Struct ReducedInt 

pub struct ReducedInt<T, R: Reducer<T>> { /* private fields */ }

An integer in a modulo ring

Implementations

impl<T, R: Reducer<T>> ReducedInt<T, R>

pub fn new(n: T, m: &T) -> Self

Convert n into the modulo ring ℤ/mℤ (i.e. n % m)

pub fn repr(&self) -> &T

pub fn inv(self) -> Option<Self>

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

Trait Implementations

impl<T: PartialEq, R: Reducer<T>> Add for ReducedInt<T, R>

type Output = ReducedInt<T, R>

The resulting type after applying the + operator.

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

Performs the + operation.

impl<T: PartialEq + Clone, R: Reducer<T>> Add<&ReducedInt<T, R>> for ReducedInt<T, R>

type Output = ReducedInt<T, R>

The resulting type after applying the + operator.

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

Performs the + operation.

impl<T: PartialEq + Clone, R: Reducer<T> + Clone> Add<&ReducedInt<T, R>> for &ReducedInt<T, R>

type Output = ReducedInt<T, R>

The resulting type after applying the + operator.

fn add(self, rhs: &ReducedInt<T, R>) -> Self::Output

Performs the + operation.

impl<T: PartialEq + Clone, R: Reducer<T>> Add<&T> for ReducedInt<T, R>

type Output = ReducedInt<T, R>

The resulting type after applying the + operator.

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

Performs the + operation.

impl<T: PartialEq + Clone, R: Reducer<T> + Clone> Add<&T> for &ReducedInt<T, R>

type Output = ReducedInt<T, R>

The resulting type after applying the + operator.

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

Performs the + operation.

impl<T: PartialEq + Clone, R: Reducer<T>> Add<ReducedInt<T, R>> for &ReducedInt<T, R>

type Output = ReducedInt<T, R>

The resulting type after applying the + operator.

fn add(self, rhs: ReducedInt<T, R>) -> Self::Output

Performs the + operation.

impl<T, R: Reducer<T>> Add<T> for ReducedInt<T, R>

type Output = ReducedInt<T, R>

The resulting type after applying the + operator.

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

Performs the + operation.

impl<T, R: Reducer<T> + Clone> Add<T> for &ReducedInt<T, R>

type Output = ReducedInt<T, R>

The resulting type after applying the + operator.

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

Performs the + operation.

impl<T: PartialEq, R: Reducer<T>> AddAssign for ReducedInt<T, R>

fn add_assign(&mut self, rhs: Self)

Performs the += operation.

impl<T: PartialEq, R: Reducer<T>> AddAssign<&ReducedInt<T, R>> for ReducedInt<T, R>

fn add_assign(&mut self, rhs: &Self)

Performs the += operation.

impl<T: PartialEq + Clone, R: Reducer<T>> AddAssign<&T> for ReducedInt<T, R>

fn add_assign(&mut self, rhs: &T)

Performs the += operation.

impl<T, R: Reducer<T>> AddAssign<T> for ReducedInt<T, R>

fn add_assign(&mut self, rhs: T)

Performs the += operation.

impl<T: Clone, R: Clone + Reducer<T>> Clone for ReducedInt<T, R>

fn clone(&self) -> ReducedInt<T, R>

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl<T: Copy, R: Copy + Reducer<T>> Copy for ReducedInt<T, R>

impl<T: Debug, R: Debug + Reducer<T>> Debug for ReducedInt<T, R>

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

Formats the value using the given formatter.

impl<T: PartialEq, R: Reducer<T>> Div for ReducedInt<T, R>

type Output = ReducedInt<T, R>

The resulting type after applying the / operator.

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

Performs the / operation.

impl<T: PartialEq + Clone, R: Reducer<T>> Div<&ReducedInt<T, R>> for ReducedInt<T, R>

type Output = ReducedInt<T, R>

The resulting type after applying the / operator.

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

Performs the / operation.

impl<T: PartialEq + Clone, R: Reducer<T> + Clone> Div<&ReducedInt<T, R>> for &ReducedInt<T, R>

type Output = ReducedInt<T, R>

The resulting type after applying the / operator.

fn div(self, rhs: &ReducedInt<T, R>) -> Self::Output

Performs the / operation.

impl<T: PartialEq + Clone, R: Reducer<T>> Div<ReducedInt<T, R>> for &ReducedInt<T, R>

type Output = ReducedInt<T, R>

The resulting type after applying the / operator.

fn div(self, rhs: ReducedInt<T, R>) -> Self::Output

Performs the / operation.

impl<T: PartialEq, R: Reducer<T>> Inv for ReducedInt<T, R>

Available on crate feature num-traits only.

type Output = ReducedInt<T, R>

The result after applying the operator.

fn inv(self) -> Self::Output

Returns the multiplicative inverse of self.

impl<T: PartialEq + Clone, R: Reducer<T> + Clone> Inv for &ReducedInt<T, R>

Available on crate feature num-traits only.

type Output = ReducedInt<T, R>

The result after applying the operator.

fn inv(self) -> Self::Output

Returns the multiplicative inverse of self.

impl<T: PartialEq + Clone, R: Reducer<T> + Clone> ModularInteger for ReducedInt<T, R>

type Base = T

The underlying representation type of the integer

fn modulus(&self) -> T

Return the modulus of the ring

fn residue(&self) -> T

Return the normalized residue of this integer in the ring

fn is_zero(&self) -> bool

Check if the integer is zero

fn convert(&self, n: T) -> Self

Convert an normal integer into the same ring.

fn double(self) -> Self

Calculate the value of self + self

fn square(self) -> Self

Calculate the value of self * self

impl<T: PartialEq, R: Reducer<T>> Mul for ReducedInt<T, R>

type Output = ReducedInt<T, R>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<T: PartialEq + Clone, R: Reducer<T>> Mul<&ReducedInt<T, R>> for ReducedInt<T, R>

type Output = ReducedInt<T, R>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<T: PartialEq + Clone, R: Reducer<T> + Clone> Mul<&ReducedInt<T, R>> for &ReducedInt<T, R>

type Output = ReducedInt<T, R>

The resulting type after applying the * operator.

fn mul(self, rhs: &ReducedInt<T, R>) -> Self::Output

Performs the * operation.

impl<T: PartialEq + Clone, R: Reducer<T>> Mul<&T> for ReducedInt<T, R>

type Output = ReducedInt<T, R>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<T: PartialEq + Clone, R: Reducer<T> + Clone> Mul<&T> for &ReducedInt<T, R>

type Output = ReducedInt<T, R>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<T: PartialEq + Clone, R: Reducer<T>> Mul<ReducedInt<T, R>> for &ReducedInt<T, R>

type Output = ReducedInt<T, R>

The resulting type after applying the * operator.

fn mul(self, rhs: ReducedInt<T, R>) -> Self::Output

Performs the * operation.

impl<T, R: Reducer<T>> Mul<T> for ReducedInt<T, R>

type Output = ReducedInt<T, R>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<T, R: Reducer<T> + Clone> Mul<T> for &ReducedInt<T, R>

type Output = ReducedInt<T, R>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<T: PartialEq, R: Reducer<T>> MulAssign for ReducedInt<T, R>

fn mul_assign(&mut self, rhs: Self)

Performs the *= operation.

impl<T: PartialEq, R: Reducer<T>> MulAssign<&ReducedInt<T, R>> for ReducedInt<T, R>

fn mul_assign(&mut self, rhs: &Self)

Performs the *= operation.

impl<T: PartialEq + Clone, R: Reducer<T>> MulAssign<&T> for ReducedInt<T, R>

fn mul_assign(&mut self, rhs: &T)

Performs the *= operation.

impl<T, R: Reducer<T>> MulAssign<T> for ReducedInt<T, R>

fn mul_assign(&mut self, rhs: T)

Performs the *= operation.

impl<T: PartialEq, R: Reducer<T>> Neg for ReducedInt<T, R>

type Output = ReducedInt<T, R>

The resulting type after applying the - operator.

fn neg(self) -> Self::Output

Performs the unary - operation.

impl<T: PartialEq + Clone, R: Reducer<T> + Clone> Neg for &ReducedInt<T, R>

type Output = ReducedInt<T, R>

The resulting type after applying the - operator.

fn neg(self) -> Self::Output

Performs the unary - operation.

impl<T: PartialEq, R: Reducer<T>> PartialEq for ReducedInt<T, R>

fn eq(&self, other: &Self) -> 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<T: PartialEq, R: Reducer<T>> Pow<T> for ReducedInt<T, R>

Available on crate feature num-traits only.

type Output = ReducedInt<T, R>

The result after applying the operator.

fn pow(self, rhs: T) -> Self::Output

Returns self to the power rhs.

impl<T: PartialEq + Clone, R: Reducer<T> + Clone> Pow<T> for &ReducedInt<T, R>

Available on crate feature num-traits only.

type Output = ReducedInt<T, R>

The result after applying the operator.

fn pow(self, rhs: T) -> Self::Output

Returns self to the power rhs.

impl<T: PartialEq, R: Reducer<T>> Sub for ReducedInt<T, R>

type Output = ReducedInt<T, R>

The resulting type after applying the - operator.

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

Performs the - operation.

impl<T: PartialEq + Clone, R: Reducer<T>> Sub<&ReducedInt<T, R>> for ReducedInt<T, R>

type Output = ReducedInt<T, R>

The resulting type after applying the - operator.

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

Performs the - operation.

impl<T: PartialEq + Clone, R: Reducer<T> + Clone> Sub<&ReducedInt<T, R>> for &ReducedInt<T, R>

type Output = ReducedInt<T, R>

The resulting type after applying the - operator.

fn sub(self, rhs: &ReducedInt<T, R>) -> Self::Output

Performs the - operation.

impl<T: PartialEq + Clone, R: Reducer<T>> Sub<&T> for ReducedInt<T, R>

type Output = ReducedInt<T, R>

The resulting type after applying the - operator.

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

Performs the - operation.

impl<T: PartialEq + Clone, R: Reducer<T> + Clone> Sub<&T> for &ReducedInt<T, R>

type Output = ReducedInt<T, R>

The resulting type after applying the - operator.

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

Performs the - operation.

impl<T: PartialEq + Clone, R: Reducer<T>> Sub<ReducedInt<T, R>> for &ReducedInt<T, R>

type Output = ReducedInt<T, R>

The resulting type after applying the - operator.

fn sub(self, rhs: ReducedInt<T, R>) -> Self::Output

Performs the - operation.

impl<T, R: Reducer<T>> Sub<T> for ReducedInt<T, R>

type Output = ReducedInt<T, R>

The resulting type after applying the - operator.

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

Performs the - operation.

impl<T, R: Reducer<T> + Clone> Sub<T> for &ReducedInt<T, R>

type Output = ReducedInt<T, R>

The resulting type after applying the - operator.

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

Performs the - operation.

impl<T: PartialEq, R: Reducer<T>> SubAssign for ReducedInt<T, R>

fn sub_assign(&mut self, rhs: Self)

Performs the -= operation.

impl<T: PartialEq, R: Reducer<T>> SubAssign<&ReducedInt<T, R>> for ReducedInt<T, R>

fn sub_assign(&mut self, rhs: &Self)

Performs the -= operation.

impl<T: PartialEq + Clone, R: Reducer<T>> SubAssign<&T> for ReducedInt<T, R>

fn sub_assign(&mut self, rhs: &T)

Performs the -= operation.

impl<T, R: Reducer<T>> SubAssign<T> for ReducedInt<T, R>

fn sub_assign(&mut self, rhs: T)

Performs the -= operation.