Struct winter_math::fields::f128::BaseElement

pub struct BaseElement(_);

Represents a base field element.

Internal values are stored in their canonical form in the range [0, M). The backing type is u128.

Implementations

impl BaseElement

pub const fn new(value: u128) -> Self

Creates a new field element from a u128 value. If the value is greater than or equal to the field modulus, modular reduction is silently preformed. This function can also be used to initialize constants.

Trait Implementations

impl Add<BaseElement> for BaseElement

type Output = Self

The resulting type after applying the + operator.

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

Performs the + operation.

impl AddAssign<BaseElement> for BaseElement

fn add_assign(&mut self, rhs: Self)

Performs the += operation.

impl AsBytes for BaseElement

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

Returns a byte representation of self.

impl Clone for BaseElement

fn clone(&self) -> BaseElement

Returns a copy of the value.

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

Performs copy-assignment from source.

impl Debug for BaseElement

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

Formats the value using the given formatter.

impl Default for BaseElement

fn default() -> BaseElement

Returns the “default value” for a type.

impl Deserializable for BaseElement

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 Display for BaseElement

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

Formats the value using the given formatter.

impl Div<BaseElement> for BaseElement

type Output = Self

The resulting type after applying the / operator.

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

Performs the / operation.

impl DivAssign<BaseElement> for BaseElement

fn div_assign(&mut self, rhs: Self)

Performs the /= operation.

impl FieldElement for BaseElement

type PositiveInteger = u128

A type defining positive integers big enough to describe a field modulus for Self::BaseField with no loss of precision.

type BaseField = Self

Base field type for this finite field. For prime fields, BaseField should be set to Self.

const ZERO: Self

The additive identity.

const ONE: Self

The multiplicative identity.

const ELEMENT_BYTES: usize

Number of bytes needed to encode an element

const IS_MALLEABLE: bool

True if internal representation of an element can be redundant - i.e., multiple internal representations map to the same canonical representation.

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 rand() -> Self

Returns a cryptographically-secure random element drawn uniformly from the entire field.

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

Returns a field element if the set of bytes forms a valid field element, otherwise returns None. The element is expected to be in canonical representation. This function is primarily intended for sampling random field elements from a hash function output.

fn elements_into_bytes(elements: Vec<Self>) -> Vec<u8>

Converts a vector of field elements into a vector of bytes. The elements may be in the internal representation rather than in the canonical representation. This conversion is intended to be zero-copy (i.e. by re-interpreting the underlying memory).

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

Converts a list of elements into a list of bytes. The elements may be in the internal representation rather than in the canonical representation. This conversion is intended to be zero-copy (i.e. by re-interpreting the underlying memory).

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

Converts a list of bytes into a list of field elements. The elements are assumed to encoded in the internal representation rather than in the canonical representation. The conversion is intended to be zero-copy (i.e. by re-interpreting the underlying memory).

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

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

fn prng_vector(seed: [u8; 32], n: usize) -> Vec<Self>

Returns a vector of n pseudo-random elements drawn uniformly from the entire field based on the provided seed.

fn normalize(&mut self)

Normalizes internal representation of this element.

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 From<[u8; 16]> for BaseElement

fn from(bytes: [u8; 16]) -> Self

Converts the value encoded in an array of 16 bytes into a field element. The bytes are assumed to be in little-endian byte order. If the value is greater than or equal to the field modulus, modular reduction is silently preformed.

impl From<u128> for BaseElement

fn from(value: u128) -> Self

Converts a 128-bit value into a filed element. If the value is greater than or equal to the field modulus, modular reduction is silently preformed.

impl From<u16> for BaseElement

fn from(value: u16) -> Self

Converts a 16-bit value into a filed element.

impl From<u32> for BaseElement

fn from(value: u32) -> Self

Converts a 32-bit value into a filed element.

impl From<u64> for BaseElement

fn from(value: u64) -> Self

Converts a 64-bit value into a filed element.

impl From<u8> for BaseElement

fn from(value: u8) -> Self

Converts an 8-bit value into a filed element.

impl Mul<BaseElement> for BaseElement

type Output = Self

The resulting type after applying the * operator.

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

Performs the * operation.

impl MulAssign<BaseElement> for BaseElement

fn mul_assign(&mut self, rhs: Self)

Performs the *= operation.

impl Neg for BaseElement

type Output = Self

The resulting type after applying the - operator.

fn neg(self) -> Self

Performs the unary - operation.

impl PartialEq<BaseElement> for BaseElement

fn eq(&self, other: &BaseElement) -> bool

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

fn ne(&self, other: &BaseElement) -> bool

This method tests for !=.

impl Serializable for BaseElement

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 StarkField for BaseElement

const MODULUS: Self::PositiveInteger

sage: MODULUS = 2^128 - 45 * 2^40 + 1
sage: GF(MODULUS).is_prime_field()
True
sage: GF(MODULUS).order()
340282366920938463463374557953744961537

const GENERATOR: Self

sage: GF(MODULUS).primitive_element()
3

const TWO_ADICITY: u32

sage: is_odd((MODULUS - 1) / 2^40)
True

const TWO_ADIC_ROOT_OF_UNITY: Self

sage: k = (MODULUS - 1) / 2^40
sage: GF(MODULUS).primitive_element()^k
23953097886125630542083529559205016746

type QuadExtension = QuadExtensionA<Self>

Type describing quadratic extension of this StarkField.

const MODULUS_BITS: u32

The number of bits needed to represents Self::MODULUS.

fn get_modulus_le_bytes() -> Vec<u8>

Returns byte representation of the field modulus in little-endian byte order.

fn as_int(&self) -> Self::PositiveInteger

Returns a canonical integer representation of the field element.

fn get_root_of_unity(n: u32) -> Self

Returns the root of unity of order 2^n.

impl Sub<BaseElement> for BaseElement

type Output = Self

The resulting type after applying the - operator.

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

Performs the - operation.

impl SubAssign<BaseElement> for BaseElement

fn sub_assign(&mut self, rhs: Self)

Performs the -= operation.

impl<'a> TryFrom<&'a [u8]> for BaseElement

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 = String

The type returned in the event of a conversion error.

impl Copy for BaseElement

impl Eq for BaseElement

impl StructuralEq for BaseElement

impl StructuralPartialEq for BaseElement