Struct winter_math::fields::f62::BaseElement
source · pub struct BaseElement(_);
Expand description
Represents base field element in the field.
Internal values are stored in Montgomery representation and can be in the range [0; 2M). The
backing type is u64
.
Implementations§
source§impl BaseElement
impl BaseElement
sourcepub const fn new(value: u64) -> BaseElement
pub const fn new(value: u64) -> BaseElement
Creates a new field element from the provided value
; the value is converted into
Montgomery representation.
Trait Implementations§
source§impl Add<BaseElement> for BaseElement
impl Add<BaseElement> for BaseElement
source§impl AddAssign<BaseElement> for BaseElement
impl AddAssign<BaseElement> for BaseElement
source§fn add_assign(&mut self, rhs: Self)
fn add_assign(&mut self, rhs: Self)
+=
operation. Read moresource§impl AsBytes for BaseElement
impl AsBytes for BaseElement
source§impl Clone for BaseElement
impl Clone for BaseElement
source§fn clone(&self) -> BaseElement
fn clone(&self) -> BaseElement
1.0.0 · source§fn clone_from(&mut self, source: &Self)
fn clone_from(&mut self, source: &Self)
source
. Read moresource§impl Debug for BaseElement
impl Debug for BaseElement
source§impl Default for BaseElement
impl Default for BaseElement
source§fn default() -> BaseElement
fn default() -> BaseElement
source§impl Deserializable for BaseElement
impl Deserializable for BaseElement
source§fn read_from<R: ByteReader>(
source: &mut R
) -> Result<Self, DeserializationError>
fn read_from<R: ByteReader>( source: &mut R ) -> Result<Self, DeserializationError>
source
, attempts to deserialize these bytes
into Self
, and returns the result. Read moresource§fn read_from_bytes(bytes: &[u8]) -> Result<Self, DeserializationError>
fn read_from_bytes(bytes: &[u8]) -> Result<Self, DeserializationError>
source§fn read_batch_from<R>(
source: &mut R,
num_elements: usize
) -> Result<Vec<Self, Global>, DeserializationError>where
R: ByteReader,
fn read_batch_from<R>( source: &mut R, num_elements: usize ) -> Result<Vec<Self, Global>, DeserializationError>where R: ByteReader,
source
, attempts to deserialize these bytes
into a vector with the specified number of Self
elements, and returns the result. Read moresource§impl Display for BaseElement
impl Display for BaseElement
source§impl Div<BaseElement> for BaseElement
impl Div<BaseElement> for BaseElement
source§impl DivAssign<BaseElement> for BaseElement
impl DivAssign<BaseElement> for BaseElement
source§fn div_assign(&mut self, rhs: Self)
fn div_assign(&mut self, rhs: Self)
/=
operation. Read moresource§impl ExtensibleField<2> for BaseElement
impl ExtensibleField<2> for BaseElement
Defines a quadratic extension of the base field over an irreducible polynomial x2 - x - 1. Thus, an extension element is defined as α + β * φ, where φ is a root of this polynomial, and α and β are base field elements.
source§fn mul(a: [Self; 2], b: [Self; 2]) -> [Self; 2]
fn mul(a: [Self; 2], b: [Self; 2]) -> [Self; 2]
a
and b
in the field defined by this extension.source§fn mul_base(a: [Self; 2], b: Self) -> [Self; 2]
fn mul_base(a: [Self; 2], b: Self) -> [Self; 2]
a
and b
in the field defined by this extension. b
represents
an element in the base field.source§fn frobenius(x: [Self; 2]) -> [Self; 2]
fn frobenius(x: [Self; 2]) -> [Self; 2]
x
in the field defined by this extension.source§fn square(a: [Self; N]) -> [Self; N]
fn square(a: [Self; N]) -> [Self; N]
a
in the field defined by this extension.source§fn is_supported() -> bool
fn is_supported() -> bool
source§impl ExtensibleField<3> for BaseElement
impl ExtensibleField<3> for BaseElement
Defines a cubic extension of the base field over an irreducible polynomial x3 + 2x + 2. Thus, an extension element is defined as α + β * φ + γ * φ^2, where φ is a root of this polynomial, and α, β and γ are base field elements.
source§fn mul(a: [Self; 3], b: [Self; 3]) -> [Self; 3]
fn mul(a: [Self; 3], b: [Self; 3]) -> [Self; 3]
a
and b
in the field defined by this extension.source§fn mul_base(a: [Self; 3], b: Self) -> [Self; 3]
fn mul_base(a: [Self; 3], b: Self) -> [Self; 3]
a
and b
in the field defined by this extension. b
represents
an element in the base field.source§fn frobenius(x: [Self; 3]) -> [Self; 3]
fn frobenius(x: [Self; 3]) -> [Self; 3]
x
in the field defined by this extension.source§fn square(a: [Self; N]) -> [Self; N]
fn square(a: [Self; N]) -> [Self; N]
a
in the field defined by this extension.source§fn is_supported() -> bool
fn is_supported() -> bool
source§impl FieldElement for BaseElement
impl FieldElement for BaseElement
§type PositiveInteger = u64
type PositiveInteger = u64
Self::BaseField
with no loss of precision.§type BaseField = BaseElement
type BaseField = BaseElement
BaseField
should be set
to Self
.source§const EXTENSION_DEGREE: usize = 1usize
const EXTENSION_DEGREE: usize = 1usize
Self::BaseField
. For prime fields,
extension degree should be set to 1.source§const ELEMENT_BYTES: usize = 8usize
const ELEMENT_BYTES: usize = 8usize
source§const IS_CANONICAL: bool = false
const IS_CANONICAL: bool = false
source§fn exp(self, power: Self::PositiveInteger) -> Self
fn exp(self, power: Self::PositiveInteger) -> Self
power
parameter.source§fn inv(self) -> Self
fn inv(self) -> Self
source§fn base_element(&self, i: usize) -> Self::BaseField
fn base_element(&self, i: usize) -> Self::BaseField
i
. Read moresource§fn slice_as_base_elements(elements: &[Self]) -> &[Self::BaseField]
fn slice_as_base_elements(elements: &[Self]) -> &[Self::BaseField]
source§fn slice_from_base_elements(elements: &[Self::BaseField]) -> &[Self]
fn slice_from_base_elements(elements: &[Self::BaseField]) -> &[Self]
source§fn elements_as_bytes(elements: &[Self]) -> &[u8] ⓘ
fn elements_as_bytes(elements: &[Self]) -> &[u8] ⓘ
source§unsafe fn bytes_as_elements(
bytes: &[u8]
) -> Result<&[Self], DeserializationError>
unsafe fn bytes_as_elements( bytes: &[u8] ) -> Result<&[Self], DeserializationError>
source§fn zeroed_vector(n: usize) -> Vec<Self>
fn zeroed_vector(n: usize) -> Vec<Self>
n
initialized with all ZERO elements. Read moresource§fn exp_vartime(self, power: Self::PositiveInteger) -> Self
fn exp_vartime(self, power: Self::PositiveInteger) -> Self
power
parameter.
This function is expressly variable time, to speed-up verifier computations.source§impl From<[u8; 8]> for BaseElement
impl From<[u8; 8]> for BaseElement
source§fn from(bytes: [u8; 8]) -> Self
fn from(bytes: [u8; 8]) -> Self
Converts the value encoded in an array of 8 bytes into a field element. The bytes are assumed to encode the element in the canonical representation in little-endian byte order. If the value is greater than or equal to the field modulus, modular reduction is silently performed.
source§impl From<BaseElement> for u128
impl From<BaseElement> for u128
source§fn from(value: BaseElement) -> Self
fn from(value: BaseElement) -> Self
source§impl From<BaseElement> for u64
impl From<BaseElement> for u64
source§fn from(value: BaseElement) -> Self
fn from(value: BaseElement) -> Self
source§impl From<u128> for BaseElement
impl From<u128> for BaseElement
source§impl From<u16> for BaseElement
impl From<u16> for BaseElement
source§impl From<u32> for BaseElement
impl From<u32> for BaseElement
source§impl From<u64> for BaseElement
impl From<u64> for BaseElement
source§impl From<u8> for BaseElement
impl From<u8> for BaseElement
source§impl Mul<BaseElement> for BaseElement
impl Mul<BaseElement> for BaseElement
source§impl MulAssign<BaseElement> for BaseElement
impl MulAssign<BaseElement> for BaseElement
source§fn mul_assign(&mut self, rhs: Self)
fn mul_assign(&mut self, rhs: Self)
*=
operation. Read moresource§impl Neg for BaseElement
impl Neg for BaseElement
source§impl PartialEq<BaseElement> for BaseElement
impl PartialEq<BaseElement> for BaseElement
source§impl Randomizable for BaseElement
impl Randomizable for BaseElement
source§const VALUE_SIZE: usize = 8usize
const VALUE_SIZE: usize = 8usize
Self
in bytes. Read moresource§fn from_random_bytes(bytes: &[u8]) -> Option<Self>
fn from_random_bytes(bytes: &[u8]) -> Option<Self>
Self
if the set of bytes forms a valid value, otherwise returns None.source§impl Serializable for BaseElement
impl Serializable for BaseElement
source§fn write_into<W: ByteWriter>(&self, target: &mut W)
fn write_into<W: ByteWriter>(&self, target: &mut W)
self
into bytes and writes these bytes into the target
.source§fn write_batch_into<W>(source: &[Self], target: &mut W)where
W: ByteWriter,
fn write_batch_into<W>(source: &[Self], target: &mut W)where W: ByteWriter,
source§fn get_size_hint(&self) -> usize
fn get_size_hint(&self) -> usize
source§impl StarkField for BaseElement
impl StarkField for BaseElement
source§const MODULUS: Self::PositiveInteger = {transmute(0x3fffc88000000001): <field::f62::BaseElement as field::traits::FieldElement>::PositiveInteger}
const MODULUS: Self::PositiveInteger = {transmute(0x3fffc88000000001): <field::f62::BaseElement as field::traits::FieldElement>::PositiveInteger}
sage: MODULUS = 2^62 - 111 * 2^39 + 1
sage: GF(MODULUS).is_prime_field()
True
sage: GF(MODULUS).order()
4611624995532046337
source§const TWO_ADICITY: u32 = 39u32
const TWO_ADICITY: u32 = 39u32
sage: is_odd((MODULUS - 1) / 2^39)
True
source§const TWO_ADIC_ROOT_OF_UNITY: Self = _
const TWO_ADIC_ROOT_OF_UNITY: Self = _
sage: k = (MODULUS - 1) / 2^39
sage: GF(MODULUS).primitive_element()^k
4421547261963328785
source§const MODULUS_BITS: u32 = 62u32
const MODULUS_BITS: u32 = 62u32
Self::MODULUS
.source§fn get_modulus_le_bytes() -> Vec<u8>
fn get_modulus_le_bytes() -> Vec<u8>
source§fn as_int(&self) -> Self::PositiveInteger
fn as_int(&self) -> Self::PositiveInteger
source§fn get_root_of_unity(n: u32) -> Self
fn get_root_of_unity(n: u32) -> Self
n
. Read moresource§impl Sub<BaseElement> for BaseElement
impl Sub<BaseElement> for BaseElement
source§impl SubAssign<BaseElement> for BaseElement
impl SubAssign<BaseElement> for BaseElement
source§fn sub_assign(&mut self, rhs: Self)
fn sub_assign(&mut self, rhs: Self)
-=
operation. Read moresource§impl<'a> TryFrom<&'a [u8]> for BaseElement
impl<'a> TryFrom<&'a [u8]> for BaseElement
source§fn try_from(bytes: &[u8]) -> Result<Self, Self::Error>
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 encode the element in the canonical representation in little-endian byte order.