Struct M31 

#[repr(transparent)]
pub struct M31(pub u32);

Tuple Fields

0: u32

Implementations

impl M31

pub fn partial_reduce(val: u32) -> Self

Returns val % P when val is in the range [0, 2P).

use stwo::core::fields::m31::{M31, P};

let val = 2 * P - 19;
assert_eq!(M31::partial_reduce(val), M31::from(P - 19));

pub const fn reduce(val: u64) -> Self

Returns val % P when val is in the range [0, P^2).

use stwo::core::fields::m31::{M31, P};

let val = (P as u64).pow(2) - 19;
assert_eq!(M31::reduce(val), M31::from(P - 19));

pub const fn from_u32_unchecked(arg: u32) -> Self

pub fn inverse(&self) -> Self

Trait Implementations

impl Add for M31

type Output = M31

The resulting type after applying the + operator.

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

Performs the + operation.

impl Add<CM31> for M31

type Output = CM31

The resulting type after applying the + operator.

fn add(self, rhs: CM31) -> Self::Output

Performs the + operation.

impl Add<M31> for CM31

type Output = CM31

The resulting type after applying the + operator.

fn add(self, rhs: M31) -> Self::Output

Performs the + operation.

impl Add<M31> for QM31

type Output = QM31

The resulting type after applying the + operator.

fn add(self, rhs: M31) -> Self::Output

Performs the + operation.

impl Add<QM31> for M31

type Output = QM31

The resulting type after applying the + operator.

fn add(self, rhs: QM31) -> Self::Output

Performs the + operation.

impl AddAssign for M31

fn add_assign(&mut self, rhs: Self)

Performs the += operation.

impl AddAssign<M31> for CM31

fn add_assign(&mut self, rhs: M31)

Performs the += operation.

impl AddAssign<M31> for QM31

fn add_assign(&mut self, rhs: M31)

Performs the += operation.

impl Clone for M31

fn clone(&self) -> M31

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl ComplexConjugate for M31

fn complex_conjugate(&self) -> Self

Example

impl Copy for M31

impl Debug for M31

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

Formats the value using the given formatter.

impl Default for M31

fn default() -> M31

Returns the “default value” for a type.

impl<'de> Deserialize<'de> for M31

fn deserialize<__D>(__deserializer: __D) -> Result<Self, __D::Error>

where __D: Deserializer<'de>,

Deserialize this value from the given Serde deserializer.

impl Display for M31

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

Formats the value using the given formatter.

impl Distribution<M31> for Standard

fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> M31

Generate a random value of T, using rng as the source of randomness.

fn sample_iter<R>(self, rng: R) -> DistIter<Self, R, T>

where R: Rng, Self: Sized,

Create an iterator that generates random values of T, using rng as the source of randomness.

fn map<F, S>(self, func: F) -> DistMap<Self, F, T, S>

where F: Fn(T) -> S, Self: Sized,

Create a distribution of values of ‘S’ by mapping the output of Self through the closure F

impl Div for M31

type Output = M31

The resulting type after applying the / operator.

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

Performs the / operation.

impl Div<CM31> for M31

type Output = CM31

The resulting type after applying the / operator.

fn div(self, rhs: CM31) -> Self::Output

Performs the / operation.

impl Div<M31> for CM31

type Output = CM31

The resulting type after applying the / operator.

fn div(self, rhs: M31) -> Self::Output

Performs the / operation.

impl Div<M31> for QM31

type Output = QM31

The resulting type after applying the / operator.

fn div(self, rhs: M31) -> Self::Output

Performs the / operation.

impl Div<QM31> for M31

type Output = QM31

The resulting type after applying the / operator.

fn div(self, rhs: QM31) -> Self::Output

Performs the / operation.

impl DivAssign for M31

fn div_assign(&mut self, rhs: Self)

Performs the /= operation.

impl DivAssign<M31> for CM31

fn div_assign(&mut self, rhs: M31)

Performs the /= operation.

impl DivAssign<M31> for QM31

fn div_assign(&mut self, rhs: M31)

Performs the /= operation.

impl Eq for M31

impl ExtensionOf<M31> for CM31

const EXTENSION_DEGREE: usize

impl ExtensionOf<M31> for QM31

const EXTENSION_DEGREE: usize

impl Field for M31

fn double(&self) -> Self

impl FieldExpOps for M31

fn inverse(&self) -> Self

use num_traits::One;
use stwo::core::fields::m31::BaseField;
use stwo::core::fields::FieldExpOps;

let v = BaseField::from(19);
assert_eq!(v.inverse() * v, BaseField::one());

fn square(&self) -> Self

fn pow(&self, exp: u128) -> Self

fn batch_inverse(column: &[Self]) -> Vec<Self>

impl From<M31> for CM31

fn from(x: M31) -> Self

Converts to this type from the input type.

impl From<M31> for QM31

fn from(x: M31) -> Self

Converts to this type from the input type.

impl From<i32> for M31

fn from(value: i32) -> Self

Converts to this type from the input type.

impl From<u32> for M31

fn from(value: u32) -> Self

Converts to this type from the input type.

impl From<usize> for M31

fn from(value: usize) -> Self

Converts to this type from the input type.

impl Hash for M31

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 Mul for M31

type Output = M31

The resulting type after applying the * operator.

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

Performs the * operation.

impl Mul<CM31> for M31

type Output = CM31

The resulting type after applying the * operator.

fn mul(self, rhs: CM31) -> Self::Output

Performs the * operation.

impl Mul<M31> for CM31

type Output = CM31

The resulting type after applying the * operator.

fn mul(self, rhs: M31) -> Self::Output

Performs the * operation.

impl Mul<M31> for QM31

type Output = QM31

The resulting type after applying the * operator.

fn mul(self, rhs: M31) -> Self::Output

Performs the * operation.

impl Mul<QM31> for M31

type Output = QM31

The resulting type after applying the * operator.

fn mul(self, rhs: QM31) -> Self::Output

Performs the * operation.

impl MulAssign for M31

fn mul_assign(&mut self, rhs: Self)

Performs the *= operation.

impl MulAssign<M31> for CM31

fn mul_assign(&mut self, rhs: M31)

Performs the *= operation.

impl MulAssign<M31> for QM31

fn mul_assign(&mut self, rhs: M31)

Performs the *= operation.

impl Neg for M31

type Output = M31

The resulting type after applying the - operator.

fn neg(self) -> Self::Output

Performs the unary - operation.

impl Num for M31

type FromStrRadixErr = Box<dyn Error>

fn from_str_radix( _str: &str, _radix: u32, ) -> Result<Self, Self::FromStrRadixErr>

Convert from a string and radix (typically 2..=36).

impl One for M31

fn one() -> Self

Returns the multiplicative identity element of Self, 1.

fn set_one(&mut self)

Sets self to the multiplicative identity element of Self, 1.

fn is_one(&self) -> bool

where Self: PartialEq,

Returns true if self is equal to the multiplicative identity.

impl Ord for M31

fn cmp(&self, other: &M31) -> 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,

Restrict a value to a certain interval.

impl PartialEq for M31

fn eq(&self, other: &M31) -> 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 M31

fn partial_cmp(&self, other: &M31) -> 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 Pod for M31

impl Product for M31

fn product<I>(iter: I) -> Self

where I: Iterator<Item = Self>,

Takes an iterator and generates Self from the elements by multiplying the items.

impl<'a> Product<&'a M31> for M31

fn product<I>(iter: I) -> Self

where I: Iterator<Item = &'a Self>,

Takes an iterator and generates Self from the elements by multiplying the items.

impl Rem for M31

type Output = M31

The resulting type after applying the % operator.

fn rem(self, _rhs: Self) -> Self::Output

Performs the % operation.

impl Rem<M31> for CM31

type Output = CM31

The resulting type after applying the % operator.

fn rem(self, _rhs: M31) -> Self::Output

Performs the % operation.

impl Rem<M31> for QM31

type Output = QM31

The resulting type after applying the % operator.

fn rem(self, _rhs: M31) -> Self::Output

Performs the % operation.

impl RemAssign for M31

fn rem_assign(&mut self, _rhs: Self)

Performs the %= operation.

impl RemAssign<M31> for CM31

fn rem_assign(&mut self, _rhs: M31)

Performs the %= operation.

impl RemAssign<M31> for QM31

fn rem_assign(&mut self, _rhs: M31)

Performs the %= operation.

impl Serialize for M31

fn serialize<__S>(&self, __serializer: __S) -> Result<__S::Ok, __S::Error>

where __S: Serializer,

Serialize this value into the given Serde serializer.

impl StructuralPartialEq for M31

impl Sub for M31

type Output = M31

The resulting type after applying the - operator.

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

Performs the - operation.

impl Sub<CM31> for M31

type Output = CM31

The resulting type after applying the - operator.

fn sub(self, rhs: CM31) -> Self::Output

Performs the - operation.

impl Sub<M31> for CM31

type Output = CM31

The resulting type after applying the - operator.

fn sub(self, rhs: M31) -> Self::Output

Performs the - operation.

impl Sub<M31> for QM31

type Output = QM31

The resulting type after applying the - operator.

fn sub(self, rhs: M31) -> Self::Output

Performs the - operation.

impl Sub<QM31> for M31

type Output = QM31

The resulting type after applying the - operator.

fn sub(self, rhs: QM31) -> Self::Output

Performs the - operation.

impl SubAssign for M31

fn sub_assign(&mut self, rhs: Self)

Performs the -= operation.

impl SubAssign<M31> for CM31

fn sub_assign(&mut self, rhs: M31)

Performs the -= operation.

impl SubAssign<M31> for QM31

fn sub_assign(&mut self, rhs: M31)

Performs the -= operation.

impl Sum for M31

fn sum<I>(iter: I) -> Self

where I: Iterator<Item = Self>,

Takes an iterator and generates Self from the elements by “summing up” the items.

impl<'a> Sum<&'a M31> for M31

fn sum<I>(iter: I) -> Self

where I: Iterator<Item = &'a Self>,

Takes an iterator and generates Self from the elements by “summing up” the items.

impl TryInto<M31> for CM31

type Error = ()

The type returned in the event of a conversion error.

fn try_into(self) -> Result<M31, Self::Error>

Performs the conversion.

impl TryInto<M31> for QM31

type Error = ()

The type returned in the event of a conversion error.

fn try_into(self) -> Result<M31, Self::Error>

Performs the conversion.

impl Zero for M31

fn zero() -> Self

Returns the additive identity element of Self, 0.

fn is_zero(&self) -> bool

Returns true if self is equal to the additive identity.

fn set_zero(&mut self)

Sets self to the additive identity element of Self, 0.

impl Zeroable for M31

fn zeroed() -> Self

Calls zeroed.