rng,
		size_t	= 0 )

inline

◆ PPerm16() [6/6]

HPCombi::PPerm16::PPerm16 ( std::initializer_list< uint8_t > il )

inline

Member Function Documentation

◆ inverse_ref()

PPerm16 HPCombi::PPerm16::inverse_ref ( ) const

inline

The inverse of a partial permutation.

Returns: the inverse of *this. The inverse of \(p\) is the unique partial permutation \(i\) such that \( p * i * p = p\) and \( i * p * i = i\)

Example:

Perm16 x = {0,3,2,4,0xFF,5,6,0xFF,8,9,11,0xFF,12,0xFF,0xFF,0xFF};

x.inverse()

HPCombi::Perm16

Permutations of : A permutation is a bijective mapping of a set of n elements onto itself.

Definition perm16.hpp:237

HPCombi::Perm16::inverse

Perm16 inverse() const

The inverse permutation.

Definition perm16.hpp:274

Returns

{0,0xFF,2,1,3,5,6,0xFF,8,9,0xFF,10,12,0xFF,0xFF,0xFF}
*

Algorithm:: \(O(n)\) algorithm using reference cast to arrays

◆ left_one()

PPerm16 HPCombi::PPerm16::left_one ( ) const

inline

◆ one()

static constexpr PPerm16 HPCombi::PPerm16::one ( )

inlinestaticconstexpr

The identity partial permutations.

◆ operator*()

PPerm16 HPCombi::PPerm16::operator* ( const PPerm16 & p ) const

inline

The product of two partial perrmutations.

◆ operator=()

PPerm16 & HPCombi::PPerm16::operator= ( const PPerm16 & )

default

◆ right_one()

PPerm16 HPCombi::PPerm16::right_one ( ) const

inline

◆ validate()

bool HPCombi::PPerm16::validate ( size_t k = 16 ) const

inline

Return whether *this is a well constructed object.

The documentation for this struct was generated from the following files:

/Users/jdm/hpcombi/include/hpcombi/perm16.hpp
/Users/jdm/hpcombi/include/hpcombi/perm16_impl.hpp

Public Member Functions

Static Public Member Functions

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ PPerm16() [1/6]

◆ PPerm16() [2/6]

◆ PPerm16() [3/6]

◆ PPerm16() [4/6]

◆ PPerm16() [5/6]

◆ PPerm16() [6/6]

Member Function Documentation

◆ inverse_ref()

◆ left_one()

◆ one()

◆ operator*()

◆ operator=()

◆ right_one()

◆ validate()