Structured polynomial class that represents the coefficients 'a' of a_0 + a_1 x ... a_n x^n of a finite field polynomial equation of degree that is at most the size of some zk circuit. Past 'n' it has a virtual size where it conceptually has coefficients all equal to 0. Notably, we allow indexing past 'n' up to our virtual size (checked only in a debug build, however). As well, we have a start index that means coefficients before start_index are also considered to be 0. The polynomial is used to represent the gates of our arithmetized zk programs. Polynomials use the majority of the memory in proving, so caution should be used in making sure unnecessary copies are avoided, both for avoiding unnecessary memory usage and performance due to unnecessary allocations. The polynomial has a maximum degree in the underlying SharedShiftedVirtualZeroesArray, dictated by the circuit size, this is just used for debugging as we represent. More...

#include <polynomial.hpp>

Public Types
enum class	DontZeroMemory { FLAG }

using	FF = Fr

Public Member Functions
	Polynomial (size_t size, size_t virtual_size, size_t start_index=0)
	Initialize a Polynomial to size 'size', zeroing memory.

	Polynomial (size_t size)

	Polynomial (size_t size, size_t virtual_size, size_t start_index, DontZeroMemory flag)
	Initialize a Polynomial to size 'size'. Important: This does NOT zero memory.

	Polynomial (size_t size, size_t virtual_size, DontZeroMemory flag)

	Polynomial (size_t size, DontZeroMemory flag)

	Polynomial (const Polynomial &other)

	Polynomial (const Polynomial &other, size_t target_size)

	Polynomial (Polynomial &&other) noexcept=default

	Polynomial (std::span< const Fr > coefficients, size_t virtual_size)

	Polynomial (std::span< const Fr > coefficients)

	Polynomial ()=default

	Polynomial (std::span< const Fr > interpolation_points, std::span< const Fr > evaluations, size_t virtual_size)
	Create the degree-(m-1) polynomial T(X) that interpolates the given evaluations. We have T(xⱼ) = yⱼ for j=1,...,m.

Polynomial &	operator= (Polynomial &&other) noexcept=default

Polynomial &	operator= (const Polynomial &other)

	~Polynomial ()=default

Polynomial	share () const

void	clear ()

bool	is_zero () const
	Check whether or not a polynomial is identically zero.

bool	operator== (Polynomial const &rhs) const

const Fr &	get (size_t i, size_t virtual_padding=0) const
	Retrieves the value at the specified index.

bool	is_empty () const

Polynomial	shifted () const
	Returns a Polynomial the left-shift of self.

Polynomial	right_shifted (const size_t magnitude) const
	Returns a Polynomial equal to the right-shift-by-magnitude of self.

Polynomial	reverse () const
	Returns the polynomial equal to the reverse of self.

Fr	evaluate_mle (std::span< const Fr > evaluation_points, bool shift=false) const
	evaluate multi-linear extension p(X_0,…,X_{n-1}) = \sum_i a_iL_i(X_0,…,X_{n-1}) at u = (u_0,…,u_{n-1}) If the polynomial is embedded into a lower dimension k<n, i.e, start_index + size <= 2^k, we evaluate it in a more efficient way. Note that a_j == 0 for any j >= 2^k. We fold over k dimensions and then multiply the result by (1 - u_k) (1 - u_{k+1}) ... * (1 - u_{n-1}). In this case, for any i < 2^k, L_i is a multiple of (1 - X_k) * (1 - X_{k+1}) ... * (1 - X_{n-1}). Dividing p by this monomial leads to a multilinear extension over variables X_0, X_1, ..X_{k-1}.

Fr	compute_barycentric_evaluation (const Fr &z, const EvaluationDomain< Fr > &domain)

void	factor_roots (const Fr &root)
	Divides p(X) by (X-r) in-place. Assumes that p(rⱼ)=0 for all j.

Fr	evaluate (const Fr &z, size_t target_size) const

Fr	evaluate (const Fr &z) const

void	add_scaled (PolynomialSpan< const Fr > other, Fr scaling_factor) &
	adds the polynomial q(X) 'other', multiplied by a scaling factor.

void	add_scaled_chunk (const ThreadChunk &chunk, PolynomialSpan< const Fr > other, Fr scaling_factor) &

Polynomial &	operator+= (PolynomialSpan< const Fr > other)
	adds the polynomial q(X) 'other'.

Polynomial &	operator-= (PolynomialSpan< const Fr > other)
	subtracts the polynomial q(X) 'other'.

Polynomial &	operator*= (Fr scaling_factor)
	sets this = p(X) to s⋅p(X)

void	multiply_chunk (const ThreadChunk &chunk, Fr scaling_factor)

void	mask ()
	Add random values to the coefficients of a polynomial. In practice, this is used for ensuring the commitment and evaluation of a polynomial don't leak information about the coefficients in the context of zero knowledge.

std::size_t	size () const

std::size_t	virtual_size () const

void	increase_virtual_size (const size_t size_in)

Fr *	data ()

const Fr *	data () const

Fr &	at (size_t index)
	Our mutable accessor, unlike operator[]. We abuse precedent a bit to differentiate at() and operator[] as mutable and immutable, respectively. This means at() can only index within start_index()..end_index() unlike operator[] which can index 0..virtual_size.

const Fr &	at (size_t index) const

const Fr &	operator[] (size_t i)

const Fr &	operator[] (size_t i) const

void	shrink_end_index (const size_t new_end_index)
	The end_index of the polynomial is decreased without any memory de-allocation. This is a very fast way to zeroize the polynomial tail from new_end_index to the end. It also means that the new end_index might be smaller than the backed memory.

Polynomial	full () const
	Copys the polynomial, but with the whole address space usable. The value of the polynomial remains the same, but defined memory region differs.

size_t	start_index () const

size_t	end_index () const

std::span< Fr >	coeffs (size_t offset=0)
	Strictly iterates the defined region of the polynomial. We keep this explicit, instead of having an implicit conversion to span. This is safer as it is more likely that we need to consider our start_index() along with the span, as in PolynomialSpan below.

std::span< const Fr >	coeffs (size_t offset=0) const

	operator PolynomialSpan< Fr > ()
	Convert to an std::span bundled with our start index.

	operator PolynomialSpan< const Fr > () const
	Convert to an std::span bundled with our start index.

auto	indices () const

auto	indexed_values ()

auto	indexed_values () const

bool	is_valid_set_index (size_t index) const
	Is this index valid for a set? i.e. calling poly.at(index) = value.

void	set_if_valid_index (size_t index, const Fr &value)
	Like setting with at(), but allows zeroes to result in no set.

template<typename T >
void	copy_vector (const std::vector< T > &vec)
	Copy over values from a vector that is of a convertible type.

Fr	debug_hash () const

Static Public Member Functions
static Polynomial	shiftable (size_t virtual_size)
	Utility to create a shiftable polynomial of given virtual size.

static Polynomial	shiftable (size_t size, size_t virtual_size)
	Utility to create a shiftable polynomial of given size and virtual size.

static Polynomial	random (size_t size, size_t start_index=0)

static Polynomial	random (size_t size, size_t virtual_size, size_t start_index)

static Polynomial	create_non_parallel_zero_init (size_t size, size_t virtual_size)
	A factory to construct a polynomial where parallel initialization is not possible (e.g. AVM code).

Private Member Functions
void	allocate_backing_memory (size_t size, size_t virtual_size, size_t start_index)

bool	in_place_operation_viable (size_t domain_size)

Private Attributes
SharedShiftedVirtualZeroesArray< Fr >	coefficients_

Detailed Description

template<typename Fr>
class bb::Polynomial< Fr >

Structured polynomial class that represents the coefficients 'a' of a_0 + a_1 x ... a_n x^n of a finite field polynomial equation of degree that is at most the size of some zk circuit. Past 'n' it has a virtual size where it conceptually has coefficients all equal to 0. Notably, we allow indexing past 'n' up to our virtual size (checked only in a debug build, however). As well, we have a start index that means coefficients before start_index are also considered to be 0. The polynomial is used to represent the gates of our arithmetized zk programs. Polynomials use the majority of the memory in proving, so caution should be used in making sure unnecessary copies are avoided, both for avoiding unnecessary memory usage and performance due to unnecessary allocations. The polynomial has a maximum degree in the underlying SharedShiftedVirtualZeroesArray, dictated by the circuit size, this is just used for debugging as we represent.

Template Parameters

Fr	the finite field type.

Definition at line 75 of file polynomial.hpp.

Member Typedef Documentation

◆ FF

template<typename Fr >

using bb::Polynomial< Fr >::FF = Fr

Definition at line 77 of file polynomial.hpp.

Member Enumeration Documentation

◆ DontZeroMemory

template<typename Fr >

enum class bb::Polynomial::DontZeroMemory

strong

Enumerator
FLAG

Definition at line 78 of file polynomial.hpp.

Constructor & Destructor Documentation

◆ Polynomial() [1/12]

template<typename Fr >

bb::Polynomial< Fr >::Polynomial	(	size_t	size,
		size_t	virtual_size,
		size_t	start_index = `0`
	)

Initialize a Polynomial to size 'size', zeroing memory.

Constructors / Destructors

Parameters

size	The size of the polynomial.

Definition at line 72 of file polynomial.cpp.

◆ Polynomial() [2/12]

template<typename Fr >

bb::Polynomial< Fr >::Polynomial ( size_t size )

inline

Definition at line 82 of file polynomial.hpp.

◆ Polynomial() [3/12]

template<typename Fr >

bb::Polynomial< Fr >::Polynomial	(	size_t	size,
		size_t	virtual_size,
		size_t	start_index,
		DontZeroMemory	flag
	)

Initialize a Polynomial to size 'size'. Important: This does NOT zero memory.

Parameters

size	The initial size of the polynomial.
flag	Signals that we do not zero memory.

Definition at line 97 of file polynomial.cpp.

◆ Polynomial() [4/12]

template<typename Fr >

bb::Polynomial< Fr >::Polynomial	(	size_t	size,
		size_t	virtual_size,
		DontZeroMemory	flag
	)

inline

Definition at line 87 of file polynomial.hpp.

◆ Polynomial() [5/12]

template<typename Fr >

bb::Polynomial< Fr >::Polynomial	(	size_t	size,
		DontZeroMemory	flag
	)

inline

Definition at line 90 of file polynomial.hpp.

◆ Polynomial() [6/12]

template<typename Fr >

bb::Polynomial< Fr >::Polynomial ( const Polynomial< Fr > & other )

◆ Polynomial() [7/12]

template<typename Fr >

bb::Polynomial< Fr >::Polynomial	(	const Polynomial< Fr > &	other,
		size_t	target_size
	)

◆ Polynomial() [8/12]

template<typename Fr >

bb::Polynomial< Fr >::Polynomial ( Polynomial< Fr > && other )

defaultnoexcept

◆ Polynomial() [9/12]

template<typename Fr >

bb::Polynomial< Fr >::Polynomial	(	std::span< const Fr >	coefficients,
		size_t	virtual_size
	)

Definition at line 127 of file polynomial.cpp.

◆ Polynomial() [10/12]

template<typename Fr >

bb::Polynomial< Fr >::Polynomial ( std::span< const Fr > coefficients )

inline

Definition at line 100 of file polynomial.hpp.

◆ Polynomial() [11/12]

template<typename Fr >

bb::Polynomial< Fr >::Polynomial ( )

default

◆ Polynomial() [12/12]

template<typename Fr >

bb::Polynomial< Fr >::Polynomial	(	std::span< const Fr >	interpolation_points,
		std::span< const Fr >	evaluations,
		size_t	virtual_size
	)

Create the degree-(m-1) polynomial T(X) that interpolates the given evaluations. We have T(xⱼ) = yⱼ for j=1,...,m.

Parameters

interpolation_points	(x₁,…,xₘ)
evaluations	(y₁,…,yₘ)

Definition at line 116 of file polynomial.cpp.

◆ ~Polynomial()

template<typename Fr >

bb::Polynomial< Fr >::~Polynomial ( )

default

Member Function Documentation

◆ add_scaled()

template<typename Fr >

void bb::Polynomial< Fr >::add_scaled	(	PolynomialSpan< const Fr >	other,
		Fr	scaling_factor
	)		&

adds the polynomial q(X) 'other', multiplied by a scaling factor.

Parameters

other	q(X)
scaling_factor	scaling factor by which all coefficients of q(X) are multiplied

Definition at line 258 of file polynomial.cpp.

◆ add_scaled_chunk()

template<typename Fr >

void bb::Polynomial< Fr >::add_scaled_chunk	(	const ThreadChunk &	chunk,
		PolynomialSpan< const Fr >	other,
		Fr	scaling_factor
	)		&

Definition at line 267 of file polynomial.cpp.

◆ allocate_backing_memory()

template<typename Fr >

void bb::Polynomial< Fr >::allocate_backing_memory	(	size_t	size,
		size_t	virtual_size,
		size_t	start_index
	)

private

Definition at line 51 of file polynomial.cpp.

◆ at() [1/2]

template<typename Fr >

Fr & bb::Polynomial< Fr >::at ( size_t index )

inline

Our mutable accessor, unlike operator[]. We abuse precedent a bit to differentiate at() and operator[] as mutable and immutable, respectively. This means at() can only index within start_index()..end_index() unlike operator[] which can index 0..virtual_size.

Parameters

index the index, to be subtracted by start_index() and read into the array memory

Returns: Fr& a mutable reference.

Definition at line 293 of file polynomial.hpp.

◆ at() [2/2]

template<typename Fr >

const Fr & bb::Polynomial< Fr >::at ( size_t index ) const

inline

Definition at line 294 of file polynomial.hpp.

◆ clear()

template<typename Fr >

void bb::Polynomial< Fr >::clear ( )

inline

Definition at line 140 of file polynomial.hpp.

◆ coeffs() [1/2]

template<typename Fr >

std::span< Fr > bb::Polynomial< Fr >::coeffs ( size_t offset = 0 )

inline

Strictly iterates the defined region of the polynomial. We keep this explicit, instead of having an implicit conversion to span. This is safer as it is more likely that we need to consider our start_index() along with the span, as in PolynomialSpan below.

Returns: std::span<Fr> a span covering start_index() to end_index()

Definition at line 351 of file polynomial.hpp.

◆ coeffs() [2/2]

template<typename Fr >

std::span< const Fr > bb::Polynomial< Fr >::coeffs ( size_t offset = 0 ) const

inline

Definition at line 352 of file polynomial.hpp.

◆ compute_barycentric_evaluation()

template<typename Fr >
requires polynomial_arithmetic::SupportsFFT<Fr>

Fr bb::Polynomial< Fr >::compute_barycentric_evaluation	(	const Fr &	z,
		const EvaluationDomain< Fr > &	domain
	)

Definition at line 205 of file polynomial.cpp.

◆ copy_vector()

template<typename Fr >

template<typename T >

void bb::Polynomial< Fr >::copy_vector ( const std::vector< T > & vec )

inline

Copy over values from a vector that is of a convertible type.

There is an underlying assumption that the relevant start index in the vector corresponds to the start_index of the destination polynomial and also that the number of elements we want to copy corresponds to the size of the polynomial. This is quirky behavior and we might want to improve the UX.

Todo:: https://github.com/AztecProtocol/barretenberg/issues/1292

Template Parameters

T	a convertible type

Parameters

vec	the vector

Definition at line 395 of file polynomial.hpp.

◆ create_non_parallel_zero_init()

template<typename Fr >

Polynomial< Fr > bb::Polynomial< Fr >::create_non_parallel_zero_init	(	size_t	size,
		size_t	virtual_size
	)

static

A factory to construct a polynomial where parallel initialization is not possible (e.g. AVM code).

Returns: a polynomial initialized with zero on the range defined by size

Definition at line 237 of file polynomial.cpp.

◆ data() [1/2]

template<typename Fr >

Fr * bb::Polynomial< Fr >::data ( )

inline

Definition at line 282 of file polynomial.hpp.

◆ data() [2/2]

template<typename Fr >

const Fr * bb::Polynomial< Fr >::data ( ) const

inline

Definition at line 283 of file polynomial.hpp.

◆ debug_hash()

template<typename Fr >

Fr bb::Polynomial< Fr >::debug_hash ( ) const

inline

Definition at line 407 of file polynomial.hpp.

◆ end_index()

template<typename Fr >

size_t bb::Polynomial< Fr >::end_index ( ) const

inline

Definition at line 341 of file polynomial.hpp.

◆ evaluate() [1/2]

template<typename Fr >

Fr bb::Polynomial< Fr >::evaluate ( const Fr & z ) const

Definition at line 193 of file polynomial.cpp.

◆ evaluate() [2/2]

template<typename Fr >

Fr bb::Polynomial< Fr >::evaluate	(	const Fr &	z,
		size_t	target_size
	)		const

Definition at line 187 of file polynomial.cpp.

◆ evaluate_mle()

template<typename Fr >

Fr bb::Polynomial< Fr >::evaluate_mle	(	std::span< const Fr >	evaluation_points,
		bool	shift = `false`
	)		const

evaluate multi-linear extension p(X_0,…,X_{n-1}) = \sum_i a_i*L_i(X_0,…,X_{n-1}) at u = (u_0,…,u_{n-1}) If the polynomial is embedded into a lower dimension k<n, i.e, start_index + size <= 2^k, we evaluate it in a more efficient way. Note that a_j == 0 for any j >= 2^k. We fold over k dimensions and then multiply the result by (1 - u_k) * (1 - u_{k+1}) ... * (1 - u_{n-1}). In this case, for any i < 2^k, L_i is a multiple of (1 - X_k) * (1 - X_{k+1}) ... * (1 - X_{n-1}). Dividing p by this monomial leads to a multilinear extension over variables X_0, X_1, ..X_{k-1}.

this function allocates a temporary buffer of size 2^(k-1)

Parameters

evaluation_points	evaluation vector of size n
shift	a boolean and when set to true, we evaluate the shifted counterpart polynomial: enforce a_0 == 0 and compute \sum_i a_{i+1}*L_i(X_0,…,X_{n-1})

Definition at line 199 of file polynomial.cpp.

◆ factor_roots()

template<typename Fr >

void bb::Polynomial< Fr >::factor_roots ( const Fr & root )

inline

Divides p(X) by (X-r) in-place. Assumes that p(rⱼ)=0 for all j.

we specialize the method when only a single root is given. if one of the roots is 0, then we first factor all other roots. dividing by X requires only a left shift of all coefficient.

Parameters

root	a single root r

Definition at line 224 of file polynomial.hpp.

◆ full()

template<typename Fr >

Polynomial< Fr > bb::Polynomial< Fr >::full ( ) const

Copys the polynomial, but with the whole address space usable. The value of the polynomial remains the same, but defined memory region differs.

Returns: a polynomial with a larger size() but same virtual_size()

Definition at line 250 of file polynomial.cpp.

◆ get()

template<typename Fr >

const Fr & bb::Polynomial< Fr >::get	(	size_t	i,
		size_t	virtual_padding = `0`
	)		const

inline

Retrieves the value at the specified index.

Parameters

index	The index from which to retrieve the value.
virtual_padding	For the rare case where we explicitly want the 0-returning behavior beyond our usual virtual_size.

Definition at line 168 of file polynomial.hpp.

◆ in_place_operation_viable()

template<typename Fr >

bool bb::Polynomial< Fr >::in_place_operation_viable ( size_t domain_size )

inlineprivate

Definition at line 422 of file polynomial.hpp.

◆ increase_virtual_size()

template<typename Fr >

void bb::Polynomial< Fr >::increase_virtual_size ( const size_t size_in )

inline

Definition at line 280 of file polynomial.hpp.

◆ indexed_values() [1/2]

template<typename Fr >

auto bb::Polynomial< Fr >::indexed_values ( )

inline

Definition at line 366 of file polynomial.hpp.

◆ indexed_values() [2/2]

template<typename Fr >

auto bb::Polynomial< Fr >::indexed_values ( ) const

inline

Definition at line 367 of file polynomial.hpp.

◆ indices()

template<typename Fr >

auto bb::Polynomial< Fr >::indices ( ) const

inline

Definition at line 365 of file polynomial.hpp.

◆ is_empty()

template<typename Fr >

bool bb::Polynomial< Fr >::is_empty ( ) const

inline

Definition at line 170 of file polynomial.hpp.

◆ is_valid_set_index()

template<typename Fr >

bool bb::Polynomial< Fr >::is_valid_set_index ( size_t index ) const

inline

Is this index valid for a set? i.e. calling poly.at(index) = value.

Definition at line 371 of file polynomial.hpp.

◆ is_zero()

template<typename Fr >

bool bb::Polynomial< Fr >::is_zero ( ) const

inline

Check whether or not a polynomial is identically zero.

Definition at line 146 of file polynomial.hpp.

◆ mask()

template<typename Fr >

void bb::Polynomial< Fr >::mask ( )

inline

Add random values to the coefficients of a polynomial. In practice, this is used for ensuring the commitment and evaluation of a polynomial don't leak information about the coefficients in the context of zero knowledge.

Definition at line 267 of file polynomial.hpp.

◆ multiply_chunk()

template<typename Fr >

void bb::Polynomial< Fr >::multiply_chunk	(	const ThreadChunk &	chunk,
		Fr	scaling_factor
	)

Definition at line 230 of file polynomial.cpp.

◆ operator PolynomialSpan< const Fr >()

template<typename Fr >

bb::Polynomial< Fr >::operator PolynomialSpan< const Fr > ( ) const

inline

Convert to an std::span bundled with our start index.

Returns: PolynomialSpan<Fr> A span covering the entire polynomial.

Definition at line 363 of file polynomial.hpp.

◆ operator PolynomialSpan< Fr >()

template<typename Fr >

bb::Polynomial< Fr >::operator PolynomialSpan< Fr > ( )

inline

Convert to an std::span bundled with our start index.

Returns: PolynomialSpan<Fr> A span covering the entire polynomial.

Definition at line 357 of file polynomial.hpp.

◆ operator*=()

template<typename Fr >

Polynomial< Fr > & bb::Polynomial< Fr >::operator*= ( Fr scaling_factor )

sets this = p(X) to s⋅p(X)

Parameters

scaling_factor s

Definition at line 224 of file polynomial.cpp.

◆ operator+=()

template<typename Fr >

Polynomial< Fr > & bb::Polynomial< Fr >::operator+= ( PolynomialSpan< const Fr > other )

adds the polynomial q(X) 'other'.

Parameters

other q(X)

Definition at line 174 of file polynomial.cpp.

◆ operator-=()

template<typename Fr >

Polynomial< Fr > & bb::Polynomial< Fr >::operator-= ( PolynomialSpan< const Fr > other )

subtracts the polynomial q(X) 'other'.

Parameters

other q(X)

Definition at line 211 of file polynomial.cpp.

◆ operator=() [1/2]

template<typename Fr >

Polynomial & bb::Polynomial< Fr >::operator= ( const Polynomial< Fr > & other )

◆ operator=() [2/2]

template<typename Fr >

Polynomial & bb::Polynomial< Fr >::operator= ( Polynomial< Fr > && other )

defaultnoexcept

◆ operator==()

template<typename Fr >

bool bb::Polynomial< Fr >::operator== ( Polynomial< Fr > const & rhs ) const

Definition at line 153 of file polynomial.cpp.

◆ operator[]() [1/2]

template<typename Fr >

const Fr & bb::Polynomial< Fr >::operator[] ( size_t i )

inline

Definition at line 296 of file polynomial.hpp.

◆ operator[]() [2/2]

template<typename Fr >

const Fr & bb::Polynomial< Fr >::operator[] ( size_t i ) const

inline

Definition at line 297 of file polynomial.hpp.

◆ random() [1/2]

template<typename Fr >

static Polynomial bb::Polynomial< Fr >::random	(	size_t	size,
		size_t	start_index = `0`
	)

inlinestatic

Definition at line 299 of file polynomial.hpp.

◆ random() [2/2]

template<typename Fr >

static Polynomial bb::Polynomial< Fr >::random	(	size_t	size,
		size_t	virtual_size,
		size_t	start_index
	)

inlinestatic

Definition at line 306 of file polynomial.hpp.

◆ reverse()

template<typename Fr >

Polynomial< Fr > bb::Polynomial< Fr >::reverse ( ) const

Returns the polynomial equal to the reverse of self.

If the coefficients of self are \((a_0, \dots, a_n)\), we return the polynomial with coefficients \((a_n, \dots, a_0)\)

Note: Resulting polynomial uses new backing memory; n = self->size()

Definition at line 297 of file polynomial.cpp.

◆ right_shifted()

template<typename Fr >

Polynomial< Fr > bb::Polynomial< Fr >::right_shifted ( const size_t magnitude ) const

Returns a Polynomial equal to the right-shift-by-magnitude of self.

Note: Resulting Polynomial shares the memory of that used to generate it

Definition at line 286 of file polynomial.cpp.

◆ set_if_valid_index()

template<typename Fr >

void bb::Polynomial< Fr >::set_if_valid_index	(	size_t	index,
		const Fr &	value
	)

inline

Like setting with at(), but allows zeroes to result in no set.

Definition at line 375 of file polynomial.hpp.

◆ share()

template<typename Fr >

Polynomial< Fr > bb::Polynomial< Fr >::share ( ) const

Return a shallow clone of the polynomial. i.e. underlying memory is shared.

Definition at line 146 of file polynomial.cpp.

◆ shiftable() [1/2]

template<typename Fr >

static Polynomial bb::Polynomial< Fr >::shiftable	(	size_t	size,
		size_t	virtual_size
	)

inlinestatic

Utility to create a shiftable polynomial of given size and virtual size.

Definition at line 114 of file polynomial.hpp.

◆ shiftable() [2/2]

template<typename Fr >

static Polynomial bb::Polynomial< Fr >::shiftable ( size_t virtual_size )

inlinestatic

Utility to create a shiftable polynomial of given virtual size.

Definition at line 107 of file polynomial.hpp.

◆ shifted()

template<typename Fr >

Polynomial< Fr > bb::Polynomial< Fr >::shifted ( ) const

Returns a Polynomial the left-shift of self.

If the n coefficients of self are (0, a₁, …, aₙ₋₁), we returns the view of the n-1 coefficients (a₁, …, aₙ₋₁).

Definition at line 276 of file polynomial.cpp.

◆ shrink_end_index()

template<typename Fr >

void bb::Polynomial< Fr >::shrink_end_index ( const size_t new_end_index )

The end_index of the polynomial is decreased without any memory de-allocation. This is a very fast way to zeroize the polynomial tail from new_end_index to the end. It also means that the new end_index might be smaller than the backed memory.

Definition at line 244 of file polynomial.cpp.

◆ size()

template<typename Fr >

std::size_t bb::Polynomial< Fr >::size ( ) const

inline

Definition at line 278 of file polynomial.hpp.

◆ start_index()

template<typename Fr >

size_t bb::Polynomial< Fr >::start_index ( ) const

inline

Definition at line 340 of file polynomial.hpp.

◆ virtual_size()

template<typename Fr >

std::size_t bb::Polynomial< Fr >::virtual_size ( ) const

inline

Definition at line 279 of file polynomial.hpp.

Member Data Documentation

◆ coefficients_

template<typename Fr >

SharedShiftedVirtualZeroesArray<Fr> bb::Polynomial< Fr >::coefficients_

private

Definition at line 426 of file polynomial.hpp.

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

src/barretenberg/polynomials/polynomial.hpp
src/barretenberg/polynomials/polynomial.cpp

Public Types

Public Member Functions

Static Public Member Functions

Private Member Functions

Private Attributes

Detailed Description

Member Typedef Documentation

◆ FF

Member Enumeration Documentation

◆ DontZeroMemory

Constructor & Destructor Documentation

◆ Polynomial() [1/12]

◆ Polynomial() [2/12]

◆ Polynomial() [3/12]

◆ Polynomial() [4/12]

◆ Polynomial() [5/12]

◆ Polynomial() [6/12]

◆ Polynomial() [7/12]

◆ Polynomial() [8/12]

◆ Polynomial() [9/12]

◆ Polynomial() [10/12]

◆ Polynomial() [11/12]

◆ Polynomial() [12/12]

◆ ~Polynomial()

Member Function Documentation

◆ add_scaled()

◆ add_scaled_chunk()

◆ allocate_backing_memory()

◆ at() [1/2]

◆ at() [2/2]

◆ clear()

◆ coeffs() [1/2]

◆ coeffs() [2/2]

◆ compute_barycentric_evaluation()

◆ copy_vector()

◆ create_non_parallel_zero_init()

◆ data() [1/2]

◆ data() [2/2]

◆ debug_hash()

◆ end_index()

◆ evaluate() [1/2]

◆ evaluate() [2/2]

◆ evaluate_mle()

◆ factor_roots()

◆ full()

◆ get()

◆ in_place_operation_viable()

◆ increase_virtual_size()

◆ indexed_values() [1/2]

◆ indexed_values() [2/2]

◆ indices()

◆ is_empty()

◆ is_valid_set_index()

◆ is_zero()

◆ mask()

◆ multiply_chunk()

◆ operator PolynomialSpan< const Fr >()

◆ operator PolynomialSpan< Fr >()

◆ operator*=()

◆ operator+=()

◆ operator-=()

◆ operator=() [1/2]

◆ operator=() [2/2]

◆ operator==()

◆ operator[]() [1/2]

◆ operator[]() [2/2]

◆ random() [1/2]

◆ random() [2/2]

◆ reverse()

◆ right_shifted()

◆ set_if_valid_index()

◆ share()

◆ shiftable() [1/2]

◆ shiftable() [2/2]

◆ shifted()

◆ shrink_end_index()

◆ size()

◆ start_index()

◆ virtual_size()

Member Data Documentation