Struct QuadExtVar

pub struct QuadExtVar<BF: FieldVar<P::BaseField, P::BasePrimeField>, P: QuadExtVarConfig<BF>>
where
    for<'a> &'a BF: FieldOpsBounds<'a, P::BaseField, BF>,
{
    pub c0: BF,
    pub c1: BF,
    /* private fields */
}

This struct is the R1CS equivalent of the quadratic extension field type in ark-ff, i.e. ark_ff::QuadExtField.

Fields

c0: BF

The zero-th coefficient of this field element.

c1: BF

The first coefficient of this field element.

Implementations

impl<BF: FieldVar<P::BaseField, P::BasePrimeField>, P: QuadExtVarConfig<BF>> QuadExtVar<BF, P>

where for<'a> &'a BF: FieldOpsBounds<'a, P::BaseField, BF>,

pub fn new(c0: BF, c1: BF) -> Self

Constructs a QuadExtVar from the underlying coefficients.

pub fn mul_base_field_by_nonresidue(fe: &BF) -> Result<BF, SynthesisError>

Multiplies a variable of the base field by the quadratic nonresidue P::NONRESIDUE that is used to construct the extension field.

pub fn mul_by_base_field_constant(&self, fe: P::BaseField) -> Self

Multiplies self by a constant from the base field.

pub fn mul_assign_by_base_field_constant(&mut self, fe: P::BaseField)

Sets self = self.mul_by_base_field_constant(fe).

pub fn unitary_inverse(&self) -> Result<Self, SynthesisError>

This is only to be used when the element is known to be in the cyclotomic subgroup.

pub fn cyclotomic_exp( &self, exponent: impl AsRef<[u64]>, ) -> Result<Self, SynthesisError>

where Self: FieldVar<QuadExtField<P>, P::BasePrimeField>,

This is only to be used when the element is known to be in the cyclotomic subgroup.

impl<P: Fp12Config> QuadExtVar<CubicExtVar<QuadExtVar<FpVar<<<<P as Fp12Config>::Fp6Config as Fp6Config>::Fp2Config as Fp2Config>::Fp>, Fp2ConfigWrapper<<<P as Fp12Config>::Fp6Config as Fp6Config>::Fp2Config>>, Fp6ConfigWrapper<<P as Fp12Config>::Fp6Config>>, Fp12ConfigWrapper<P>>

pub fn mul_by_014( &self, c0: &Fp2Var<<<P as Fp12Config>::Fp6Config as Fp6Config>::Fp2Config>, c1: &Fp2Var<<<P as Fp12Config>::Fp6Config as Fp6Config>::Fp2Config>, d1: &Fp2Var<<<P as Fp12Config>::Fp6Config as Fp6Config>::Fp2Config>, ) -> Result<Self, SynthesisError>

Multiplies by a sparse element of the form (c0 = (c0, c1, 0), c1 = (0, d1, 0)).

pub fn mul_by_034( &self, c0: &Fp2Var<<<P as Fp12Config>::Fp6Config as Fp6Config>::Fp2Config>, d0: &Fp2Var<<<P as Fp12Config>::Fp6Config as Fp6Config>::Fp2Config>, d1: &Fp2Var<<<P as Fp12Config>::Fp6Config as Fp6Config>::Fp2Config>, ) -> Result<Self, SynthesisError>

Multiplies by a sparse element of the form (c0 = (c0, 0, 0), c1 = (d0, d1, 0)).

pub fn cyclotomic_square(&self) -> Result<Self, SynthesisError>

Squares self when self is in the cyclotomic subgroup.

pub fn optimized_cyclotomic_exp( &self, exponent: impl AsRef<[u64]>, ) -> Result<Self, SynthesisError>

Like Self::cyclotomic_exp, but additionally uses cyclotomic squaring.

Trait Implementations

impl<'a, BF: FieldVar<P::BaseField, P::BasePrimeField>, P: QuadExtVarConfig<BF>> Add<&'a QuadExtVar<BF, P>> for QuadExtVar<BF, P>

where for<'b> &'b BF: FieldOpsBounds<'b, P::BaseField, BF>,

type Output = QuadExtVar<BF, P>

The resulting type after applying the + operator.

fn add(self, other: &'a QuadExtVar<BF, P>) -> Self::Output

Performs the + operation.

impl<'a, BF: FieldVar<P::BaseField, P::BasePrimeField>, P: QuadExtVarConfig<BF>> Add<QuadExtField<P>> for &'a QuadExtVar<BF, P>

where for<'b> &'b BF: FieldOpsBounds<'b, P::BaseField, BF>,

type Output = QuadExtVar<BF, P>

The resulting type after applying the + operator.

fn add(self, other: QuadExtField<P>) -> Self::Output

Performs the + operation.

impl<BF: FieldVar<P::BaseField, P::BasePrimeField>, P: QuadExtVarConfig<BF>> Add<QuadExtField<P>> for QuadExtVar<BF, P>

where for<'b> &'b BF: FieldOpsBounds<'b, P::BaseField, BF>,

type Output = QuadExtVar<BF, P>

The resulting type after applying the + operator.

fn add(self, other: QuadExtField<P>) -> Self::Output

Performs the + operation.

impl<'a, BF: FieldVar<P::BaseField, P::BasePrimeField>, P: QuadExtVarConfig<BF>> Add<QuadExtVar<BF, P>> for &'a QuadExtVar<BF, P>

where for<'b> &'b BF: FieldOpsBounds<'b, P::BaseField, BF>,

type Output = QuadExtVar<BF, P>

The resulting type after applying the + operator.

fn add(self, other: QuadExtVar<BF, P>) -> Self::Output

Performs the + operation.

impl<'a, BF: FieldVar<P::BaseField, P::BasePrimeField>, P: QuadExtVarConfig<BF>> Add for &'a QuadExtVar<BF, P>

where for<'b> &'b BF: FieldOpsBounds<'b, P::BaseField, BF>,

type Output = QuadExtVar<BF, P>

The resulting type after applying the + operator.

fn add(self, other: &'a QuadExtVar<BF, P>) -> Self::Output

Performs the + operation.

impl<BF: FieldVar<P::BaseField, P::BasePrimeField>, P: QuadExtVarConfig<BF>> Add for QuadExtVar<BF, P>

where for<'b> &'b BF: FieldOpsBounds<'b, P::BaseField, BF>,

type Output = QuadExtVar<BF, P>

The resulting type after applying the + operator.

fn add(self, other: QuadExtVar<BF, P>) -> Self::Output

Performs the + operation.

impl<'a, BF: FieldVar<P::BaseField, P::BasePrimeField>, P: QuadExtVarConfig<BF>> AddAssign<&'a QuadExtVar<BF, P>> for QuadExtVar<BF, P>

where for<'b> &'b BF: FieldOpsBounds<'b, P::BaseField, BF>,

fn add_assign(&mut self, other: &'a QuadExtVar<BF, P>)

Performs the += operation.

impl<BF: FieldVar<P::BaseField, P::BasePrimeField>, P: QuadExtVarConfig<BF>> AddAssign<QuadExtField<P>> for QuadExtVar<BF, P>

where for<'b> &'b BF: FieldOpsBounds<'b, P::BaseField, BF>,

fn add_assign(&mut self, other: QuadExtField<P>)

Performs the += operation.

impl<BF: FieldVar<P::BaseField, P::BasePrimeField>, P: QuadExtVarConfig<BF>> AddAssign for QuadExtVar<BF, P>

where for<'b> &'b BF: FieldOpsBounds<'b, P::BaseField, BF>,

fn add_assign(&mut self, other: QuadExtVar<BF, P>)

Performs the += operation.

impl<BF, P> AllocVar<QuadExtField<P>, <P as QuadExtConfig>::BasePrimeField> for QuadExtVar<BF, P>

where BF: FieldVar<P::BaseField, P::BasePrimeField>, for<'b> &'b BF: FieldOpsBounds<'b, P::BaseField, BF>, P: QuadExtVarConfig<BF>,

fn new_variable<T: Borrow<QuadExtField<P>>>( cs: impl Into<Namespace<P::BasePrimeField>>, f: impl FnOnce() -> Result<T, SynthesisError>, mode: AllocationMode, ) -> Result<Self, SynthesisError>

Allocates a new variable of type Self in the ConstraintSystem cs. The mode of allocation is decided by mode.

fn new_constant( cs: impl Into<Namespace<F>>, t: impl Borrow<V>, ) -> Result<Self, SynthesisError>

Allocates a new constant of type Self in the ConstraintSystem cs.

fn new_input<T: Borrow<V>>( cs: impl Into<Namespace<F>>, f: impl FnOnce() -> Result<T, SynthesisError>, ) -> Result<Self, SynthesisError>

Allocates a new public input of type Self in the ConstraintSystem cs.

fn new_witness<T: Borrow<V>>( cs: impl Into<Namespace<F>>, f: impl FnOnce() -> Result<T, SynthesisError>, ) -> Result<Self, SynthesisError>

Allocates a new private witness of type Self in the ConstraintSystem cs.

fn new_variable_with_inferred_mode<T: Borrow<V>>( cs: impl Into<Namespace<F>>, f: impl FnOnce() -> Result<T, SynthesisError>, ) -> Result<Self, SynthesisError>

Allocates a new constant or private witness of type Self in the ConstraintSystem cs with the allocation mode inferred from cs. A constant is allocated if cs is None, and a private witness is allocated otherwise.

impl<BF, P: QuadExtVarConfig<BF>> Clone for QuadExtVar<BF, P>

where for<'a> &'a BF: FieldOpsBounds<'a, P::BaseField, BF>, BF: Clone + FieldVar<P::BaseField, P::BasePrimeField>, PhantomData<P>: Clone,

fn clone(&self) -> Self

Returns a copy of the value.

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl<BF, P> CondSelectGadget<<P as QuadExtConfig>::BasePrimeField> for QuadExtVar<BF, P>

where BF: FieldVar<P::BaseField, P::BasePrimeField>, for<'b> &'b BF: FieldOpsBounds<'b, P::BaseField, BF>, P: QuadExtVarConfig<BF>,

fn conditionally_select( cond: &Boolean<P::BasePrimeField>, true_value: &Self, false_value: &Self, ) -> Result<Self, SynthesisError>

If cond == &Boolean::TRUE, then this returns true_value; else, returns false_value.

fn conditionally_select_power_of_two_vector( position: &[Boolean<ConstraintF>], values: &[Self], ) -> Result<Self, SynthesisError>

Returns an element of values whose index in represented by position. position is an array of boolean that represents an unsigned integer in big endian order.

impl<P: Fp6Config> CubicExtVarConfig<QuadExtVar<FpVar<<<P as Fp6Config>::Fp2Config as Fp2Config>::Fp>, Fp2ConfigWrapper<<P as Fp6Config>::Fp2Config>>> for Fp6ConfigWrapper<P>

fn mul_base_field_vars_by_frob_coeff( c1: &mut Fp2Var<P::Fp2Config>, c2: &mut Fp2Var<P::Fp2Config>, power: usize, )

Multiply the base field of the CubicExtVar by the appropriate Frobenius coefficient. This is equivalent to Self::mul_base_field_by_frob_coeff(c1, c2, power).

impl<BF, P: QuadExtVarConfig<BF>> Debug for QuadExtVar<BF, P>

where for<'a> &'a BF: FieldOpsBounds<'a, P::BaseField, BF>, BF: Debug + FieldVar<P::BaseField, P::BasePrimeField>,

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.

impl<BF, P> EqGadget<<P as QuadExtConfig>::BasePrimeField> for QuadExtVar<BF, P>

where BF: FieldVar<P::BaseField, P::BasePrimeField>, for<'b> &'b BF: FieldOpsBounds<'b, P::BaseField, BF>, P: QuadExtVarConfig<BF>,

fn is_eq( &self, other: &Self, ) -> Result<Boolean<P::BasePrimeField>, SynthesisError>

Output a Boolean value representing whether self.value() == other.value().

fn conditional_enforce_equal( &self, other: &Self, condition: &Boolean<P::BasePrimeField>, ) -> Result<(), SynthesisError>

If should_enforce == true, enforce that self and other are equal; else, enforce a vacuously true statement.

fn conditional_enforce_not_equal( &self, other: &Self, condition: &Boolean<P::BasePrimeField>, ) -> Result<(), SynthesisError>

If should_enforce == true, enforce that self and other are not equal; else, enforce a vacuously true statement.

fn is_neq(&self, other: &Self) -> Result<Boolean<F>, SynthesisError>

Output a Boolean value representing whether self.value() != other.value().

fn enforce_equal(&self, other: &Self) -> Result<(), SynthesisError>

Enforce that self and other are equal.

fn enforce_not_equal(&self, other: &Self) -> Result<(), SynthesisError>

Enforce that self and other are not equal.

impl<BF, P> FieldVar<QuadExtField<P>, <P as QuadExtConfig>::BasePrimeField> for QuadExtVar<BF, P>

where BF: FieldVar<P::BaseField, P::BasePrimeField>, for<'a> &'a BF: FieldOpsBounds<'a, P::BaseField, BF>, P: QuadExtVarConfig<BF>,

fn constant(other: QuadExtField<P>) -> Self

Returns a constant with value v.

fn zero() -> Self

Returns the constant F::zero().

fn one() -> Self

Returns the constant F::one().

fn double(&self) -> Result<Self, SynthesisError>

Computes self + self.

fn negate(&self) -> Result<Self, SynthesisError>

Coputes -self.

fn square(&self) -> Result<Self, SynthesisError>

Computes self * self.

fn mul_equals(&self, other: &Self, result: &Self) -> Result<(), SynthesisError>

Enforces that self * other == result.

fn frobenius_map(&self, power: usize) -> Result<Self, SynthesisError>

Computes the frobenius map over self.

fn inverse(&self) -> Result<Self, SynthesisError>

Computes result such that self * result == Self::one().

fn is_zero(&self) -> Result<Boolean<ConstraintF>, SynthesisError>

Returns a Boolean representing whether self == Self::zero().

fn is_one(&self) -> Result<Boolean<ConstraintF>, SynthesisError>

Returns a Boolean representing whether self == Self::one().

fn double_in_place(&mut self) -> Result<&mut Self, SynthesisError>

Sets self = self + self.

fn negate_in_place(&mut self) -> Result<&mut Self, SynthesisError>

Sets self = -self.

fn square_in_place(&mut self) -> Result<&mut Self, SynthesisError>

Sets self = self.square().

fn square_equals(&self, result: &Self) -> Result<(), SynthesisError>

Enforces that self * self == result.

fn mul_by_inverse(&self, d: &Self) -> Result<Self, SynthesisError>

Returns (self / d). The constraint system will be unsatisfiable when d = 0.

fn mul_by_inverse_unchecked(&self, d: &Self) -> Result<Self, SynthesisError>

Returns (self / d).

fn frobenius_map_in_place( &mut self, power: usize, ) -> Result<&mut Self, SynthesisError>

Sets self = self.frobenius_map().

fn pow_le(&self, bits: &[Boolean<ConstraintF>]) -> Result<Self, SynthesisError>

Comptues self^bits, where bits is a little-endian bit-wise decomposition of the exponent.

fn pow_by_constant<S: AsRef<[u64]>>( &self, exp: S, ) -> Result<Self, SynthesisError>

Computes self^S, where S is interpreted as an little-endian u64-decomposition of an integer.

impl<BF, P> From<Boolean<<P as QuadExtConfig>::BasePrimeField>> for QuadExtVar<BF, P>

where BF: FieldVar<P::BaseField, P::BasePrimeField>, for<'a> &'a BF: FieldOpsBounds<'a, P::BaseField, BF>, P: QuadExtVarConfig<BF>,

fn from(other: Boolean<P::BasePrimeField>) -> Self

Converts to this type from the input type.

impl<'a, BF: FieldVar<P::BaseField, P::BasePrimeField>, P: QuadExtVarConfig<BF>> Mul<&'a QuadExtVar<BF, P>> for QuadExtVar<BF, P>

where for<'b> &'b BF: FieldOpsBounds<'b, P::BaseField, BF>,

type Output = QuadExtVar<BF, P>

The resulting type after applying the * operator.

fn mul(self, other: &'a QuadExtVar<BF, P>) -> Self::Output

Performs the * operation.

impl<'a, BF: FieldVar<P::BaseField, P::BasePrimeField>, P: QuadExtVarConfig<BF>> Mul<QuadExtField<P>> for &'a QuadExtVar<BF, P>

where for<'b> &'b BF: FieldOpsBounds<'b, P::BaseField, BF>,

type Output = QuadExtVar<BF, P>

The resulting type after applying the * operator.

fn mul(self, other: QuadExtField<P>) -> Self::Output

Performs the * operation.

impl<BF: FieldVar<P::BaseField, P::BasePrimeField>, P: QuadExtVarConfig<BF>> Mul<QuadExtField<P>> for QuadExtVar<BF, P>

where for<'b> &'b BF: FieldOpsBounds<'b, P::BaseField, BF>,

type Output = QuadExtVar<BF, P>

The resulting type after applying the * operator.

fn mul(self, other: QuadExtField<P>) -> Self::Output

Performs the * operation.

impl<'a, BF: FieldVar<P::BaseField, P::BasePrimeField>, P: QuadExtVarConfig<BF>> Mul<QuadExtVar<BF, P>> for &'a QuadExtVar<BF, P>

where for<'b> &'b BF: FieldOpsBounds<'b, P::BaseField, BF>,

type Output = QuadExtVar<BF, P>

The resulting type after applying the * operator.

fn mul(self, other: QuadExtVar<BF, P>) -> Self::Output

Performs the * operation.

impl<'a, BF: FieldVar<P::BaseField, P::BasePrimeField>, P: QuadExtVarConfig<BF>> Mul for &'a QuadExtVar<BF, P>

where for<'b> &'b BF: FieldOpsBounds<'b, P::BaseField, BF>,

type Output = QuadExtVar<BF, P>

The resulting type after applying the * operator.

fn mul(self, other: &'a QuadExtVar<BF, P>) -> Self::Output

Performs the * operation.

impl<BF: FieldVar<P::BaseField, P::BasePrimeField>, P: QuadExtVarConfig<BF>> Mul for QuadExtVar<BF, P>

where for<'b> &'b BF: FieldOpsBounds<'b, P::BaseField, BF>,

type Output = QuadExtVar<BF, P>

The resulting type after applying the * operator.

fn mul(self, other: QuadExtVar<BF, P>) -> Self::Output

Performs the * operation.

impl<'a, BF: FieldVar<P::BaseField, P::BasePrimeField>, P: QuadExtVarConfig<BF>> MulAssign<&'a QuadExtVar<BF, P>> for QuadExtVar<BF, P>

where for<'b> &'b BF: FieldOpsBounds<'b, P::BaseField, BF>,

fn mul_assign(&mut self, other: &'a QuadExtVar<BF, P>)

Performs the *= operation.

impl<BF: FieldVar<P::BaseField, P::BasePrimeField>, P: QuadExtVarConfig<BF>> MulAssign<QuadExtField<P>> for QuadExtVar<BF, P>

where for<'b> &'b BF: FieldOpsBounds<'b, P::BaseField, BF>,

fn mul_assign(&mut self, other: QuadExtField<P>)

Performs the *= operation.

impl<BF: FieldVar<P::BaseField, P::BasePrimeField>, P: QuadExtVarConfig<BF>> MulAssign for QuadExtVar<BF, P>

where for<'b> &'b BF: FieldOpsBounds<'b, P::BaseField, BF>,

fn mul_assign(&mut self, other: QuadExtVar<BF, P>)

Performs the *= operation.

impl<P: Fp4Config> QuadExtVarConfig<QuadExtVar<FpVar<<<P as Fp4Config>::Fp2Config as Fp2Config>::Fp>, Fp2ConfigWrapper<<P as Fp4Config>::Fp2Config>>> for Fp4ConfigWrapper<P>

fn mul_base_field_var_by_frob_coeff(fe: &mut Fp2Var<P::Fp2Config>, power: usize)

Multiply the base field of the QuadExtVar by the appropriate Frobenius coefficient. This is equivalent to Self::mul_base_field_by_frob_coeff(power).

impl<'a, BF: FieldVar<P::BaseField, P::BasePrimeField>, P: QuadExtVarConfig<BF>> Sub<&'a QuadExtVar<BF, P>> for QuadExtVar<BF, P>

where for<'b> &'b BF: FieldOpsBounds<'b, P::BaseField, BF>,

type Output = QuadExtVar<BF, P>

The resulting type after applying the - operator.

fn sub(self, other: &'a QuadExtVar<BF, P>) -> Self::Output

Performs the - operation.

impl<'a, BF: FieldVar<P::BaseField, P::BasePrimeField>, P: QuadExtVarConfig<BF>> Sub<QuadExtField<P>> for &'a QuadExtVar<BF, P>

where for<'b> &'b BF: FieldOpsBounds<'b, P::BaseField, BF>,

type Output = QuadExtVar<BF, P>

The resulting type after applying the - operator.

fn sub(self, other: QuadExtField<P>) -> Self::Output

Performs the - operation.

impl<BF: FieldVar<P::BaseField, P::BasePrimeField>, P: QuadExtVarConfig<BF>> Sub<QuadExtField<P>> for QuadExtVar<BF, P>

where for<'b> &'b BF: FieldOpsBounds<'b, P::BaseField, BF>,

type Output = QuadExtVar<BF, P>

The resulting type after applying the - operator.

fn sub(self, other: QuadExtField<P>) -> Self::Output

Performs the - operation.

impl<'a, BF: FieldVar<P::BaseField, P::BasePrimeField>, P: QuadExtVarConfig<BF>> Sub<QuadExtVar<BF, P>> for &'a QuadExtVar<BF, P>

where for<'b> &'b BF: FieldOpsBounds<'b, P::BaseField, BF>,

type Output = QuadExtVar<BF, P>

The resulting type after applying the - operator.

fn sub(self, other: QuadExtVar<BF, P>) -> Self::Output

Performs the - operation.

impl<'a, BF: FieldVar<P::BaseField, P::BasePrimeField>, P: QuadExtVarConfig<BF>> Sub for &'a QuadExtVar<BF, P>

where for<'b> &'b BF: FieldOpsBounds<'b, P::BaseField, BF>,

type Output = QuadExtVar<BF, P>

The resulting type after applying the - operator.

fn sub(self, other: &'a QuadExtVar<BF, P>) -> Self::Output

Performs the - operation.

impl<BF: FieldVar<P::BaseField, P::BasePrimeField>, P: QuadExtVarConfig<BF>> Sub for QuadExtVar<BF, P>

where for<'b> &'b BF: FieldOpsBounds<'b, P::BaseField, BF>,

type Output = QuadExtVar<BF, P>

The resulting type after applying the - operator.

fn sub(self, other: QuadExtVar<BF, P>) -> Self::Output

Performs the - operation.

impl<'a, BF: FieldVar<P::BaseField, P::BasePrimeField>, P: QuadExtVarConfig<BF>> SubAssign<&'a QuadExtVar<BF, P>> for QuadExtVar<BF, P>

where for<'b> &'b BF: FieldOpsBounds<'b, P::BaseField, BF>,

fn sub_assign(&mut self, other: &'a QuadExtVar<BF, P>)

Performs the -= operation.

impl<BF: FieldVar<P::BaseField, P::BasePrimeField>, P: QuadExtVarConfig<BF>> SubAssign<QuadExtField<P>> for QuadExtVar<BF, P>

where for<'b> &'b BF: FieldOpsBounds<'b, P::BaseField, BF>,

fn sub_assign(&mut self, other: QuadExtField<P>)

Performs the -= operation.

impl<BF: FieldVar<P::BaseField, P::BasePrimeField>, P: QuadExtVarConfig<BF>> SubAssign for QuadExtVar<BF, P>

where for<'b> &'b BF: FieldOpsBounds<'b, P::BaseField, BF>,

fn sub_assign(&mut self, other: QuadExtVar<BF, P>)

Performs the -= operation.

impl<BF, P> ThreeBitCondNegLookupGadget<<P as QuadExtConfig>::BasePrimeField> for QuadExtVar<BF, P>

where BF: FieldVar<P::BaseField, P::BasePrimeField> + ThreeBitCondNegLookupGadget<P::BasePrimeField, TableConstant = P::BaseField>, for<'b> &'b BF: FieldOpsBounds<'b, P::BaseField, BF>, P: QuadExtVarConfig<BF>,

type TableConstant = QuadExtField<P>

The type of values being looked up.

fn three_bit_cond_neg_lookup( b: &[Boolean<P::BasePrimeField>], b0b1: &Boolean<P::BasePrimeField>, c: &[Self::TableConstant], ) -> Result<Self, SynthesisError>

Interprets the slice bits as a two-bit integer b = bits[0] + (bits[1] << 1), and then outputs constants[b] * c, where c = if bits[2] { -1 } else { 1 };.

impl<BF, P> ToBitsGadget<<P as QuadExtConfig>::BasePrimeField> for QuadExtVar<BF, P>

where BF: FieldVar<P::BaseField, P::BasePrimeField>, for<'b> &'b BF: FieldOpsBounds<'b, P::BaseField, BF>, P: QuadExtVarConfig<BF>,

fn to_bits_le(&self) -> Result<Vec<Boolean<P::BasePrimeField>>, SynthesisError>

Outputs the canonical little-endian bit-wise representation of self.

fn to_non_unique_bits_le( &self, ) -> Result<Vec<Boolean<P::BasePrimeField>>, SynthesisError>

Outputs a possibly non-unique little-endian bit-wise representation of self.

fn to_bits_be(&self) -> Result<Vec<Boolean<F>>, SynthesisError>

Outputs the canonical big-endian bit-wise representation of self.

fn to_non_unique_bits_be(&self) -> Result<Vec<Boolean<F>>, SynthesisError>

Outputs a possibly non-unique big-endian bit-wise representation of self.

impl<BF, P> ToBytesGadget<<P as QuadExtConfig>::BasePrimeField> for QuadExtVar<BF, P>

where BF: FieldVar<P::BaseField, P::BasePrimeField>, for<'b> &'b BF: FieldOpsBounds<'b, P::BaseField, BF>, P: QuadExtVarConfig<BF>,

fn to_bytes_le(&self) -> Result<Vec<UInt8<P::BasePrimeField>>, SynthesisError>

Outputs a canonical, little-endian, byte decomposition of self.

fn to_non_unique_bytes_le( &self, ) -> Result<Vec<UInt8<P::BasePrimeField>>, SynthesisError>

Outputs a possibly non-unique byte decomposition of self.

impl<BF, P> ToConstraintFieldGadget<<P as QuadExtConfig>::BasePrimeField> for QuadExtVar<BF, P>

where BF: FieldVar<P::BaseField, P::BasePrimeField> + ToConstraintFieldGadget<P::BasePrimeField>, for<'a> &'a BF: FieldOpsBounds<'a, P::BaseField, BF>, P: QuadExtVarConfig<BF>,

fn to_constraint_field( &self, ) -> Result<Vec<FpVar<P::BasePrimeField>>, SynthesisError>

Converts self to FpVar<ConstraintF> variables.

impl<BF, P> TwoBitLookupGadget<<P as QuadExtConfig>::BasePrimeField> for QuadExtVar<BF, P>

where BF: FieldVar<P::BaseField, P::BasePrimeField> + TwoBitLookupGadget<P::BasePrimeField, TableConstant = P::BaseField>, for<'b> &'b BF: FieldOpsBounds<'b, P::BaseField, BF>, P: QuadExtVarConfig<BF>,

type TableConstant = QuadExtField<P>

The type of values being looked up.

fn two_bit_lookup( b: &[Boolean<P::BasePrimeField>], c: &[Self::TableConstant], ) -> Result<Self, SynthesisError>

Interprets the slice bits as a two-bit integer b = bits[0] + (bits[1] << 1), and then outputs constants[b].

impl<'a, BF, P> FieldOpsBounds<'a, QuadExtField<P>, QuadExtVar<BF, P>> for &'a QuadExtVar<BF, P>

where BF: FieldVar<P::BaseField, P::BasePrimeField>, for<'b> &'b BF: FieldOpsBounds<'b, P::BaseField, BF>, P: QuadExtVarConfig<BF>,

impl<'a, BF, P> FieldOpsBounds<'a, QuadExtField<P>, QuadExtVar<BF, P>> for QuadExtVar<BF, P>

where BF: FieldVar<P::BaseField, P::BasePrimeField>, for<'b> &'b BF: FieldOpsBounds<'b, P::BaseField, BF>, P: QuadExtVarConfig<BF>,