Struct lambdaworks_math::field::fields::u64_goldilocks_field::Goldilocks64Field

pub struct Goldilocks64Field;

Goldilocks Prime Field F_p where p = 2^64 - 2^32 + 1;

Implementations

impl Goldilocks64Field

pub const ORDER: u64 = 18_446_744_069_414_584_321u64

pub const NEG_ORDER: u64 = 4_294_967_295u64

Trait Implementations

impl Clone for Goldilocks64Field

fn clone(&self) -> Goldilocks64Field

Returns a copy of the value.

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

Performs copy-assignment from source.

impl Debug for Goldilocks64Field

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

Formats the value using the given formatter.

impl HasQuadraticNonResidue<Goldilocks64Field> for Goldilocks64Field

fn residue() -> FieldElement<Goldilocks64Field>

impl Hash for Goldilocks64Field

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 IsField for Goldilocks64Field

fn inv(a: &u64) -> Result<u64, FieldError>

Returns the multiplicative inverse of a.

fn div(a: &u64, b: &u64) -> u64

Returns the division of a and b.

fn eq(a: &u64, b: &u64) -> bool

Returns a boolean indicating whether a and b are equal or not.

fn zero() -> u64

Returns the additive neutral element.

fn one() -> u64

Returns the multiplicative neutral element.

fn from_u64(x: u64) -> u64

Returns the element x * 1 where 1 is the multiplicative neutral element.

fn from_base_type(x: u64) -> u64

Takes as input an element of BaseType and returns the internal representation of that element in the field.

type BaseType = u64

fn add(a: &u64, b: &u64) -> u64

Returns the sum of a and b.

fn mul(a: &u64, b: &u64) -> u64

Returns the multiplication of a and b.

fn sub(a: &u64, b: &u64) -> u64

Returns the subtraction of a and b.

fn neg(a: &u64) -> u64

Returns the additive inverse of a.

fn double(a: &Self::BaseType) -> Self::BaseType

Returns the double of a.

fn square(a: &Self::BaseType) -> Self::BaseType

Returns the multiplication of a and a.

fn pow<T>(a: &Self::BaseType, exponent: T) -> Self::BaseType

where T: IsUnsignedInteger,

impl IsPrimeField for Goldilocks64Field

type RepresentativeType = u64

fn representative(x: &u64) -> u64

Returns the integer representative in the range [0, p-1], where p the modulus

fn field_bit_size() -> usize

Returns the number of bits of the max element of the field, as per field documentation, not internal representation. This is log2(max FE) rounded up

fn from_hex(hex_string: &str) -> Result<Self::BaseType, CreationError>

Creates a BaseType from a Hex String 0x is optional Returns an CreationError::InvalidHexStringif the value is not a hexstring

fn to_hex(x: &u64) -> String

Creates a hexstring from a FieldElement without 0x.

fn modulus_minus_one() -> Self::RepresentativeType

fn legendre_symbol(a: &Self::BaseType) -> LegendreSymbol

fn sqrt(a: &Self::BaseType) -> Option<(Self::BaseType, Self::BaseType)>

Returns the two square roots of self if they exist and None otherwise

impl Ord for Goldilocks64Field

fn cmp(&self, other: &Goldilocks64Field) -> Ordering

This method returns an Ordering between self and other.

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

where Self: Sized,

Compares and returns the maximum of two values.

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

where Self: Sized,

Compares and returns the minimum of two values.

fn clamp(self, min: Self, max: Self) -> Self

where Self: Sized + PartialOrd,

Restrict a value to a certain interval.

impl PartialEq for Goldilocks64Field

fn eq(&self, other: &Goldilocks64Field) -> 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 PartialOrd for Goldilocks64Field

fn partial_cmp(&self, other: &Goldilocks64Field) -> Option<Ordering>

This method returns an ordering between self and other values if one exists.

fn lt(&self, other: &Rhs) -> bool

Tests less than (for self and other) and is used by the < operator.

fn le(&self, other: &Rhs) -> bool

Tests less than or equal to (for self and other) and is used by the <= operator.

fn gt(&self, other: &Rhs) -> bool

Tests greater than (for self and other) and is used by the > operator.

fn ge(&self, other: &Rhs) -> bool

Tests greater than or equal to (for self and other) and is used by the >= operator.

impl Copy for Goldilocks64Field

impl Eq for Goldilocks64Field

impl StructuralPartialEq for Goldilocks64Field