Struct ark_r1cs_std::fields::cubic_extension::CubicExtVar

pub struct CubicExtVar<BF: FieldVar<P::BaseField, P::BasePrimeField>, P: CubicExtVarParams<BF>> where
    for<'a> &'a BF: FieldOpsBounds<'a, P::BaseField, BF>,  {
    pub c0: BF,
    pub c1: BF,
    pub c2: BF,
    // some fields omitted
}

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

Fields

c0: BF

The zero-th coefficient of this field element.

c1: BF

The first coefficient of this field element.

c2: BF

The second coefficient of this field element.

Implementations

impl<BF: FieldVar<P::BaseField, P::BasePrimeField>, P: CubicExtVarParams<BF>> CubicExtVar<BF, P> where
    for<'a> &'a BF: FieldOpsBounds<'a, P::BaseField, BF>, 

pub fn new(c0: BF, c1: BF, c2: BF) -> Self

Constructs a CubicExtVar 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 cubic 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).

impl<P: Fp6Parameters> CubicExtVar<QuadExtVar<FpVar<<<P as Fp6Parameters>::Fp2Params as Fp2Parameters>::Fp>, Fp2ParamsWrapper<<P as Fp6Parameters>::Fp2Params>>, Fp6ParamsWrapper<P>>

pub fn mul_by_0_c1_0(
    &self,
    c1: &Fp2Var<P::Fp2Params>
) -> Result<Self, SynthesisError>

Multiplies self by a sparse element which has c0 == c2 == zero.

pub fn mul_by_c0_c1_0(
    &self,
    c0: &Fp2Var<P::Fp2Params>,
    c1: &Fp2Var<P::Fp2Params>
) -> Result<Self, SynthesisError>

Multiplies self by a sparse element which has c2 == zero.

Trait Implementations

impl<'a, BF: FieldVar<P::BaseField, P::BasePrimeField>, P: CubicExtVarParams<BF>> Add<&'a CubicExtVar<BF, P>> for &'a CubicExtVar<BF, P> where
    for<'b> &'b BF: FieldOpsBounds<'b, P::BaseField, BF>, 

type Output = CubicExtVar<BF, P>

The resulting type after applying the + operator.

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

Performs the + operation.

impl<'a, BF: FieldVar<P::BaseField, P::BasePrimeField>, P: CubicExtVarParams<BF>> Add<&'a CubicExtVar<BF, P>> for CubicExtVar<BF, P> where
    for<'b> &'b BF: FieldOpsBounds<'b, P::BaseField, BF>, 

type Output = CubicExtVar<BF, P>

The resulting type after applying the + operator.

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

Performs the + operation.

impl<'a, BF: FieldVar<P::BaseField, P::BasePrimeField>, P: CubicExtVarParams<BF>> Add<CubicExtField<P>> for &'a CubicExtVar<BF, P> where
    for<'b> &'b BF: FieldOpsBounds<'b, P::BaseField, BF>, 

type Output = CubicExtVar<BF, P>

The resulting type after applying the + operator.

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

Performs the + operation.

impl<BF: FieldVar<P::BaseField, P::BasePrimeField>, P: CubicExtVarParams<BF>> Add<CubicExtField<P>> for CubicExtVar<BF, P> where
    for<'b> &'b BF: FieldOpsBounds<'b, P::BaseField, BF>, 

type Output = CubicExtVar<BF, P>

The resulting type after applying the + operator.

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

Performs the + operation.

impl<'a, BF: FieldVar<P::BaseField, P::BasePrimeField>, P: CubicExtVarParams<BF>> Add<CubicExtVar<BF, P>> for &'a CubicExtVar<BF, P> where
    for<'b> &'b BF: FieldOpsBounds<'b, P::BaseField, BF>, 

type Output = CubicExtVar<BF, P>

The resulting type after applying the + operator.

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

Performs the + operation.

impl<BF: FieldVar<P::BaseField, P::BasePrimeField>, P: CubicExtVarParams<BF>> Add<CubicExtVar<BF, P>> for CubicExtVar<BF, P> where
    for<'b> &'b BF: FieldOpsBounds<'b, P::BaseField, BF>, 

type Output = CubicExtVar<BF, P>

The resulting type after applying the + operator.

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

Performs the + operation.

impl<'a, BF: FieldVar<P::BaseField, P::BasePrimeField>, P: CubicExtVarParams<BF>> AddAssign<&'a CubicExtVar<BF, P>> for CubicExtVar<BF, P> where
    for<'b> &'b BF: FieldOpsBounds<'b, P::BaseField, BF>, 

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

Performs the += operation.

impl<BF: FieldVar<P::BaseField, P::BasePrimeField>, P: CubicExtVarParams<BF>> AddAssign<CubicExtField<P>> for CubicExtVar<BF, P> where
    for<'b> &'b BF: FieldOpsBounds<'b, P::BaseField, BF>, 

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

Performs the += operation.

impl<BF: FieldVar<P::BaseField, P::BasePrimeField>, P: CubicExtVarParams<BF>> AddAssign<CubicExtVar<BF, P>> for CubicExtVar<BF, P> where
    for<'b> &'b BF: FieldOpsBounds<'b, P::BaseField, BF>, 

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

Performs the += operation.

impl<BF, P> AllocVar<CubicExtField<P>, <P as CubicExtParameters>::BasePrimeField> for CubicExtVar<BF, P> where
    BF: FieldVar<P::BaseField, P::BasePrimeField>,
    for<'a> &'a BF: FieldOpsBounds<'a, P::BaseField, BF>,
    P: CubicExtVarParams<BF>, 

fn new_variable<T: Borrow<CubicExtField<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.

impl<BF: FieldVar<P::BaseField, P::BasePrimeField>, P: CubicExtVarParams<BF>> Clone for CubicExtVar<BF, P> where
    for<'a> &'a BF: FieldOpsBounds<'a, P::BaseField, BF>,
    BF: 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 CubicExtParameters>::BasePrimeField> for CubicExtVar<BF, P> where
    BF: FieldVar<P::BaseField, P::BasePrimeField>,
    for<'a> &'a BF: FieldOpsBounds<'a, P::BaseField, BF>,
    P: CubicExtVarParams<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<BF: FieldVar<P::BaseField, P::BasePrimeField>, P: CubicExtVarParams<BF>> Debug for CubicExtVar<BF, P> where
    for<'a> &'a BF: FieldOpsBounds<'a, P::BaseField, BF>,
    BF: Debug, 

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

Formats the value using the given formatter.

impl<BF, P> EqGadget<<P as CubicExtParameters>::BasePrimeField> for CubicExtVar<BF, P> where
    BF: FieldVar<P::BaseField, P::BasePrimeField>,
    for<'a> &'a BF: FieldOpsBounds<'a, P::BaseField, BF>,
    P: CubicExtVarParams<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<CubicExtField<P>, <P as CubicExtParameters>::BasePrimeField> for CubicExtVar<BF, P> where
    BF: FieldVar<P::BaseField, P::BasePrimeField>,
    for<'a> &'a BF: FieldOpsBounds<'a, P::BaseField, BF>,
    P: CubicExtVarParams<BF>, 

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

Use the Chung-Hasan asymmetric squaring formula.

(Devegili OhEig Scott Dahab — Multiplication and Squaring on Abstract Pairing-Friendly Fields.pdf; Section 4 (CH-SQR2))

fn constant(other: CubicExtField<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 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 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 CubicExtParameters>::BasePrimeField>> for CubicExtVar<BF, P> where
    BF: FieldVar<P::BaseField, P::BasePrimeField>,
    for<'a> &'a BF: FieldOpsBounds<'a, P::BaseField, BF>,
    P: CubicExtVarParams<BF>, 

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

Performs the conversion.

impl<'a, BF: FieldVar<P::BaseField, P::BasePrimeField>, P: CubicExtVarParams<BF>> Mul<&'a CubicExtVar<BF, P>> for &'a CubicExtVar<BF, P> where
    for<'b> &'b BF: FieldOpsBounds<'b, P::BaseField, BF>, 

type Output = CubicExtVar<BF, P>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<'a, BF: FieldVar<P::BaseField, P::BasePrimeField>, P: CubicExtVarParams<BF>> Mul<&'a CubicExtVar<BF, P>> for CubicExtVar<BF, P> where
    for<'b> &'b BF: FieldOpsBounds<'b, P::BaseField, BF>, 

type Output = CubicExtVar<BF, P>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<'a, BF: FieldVar<P::BaseField, P::BasePrimeField>, P: CubicExtVarParams<BF>> Mul<CubicExtField<P>> for &'a CubicExtVar<BF, P> where
    for<'b> &'b BF: FieldOpsBounds<'b, P::BaseField, BF>, 

type Output = CubicExtVar<BF, P>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<BF: FieldVar<P::BaseField, P::BasePrimeField>, P: CubicExtVarParams<BF>> Mul<CubicExtField<P>> for CubicExtVar<BF, P> where
    for<'b> &'b BF: FieldOpsBounds<'b, P::BaseField, BF>, 

type Output = CubicExtVar<BF, P>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<'a, BF: FieldVar<P::BaseField, P::BasePrimeField>, P: CubicExtVarParams<BF>> Mul<CubicExtVar<BF, P>> for &'a CubicExtVar<BF, P> where
    for<'b> &'b BF: FieldOpsBounds<'b, P::BaseField, BF>, 

type Output = CubicExtVar<BF, P>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<BF: FieldVar<P::BaseField, P::BasePrimeField>, P: CubicExtVarParams<BF>> Mul<CubicExtVar<BF, P>> for CubicExtVar<BF, P> where
    for<'b> &'b BF: FieldOpsBounds<'b, P::BaseField, BF>, 

type Output = CubicExtVar<BF, P>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<'a, BF: FieldVar<P::BaseField, P::BasePrimeField>, P: CubicExtVarParams<BF>> MulAssign<&'a CubicExtVar<BF, P>> for CubicExtVar<BF, P> where
    for<'b> &'b BF: FieldOpsBounds<'b, P::BaseField, BF>, 

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

Performs the *= operation.

impl<BF: FieldVar<P::BaseField, P::BasePrimeField>, P: CubicExtVarParams<BF>> MulAssign<CubicExtField<P>> for CubicExtVar<BF, P> where
    for<'b> &'b BF: FieldOpsBounds<'b, P::BaseField, BF>, 

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

Performs the *= operation.

impl<BF: FieldVar<P::BaseField, P::BasePrimeField>, P: CubicExtVarParams<BF>> MulAssign<CubicExtVar<BF, P>> for CubicExtVar<BF, P> where
    for<'b> &'b BF: FieldOpsBounds<'b, P::BaseField, BF>, 

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

Performs the *= operation.

impl<P: Fp6Parameters> QuadExtVarParams<CubicExtVar<FpVar<<<P as Fp6Parameters>::Fp3Params as Fp3Parameters>::Fp>, Fp3ParamsWrapper<<P as Fp6Parameters>::Fp3Params>>> for Fp6ParamsWrapper<P>

fn mul_base_field_var_by_frob_coeff(fe: &mut Fp3Var<P::Fp3Params>, 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<P: Fp12Parameters> QuadExtVarParams<CubicExtVar<QuadExtVar<FpVar<<<<P as Fp12Parameters>::Fp6Params as Fp6Parameters>::Fp2Params as Fp2Parameters>::Fp>, Fp2ParamsWrapper<<<P as Fp12Parameters>::Fp6Params as Fp6Parameters>::Fp2Params>>, Fp6ParamsWrapper<<P as Fp12Parameters>::Fp6Params>>> for Fp12ParamsWrapper<P>

fn mul_base_field_var_by_frob_coeff(fe: &mut Fp6Var<P::Fp6Params>, 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<BF, P> R1CSVar<<P as CubicExtParameters>::BasePrimeField> for CubicExtVar<BF, P> where
    BF: FieldVar<P::BaseField, P::BasePrimeField>,
    for<'a> &'a BF: FieldOpsBounds<'a, P::BaseField, BF>,
    P: CubicExtVarParams<BF>, 

type Value = CubicExtField<P>

The type of the “native” value that Self represents in the constraint system.

fn cs(&self) -> ConstraintSystemRef<P::BasePrimeField>

Returns the underlying ConstraintSystemRef.

fn value(&self) -> Result<Self::Value, SynthesisError>

Returns the value that is assigned to self in the underlying ConstraintSystem.

fn is_constant(&self) -> bool

Returns true if self is a circuit-generation-time constant.

impl<'a, BF: FieldVar<P::BaseField, P::BasePrimeField>, P: CubicExtVarParams<BF>> Sub<&'a CubicExtVar<BF, P>> for &'a CubicExtVar<BF, P> where
    for<'b> &'b BF: FieldOpsBounds<'b, P::BaseField, BF>, 

type Output = CubicExtVar<BF, P>

The resulting type after applying the - operator.

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

Performs the - operation.

impl<'a, BF: FieldVar<P::BaseField, P::BasePrimeField>, P: CubicExtVarParams<BF>> Sub<&'a CubicExtVar<BF, P>> for CubicExtVar<BF, P> where
    for<'b> &'b BF: FieldOpsBounds<'b, P::BaseField, BF>, 

type Output = CubicExtVar<BF, P>

The resulting type after applying the - operator.

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

Performs the - operation.

impl<'a, BF: FieldVar<P::BaseField, P::BasePrimeField>, P: CubicExtVarParams<BF>> Sub<CubicExtField<P>> for &'a CubicExtVar<BF, P> where
    for<'b> &'b BF: FieldOpsBounds<'b, P::BaseField, BF>, 

type Output = CubicExtVar<BF, P>

The resulting type after applying the - operator.

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

Performs the - operation.

impl<BF: FieldVar<P::BaseField, P::BasePrimeField>, P: CubicExtVarParams<BF>> Sub<CubicExtField<P>> for CubicExtVar<BF, P> where
    for<'b> &'b BF: FieldOpsBounds<'b, P::BaseField, BF>, 

type Output = CubicExtVar<BF, P>

The resulting type after applying the - operator.

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

Performs the - operation.

impl<'a, BF: FieldVar<P::BaseField, P::BasePrimeField>, P: CubicExtVarParams<BF>> Sub<CubicExtVar<BF, P>> for &'a CubicExtVar<BF, P> where
    for<'b> &'b BF: FieldOpsBounds<'b, P::BaseField, BF>, 

type Output = CubicExtVar<BF, P>

The resulting type after applying the - operator.

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

Performs the - operation.

impl<BF: FieldVar<P::BaseField, P::BasePrimeField>, P: CubicExtVarParams<BF>> Sub<CubicExtVar<BF, P>> for CubicExtVar<BF, P> where
    for<'b> &'b BF: FieldOpsBounds<'b, P::BaseField, BF>, 

type Output = CubicExtVar<BF, P>

The resulting type after applying the - operator.

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

Performs the - operation.

impl<'a, BF: FieldVar<P::BaseField, P::BasePrimeField>, P: CubicExtVarParams<BF>> SubAssign<&'a CubicExtVar<BF, P>> for CubicExtVar<BF, P> where
    for<'b> &'b BF: FieldOpsBounds<'b, P::BaseField, BF>, 

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

Performs the -= operation.

impl<BF: FieldVar<P::BaseField, P::BasePrimeField>, P: CubicExtVarParams<BF>> SubAssign<CubicExtField<P>> for CubicExtVar<BF, P> where
    for<'b> &'b BF: FieldOpsBounds<'b, P::BaseField, BF>, 

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

Performs the -= operation.

impl<BF: FieldVar<P::BaseField, P::BasePrimeField>, P: CubicExtVarParams<BF>> SubAssign<CubicExtVar<BF, P>> for CubicExtVar<BF, P> where
    for<'b> &'b BF: FieldOpsBounds<'b, P::BaseField, BF>, 

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

Performs the -= operation.

impl<BF, P> ThreeBitCondNegLookupGadget<<P as CubicExtParameters>::BasePrimeField> for CubicExtVar<BF, P> where
    BF: FieldVar<P::BaseField, P::BasePrimeField> + ThreeBitCondNegLookupGadget<P::BasePrimeField, TableConstant = P::BaseField>,
    for<'a> &'a BF: FieldOpsBounds<'a, P::BaseField, BF>,
    P: CubicExtVarParams<BF>, 

type TableConstant = CubicExtField<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 CubicExtParameters>::BasePrimeField> for CubicExtVar<BF, P> where
    BF: FieldVar<P::BaseField, P::BasePrimeField>,
    for<'a> &'a BF: FieldOpsBounds<'a, P::BaseField, BF>,
    P: CubicExtVarParams<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 CubicExtParameters>::BasePrimeField> for CubicExtVar<BF, P> where
    BF: FieldVar<P::BaseField, P::BasePrimeField>,
    for<'a> &'a BF: FieldOpsBounds<'a, P::BaseField, BF>,
    P: CubicExtVarParams<BF>, 

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

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

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

Outputs a possibly non-unique byte decomposition of self.

impl<BF, P> ToConstraintFieldGadget<<P as CubicExtParameters>::BasePrimeField> for CubicExtVar<BF, P> where
    BF: FieldVar<P::BaseField, P::BasePrimeField>,
    for<'a> &'a BF: FieldOpsBounds<'a, P::BaseField, BF>,
    P: CubicExtVarParams<BF>,
    BF: ToConstraintFieldGadget<P::BasePrimeField>, 

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

Converts self to FpVar<ConstraintF> variables.

impl<BF, P> TwoBitLookupGadget<<P as CubicExtParameters>::BasePrimeField> for CubicExtVar<BF, P> where
    BF: FieldVar<P::BaseField, P::BasePrimeField> + TwoBitLookupGadget<P::BasePrimeField, TableConstant = P::BaseField>,
    for<'a> &'a BF: FieldOpsBounds<'a, P::BaseField, BF>,
    P: CubicExtVarParams<BF>, 

type TableConstant = CubicExtField<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, CubicExtField<P>, CubicExtVar<BF, P>> for CubicExtVar<BF, P> where
    BF: FieldVar<P::BaseField, P::BasePrimeField>,
    for<'b> &'b BF: FieldOpsBounds<'b, P::BaseField, BF>,
    P: CubicExtVarParams<BF>, 

impl<'a, BF, P> FieldOpsBounds<'a, CubicExtField<P>, CubicExtVar<BF, P>> for &'a CubicExtVar<BF, P> where
    BF: FieldVar<P::BaseField, P::BasePrimeField>,
    for<'b> &'b BF: FieldOpsBounds<'b, P::BaseField, BF>,
    P: CubicExtVarParams<BF>,