proof_system::LookupRelationImpl< FF_ > Class Template Reference

LookupRelationImpl defines the algebra for the lookup polynomial: More...

#include <lookup_relation.hpp>

Public Types
using	FF = FF_

Static Public Member Functions
static auto &	get_grand_product_polynomial (auto &input)
	Get the grand product polynomial object (either from the proving key or AllEntities depending on context)
static auto &	get_shifted_grand_product_polynomial (auto &input)
	Get the shifted grand product polynomial object (either from the proving key or AllEntities depending on context)
template<typename Accumulator , typename AllEntities , typename Parameters >
static Accumulator	compute_grand_product_numerator (const AllEntities &in, const Parameters &params)
	Compute numerator term of the lookup relation:
template<typename Accumulator , typename AllEntities , typename Parameters >
static Accumulator	compute_grand_product_denominator (const AllEntities &in, const Parameters &params)
	Compute denominator term of the lookup relation:
template<typename ContainerOverSubrelations , typename AllEntities , typename Parameters >
static void	accumulate (ContainerOverSubrelations &accumulators, const AllEntities &in, const Parameters &params, const FF &scaling_factor)
	Compute contribution of the lookup grand prod relation for a given edge (internal function)

Static Public Attributes
static constexpr std::array< size_t, 2 >	SUBRELATION_PARTIAL_LENGTHS
static constexpr std::array< size_t, 2 >	TOTAL_LENGTH_ADJUSTMENTS

Detailed Description

template<typename FF_>
class proof_system::LookupRelationImpl< FF_ >

LookupRelationImpl defines the algebra for the lookup polynomial:

                  ∏ (1 + β) ⋅ (q_lookup*f_k + γ) ⋅ (t_k + βt_{k+1} + γ(1 + β))

Z_lookup(g^j) = -----------------------------------------------------------------------— ∏ (s_k + βs_{k+1} + γ(1 + β))

The method compute_numerator_term computes polynomials f, t and incorporate them into terms that are ultimately needed to construct the grand product polynomial Z_lookup(X): Note 1: In the above, 't' is associated with table values (and is not to be confused with the quotient polynomial, also refered to as 't' elsewhere). Polynomial 's' is the sorted concatenation of the witnesses and the table values.

Template Parameters

FF	parametrises the prime field class being used

Member Function Documentation

accumulate()

template<typename FF_ >

template<typename ContainerOverSubrelations , typename AllEntities , typename Parameters >

static void proof_system::LookupRelationImpl< FF_ >::accumulate ( ContainerOverSubrelations &  accumulators, const AllEntities &  in, const Parameters &  params, const FF &  scaling_factor  )

inlinestatic

Compute contribution of the lookup grand prod relation for a given edge (internal function)

This the relation confirms faithful calculation of the lookup grand product polynomial Z_lookup. The contribution is z_lookup * (1 + β) * [q_lookup * f + γ] * (t_accum_k + βt_accum_{k+1} + γ(1 + β)) - z_lookup_shift * (s_accum_k + βs_accum_{k+1} + γ(1 + β)) where f = (w_1 + q_2*w_1_shift) + η(w_2 + q_m*w_2_shift) + η²(w_3 + q_c*w_3_shift) + η³q_index, t_accum = table_1 + ηtable_2 + η²table_3 + η³table_4, and s_accum = s_1 + ηs_2 + η²s_3 + η³s_4. Note: Selectors q_2, q_m and q_c are repurposed as 'column step size' for lookup gates.

Parameters

evals	transformed to evals + C(in(X)...)*scaling_factor
in	an std::array containing the fully extended Univariate edges.
parameters	contains beta, gamma, and public_input_delta, ....
scaling_factor	optional term to scale the evaluation before adding to evals.

compute_grand_product_denominator()

template<typename FF_ >

template<typename Accumulator , typename AllEntities , typename Parameters >

static Accumulator proof_system::LookupRelationImpl< FF_ >::compute_grand_product_denominator ( const AllEntities &  in, const Parameters &  params  )

inlinestatic

Compute denominator term of the lookup relation:

 (s_k + βs_{k+1} + γ(1 + β))

Template Parameters

AccumulatorTypes

Parameters

in
relation_parameters
index

compute_grand_product_numerator()

template<typename FF_ >

template<typename Accumulator , typename AllEntities , typename Parameters >

static Accumulator proof_system::LookupRelationImpl< FF_ >::compute_grand_product_numerator ( const AllEntities &  in, const Parameters &  params  )

inlinestatic

Compute numerator term of the lookup relation:

N_{index} = (1 + β) ⋅ ∏ (q_lookup*f_k + γ) ⋅ (t_k + βt_{k+1} + γ(1 + β))

Template Parameters

AccumulatorTypes

Parameters

in
relation_parameters
index	If calling this method over vector inputs, index >= 0

get_grand_product_polynomial()

template<typename FF_ >

static auto & proof_system::LookupRelationImpl< FF_ >::get_grand_product_polynomial ( auto &  input )

inlinestatic

Get the grand product polynomial object (either from the proving key or AllEntities depending on context)

Parameters

input

Returns

auto& either std::span<FF> or Flavor::Polynomial depending on context

get_shifted_grand_product_polynomial()

template<typename FF_ >

static auto & proof_system::LookupRelationImpl< FF_ >::get_shifted_grand_product_polynomial ( auto &  input )

inlinestatic

Get the shifted grand product polynomial object (either from the proving key or AllEntities depending on context)

Parameters

input

Returns

auto& either std::span<FF> or Flavor::Polynomial depending on context

Member Data Documentation

SUBRELATION_PARTIAL_LENGTHS

template<typename FF_ >

constexpr std::array<size_t, 2> proof_system::LookupRelationImpl< FF_ >::SUBRELATION_PARTIAL_LENGTHS

staticconstexpr

Initial value:

{
        6, 
        3  
    }

TOTAL_LENGTH_ADJUSTMENTS

template<typename FF_ >

constexpr std::array<size_t, 2> proof_system::LookupRelationImpl< FF_ >::TOTAL_LENGTH_ADJUSTMENTS

staticconstexpr

Initial value:

{
        6, 
        0  
    }

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

• src/barretenberg/relations/lookup_relation.hpp