Struct FixedMersenne64 

pub struct FixedMersenne64<const P: u8, const K: u64>();

A modular reducer for (pseudo) Mersenne numbers 2^P - K as modulus with 64-bit operands.

Supports P up to 64 and K < 2^(P-1). All inputs and outputs are u64. Uses u128 as the double-width intermediate for multiplication and reduction. The modulus 2^P - K must be prime for modular inverse and Fermat-based operations to be valid.

Example

use num_modular::{FixedMersenne64, Reducer};

const P: u8 = 61;
const K: u64 = 1;
let modulus = (1u64 << P) - K; // 2^61 - 1 (Mersenne prime)
let reducer = FixedMersenne64::<P, K>::new(&modulus);
let a = reducer.transform(1000);
let b = reducer.transform(2000);
assert_eq!(reducer.residue(reducer.mul(&a, &b)), (1000u64 * 2000) % modulus);

Implementations

impl<const P: u8, const K: u64> FixedMersenne64<P, K>

pub const MODULUS: u64

Trait Implementations

impl<const P: u8, const K: u64> Clone for FixedMersenne64<P, K>

fn clone(&self) -> FixedMersenne64<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: u64> Copy for FixedMersenne64<P, K>

impl<const P: u8, const K: u64> Debug for FixedMersenne64<P, K>

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

Formats the value using the given formatter.

impl<const P: u8, const K: u64> Reducer<u64> for FixedMersenne64<P, K>

fn new(m: &u64) -> Self

Create a reducer for a modulus m

fn transform(&self, target: u64) -> u64

Transform a normal integer into reduced form

fn check(&self, target: &u64) -> bool

Check whether target is a valid reduced form

fn residue(&self, target: u64) -> u64

Transform a reduced form back to normal integer

fn modulus(&self) -> u64

Get the modulus in original integer type

fn is_zero(&self, target: &u64) -> bool

Test if the residue() == 0

fn add(&self, lhs: &u64, rhs: &u64) -> u64

Calculate (lhs + rhs) mod m in reduced form

fn sub(&self, lhs: &u64, rhs: &u64) -> u64

Calculate (lhs - rhs) mod m in reduced form

fn dbl(&self, target: u64) -> u64

Calculate 2*target mod m

fn neg(&self, target: u64) -> u64

Calculate -monty mod m in reduced form

fn mul(&self, lhs: &u64, rhs: &u64) -> u64

Calculate (lhs * rhs) mod m in reduced form

fn inv(&self, target: u64) -> Option<u64>

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

fn sqr(&self, target: u64) -> u64

Calculate target^2 mod m in reduced form

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

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)