Struct winter_math::fields::QuadExtension

#[repr(C)]
pub struct QuadExtension<B: ExtensibleField<2>>(_, _);

Represents an element in a quadratic extension of a StarkField.

The extension element is defined as α + β * φ, where φ is a root of in irreducible polynomial defined by the implementation of the ExtensibleField trait, and α and β are base field elements.

Implementations

impl<B: ExtensibleField<2>> QuadExtension<B>

pub fn new(a: B, b: B) -> Self

Returns a new extension element instantiated from the provided base elements.

pub fn is_supported() -> bool

Returns true if the base field specified by B type parameter supports quadratic extensions.

Trait Implementations

impl<B: ExtensibleField<2>> Add<QuadExtension<B>> for QuadExtension<B>

type Output = QuadExtension<B>

The resulting type after applying the + operator.

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

Performs the + operation.

impl<B: ExtensibleField<2>> AddAssign<QuadExtension<B>> for QuadExtension<B>

fn add_assign(&mut self, rhs: Self)

Performs the += operation.

impl<B: ExtensibleField<2>> AsBytes for QuadExtension<B>

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

Returns a byte representation of self.

impl<B: Clone + ExtensibleField<2>> Clone for QuadExtension<B>

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

Returns a copy of the value.

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

Performs copy-assignment from source.

impl<B: Debug + ExtensibleField<2>> Debug for QuadExtension<B>

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

Formats the value using the given formatter.

impl<B: Default + ExtensibleField<2>> Default for QuadExtension<B>

fn default() -> QuadExtension<B>

Returns the “default value” for a type.

impl<B: ExtensibleField<2>> Deserializable for QuadExtension<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: ExtensibleField<2>> Display for QuadExtension<B>

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

Formats the value using the given formatter.

impl<B: ExtensibleField<2>> Div<QuadExtension<B>> for QuadExtension<B>

type Output = QuadExtension<B>

The resulting type after applying the / operator.

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

Performs the / operation.

impl<B: ExtensibleField<2>> DivAssign<QuadExtension<B>> for QuadExtension<B>

fn div_assign(&mut self, rhs: Self)

Performs the /= operation.

impl<B: ExtensibleField<2>> ExtensionOf<B> for QuadExtension<B>

fn mul_base(self, other: B) -> Self

impl<B: ExtensibleField<2>> FieldElement for QuadExtension<B>

type PositiveInteger = <B as FieldElement>::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 = B::ELEMENT_BYTES * 2

Number of bytes needed to encode an element

const IS_CANONICAL: bool = B::IS_CANONICAL

True if internal representation of the element is the same as its canonical representation.

const ZERO: Self = Self(B::ZERO, B::ZERO)

The additive identity.

const ONE: Self = Self(B::ONE, B::ZERO)

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

Converts a list of elements into a list of bytes.

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

Converts a list of bytes into a list of field elements.

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

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

fn as_base_elements(elements: &[Self]) -> &[Self::BaseField]

Converts a list of field elements into a list of elements in the underlying base field.

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: ExtensibleField<2>> From<B> for QuadExtension<B>

fn from(value: B) -> Self

Converts to this type from the input type.

impl<B: ExtensibleField<2>> From<u128> for QuadExtension<B>

fn from(value: u128) -> Self

Converts to this type from the input type.

impl<B: ExtensibleField<2>> From<u16> for QuadExtension<B>

fn from(value: u16) -> Self

Converts to this type from the input type.

impl<B: ExtensibleField<2>> From<u32> for QuadExtension<B>

fn from(value: u32) -> Self

Converts to this type from the input type.

impl<B: ExtensibleField<2>> From<u64> for QuadExtension<B>

fn from(value: u64) -> Self

Converts to this type from the input type.

impl<B: ExtensibleField<2>> From<u8> for QuadExtension<B>

fn from(value: u8) -> Self

Converts to this type from the input type.

impl<B: ExtensibleField<2>> Mul<QuadExtension<B>> for QuadExtension<B>

type Output = QuadExtension<B>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<B: ExtensibleField<2>> MulAssign<QuadExtension<B>> for QuadExtension<B>

fn mul_assign(&mut self, rhs: Self)

Performs the *= operation.

impl<B: ExtensibleField<2>> Neg for QuadExtension<B>

type Output = QuadExtension<B>

The resulting type after applying the - operator.

fn neg(self) -> Self

Performs the unary - operation.

impl<B: PartialEq + ExtensibleField<2>> PartialEq<QuadExtension<B>> for QuadExtension<B>

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

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

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

This method tests for !=.

impl<B: ExtensibleField<2>> Randomizable for QuadExtension<B>

const VALUE_SIZE: usize = Self::ELEMENT_BYTES

Size of Self in bytes.

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

Returns Self if the set of bytes forms a valid value, otherwise returns None.

impl<B: ExtensibleField<2>> Serializable for QuadExtension<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: ExtensibleField<2>> Sub<QuadExtension<B>> for QuadExtension<B>

type Output = QuadExtension<B>

The resulting type after applying the - operator.

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

Performs the - operation.

impl<B: ExtensibleField<2>> SubAssign<QuadExtension<B>> for QuadExtension<B>

fn sub_assign(&mut self, rhs: Self)

Performs the -= operation.

impl<'a, B: ExtensibleField<2>> TryFrom<&'a [u8]> for QuadExtension<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 = DeserializationError

The type returned in the event of a conversion error.

impl<B: Copy + ExtensibleField<2>> Copy for QuadExtension<B>

impl<B: Eq + ExtensibleField<2>> Eq for QuadExtension<B>

impl<B: ExtensibleField<2>> StructuralEq for QuadExtension<B>

impl<B: ExtensibleField<2>> StructuralPartialEq for QuadExtension<B>