Struct ibig::modular::Modulo

pub struct Modulo<'a>(_);

Modular arithmetic.

Examples

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

Implementations

impl Modulo<'_>

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.from(-1234);
assert_eq!(x.residue(), ubig!(66));

impl Modulo<'_>

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

Exponentiation.

Examples

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

Trait Implementations

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

type Output = Modulo<'a>

The resulting type after applying the + operator.

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

Performs the + operation.

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

type Output = Modulo<'a>

The resulting type after applying the + operator.

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

Performs the + operation.

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

type Output = Modulo<'a>

The resulting type after applying the + operator.

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

Performs the + operation.

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

type Output = Modulo<'a>

The resulting type after applying the + operator.

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

Performs the + operation.

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

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

Performs the += operation.

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

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

Performs the += operation.

impl Binary for Modulo<'_>

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

Formats the value using the given formatter.

impl Clone for Modulo<'_>

fn clone(&self) -> Self

Returns a copy of the value.

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

Performs copy-assignment from source.

impl Debug for Modulo<'_>

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

Formats the value using the given formatter.

impl Display for Modulo<'_>

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

Formats the value using the given formatter.

impl Eq for Modulo<'_>

impl LowerHex for Modulo<'_>

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

Formats the value using the given formatter.

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

type Output = Modulo<'a>

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Modulo<'a>

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Modulo<'a>

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Modulo<'a>

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

Performs the *= operation.

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

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

Performs the *= operation.

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

type Output = Modulo<'a>

The resulting type after applying the - operator.

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

Performs the unary - operation.

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

type Output = Modulo<'a>

The resulting type after applying the - operator.

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

Performs the unary - operation.

impl Octal for Modulo<'_>

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

Formats the value using the given formatter.

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

Equality within a ring.

Panics

Panics if the two values are from different rings.

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

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

#[must_use]

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

This method tests for !=.

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

type Output = Modulo<'a>

The resulting type after applying the - operator.

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

Performs the - operation.

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

type Output = Modulo<'a>

The resulting type after applying the - operator.

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

Performs the - operation.

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

type Output = Modulo<'a>

The resulting type after applying the - operator.

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

Performs the - operation.

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

type Output = Modulo<'a>

The resulting type after applying the - operator.

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

Performs the - operation.

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

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

Performs the -= operation.

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

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

Performs the -= operation.

impl UpperHex for Modulo<'_>

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

Formats the value using the given formatter.