Struct F 

pub struct F(/* private fields */);

An element of the Goldilocks field.

Implementations

impl F

pub const ROOT_OF_UNITY: Self

An element of order 2^32.

This is specifically chosen such that ROOT_OF_UNITY^(2^26) = 8.

That enables optimizations when doing NTTs, and things like that.

pub const NOT_ROOT_OF_UNITY: Self

An element guaranteed not to be any power of Self::ROOT_OF_UNITY.

pub const NOT_ROOT_OF_UNITY_INV: Self

The inverse of Self::NOT_ROOT_OF_UNITY.

pub fn inv(self) -> Self

Return the multiplicative inverse of a field element.

Self::zero will return Self::zero.

pub fn root_of_unity(lg_k: u8) -> Option<Self>

Construct a 2^lg_k root of unity.

This will fail for lg_k > 32.

pub fn div_2(self) -> Self

Return self / 2.

pub fn stream_from_u64s( inner: impl Iterator<Item = u64>, ) -> impl Iterator<Item = Self>

Convert a stream of u64s into a stream of field elements.

pub fn stream_to_u64s( inner: impl Iterator<Item = Self>, ) -> impl Iterator<Item = u64>

Convert a stream produced by F::stream_from_u64s back to the original stream.

This may produce a single extra 0 element.

pub const fn bits_to_elements(bits: usize) -> usize

How many elements are used to encode a given number of bits?

This is based on what F::stream_from_u64s does.

pub const fn to_le_bytes(&self) -> [u8; 8]

Convert this element to little-endian bytes.

pub fn rand(rng: impl CryptoRngCore) -> Self

Create a random field element.

This will be uniformly distributed.

Trait Implementations

impl<'a> Add<&'a F> for F

type Output = F

The resulting type after applying the + operator.

fn add(self, rhs: &'a F) -> Self::Output

Performs the + operation.

impl Add for F

type Output = F

The resulting type after applying the + operator.

fn add(self, b: Self) -> Self::Output

Performs the + operation.

impl<'a> AddAssign<&'a F> for F

fn add_assign(&mut self, rhs: &'a F)

Performs the += operation.

impl Additive for F

fn zero() -> Self

The neutral element for addition.

fn double(&mut self)

Add an element to itself.

fn scale(&self, bits_le: &[u64]) -> Self

Scale this number by a positive integer.

impl Clone for F

fn clone(&self) -> F

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl Debug for F

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

Formats the value using the given formatter.

impl Field for F

fn inv(&self) -> Self

The multiplicative inverse of an element.

impl FixedSize for F

const SIZE: usize = 8usize

The size of the encoded value (in bytes).

impl From<u64> for F

fn from(value: u64) -> Self

Converts to this type from the input type.

impl<'a> Mul<&'a F> for F

type Output = F

The resulting type after applying the * operator.

fn mul(self, rhs: &'a F) -> Self::Output

Performs the * operation.

impl Mul for F

type Output = F

The resulting type after applying the * operator.

fn mul(self, b: Self) -> Self::Output

Performs the * operation.

impl<'a> MulAssign<&'a F> for F

fn mul_assign(&mut self, rhs: &'a F)

Performs the *= operation.

impl Multiplicative for F

fn square(&mut self)

Multiply an element with itself.

impl Neg for F

type Output = F

The resulting type after applying the - operator.

fn neg(self) -> Self::Output

Performs the unary - operation.

impl PartialEq for F

fn eq(&self, other: &F) -> 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 Read for F

type Cfg = <u64 as Read>::Cfg

The Cfg type parameter allows passing configuration during the read process. This is crucial for safely decoding untrusted data, for example, by providing size limits for collections or strings.

fn read_cfg(buf: &mut impl Buf, cfg: &Self::Cfg) -> Result<Self, Error>

Reads a value from the buffer using the provided configuration cfg.

impl Ring for F

fn one() -> Self

The neutral element for multiplication.

fn exp(&self, bits_le: &[u64]) -> Self

Exponentiate this number by a positive integer.

impl<'a> Sub<&'a F> for F

type Output = F

The resulting type after applying the - operator.

fn sub(self, rhs: &'a F) -> Self::Output

Performs the - operation.

impl Sub for F

type Output = F

The resulting type after applying the - operator.

fn sub(self, b: Self) -> Self::Output

Performs the - operation.

impl<'a> SubAssign<&'a F> for F

fn sub_assign(&mut self, rhs: &'a F)

Performs the -= operation.

impl Write for F

fn write(&self, buf: &mut impl BufMut)

Writes the binary representation of self to the provided buffer buf.

impl Copy for F

impl Eq for F

impl Object for F

impl StructuralPartialEq for F