Struct QuadExtension 

pub struct QuadExtension<B>(/* private fields */)
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 const 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.

pub const fn to_base_elements(self) -> [B; 2]

Returns an array of base field elements comprising this extension field element.

The order of abase elements in the returned array is the same as the order in which the elements are provided to the QuadExtension::new() constructor.

Trait Implementations

impl<B> Add 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 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 duplicate 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_from_bytes(bytes: &[u8]) -> Result<Self, DeserializationError>

Attempts to deserialize the provided bytes into Self 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 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 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>,

const EXTENSION_DEGREE: usize = 2usize

Extension degree of this field with respect to Self::BaseField. For prime fields, extension degree should be set to 1.

const ELEMENT_BYTES: usize

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>

The additive identity.

const ONE: QuadExtension<B>

The multiplicative identity.

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.

fn double(self) -> QuadExtension<B>

Returns this field element added to itself.

fn square(self) -> QuadExtension<B>

Returns this field element raised to power 2.

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 base_element( &self, i: usize, ) -> <QuadExtension<B> as FieldElement>::BaseField

Return base filed element component of this field element at the specified index i.

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

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

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

Convert a slice of base field elements into a slice of field elements.

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 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.

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

Exponentiates this field element by power parameter. This function is expressly variable time, to speed-up verifier computations.

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<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<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 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 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 for QuadExtension<B>

where B: PartialEq + ExtensibleField<2>,

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

Serializes self into a vector of bytes.

fn get_size_hint(&self) -> usize

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

impl<B> Sub 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 for QuadExtension<B>

where B: ExtensibleField<2>,

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

Performs the -= operation.

impl<B> TryFrom<&[u8]> for QuadExtension<B>

where B: ExtensibleField<2>,

fn try_from( bytes: &[u8], ) -> Result<QuadExtension<B>, <QuadExtension<B> as TryFrom<&[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> TryFrom<u128> for QuadExtension<B>

where B: ExtensibleField<2>,

type Error = String

The type returned in the event of a conversion error.

fn try_from( value: u128, ) -> Result<QuadExtension<B>, <QuadExtension<B> as TryFrom<u128>>::Error>

Performs the conversion.

impl<B> TryFrom<u64> for QuadExtension<B>

where B: ExtensibleField<2>,

type Error = String

The type returned in the event of a conversion error.

fn try_from( value: u64, ) -> Result<QuadExtension<B>, <QuadExtension<B> as TryFrom<u64>>::Error>

Performs the conversion.

impl<B> Copy for QuadExtension<B>

where B: Copy + ExtensibleField<2>,

impl<B> Eq for QuadExtension<B>

where B: Eq + ExtensibleField<2>,

impl<B> StructuralPartialEq for QuadExtension<B>

where B: ExtensibleField<2>,