Struct winter_math::fields::QuadExtensionA

#[repr(C)]
pub struct QuadExtensionA<B: StarkField>(_, _);

Represents an element in a quadratic extensions field defined as F[x]/(x^2-x-1).

The extension element is α + β * φ, where φ is a root of the polynomial x^2 - x - 1, and α and β are base field elements.

Trait Implementations

impl<B: StarkField> Add<QuadExtensionA<B>> for QuadExtensionA<B>

type Output = Self

The resulting type after applying the + operator.

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

Performs the + operation.

impl<B: StarkField> AddAssign<QuadExtensionA<B>> for QuadExtensionA<B>

fn add_assign(&mut self, rhs: Self)

Performs the += operation.

impl<B: StarkField> AsBytes for QuadExtensionA<B>

fn as_bytes(&self) -> &[u8]

Returns a byte representation of self.

impl<B: Clone + StarkField> Clone for QuadExtensionA<B>

fn clone(&self) -> QuadExtensionA<B>

Returns a copy of the value.

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

Performs copy-assignment from source.

impl<B: Debug + StarkField> Debug for QuadExtensionA<B>

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

Formats the value using the given formatter.

impl<B: Default + StarkField> Default for QuadExtensionA<B>

fn default() -> QuadExtensionA<B>

Returns the “default value” for a type.

impl<B: StarkField> Deserializable for QuadExtensionA<B>

fn read_from<R: ByteReader>(
    source: &mut R
) -> Result<Self, DeserializationError>

Reads a sequence of bytes from the provided source, attempts to deserialize these bytes into Self, and returns the result.

fn read_batch_from<R>(
    source: &mut R,
    num_elements: usize
) -> Result<Vec<Self, Global>, DeserializationError> where
    R: ByteReader, 

Reads a sequence of bytes from the provided source, attempts to deserialize these bytes into a vector with the specified number of Self elements, and returns the result.

impl<B: StarkField> Display for QuadExtensionA<B>

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

Formats the value using the given formatter.

impl<B: StarkField> Div<QuadExtensionA<B>> for QuadExtensionA<B>

type Output = Self

The resulting type after applying the / operator.

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

Performs the / operation.

impl<B: StarkField> DivAssign<QuadExtensionA<B>> for QuadExtensionA<B>

fn div_assign(&mut self, rhs: Self)

Performs the /= operation.

impl<B: StarkField> FieldElement for QuadExtensionA<B>

type PositiveInteger = B::PositiveInteger

A type defining positive integers big enough to describe a field modulus for Self::BaseField with no loss of precision.

type BaseField = B

Base field type for this finite field. For prime fields, BaseField should be set to Self.

const ELEMENT_BYTES: usize

Number of bytes needed to encode an element

const IS_MALLEABLE: bool

True if internal representation of an element can be redundant - i.e., multiple internal representations map to the same canonical representation.

const ZERO: Self

The additive identity.

const ONE: Self

The multiplicative identity.

fn inv(self) -> Self

Returns a multiplicative inverse of this field element. If this element is ZERO, ZERO is returned.

fn conjugate(&self) -> Self

Returns a conjugate of this field element.

fn rand() -> Self

Returns a cryptographically-secure random element drawn uniformly from the entire field.

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

Returns a field element if the set of bytes forms a valid field element, otherwise returns None. The element is expected to be in canonical representation. This function is primarily intended for sampling random field elements from a hash function output.

fn elements_into_bytes(elements: Vec<Self>) -> Vec<u8>

Converts a vector of field elements into a vector of bytes. The elements may be in the internal representation rather than in the canonical representation. This conversion is intended to be zero-copy (i.e. by re-interpreting the underlying memory).

fn elements_as_bytes(elements: &[Self]) -> &[u8]

Converts a list of elements into a list of bytes. The elements may be in the internal representation rather than in the canonical representation. This conversion is intended to be zero-copy (i.e. by re-interpreting the underlying memory).

unsafe fn bytes_as_elements(
    bytes: &[u8]
) -> Result<&[Self], DeserializationError>

Converts a list of bytes into a list of field elements. The elements are assumed to encoded in the internal representation rather than in the canonical representation. The conversion is intended to be zero-copy (i.e. by re-interpreting the underlying memory).

fn zeroed_vector(n: usize) -> Vec<Self>

Returns a vector of length n initialized with all ZERO elements.

fn prng_vector(seed: [u8; 32], n: usize) -> Vec<Self>

Returns a vector of n pseudo-random elements drawn uniformly from the entire field based on the provided seed.

fn normalize(&mut self)

Normalizes internal representation of this element.

fn double(self) -> Self

Returns this field element added to itself.

fn square(self) -> Self

Returns this field element raised to power 2.

fn cube(self) -> Self

Returns this field element raised to power 3.

fn exp(self, power: Self::PositiveInteger) -> Self

Exponentiates this field element by power parameter.

impl<B: StarkField> From<B> for QuadExtensionA<B>

fn from(e: B) -> Self

Performs the conversion.

impl<B: StarkField> From<u128> for QuadExtensionA<B>

fn from(value: u128) -> Self

Performs the conversion.

impl<B: StarkField> From<u16> for QuadExtensionA<B>

fn from(value: u16) -> Self

Performs the conversion.

impl<B: StarkField> From<u32> for QuadExtensionA<B>

fn from(value: u32) -> Self

Performs the conversion.

impl<B: StarkField> From<u64> for QuadExtensionA<B>

fn from(value: u64) -> Self

Performs the conversion.

impl<B: StarkField> From<u8> for QuadExtensionA<B>

fn from(value: u8) -> Self

Performs the conversion.

impl<B: StarkField> Mul<QuadExtensionA<B>> for QuadExtensionA<B>

type Output = Self

The resulting type after applying the * operator.

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

Performs the * operation.

impl<B: StarkField> MulAssign<QuadExtensionA<B>> for QuadExtensionA<B>

fn mul_assign(&mut self, rhs: Self)

Performs the *= operation.

impl<B: StarkField> Neg for QuadExtensionA<B>

type Output = Self

The resulting type after applying the - operator.

fn neg(self) -> Self

Performs the unary - operation.

impl<B: PartialEq + StarkField> PartialEq<QuadExtensionA<B>> for QuadExtensionA<B>

fn eq(&self, other: &QuadExtensionA<B>) -> bool

This method tests for self and other values to be equal, and is used by ==.

fn ne(&self, other: &QuadExtensionA<B>) -> bool

This method tests for !=.

impl<B: StarkField> Serializable for QuadExtensionA<B>

fn write_into<W: ByteWriter>(&self, target: &mut W)

Serializes self into bytes and writes these bytes into the target.

fn to_bytes(&self) -> Vec<u8, Global>

Serializes self into a vector of bytes.

fn write_batch_into<W>(source: &[Self], target: &mut W) where
    W: ByteWriter, 

Serializes all elements of the source and writes these bytes into the target.

fn get_size_hint(&self) -> usize

Returns an estimate of how many bytes are needed to represent self.

impl<B: StarkField> Sub<QuadExtensionA<B>> for QuadExtensionA<B>

type Output = Self

The resulting type after applying the - operator.

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

Performs the - operation.

impl<B: StarkField> SubAssign<QuadExtensionA<B>> for QuadExtensionA<B>

fn sub_assign(&mut self, rhs: Self)

Performs the -= operation.

impl<'a, B: StarkField> TryFrom<&'a [u8]> for QuadExtensionA<B>

fn try_from(bytes: &[u8]) -> Result<Self, Self::Error>

Converts a slice of bytes into a field element; returns error if the value encoded in bytes is not a valid field element. The bytes are assumed to be in little-endian byte order.

type Error = String

The type returned in the event of a conversion error.

impl<B: Copy + StarkField> Copy for QuadExtensionA<B>

impl<B: Eq + StarkField> Eq for QuadExtensionA<B>

impl<B: StarkField> StructuralEq for QuadExtensionA<B>

impl<B: StarkField> StructuralPartialEq for QuadExtensionA<B>