Struct miden_core::QuadExtension

pub struct QuadExtension<B>(_, _)
where
    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> QuadExtension<B>where
    B: ExtensibleField<2>,

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

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> Add<QuadExtension<B>> for QuadExtension<B>where
    B: ExtensibleField<2>,

type Output = QuadExtension<B>

The resulting type after applying the + operator.

fn add(self, rhs: QuadExtension<B>) -> QuadExtension<B>

Performs the + operation.

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

fn add_assign(&mut self, rhs: QuadExtension<B>)

Performs the += operation.

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

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

Returns a byte representation of self.

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

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 for QuadExtension<B>where
    B: Debug + ExtensibleField<2>,

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

Formats the value using the given formatter.

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

fn default() -> QuadExtension<B>

Returns the “default value” for a type.

impl<B> Deserializable for QuadExtension<B>where
    B: ExtensibleField<2>,

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

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> Display for QuadExtension<B>where
    B: ExtensibleField<2>,

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

Formats the value using the given formatter.

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

type Output = QuadExtension<B>

The resulting type after applying the / operator.

fn div(self, rhs: QuadExtension<B>) -> QuadExtension<B>

Performs the / operation.

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

fn div_assign(&mut self, rhs: QuadExtension<B>)

Performs the /= operation.

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

fn mul_base(self, other: B) -> QuadExtension<B>

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

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: QuadExtension<B> = Self(B::ZERO, B::ZERO)

The additive identity.

const ONE: QuadExtension<B> = Self(B::ONE, B::ZERO)

The multiplicative identity.

fn double(self) -> QuadExtension<B>

Returns this field element added to itself.

fn inv(self) -> QuadExtension<B>

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

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

Returns a conjugate of this field element.

fn elements_as_bytes(elements: &[QuadExtension<B>]) -> &[u8]

Converts a list of elements into a list of bytes.

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

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

fn zeroed_vector(n: usize) -> Vec<QuadExtension<B>, Global>

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

fn as_base_elements(
    elements: &[QuadExtension<B>]
) -> &[<QuadExtension<B> as FieldElement>::BaseField]

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

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

fn from(value: B) -> QuadExtension<B>

Converts to this type from the input type.

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

fn from(value: u128) -> QuadExtension<B>

Converts to this type from the input type.

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

fn from(value: u16) -> QuadExtension<B>

Converts to this type from the input type.

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

fn from(value: u32) -> QuadExtension<B>

Converts to this type from the input type.

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

fn from(value: u64) -> QuadExtension<B>

Converts to this type from the input type.

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

fn from(value: u8) -> QuadExtension<B>

Converts to this type from the input type.

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

type Output = QuadExtension<B>

The resulting type after applying the * operator.

fn mul(self, rhs: QuadExtension<B>) -> QuadExtension<B>

Performs the * operation.

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

fn mul_assign(&mut self, rhs: QuadExtension<B>)

Performs the *= operation.

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

type Output = QuadExtension<B>

The resulting type after applying the - operator.

fn neg(self) -> QuadExtension<B>

Performs the unary - operation.

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

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: &Rhs) -> bool

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

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

const VALUE_SIZE: usize = Self::ELEMENT_BYTES

Size of Self in bytes.

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

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

impl<B> Serializable for QuadExtension<B>where
    B: ExtensibleField<2>,

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

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> Sub<QuadExtension<B>> for QuadExtension<B>where
    B: ExtensibleField<2>,

type Output = QuadExtension<B>

The resulting type after applying the - operator.

fn sub(self, rhs: QuadExtension<B>) -> QuadExtension<B>

Performs the - operation.

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

fn sub_assign(&mut self, rhs: QuadExtension<B>)

Performs the -= operation.

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

fn try_from(
    bytes: &[u8]
) -> Result<QuadExtension<B>, <QuadExtension<B> as TryFrom<&'a [u8]>>::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 for QuadExtension<B>where
    B: Copy + ExtensibleField<2>,

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

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

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