Struct QuadExtField

pub struct QuadExtField<P: QuadExtConfig> {
    pub c0: P::BaseField,
    pub c1: P::BaseField,
}

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

Fields

c0: P::BaseField

Coefficient c0 in the representation of the field element c = c0 + c1 * X

c1: P::BaseField

Coefficient c1 in the representation of the field element c = c0 + c1 * X

Implementations

impl<P: Fp2Config> QuadExtField<Fp2ConfigWrapper<P>>

pub fn mul_assign_by_fp(&mut self, other: &P::Fp)

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

Examples

let c0: Fp = Fp::rand(&mut test_rng());
let c1: Fp = Fp::rand(&mut test_rng());
let mut ext_element: Fp2 = Fp2::new(c0, c1);

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);

impl<P: Fp4Config> QuadExtField<Fp4ConfigWrapper<P>>

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

pub fn mul_by_fp2(&mut self, element: &Fp2<P::Fp2Config>)

impl<P: Fp6Config> QuadExtField<Fp6ConfigWrapper<P>>

pub fn mul_by_034( &mut self, c0: &<P::Fp3Config as Fp3Config>::Fp, c3: &<P::Fp3Config as Fp3Config>::Fp, c4: &<P::Fp3Config as Fp3Config>::Fp, )

pub fn mul_by_014( &mut self, c0: &<P::Fp3Config as Fp3Config>::Fp, c1: &<P::Fp3Config as Fp3Config>::Fp, c4: &<P::Fp3Config as Fp3Config>::Fp, )

impl<P: Fp12Config> QuadExtField<Fp12ConfigWrapper<P>>

pub fn mul_by_fp(&mut self, element: &<Self as Field>::BasePrimeField)

pub fn mul_by_034( &mut self, c0: &Fp2<<<P as Fp12Config>::Fp6Config as Fp6Config>::Fp2Config>, c3: &Fp2<<<P as Fp12Config>::Fp6Config as Fp6Config>::Fp2Config>, c4: &Fp2<<<P as Fp12Config>::Fp6Config as Fp6Config>::Fp2Config>, )

pub fn mul_by_014( &mut self, c0: &Fp2<<<P as Fp12Config>::Fp6Config as Fp6Config>::Fp2Config>, c1: &Fp2<<<P as Fp12Config>::Fp6Config as Fp6Config>::Fp2Config>, c4: &Fp2<<<P as Fp12Config>::Fp6Config as Fp6Config>::Fp2Config>, )

impl<P: QuadExtConfig> QuadExtField<P>

pub const fn new(c0: P::BaseField, c1: P::BaseField) -> Self

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

Examples

let c0: Fp = Fp::rand(&mut test_rng());
let c1: Fp = Fp::rand(&mut test_rng());
// `Fp2` a degree-2 extension over `Fp`.
let c: Fp2 = Fp2::new(c0, c1);

pub fn conjugate_in_place(&mut self) -> &mut Self

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

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

Norm of QuadExtField over P::BaseField:Norm(a) = a * a.conjugate(). This simplifies to: Norm(a) = a.x^2 - P::NON_RESIDUE * a.y^2. This is alternatively expressed as Norm(a) = a^(1 + p).

Examples

let c: Fp2 = Fp2::rand(&mut test_rng());
let norm = c.norm();
// We now compute the norm using the `a * a.conjugate()` approach.
// A Frobenius map sends an element of `Fp2` to one of its p_th powers:
// `a.frobenius_map_in_place(1) -> a^p` and `a^p` is also `a`'s Galois conjugate.
let mut c_conjugate = c;
c_conjugate.frobenius_map_in_place(1);
let norm2 = c * c_conjugate;
// Computing the norm of an `Fp2` element should result in an element
// in BaseField `Fp`, i.e. `c1 == 0`
assert!(norm2.c1.is_zero());
assert_eq!(norm, norm2.c0);

pub fn mul_assign_by_basefield(&mut self, element: &P::BaseField)

In-place multiply both coefficients c0 & c1 of the quadratic extension field by an element from the base field.

Trait Implementations

impl<'a, 'b, P: QuadExtConfig> Add<&'a QuadExtField<P>> for &'b QuadExtField<P>

type Output = QuadExtField<P>

The resulting type after applying the + operator.

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

Performs the + operation.

impl<'a, P: QuadExtConfig> Add<&'a QuadExtField<P>> for QuadExtField<P>

type Output = QuadExtField<P>

The resulting type after applying the + operator.

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

Performs the + operation.

impl<'a, 'b, P: QuadExtConfig> Add<&'a mut QuadExtField<P>> for &'b QuadExtField<P>

type Output = QuadExtField<P>

The resulting type after applying the + operator.

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

Performs the + operation.

impl<'a, P: QuadExtConfig> Add<&'a mut QuadExtField<P>> for QuadExtField<P>

type Output = QuadExtField<P>

The resulting type after applying the + operator.

fn add(self, other: &'a mut Self) -> Self

Performs the + operation.

impl<'b, P: QuadExtConfig> Add<QuadExtField<P>> for &'b QuadExtField<P>

type Output = QuadExtField<P>

The resulting type after applying the + operator.

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

Performs the + operation.

impl<P: QuadExtConfig> Add for QuadExtField<P>

type Output = QuadExtField<P>

The resulting type after applying the + operator.

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

Performs the + operation.

impl<'a, P: QuadExtConfig> AddAssign<&'a QuadExtField<P>> for QuadExtField<P>

fn add_assign(&mut self, other: &Self)

Performs the += operation.

impl<'a, P: QuadExtConfig> AddAssign<&'a mut QuadExtField<P>> for QuadExtField<P>

fn add_assign(&mut self, other: &'a mut Self)

Performs the += operation.

impl<P: QuadExtConfig> AddAssign for QuadExtField<P>

fn add_assign(&mut self, other: Self)

Performs the += operation.

impl<P: QuadExtConfig> AdditiveGroup for QuadExtField<P>

const ZERO: Self = _

The additive identity of the field.

type Scalar = QuadExtField<P>

fn double(&self) -> Self

Doubles self.

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

Doubles self in place.

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

Negates self in place.

impl<P: QuadExtConfig> CanonicalDeserialize for QuadExtField<P>

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

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: QuadExtConfig> CanonicalDeserializeWithFlags for QuadExtField<P>

fn deserialize_with_flags<R: Read, F: Flags>( reader: R, ) -> Result<(Self, F), SerializationError>

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

impl<P: QuadExtConfig> CanonicalSerialize for QuadExtField<P>

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

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: QuadExtConfig> CanonicalSerializeWithFlags for QuadExtField<P>

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

Serializes self and flags into writer.

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

Serializes self and flags into writer.

impl<P: QuadExtConfig> Clone for QuadExtField<P>

where P::BaseField: Copy,

fn clone(&self) -> Self

Returns a copy of the value.

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

Performs copy-assignment from source.

impl<P: QuadExtConfig> Debug for QuadExtField<P>

where P::BaseField: Debug,

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

Formats the value using the given formatter.

impl<P: QuadExtConfig> Default for QuadExtField<P>

where P::BaseField: Default,

fn default() -> Self

Returns the “default value” for a type.

impl<P: QuadExtConfig> Display for QuadExtField<P>

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

Formats the value using the given formatter.

impl<P: QuadExtConfig> Distribution<QuadExtField<P>> for Standard

fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> QuadExtField<P>

Generate a random value of T, using rng as the source of randomness.

fn sample_iter<R>(self, rng: R) -> DistIter<Self, R, T>

where R: Rng, Self: Sized,

Create an iterator that generates random values of T, using rng as the source of randomness.

fn map<F, S>(self, func: F) -> DistMap<Self, F, T, S>

where F: Fn(T) -> S, Self: Sized,

Create a distribution of values of ‘S’ by mapping the output of Self through the closure F

impl<'a, 'b, P: QuadExtConfig> Div<&'a QuadExtField<P>> for &'b QuadExtField<P>

type Output = QuadExtField<P>

The resulting type after applying the / operator.

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

Performs the / operation.

impl<'a, P: QuadExtConfig> Div<&'a QuadExtField<P>> for QuadExtField<P>

type Output = QuadExtField<P>

The resulting type after applying the / operator.

fn div(self, other: &Self) -> Self

Performs the / operation.

impl<'a, 'b, P: QuadExtConfig> Div<&'a mut QuadExtField<P>> for &'b QuadExtField<P>

type Output = QuadExtField<P>

The resulting type after applying the / operator.

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

Performs the / operation.

impl<'a, P: QuadExtConfig> Div<&'a mut QuadExtField<P>> for QuadExtField<P>

type Output = QuadExtField<P>

The resulting type after applying the / operator.

fn div(self, other: &'a mut Self) -> Self

Performs the / operation.

impl<'b, P: QuadExtConfig> Div<QuadExtField<P>> for &'b QuadExtField<P>

type Output = QuadExtField<P>

The resulting type after applying the / operator.

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

Performs the / operation.

impl<P: QuadExtConfig> Div for QuadExtField<P>

type Output = QuadExtField<P>

The resulting type after applying the / operator.

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

Performs the / operation.

impl<'a, P: QuadExtConfig> DivAssign<&'a QuadExtField<P>> for QuadExtField<P>

fn div_assign(&mut self, other: &Self)

Performs the /= operation.

impl<'a, P: QuadExtConfig> DivAssign<&'a mut QuadExtField<P>> for QuadExtField<P>

fn div_assign(&mut self, other: &'a mut Self)

Performs the /= operation.

impl<P: QuadExtConfig> DivAssign for QuadExtField<P>

fn div_assign(&mut self, other: Self)

Performs the /= operation.

impl<P: QuadExtConfig> FftField for QuadExtField<P>

where P::BaseField: FftField,

const GENERATOR: Self = _

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: Self = _

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<Self> = _

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: QuadExtConfig> Field for QuadExtField<P>

const SQRT_PRECOMP: Option<SqrtPrecomputation<Self>> = None

Determines the algorithm for computing square roots.

const ONE: Self = _

The multiplicative identity of the field.

type BasePrimeField = <P as QuadExtConfig>::BasePrimeField

fn extension_degree() -> u64

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

fn from_base_prime_field(elem: Self::BasePrimeField) -> Self

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

fn to_base_prime_field_elements( &self, ) -> impl Iterator<Item = Self::BasePrimeField>

fn from_base_prime_field_elems( elems: impl IntoIterator<Item = Self::BasePrimeField>, ) -> Option<Self>

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

fn square(&self) -> Self

Returns self * self.

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

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<Self>

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

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

Squares self in place.

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

Computes the multiplicative inverse of self if self is nonzero.

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

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 legendre(&self) -> LegendreSymbol

Returns a LegendreSymbol, which indicates whether this field element is 1 : a quadratic residue 0 : equal to 0 -1 : a quadratic non-residue

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 mul_by_base_prime_field(&self, elem: &Self::BasePrimeField) -> Self

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

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

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

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

fn pow_with_table<S: AsRef<[u64]>>(powers_of_2: &[Self], exp: S) -> Option<Self>

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: QuadExtConfig> From<bool> for QuadExtField<P>

fn from(other: bool) -> Self

Converts to this type from the input type.

impl<P: QuadExtConfig> From<i128> for QuadExtField<P>

fn from(val: i128) -> Self

Converts to this type from the input type.

impl<P: QuadExtConfig> From<i16> for QuadExtField<P>

fn from(val: i16) -> Self

Converts to this type from the input type.

impl<P: QuadExtConfig> From<i32> for QuadExtField<P>

fn from(val: i32) -> Self

Converts to this type from the input type.

impl<P: QuadExtConfig> From<i64> for QuadExtField<P>

fn from(val: i64) -> Self

Converts to this type from the input type.

impl<P: QuadExtConfig> From<i8> for QuadExtField<P>

fn from(val: i8) -> Self

Converts to this type from the input type.

impl<P: QuadExtConfig> From<u128> for QuadExtField<P>

fn from(other: u128) -> Self

Converts to this type from the input type.

impl<P: QuadExtConfig> From<u16> for QuadExtField<P>

fn from(other: u16) -> Self

Converts to this type from the input type.

impl<P: QuadExtConfig> From<u32> for QuadExtField<P>

fn from(other: u32) -> Self

Converts to this type from the input type.

impl<P: QuadExtConfig> From<u64> for QuadExtField<P>

fn from(other: u64) -> Self

Converts to this type from the input type.

impl<P: QuadExtConfig> From<u8> for QuadExtField<P>

fn from(other: u8) -> Self

Converts to this type from the input type.

impl<P: QuadExtConfig> Hash for QuadExtField<P>

where P::BaseField: Hash,

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

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: QuadExtConfig> Mul<&'a QuadExtField<P>> for &'b QuadExtField<P>

type Output = QuadExtField<P>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<'a, P: QuadExtConfig> Mul<&'a QuadExtField<P>> for QuadExtField<P>

type Output = QuadExtField<P>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<'a, 'b, P: QuadExtConfig> Mul<&'a mut QuadExtField<P>> for &'b QuadExtField<P>

type Output = QuadExtField<P>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<'a, P: QuadExtConfig> Mul<&'a mut QuadExtField<P>> for QuadExtField<P>

type Output = QuadExtField<P>

The resulting type after applying the * operator.

fn mul(self, other: &'a mut Self) -> Self

Performs the * operation.

impl<'b, P: QuadExtConfig> Mul<QuadExtField<P>> for &'b QuadExtField<P>

type Output = QuadExtField<P>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<P: QuadExtConfig> Mul for QuadExtField<P>

type Output = QuadExtField<P>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<'a, P: QuadExtConfig> MulAssign<&'a QuadExtField<P>> for QuadExtField<P>

fn mul_assign(&mut self, other: &Self)

Performs the *= operation.

impl<'a, P: QuadExtConfig> MulAssign<&'a mut QuadExtField<P>> for QuadExtField<P>

fn mul_assign(&mut self, other: &'a mut Self)

Performs the *= operation.

impl<P: QuadExtConfig> MulAssign for QuadExtField<P>

fn mul_assign(&mut self, other: Self)

Performs the *= operation.

impl<P: QuadExtConfig> Neg for QuadExtField<P>

type Output = QuadExtField<P>

The resulting type after applying the - operator.

fn neg(self) -> Self

Performs the unary - operation.

impl<P: QuadExtConfig> One for QuadExtField<P>

fn one() -> Self

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: QuadExtConfig> Ord for QuadExtField<P>

QuadExtField elements are ordered lexicographically.

fn cmp(&self, other: &Self) -> 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: QuadExtConfig> PartialEq for QuadExtField<P>

where P::BaseField: PartialEq,

fn eq(&self, other: &Self) -> 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: QuadExtConfig> PartialOrd for QuadExtField<P>

fn partial_cmp(&self, other: &Self) -> 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: QuadExtConfig> Product<&'a QuadExtField<P>> for QuadExtField<P>

fn product<I: Iterator<Item = &'a Self>>(iter: I) -> Self

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

impl<P: QuadExtConfig> Product for QuadExtField<P>

fn product<I: Iterator<Item = Self>>(iter: I) -> Self

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

impl<'a, 'b, P: QuadExtConfig> Sub<&'a QuadExtField<P>> for &'b QuadExtField<P>

type Output = QuadExtField<P>

The resulting type after applying the - operator.

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

Performs the - operation.

impl<'a, P: QuadExtConfig> Sub<&'a QuadExtField<P>> for QuadExtField<P>

type Output = QuadExtField<P>

The resulting type after applying the - operator.

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

Performs the - operation.

impl<'a, 'b, P: QuadExtConfig> Sub<&'a mut QuadExtField<P>> for &'b QuadExtField<P>

type Output = QuadExtField<P>

The resulting type after applying the - operator.

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

Performs the - operation.

impl<'a, P: QuadExtConfig> Sub<&'a mut QuadExtField<P>> for QuadExtField<P>

type Output = QuadExtField<P>

The resulting type after applying the - operator.

fn sub(self, other: &'a mut Self) -> Self

Performs the - operation.

impl<'b, P: QuadExtConfig> Sub<QuadExtField<P>> for &'b QuadExtField<P>

type Output = QuadExtField<P>

The resulting type after applying the - operator.

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

Performs the - operation.

impl<P: QuadExtConfig> Sub for QuadExtField<P>

type Output = QuadExtField<P>

The resulting type after applying the - operator.

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

Performs the - operation.

impl<'a, P: QuadExtConfig> SubAssign<&'a QuadExtField<P>> for QuadExtField<P>

fn sub_assign(&mut self, other: &Self)

Performs the -= operation.

impl<'a, P: QuadExtConfig> SubAssign<&'a mut QuadExtField<P>> for QuadExtField<P>

fn sub_assign(&mut self, other: &'a mut Self)

Performs the -= operation.

impl<P: QuadExtConfig> SubAssign for QuadExtField<P>

fn sub_assign(&mut self, other: Self)

Performs the -= operation.

impl<'a, P: QuadExtConfig> Sum<&'a QuadExtField<P>> for QuadExtField<P>

fn sum<I: Iterator<Item = &'a Self>>(iter: I) -> Self

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

impl<P: QuadExtConfig> Sum for QuadExtField<P>

fn sum<I: Iterator<Item = Self>>(iter: I) -> Self

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

impl<P: QuadExtConfig> ToConstraintField<<P as QuadExtConfig>::BasePrimeField> for QuadExtField<P>

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

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

impl<P: QuadExtConfig> Valid for QuadExtField<P>

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

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

where Self: 'a,

impl<P: QuadExtConfig> Zero for QuadExtField<P>

fn zero() -> Self

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: QuadExtConfig> Zeroize for QuadExtField<P>

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: QuadExtConfig> Copy for QuadExtField<P>

where P::BaseField: Copy,

impl<P: QuadExtConfig> Eq for QuadExtField<P>

where P::BaseField: PartialEq,