Struct FixedMersenne 

pub struct FixedMersenne<const P: u8, const K: umax>();

A modular reducer for (pseudo) Mersenne numbers 2^P - K as modulus.

Supports P up to 128 and K < 2^(P-1). All inputs and outputs are umax (currently u128).

The P is limited to 128 so that overflow checks aren’t necessary. This covers all Mersenne primes within the range of umax (i.e. u128).

Example

use num_modular::{FixedMersenne, Reducer, umax};

const P: u8 = 31;
const K: umax = 1;
let modulus = (1 << P) - K; // 2^31 - 1 (Mersenne prime)
let reducer = FixedMersenne::<P, K>::new(&modulus);
let a = reducer.transform(1000);
let b = reducer.transform(2000);
assert_eq!(reducer.residue(reducer.mul(&a, &b)), (1000 * 2000) % modulus);

Implementations

impl<const P: u8, const K: umax> FixedMersenne<P, K>

pub const MODULUS: umax

Trait Implementations

impl<const P: u8, const K: umax> Clone for FixedMersenne<P, K>

fn clone(&self) -> FixedMersenne<P, K>

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl<const P: u8, const K: umax> Copy for FixedMersenne<P, K>

impl<const P: u8, const K: umax> Debug for FixedMersenne<P, K>

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

Formats the value using the given formatter.

impl<const P: u8, const K: umax> Reducer<u128> for FixedMersenne<P, K>

fn new(m: &umax) -> Self

Create a reducer for a modulus m

fn transform(&self, target: umax) -> umax

Transform a normal integer into reduced form

fn check(&self, target: &umax) -> bool

Check whether target is a valid reduced form

fn residue(&self, target: umax) -> umax

Transform a reduced form back to normal integer

fn modulus(&self) -> umax

Get the modulus in original integer type

fn is_zero(&self, target: &umax) -> bool

Test if the residue() == 0

fn add(&self, lhs: &umax, rhs: &umax) -> umax

Calculate (lhs + rhs) mod m in reduced form

fn sub(&self, lhs: &umax, rhs: &umax) -> umax

Calculate (lhs - rhs) mod m in reduced form

fn dbl(&self, target: umax) -> umax

Calculate 2*target mod m

fn neg(&self, target: umax) -> umax

Calculate -monty mod m in reduced form

fn mul(&self, lhs: &umax, rhs: &umax) -> umax

Calculate (lhs * rhs) mod m in reduced form

fn inv(&self, target: umax) -> Option<umax>

Calculate target^-1 mod m in reduced form, it may return None when there is no modular inverse.

fn sqr(&self, target: umax) -> umax

Calculate target^2 mod m in reduced form

fn pow(&self, base: umax, exp: &umax) -> umax

Calculate base ^ exp mod m in reduced form

fn add_in_place(&self, lhs: &mut T, rhs: &T)

fn sub_in_place(&self, lhs: &mut T, rhs: &T)

fn mul_in_place(&self, lhs: &mut T, rhs: &T)