Struct r1cs::Element

pub struct Element<F: Field> { /* fields omitted */ }

An element of a prime field.

Methods

impl<F: Field> Element<F>

pub fn zero() -> Self

pub fn one() -> Self

pub fn largest_element() -> Self

pub fn to_biguint(&self) -> &BigUint

pub fn is_zero(&self) -> bool

pub fn is_nonzero(&self) -> bool

pub fn is_one(&self) -> bool

pub fn multiplicative_inverse(&self) -> Self

pub fn multiplicative_inverse_or_zero(&self) -> Self

Like multiplicative_inverse, except that zero is mapped to itself rather than causing a panic.

pub fn exponentiation(&self, power: &Self) -> Self

pub fn integer_division(&self, rhs: &Self) -> Self

pub fn integer_modulus(&self, rhs: &Self) -> Self

pub fn gcd(&self, rhs: &Self) -> Self

pub fn is_prime(&self) -> bool

pub fn max_bits() -> usize

The number of bits needed to encode every element of F.

pub fn bits(&self) -> usize

The number of bits needed to encode this particular field element.

pub fn bit(&self, i: usize) -> bool

Return the i'th least significant bit. So, for example, x.bit(0) returns the least significant bit of x. Return false for outside of range.

Trait Implementations

impl<F: Field> From<Element<F>> for Expression<F>

fn from(value: Element<F>) -> Self

Performs the conversion.

impl<'_, F: Field> From<&'_ Element<F>> for Expression<F>

fn from(value: &Element<F>) -> Self

Performs the conversion.

impl<F: Field> From<BigUint> for Element<F>

fn from(n: BigUint) -> Element<F>

Performs the conversion.

impl<F: Field> From<usize> for Element<F>

fn from(n: usize) -> Element<F>

Performs the conversion.

impl<F: Field> From<u128> for Element<F>

fn from(n: u128) -> Element<F>

Performs the conversion.

impl<F: Field> From<u64> for Element<F>

fn from(n: u64) -> Element<F>

Performs the conversion.

impl<F: Field> From<u32> for Element<F>

fn from(n: u32) -> Element<F>

Performs the conversion.

impl<F: Field> From<u16> for Element<F>

fn from(n: u16) -> Element<F>

Performs the conversion.

impl<F: Field> From<u8> for Element<F>

fn from(n: u8) -> Element<F>

Performs the conversion.

impl<F: Field> From<bool> for Element<F>

fn from(b: bool) -> Element<F>

Performs the conversion.

impl<F: Field> Clone for Element<F>

fn clone(&self) -> Self

Returns a copy of the value.

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

Performs copy-assignment from source.

impl<F: Field> Eq for Element<F>

impl<F: Field> Ord for Element<F>

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

This method returns an Ordering between self and other.

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

Compares and returns the maximum of two values.

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

Compares and returns the minimum of two values.

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

🔬 This is a nightly-only experimental API. (clamp)

Restrict a value to a certain interval.

impl<F: Field> PartialEq<Element<F>> for Element<F>

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

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

#[must_use] fn ne(&self, other: &Rhs) -> bool

This method tests for !=.

impl<F: Field> PartialOrd<Element<F>> for Element<F>

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

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

#[must_use] fn lt(&self, other: &Rhs) -> bool

This method tests less than (for self and other) and is used by the < operator.

#[must_use] fn le(&self, other: &Rhs) -> bool

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

#[must_use] fn gt(&self, other: &Rhs) -> bool

This method tests greater than (for self and other) and is used by the > operator.

#[must_use] fn ge(&self, other: &Rhs) -> bool

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

impl<F: Field> Display for Element<F>

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

Formats the value using the given formatter.

impl<F: Debug + Field> Debug for Element<F>

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

Formats the value using the given formatter.

impl<F: Field> Div<Element<F>> for Expression<F>

type Output = Expression<F>

The resulting type after applying the / operator.

fn div(self, rhs: Element<F>) -> Expression<F>

Performs the / operation.

impl<'_, F: Field> Div<&'_ Element<F>> for Expression<F>

type Output = Expression<F>

The resulting type after applying the / operator.

fn div(self, rhs: &Element<F>) -> Expression<F>

Performs the / operation.

impl<'_, F: Field> Div<Element<F>> for &'_ Expression<F>

type Output = Expression<F>

The resulting type after applying the / operator.

fn div(self, rhs: Element<F>) -> Expression<F>

Performs the / operation.

impl<'_, '_, F: Field> Div<&'_ Element<F>> for &'_ Expression<F>

type Output = Expression<F>

The resulting type after applying the / operator.

fn div(self, rhs: &Element<F>) -> Expression<F>

Performs the / operation.

impl<F: Field> Div<Element<F>> for Element<F>

type Output = Element<F>

The resulting type after applying the / operator.

fn div(self, rhs: Element<F>) -> Element<F>

Performs the / operation.

impl<'_, F: Field> Div<&'_ Element<F>> for Element<F>

type Output = Element<F>

The resulting type after applying the / operator.

fn div(self, rhs: &Element<F>) -> Element<F>

Performs the / operation.

impl<'_, F: Field> Div<Element<F>> for &'_ Element<F>

type Output = Element<F>

The resulting type after applying the / operator.

fn div(self, rhs: Element<F>) -> Element<F>

Performs the / operation.

impl<'_, '_, F: Field> Div<&'_ Element<F>> for &'_ Element<F>

type Output = Element<F>

The resulting type after applying the / operator.

fn div(self, rhs: &Element<F>) -> Element<F>

Performs the / operation.

impl<F: Field> Div<u128> for Element<F>

type Output = Element<F>

The resulting type after applying the / operator.

fn div(self, rhs: u128) -> Element<F>

Performs the / operation.

impl<'_, F: Field> Div<u128> for &'_ Element<F>

type Output = Element<F>

The resulting type after applying the / operator.

fn div(self, rhs: u128) -> Element<F>

Performs the / operation.

impl<F: Field> Sub<Element<F>> for Element<F>

type Output = Element<F>

The resulting type after applying the - operator.

fn sub(self, rhs: Element<F>) -> Element<F>

Performs the - operation.

impl<'_, F: Field> Sub<&'_ Element<F>> for Element<F>

type Output = Element<F>

The resulting type after applying the - operator.

fn sub(self, rhs: &Element<F>) -> Element<F>

Performs the - operation.

impl<'_, F: Field> Sub<Element<F>> for &'_ Element<F>

type Output = Element<F>

The resulting type after applying the - operator.

fn sub(self, rhs: Element<F>) -> Element<F>

Performs the - operation.

impl<'_, '_, F: Field> Sub<&'_ Element<F>> for &'_ Element<F>

type Output = Element<F>

The resulting type after applying the - operator.

fn sub(self, rhs: &Element<F>) -> Element<F>

Performs the - operation.

impl<F: Field> FromStr for Element<F>

type Err = ParseBigIntError

The associated error which can be returned from parsing.

fn from_str(s: &str) -> Result<Self, Self::Err>

Parses a string s to return a value of this type.

impl<F: Field> Add<Element<F>> for Element<F>

type Output = Element<F>

The resulting type after applying the + operator.

fn add(self, rhs: Element<F>) -> Element<F>

Performs the + operation.

impl<'_, F: Field> Add<&'_ Element<F>> for Element<F>

type Output = Element<F>

The resulting type after applying the + operator.

fn add(self, rhs: &Element<F>) -> Element<F>

Performs the + operation.

impl<'_, F: Field> Add<Element<F>> for &'_ Element<F>

type Output = Element<F>

The resulting type after applying the + operator.

fn add(self, rhs: Element<F>) -> Element<F>

Performs the + operation.

impl<'_, '_, F: Field> Add<&'_ Element<F>> for &'_ Element<F>

type Output = Element<F>

The resulting type after applying the + operator.

fn add(self, rhs: &Element<F>) -> Element<F>

Performs the + operation.

impl<F: Field> Mul<Element<F>> for Expression<F>

type Output = Expression<F>

The resulting type after applying the * operator.

fn mul(self, rhs: Element<F>) -> Expression<F>

Performs the * operation.

impl<'_, F: Field> Mul<&'_ Element<F>> for Expression<F>

type Output = Expression<F>

The resulting type after applying the * operator.

fn mul(self, rhs: &Element<F>) -> Expression<F>

Performs the * operation.

impl<'_, F: Field> Mul<Element<F>> for &'_ Expression<F>

type Output = Expression<F>

The resulting type after applying the * operator.

fn mul(self, rhs: Element<F>) -> Expression<F>

Performs the * operation.

impl<'_, '_, F: Field> Mul<&'_ Element<F>> for &'_ Expression<F>

type Output = Expression<F>

The resulting type after applying the * operator.

fn mul(self, rhs: &Element<F>) -> Expression<F>

Performs the * operation.

impl<F: Field> Mul<Element<F>> for Element<F>

type Output = Element<F>

The resulting type after applying the * operator.

fn mul(self, rhs: Element<F>) -> Element<F>

Performs the * operation.

impl<'_, F: Field> Mul<&'_ Element<F>> for Element<F>

type Output = Element<F>

The resulting type after applying the * operator.

fn mul(self, rhs: &Element<F>) -> Element<F>

Performs the * operation.

impl<'_, F: Field> Mul<Element<F>> for &'_ Element<F>

type Output = Element<F>

The resulting type after applying the * operator.

fn mul(self, rhs: Element<F>) -> Element<F>

Performs the * operation.

impl<'_, '_, F: Field> Mul<&'_ Element<F>> for &'_ Element<F>

type Output = Element<F>

The resulting type after applying the * operator.

fn mul(self, rhs: &Element<F>) -> Element<F>

Performs the * operation.

impl<F: Field> Mul<u128> for Element<F>

type Output = Element<F>

The resulting type after applying the * operator.

fn mul(self, rhs: u128) -> Element<F>

Performs the * operation.

impl<'_, F: Field> Mul<u128> for &'_ Element<F>

type Output = Element<F>

The resulting type after applying the * operator.

fn mul(self, rhs: u128) -> Element<F>

Performs the * operation.

impl<F: Field> Neg for Element<F>

type Output = Element<F>

The resulting type after applying the - operator.

fn neg(self) -> Element<F>

Performs the unary - operation.

impl<'_, F: Field> Neg for &'_ Element<F>

type Output = Element<F>

The resulting type after applying the - operator.

fn neg(self) -> Element<F>

Performs the unary - operation.

impl<F: Field> AddAssign<Element<F>> for Element<F>

fn add_assign(&mut self, rhs: Element<F>)

Performs the += operation.

impl<'_, F: Field> AddAssign<&'_ Element<F>> for Element<F>

fn add_assign(&mut self, rhs: &Element<F>)

Performs the += operation.

impl<F: Field> SubAssign<Element<F>> for Element<F>

fn sub_assign(&mut self, rhs: Element<F>)

Performs the -= operation.

impl<'_, F: Field> SubAssign<&'_ Element<F>> for Element<F>

fn sub_assign(&mut self, rhs: &Element<F>)

Performs the -= operation.

impl<F: Field> MulAssign<Element<F>> for Expression<F>

fn mul_assign(&mut self, rhs: Element<F>)

Performs the *= operation.

impl<'_, F: Field> MulAssign<&'_ Element<F>> for Expression<F>

fn mul_assign(&mut self, rhs: &Element<F>)

Performs the *= operation.

impl<F: Field> MulAssign<Element<F>> for Element<F>

fn mul_assign(&mut self, rhs: Element<F>)

Performs the *= operation.

impl<'_, F: Field> MulAssign<&'_ Element<F>> for Element<F>

fn mul_assign(&mut self, rhs: &Element<F>)

Performs the *= operation.

impl<F: Field> MulAssign<u128> for Element<F>

fn mul_assign(&mut self, rhs: u128)

Performs the *= operation.

impl<F: Field> DivAssign<Element<F>> for Expression<F>

fn div_assign(&mut self, rhs: Element<F>)

Performs the /= operation.

impl<'_, F: Field> DivAssign<&'_ Element<F>> for Expression<F>

fn div_assign(&mut self, rhs: &Element<F>)

Performs the /= operation.

impl<F: Field> DivAssign<Element<F>> for Element<F>

fn div_assign(&mut self, rhs: Element<F>)

Performs the /= operation.

impl<'_, F: Field> DivAssign<&'_ Element<F>> for Element<F>

fn div_assign(&mut self, rhs: &Element<F>)

Performs the /= operation.

impl<F: Field> DivAssign<u128> for Element<F>

fn div_assign(&mut self, rhs: u128)

Performs the /= operation.

impl<F: Field> Shl<usize> for Element<F>

type Output = Element<F>

The resulting type after applying the << operator.

fn shl(self, rhs: usize) -> Element<F>

Performs the << operation.

impl<'_, F: Field> Shl<usize> for &'_ Element<F>

type Output = Element<F>

The resulting type after applying the << operator.

fn shl(self, rhs: usize) -> Element<F>

Performs the << operation.

impl<F: Field> Hash for Element<F>

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, 

Feeds a slice of this type into the given [Hasher].