bb::NonNativeFieldRelationImpl< FF_ > Class Template Reference

Non-Native Field Relation for emulating arithmetic over fields larger than the native circuit field. More...

#include <non_native_field_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 &accumulators, const AllEntities &in, BB_UNUSED const Parameters &params, const FF &scaling_factor)
	Accumulates constraints for non-native field multiplication and limb decomposition.

Static Public Attributes
static constexpr std::array< size_t, 1 >	SUBRELATION_PARTIAL_LENGTHS

Detailed Description

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

Non-Native Field Relation for emulating arithmetic over fields larger than the native circuit field.

This relation enables arithmetic operations (multiplication, reduction) on "bigfield" elements, which represent values in a field larger than the circuit's native field (e.g., secp256k1's base field when proving over BN254). A bigfield element is decomposed into 68-bit limbs that fit within the native field, and this relation enforces correct limb-wise arithmetic with carry propagation.

The relation handles two types of constraints:

1. Bigfield Product Gates (3 variants): Verify that limb products and cross-terms combine correctly when multiplying two bigfield elements. The product of two 4-limb numbers produces terms that must be accumulated with appropriate powers of 2^68.
2. Limb Accumulation Gates (2 variants): Verify that 14-bit sublimbs correctly reconstruct a 68-bit limb. Each 68-bit limb is decomposed into five 14-bit chunks (with 2 bits of slack), enabling efficient range checks via the delta range constraint relation.

Definition at line 31 of file non_native_field_relation.hpp.

Member Typedef Documentation

FF

template<typename FF_ >

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

Definition at line 33 of file non_native_field_relation.hpp.

Member Function Documentation

accumulate()

template<typename FF_ >

template<typename ContainerOverSubrelations , typename AllEntities , typename Parameters >

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

inlinestatic

Accumulates constraints for non-native field multiplication and limb decomposition.

Multiple selectors toggle different gate types within this single relation:

gate type	q_nnf	q_2	q_3	q_4	q_m
Bigfield Limb Accumulation 1	1	0	1	1	0
Bigfield Limb Accumulation 2	1	0	1	0	1
Bigfield Product 1	1	1	1	0	0
Bigfield Product 2	1	1	0	1	0
Bigfield Product 3	1	1	0	0	1

Parameters

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

Definition at line 64 of file non_native_field_relation.hpp.

skip()

template<typename FF_ >

template<typename AllEntities >

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

inlinestatic

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

Definition at line 43 of file non_native_field_relation.hpp.

Member Data Documentation

SUBRELATION_PARTIAL_LENGTHS

template<typename FF_ >

constexpr std::array<size_t, 1> bb::NonNativeFieldRelationImpl< FF_ >::SUBRELATION_PARTIAL_LENGTHS

staticconstexpr

Initial value:

{
        6 
    }

Definition at line 35 of file non_native_field_relation.hpp.

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

• src/barretenberg/relations/non_native_field_relation.hpp