Namespaces
namespace	detail

namespace	power_helper

Classes
class	BMat8
	Class for fast boolean matrices of dimension up to 8 x 8. More...

struct	Perm16
	Permutations of \(\{0\dots 15\}\). More...

struct	PermGeneric

struct	PPerm16
	Partial permutation of \(\{0, \dots, 15\}\). More...

struct	PTransf16
	Partial transformation of \(\{0\dots 15\}\). More...

struct	TPUBuild
	Class for factory object associated to a SIMD packed unsigned integers. More...

struct	Transf16
	Full transformation of \(\{0\dots 15\}\). More...

struct	Vect16

struct	VectGeneric
	A generic class for combinatorial integer vectors. More...

Typedefs
using	epu64 = uint64_t __attribute__((__vector_size__(16), __may_alias__))

using	epu8 = uint8_t __attribute__((vector_size(16)))
	SIMD vector of 16 unsigned bytes.

Functions
template<class TPU >
TPUBuild< TPU >::array &	as_array (TPU &v) noexcept
	Cast a TPU to a c++ `std::array`.

template<class TPU >
const TPUBuild< TPU >::array &	as_array (const TPU &v) noexcept
	Cast a constant TPU to a constant c++ `std::array`.

template<class TPU >
VectGeneric< TPUBuild< TPU >::size > &	as_VectGeneric (TPU &v)
	Cast a HPCombi::epu8 to a c++ HPCombi::VectGeneric.

template<class TPU >
const VectGeneric< TPUBuild< TPU >::size > &	as_VectGeneric (const TPU &v)
	Cast a HPCombi::epu8 to a c++ HPCombi::VectGeneric.

constexpr uint8_t	operator""_u8 (unsigned long long arg) noexcept
	Unsigned 8 bits int constant.

bool	is_all_zero (epu8 a) noexcept
	Test whether all the entries of a HPCombi::epu8 are zero.

bool	is_all_one (epu8 a) noexcept
	Test whether all the entries of a HPCombi::epu8 are one.

bool	equal (epu8 a, epu8 b) noexcept
	Equality of HPCombi::epu8.

bool	not_equal (epu8 a, epu8 b) noexcept
	Non equality of HPCombi::epu8.

epu8	permuted_ref (epu8 a, epu8 b) noexcept
	Permuting a HPCombi::epu8.

epu8	permuted (epu8 a, epu8 b) noexcept
	Permuting a HPCombi::epu8.

epu8	shifted_right (epu8 a) noexcept
	Left shifted of a HPCombi::epu8 inserting a 0.

epu8	shifted_left (epu8 a) noexcept
	Right shifted of a HPCombi::epu8 inserting a 0.

epu8	reverted (epu8 a) noexcept
	Reverting a HPCombi::epu8.

epu8	min (epu8 a, epu8 b) noexcept
	Vector min between two HPCombi::epu8 0.

epu8	max (epu8 a, epu8 b) noexcept
	Vector max between two HPCombi::epu8 0.

bool	is_sorted (epu8 a) noexcept
	Testing if a HPCombi::epu8 is sorted.

epu8	sorted (epu8 a) noexcept
	Return a sorted HPCombi::epu8.

epu8	sorted8 (epu8 a) noexcept
	Return a HPCombi::epu8 with the two half sorted.

epu8	revsorted (epu8 a) noexcept
	Return a reverse sorted HPCombi::epu8.

epu8	revsorted8 (epu8 a) noexcept
	Return a HPCombi::epu8 with the two half reverse sorted.

epu8	sort_perm (epu8 &a) noexcept
	Sort `this` and return the sorting permutation.

epu8	sort8_perm (epu8 &a) noexcept
	Sort `this` and return the sorting permutation.

void	merge (epu8 &a, epu8 &b) noexcept
	Merge two sorted epu8.

epu8	permutation_of_ref (epu8 a, epu8 b) noexcept
	Find if a vector is a permutation of one other.

epu8	permutation_of (epu8 a, epu8 b) noexcept
	Find if a vector is a permutation of one other.

epu8	random_epu8 (uint16_t bnd)
	A random HPCombi::epu8.

epu8	remove_dups (epu8 a, uint8_t repl=0) noexcept
	Remove duplicates in a sorted HPCombi::epu8.

uint8_t	horiz_sum_ref (epu8) noexcept
	Horizontal sum of a HPCombi::epu8.

uint8_t	horiz_sum_gen (epu8) noexcept
	Horizontal sum of a HPCombi::epu8.

uint8_t	horiz_sum4 (epu8) noexcept
	Horizontal sum of a HPCombi::epu8.

uint8_t	horiz_sum3 (epu8) noexcept
	Horizontal sum of a HPCombi::epu8.

uint8_t	horiz_sum (epu8 v) noexcept
	Horizontal sum of a HPCombi::epu8.

epu8	partial_sums_ref (epu8) noexcept
	Horizontal partial sum of a HPCombi::epu8.

epu8	partial_sums_gen (epu8) noexcept
	Horizontal partial sum of a HPCombi::epu8.

epu8	partial_sums_round (epu8) noexcept
	Horizontal partial sum of a HPCombi::epu8.

epu8	partial_sums (epu8 v) noexcept
	Horizontal partial sum of a HPCombi::epu8.

uint8_t	horiz_max_ref (epu8) noexcept
	Horizontal sum of a HPCombi::epu8.

uint8_t	horiz_max_gen (epu8) noexcept
	Horizontal sum of a HPCombi::epu8.

uint8_t	horiz_max4 (epu8) noexcept
	Horizontal sum of a HPCombi::epu8.

uint8_t	horiz_max3 (epu8) noexcept
	Horizontal sum of a HPCombi::epu8.

uint8_t	horiz_max (epu8 v) noexcept
	Horizontal sum of a HPCombi::epu8.

epu8	partial_max_ref (epu8) noexcept
	Horizontal partial sum of a HPCombi::epu8.

epu8	partial_max_gen (epu8) noexcept
	Horizontal partial sum of a HPCombi::epu8.

epu8	partial_max_round (epu8) noexcept
	Horizontal partial sum of a HPCombi::epu8.

epu8	partial_max (epu8 v) noexcept
	Horizontal partial sum of a HPCombi::epu8.

uint8_t	horiz_min_ref (epu8) noexcept
	Horizontal sum of a HPCombi::epu8.

uint8_t	horiz_min_gen (epu8) noexcept
	Horizontal sum of a HPCombi::epu8.

uint8_t	horiz_min4 (epu8) noexcept
	Horizontal sum of a HPCombi::epu8.

uint8_t	horiz_min3 (epu8) noexcept
	Horizontal sum of a HPCombi::epu8.

uint8_t	horiz_min (epu8 v) noexcept
	Horizontal sum of a HPCombi::epu8.

epu8	partial_min_ref (epu8) noexcept
	Horizontal partial sum of a HPCombi::epu8.

epu8	partial_min_gen (epu8) noexcept
	Horizontal partial sum of a HPCombi::epu8.

epu8	partial_min_round (epu8) noexcept
	Horizontal partial sum of a HPCombi::epu8.

epu8	partial_min (epu8 v) noexcept
	Horizontal partial sum of a HPCombi::epu8.

epu8	eval16_ref (epu8 v) noexcept
	Evaluation of a HPCombi::epu8.

epu8	eval16_arr (epu8 v) noexcept
	Evaluation of a HPCombi::epu8.

epu8	eval16_cycle (epu8 v) noexcept
	Evaluation of a HPCombi::epu8.

epu8	eval16_popcount (epu8 v) noexcept
	Evaluation of a HPCombi::epu8.

epu8	eval16 (epu8 v) noexcept
	Evaluation of a HPCombi::epu8.

uint64_t	first_diff_ref (epu8 a, epu8 b, size_t bound=16) noexcept
	The first difference between two HPCombi::epu8.

uint64_t	first_diff_mask (epu8 a, epu8 b, size_t bound=16) noexcept
	The first difference between two HPCombi::epu8.

uint64_t	first_diff (epu8 a, epu8 b, size_t bound=16) noexcept
	The first difference between two HPCombi::epu8.

uint64_t	last_diff_ref (epu8 a, epu8 b, size_t bound=16) noexcept
	The last difference between two HPCombi::epu8.

uint64_t	last_diff_mask (epu8 a, epu8 b, size_t bound=16) noexcept
	The last difference between two HPCombi::epu8.

uint64_t	last_diff (epu8 a, epu8 b, size_t bound=16) noexcept
	The last difference between two HPCombi::epu8.

bool	less (epu8 a, epu8 b) noexcept
	Lexicographic comparison between two HPCombi::epu8.

int8_t	less_partial (epu8 a, epu8 b, int k) noexcept
	Partial lexicographic comparison between two HPCombi::epu8.

uint64_t	first_zero (epu8 v, int bnd) noexcept
	return the index of the first zero entry or 16 if there are none Only index smaller than bound are taken into account.

uint64_t	last_zero (epu8 v, int bnd) noexcept
	return the index of the last zero entry or 16 if there are none Only index smaller than bound are taken into account.

uint64_t	first_non_zero (epu8 v, int bnd) noexcept
	return the index of the first non zero entry or 16 if there are none Only index smaller than bound are taken into account.

uint64_t	last_non_zero (epu8 v, int bnd) noexcept
	return the index of the last non zero entry or 16 if there are none Only index smaller than bound are taken into account.

epu8	popcount16 (epu8 v) noexcept
	a vector popcount function

bool	is_partial_transformation (epu8 v, const size_t k=16) noexcept
	Test for partial transformation.

bool	is_transformation (epu8 v, const size_t k=16) noexcept
	Test for transformation.

bool	is_partial_permutation (epu8 v, const size_t k=16) noexcept
	Test for partial permutations.

bool	is_permutation_sort (epu8 v, const size_t k=16) noexcept

bool	is_permutation_eval (epu8 v, const size_t k=16) noexcept

bool	is_permutation (epu8 v, const size_t k=16) noexcept

uint64_t	first_mask (epu8 msk, size_t bound)

uint64_t	last_mask (epu8 msk, size_t bound)

template<bool Increasing = true, size_t sz>
epu8	network_sort (epu8 res, std::array< epu8, sz > rounds)
	Apply a sorting network.

template<bool Increasing = true, size_t sz>
epu8	network_sort_perm (epu8 &v, std::array< epu8, sz > rounds)
	Apply a sorting network in place and return the permutation.

void	merge_rev (epu8 &a, epu8 &b) noexcept

epu8	eval16_gen (epu8 v) noexcept

template<typename T , typename M = power_helper::Monoid<T>>
const T	square (const T x)
	A generic compile time squaring function.

template<unsigned exp, typename T , typename M = power_helper::Monoid<T>>
const T	pow (const T x)
	A generic compile time exponentiation function.

template<size_t Size, typename Expo = uint8_t>
std::array< Expo, Size >	sorted_vect (std::array< Expo, Size > v)

Variables
constexpr std::array< epu8, 4 >	masks

constexpr TPUBuild< epu8 >	Epu8 {}
	Factory object acting as a class constructor for type HPCombi::epu8.

constexpr uint64_t	prime = 0x9e3779b97f4a7bb9
	A prime number good for hashing.

constexpr std::array< epu8, 9 >	sorting_rounds
	A 16-way sorting network.

constexpr std::array< epu8, 6 >	sorting_rounds8
	A duplicated 8-way sorting network.

constexpr std::array< epu8, 6 >	merge_rounds

constexpr std::array< epu8, 3 >	inverting_rounds

constexpr std::array< epu8, 4 >	summing_rounds
	Permutation Round for partial and horizontal sums.

constexpr std::array< epu8, 4 >	mining_rounds

Typedef Documentation

◆ epu64

using HPCombi::epu64 = typedef uint64_t __attribute__((__vector_size__(16), __may_alias__))

◆ epu8

using HPCombi::epu8 = typedef uint8_t __attribute__((vector_size(16)))

SIMD vector of 16 unsigned bytes.

Function Documentation

◆ as_array() [1/2]

template<class TPU >

const TPUBuild< TPU >::array & HPCombi::as_array ( const TPU & v )

inlinenoexcept

Cast a constant TPU to a constant c++ std::array.

This is usually faster for algorithm using a lot of indexed access.

◆ as_array() [2/2]

template<class TPU >

TPUBuild< TPU >::array & HPCombi::as_array ( TPU & v )

inlinenoexcept

Cast a TPU to a c++ std::array.

This is usually faster for algorithm using a lot of indexed access.

◆ as_VectGeneric() [1/2]

template<class TPU >

const VectGeneric< TPUBuild< TPU >::size > & HPCombi::as_VectGeneric ( const TPU & v )

inline

Cast a HPCombi::epu8 to a c++ HPCombi::VectGeneric.

This is usually faster for algorithm using a lot of indexed access.

◆ as_VectGeneric() [2/2]

template<class TPU >

VectGeneric< TPUBuild< TPU >::size > & HPCombi::as_VectGeneric ( TPU & v )

inline

Cast a HPCombi::epu8 to a c++ HPCombi::VectGeneric.

This is usually faster for algorithm using a lot of indexed access.

◆ equal()

bool HPCombi::equal	(	epu8	a,
		epu8	b
	)

inlinenoexcept

Equality of HPCombi::epu8.

◆ eval16()

epu8 HPCombi::eval16 ( epu8 v )

inlinenoexcept

Evaluation of a HPCombi::epu8.

Parameters

v	: a HPCombi::epu8

Returns: the evaluation, that is the HPCombi::epu8 r such that r[i] is the number of occurrence of i in the input v

Example:: eval16(epu8 { 5, 5, 2, 5, 1, 6,12, 4, 0, 3, 2,11,12,13,14,15});

HPCombi::eval16
epu8 eval16(epu8 v) noexcept
Evaluation of a HPCombi::epu8.
Definition epu8.hpp:408

HPCombi::epu8
uint8_t __attribute__((vector_size(16))) epu8
SIMD vector of 16 unsigned bytes.
Definition epu8.hpp:45

Returns { 1, 1, 2, 1, 1, 3, 1, 0, 0, 0, 0, 1, 2, 1, 1, 1}

Warning: The entries larger than 15 are ignored

◆ eval16_arr()

epu8 HPCombi::eval16_arr ( epu8 v )

inlinenoexcept

Evaluation of a HPCombi::epu8.

Parameters

v	: a HPCombi::epu8

Returns: the evaluation, that is the HPCombi::epu8 r such that r[i] is the number of occurrence of i in the input v

Example:: eval16(epu8 { 5, 5, 2, 5, 1, 6,12, 4, 0, 3, 2,11,12,13,14,15});

Returns { 1, 1, 2, 1, 1, 3, 1, 0, 0, 0, 0, 1, 2, 1, 1, 1}

Warning: The entries larger than 15 are ignored

Algorithm:: Reference \(O(n)\) algorithm using loop and cast to array

◆ eval16_cycle()

epu8 HPCombi::eval16_cycle ( epu8 v )

inlinenoexcept

Evaluation of a HPCombi::epu8.

Parameters

v	: a HPCombi::epu8

Returns: the evaluation, that is the HPCombi::epu8 r such that r[i] is the number of occurrence of i in the input v

Example:: eval16(epu8 { 5, 5, 2, 5, 1, 6,12, 4, 0, 3, 2,11,12,13,14,15});

Returns { 1, 1, 2, 1, 1, 3, 1, 0, 0, 0, 0, 1, 2, 1, 1, 1}

Warning: The entries larger than 15 are ignored

Algorithm:: Vector \(O(n)\) using cyclic shifting

◆ eval16_gen()

epu8 HPCombi::eval16_gen ( epu8 v )

inlinenoexcept

◆ eval16_popcount()

epu8 HPCombi::eval16_popcount ( epu8 v )

inlinenoexcept

Evaluation of a HPCombi::epu8.

Parameters

v	: a HPCombi::epu8

Returns: the evaluation, that is the HPCombi::epu8 r such that r[i] is the number of occurrence of i in the input v

Example:: eval16(epu8 { 5, 5, 2, 5, 1, 6,12, 4, 0, 3, 2,11,12,13,14,15});

Returns { 1, 1, 2, 1, 1, 3, 1, 0, 0, 0, 0, 1, 2, 1, 1, 1}

Warning: The entries larger than 15 are ignored

Algorithm:: Vector \(O(n)\) using popcount

◆ eval16_ref()

epu8 HPCombi::eval16_ref ( epu8 v )

inlinenoexcept

Evaluation of a HPCombi::epu8.

Parameters

v	: a HPCombi::epu8

Returns: the evaluation, that is the HPCombi::epu8 r such that r[i] is the number of occurrence of i in the input v

Example:: eval16(epu8 { 5, 5, 2, 5, 1, 6,12, 4, 0, 3, 2,11,12,13,14,15});

Returns { 1, 1, 2, 1, 1, 3, 1, 0, 0, 0, 0, 1, 2, 1, 1, 1}

Warning: The entries larger than 15 are ignored

Algorithm:: Reference \(O(n)\) algorithm using loop and indexed access

◆ first_diff()

uint64_t HPCombi::first_diff	(	epu8	a,
		epu8	b,
		size_t	bound = `16`
	)

inlinenoexcept

The first difference between two HPCombi::epu8.

Parameters

a,b	: two HPCombi::epu8
bound	: a `size_t`

Returns: the smallest index \(i<bound\) such that a[i] and b[i] differ, 16 if there is no differences before bound.

Example:: epu8 a { 5, 5, 2, 5, 1, 6,12, 4, 0, 3, 2,11,12,13,14,15};

epu8 b { 5, 5, 2, 9, 1, 6,12, 4, 0, 4, 4, 4,12,13,14,15};

then first_diff(a, b) returns 3, first_diff(a, b, 3) returns 16, first_diff(a, b, 4) returns 3, first_diff(a, b, 7) returns 3.

Warning: bound is assumed to be smaller or equal than 16

◆ first_diff_mask()

uint64_t HPCombi::first_diff_mask	(	epu8	a,
		epu8	b,
		size_t	bound = `16`
	)

inlinenoexcept

The first difference between two HPCombi::epu8.

Parameters

a,b	: two HPCombi::epu8
bound	: a `size_t`

Returns: the smallest index \(i<bound\) such that a[i] and b[i] differ, 16 if there is no differences before bound.

Example:: epu8 a { 5, 5, 2, 5, 1, 6,12, 4, 0, 3, 2,11,12,13,14,15};

epu8 b { 5, 5, 2, 9, 1, 6,12, 4, 0, 4, 4, 4,12,13,14,15};

then first_diff(a, b) returns 3, first_diff(a, b, 3) returns 16, first_diff(a, b, 4) returns 3, first_diff(a, b, 7) returns 3.

Warning: bound is assumed to be smaller or equal than 16

Algorithm:: Using vector comparison and mask

◆ first_diff_ref()

uint64_t HPCombi::first_diff_ref	(	epu8	a,
		epu8	b,
		size_t	bound = `16`
	)

inlinenoexcept

The first difference between two HPCombi::epu8.

Parameters

a,b	: two HPCombi::epu8
bound	: a `size_t`

Returns: the smallest index \(i<bound\) such that a[i] and b[i] differ, 16 if there is no differences before bound.

Example:: epu8 a { 5, 5, 2, 5, 1, 6,12, 4, 0, 3, 2,11,12,13,14,15};

epu8 b { 5, 5, 2, 9, 1, 6,12, 4, 0, 4, 4, 4,12,13,14,15};

then first_diff(a, b) returns 3, first_diff(a, b, 3) returns 16, first_diff(a, b, 4) returns 3, first_diff(a, b, 7) returns 3.

Warning: bound is assumed to be smaller or equal than 16

Algorithm:: Reference \(O(n)\) algorithm using loop and indexed access

◆ first_mask()

uint64_t HPCombi::first_mask	(	epu8	msk,
		size_t	bound
	)

inline

◆ first_non_zero()

uint64_t HPCombi::first_non_zero	(	epu8	v,
		int	bnd
	)

inlinenoexcept

return the index of the first non zero entry or 16 if there are none Only index smaller than bound are taken into account.

◆ first_zero()

uint64_t HPCombi::first_zero	(	epu8	v,
		int	bnd
	)

inlinenoexcept

return the index of the first zero entry or 16 if there are none Only index smaller than bound are taken into account.

◆ horiz_max()

uint8_t HPCombi::horiz_max ( epu8 v )

inlinenoexcept

Horizontal sum of a HPCombi::epu8.

Returns: the horizontal sum of the input

Example:: horiz_max(epu8 { 5, 5, 2, 5, 1, 6,12, 4, 0, 3, 2, 0,12, 0, 0, 0});

HPCombi::horiz_max
uint8_t horiz_max(epu8 v) noexcept
Horizontal sum of a HPCombi::epu8.
Definition epu8.hpp:280

Returns 12

◆ horiz_max3()

uint8_t HPCombi::horiz_max3 ( epu8 v )

inlinenoexcept

Horizontal sum of a HPCombi::epu8.

Returns: the horizontal sum of the input

Example:: horiz_max(epu8 { 5, 5, 2, 5, 1, 6,12, 4, 0, 3, 2, 0,12, 0, 0, 0});

Returns 12

Algorithm:: 3-stages parallel algorithm + indexed access

◆ horiz_max4()

uint8_t HPCombi::horiz_max4 ( epu8 v )

inlinenoexcept

Horizontal sum of a HPCombi::epu8.

Returns: the horizontal sum of the input

Example:: horiz_max(epu8 { 5, 5, 2, 5, 1, 6,12, 4, 0, 3, 2, 0,12, 0, 0, 0});

Returns 12

Algorithm:: 4-stages parallel algorithm

◆ horiz_max_gen()

uint8_t HPCombi::horiz_max_gen ( epu8 v )

inlinenoexcept

Horizontal sum of a HPCombi::epu8.

Returns: the horizontal sum of the input

Example:: horiz_max(epu8 { 5, 5, 2, 5, 1, 6,12, 4, 0, 3, 2, 0,12, 0, 0, 0});

Returns 12

Algorithm:: Reference \(O(n)\) algorithm using loop and indexed access through HPCombi::VectGeneric

◆ horiz_max_ref()

uint8_t HPCombi::horiz_max_ref ( epu8 v )

inlinenoexcept

Horizontal sum of a HPCombi::epu8.

Returns: the horizontal sum of the input

Example:: horiz_max(epu8 { 5, 5, 2, 5, 1, 6,12, 4, 0, 3, 2, 0,12, 0, 0, 0});

Returns 12

Algorithm:: Reference \(O(n)\) algorithm using loop and indexed access

◆ horiz_min()

uint8_t HPCombi::horiz_min ( epu8 v )

inlinenoexcept

Horizontal sum of a HPCombi::epu8.

Returns: the horizontal sum of the input

Example:: horiz_min(epu8 { 5, 5, 2, 5, 1, 6,12, 4, 1, 3, 2, 2,12, 3, 4, 4});

HPCombi::horiz_min
uint8_t horiz_min(epu8 v) noexcept
Horizontal sum of a HPCombi::epu8.
Definition epu8.hpp:343

Returns 1

◆ horiz_min3()

uint8_t HPCombi::horiz_min3 ( epu8 v )

inlinenoexcept

Horizontal sum of a HPCombi::epu8.

Returns: the horizontal sum of the input

Example:: horiz_min(epu8 { 5, 5, 2, 5, 1, 6,12, 4, 1, 3, 2, 2,12, 3, 4, 4});

Returns 1

Algorithm:: 3-stages parallel algorithm + indexed access

◆ horiz_min4()

uint8_t HPCombi::horiz_min4 ( epu8 v )

inlinenoexcept

Horizontal sum of a HPCombi::epu8.

Returns: the horizontal sum of the input

Example:: horiz_min(epu8 { 5, 5, 2, 5, 1, 6,12, 4, 1, 3, 2, 2,12, 3, 4, 4});

Returns 1

Algorithm:: 4-stages parallel algorithm

◆ horiz_min_gen()

uint8_t HPCombi::horiz_min_gen ( epu8 v )

inlinenoexcept

Horizontal sum of a HPCombi::epu8.

Returns: the horizontal sum of the input

Example:: horiz_min(epu8 { 5, 5, 2, 5, 1, 6,12, 4, 1, 3, 2, 2,12, 3, 4, 4});

Returns 1

Algorithm:: Reference \(O(n)\) algorithm using loop and indexed access through HPCombi::VectGeneric

◆ horiz_min_ref()

uint8_t HPCombi::horiz_min_ref ( epu8 v )

inlinenoexcept

Horizontal sum of a HPCombi::epu8.

Returns: the horizontal sum of the input

Example:: horiz_min(epu8 { 5, 5, 2, 5, 1, 6,12, 4, 1, 3, 2, 2,12, 3, 4, 4});

Returns 1

Algorithm:: Reference \(O(n)\) algorithm using loop and indexed access

◆ horiz_sum()

uint8_t HPCombi::horiz_sum ( epu8 v )

inlinenoexcept

Horizontal sum of a HPCombi::epu8.

Returns: the horizontal sum of the input

Example:: horiz_sum(epu8 { 5, 5, 2, 5, 1, 6,12, 4, 0, 3, 2,11,12,13,14,15});

HPCombi::horiz_sum
uint8_t horiz_sum(epu8 v) noexcept
Horizontal sum of a HPCombi::epu8.
Definition epu8.hpp:217

Returns 110

Warning: The result is supposed to fit in a uint8_t

◆ horiz_sum3()

uint8_t HPCombi::horiz_sum3 ( epu8 v )

inlinenoexcept

Horizontal sum of a HPCombi::epu8.

Returns: the horizontal sum of the input

Example:: horiz_sum(epu8 { 5, 5, 2, 5, 1, 6,12, 4, 0, 3, 2,11,12,13,14,15});

Returns 110

Warning: The result is supposed to fit in a uint8_t

Algorithm:: 3-stages parallel algorithm + indexed access

◆ horiz_sum4()

uint8_t HPCombi::horiz_sum4 ( epu8 v )

inlinenoexcept

Horizontal sum of a HPCombi::epu8.

Returns: the horizontal sum of the input

Example:: horiz_sum(epu8 { 5, 5, 2, 5, 1, 6,12, 4, 0, 3, 2,11,12,13,14,15});

Returns 110

Warning: The result is supposed to fit in a uint8_t

Algorithm:: 4-stages parallel algorithm

◆ horiz_sum_gen()

uint8_t HPCombi::horiz_sum_gen ( epu8 v )

inlinenoexcept

Horizontal sum of a HPCombi::epu8.

Returns: the horizontal sum of the input

Example:: horiz_sum(epu8 { 5, 5, 2, 5, 1, 6,12, 4, 0, 3, 2,11,12,13,14,15});

Returns 110

Warning: The result is supposed to fit in a uint8_t

Algorithm:: Reference \(O(n)\) algorithm using loop and indexed access through HPCombi::VectGeneric

◆ horiz_sum_ref()

uint8_t HPCombi::horiz_sum_ref ( epu8 v )

inlinenoexcept

Horizontal sum of a HPCombi::epu8.

Returns: the horizontal sum of the input

Example:: horiz_sum(epu8 { 5, 5, 2, 5, 1, 6,12, 4, 0, 3, 2,11,12,13,14,15});

Returns 110

Warning: The result is supposed to fit in a uint8_t

Algorithm:: Reference \(O(n)\) algorithm using loop and indexed access

◆ is_all_one()

bool HPCombi::is_all_one ( epu8 a )

inlinenoexcept

Test whether all the entries of a HPCombi::epu8 are one.

◆ is_all_zero()

bool HPCombi::is_all_zero ( epu8 a )

inlinenoexcept

Test whether all the entries of a HPCombi::epu8 are zero.

◆ is_partial_permutation()

bool HPCombi::is_partial_permutation	(	epu8	v,
		const size_t	k = `16`
	)

inlinenoexcept

Test for partial permutations.

Returns: whether *this is a partial permutation.

Parameters

v	the vector to test
k	the size of `*this` (default 16)

Points where the function is undefined are mapped to 0xff. If *this is a partial permutation of \(0\dots n-1\) for \(n<16\), it should be completed to a partial permutation of \(0\dots 15\) by adding fixed points. That is the values \(i\geq n\) should be mapped to themself.

Example:: The permutation \(\begin{matrix}0 1 2 3 4 5\\ 2 0 5 . . 4 \end{matrix}\) is encoded by the array {2,0,5,0xFF,0xFF,4,6,7,8,9,10,11,12,13,14,15}

◆ is_partial_transformation()

bool HPCombi::is_partial_transformation	(	epu8	v,
		const size_t	k = `16`
	)

inlinenoexcept

Test for partial transformation.

Returns: whether v is a partial transformation.

Parameters

v	the vector to test
k	the size of `*this` (default 16)

Points where the function is undefined are mapped to 0xff. If *this is a transformation of \(0\dots n-1\) for \(n<16\), it should be completed to a transformation of \(0\dots 15\) by adding fixed points. That is the values \(i\geq n\) should be mapped to themself.

Example:: The partial transformation \(\begin{matrix}0 1 2 3 4 5\\ 2 0 5 . . 4 \end{matrix}\) is encoded by the array {2,0,5,0xff,0xff,4,6,7,8,9,10,11,12,13,14,15}

◆ is_permutation()

bool HPCombi::is_permutation	(	epu8	v,
		const size_t	k = `16`
	)

inlinenoexcept

Returns: whether *this is a permutation.

Parameters

v	the vector to test
k	the size of `*this` (default 16)

If *this is a permutation of \(0\dots n-1\) for \(n<16\), it should be completed to a permutation of \(0\dots 15\) by adding fixed points. That is the values \(i\geq n\) should be mapped to themself.

Example:: The permutation \(\begin{matrix}0 1 2 3 4 5\\ 2 0 5 3 1 4 \end{matrix}\) is encoded by the array {2,0,5,3,1,4,6,7,8,9,10,11,12,13,14,15}

Algorithm: architecture dependent

◆ is_permutation_eval()

bool HPCombi::is_permutation_eval	(	epu8	v,
		const size_t	k = `16`
	)

inlinenoexcept

Returns: whether *this is a permutation.

Parameters

v	the vector to test
k	the size of `*this` (default 16)

If *this is a permutation of \(0\dots n-1\) for \(n<16\), it should be completed to a permutation of \(0\dots 15\) by adding fixed points. That is the values \(i\geq n\) should be mapped to themself.

Example:: The permutation \(\begin{matrix}0 1 2 3 4 5\\ 2 0 5 3 1 4 \end{matrix}\) is encoded by the array {2,0,5,3,1,4,6,7,8,9,10,11,12,13,14,15}

Algorithm: uses evaluation

◆ is_permutation_sort()

bool HPCombi::is_permutation_sort	(	epu8	v,
		const size_t	k = `16`
	)

inlinenoexcept

Returns: whether *this is a permutation.

Parameters

v	the vector to test
k	the size of `*this` (default 16)

If *this is a permutation of \(0\dots n-1\) for \(n<16\), it should be completed to a permutation of \(0\dots 15\) by adding fixed points. That is the values \(i\geq n\) should be mapped to themself.

Example:: The permutation \(\begin{matrix}0 1 2 3 4 5\\ 2 0 5 3 1 4 \end{matrix}\) is encoded by the array {2,0,5,3,1,4,6,7,8,9,10,11,12,13,14,15}

Algorithm: sort the vector and compare to identity

◆ is_sorted()

bool HPCombi::is_sorted ( epu8 a )

inlinenoexcept

Testing if a HPCombi::epu8 is sorted.

◆ is_transformation()

bool HPCombi::is_transformation	(	epu8	v,
		const size_t	k = `16`
	)

inlinenoexcept

Test for transformation.

Returns: whether *this is a transformation.

Parameters

v	the vector to test
k	the size of `*this` (default 16)

If *this is a transformation of \(0\dots n-1\) for \(n<16\), it should be completed to a transformation of \(0\dots 15\) by adding fixed points. That is the values \(i\geq n\) should be mapped to themself.

Example:: The transformation \(\begin{matrix}0 1 2 3 4 5\\ 2 0 5 2 1 4 \end{matrix}\) is encoded by the array {2,0,5,2,1,4,6,7,8,9,10,11,12,13,14,15}

◆ last_diff()

uint64_t HPCombi::last_diff	(	epu8	a,
		epu8	b,
		size_t	bound = `16`
	)

inlinenoexcept

The last difference between two HPCombi::epu8.

Parameters

a,b	: two HPCombi::epu8
bound	: a `size_t`

Returns: the largest index \(i<bound\) such that a[i] and b[i] differ, 16 if there is no differences before bound.

Example:: epu8 a { 5, 5, 2, 5, 1, 6,12, 4, 0, 3, 2,11,12,13,14,15};

epu8 b { 5, 5, 2, 9, 1, 6,12, 4, 0, 4, 4, 4,12,13,14,15};

then last_diff(a, b) returns 11, last_diff(a, b, 3) returns 16, last_diff(a, b, 4) returns 3, last_diff(a, b, 7) returns 3.

Warning: bound is assumed to be smaller or equal than 16

◆ last_diff_mask()

uint64_t HPCombi::last_diff_mask	(	epu8	a,
		epu8	b,
		size_t	bound = `16`
	)

inlinenoexcept

The last difference between two HPCombi::epu8.

Parameters

a,b	: two HPCombi::epu8
bound	: a `size_t`

Returns: the largest index \(i<bound\) such that a[i] and b[i] differ, 16 if there is no differences before bound.

Example:: epu8 a { 5, 5, 2, 5, 1, 6,12, 4, 0, 3, 2,11,12,13,14,15};

epu8 b { 5, 5, 2, 9, 1, 6,12, 4, 0, 4, 4, 4,12,13,14,15};

then last_diff(a, b) returns 11, last_diff(a, b, 3) returns 16, last_diff(a, b, 4) returns 3, last_diff(a, b, 7) returns 3.

Warning: bound is assumed to be smaller or equal than 16

Algorithm:: Using vector comparison and mask

◆ last_diff_ref()

uint64_t HPCombi::last_diff_ref	(	epu8	a,
		epu8	b,
		size_t	bound = `16`
	)

inlinenoexcept

The last difference between two HPCombi::epu8.

Parameters

a,b	: two HPCombi::epu8
bound	: a `size_t`

Returns: the largest index \(i<bound\) such that a[i] and b[i] differ, 16 if there is no differences before bound.

Example:: epu8 a { 5, 5, 2, 5, 1, 6,12, 4, 0, 3, 2,11,12,13,14,15};

epu8 b { 5, 5, 2, 9, 1, 6,12, 4, 0, 4, 4, 4,12,13,14,15};

then last_diff(a, b) returns 11, last_diff(a, b, 3) returns 16, last_diff(a, b, 4) returns 3, last_diff(a, b, 7) returns 3.

Warning: bound is assumed to be smaller or equal than 16

Algorithm:: Reference \(O(n)\) algorithm using loop and indexed access

◆ last_mask()

uint64_t HPCombi::last_mask	(	epu8	msk,
		size_t	bound
	)

inline

◆ last_non_zero()

uint64_t HPCombi::last_non_zero	(	epu8	v,
		int	bnd
	)

inlinenoexcept

return the index of the last non zero entry or 16 if there are none Only index smaller than bound are taken into account.

◆ last_zero()

uint64_t HPCombi::last_zero	(	epu8	v,
		int	bnd
	)

inlinenoexcept

return the index of the last zero entry or 16 if there are none Only index smaller than bound are taken into account.

◆ less()

bool HPCombi::less	(	epu8	a,
		epu8	b
	)

inlinenoexcept

Lexicographic comparison between two HPCombi::epu8.

◆ less_partial()

int8_t HPCombi::less_partial	(	epu8	a,
		epu8	b,
		int	k
	)

inlinenoexcept

Partial lexicographic comparison between two HPCombi::epu8.

Parameters

a,b	: the vectors to compare
k	: the bound for the lexicographic comparison

Returns: a positive, negative or zero int8_t depending on the result

◆ max()

epu8 HPCombi::max	(	epu8	a,
		epu8	b
	)

inlinenoexcept

Vector max between two HPCombi::epu8 0.

◆ merge()

void HPCombi::merge	(	epu8 &	a,
		epu8 &	b
	)

inlinenoexcept

Merge two sorted epu8.

Parameters

a,b	two HPCombi::epu8 after executing merge, `a` and `are` sorted `a`[15] <= `b`[0]

Algorithm: bitonic merge sorting network

◆ merge_rev()

void HPCombi::merge_rev	(	epu8 &	a,
		epu8 &	b
	)

inlinenoexcept

◆ min()

epu8 HPCombi::min	(	epu8	a,
		epu8	b
	)

inlinenoexcept

Vector min between two HPCombi::epu8 0.

◆ network_sort()

template<bool Increasing = true, size_t sz>

epu8 HPCombi::network_sort	(	epu8	res,
		std::array< epu8, sz >	rounds
	)

inline

Apply a sorting network.

◆ network_sort_perm()

template<bool Increasing = true, size_t sz>

epu8 HPCombi::network_sort_perm	(	epu8 &	v,
		std::array< epu8, sz >	rounds
	)

inline

Apply a sorting network in place and return the permutation.

◆ not_equal()

bool HPCombi::not_equal	(	epu8	a,
		epu8	b
	)

inlinenoexcept

Non equality of HPCombi::epu8.

◆ operator""_u8()

constexpr uint8_t HPCombi::operator""_u8 ( unsigned long long arg )

inlineconstexprnoexcept

Unsigned 8 bits int constant.

◆ partial_max()

epu8 HPCombi::partial_max ( epu8 v )

inlinenoexcept

Horizontal partial sum of a HPCombi::epu8.

Returns: the partials max of the input

Example:: partial_max(epu8 { 5, 5, 2, 5, 1, 6,12, 4, 0, 3, 2,11,12,13,14,15});

HPCombi::partial_max
epu8 partial_max(epu8 v) noexcept
Horizontal partial sum of a HPCombi::epu8.
Definition epu8.hpp:309

Returns { 5, 5, 5, 5, 5, 6,12,12,12,12,12,12,12,13,14,15}

◆ partial_max_gen()

epu8 HPCombi::partial_max_gen ( epu8 v )

inlinenoexcept

Horizontal partial sum of a HPCombi::epu8.

Returns: the partials max of the input

Example:: partial_max(epu8 { 5, 5, 2, 5, 1, 6,12, 4, 0, 3, 2,11,12,13,14,15});

Returns { 5, 5, 5, 5, 5, 6,12,12,12,12,12,12,12,13,14,15}

Algorithm:: Reference \(O(n)\) algorithm using loop and indexed access through HPCombi::VectGeneric

◆ partial_max_ref()

epu8 HPCombi::partial_max_ref ( epu8 v )

inlinenoexcept

Horizontal partial sum of a HPCombi::epu8.

Returns: the partials max of the input

Example:: partial_max(epu8 { 5, 5, 2, 5, 1, 6,12, 4, 0, 3, 2,11,12,13,14,15});

Returns { 5, 5, 5, 5, 5, 6,12,12,12,12,12,12,12,13,14,15}

Algorithm:: Reference \(O(n)\) algorithm using loop and indexed access

◆ partial_max_round()

epu8 HPCombi::partial_max_round ( epu8 v )

inlinenoexcept

Horizontal partial sum of a HPCombi::epu8.

Returns: the partials max of the input

Example:: partial_max(epu8 { 5, 5, 2, 5, 1, 6,12, 4, 0, 3, 2,11,12,13,14,15});

Returns { 5, 5, 5, 5, 5, 6,12,12,12,12,12,12,12,13,14,15}

Algorithm:: 4-stages parallel algorithm

◆ partial_min()

epu8 HPCombi::partial_min ( epu8 v )

inlinenoexcept

Horizontal partial sum of a HPCombi::epu8.

Returns: the partials min of the input

Example:: partial_min(epu8 { 5, 5, 2, 5, 1, 6,12, 4, 0, 3, 2,11,12,13,14,15});

HPCombi::partial_min
epu8 partial_min(epu8 v) noexcept
Horizontal partial sum of a HPCombi::epu8.
Definition epu8.hpp:372

Returns { 5, 5, 2, 2, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0}

◆ partial_min_gen()

epu8 HPCombi::partial_min_gen ( epu8 v )

inlinenoexcept

Horizontal partial sum of a HPCombi::epu8.

Returns: the partials min of the input

Example:: partial_min(epu8 { 5, 5, 2, 5, 1, 6,12, 4, 0, 3, 2,11,12,13,14,15});

Returns { 5, 5, 2, 2, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0}

Algorithm:: Reference \(O(n)\) algorithm using loop and indexed access through HPCombi::VectGeneric

◆ partial_min_ref()

epu8 HPCombi::partial_min_ref ( epu8 v )

inlinenoexcept

Horizontal partial sum of a HPCombi::epu8.

Returns: the partials min of the input

Example:: partial_min(epu8 { 5, 5, 2, 5, 1, 6,12, 4, 0, 3, 2,11,12,13,14,15});

Returns { 5, 5, 2, 2, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0}

Algorithm:: Reference \(O(n)\) algorithm using loop and indexed access

◆ partial_min_round()

epu8 HPCombi::partial_min_round ( epu8 v )

inlinenoexcept

Horizontal partial sum of a HPCombi::epu8.

Returns: the partials min of the input

Example:: partial_min(epu8 { 5, 5, 2, 5, 1, 6,12, 4, 0, 3, 2,11,12,13,14,15});

Returns { 5, 5, 2, 2, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0}

Algorithm:: 4-stages parallel algorithm

◆ partial_sums()

epu8 HPCombi::partial_sums ( epu8 v )

inlinenoexcept

Horizontal partial sum of a HPCombi::epu8.

Returns: the partials sums of the input

Example:: partial_sums(epu8 { 5, 5, 2, 5, 1, 6,12, 4, 0, 3, 2,11,12,13,14,15});

HPCombi::partial_sums
epu8 partial_sums(epu8 v) noexcept
Horizontal partial sum of a HPCombi::epu8.
Definition epu8.hpp:246

Returns { 5,10,12,17,18,24,36,40,40,43,45,56,68,81,95,110}

◆ partial_sums_gen()

epu8 HPCombi::partial_sums_gen ( epu8 v )

inlinenoexcept

Horizontal partial sum of a HPCombi::epu8.

Returns: the partials sums of the input

Example:: partial_sums(epu8 { 5, 5, 2, 5, 1, 6,12, 4, 0, 3, 2,11,12,13,14,15});

Returns { 5,10,12,17,18,24,36,40,40,43,45,56,68,81,95,110}

Algorithm:: Reference \(O(n)\) algorithm using loop and indexed access through HPCombi::VectGeneric

◆ partial_sums_ref()

epu8 HPCombi::partial_sums_ref ( epu8 v )

inlinenoexcept

Horizontal partial sum of a HPCombi::epu8.

Returns: the partials sums of the input

Example:: partial_sums(epu8 { 5, 5, 2, 5, 1, 6,12, 4, 0, 3, 2,11,12,13,14,15});

Returns { 5,10,12,17,18,24,36,40,40,43,45,56,68,81,95,110}

Algorithm:: Reference \(O(n)\) algorithm using loop and indexed access

◆ partial_sums_round()

epu8 HPCombi::partial_sums_round ( epu8 v )

inlinenoexcept

Horizontal partial sum of a HPCombi::epu8.

Returns: the partials sums of the input

Example:: partial_sums(epu8 { 5, 5, 2, 5, 1, 6,12, 4, 0, 3, 2,11,12,13,14,15});

Returns { 5,10,12,17,18,24,36,40,40,43,45,56,68,81,95,110}

Algorithm:: 4-stages parallel algorithm

◆ permutation_of()

epu8 HPCombi::permutation_of	(	epu8	a,
		epu8	b
	)

inlinenoexcept

Find if a vector is a permutation of one other.

Parameters

a,b	two HPCombi::epu8

Returns: a HPCombi::epu8 For each \(0 \leq i < 16\), res[i] is the position in a of b[i] if b[i] appears exactly once in a, or undefined if not.

Algorithm: architecture dependent

◆ permutation_of_ref()

epu8 HPCombi::permutation_of_ref	(	epu8	a,
		epu8	b
	)

inlinenoexcept

Find if a vector is a permutation of one other.

Parameters

a,b	two HPCombi::epu8

Returns: a HPCombi::epu8 For each \(0 \leq i < 16\), res[i] is the position in a of b[i] if b[i] appears exactly once in a, or undefined if not.

Algorithm: reference implementation

◆ permuted()

epu8 HPCombi::permuted	(	epu8	a,
		epu8	b
	)

inlinenoexcept

Permuting a HPCombi::epu8.

◆ permuted_ref()

epu8 HPCombi::permuted_ref	(	epu8	a,
		epu8	b
	)

inlinenoexcept

Permuting a HPCombi::epu8.

◆ popcount16()

epu8 HPCombi::popcount16 ( epu8 v )

inlinenoexcept

a vector popcount function

◆ pow()

template<unsigned exp, typename T , typename M = power_helper::Monoid<T>>

const T HPCombi::pow ( const T x )

A generic compile time exponentiation function.

Template Parameters

exp the power

Parameters

x	the number to exponentiate

Returns: x to the power exp

Raise x to the exponent exp where exp is known at compile time. We use the classical recursive binary algorithm, but the recursion is unfolded and optimized at compile time giving an assembly code which is just a sequence of multiplication.

To use for a specific type the user should pass a Monoid structure (see below) as third parameter to the template. Alternatively a default monoid structure can be defined for a given type by specializing the template struct HPCombi::power_helper::Monoid

◆ random_epu8()

epu8 HPCombi::random_epu8 ( uint16_t bnd )

inline

A random HPCombi::epu8.

Parameters

bnd	: the upper bound for the value of the entries. `bnd` must verify \( 0 < bnd \leq 256 \). This is not checked.

Returns: a random HPCombi::epu8 with value in the interval \([0, 1, 2, ..., bnd-1]\).

◆ remove_dups()

epu8 HPCombi::remove_dups	(	epu8	a,
		uint8_t	repl = `0`
	)

inlinenoexcept

Remove duplicates in a sorted HPCombi::epu8.

Parameters

a	supposed to be sorted
repl	the value replacing the duplicate entries (default to 0)

Returns: the vector a where repeated occurrences of entries are replaced by repl

◆ reverted()

epu8 HPCombi::reverted ( epu8 a )

inlinenoexcept

Reverting a HPCombi::epu8.

◆ revsorted()

epu8 HPCombi::revsorted ( epu8 a )

inlinenoexcept

Return a reverse sorted HPCombi::epu8.

Algorithm:: Uses the 9 stages sorting network sorting_rounds

◆ revsorted8()

epu8 HPCombi::revsorted8 ( epu8 a )

inlinenoexcept

Return a HPCombi::epu8 with the two half reverse sorted.

Algorithm: Uses a 6 stages sorting network #sorting_rounds8

◆ shifted_left()

epu8 HPCombi::shifted_left ( epu8 a )

inlinenoexcept

Right shifted of a HPCombi::epu8 inserting a 0.

Warning: we use the convention that the 0 entry is on the left !

◆ shifted_right()

epu8 HPCombi::shifted_right ( epu8 a )

inlinenoexcept

Left shifted of a HPCombi::epu8 inserting a 0.

Warning: we use the convention that the 0 entry is on the left !

◆ sort8_perm()

epu8 HPCombi::sort8_perm ( epu8 & a )

inlinenoexcept

Sort this and return the sorting permutation.

Algorithm: Uses a 6 stages sorting network #sorting_rounds8

◆ sort_perm()

epu8 HPCombi::sort_perm ( epu8 & a )

inlinenoexcept

Sort this and return the sorting permutation.

Algorithm: Uses a 9 stages sorting network #sorting_rounds8

◆ sorted()

epu8 HPCombi::sorted ( epu8 a )

inlinenoexcept

Return a sorted HPCombi::epu8.

Algorithm:: Uses the 9 stages sorting network sorting_rounds

◆ sorted8()

epu8 HPCombi::sorted8 ( epu8 a )

inlinenoexcept

Return a HPCombi::epu8 with the two half sorted.

Algorithm: Uses a 6 stages sorting network #sorting_rounds8

◆ sorted_vect()

template<size_t Size, typename Expo = uint8_t>

std::array< Expo, Size > HPCombi::sorted_vect ( std::array< Expo, Size > v )

◆ square()

template<typename T , typename M = power_helper::Monoid<T>>

const T HPCombi::square ( const T x )

A generic compile time squaring function.

Parameters

x	the number to square

Returns: x squared

To use for a specific type the user should pass a monoid structure as second parameter to the template. Alternatively a default monoid structure can be defined for a given type by specializing the template struct HPCombi::power_helper::Monoid

Variable Documentation

◆ Epu8

constexpr TPUBuild<epu8> HPCombi::Epu8 {}

constexpr

Factory object acting as a class constructor for type HPCombi::epu8.

see HPCombi::TPUBuild for usage and capability

◆ inverting_rounds

constexpr std::array<epu8, 3> HPCombi::inverting_rounds

constexpr

Initial value:

{{
    
    
    epu8 { 0,  1,  2,  3,  8,  9, 10, 11,  4,  5,  6,  7, 12, 13, 14, 15},
    epu8 { 0,  1,  4,  5,  8,  9, 12, 13,  2,  3,  6,  7, 10, 11, 14, 15},
    epu8 { 0,  2,  4,  6,  8, 10, 12, 14,  1,  3,  5,  7,  9, 11, 13, 15}
    
}}

◆ masks

constexpr std::array<epu8, 4> HPCombi::masks

constexpr

Initial value:

{{
    
      {FF, 0,FF, 0,FF, 0,FF, 0,FF, 0,FF, 0,FF, 0,FF, 0}, 
      {FF,FF, 1, 1,FF,FF, 1, 1,FF,FF, 1, 1,FF,FF, 1, 1}, 
      {FF,FF,FF,FF, 2, 2, 2, 2,FF,FF,FF,FF, 2, 2, 2, 2}, 
      {FF,FF,FF,FF,FF,FF,FF,FF, 3, 3, 3, 3, 3, 3, 3, 3}  
    }}

◆ merge_rounds

constexpr std::array<epu8, 6> HPCombi::merge_rounds

constexpr

Initial value:

{{
    epu8 { 8,  9, 10, 11, 12, 13, 14, 15,  0,  1,  2,  3,  4,  5,  6,  7},
    epu8 { 4,  5,  6,  7,  0,  1,  2,  3, 12, 13, 14, 15,  8,  9, 10, 11},
    epu8 { 2,  3,  0,  1,  6,  7,  4,  5, 10, 11,  8,  9, 14, 15, 12, 13},
    epu8 { 1,  0,  3,  2,  5,  4,  7,  6,  9,  8, 11, 10, 13, 12, 15, 14},
}}

◆ mining_rounds

constexpr std::array<epu8, 4> HPCombi::mining_rounds

constexpr

Initial value:

{{
    
    
    epu8 {  0,  0,  2,  2,  4,  4,  6,  6,  8,  8, 10, 10, 12, 12, 14, 14},
    epu8 {  0,  1,  1,  1,  4,  5,  5,  5,  8,  9,  9,  9, 12, 13, 13, 13},
    epu8 {  0,  1,  2,  3,  3,  3,  3,  3,  8,  9, 10, 11, 11, 11, 11, 11},
    epu8 {  0,  1,  2,  3,  4,  5,  6,  7,  7,  7,  7,  7,  7,  7,  7,  7}
    
}}

◆ prime

constexpr uint64_t HPCombi::prime = 0x9e3779b97f4a7bb9

constexpr

A prime number good for hashing.

◆ sorting_rounds

constexpr std::array<epu8, 9> HPCombi::sorting_rounds

constexpr

Initial value:

{{epu8{1, 0, 3, 2, 5, 4, 7, 6, 9, 8, 11, 10, 13, 12, 15, 14},
      epu8{2, 3, 0, 1, 6, 7, 4, 5, 10, 11, 8, 9, 14, 15, 12, 13},
      epu8{4, 5, 6, 7, 0, 1, 2, 3, 12, 13, 14, 15, 8, 9, 10, 11},
      epu8{8, 9, 10, 11, 12, 13, 14, 15, 0, 1, 2, 3, 4, 5, 6, 7},
      epu8{0, 2, 1, 12, 8, 10, 9, 11, 4, 6, 5, 7, 3, 14, 13, 15},
      epu8{0, 4, 8, 10, 1, 9, 12, 13, 2, 5, 3, 14, 6, 7, 11, 15},
      epu8{0, 1, 4, 5, 2, 3, 8, 9, 6, 7, 12, 13, 10, 11, 14, 15},
      epu8{0, 1, 2, 6, 4, 8, 3, 10, 5, 12, 7, 11, 9, 13, 14, 15},
      epu8{0, 1, 2, 4, 3, 6, 5, 8, 7, 10, 9, 12, 11, 13, 14, 15}}}

A 16-way sorting network.

Sorting network from Knuth [AoCP3] Fig. 51 p 229. used by the sorted function

[AoCP3]: "D. Knuth, The art of computer programming vol. 3"

◆ sorting_rounds8

constexpr std::array<epu8, 6> HPCombi::sorting_rounds8

constexpr

Initial value:

{{
    epu8 { 1,  0,  3,  2,  5,  4,  7,  6,  9,  8, 11, 10, 13, 12, 15, 14},
    epu8 { 2,  3,  0,  1,  6,  7,  4,  5, 10, 11,  8,  9, 14, 15, 12, 13},
    epu8 { 0,  2,  1,  3,  4,  6,  5,  7,  8, 10,  9, 11, 12, 14, 13, 15},
    epu8 { 4,  5,  6,  7,  0,  1,  2,  3, 12, 13, 14, 15,  8,  9, 10, 11},
    epu8 { 0,  1,  4,  5,  2,  3,  6,  7,  8,  9, 12, 13, 10, 11, 14, 15},
    epu8 { 0,  2,  1,  4,  3,  6,  5,  7,  8, 10,  9, 12, 11, 14, 13, 15}
}}

A duplicated 8-way sorting network.

Batcher odd-Even mergesort sorting network used by the sorted function

◆ summing_rounds

constexpr std::array<epu8, 4> HPCombi::summing_rounds

constexpr

Initial value:

{{
    
    
    epu8 { FF,  0, FF,  2, FF,  4, FF,  6, FF,  8, FF, 10, FF, 12, FF, 14},
    epu8 { FF, FF,  1,  1, FF, FF,  5,  5, FF, FF,  9,  9, FF, FF, 13, 13},
    epu8 { FF, FF, FF, FF,  3,  3,  3,  3, FF, FF, FF, FF, 11, 11, 11, 11},
    epu8 { FF, FF, FF, FF, FF, FF, FF, FF,  7,  7,  7,  7,  7,  7,  7,  7}
    
}}

Permutation Round for partial and horizontal sums.

Namespaces

Classes

Typedefs

Functions

Variables

Typedef Documentation

◆ epu64

◆ epu8

Function Documentation

◆ as_array() [1/2]

◆ as_array() [2/2]

◆ as_VectGeneric() [1/2]

◆ as_VectGeneric() [2/2]

◆ equal()

◆ eval16()

◆ eval16_arr()

◆ eval16_cycle()

◆ eval16_gen()

◆ eval16_popcount()

◆ eval16_ref()

◆ first_diff()

◆ first_diff_mask()

◆ first_diff_ref()

◆ first_mask()

◆ first_non_zero()

◆ first_zero()

◆ horiz_max()

◆ horiz_max3()

◆ horiz_max4()

◆ horiz_max_gen()

◆ horiz_max_ref()

◆ horiz_min()

◆ horiz_min3()

◆ horiz_min4()

◆ horiz_min_gen()

◆ horiz_min_ref()

◆ horiz_sum()

◆ horiz_sum3()

◆ horiz_sum4()

◆ horiz_sum_gen()

◆ horiz_sum_ref()

◆ is_all_one()

◆ is_all_zero()

◆ is_partial_permutation()

◆ is_partial_transformation()

◆ is_permutation()

◆ is_permutation_eval()

◆ is_permutation_sort()

◆ is_sorted()

◆ is_transformation()

◆ last_diff()

◆ last_diff_mask()

◆ last_diff_ref()

◆ last_mask()

◆ last_non_zero()

◆ last_zero()

◆ less()

◆ less_partial()

◆ max()

◆ merge()

◆ merge_rev()

◆ min()

◆ network_sort()

◆ network_sort_perm()

◆ not_equal()

◆ operator""_u8()

◆ partial_max()

◆ partial_max_gen()

◆ partial_max_ref()

◆ partial_max_round()

◆ partial_min()

◆ partial_min_gen()

◆ partial_min_ref()

◆ partial_min_round()

◆ partial_sums()

◆ partial_sums_gen()

◆ partial_sums_ref()

◆ partial_sums_round()

◆ permutation_of()

◆ permutation_of_ref()