Struct twenty_first::shared_math::x_field_element::XFieldElement

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

Fields

coefficients: [BFieldElement; 3]

Implementations

impl XFieldElement

pub fn shah_polynomial() -> Polynomial<BFieldElement>

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

pub const fn new_u64(coeffs: [u64; 3]) -> Self

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

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

pub fn sample(digest: Digest) -> Self

Derive a sample XFieldElement from a random Digest.

The specific elements of the digest (element 2, 3 and 4) were chosen because the tasm equivalent of this function can more efficiently pop elements 0 and 1, leading to a more efficient sample_weights() implementation:

https://github.com/Neptune-Crypto/twenty-first/pull/66#discussion_r1049771105

pub fn xgcd( x: Polynomial<BFieldElement>, y: Polynomial<BFieldElement> ) -> (Polynomial<BFieldElement>, Polynomial<BFieldElement>, Polynomial<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) -> Self

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: Self) -> Self

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: Self)

Performs the += operation.

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

fn arbitrary(u: &mut Unstructured<'arbitrary>) -> Result<Self>

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

fn arbitrary_take_rest(u: Unstructured<'arbitrary>) -> Result<Self>

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

fn decode(sequence: &[BFieldElement]) -> Result<Box<Self>>

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 CyclicGroupGenerator for XFieldElement

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

impl Debug for XFieldElement

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

Formats the value using the given formatter.

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

fn deserialize<__D>(__deserializer: __D) -> Result<Self, __D::Error>

where __D: Deserializer<'de>,

Deserialize this value from the given Serde deserializer.

impl Display for XFieldElement

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

Formats the value using the given formatter.

impl Distribution<XFieldElement> for Standard

fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> XFieldElement

Generate a random value of T, using rng as the source of randomness.

fn sample_iter<R>(self, rng: R) -> DistIter<Self, R, T>

where R: Rng, Self: Sized,

Create an iterator that generates random values of T, using rng as the source of randomness.

fn map<F, S>(self, func: F) -> DistMap<Self, F, T, S>

where F: Fn(T) -> S, Self: Sized,

Create a distribution of values of ‘S’ by mapping the output of Self through the closure F

impl Div for XFieldElement

type Output = XFieldElement

The resulting type after applying the / operator.

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

Performs the / operation.

impl Emojihash for XFieldElement

fn emojihash(&self) -> String

impl FiniteField for XFieldElement

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

Montgomery Batch Inversion

fn square(self) -> Self

impl From<BFieldElement> for XFieldElement

fn from(bfe: BFieldElement) -> Self

Converts to this type from the input type.

impl From<Polynomial<BFieldElement>> for XFieldElement

fn from(poly: Polynomial<BFieldElement>) -> Self

Converts to this type from the input type.

impl From<XFieldElement> for Digest

fn from(xfe: XFieldElement) -> Self

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 From<XFieldElement> for Polynomial<BFieldElement>

fn from(item: XFieldElement) -> Self

Converts to this type from the input type.

impl From<u32> for XFieldElement

fn from(value: u32) -> Self

Converts to this type from the input type.

impl FromVecu8 for XFieldElement

fn from_vecu8(bytes: Vec<u8>) -> Self

impl Hash for XFieldElement

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

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) -> Self

fn inverse_or_zero(&self) -> Self

impl ModPowU32 for XFieldElement

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

impl ModPowU64 for XFieldElement

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

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) -> Self

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

XField * XField means:

(ax^2 + bx + c) * (dx^2 + ex + f) (mod x^3 - x + 1)

= adx^4 + aex^3 + afx^2

• bdx^3 + bex^2 + bfx
• cdx^2 + cex + cf

= adx^4 + (ae + bd)x^3 + (af + be + cd)x^2 + (bf + ce)x + cf (mod x^3 - x + 1)

type Output = XFieldElement

The resulting type after applying the * operator.

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

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: Self)

Performs the *= operation.

impl Neg for XFieldElement

type Output = XFieldElement

The resulting type after applying the - operator.

fn neg(self) -> Self

Performs the unary - operation.

impl New for XFieldElement

fn new_from_usize(&self, value: usize) -> Self

impl One for XFieldElement

fn one() -> Self

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

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 PrimitiveRootOfUnity for XFieldElement

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

impl Serialize for XFieldElement

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

where __S: Serializer,

Serialize this value into the given Serde serializer.

impl Sub<BFieldElement> for XFieldElement

Subtracting a BFieldElement from an XFieldElement

self - other = self + (-other)

This overloads to Add and Neg

type Output = XFieldElement

The resulting type after applying the - operator.

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

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: Self) -> Self

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: Self)

Performs the -= operation.

impl Sum for XFieldElement

fn sum<I: Iterator<Item = Self>>(iter: I) -> Self

Method which takes an iterator and generates Self from the elements by “summing up” the items.

impl TryFrom<&[BFieldElement]> for XFieldElement

type Error = String

The type returned in the event of a conversion error.

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

Performs the conversion.

impl TryFrom<Digest> for XFieldElement

type Error = &'static str

The type returned in the event of a conversion error.

fn try_from(digest: Digest) -> Result<Self, Self::Error>

Performs the conversion.

impl TryFrom<Vec<BFieldElement>> for XFieldElement

type Error = String

The type returned in the event of a conversion error.

fn try_from(value: Vec<BFieldElement>) -> Result<Self, Self::Error>

Performs the conversion.

impl Zero for XFieldElement

fn zero() -> Self

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 StructuralEq for XFieldElement

impl StructuralPartialEq for XFieldElement