Struct CubicExtField

pub struct CubicExtField<P>
where
    P: CubicExtConfig,
{
    pub c0: <P as CubicExtConfig>::BaseField,
    pub c1: <P as CubicExtConfig>::BaseField,
    pub c2: <P as CubicExtConfig>::BaseField,
}

An element of a cubic extension field F_p[X]/(X^3 - P::NONRESIDUE) is represented as c0 + c1 * X + c2 * X^2, for c0, c1, c2 in P::BaseField.

Fields

c0: <P as CubicExtConfig>::BaseField

c1: <P as CubicExtConfig>::BaseField

c2: <P as CubicExtConfig>::BaseField

Implementations

impl<P> CubicExtField<Fp3ConfigWrapper<P>>

where P: Fp3Config,

pub fn mul_assign_by_fp(&mut self, value: &<P as Fp3Config>::Fp)

In-place multiply all coefficients c0, c1, and c2 of self by an element from Fp.

Examples

use ark_mnt6_753::{Fq as Fp, Fq3 as Fp3};
let c0: Fp = Fp::rand(&mut test_rng());
let c1: Fp = Fp::rand(&mut test_rng());
let c2: Fp = Fp::rand(&mut test_rng());
let mut ext_element: Fp3 = Fp3::new(c0, c1, c2);

let base_field_element: Fp = Fp::rand(&mut test_rng());
ext_element.mul_assign_by_fp(&base_field_element);

assert_eq!(ext_element.c0, c0 * base_field_element);
assert_eq!(ext_element.c1, c1 * base_field_element);
assert_eq!(ext_element.c2, c2 * base_field_element);

impl<P> CubicExtField<Fp6ConfigWrapper<P>>

where P: Fp6Config,

pub fn mul_assign_by_fp2( &mut self, other: QuadExtField<Fp2ConfigWrapper<<P as Fp6Config>::Fp2Config>>, )

pub fn mul_by_fp( &mut self, element: &<<P as Fp6Config>::Fp2Config as Fp2Config>::Fp, )

pub fn mul_by_fp2( &mut self, element: &QuadExtField<Fp2ConfigWrapper<<P as Fp6Config>::Fp2Config>>, )

pub fn mul_by_1( &mut self, c1: &QuadExtField<Fp2ConfigWrapper<<P as Fp6Config>::Fp2Config>>, )

pub fn mul_by_01( &mut self, c0: &QuadExtField<Fp2ConfigWrapper<<P as Fp6Config>::Fp2Config>>, c1: &QuadExtField<Fp2ConfigWrapper<<P as Fp6Config>::Fp2Config>>, )

impl<P> CubicExtField<P>

where P: CubicExtConfig,

pub const fn new( c0: <P as CubicExtConfig>::BaseField, c1: <P as CubicExtConfig>::BaseField, c2: <P as CubicExtConfig>::BaseField, ) -> CubicExtField<P>

Create a new field element from coefficients c0, c1 and c2 so that the result is of the form c0 + c1 * X + c2 * X^2.

Examples

use ark_ff::models::cubic_extension::CubicExtField;

let c0: Fp2 = Fp2::rand(&mut test_rng());
let c1: Fp2 = Fp2::rand(&mut test_rng());
let c2: Fp2 = Fp2::rand(&mut test_rng());
// `Fp6` a degree-3 extension over `Fp2`.
let c: CubicExtField<Config> = Fp6::new(c0, c1, c2);

pub fn mul_assign_by_base_field( &mut self, value: &<P as CubicExtConfig>::BaseField, )

pub fn norm(&self) -> <P as CubicExtConfig>::BaseField

Calculate the norm of an element with respect to the base field P::BaseField. The norm maps an element a in the extension field Fq^m to an element in the BaseField Fq. Norm(a) = a * a^q * a^(q^2)

Trait Implementations

impl<'a, 'b, P> Add<&'a CubicExtField<P>> for &'b CubicExtField<P>

where P: CubicExtConfig,

type Output = CubicExtField<P>

The resulting type after applying the + operator.

fn add(self, other: &'a CubicExtField<P>) -> CubicExtField<P>

Performs the + operation.

impl<'a, P> Add<&'a CubicExtField<P>> for CubicExtField<P>

where P: CubicExtConfig,

type Output = CubicExtField<P>

The resulting type after applying the + operator.

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

Performs the + operation.

impl<'a, 'b, P> Add<&'a mut CubicExtField<P>> for &'b CubicExtField<P>

where P: CubicExtConfig,

type Output = CubicExtField<P>

The resulting type after applying the + operator.

fn add(self, other: &'a mut CubicExtField<P>) -> CubicExtField<P>

Performs the + operation.

impl<'a, P> Add<&'a mut CubicExtField<P>> for CubicExtField<P>

where P: CubicExtConfig,

type Output = CubicExtField<P>

The resulting type after applying the + operator.

fn add(self, other: &'a mut CubicExtField<P>) -> CubicExtField<P>

Performs the + operation.

impl<'b, P> Add<CubicExtField<P>> for &'b CubicExtField<P>

where P: CubicExtConfig,

type Output = CubicExtField<P>

The resulting type after applying the + operator.

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

Performs the + operation.

impl<P> Add for CubicExtField<P>

where P: CubicExtConfig,

type Output = CubicExtField<P>

The resulting type after applying the + operator.

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

Performs the + operation.

impl<'a, P> AddAssign<&'a CubicExtField<P>> for CubicExtField<P>

where P: CubicExtConfig,

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

Performs the += operation.

impl<'a, P> AddAssign<&'a mut CubicExtField<P>> for CubicExtField<P>

where P: CubicExtConfig,

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

Performs the += operation.

impl<P> AddAssign for CubicExtField<P>

where P: CubicExtConfig,

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

Performs the += operation.

impl<P> AdditiveGroup for CubicExtField<P>

where P: CubicExtConfig,

const ZERO: CubicExtField<P> = _

The additive identity of the field.

type Scalar = CubicExtField<P>

fn double(&self) -> CubicExtField<P>

Doubles self.

fn double_in_place(&mut self) -> &mut CubicExtField<P>

Doubles self in place.

fn neg_in_place(&mut self) -> &mut CubicExtField<P>

Negates self in place.

impl<P> CanonicalDeserialize for CubicExtField<P>

where P: CubicExtConfig,

fn deserialize_with_mode<R>( reader: R, compress: Compress, validate: Validate, ) -> Result<CubicExtField<P>, SerializationError>

where R: Read,

The general deserialize method that takes in customization flags.

fn deserialize_compressed<R>(reader: R) -> Result<Self, SerializationError>

where R: Read,

fn deserialize_compressed_unchecked<R>( reader: R, ) -> Result<Self, SerializationError>

where R: Read,

fn deserialize_uncompressed<R>(reader: R) -> Result<Self, SerializationError>

where R: Read,

fn deserialize_uncompressed_unchecked<R>( reader: R, ) -> Result<Self, SerializationError>

where R: Read,

impl<P> CanonicalDeserializeWithFlags for CubicExtField<P>

where P: CubicExtConfig,

fn deserialize_with_flags<R, F>( reader: R, ) -> Result<(CubicExtField<P>, F), SerializationError>

where R: Read, F: Flags,

Reads Self and Flags from reader. Returns empty flags by default.

impl<P> CanonicalSerialize for CubicExtField<P>

where P: CubicExtConfig,

fn serialize_with_mode<W>( &self, writer: W, _compress: Compress, ) -> Result<(), SerializationError>

where W: Write,

The general serialize method that takes in customization flags.

fn serialized_size(&self, _compress: Compress) -> usize

fn serialize_compressed<W>(&self, writer: W) -> Result<(), SerializationError>

where W: Write,

fn compressed_size(&self) -> usize

fn serialize_uncompressed<W>(&self, writer: W) -> Result<(), SerializationError>

where W: Write,

fn uncompressed_size(&self) -> usize

impl<P> CanonicalSerializeWithFlags for CubicExtField<P>

where P: CubicExtConfig,

fn serialize_with_flags<W, F>( &self, writer: W, flags: F, ) -> Result<(), SerializationError>

where W: Write, F: Flags,

Serializes self and flags into writer.

fn serialized_size_with_flags<F>(&self) -> usize

where F: Flags,

Serializes self and flags into writer.

impl<P> Clone for CubicExtField<P>

where P: CubicExtConfig, <P as CubicExtConfig>::BaseField: Copy,

fn clone(&self) -> CubicExtField<P>

Returns a copy of the value.

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

Performs copy-assignment from source.

impl<P> CyclotomicMultSubgroup for CubicExtField<Fp3ConfigWrapper<P>>

where P: Fp3Config,

const INVERSE_IS_FAST: bool = false

Is the inverse fast to compute? For example, in quadratic extensions, the inverse can be computed at the cost of negating one coordinate, which is much faster than standard inversion. By default this is false, but should be set to true for quadratic extensions.

fn cyclotomic_square(&self) -> Self

Compute a square in the cyclotomic subgroup. By default this is computed using Field::square, but for degree 12 extensions, this can be computed faster than normal squaring.

fn cyclotomic_square_in_place(&mut self) -> &mut Self

Square self in place. By default this is computed using Field::square_in_place, but for degree 12 extensions, this can be computed faster than normal squaring.

fn cyclotomic_inverse(&self) -> Option<Self>

Compute the inverse of self. See Self::INVERSE_IS_FAST for details. Returns None if self.is_zero(), and Some otherwise.

fn cyclotomic_inverse_in_place(&mut self) -> Option<&mut Self>

Compute the inverse of self. See Self::INVERSE_IS_FAST for details. Returns None if self.is_zero(), and Some otherwise.

fn cyclotomic_exp(&self, e: impl AsRef<[u64]>) -> Self

Compute a cyclotomic exponentiation of self with respect to e.

fn cyclotomic_exp_in_place(&mut self, e: impl AsRef<[u64]>)

Set self to be the result of exponentiating self by e, using efficient cyclotomic algorithms.

impl<P> CyclotomicMultSubgroup for CubicExtField<Fp6ConfigWrapper<P>>

where P: Fp6Config,

const INVERSE_IS_FAST: bool = false

Is the inverse fast to compute? For example, in quadratic extensions, the inverse can be computed at the cost of negating one coordinate, which is much faster than standard inversion. By default this is false, but should be set to true for quadratic extensions.

fn cyclotomic_square(&self) -> Self

Compute a square in the cyclotomic subgroup. By default this is computed using Field::square, but for degree 12 extensions, this can be computed faster than normal squaring.

fn cyclotomic_square_in_place(&mut self) -> &mut Self

Square self in place. By default this is computed using Field::square_in_place, but for degree 12 extensions, this can be computed faster than normal squaring.

fn cyclotomic_inverse(&self) -> Option<Self>

Compute the inverse of self. See Self::INVERSE_IS_FAST for details. Returns None if self.is_zero(), and Some otherwise.

fn cyclotomic_inverse_in_place(&mut self) -> Option<&mut Self>

Compute the inverse of self. See Self::INVERSE_IS_FAST for details. Returns None if self.is_zero(), and Some otherwise.

fn cyclotomic_exp(&self, e: impl AsRef<[u64]>) -> Self

Compute a cyclotomic exponentiation of self with respect to e.

fn cyclotomic_exp_in_place(&mut self, e: impl AsRef<[u64]>)

Set self to be the result of exponentiating self by e, using efficient cyclotomic algorithms.

impl<P> Debug for CubicExtField<P>

where P: CubicExtConfig, <P as CubicExtConfig>::BaseField: Debug,

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

Formats the value using the given formatter.

impl<P> Default for CubicExtField<P>

where P: CubicExtConfig, <P as CubicExtConfig>::BaseField: Default,

fn default() -> CubicExtField<P>

Returns the “default value” for a type.

impl<P> Display for CubicExtField<P>

where P: CubicExtConfig,

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

Formats the value using the given formatter.

impl<'a, 'b, P> Div<&'a CubicExtField<P>> for &'b CubicExtField<P>

where P: CubicExtConfig,

type Output = CubicExtField<P>

The resulting type after applying the / operator.

fn div(self, other: &'a CubicExtField<P>) -> CubicExtField<P>

Performs the / operation.

impl<'a, P> Div<&'a CubicExtField<P>> for CubicExtField<P>

where P: CubicExtConfig,

type Output = CubicExtField<P>

The resulting type after applying the / operator.

fn div(self, other: &CubicExtField<P>) -> CubicExtField<P>

Performs the / operation.

impl<'a, 'b, P> Div<&'a mut CubicExtField<P>> for &'b CubicExtField<P>

where P: CubicExtConfig,

type Output = CubicExtField<P>

The resulting type after applying the / operator.

fn div(self, other: &'a mut CubicExtField<P>) -> CubicExtField<P>

Performs the / operation.

impl<'a, P> Div<&'a mut CubicExtField<P>> for CubicExtField<P>

where P: CubicExtConfig,

type Output = CubicExtField<P>

The resulting type after applying the / operator.

fn div(self, other: &'a mut CubicExtField<P>) -> CubicExtField<P>

Performs the / operation.

impl<'b, P> Div<CubicExtField<P>> for &'b CubicExtField<P>

where P: CubicExtConfig,

type Output = CubicExtField<P>

The resulting type after applying the / operator.

fn div(self, other: CubicExtField<P>) -> CubicExtField<P>

Performs the / operation.

impl<P> Div for CubicExtField<P>

where P: CubicExtConfig,

type Output = CubicExtField<P>

The resulting type after applying the / operator.

fn div(self, other: CubicExtField<P>) -> CubicExtField<P>

Performs the / operation.

impl<'a, P> DivAssign<&'a CubicExtField<P>> for CubicExtField<P>

where P: CubicExtConfig,

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

Performs the /= operation.

impl<'a, P> DivAssign<&'a mut CubicExtField<P>> for CubicExtField<P>

where P: CubicExtConfig,

fn div_assign(&mut self, other: &'a mut CubicExtField<P>)

Performs the /= operation.

impl<P> DivAssign for CubicExtField<P>

where P: CubicExtConfig,

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

Performs the /= operation.

impl<P> FftField for CubicExtField<P>

where P: CubicExtConfig, <P as CubicExtConfig>::BaseField: FftField,

const GENERATOR: CubicExtField<P> = _

The generator of the multiplicative group of the field

const TWO_ADICITY: u32 = <P::BaseField>::TWO_ADICITY

Let N be the size of the multiplicative group defined by the field. Then TWO_ADICITY is the two-adicity of N, i.e. the integer s such that N = 2^s * t for some odd integer t.

const TWO_ADIC_ROOT_OF_UNITY: CubicExtField<P> = _

2^s root of unity computed by GENERATOR^t

const SMALL_SUBGROUP_BASE: Option<u32> = <P::BaseField>::SMALL_SUBGROUP_BASE

An integer b such that there exists a multiplicative subgroup of size b^k for some integer k.

const SMALL_SUBGROUP_BASE_ADICITY: Option<u32> = <P::BaseField>::SMALL_SUBGROUP_BASE_ADICITY

The integer k such that there exists a multiplicative subgroup of size Self::SMALL_SUBGROUP_BASE^k.

const LARGE_SUBGROUP_ROOT_OF_UNITY: Option<CubicExtField<P>> = _

GENERATOR^((MODULUS-1) / (2^s * SMALL_SUBGROUP_BASE^SMALL_SUBGROUP_BASE_ADICITY)) Used for mixed-radix FFT.

fn get_root_of_unity(n: u64) -> Option<Self>

Returns the root of unity of order n, if one exists. If no small multiplicative subgroup is defined, this is the 2-adic root of unity of order n (for n a power of 2). If a small multiplicative subgroup is defined, this is the root of unity of order n for the larger subgroup generated by FftConfig::LARGE_SUBGROUP_ROOT_OF_UNITY (for n = 2^i * FftConfig::SMALL_SUBGROUP_BASE^j for some i, j).

impl<P> Field for CubicExtField<P>

where P: CubicExtConfig,

fn legendre(&self) -> LegendreSymbol

Returns the Legendre symbol.

const SQRT_PRECOMP: Option<SqrtPrecomputation<CubicExtField<P>>> = P::SQRT_PRECOMP

Determines the algorithm for computing square roots.

const ONE: CubicExtField<P> = _

The multiplicative identity of the field.

type BasePrimeField = <P as CubicExtConfig>::BasePrimeField

fn extension_degree() -> u64

Returns the extension degree of this field with respect to Self::BasePrimeField.

fn from_base_prime_field( elem: <CubicExtField<P> as Field>::BasePrimeField, ) -> CubicExtField<P>

Constructs a field element from a single base prime field elements.

fn to_base_prime_field_elements( &self, ) -> impl Iterator<Item = <CubicExtField<P> as Field>::BasePrimeField>

fn from_base_prime_field_elems( elems: impl IntoIterator<Item = <CubicExtField<P> as Field>::BasePrimeField>, ) -> Option<CubicExtField<P>>

Convert a slice of base prime field elements into a field element. If the slice length != Self::extension_degree(), must return None.

fn from_random_bytes_with_flags<F>( bytes: &[u8], ) -> Option<(CubicExtField<P>, F)>

where F: Flags,

Attempt to deserialize a field element, splitting the bitflags metadata according to F specification. Returns None if the deserialization fails.

fn from_random_bytes(bytes: &[u8]) -> Option<CubicExtField<P>>

Attempt to deserialize a field element. Returns None if the deserialization fails.

fn square(&self) -> CubicExtField<P>

Returns self * self.

fn square_in_place(&mut self) -> &mut CubicExtField<P>

Squares self in place.

fn inverse(&self) -> Option<CubicExtField<P>>

Computes the multiplicative inverse of self if self is nonzero.

fn inverse_in_place(&mut self) -> Option<&mut CubicExtField<P>>

If self.inverse().is_none(), this just returns None. Otherwise, it sets self to self.inverse().unwrap().

fn frobenius_map_in_place(&mut self, power: usize)

Sets self to self^s, where s = Self::BasePrimeField::MODULUS^power. This is also called the Frobenius automorphism.

fn mul_by_base_prime_field( &self, elem: &<CubicExtField<P> as Field>::BasePrimeField, ) -> CubicExtField<P>

fn characteristic() -> &'static [u64]

Returns the characteristic of the field, in little-endian representation.

fn sqrt(&self) -> Option<Self>

Returns the square root of self, if it exists.

fn sqrt_in_place(&mut self) -> Option<&mut Self>

Sets self to be the square root of self, if it exists.

fn sum_of_products<const T: usize>(a: &[Self; T], b: &[Self; T]) -> Self

Returns sum([a_i * b_i]).

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

Returns self^s, where s = Self::BasePrimeField::MODULUS^power. This is also called the Frobenius automorphism.

fn pow<S>(&self, exp: S) -> Self

where S: AsRef<[u64]>,

Returns self^exp, where exp is an integer represented with u64 limbs, least significant limb first.

fn pow_with_table<S>(powers_of_2: &[Self], exp: S) -> Option<Self>

where S: AsRef<[u64]>,

Exponentiates a field element f by a number represented with u64 limbs, using a precomputed table containing as many powers of 2 of f as the 1 + the floor of log2 of the exponent exp, starting from the 1st power. That is, powers_of_2 should equal &[p, p^2, p^4, ..., p^(2^n)] when exp has at most n bits.

impl<P> From<bool> for CubicExtField<P>

where P: CubicExtConfig,

fn from(other: bool) -> CubicExtField<P>

Converts to this type from the input type.

impl<P> From<i128> for CubicExtField<P>

where P: CubicExtConfig,

fn from(val: i128) -> CubicExtField<P>

Converts to this type from the input type.

impl<P> From<i16> for CubicExtField<P>

where P: CubicExtConfig,

fn from(val: i16) -> CubicExtField<P>

Converts to this type from the input type.

impl<P> From<i32> for CubicExtField<P>

where P: CubicExtConfig,

fn from(val: i32) -> CubicExtField<P>

Converts to this type from the input type.

impl<P> From<i64> for CubicExtField<P>

where P: CubicExtConfig,

fn from(val: i64) -> CubicExtField<P>

Converts to this type from the input type.

impl<P> From<i8> for CubicExtField<P>

where P: CubicExtConfig,

fn from(val: i8) -> CubicExtField<P>

Converts to this type from the input type.

impl<P> From<u128> for CubicExtField<P>

where P: CubicExtConfig,

fn from(other: u128) -> CubicExtField<P>

Converts to this type from the input type.

impl<P> From<u16> for CubicExtField<P>

where P: CubicExtConfig,

fn from(other: u16) -> CubicExtField<P>

Converts to this type from the input type.

impl<P> From<u32> for CubicExtField<P>

where P: CubicExtConfig,

fn from(other: u32) -> CubicExtField<P>

Converts to this type from the input type.

impl<P> From<u64> for CubicExtField<P>

where P: CubicExtConfig,

fn from(other: u64) -> CubicExtField<P>

Converts to this type from the input type.

impl<P> From<u8> for CubicExtField<P>

where P: CubicExtConfig,

fn from(other: u8) -> CubicExtField<P>

Converts to this type from the input type.

impl<P> Hash for CubicExtField<P>

where P: CubicExtConfig, <P as CubicExtConfig>::BaseField: Hash,

fn hash<H>(&self, state: &mut H)

where H: Hasher,

Feeds this value into the given Hasher.

fn hash_slice<H>(data: &[Self], state: &mut H)

where H: Hasher, Self: Sized,

Feeds a slice of this type into the given Hasher.

impl<'a, 'b, P> Mul<&'a CubicExtField<P>> for &'b CubicExtField<P>

where P: CubicExtConfig,

type Output = CubicExtField<P>

The resulting type after applying the * operator.

fn mul(self, other: &'a CubicExtField<P>) -> CubicExtField<P>

Performs the * operation.

impl<'a, P> Mul<&'a CubicExtField<P>> for CubicExtField<P>

where P: CubicExtConfig,

type Output = CubicExtField<P>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<'a, 'b, P> Mul<&'a mut CubicExtField<P>> for &'b CubicExtField<P>

where P: CubicExtConfig,

type Output = CubicExtField<P>

The resulting type after applying the * operator.

fn mul(self, other: &'a mut CubicExtField<P>) -> CubicExtField<P>

Performs the * operation.

impl<'a, P> Mul<&'a mut CubicExtField<P>> for CubicExtField<P>

where P: CubicExtConfig,

type Output = CubicExtField<P>

The resulting type after applying the * operator.

fn mul(self, other: &'a mut CubicExtField<P>) -> CubicExtField<P>

Performs the * operation.

impl<'b, P> Mul<CubicExtField<P>> for &'b CubicExtField<P>

where P: CubicExtConfig,

type Output = CubicExtField<P>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<P> Mul for CubicExtField<P>

where P: CubicExtConfig,

type Output = CubicExtField<P>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<'a, P> MulAssign<&'a CubicExtField<P>> for CubicExtField<P>

where P: CubicExtConfig,

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

Performs the *= operation.

impl<'a, P> MulAssign<&'a mut CubicExtField<P>> for CubicExtField<P>

where P: CubicExtConfig,

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

Performs the *= operation.

impl<P> MulAssign for CubicExtField<P>

where P: CubicExtConfig,

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

Performs the *= operation.

impl<P> Neg for CubicExtField<P>

where P: CubicExtConfig,

type Output = CubicExtField<P>

The resulting type after applying the - operator.

fn neg(self) -> CubicExtField<P>

Performs the unary - operation.

impl<P> One for CubicExtField<P>

where P: CubicExtConfig,

fn one() -> CubicExtField<P>

Returns the multiplicative identity element of Self, 1.

fn is_one(&self) -> bool

Returns true if self is equal to the multiplicative identity.

fn set_one(&mut self)

Sets self to the multiplicative identity element of Self, 1.

impl<P> Ord for CubicExtField<P>

where P: CubicExtConfig,

CubicExtField elements are ordered lexicographically.

fn cmp(&self, other: &CubicExtField<P>) -> Ordering

This method returns an Ordering between self and other.

fn max(self, other: Self) -> Self

where Self: Sized,

Compares and returns the maximum of two values.

fn min(self, other: Self) -> Self

where Self: Sized,

Compares and returns the minimum of two values.

fn clamp(self, min: Self, max: Self) -> Self

where Self: Sized,

Restrict a value to a certain interval.

impl<P> PartialEq for CubicExtField<P>

where P: CubicExtConfig, <P as CubicExtConfig>::BaseField: PartialEq,

fn eq(&self, other: &CubicExtField<P>) -> bool

Tests for self and other values to be equal, and is used by ==.

fn ne(&self, other: &Rhs) -> bool

Tests for !=. The default implementation is almost always sufficient, and should not be overridden without very good reason.

impl<P> PartialOrd for CubicExtField<P>

where P: CubicExtConfig,

fn partial_cmp(&self, other: &CubicExtField<P>) -> Option<Ordering>

This method returns an ordering between self and other values if one exists.

fn lt(&self, other: &Rhs) -> bool

Tests less than (for self and other) and is used by the < operator.

fn le(&self, other: &Rhs) -> bool

Tests less than or equal to (for self and other) and is used by the <= operator.

fn gt(&self, other: &Rhs) -> bool

Tests greater than (for self and other) and is used by the > operator.

fn ge(&self, other: &Rhs) -> bool

Tests greater than or equal to (for self and other) and is used by the >= operator.

impl<'a, P> Product<&'a CubicExtField<P>> for CubicExtField<P>

where P: CubicExtConfig,

fn product<I>(iter: I) -> CubicExtField<P>

where I: Iterator<Item = &'a CubicExtField<P>>,

Takes an iterator and generates Self from the elements by multiplying the items.

impl<P> Product for CubicExtField<P>

where P: CubicExtConfig,

fn product<I>(iter: I) -> CubicExtField<P>

where I: Iterator<Item = CubicExtField<P>>,

Takes an iterator and generates Self from the elements by multiplying the items.

impl<'a, 'b, P> Sub<&'a CubicExtField<P>> for &'b CubicExtField<P>

where P: CubicExtConfig,

type Output = CubicExtField<P>

The resulting type after applying the - operator.

fn sub(self, other: &'a CubicExtField<P>) -> CubicExtField<P>

Performs the - operation.

impl<'a, P> Sub<&'a CubicExtField<P>> for CubicExtField<P>

where P: CubicExtConfig,

type Output = CubicExtField<P>

The resulting type after applying the - operator.

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

Performs the - operation.

impl<'a, 'b, P> Sub<&'a mut CubicExtField<P>> for &'b CubicExtField<P>

where P: CubicExtConfig,

type Output = CubicExtField<P>

The resulting type after applying the - operator.

fn sub(self, other: &'a mut CubicExtField<P>) -> CubicExtField<P>

Performs the - operation.

impl<'a, P> Sub<&'a mut CubicExtField<P>> for CubicExtField<P>

where P: CubicExtConfig,

type Output = CubicExtField<P>

The resulting type after applying the - operator.

fn sub(self, other: &'a mut CubicExtField<P>) -> CubicExtField<P>

Performs the - operation.

impl<'b, P> Sub<CubicExtField<P>> for &'b CubicExtField<P>

where P: CubicExtConfig,

type Output = CubicExtField<P>

The resulting type after applying the - operator.

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

Performs the - operation.

impl<P> Sub for CubicExtField<P>

where P: CubicExtConfig,

type Output = CubicExtField<P>

The resulting type after applying the - operator.

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

Performs the - operation.

impl<'a, P> SubAssign<&'a CubicExtField<P>> for CubicExtField<P>

where P: CubicExtConfig,

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

Performs the -= operation.

impl<'a, P> SubAssign<&'a mut CubicExtField<P>> for CubicExtField<P>

where P: CubicExtConfig,

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

Performs the -= operation.

impl<P> SubAssign for CubicExtField<P>

where P: CubicExtConfig,

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

Performs the -= operation.

impl<'a, P> Sum<&'a CubicExtField<P>> for CubicExtField<P>

where P: CubicExtConfig,

fn sum<I>(iter: I) -> CubicExtField<P>

where I: Iterator<Item = &'a CubicExtField<P>>,

Takes an iterator and generates Self from the elements by “summing up” the items.

impl<P> Sum for CubicExtField<P>

where P: CubicExtConfig,

fn sum<I>(iter: I) -> CubicExtField<P>

where I: Iterator<Item = CubicExtField<P>>,

Takes an iterator and generates Self from the elements by “summing up” the items.

impl<P> ToConstraintField<<P as CubicExtConfig>::BasePrimeField> for CubicExtField<P>

where P: CubicExtConfig, <P as CubicExtConfig>::BaseField: ToConstraintField<<P as CubicExtConfig>::BasePrimeField>,

fn to_field_elements( &self, ) -> Option<Vec<<P as CubicExtConfig>::BasePrimeField>>

impl<P> Valid for CubicExtField<P>

where P: CubicExtConfig,

fn check(&self) -> Result<(), SerializationError>

fn batch_check<'a>( batch: impl Iterator<Item = &'a Self> + Send, ) -> Result<(), SerializationError>

where Self: 'a,

impl<P> Zero for CubicExtField<P>

where P: CubicExtConfig,

fn zero() -> CubicExtField<P>

Returns the additive identity element of Self, 0.

fn is_zero(&self) -> bool

Returns true if self is equal to the additive identity.

fn set_zero(&mut self)

Sets self to the additive identity element of Self, 0.

impl<P> Zeroize for CubicExtField<P>

where P: CubicExtConfig,

fn zeroize(&mut self)

Zero out this object from memory using Rust intrinsics which ensure the zeroization operation is not “optimized away” by the compiler.

impl<P> Copy for CubicExtField<P>

where P: CubicExtConfig, <P as CubicExtConfig>::BaseField: Copy,

impl<P> Eq for CubicExtField<P>

where P: CubicExtConfig, <P as CubicExtConfig>::BaseField: PartialEq,