Single logical field unifying several pairwise-isomorphic representations. More...

#include <fields.hpp>

Inheritance diagram for CECCO::Iso< MAIN, OTHERS >:

Public Types
using	label_t = typename MAIN::label_t
using	BASE_FIELD = typename MAIN::BASE_FIELD

Public Member Functions
constexpr	Iso () noexcept
	Default constructor: 0 (consistent across all representations).
constexpr	Iso (int l)
	Construct from a signed element label via the MAIN representation.
constexpr	Iso (const MAIN &other) noexcept
	Wrap a MAIN-representation element.
constexpr	Iso (MAIN &&other) noexcept
	Wrap a MAIN-representation rvalue.
template<BelongsTo< OTHERS... > OTHER>
constexpr	Iso (const OTHER &other)
	Wrap an OTHERS element by converting to MAIN.
template<BelongsTo< OTHERS... > OTHER>
constexpr	Iso (OTHER &&other)
	Wrap an OTHERS rvalue by converting to MAIN.
constexpr	Iso (const Iso &other) noexcept=default
constexpr	Iso (Iso &&other) noexcept=default
template<FiniteFieldType T>
	Iso (const Vector< T > &v)
	Construct from a coefficient vector over a subfield T.
template<FiniteFieldType B, MOD modulus, LutMode mode>
	Iso (const Ext< B, modulus, mode > &other)
	Cross-field conversion from an extension field.
template<uint16_t p> requires SubfieldOf<Iso<MAIN, OTHERS...>, Fp<p>> && (!std::is_same_v<MAIN, Fp<p>>) && (!BelongsTo<Fp<p>, OTHERS...>)
constexpr	Iso (const Fp< p > &other)
	Embed a prime-field element when 𝔽_p is a (possibly indirect) subfield of the Iso.
template<FiniteFieldType OTHER_MAIN, FiniteFieldType... OTHER_OTHERS>
	Iso (const Iso< OTHER_MAIN, OTHER_OTHERS... > &other)
	Cross-field conversion from another Iso of the same characteristic.
constexpr Iso	operator- () const
	Additive inverse (delegates to MAIN).
constexpr Iso &	operator+= (const Iso &other)
	*this += other (delegates to MAIN)
template<typename OTHER> requires BelongsTo<OTHER, OTHERS...>
constexpr Iso &	operator+= (const OTHER &other)
	*this += other after converting an OTHERS operand to MAIN
constexpr Iso &	operator-= (const Iso &other)
	*this -= other (delegates to MAIN)
template<typename OTHER> requires BelongsTo<OTHER, OTHERS...>
constexpr Iso &	operator-= (const OTHER &other)
	*this -= other after converting an OTHERS operand to MAIN
constexpr Iso &	operator*= (const Iso &other)
	this = other (delegates to MAIN)
template<typename OTHER> requires BelongsTo<OTHER, OTHERS...>
constexpr Iso &	operator*= (const OTHER &other)
	this = other after converting an OTHERS operand to MAIN
constexpr Iso &	operator*= (int s)
	Scalar multiplication by an int (delegates to MAIN).
Iso &	operator/= (const Iso &other)
	*this /= other; throws std::invalid_argument if other is zero
template<typename OTHER> requires BelongsTo<OTHER, OTHERS...>
Iso &	operator/= (const OTHER &other)
	*this /= other after converting an OTHERS operand to MAIN; same exception
template<typename TO> requires BelongsTo<TO, OTHERS...>
constexpr TO	as () const
	Project to a specific representation by applying the cached Isomorphism.
constexpr const MAIN &	main () const noexcept
	Read-only access to the underlying MAIN-representation element.
constexpr bool	is_zero () const noexcept
constexpr bool	has_positive_sign () const noexcept
constexpr Iso &	randomize ()
constexpr Iso &	randomize_force_change ()
size_t	get_multiplicative_order () const
size_t	get_additive_order () const
constexpr auto	get_label () const noexcept
constexpr Iso &	erase () noexcept
	Mark this element as erased (delegates to MAIN).
constexpr Iso &	unerase () noexcept
	Clear the erasure flag, resetting MAIN to its additive identity.
constexpr bool	is_erased () const noexcept
	Test whether this element is currently erased.
constexpr Iso &	operator= (const Iso &other)=default
constexpr Iso &	operator= (Iso &&other) noexcept=default
constexpr Iso &	operator= (const MAIN &other)
	Assign a MAIN-representation element directly.
constexpr Iso &	operator= (int other)
	Assign a signed element label via MAIN.
template<typename OTHER> requires BelongsTo<OTHER, OTHERS...>
Iso &	operator= (const OTHER &other)
	Assign from an OTHERS representation (copy-and-swap; same semantics as the constructor).
template<uint16_t p>
Iso &	operator= (const Fp< p > &other)
	Assign from an Fp of matching characteristic (copy-and-swap).
template<FiniteFieldType B, MOD ext_modulus, LutMode mode>
Iso &	operator= (const Ext< B, ext_modulus, mode > &other)
	Assign from an Ext of matching characteristic (copy-and-swap).
template<FiniteFieldType OTHER_MAIN, FiniteFieldType... OTHER_OTHERS> requires (OTHER_MAIN::get_characteristic() == MAIN::get_characteristic()) && (!std::is_same_v<Iso<OTHER_MAIN, OTHER_OTHERS...>, Iso<MAIN, OTHERS...>>)
Iso &	operator= (const Iso< OTHER_MAIN, OTHER_OTHERS... > &other)
	Assign from another Iso of matching characteristic (copy-and-swap).
constexpr bool	operator== (const Iso &other) const noexcept
constexpr bool	operator== (const MAIN &other) const noexcept
constexpr bool	operator!= (const Iso &other) const
constexpr bool	operator!= (const MAIN &other) const
template<FiniteFieldType T> requires ((SubfieldOf<MAIN, T> \|\| ((SubfieldOf<OTHERS, T>) \|\| ...))) && (!std::is_same_v<Iso<MAIN, OTHERS...>, T>)
Vector< T >	as_vector () const
	Coordinate vector over a subfield T of MAIN or any OTHERS representation.
template<typename OTHER> requires BelongsTo<OTHER, OTHERS...>
Iso< MAIN, OTHERS... > &	operator= (const OTHER &other)
template<uint16_t p>
Iso< MAIN, OTHERS... > &	operator= (const Fp< p > &other)
template<FiniteFieldType B, MOD ext_modulus, LutMode mode>
Iso< MAIN, OTHERS... > &	operator= (const Ext< B, ext_modulus, mode > &other)
template<FiniteFieldType OTHER_MAIN, FiniteFieldType... OTHER_OTHERS> requires (OTHER_MAIN::get_characteristic() == MAIN::get_characteristic()) && (!std::is_same_v<Iso<OTHER_MAIN, OTHER_OTHERS...>, Iso<MAIN, OTHERS...>>)
Iso< MAIN, OTHERS... > &	operator= (const Iso< OTHER_MAIN, OTHER_OTHERS... > &other)
template<typename OTHER> requires BelongsTo<OTHER, OTHERS...>
constexpr Iso< MAIN, OTHERS... > &	operator+= (const OTHER &other)
template<typename OTHER> requires BelongsTo<OTHER, OTHERS...>
constexpr Iso< MAIN, OTHERS... > &	operator-= (const OTHER &other)
template<typename OTHER> requires BelongsTo<OTHER, OTHERS...>
constexpr Iso< MAIN, OTHERS... > &	operator*= (const OTHER &other)
template<typename OTHER> requires BelongsTo<OTHER, OTHERS...>
Iso< MAIN, OTHERS... > &	operator/= (const OTHER &other)

Static Public Member Functions
static std::string	get_info ()
static constexpr size_t	get_characteristic () noexcept
static constexpr size_t	get_p () noexcept
static constexpr size_t	get_q () noexcept
static constexpr size_t	get_m () noexcept
static constexpr size_t	get_size () noexcept
static constexpr Polynomial< BASE_FIELD >	get_modulus ()
static constexpr Iso	get_generator ()
static constexpr bool	is_constexpr_ready () noexcept
	Inherits constexpr-readiness from MAIN (OTHERS may differ; isomorphisms run at runtime).
static constexpr bool	ready ()
static constexpr auto &	lut_add ()
static constexpr auto &	lut_neg ()
static constexpr auto &	lut_mul ()
static constexpr auto &	lut_inv ()
static constexpr label_t	lut_add (label_t a, label_t b)
static constexpr label_t	lut_mul (label_t a, label_t b)
static constexpr label_t	lut_neg (label_t a)
static constexpr label_t	lut_inv (label_t a)

Friends
std::ostream &	operator<< (std::ostream &os, const Iso &iso)

Additional Inherited Members
Protected Member Functions inherited from CECCO::details::Base
	Base ()=default

Detailed Description

template<FiniteFieldType MAIN, FiniteFieldType... OTHERS>
class CECCO::Iso< MAIN, OTHERS >

Single logical field unifying several pairwise-isomorphic representations.

Template Parameters

MAIN	Primary representation; satisfies CECCO::FiniteFieldType. All operations are forwarded to it, so the Iso inherits its CECCO::LutMode and performance characteristics.
OTHERS	Alternative representations of the same abstract field (each Isomorphic<MAIN, OTHER>). Pairwise distinctness is enforced at instantiation.

Useful for merging two construction towers that meet at the same mathematical field, e.g. 𝔽₁₆ built once from 𝔽₂ and once from 𝔽₄. With those two Ext types wrapped in an Iso, CECCO::SubfieldOf can recognise both as containing 𝔽₂ and 𝔽₄, which makes the cross-field constructors of CECCO::Ext and CECCO::Iso pick optimal paths. The OTHERS representations may use different LUT modes from MAIN; isomorphism conversions across representations happen at runtime via cached maps.

Usage_Example

using F2   = Fp<2>;
using F4_a = Ext<F2, {1, 1, 1}>;
using F4_b = Ext<F2, {1, 0, 1}>;
using F4   = Iso<F4_a, F4_b>;
 
F4_a a(2);
F4_b b(3);
F4 c(a);                   // wrap a into the unified field
c += b;                    // OTHERS-overload converts b into MAIN behind the scenes
F4_b d = c.as<F4_b>();     // explicit projection back to F4_b

Definition at line 3159 of file fields.hpp.

Member Typedef Documentation

◆ BASE_FIELD

template<FiniteFieldType MAIN, FiniteFieldType... OTHERS>

using CECCO::Iso< MAIN, OTHERS >::BASE_FIELD = typename MAIN::BASE_FIELD

Definition at line 3171 of file fields.hpp.

◆ label_t

template<FiniteFieldType MAIN, FiniteFieldType... OTHERS>

using CECCO::Iso< MAIN, OTHERS >::label_t = typename MAIN::label_t

Definition at line 3170 of file fields.hpp.

Constructor & Destructor Documentation

◆ Iso() [1/12]

template<FiniteFieldType MAIN, FiniteFieldType... OTHERS>

CECCO::Iso< MAIN, OTHERS >::Iso ( )

inlineconstexprnoexcept

Default constructor: 0 (consistent across all representations).

Definition at line 3178 of file fields.hpp.

◆ Iso() [2/12]

template<FiniteFieldType MAIN, FiniteFieldType... OTHERS>

CECCO::Iso< MAIN, OTHERS >::Iso ( int l )

inlineconstexpr

Construct from a signed element label via the MAIN representation.

Definition at line 3181 of file fields.hpp.

◆ Iso() [3/12]

template<FiniteFieldType MAIN, FiniteFieldType... OTHERS>

CECCO::Iso< MAIN, OTHERS >::Iso ( const MAIN & other )

inlineconstexprnoexcept

Wrap a MAIN-representation element.

Definition at line 3184 of file fields.hpp.

◆ Iso() [4/12]

template<FiniteFieldType MAIN, FiniteFieldType... OTHERS>

CECCO::Iso< MAIN, OTHERS >::Iso ( MAIN && other )

inlineconstexprnoexcept

Wrap a MAIN-representation rvalue.

Definition at line 3186 of file fields.hpp.

◆ Iso() [5/12]

template<FiniteFieldType MAIN, FiniteFieldType... OTHERS>

template<BelongsTo< OTHERS... > OTHER>

CECCO::Iso< MAIN, OTHERS >::Iso ( const OTHER & other )

inlineconstexpr

Wrap an OTHERS element by converting to MAIN.

Definition at line 3190 of file fields.hpp.

◆ Iso() [6/12]

template<FiniteFieldType MAIN, FiniteFieldType... OTHERS>

template<BelongsTo< OTHERS... > OTHER>

CECCO::Iso< MAIN, OTHERS >::Iso ( OTHER && other )

inlineconstexpr

Wrap an OTHERS rvalue by converting to MAIN.

Definition at line 3193 of file fields.hpp.

◆ Iso() [7/12]

template<FiniteFieldType MAIN, FiniteFieldType... OTHERS>

CECCO::Iso< MAIN, OTHERS >::Iso ( const Iso< MAIN, OTHERS > & other )

constexprdefaultnoexcept

◆ Iso() [8/12]

template<FiniteFieldType MAIN, FiniteFieldType... OTHERS>

CECCO::Iso< MAIN, OTHERS >::Iso ( Iso< MAIN, OTHERS > && other )

constexprdefaultnoexcept

◆ Iso() [9/12]

template<FiniteFieldType MAIN, FiniteFieldType... OTHERS>

template<FiniteFieldType T>

CECCO::Iso< MAIN, OTHERS >::Iso ( const Vector< T > & v )

Construct from a coefficient vector over a subfield T.

Template Parameters

T	Subfield type

Exceptions

std::invalid_argument if no representation in the Iso can be constructed from v

Tries MAIN first, then each of OTHERS until one succeeds. Round-trip correct with as_vector.

Definition at line 3729 of file fields.hpp.

◆ Iso() [10/12]

template<FiniteFieldType MAIN, FiniteFieldType... OTHERS>

template<FiniteFieldType B, MOD modulus, LutMode mode>

CECCO::Iso< MAIN, OTHERS >::Iso ( const Ext< B, modulus, mode > & other )

Cross-field conversion from an extension field.

Delegates to MAIN(Ext(...)) (or to an OTHERS representation when MAIN cannot reach the source directly), then stores the MAIN result. All paths supported by the Ext-from-Ext constructor are available: direct copy, isomorphism, upcast, downcast, cross-tower bridge.

Exceptions

std::invalid_argument if no conversion path exists (typically a downcast where the source value lies outside the target)

Definition at line 3481 of file fields.hpp.

◆ Iso() [11/12]

template<FiniteFieldType MAIN, FiniteFieldType... OTHERS>
requires SubfieldOf<Iso<MAIN, OTHERS...>, Fp<p>> && (!std::is_same_v<MAIN, Fp<p>>) && (!BelongsTo<Fp<p>, OTHERS...>)

template<uint16_t p>
requires SubfieldOf<Iso<MAIN, OTHERS...>, Fp<p>> && (!std::is_same_v<MAIN, Fp<p>>) && (!BelongsTo<Fp<p>, OTHERS...>)

CECCO::Iso< MAIN, OTHERS >::Iso ( const Fp< p > & other )

constexpr

Embed a prime-field element when 𝔽_p is a (possibly indirect) subfield of the Iso.

Picks the first of MAIN / OTHERS that contains 𝔽_p and embeds via the corresponding Embedding. The constraints rule out the trivial cases where 𝔽_p already appears literally as MAIN or one of OTHERS (those use the wrapping constructors above).

Definition at line 3553 of file fields.hpp.

◆ Iso() [12/12]

template<FiniteFieldType MAIN, FiniteFieldType... OTHERS>

template<FiniteFieldType OTHER_MAIN, FiniteFieldType... OTHER_OTHERS>

CECCO::Iso< MAIN, OTHERS >::Iso ( const Iso< OTHER_MAIN, OTHER_OTHERS... > & other )

Cross-field conversion from another Iso of the same characteristic.

Same four-way decision as the Ext cross-field constructor (direct isomorphism, upcast, downcast, or bridge via details::largest_common_subfield_t), but extended to handle every (MAIN, OTHERS...) pairing on both sides. Each side's representation tower is searched for the cheapest viable path.

Exceptions

std::invalid_argument on a downcast whose source value lies outside the target

Definition at line 3588 of file fields.hpp.

Member Function Documentation

◆ as()

template<FiniteFieldType MAIN, FiniteFieldType... OTHERS>
requires BelongsTo<TO, OTHERS...>

template<typename TO>
requires BelongsTo<TO, OTHERS...>

TO CECCO::Iso< MAIN, OTHERS >::as ( ) const

constexpr

Project to a specific representation by applying the cached Isomorphism.

Template Parameters

TO	Target representation, one of the OTHERS

Definition at line 3825 of file fields.hpp.

◆ as_vector()

template<FiniteFieldType MAIN, FiniteFieldType... OTHERS>
requires ((SubfieldOf<MAIN, T> || ((SubfieldOf<OTHERS, T>) || ...))) && (!std::is_same_v<Iso<MAIN, OTHERS...>, T>)

template<FiniteFieldType T>
requires ((SubfieldOf<MAIN, T> || ((SubfieldOf<OTHERS, T>) || ...))) && (!std::is_same_v<Iso<MAIN, OTHERS...>, T>)

Vector< T > CECCO::Iso< MAIN, OTHERS >::as_vector ( ) const

Coordinate vector over a subfield T of MAIN or any OTHERS representation.

Template Parameters

T	Subfield reachable from MAIN or one of OTHERS

Definition at line 3844 of file fields.hpp.

◆ erase()

template<FiniteFieldType MAIN, FiniteFieldType... OTHERS>

Iso< MAIN, OTHERS... > & CECCO::Iso< MAIN, OTHERS >::erase ( )

constexprnoexcept

Mark this element as erased (delegates to MAIN).

Warning: Erased elements must not participate in field arithmetic, see CECCO_ERASURE_SUPPORT.

Definition at line 3874 of file fields.hpp.

◆ get_additive_order()

template<FiniteFieldType MAIN, FiniteFieldType... OTHERS>

size_t CECCO::Iso< MAIN, OTHERS >::get_additive_order ( ) const

inline

Definition at line 3311 of file fields.hpp.

◆ get_characteristic()

template<FiniteFieldType MAIN, FiniteFieldType... OTHERS>

constexpr size_t CECCO::Iso< MAIN, OTHERS >::get_characteristic ( )

inlinestaticconstexprnoexcept

Definition at line 3375 of file fields.hpp.

◆ get_generator()

template<FiniteFieldType MAIN, FiniteFieldType... OTHERS>

constexpr Iso CECCO::Iso< MAIN, OTHERS >::get_generator ( )

inlinestaticconstexpr

Definition at line 3387 of file fields.hpp.

◆ get_info()

template<FiniteFieldType MAIN, FiniteFieldType... OTHERS>

std::string CECCO::Iso< MAIN, OTHERS >::get_info ( )

static

Definition at line 3837 of file fields.hpp.

◆ get_label()

template<FiniteFieldType MAIN, FiniteFieldType... OTHERS>

auto CECCO::Iso< MAIN, OTHERS >::get_label ( ) const

inlineconstexprnoexcept

Definition at line 3313 of file fields.hpp.

◆ get_m()

template<FiniteFieldType MAIN, FiniteFieldType... OTHERS>

constexpr size_t CECCO::Iso< MAIN, OTHERS >::get_m ( )

inlinestaticconstexprnoexcept

Definition at line 3381 of file fields.hpp.

◆ get_modulus()

template<FiniteFieldType MAIN, FiniteFieldType... OTHERS>

constexpr Polynomial< BASE_FIELD > CECCO::Iso< MAIN, OTHERS >::get_modulus ( )

inlinestaticconstexpr

Definition at line 3385 of file fields.hpp.

◆ get_multiplicative_order()

template<FiniteFieldType MAIN, FiniteFieldType... OTHERS>

size_t CECCO::Iso< MAIN, OTHERS >::get_multiplicative_order ( ) const

inline

Definition at line 3309 of file fields.hpp.

◆ get_p()

template<FiniteFieldType MAIN, FiniteFieldType... OTHERS>

constexpr size_t CECCO::Iso< MAIN, OTHERS >::get_p ( )

inlinestaticconstexprnoexcept

Definition at line 3377 of file fields.hpp.

◆ get_q()

template<FiniteFieldType MAIN, FiniteFieldType... OTHERS>

constexpr size_t CECCO::Iso< MAIN, OTHERS >::get_q ( )

inlinestaticconstexprnoexcept

Definition at line 3379 of file fields.hpp.

◆ get_size()

template<FiniteFieldType MAIN, FiniteFieldType... OTHERS>

constexpr size_t CECCO::Iso< MAIN, OTHERS >::get_size ( )

inlinestaticconstexprnoexcept

Definition at line 3383 of file fields.hpp.

◆ has_positive_sign()

template<FiniteFieldType MAIN, FiniteFieldType... OTHERS>

bool CECCO::Iso< MAIN, OTHERS >::has_positive_sign ( ) const

inlineconstexprnoexcept

Definition at line 3297 of file fields.hpp.

◆ is_constexpr_ready()

template<FiniteFieldType MAIN, FiniteFieldType... OTHERS>

constexpr bool CECCO::Iso< MAIN, OTHERS >::is_constexpr_ready ( )

inlinestaticconstexprnoexcept

Inherits constexpr-readiness from MAIN (OTHERS may differ; isomorphisms run at runtime).

Definition at line 3390 of file fields.hpp.

◆ is_erased()

template<FiniteFieldType MAIN, FiniteFieldType... OTHERS>

bool CECCO::Iso< MAIN, OTHERS >::is_erased ( ) const

inlineconstexprnoexcept

Test whether this element is currently erased.

Definition at line 3326 of file fields.hpp.

◆ is_zero()

template<FiniteFieldType MAIN, FiniteFieldType... OTHERS>

bool CECCO::Iso< MAIN, OTHERS >::is_zero ( ) const

inlineconstexprnoexcept

Definition at line 3295 of file fields.hpp.

◆ lut_add() [1/2]

template<FiniteFieldType MAIN, FiniteFieldType... OTHERS>

constexpr auto & CECCO::Iso< MAIN, OTHERS >::lut_add ( )

inlinestaticconstexpr

Definition at line 3397 of file fields.hpp.

◆ lut_add() [2/2]

template<FiniteFieldType MAIN, FiniteFieldType... OTHERS>

constexpr label_t CECCO::Iso< MAIN, OTHERS >::lut_add	(	label_t	a,
		label_t	b )

inlinestaticconstexpr

Definition at line 3407 of file fields.hpp.

◆ lut_inv() [1/2]

template<FiniteFieldType MAIN, FiniteFieldType... OTHERS>

constexpr auto & CECCO::Iso< MAIN, OTHERS >::lut_inv ( )

inlinestaticconstexpr

Definition at line 3403 of file fields.hpp.

◆ lut_inv() [2/2]

template<FiniteFieldType MAIN, FiniteFieldType... OTHERS>

constexpr label_t CECCO::Iso< MAIN, OTHERS >::lut_inv ( label_t a )

inlinestaticconstexpr

Definition at line 3413 of file fields.hpp.

◆ lut_mul() [1/2]

template<FiniteFieldType MAIN, FiniteFieldType... OTHERS>

constexpr auto & CECCO::Iso< MAIN, OTHERS >::lut_mul ( )

inlinestaticconstexpr

Definition at line 3401 of file fields.hpp.

◆ lut_mul() [2/2]

template<FiniteFieldType MAIN, FiniteFieldType... OTHERS>

constexpr label_t CECCO::Iso< MAIN, OTHERS >::lut_mul	(	label_t	a,
		label_t	b )

inlinestaticconstexpr

Definition at line 3409 of file fields.hpp.

◆ lut_neg() [1/2]

template<FiniteFieldType MAIN, FiniteFieldType... OTHERS>

constexpr auto & CECCO::Iso< MAIN, OTHERS >::lut_neg ( )

inlinestaticconstexpr

Definition at line 3399 of file fields.hpp.

◆ lut_neg() [2/2]

template<FiniteFieldType MAIN, FiniteFieldType... OTHERS>

constexpr label_t CECCO::Iso< MAIN, OTHERS >::lut_neg ( label_t a )

inlinestaticconstexpr

Definition at line 3411 of file fields.hpp.

◆ main()

template<FiniteFieldType MAIN, FiniteFieldType... OTHERS>

const MAIN & CECCO::Iso< MAIN, OTHERS >::main ( ) const

inlineconstexprnoexcept

Read-only access to the underlying MAIN-representation element.

Definition at line 3293 of file fields.hpp.

◆ operator!=() [1/2]

template<FiniteFieldType MAIN, FiniteFieldType... OTHERS>

bool CECCO::Iso< MAIN, OTHERS >::operator!= ( const Iso< MAIN, OTHERS > & other ) const

inlineconstexpr

Definition at line 3363 of file fields.hpp.

◆ operator!=() [2/2]

template<FiniteFieldType MAIN, FiniteFieldType... OTHERS>

bool CECCO::Iso< MAIN, OTHERS >::operator!= ( const MAIN & other ) const

inlineconstexpr

Definition at line 3365 of file fields.hpp.

◆ operator*=() [1/4]

template<FiniteFieldType MAIN, FiniteFieldType... OTHERS>

Iso< MAIN, OTHERS... > & CECCO::Iso< MAIN, OTHERS >::operator*= ( const Iso< MAIN, OTHERS > & other )

constexpr

*this *= other (delegates to MAIN)

Definition at line 3788 of file fields.hpp.

◆ operator*=() [2/4]

template<FiniteFieldType MAIN, FiniteFieldType... OTHERS>

template<typename OTHER>
requires BelongsTo<OTHER, OTHERS...>

Iso< MAIN, OTHERS... > & CECCO::Iso< MAIN, OTHERS >::operator*= ( const OTHER & other )

constexpr

Definition at line 3795 of file fields.hpp.

◆ operator*=() [3/4]

template<FiniteFieldType MAIN, FiniteFieldType... OTHERS>

template<typename OTHER>
requires BelongsTo<OTHER, OTHERS...>

Iso & CECCO::Iso< MAIN, OTHERS >::operator*= ( const OTHER & other )

constexpr

*this *= other after converting an OTHERS operand to MAIN

◆ operator*=() [4/4]

template<FiniteFieldType MAIN, FiniteFieldType... OTHERS>

Iso< MAIN, OTHERS... > & CECCO::Iso< MAIN, OTHERS >::operator*= ( int s )

constexpr

Scalar multiplication by an int (delegates to MAIN).

Definition at line 3803 of file fields.hpp.

◆ operator+=() [1/3]

template<FiniteFieldType MAIN, FiniteFieldType... OTHERS>

Iso< MAIN, OTHERS... > & CECCO::Iso< MAIN, OTHERS >::operator+= ( const Iso< MAIN, OTHERS > & other )

constexpr

*this += other (delegates to MAIN)

Definition at line 3758 of file fields.hpp.

◆ operator+=() [2/3]

template<FiniteFieldType MAIN, FiniteFieldType... OTHERS>

template<typename OTHER>
requires BelongsTo<OTHER, OTHERS...>

Iso< MAIN, OTHERS... > & CECCO::Iso< MAIN, OTHERS >::operator+= ( const OTHER & other )

constexpr

Definition at line 3765 of file fields.hpp.

◆ operator+=() [3/3]

template<FiniteFieldType MAIN, FiniteFieldType... OTHERS>

template<typename OTHER>
requires BelongsTo<OTHER, OTHERS...>

Iso & CECCO::Iso< MAIN, OTHERS >::operator+= ( const OTHER & other )

constexpr

*this += other after converting an OTHERS operand to MAIN

◆ operator-()

template<FiniteFieldType MAIN, FiniteFieldType... OTHERS>

Iso CECCO::Iso< MAIN, OTHERS >::operator- ( ) const

inlineconstexpr

Additive inverse (delegates to MAIN).

Definition at line 3250 of file fields.hpp.

◆ operator-=() [1/3]

template<FiniteFieldType MAIN, FiniteFieldType... OTHERS>

Iso< MAIN, OTHERS... > & CECCO::Iso< MAIN, OTHERS >::operator-= ( const Iso< MAIN, OTHERS > & other )

constexpr

*this -= other (delegates to MAIN)

Definition at line 3773 of file fields.hpp.

◆ operator-=() [2/3]

template<FiniteFieldType MAIN, FiniteFieldType... OTHERS>

template<typename OTHER>
requires BelongsTo<OTHER, OTHERS...>

Iso< MAIN, OTHERS... > & CECCO::Iso< MAIN, OTHERS >::operator-= ( const OTHER & other )

constexpr

Definition at line 3780 of file fields.hpp.

◆ operator-=() [3/3]

template<FiniteFieldType MAIN, FiniteFieldType... OTHERS>

template<typename OTHER>
requires BelongsTo<OTHER, OTHERS...>

Iso & CECCO::Iso< MAIN, OTHERS >::operator-= ( const OTHER & other )

constexpr

*this -= other after converting an OTHERS operand to MAIN

◆ operator/=() [1/3]

template<FiniteFieldType MAIN, FiniteFieldType... OTHERS>

Iso< MAIN, OTHERS... > & CECCO::Iso< MAIN, OTHERS >::operator/= ( const Iso< MAIN, OTHERS > & other )

*this /= other; throws std::invalid_argument if other is zero

Definition at line 3809 of file fields.hpp.

◆ operator/=() [2/3]

template<FiniteFieldType MAIN, FiniteFieldType... OTHERS>

template<typename OTHER>
requires BelongsTo<OTHER, OTHERS...>

Iso< MAIN, OTHERS... > & CECCO::Iso< MAIN, OTHERS >::operator/= ( const OTHER & other )

Definition at line 3816 of file fields.hpp.

◆ operator/=() [3/3]

template<FiniteFieldType MAIN, FiniteFieldType... OTHERS>

template<typename OTHER>
requires BelongsTo<OTHER, OTHERS...>

Iso & CECCO::Iso< MAIN, OTHERS >::operator/= ( const OTHER & other )

*this /= other after converting an OTHERS operand to MAIN; same exception

◆ operator=() [1/12]

template<FiniteFieldType MAIN, FiniteFieldType... OTHERS>

template<FiniteFieldType B, MOD ext_modulus, LutMode mode>

Iso< MAIN, OTHERS... > & CECCO::Iso< MAIN, OTHERS >::operator= ( const Ext< B, ext_modulus, mode > & other )

Definition at line 3462 of file fields.hpp.

◆ operator=() [2/12]

template<FiniteFieldType MAIN, FiniteFieldType... OTHERS>

template<FiniteFieldType B, MOD ext_modulus, LutMode mode>

Iso & CECCO::Iso< MAIN, OTHERS >::operator= ( const Ext< B, ext_modulus, mode > & other )

Assign from an Ext of matching characteristic (copy-and-swap).

◆ operator=() [3/12]

template<FiniteFieldType MAIN, FiniteFieldType... OTHERS>

template<uint16_t p>

Iso< MAIN, OTHERS... > & CECCO::Iso< MAIN, OTHERS >::operator= ( const Fp< p > & other )

Definition at line 3453 of file fields.hpp.

◆ operator=() [4/12]

template<FiniteFieldType MAIN, FiniteFieldType... OTHERS>

template<uint16_t p>

Iso & CECCO::Iso< MAIN, OTHERS >::operator= ( const Fp< p > & other )

Assign from an Fp of matching characteristic (copy-and-swap).

◆ operator=() [5/12]

template<FiniteFieldType MAIN, FiniteFieldType... OTHERS>

Iso & CECCO::Iso< MAIN, OTHERS >::operator= ( const Iso< MAIN, OTHERS > & other )

constexprdefault

◆ operator=() [6/12]

template<FiniteFieldType MAIN, FiniteFieldType... OTHERS>

template<FiniteFieldType OTHER_MAIN, FiniteFieldType... OTHER_OTHERS>
requires (OTHER_MAIN::get_characteristic() == MAIN::get_characteristic()) && (!std::is_same_v<Iso<OTHER_MAIN, OTHER_OTHERS...>, Iso<MAIN, OTHERS...>>)

Iso< MAIN, OTHERS... > & CECCO::Iso< MAIN, OTHERS >::operator= ( const Iso< OTHER_MAIN, OTHER_OTHERS... > & other )

Definition at line 3470 of file fields.hpp.

◆ operator=() [7/12]

template<FiniteFieldType MAIN, FiniteFieldType... OTHERS>

template<FiniteFieldType OTHER_MAIN, FiniteFieldType... OTHER_OTHERS>
requires (OTHER_MAIN::get_characteristic() == MAIN::get_characteristic()) && (!std::is_same_v<Iso<OTHER_MAIN, OTHER_OTHERS...>, Iso<MAIN, OTHERS...>>)

Iso & CECCO::Iso< MAIN, OTHERS >::operator= ( const Iso< OTHER_MAIN, OTHER_OTHERS... > & other )

Assign from another Iso of matching characteristic (copy-and-swap).

◆ operator=() [8/12]

template<FiniteFieldType MAIN, FiniteFieldType... OTHERS>

Iso< MAIN, OTHERS... > & CECCO::Iso< MAIN, OTHERS >::operator= ( const MAIN & other )

constexpr

Assign a MAIN-representation element directly.

Definition at line 3429 of file fields.hpp.

◆ operator=() [9/12]

template<FiniteFieldType MAIN, FiniteFieldType... OTHERS>

template<typename OTHER>
requires BelongsTo<OTHER, OTHERS...>

Iso< MAIN, OTHERS... > & CECCO::Iso< MAIN, OTHERS >::operator= ( const OTHER & other )

Definition at line 3442 of file fields.hpp.

◆ operator=() [10/12]

template<FiniteFieldType MAIN, FiniteFieldType... OTHERS>

template<typename OTHER>
requires BelongsTo<OTHER, OTHERS...>

Iso & CECCO::Iso< MAIN, OTHERS >::operator= ( const OTHER & other )

Assign from an OTHERS representation (copy-and-swap; same semantics as the constructor).

◆ operator=() [11/12]

template<FiniteFieldType MAIN, FiniteFieldType... OTHERS>

Iso< MAIN, OTHERS... > & CECCO::Iso< MAIN, OTHERS >::operator= ( int other )

constexpr

Assign a signed element label via MAIN.

Definition at line 3435 of file fields.hpp.

◆ operator=() [12/12]

template<FiniteFieldType MAIN, FiniteFieldType... OTHERS>

Iso & CECCO::Iso< MAIN, OTHERS >::operator= ( Iso< MAIN, OTHERS > && other )

constexprdefaultnoexcept

◆ operator==() [1/2]

template<FiniteFieldType MAIN, FiniteFieldType... OTHERS>

bool CECCO::Iso< MAIN, OTHERS >::operator== ( const Iso< MAIN, OTHERS > & other ) const

inlineconstexprnoexcept

Definition at line 3359 of file fields.hpp.

◆ operator==() [2/2]

template<FiniteFieldType MAIN, FiniteFieldType... OTHERS>

bool CECCO::Iso< MAIN, OTHERS >::operator== ( const MAIN & other ) const

inlineconstexprnoexcept

Definition at line 3361 of file fields.hpp.

◆ randomize()

template<FiniteFieldType MAIN, FiniteFieldType... OTHERS>

Iso & CECCO::Iso< MAIN, OTHERS >::randomize ( )

inlineconstexpr

Definition at line 3299 of file fields.hpp.

◆ randomize_force_change()

template<FiniteFieldType MAIN, FiniteFieldType... OTHERS>

Iso & CECCO::Iso< MAIN, OTHERS >::randomize_force_change ( )

inlineconstexpr

Definition at line 3304 of file fields.hpp.

◆ ready()

template<FiniteFieldType MAIN, FiniteFieldType... OTHERS>

constexpr bool CECCO::Iso< MAIN, OTHERS >::ready ( )

inlinestaticconstexpr

Definition at line 3393 of file fields.hpp.

◆ unerase()

template<FiniteFieldType MAIN, FiniteFieldType... OTHERS>

Iso< MAIN, OTHERS... > & CECCO::Iso< MAIN, OTHERS >::unerase ( )

constexprnoexcept

Clear the erasure flag, resetting MAIN to its additive identity.

Definition at line 3880 of file fields.hpp.

◆ operator<<

template<FiniteFieldType MAIN, FiniteFieldType... OTHERS>

std::ostream & operator<<	(	std::ostream &	os,
		const Iso< MAIN, OTHERS > &	iso )

friend

Definition at line 3370 of file fields.hpp.

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

Public Types

Public Member Functions

Static Public Member Functions

Friends

Additional Inherited Members

Detailed Description

Usage_Example

Member Typedef Documentation

◆ BASE_FIELD

◆ label_t

Constructor & Destructor Documentation

◆ Iso() [1/12]

◆ Iso() [2/12]

◆ Iso() [3/12]

◆ Iso() [4/12]

◆ Iso() [5/12]

◆ Iso() [6/12]

◆ Iso() [7/12]

◆ Iso() [8/12]

◆ Iso() [9/12]

◆ Iso() [10/12]

◆ Iso() [11/12]

◆ Iso() [12/12]

Member Function Documentation

◆ as()

◆ as_vector()

◆ erase()

◆ get_additive_order()

◆ get_characteristic()

◆ get_generator()

◆ get_info()

◆ get_label()

◆ get_m()

◆ get_modulus()

◆ get_multiplicative_order()

◆ get_p()

◆ get_q()

◆ get_size()

◆ has_positive_sign()

◆ is_constexpr_ready()

◆ is_erased()

◆ is_zero()

◆ lut_add() [1/2]

◆ lut_add() [2/2]

◆ lut_inv() [1/2]

◆ lut_inv() [2/2]

◆ lut_mul() [1/2]

◆ lut_mul() [2/2]

◆ lut_neg() [1/2]

◆ lut_neg() [2/2]

◆ main()

◆ operator!=() [1/2]

◆ operator!=() [2/2]

◆ operator*=() [1/4]

◆ operator*=() [2/4]

◆ operator*=() [3/4]

◆ operator*=() [4/4]

◆ operator+=() [1/3]

◆ operator+=() [2/3]

◆ operator+=() [3/3]

◆ operator-()

◆ operator-=() [1/3]

◆ operator-=() [2/3]

◆ operator-=() [3/3]

◆ operator/=() [1/3]

◆ operator/=() [2/3]

◆ operator/=() [3/3]

◆ operator=() [1/12]

◆ operator=() [2/12]

◆ operator=() [3/12]

◆ operator=() [4/12]

◆ operator=() [5/12]

◆ operator=() [6/12]

◆ operator=() [7/12]

◆ operator=() [8/12]

◆ operator=() [9/12]

◆ operator=() [10/12]

◆ operator=() [11/12]

◆ operator=() [12/12]

◆ operator==() [1/2]