bb::Univariate< Fr, domain_end > Class Template Reference

A univariate polynomial represented by its values on {0, 1,..., domain_end - 1}. More...

#include <univariate.hpp>

Public Types
using	View = UnivariateView< Fr, domain_end >
using	CoefficientAccumulator = UnivariateCoefficientBasis< Fr, MONOMIAL_LENGTH, true >
using	value_type = Fr

Public Member Functions
	Univariate ()=default
	Univariate (const std::array< Fr, LENGTH > &evaluations)
	~Univariate ()=default
	Univariate (const Univariate &other)=default
	Univariate (Univariate &&other) noexcept=default
Univariate &	operator= (const Univariate &other)=default
Univariate &	operator= (Univariate &&other) noexcept=default
	operator UnivariateCoefficientBasis< Fr, 2, true > () const
template<bool has_a0_plus_a1>
	Univariate (const UnivariateCoefficientBasis< Fr, 2, has_a0_plus_a1 > &monomial)
template<bool has_a0_plus_a1>
	Univariate (const UnivariateCoefficientBasis< Fr, 3, has_a0_plus_a1 > &monomial)
	Univariate (const Fr &value)
	Univariate (const UnivariateView< Fr, domain_end > &in)
Fr &	value_at (size_t i)
const Fr &	value_at (size_t i) const
size_t	size ()
bool	is_zero () const
std::vector< uint8_t >	to_buffer () const
bool	operator== (const Univariate &other) const =default
Univariate &	operator+= (const Univariate &other)
Univariate &	operator-= (const Univariate &other)
Univariate &	operator*= (const Univariate &other)
Univariate &	self_sqr ()
Univariate	operator+ (const Univariate &other) const
Univariate	operator- (const Univariate &other) const
Univariate	operator- () const
Univariate	operator* (const Univariate &other) const
Univariate	sqr () const
Univariate &	operator+= (const Fr &scalar)
Univariate &	operator-= (const Fr &scalar)
Univariate &	operator*= (const Fr &scalar)
Univariate	operator+ (const Fr &scalar) const
Univariate	operator- (const Fr &scalar) const
Univariate	operator* (const Fr &scalar) const
Univariate &	operator+= (const UnivariateView< Fr, domain_end > &view)
Univariate &	operator-= (const UnivariateView< Fr, domain_end > &view)
Univariate &	operator*= (const UnivariateView< Fr, domain_end > &view)
Univariate	operator+ (const UnivariateView< Fr, domain_end > &view) const
Univariate	operator- (const UnivariateView< Fr, domain_end > &view) const
Univariate	operator* (const UnivariateView< Fr, domain_end > &view) const
template<size_t EXTENDED_DOMAIN_END> requires (domain_end == 2)
	operator Univariate< Fr, EXTENDED_DOMAIN_END > ()
template<size_t EXTENDED_DOMAIN_END>
Univariate< Fr, EXTENDED_DOMAIN_END >	extend_to () const
	Given a univariate f represented by {f(0), ..., f(domain_end - 1)}, compute the evaluations {f(domain_end),..., f(extended_domain_end -1)} and return the Univariate represented by {f(0),..., f(extended_domain_end -1)}.
template<size_t INITIAL_LENGTH>
void	self_extend_from ()
	Compute the evaluations of the polynomial from the INITIAL_LENGTH up to the total LENGTH. Currently only supports INITIAL_LENGTH = 2.
Fr	evaluate (const Fr &u) const
	Evaluate a univariate at a point u not known at compile time and assumed not to be in the domain (else we divide by zero).
auto	begin ()
auto	begin () const
auto	end ()
auto	end () const

Static Public Member Functions
static Univariate	serialize_from_buffer (uint8_t const *buffer)
static Univariate	get_random ()
static Univariate	zero ()

Public Attributes
std::array< Fr, LENGTH >	evaluations

Static Public Attributes
static constexpr size_t	LENGTH = domain_end
static constexpr size_t	MONOMIAL_LENGTH = LENGTH > 1 ? 2 : 1

Friends
std::ostream &	operator<< (std::ostream &os, const Univariate &u)

Detailed Description

template<class Fr, size_t domain_end>
class bb::Univariate< Fr, domain_end >

A univariate polynomial represented by its values on {0, 1,..., domain_end - 1}.

Definition at line 32 of file univariate.hpp.

Member Typedef Documentation

CoefficientAccumulator

template<class Fr , size_t domain_end>

using bb::Univariate< Fr, domain_end >::CoefficientAccumulator = UnivariateCoefficientBasis<Fr, MONOMIAL_LENGTH, true>

Definition at line 37 of file univariate.hpp.

value_type

template<class Fr , size_t domain_end>

using bb::Univariate< Fr, domain_end >::value_type = Fr

Definition at line 39 of file univariate.hpp.

View

template<class Fr , size_t domain_end>

using bb::Univariate< Fr, domain_end >::View = UnivariateView<Fr, domain_end>

Definition at line 35 of file univariate.hpp.

Constructor & Destructor Documentation

Univariate() [1/8]

template<class Fr , size_t domain_end>

bb::Univariate< Fr, domain_end >::Univariate ( )

default

Univariate() [2/8]

template<class Fr , size_t domain_end>

bb::Univariate< Fr, domain_end >::Univariate ( const std::array< Fr, LENGTH > &  evaluations )

inlineexplicit

Definition at line 45 of file univariate.hpp.

~Univariate()

template<class Fr , size_t domain_end>

bb::Univariate< Fr, domain_end >::~Univariate ( )

default

Univariate() [3/8]

template<class Fr , size_t domain_end>

bb::Univariate< Fr, domain_end >::Univariate ( const Univariate< Fr, domain_end > &  other )

default

Univariate() [4/8]

template<class Fr , size_t domain_end>

bb::Univariate< Fr, domain_end >::Univariate ( Univariate< Fr, domain_end > &&  other )

defaultnoexcept

Univariate() [5/8]

template<class Fr , size_t domain_end>

template<bool has_a0_plus_a1>

bb::Univariate< Fr, domain_end >::Univariate ( const UnivariateCoefficientBasis< Fr, 2, has_a0_plus_a1 > &  monomial )

inline

Definition at line 67 of file univariate.hpp.

Univariate() [6/8]

template<class Fr , size_t domain_end>

template<bool has_a0_plus_a1>

bb::Univariate< Fr, domain_end >::Univariate ( const UnivariateCoefficientBasis< Fr, 3, has_a0_plus_a1 > &  monomial )

inline

Definition at line 80 of file univariate.hpp.

Univariate() [7/8]

template<class Fr , size_t domain_end>

bb::Univariate< Fr, domain_end >::Univariate ( const Fr &  value )

inlineexplicit

Definition at line 98 of file univariate.hpp.

Univariate() [8/8]

template<class Fr , size_t domain_end>

bb::Univariate< Fr, domain_end >::Univariate ( const UnivariateView< Fr, domain_end > &  in )

inlineexplicit

Definition at line 106 of file univariate.hpp.

Member Function Documentation

begin() [1/2]

template<class Fr , size_t domain_end>

auto bb::Univariate< Fr, domain_end >::begin ( )

inline

Definition at line 533 of file univariate.hpp.

begin() [2/2]

template<class Fr , size_t domain_end>

auto bb::Univariate< Fr, domain_end >::begin ( ) const

inline

Definition at line 534 of file univariate.hpp.

end() [1/2]

template<class Fr , size_t domain_end>

auto bb::Univariate< Fr, domain_end >::end ( )

inline

Definition at line 536 of file univariate.hpp.

end() [2/2]

template<class Fr , size_t domain_end>

auto bb::Univariate< Fr, domain_end >::end ( ) const

inline

Definition at line 537 of file univariate.hpp.

evaluate()

template<class Fr , size_t domain_end>

Fr bb::Univariate< Fr, domain_end >::evaluate ( const Fr &  u ) const

inline

Evaluate a univariate at a point u not known at compile time and assumed not to be in the domain (else we divide by zero).

Parameters

f

Returns

Fr

Definition at line 502 of file univariate.hpp.

extend_to()

template<class Fr , size_t domain_end>

template<size_t EXTENDED_DOMAIN_END>

Univariate< Fr, EXTENDED_DOMAIN_END > bb::Univariate< Fr, domain_end >::extend_to ( ) const

inline

Given a univariate f represented by {f(0), ..., f(domain_end - 1)}, compute the evaluations {f(domain_end),..., f(extended_domain_end -1)} and return the Univariate represented by {f(0),..., f(extended_domain_end -1)}.

Write v_i = f(x_i) on the domain {x_0, ..., x_{domain_end-1}}. To efficiently compute the needed values of f, we use the barycentric formula

• f(x) = B(x) Σ_{i=0}^{domain_end-1} v_i / (d_i*(x-x_i)) where
• B(x) = Π_{i=0}^{domain_end-1} (x-x_i)
• d_i = Π_{j ∈ {0, ..., domain_end-1}, j≠i} (x_i-x_j) for i ∈ {0, ..., domain_end-1}

When the domain size is two, extending f = v0(1-X) + v1X to a new value involves just one addition and a subtraction: setting Δ = v1-v0, the values of f(X) are f(0)=v0, f(1)= v0 + Δ, v2 = f(1) + Δ, v3 = f(2) + Δ...

Definition at line 351 of file univariate.hpp.

get_random()

template<class Fr , size_t domain_end>

static Univariate bb::Univariate< Fr, domain_end >::get_random ( )

inlinestatic

Definition at line 142 of file univariate.hpp.

is_zero()

template<class Fr , size_t domain_end>

bool bb::Univariate< Fr, domain_end >::is_zero ( ) const

inline

Definition at line 119 of file univariate.hpp.

operator Univariate< Fr, EXTENDED_DOMAIN_END >()

template<class Fr , size_t domain_end>

template<size_t EXTENDED_DOMAIN_END>
requires (domain_end == 2)

bb::Univariate< Fr, domain_end >::operator Univariate< Fr, EXTENDED_DOMAIN_END > ( )

inlineexplicit

Definition at line 328 of file univariate.hpp.

operator UnivariateCoefficientBasis< Fr, 2, true >()

template<class Fr , size_t domain_end>

bb::Univariate< Fr, domain_end >::operator UnivariateCoefficientBasis< Fr, 2, true > ( ) const

inlineexplicit

Definition at line 54 of file univariate.hpp.

operator*() [1/3]

template<class Fr , size_t domain_end>

Univariate bb::Univariate< Fr, domain_end >::operator* ( const Fr &  scalar ) const

inline

Definition at line 258 of file univariate.hpp.

operator*() [2/3]

template<class Fr , size_t domain_end>

Univariate bb::Univariate< Fr, domain_end >::operator* ( const Univariate< Fr, domain_end > &  other ) const

inline

Definition at line 206 of file univariate.hpp.

operator*() [3/3]

template<class Fr , size_t domain_end>

Univariate bb::Univariate< Fr, domain_end >::operator* ( const UnivariateView< Fr, domain_end > &  view ) const

inline

Definition at line 304 of file univariate.hpp.

operator*=() [1/3]

template<class Fr , size_t domain_end>

Univariate & bb::Univariate< Fr, domain_end >::operator*= ( const Fr &  scalar )

inline

Definition at line 236 of file univariate.hpp.

operator*=() [2/3]

template<class Fr , size_t domain_end>

Univariate & bb::Univariate< Fr, domain_end >::operator*= ( const Univariate< Fr, domain_end > &  other )

inline

Definition at line 170 of file univariate.hpp.

operator*=() [3/3]

template<class Fr , size_t domain_end>

Univariate & bb::Univariate< Fr, domain_end >::operator*= ( const UnivariateView< Fr, domain_end > &  view )

inline

Definition at line 282 of file univariate.hpp.

operator+() [1/3]

template<class Fr , size_t domain_end>

Univariate bb::Univariate< Fr, domain_end >::operator+ ( const Fr &  scalar ) const

inline

Definition at line 244 of file univariate.hpp.

operator+() [2/3]

template<class Fr , size_t domain_end>

Univariate bb::Univariate< Fr, domain_end >::operator+ ( const Univariate< Fr, domain_end > &  other ) const

inline

Definition at line 184 of file univariate.hpp.

operator+() [3/3]

template<class Fr , size_t domain_end>

Univariate bb::Univariate< Fr, domain_end >::operator+ ( const UnivariateView< Fr, domain_end > &  view ) const

inline

Definition at line 290 of file univariate.hpp.

operator+=() [1/3]

template<class Fr , size_t domain_end>

Univariate & bb::Univariate< Fr, domain_end >::operator+= ( const Fr &  scalar )

inline

Definition at line 221 of file univariate.hpp.

operator+=() [2/3]

template<class Fr , size_t domain_end>

Univariate & bb::Univariate< Fr, domain_end >::operator+= ( const Univariate< Fr, domain_end > &  other )

inline

Definition at line 156 of file univariate.hpp.

operator+=() [3/3]

template<class Fr , size_t domain_end>

Univariate & bb::Univariate< Fr, domain_end >::operator+= ( const UnivariateView< Fr, domain_end > &  view )

inline

Definition at line 266 of file univariate.hpp.

operator-() [1/4]

template<class Fr , size_t domain_end>

Univariate bb::Univariate< Fr, domain_end >::operator- ( ) const

inline

Definition at line 197 of file univariate.hpp.

operator-() [2/4]

template<class Fr , size_t domain_end>

Univariate bb::Univariate< Fr, domain_end >::operator- ( const Fr &  scalar ) const

inline

Definition at line 251 of file univariate.hpp.

operator-() [3/4]

template<class Fr , size_t domain_end>

Univariate bb::Univariate< Fr, domain_end >::operator- ( const Univariate< Fr, domain_end > &  other ) const

inline

Definition at line 191 of file univariate.hpp.

operator-() [4/4]

template<class Fr , size_t domain_end>

Univariate bb::Univariate< Fr, domain_end >::operator- ( const UnivariateView< Fr, domain_end > &  view ) const

inline

Definition at line 297 of file univariate.hpp.

operator-=() [1/3]

template<class Fr , size_t domain_end>

Univariate & bb::Univariate< Fr, domain_end >::operator-= ( const Fr &  scalar )

inline

Definition at line 229 of file univariate.hpp.

operator-=() [2/3]

template<class Fr , size_t domain_end>

Univariate & bb::Univariate< Fr, domain_end >::operator-= ( const Univariate< Fr, domain_end > &  other )

inline

Definition at line 163 of file univariate.hpp.

operator-=() [3/3]

template<class Fr , size_t domain_end>

Univariate & bb::Univariate< Fr, domain_end >::operator-= ( const UnivariateView< Fr, domain_end > &  view )

inline

Definition at line 274 of file univariate.hpp.

operator=() [1/2]

template<class Fr , size_t domain_end>

Univariate & bb::Univariate< Fr, domain_end >::operator= ( const Univariate< Fr, domain_end > &  other )

default

operator=() [2/2]

template<class Fr , size_t domain_end>

Univariate & bb::Univariate< Fr, domain_end >::operator= ( Univariate< Fr, domain_end > &&  other )

defaultnoexcept

operator==()

template<class Fr , size_t domain_end>

bool bb::Univariate< Fr, domain_end >::operator== ( const Univariate< Fr, domain_end > &  other ) const

default

self_extend_from()

template<class Fr , size_t domain_end>

template<size_t INITIAL_LENGTH>

void bb::Univariate< Fr, domain_end >::self_extend_from ( )

inline

Compute the evaluations of the polynomial from the INITIAL_LENGTH up to the total LENGTH. Currently only supports INITIAL_LENGTH = 2.

Template Parameters

INITIAL_LENGTH

Definition at line 482 of file univariate.hpp.

self_sqr()

template<class Fr , size_t domain_end>

Univariate & bb::Univariate< Fr, domain_end >::self_sqr ( )

inline

Definition at line 177 of file univariate.hpp.

serialize_from_buffer()

template<class Fr , size_t domain_end>

static Univariate bb::Univariate< Fr, domain_end >::serialize_from_buffer ( uint8_t const *  buffer )

inlinestatic

Definition at line 135 of file univariate.hpp.

size()

template<class Fr , size_t domain_end>

size_t bb::Univariate< Fr, domain_end >::size ( )

inline

Definition at line 116 of file univariate.hpp.

sqr()

template<class Fr , size_t domain_end>

Univariate bb::Univariate< Fr, domain_end >::sqr ( ) const

inline

Definition at line 213 of file univariate.hpp.

to_buffer()

template<class Fr , size_t domain_end>

std::vector< uint8_t > bb::Univariate< Fr, domain_end >::to_buffer ( ) const

inline

Definition at line 130 of file univariate.hpp.

value_at() [1/2]

template<class Fr , size_t domain_end>

Fr & bb::Univariate< Fr, domain_end >::value_at ( size_t  i )

inline

Definition at line 114 of file univariate.hpp.

value_at() [2/2]

template<class Fr , size_t domain_end>

const Fr & bb::Univariate< Fr, domain_end >::value_at ( size_t  i ) const

inline

Definition at line 115 of file univariate.hpp.

zero()

template<class Fr , size_t domain_end>

static Univariate bb::Univariate< Fr, domain_end >::zero ( )

inlinestatic

Definition at line 151 of file univariate.hpp.

Friends And Related Symbol Documentation

operator<<

template<class Fr , size_t domain_end>

std::ostream & operator<< ( std::ostream &  os, const Univariate< Fr, domain_end > &  u  )

friend

Definition at line 312 of file univariate.hpp.

Member Data Documentation

evaluations

template<class Fr , size_t domain_end>

std::array<Fr, LENGTH> bb::Univariate< Fr, domain_end >::evaluations

Definition at line 41 of file univariate.hpp.

LENGTH

template<class Fr , size_t domain_end>

constexpr size_t bb::Univariate< Fr, domain_end >::LENGTH = domain_end

staticconstexpr

Definition at line 34 of file univariate.hpp.

MONOMIAL_LENGTH

template<class Fr , size_t domain_end>

constexpr size_t bb::Univariate< Fr, domain_end >::MONOMIAL_LENGTH = LENGTH > 1 ? 2 : 1

staticconstexpr

Definition at line 36 of file univariate.hpp.

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

• src/barretenberg/polynomials/univariate.hpp