Struct Modular 

pub struct Modular { /* private fields */ }

An element of the ring ℤ/nℤ — an integer taken modulo a fixed modulus. This is the arbitrary-modulus generalisation of crate::Word8/…/crate::Word64 (whose modulus is a power of two): arithmetic WRAPS into [0, modulus), the cyclic group where overflow is the point, not a bug. The number-theory / crypto substrate — modular exponentiation and the extended-Euclid inverse live here, so RSA-style and finite-field code is exact.

INVARIANT: 0 ≤ value < modulus and modulus ≥ 1 (built via Modular::new, which reduces into range), so equal residues share one representation (Eq/Hash are structural). NOT ordered (ℤ/nℤ has no canonical total order).

Implementations

impl Modular

pub fn new(value: BigInt, modulus: BigInt) -> Option<Modular>

Reduce value into the ring ℤ/modulusℤ. None for a non-positive modulus.

pub fn from_i64(value: i64, modulus: i64) -> Option<Modular>

Convenience over machine integers (None if modulus ≤ 0).

pub fn value(&self) -> &BigInt

The canonical representative in [0, modulus).

pub fn modulus(&self) -> &BigInt

pub fn is_zero(&self) -> bool

pub fn add(&self, other: &Modular) -> Option<Modular>

self + other — None when the moduli differ (a ring mismatch, like a Word width mismatch).

pub fn sub(&self, other: &Modular) -> Option<Modular>

pub fn mul(&self, other: &Modular) -> Option<Modular>

pub fn negated(&self) -> Modular

The additive inverse −self (i.e. modulus − value, reduced).

pub fn pow(&self, exp: u64) -> Modular

self^exp by fast modular exponentiation (square-and-multiply). 0^0 == 1.

pub fn inverse(&self) -> Option<Modular>

The multiplicative inverse self⁻¹ (extended Euclid). None unless gcd(value, modulus) == 1 (the value must be a unit of the ring).

pub fn div(&self, other: &Modular) -> Option<Modular>

self / other = self · other⁻¹ — None on a modulus mismatch or a non-invertible divisor.

Trait Implementations

impl Clone for Modular

fn clone(&self) -> Modular

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl Debug for Modular

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

Formats the value using the given formatter.

impl Display for Modular

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

Formats the value using the given formatter.

impl Eq for Modular

impl Hash for Modular

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 PartialEq for Modular

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

Equality operator ==.

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

Inequality operator !=.

impl StructuralPartialEq for Modular