Struct miden_core::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) -> BaseElement

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 = BaseElement

The resulting type after applying the + operator.

pub fn add(self, rhs: BaseElement) -> BaseElement

Performs the + operation.

impl AddAssign<BaseElement> for BaseElement

pub fn add_assign(&mut self, rhs: BaseElement)

Performs the += operation.

impl AsBytes for BaseElement

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

Returns a byte representation of self.

impl Clone for BaseElement

pub 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

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

Formats the value using the given formatter.

impl Default for BaseElement

pub fn default() -> BaseElement

Returns the “default value” for a type.

impl Deserializable for BaseElement

pub fn read_from<R>(source: &mut R) -> Result<BaseElement, 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 Display for BaseElement

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

Formats the value using the given formatter.

impl Div<BaseElement> for BaseElement

type Output = BaseElement

The resulting type after applying the / operator.

pub fn div(self, rhs: BaseElement) -> BaseElement

Performs the / operation.

impl DivAssign<BaseElement> for BaseElement

pub fn div_assign(&mut self, rhs: BaseElement)

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 = BaseElement

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

pub const ZERO: BaseElement

The additive identity.

pub const ONE: BaseElement

The multiplicative identity.

pub const ELEMENT_BYTES: usize

Number of bytes needed to encode an element

pub const IS_CANONICAL: bool

True if internal representation of the element is the same as its canonical representation.

pub fn inv(self) -> BaseElement

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

pub fn conjugate(&self) -> BaseElement

Returns a conjugate of this field element.

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

Converts a list of elements into a list of bytes.

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

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

pub fn zeroed_vector(n: usize) -> Vec<BaseElement, Global>

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

pub fn as_base_elements(
    elements: &[BaseElement]
) -> &[<BaseElement as FieldElement>::BaseField]

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

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

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

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

pub fn from(value: u128) -> BaseElement

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

pub fn from(value: u16) -> BaseElement

Converts a 16-bit value into a filed element.

impl From<u32> for BaseElement

pub fn from(value: u32) -> BaseElement

Converts a 32-bit value into a filed element.

impl From<u64> for BaseElement

pub fn from(value: u64) -> BaseElement

Converts a 64-bit value into a filed element.

impl From<u8> for BaseElement

pub fn from(value: u8) -> BaseElement

Converts an 8-bit value into a filed element.

impl Mul<BaseElement> for BaseElement

type Output = BaseElement

The resulting type after applying the * operator.

pub fn mul(self, rhs: BaseElement) -> BaseElement

Performs the * operation.

impl MulAssign<BaseElement> for BaseElement

pub fn mul_assign(&mut self, rhs: BaseElement)

Performs the *= operation.

impl Neg for BaseElement

type Output = BaseElement

The resulting type after applying the - operator.

pub fn neg(self) -> BaseElement

Performs the unary - operation.

impl PartialEq<BaseElement> for BaseElement

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

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

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

This method tests for !=.

impl Randomizable for BaseElement

pub const VALUE_SIZE: usize

Size of Self in bytes.

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

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

impl Serializable for BaseElement

pub 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 StarkField for BaseElement

pub const MODULUS: <BaseElement as FieldElement>::PositiveInteger

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

pub const GENERATOR: BaseElement

sage: GF(MODULUS).primitive_element()
3

pub const TWO_ADICITY: u32

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

pub const TWO_ADIC_ROOT_OF_UNITY: BaseElement

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

type QuadExtension = QuadExtensionA<BaseElement>

Type describing quadratic extension of this StarkField.

pub const MODULUS_BITS: u32

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

pub fn get_modulus_le_bytes() -> Vec<u8, Global>

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

pub fn as_int(&self) -> <BaseElement as FieldElement>::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 = BaseElement

The resulting type after applying the - operator.

pub fn sub(self, rhs: BaseElement) -> BaseElement

Performs the - operation.

impl SubAssign<BaseElement> for BaseElement

pub fn sub_assign(&mut self, rhs: BaseElement)

Performs the -= operation.

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

pub fn try_from(
    bytes: &[u8]
) -> Result<BaseElement, <BaseElement 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 = 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