#include <gate_separator.hpp>

Public Member Functions
	GateSeparatorPolynomial (const std::vector< FF > &betas, const size_t log_num_monomials)
	Construct a new GateSeparatorPolynomial.

	GateSeparatorPolynomial (const std::vector< FF > &betas)
	Construct a new GateSeparatorPolynomial object without expanding to a vector of monomials.

	GateSeparatorPolynomial (const std::vector< FF > &betas, const std::vector< FF > &challenge)
	Constructs a virtual GateSeparator used by the prover in rounds k > d - 1, and computes its partial evaluation at (u_0, ..., u_{d-1}).

FF const &	operator[] (size_t idx) const
	Retruns the element in beta_products at place #idx.

template<typename Element >
Element	gather (size_t edge_idx) const
	Read `Element::SIZE` consecutive edge-pair `pow_beta` factors starting at `edge_idx`, packed as a single `Element` value. Lane j reads `(*this)[edge_idx + 2j]`.

FF	current_element () const
	Computes the component at index current_element_idx in betas.

FF	univariate_eval (FF challenge) const
	Evaluate \( ((1−X_{i}) + X_{i}\cdot \beta_{i})\) at the challenge point \( X_{i}=u_{i} \).

void	partially_evaluate (FF challenge)
	Partially evaluate the \(pow_{\beta} \)-polynomial at the new challenge and update \( c_i \).

Static Public Member Functions
static FF	univariate_factor (const FF &challenge, const FF &beta)
	The pow_β per-variable factor \( (1 - X) + X\cdot \beta \) at \( X = \mathrm{challenge} \).

static BB_PROFILE Polynomial< FF >	compute_beta_products (const std::vector< FF > &betas, const size_t log_num_monomials, const FF &scaling_factor=FF(1))
	Given \( \vec\beta = (\beta_0,...,\beta_{d-1})\) compute \( pow_{\ell}(\vec \beta) = pow_{\beta}(\vec \ell)\) for \( \ell =0,\ldots,2^{d}-1\).

Public Attributes
std::vector< FF >	betas
	The challenges \((\beta_0,\ldots, \beta_{d-1}) \).

Polynomial< FF >	beta_products
	The consecutive evaluations \( pow_{\ell}(\beta) = pow_{\beta}(\vec \ell) \) for \(\vec \ell\) identified with the integers \(\ell = 0,\ldots, 2^d-1\).

size_t	current_element_idx = 0
	In Round \( i\) of Sumcheck, it points to the \( i \)-th element in \( \vec \beta \).

size_t	periodicity = 2
	In Round \( i\) of Sumcheck, the periodicity equals to \( 2^{i+1}\) and represents the fixed interval at which elements not containing either of \( (\beta_0,\ldots ,β_i)\) appear in beta_products.

FF	partial_evaluation_result = FF(1)
	The value \(c_i\) obtained by partially evaluating one variable in the power polynomial at each round. At the end of Round \( i \) in the sumcheck protocol, variable \(X_i\) is replaced by the challenge \(u_i \). The partial evaluation result is updated to represent \( pow_{\beta}(u_0,.., u_{i}) = \prod_{k=0}^{i} ( (1-u_k) + u_k\cdot \beta_k) \).

Detailed Description

template<typename FF>
struct bb::GateSeparatorPolynomial< FF >

Definition at line 19 of file gate_separator.hpp.

Constructor & Destructor Documentation

◆ GateSeparatorPolynomial() [1/3]

template<typename FF >

bb::GateSeparatorPolynomial< FF >::GateSeparatorPolynomial	(	const std::vector< FF > &	betas,
		const size_t	log_num_monomials
	)

inline

Construct a new GateSeparatorPolynomial.

Parameters

betas
log_num_monomials

Definition at line 58 of file gate_separator.hpp.

◆ GateSeparatorPolynomial() [2/3]

template<typename FF >

bb::GateSeparatorPolynomial< FF >::GateSeparatorPolynomial ( const std::vector< FF > & betas )

inline

Construct a new GateSeparatorPolynomial object without expanding to a vector of monomials.

The sumcheck verifier does not use beta_products

Parameters

betas

Definition at line 69 of file gate_separator.hpp.

◆ GateSeparatorPolynomial() [3/3]

template<typename FF >

bb::GateSeparatorPolynomial< FF >::GateSeparatorPolynomial	(	const std::vector< FF > &	betas,
		const std::vector< FF > &	challenge
	)

inline

Constructs a virtual GateSeparator used by the prover in rounds k > d - 1, and computes its partial evaluation at (u_0, ..., u_{d-1}).

Definition at line 78 of file gate_separator.hpp.

Member Function Documentation

◆ compute_beta_products()

template<typename FF >

static BB_PROFILE Polynomial< FF > bb::GateSeparatorPolynomial< FF >::compute_beta_products	(	const std::vector< FF > &	betas,
		const size_t	log_num_monomials,
		const FF &	scaling_factor = `FF(1)`
	)

inlinestatic

Given \( \vec\beta = (\beta_0,...,\beta_{d-1})\) compute \( pow_{\ell}(\vec \beta) = pow_{\beta}(\vec \ell)\) for \( \ell =0,\ldots,2^{d}-1\).

Parameters

log_num_monomials Determines the number of beta challenges used to compute beta_products (required because when we generate CONST_SIZE_PROOF_LOG_N, currently 28, challenges but the real circuit size is less than 1 << CONST_SIZE_PROOF_LOG_N, we should compute unnecessarily a vector of beta_products of length 1 << 28 )

Definition at line 163 of file gate_separator.hpp.

◆ current_element()

template<typename FF >

FF bb::GateSeparatorPolynomial< FF >::current_element ( ) const

inline

Computes the component at index current_element_idx in betas.

Returns: FF

Definition at line 119 of file gate_separator.hpp.

◆ gather()

template<typename FF >

template<typename Element >

Element bb::GateSeparatorPolynomial< FF >::gather ( size_t edge_idx ) const

inline

Read Element::SIZE consecutive edge-pair pow_beta factors starting at edge_idx, packed as a single Element value. Lane j reads (*this)[edge_idx + 2j].

Uniform stride-2 gather for the scalar (Element = FF) and SIMD (Element = VectorField<...>) sumcheck paths: FF::from_lanes is a width-1 identity so this reduces to (*this)[edge_idx] for scalar; for VectorField it fills all lanes.

Definition at line 110 of file gate_separator.hpp.

◆ operator[]()

template<typename FF >

FF const & bb::GateSeparatorPolynomial< FF >::operator[] ( size_t idx ) const

inline

Retruns the element in beta_products at place #idx.

Parameters

idx

Returns: FF const&

Definition at line 94 of file gate_separator.hpp.

◆ partially_evaluate()

template<typename FF >

void bb::GateSeparatorPolynomial< FF >::partially_evaluate ( FF challenge )

inline

Partially evaluate the \(pow_{\beta} \)-polynomial at the new challenge and update \( c_i \).

Update the constant \(c_{i} \to c_{i+1} \) multiplying it by \(pow_{\beta}\)'s factor \(\left( (1-X_i) + X_i\cdot \beta_i\right)\vert_{X_i = u_i}\) computed by univariate_eval.

Parameters

challenge \( i \)-th verifier challenge \( u_{i}\)

Definition at line 145 of file gate_separator.hpp.

◆ univariate_eval()

template<typename FF >

FF bb::GateSeparatorPolynomial< FF >::univariate_eval ( FF challenge ) const

inline

Evaluate \( ((1−X_{i}) + X_{i}\cdot \beta_{i})\) at the challenge point \( X_{i}=u_{i} \).

Definition at line 137 of file gate_separator.hpp.

◆ univariate_factor()

template<typename FF >

static FF bb::GateSeparatorPolynomial< FF >::univariate_factor	(	const FF &	challenge,
		const FF &	beta
	)

inlinestatic

The pow_β per-variable factor \( (1 - X) + X\cdot \beta \) at \( X = \mathrm{challenge} \).

The building block of every pow_β / eq / shifted-eq fold; shared with ShiftedEqPolynomial so the factor has a single definition.

Definition at line 132 of file gate_separator.hpp.

Member Data Documentation

◆ beta_products

template<typename FF >

Polynomial<FF> bb::GateSeparatorPolynomial< FF >::beta_products

The consecutive evaluations \( pow_{\ell}(\beta) = pow_{\beta}(\vec \ell) \) for \(\vec \ell\) identified with the integers \(\ell = 0,\ldots, 2^d-1\).

Definition at line 31 of file gate_separator.hpp.

◆ betas

template<typename FF >

std::vector<FF> bb::GateSeparatorPolynomial< FF >::betas

The challenges \((\beta_0,\ldots, \beta_{d-1}) \).

Definition at line 24 of file gate_separator.hpp.

◆ current_element_idx

template<typename FF >

size_t bb::GateSeparatorPolynomial< FF >::current_element_idx = 0

In Round \( i\) of Sumcheck, it points to the \( i \)-th element in \( \vec \beta \).

Definition at line 36 of file gate_separator.hpp.

◆ partial_evaluation_result

template<typename FF >

FF bb::GateSeparatorPolynomial< FF >::partial_evaluation_result = FF(1)

The value \(c_i\) obtained by partially evaluating one variable in the power polynomial at each round. At the end of Round \( i \) in the sumcheck protocol, variable \(X_i\) is replaced by the challenge \(u_i \). The partial evaluation result is updated to represent \( pow_{\beta}(u_0,.., u_{i}) = \prod_{k=0}^{i} ( (1-u_k) + u_k\cdot \beta_k) \).

Definition at line 50 of file gate_separator.hpp.

◆ periodicity

template<typename FF >

size_t bb::GateSeparatorPolynomial< FF >::periodicity = 2

In Round \( i\) of Sumcheck, the periodicity equals to \( 2^{i+1}\) and represents the fixed interval at which elements not containing either of \( (\beta_0,\ldots ,β_i)\) appear in beta_products.

Definition at line 42 of file gate_separator.hpp.

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

src/barretenberg/polynomials/gate_separator.hpp

Public Member Functions

Static Public Member Functions

Public Attributes

Detailed Description

Constructor & Destructor Documentation

◆ GateSeparatorPolynomial() [1/3]

◆ GateSeparatorPolynomial() [2/3]

◆ GateSeparatorPolynomial() [3/3]

Member Function Documentation

◆ compute_beta_products()

◆ current_element()

◆ gather()

◆ operator[]()

◆ partially_evaluate()

◆ univariate_eval()

◆ univariate_factor()

Member Data Documentation

◆ beta_products

◆ betas

◆ current_element_idx

◆ partial_evaluation_result

◆ periodicity