Struct dashu_int::modular::Modulo

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pub struct Modulo<'a>(_);

Expand description

Modular arithmetic.

Examples

let ring = ModuloRing::new(ubig!(10000));
let x = ring.convert(12345);
let y = ring.convert(55443);
assert_eq!((x - y).residue(), ubig!(6902));

Implementations

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impl Modulo<'_>

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pub fn residue(&self) -> UBig

Get the residue in range 0..n in an n-element ring.

Examples

let ring = ModuloRing::new(ubig!(100));
let x = ring.convert(-1234);
assert_eq!(x.residue(), ubig!(66));

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impl<'a> Modulo<'a>

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pub fn panic_different_rings() -> !

Panics when trying to do operations on Modulo values from different rings.

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impl<'a> Modulo<'a>

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pub fn pow(&self, exp: &UBig) -> Modulo<'a>

Exponentiation.

Examples

// A Mersenne prime.
let p = ubig!(2).pow(607) - ubig!(1);
let ring = ModuloRing::new(p.clone());
// Fermat's little theorem: a^(p-1) = 1 (mod p)
let a = ring.convert(123);
assert_eq!(a.pow(&(p - ubig!(1))), ring.convert(1));

Trait Implementations

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

type Output = Modulo<'a>

The resulting type after applying the + operator.

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fn add(self, rhs: &Modulo<'a>) -> Modulo<'a>

Performs the + operation. Read more

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

type Output = Modulo<'a>

The resulting type after applying the + operator.

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fn add(self, rhs: &Modulo<'a>) -> Modulo<'a>

Performs the + operation. Read more

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

type Output = Modulo<'a>

The resulting type after applying the + operator.

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fn add(self, rhs: Modulo<'a>) -> Modulo<'a>

Performs the + operation. Read more

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impl<'a> Add<Modulo<'a>> for Modulo<'a>

type Output = Modulo<'a>

The resulting type after applying the + operator.

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fn add(self, rhs: Modulo<'a>) -> Modulo<'a>

Performs the + operation. Read more

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

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fn add_assign(&mut self, rhs: &Modulo<'a>)

Performs the += operation. Read more

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impl<'a> AddAssign<Modulo<'a>> for Modulo<'a>

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fn add_assign(&mut self, rhs: Modulo<'a>)

Performs the += operation. Read more

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impl Binary for Modulo<'_>

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

Formats the value using the given formatter.

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impl Clone for Modulo<'_>

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fn clone(&self) -> Self

Returns a copy of the value. Read more

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

Performs copy-assignment from source. Read more

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impl Debug for Modulo<'_>

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

Formats the value using the given formatter. Read more

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impl Display for Modulo<'_>

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

Formats the value using the given formatter. Read more

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impl LowerHex for Modulo<'_>

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

Formats the value using the given formatter.

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

type Output = Modulo<'a>

The resulting type after applying the * operator.

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fn mul(self, rhs: &Modulo<'a>) -> Modulo<'a>

Performs the * operation. Read more

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

type Output = Modulo<'a>

The resulting type after applying the * operator.

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fn mul(self, rhs: &Modulo<'a>) -> Modulo<'a>

Performs the * operation. Read more

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

type Output = Modulo<'a>

The resulting type after applying the * operator.

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fn mul(self, rhs: Modulo<'a>) -> Modulo<'a>

Performs the * operation. Read more

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impl<'a> Mul<Modulo<'a>> for Modulo<'a>

type Output = Modulo<'a>

The resulting type after applying the * operator.

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fn mul(self, rhs: Modulo<'a>) -> Modulo<'a>

Performs the * operation. Read more

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

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fn mul_assign(&mut self, rhs: &Modulo<'a>)

Performs the *= operation. Read more

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impl<'a> MulAssign<Modulo<'a>> for Modulo<'a>

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fn mul_assign(&mut self, rhs: Modulo<'a>)

Performs the *= operation. Read more

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impl<'a> Neg for &Modulo<'a>

type Output = Modulo<'a>

The resulting type after applying the - operator.

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fn neg(self) -> Modulo<'a>

Performs the unary - operation. Read more

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impl<'a> Neg for Modulo<'a>

type Output = Modulo<'a>

The resulting type after applying the - operator.

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fn neg(self) -> Modulo<'a>

Performs the unary - operation. Read more

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impl Octal for Modulo<'_>

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

Formats the value using the given formatter.

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impl PartialEq<Modulo<'_>> for Modulo<'_>

Equality within a ring.

Panics

Panics if the two values are from different rings.

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

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

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

This method tests for !=.

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

type Output = Modulo<'a>

The resulting type after applying the - operator.

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fn sub(self, rhs: &Modulo<'a>) -> Modulo<'a>

Performs the - operation. Read more

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

type Output = Modulo<'a>

The resulting type after applying the - operator.

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fn sub(self, rhs: &Modulo<'a>) -> Modulo<'a>

Performs the - operation. Read more

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

type Output = Modulo<'a>

The resulting type after applying the - operator.

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fn sub(self, rhs: Modulo<'a>) -> Modulo<'a>

Performs the - operation. Read more

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impl<'a> Sub<Modulo<'a>> for Modulo<'a>

type Output = Modulo<'a>

The resulting type after applying the - operator.

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fn sub(self, rhs: Modulo<'a>) -> Modulo<'a>

Performs the - operation. Read more

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

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fn sub_assign(&mut self, rhs: &Modulo<'a>)

Performs the -= operation. Read more

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impl<'a> SubAssign<Modulo<'a>> for Modulo<'a>

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fn sub_assign(&mut self, rhs: Modulo<'a>)

Performs the -= operation. Read more

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impl UpperHex for Modulo<'_>

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

Formats the value using the given formatter.

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impl Eq for Modulo<'_>

Auto Trait Implementations

impl<'a> RefUnwindSafe for Modulo<'a>

impl<'a> Send for Modulo<'a>

impl<'a> Sync for Modulo<'a>

impl<'a> Unpin for Modulo<'a>

impl<'a> UnwindSafe for Modulo<'a>

Blanket Implementations

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impl<T> Any for T where
T: 'static + ?Sized,

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fn type_id(&self) -> TypeId

Gets the TypeId of self. Read more

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impl<T> Borrow<T> for T where
T: ?Sized,

const: unstable · source

fn borrow(&self) -> &T

Immutably borrows from an owned value. Read more

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impl<T> BorrowMut<T> for T where
T: ?Sized,

const: unstable · source

fn borrow_mut(&mut self) -> &mut T

Mutably borrows from an owned value. Read more

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impl<T> From<T> for T

const: unstable · source

fn from(t: T) -> T

Returns the argument unchanged.

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impl<T, U> Into for T where
U: From<T>,

const: unstable · source

fn into(self) -> U

Calls U::from(self).

That is, this conversion is whatever the implementation of From<T> for U chooses to do.

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impl<T> ToOwned for T where
T: Clone,

type Owned = T

The resulting type after obtaining ownership.

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fn to_owned(&self) -> T

Creates owned data from borrowed data, usually by cloning. Read more

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fn clone_into(&self, target: &mut T)

Uses borrowed data to replace owned data, usually by cloning. Read more

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impl<T> ToString for T where
T: Display + ?Sized,

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default fn to_string(&self) -> String

Converts the given value to a String. Read more

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impl<T, U> TryFrom for T where
U: Into<T>,

type Error = Infallible

The type returned in the event of a conversion error.

const: unstable · source

fn try_from(value: U) -> Result<T, <T as TryFrom>::Error>

Performs the conversion.

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impl<T, U> TryInto for T where
U: TryFrom<T>,

type Error = >::Error

The type returned in the event of a conversion error.

const: unstable · source

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

Performs the conversion.