bb::ArithmeticRelationImpl< FF_ > Class Template Reference

#include <ultra_arithmetic_relation.hpp>

Public Types
using	FF = FF_

Static Public Member Functions
template<typename AllEntities >
static bool	skip (const AllEntities &in)
	Returns true if the contribution from all subrelations for the provided inputs is identically zero.
template<typename ContainerOverSubrelations , typename AllEntities , typename Parameters >
static void	accumulate (ContainerOverSubrelations &evals, const AllEntities &in, BB_UNUSED const Parameters &params, const FF &scaling_factor)
	Expression for the Ultra (width-4) Arithmetic gate.

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

Detailed Description

template<typename FF_>
class bb::ArithmeticRelationImpl< FF_ >

Definition at line 12 of file ultra_arithmetic_relation.hpp.

Member Typedef Documentation

FF

template<typename FF_ >

using bb::ArithmeticRelationImpl< FF_ >::FF = FF_

Definition at line 14 of file ultra_arithmetic_relation.hpp.

Member Function Documentation

accumulate()

template<typename FF_ >

template<typename ContainerOverSubrelations , typename AllEntities , typename Parameters >

static void bb::ArithmeticRelationImpl< FF_ >::accumulate ( ContainerOverSubrelations &  evals, const AllEntities &  in, BB_UNUSED const Parameters &  params, const FF &  scaling_factor  )

inlinestatic

Expression for the Ultra (width-4) Arithmetic gate.

This relation contains two subrelations and encapsulates several identities, toggled by the value of q_arith in [0, 1, 2, 3].

Subrelation 1: q_arith * [ (-1/2) * (q_arith - 3) * (q_m * w_1 * w_2) + \sum_{i=1..4} q_i * w_i + q_c + (q_arith - 1) * w_4_shift]

Subrelation 2: q_arith * (q_arith - 1) * (q_arith - 2) * (w_1 + w_4 - w_1_shift + q_m)

These formulas result in several cases depending on q_arith:

CASE q_arith == 0: Arithmetic gate is completely disabled

CASE q_arith == 1: Conventional 4-wire Ultra arithmetic relation Subrelation 1: q_m * w_1 * w_2 + \sum_{i=1..4} q_i * w_i + q_c Subrelation 2: Disabled

CASE q_arith == 2: Same as above but with an additional linear term: +w_4_shift Subrelation 1: q_m * w_1 * w_2 + [ \sum_{i=1..4} q_i * w_i + q_c + w_4_shift ] * 2 Subrelation 2: Disabled Note: Factor of 2 on the linear term must be accounted for when constructing inputs to the relation.

CASE q_arith == 3: Subrelation 1: [ \sum_{i=1..4} q_i * w_i + q_c + (2 * w_4_shift) ] * 3 Subrelation 2: [ w_1 + w_4 - w_1_shift + q_m ] * 6 Note: We are repurposing q_m here as an additive term in the second subrelation. Note: Factor of 2 on the w_4_shift term must be accounted for when constructing inputs to the relation.

Parameters

evals	transformed to evals + C(in(X)...)*scaling_factor
in	Inputs to the relation algebra
parameters	Unused in this relation
scaling_factor	optional term to scale the evaluation before adding to evals.

Definition at line 64 of file ultra_arithmetic_relation.hpp.

skip()

template<typename FF_ >

template<typename AllEntities >

static bool bb::ArithmeticRelationImpl< FF_ >::skip ( const AllEntities &  in )

inlinestatic

Returns true if the contribution from all subrelations for the provided inputs is identically zero.

Definition at line 25 of file ultra_arithmetic_relation.hpp.

Member Data Documentation

SUBRELATION_PARTIAL_LENGTHS

template<typename FF_ >

constexpr std::array<size_t, 2> bb::ArithmeticRelationImpl< FF_ >::SUBRELATION_PARTIAL_LENGTHS

staticconstexpr

Initial value:

{
        6, 
        5  
    }

Definition at line 16 of file ultra_arithmetic_relation.hpp.

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

• src/barretenberg/relations/ultra_arithmetic_relation.hpp