Struct XFieldElement

pub struct XFieldElement {
    pub coefficients: [BFieldElement; 3],
}

Fields

coefficients: [BFieldElement; 3]

Implementations

impl XFieldElement

pub fn shah_polynomial() -> Polynomial<'static, BFieldElement>

The quotient defining the field extension over the base field, namely x³ - x + 1.

pub const fn new(coefficients: [BFieldElement; 3]) -> XFieldElement

pub const fn new_const(element: BFieldElement) -> XFieldElement

pub fn unlift(&self) -> Option<BFieldElement>

pub fn increment(&mut self, index: usize)

pub fn decrement(&mut self, index: usize)

Trait Implementations

impl Add<BFieldElement> for XFieldElement

type Output = XFieldElement

The resulting type after applying the + operator.

fn add(self, other: BFieldElement) -> XFieldElement

Performs the + operation.

impl Add<XFieldElement> for BFieldElement

The bfe + xfe -> xfe instance belongs to BFieldElement.

type Output = XFieldElement

The resulting type after applying the + operator.

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

Performs the + operation.

impl Add for XFieldElement

type Output = XFieldElement

The resulting type after applying the + operator.

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

Performs the + operation.

impl AddAssign<BFieldElement> for XFieldElement

fn add_assign(&mut self, rhs: BFieldElement)

Performs the += operation.

impl AddAssign for XFieldElement

fn add_assign(&mut self, rhs: XFieldElement)

Performs the += operation.

impl<'arbitrary> Arbitrary<'arbitrary> for XFieldElement

fn arbitrary(u: &mut Unstructured<'arbitrary>) -> Result<XFieldElement, Error>

Generate an arbitrary value of Self from the given unstructured data.

fn arbitrary_take_rest( u: Unstructured<'arbitrary>, ) -> Result<XFieldElement, Error>

Generate an arbitrary value of Self from the entirety of the given unstructured data.

fn size_hint(depth: usize) -> (usize, Option<usize>)

Get a size hint for how many bytes out of an Unstructured this type needs to construct itself.

impl BFieldCodec for XFieldElement

type Error = XFieldElementBFieldDecodingError

fn decode( sequence: &[BFieldElement], ) -> Result<Box<XFieldElement>, <XFieldElement as BFieldCodec>::Error>

fn encode(&self) -> Vec<BFieldElement>

fn static_length() -> Option<usize>

Returns the length in number of BFieldElements if it is known at compile-time. Otherwise, None.

impl Clone for XFieldElement

fn clone(&self) -> XFieldElement

Returns a copy of the value.

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

Performs copy-assignment from source.

impl ConstOne for XFieldElement

const ONE: XFieldElement = _

The multiplicative identity element of Self, 1.

impl ConstZero for XFieldElement

const ZERO: XFieldElement = _

The additive identity element of Self, 0.

impl CyclicGroupGenerator for XFieldElement

fn get_cyclic_group_elements(&self, max: Option<usize>) -> Vec<XFieldElement>

impl Debug for XFieldElement

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

Formats the value using the given formatter.

impl<'de> Deserialize<'de> for XFieldElement

fn deserialize<__D>( __deserializer: __D, ) -> Result<XFieldElement, <__D as Deserializer<'de>>::Error>

where __D: Deserializer<'de>,

Deserialize this value from the given Serde deserializer.

impl Display for XFieldElement

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

Formats the value using the given formatter.

impl Div for XFieldElement

type Output = XFieldElement

The resulting type after applying the / operator.

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

Performs the / operation.

impl Evaluable<XFieldElement> for MasterAuxTable

fn evaluate_initial_constraints( main_row: ArrayView1<'_, XFieldElement>, aux_row: ArrayView1<'_, XFieldElement>, challenges: &Challenges, ) -> Vec<XFieldElement>

fn evaluate_consistency_constraints( main_row: ArrayView1<'_, XFieldElement>, aux_row: ArrayView1<'_, XFieldElement>, challenges: &Challenges, ) -> Vec<XFieldElement>

fn evaluate_transition_constraints( current_main_row: ArrayView1<'_, XFieldElement>, current_aux_row: ArrayView1<'_, XFieldElement>, next_main_row: ArrayView1<'_, XFieldElement>, next_aux_row: ArrayView1<'_, XFieldElement>, challenges: &Challenges, ) -> Vec<XFieldElement>

fn evaluate_terminal_constraints( main_row: ArrayView1<'_, XFieldElement>, aux_row: ArrayView1<'_, XFieldElement>, challenges: &Challenges, ) -> Vec<XFieldElement>

impl FiniteField for XFieldElement

fn batch_inversion(input: Vec<Self>) -> Vec<Self>

Montgomery Batch Inversion

fn square(self) -> Self

impl<T> From<[T; 3]> for XFieldElement

where T: Into<BFieldElement>,

fn from(value: [T; 3]) -> XFieldElement

Converts to this type from the input type.

impl From<Polynomial<'_, BFieldElement>> for XFieldElement

fn from(poly: Polynomial<'_, BFieldElement>) -> XFieldElement

Converts to this type from the input type.

impl<T> From<T> for XFieldElement

where T: Into<BFieldElement>,

fn from(value: T) -> XFieldElement

Converts to this type from the input type.

impl From<XFieldElement> for Digest

fn from(xfe: XFieldElement) -> Digest

Interpret the XFieldElement as a Digest. No hashing is performed. This interpretation can be useful for the AlgebraicHasher trait and, by extension, allows building MerkleTrees directly from XFieldElements.

impl Hash for XFieldElement

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

where __H: Hasher,

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 Inverse for XFieldElement

fn inverse(&self) -> XFieldElement

fn inverse_or_zero(&self) -> Self

impl ModPowU32 for XFieldElement

fn mod_pow_u32(&self, exp: u32) -> XFieldElement

impl ModPowU64 for XFieldElement

fn mod_pow_u64(&self, exponent: u64) -> XFieldElement

impl Mul<BFieldElement> for XFieldElement

XField * BField means scalar multiplication of the BFieldElement onto each coefficient of the XField.

type Output = XFieldElement

The resulting type after applying the * operator.

fn mul(self, other: BFieldElement) -> XFieldElement

Performs the * operation.

impl<FF, FF2> Mul<Polynomial<'_, FF>> for XFieldElement

where FF: FiniteField<Output = FF2> + Mul<XFieldElement>, FF2: 'static + FiniteField,

type Output = Polynomial<'static, FF2>

The resulting type after applying the * operator.

fn mul( self, other: Polynomial<'_, FF>, ) -> <XFieldElement as Mul<Polynomial<'_, FF>>>::Output

Performs the * operation.

impl Mul<XFieldElement> for BFieldElement

type Output = XFieldElement

The resulting type after applying the * operator.

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

Performs the * operation.

impl Mul for XFieldElement

type Output = XFieldElement

The resulting type after applying the * operator.

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

Performs the * operation.

impl MulAssign<BFieldElement> for XFieldElement

fn mul_assign(&mut self, rhs: BFieldElement)

Performs the *= operation.

impl MulAssign for XFieldElement

fn mul_assign(&mut self, rhs: XFieldElement)

Performs the *= operation.

impl Neg for XFieldElement

type Output = XFieldElement

The resulting type after applying the - operator.

fn neg(self) -> XFieldElement

Performs the unary - operation.

impl One for XFieldElement

fn one() -> XFieldElement

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 PartialEq for XFieldElement

fn eq(&self, other: &XFieldElement) -> 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 PrimitiveRootOfUnity for XFieldElement

fn primitive_root_of_unity(n: u64) -> Option<XFieldElement>

impl Serialize for XFieldElement

fn serialize<__S>( &self, __serializer: __S, ) -> Result<<__S as Serializer>::Ok, <__S as Serializer>::Error>

where __S: Serializer,

Serialize this value into the given Serde serializer.

impl Sub<BFieldElement> for XFieldElement

type Output = XFieldElement

The resulting type after applying the - operator.

fn sub(self, other: BFieldElement) -> XFieldElement

Performs the - operation.

impl Sub<XFieldElement> for BFieldElement

type Output = XFieldElement

The resulting type after applying the - operator.

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

Performs the - operation.

impl Sub for XFieldElement

type Output = XFieldElement

The resulting type after applying the - operator.

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

Performs the - operation.

impl SubAssign<BFieldElement> for XFieldElement

fn sub_assign(&mut self, rhs: BFieldElement)

Performs the -= operation.

impl SubAssign for XFieldElement

fn sub_assign(&mut self, rhs: XFieldElement)

Performs the -= operation.

impl Sum for XFieldElement

fn sum<I>(iter: I) -> XFieldElement

where I: Iterator<Item = XFieldElement>,

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

impl TryFrom<&[BFieldElement]> for XFieldElement

type Error = TryFromXFieldElementError

The type returned in the event of a conversion error.

fn try_from( value: &[BFieldElement], ) -> Result<XFieldElement, <XFieldElement as TryFrom<&[BFieldElement]>>::Error>

Performs the conversion.

impl TryFrom<Digest> for XFieldElement

type Error = TryFromXFieldElementError

The type returned in the event of a conversion error.

fn try_from( digest: Digest, ) -> Result<XFieldElement, <XFieldElement as TryFrom<Digest>>::Error>

Performs the conversion.

impl TryFrom<Vec<BFieldElement>> for XFieldElement

type Error = TryFromXFieldElementError

The type returned in the event of a conversion error.

fn try_from( value: Vec<BFieldElement>, ) -> Result<XFieldElement, <XFieldElement as TryFrom<Vec<BFieldElement>>>::Error>

Performs the conversion.

impl Zero for XFieldElement

fn zero() -> XFieldElement

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 Copy for XFieldElement

impl Eq for XFieldElement

impl StructuralPartialEq for XFieldElement