Struct FixedMersenne32 

pub struct FixedMersenne32<const P: u8, const K: u32>();

A modular reducer for (pseudo) Mersenne numbers 2^P - K as modulus with 32-bit operands.

Supports P up to 32 and K < 2^(P-1). All inputs and outputs are u32. The modulus 2^P - K must be prime for modular inverse and Fermat-based operations to be valid.

Example

use num_modular::{FixedMersenne32, Reducer};

const P: u8 = 13;
const K: u32 = 1;
let modulus = (1u32 << P) - K; // 2^13 - 1 = 8191 (Mersenne prime)
let reducer = FixedMersenne32::<P, K>::new(&modulus);
let a = reducer.transform(100);
let b = reducer.transform(200);
assert_eq!(reducer.residue(reducer.add(&a, &b)), 300 % modulus);

Implementations

impl<const P: u8, const K: u32> FixedMersenne32<P, K>

pub const MODULUS: u32

pub const fn reduce_single(v: u32) -> u32

Reduces a single-width value v modulo 2^P - K.

For the result of a widening multiplication or square, use reduce_double instead.

pub fn reduce_double(v: u64) -> u32

Reduces a double-width value v modulo 2^P - K.

This handles widening-multiplication or widening-square results. For single-width values, use reduce_single.

Trait Implementations

impl<const P: u8, const K: u32> Clone for FixedMersenne32<P, K>

fn clone(&self) -> FixedMersenne32<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: u32> Copy for FixedMersenne32<P, K>

impl<const P: u8, const K: u32> Debug for FixedMersenne32<P, K>

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

Formats the value using the given formatter.

impl<const P: u8, const K: u32> Reducer<u32> for FixedMersenne32<P, K>

fn new(m: &u32) -> Self

Create a reducer for a modulus m

fn transform(&self, target: u32) -> u32

Transform a normal integer into reduced form

fn residue(&self, target: u32) -> u32

Transform a reduced form back to normal integer

fn check(&self, target: &u32) -> bool

Check whether target is a valid reduced form

fn modulus(&self) -> u32

Get the modulus in original integer type

fn is_zero(&self, target: &u32) -> bool

Test if the residue() == 0

fn add(&self, lhs: &u32, rhs: &u32) -> u32

Calculate (lhs + rhs) mod m in reduced form

fn sub(&self, lhs: &u32, rhs: &u32) -> u32

Calculate (lhs - rhs) mod m in reduced form

fn dbl(&self, target: u32) -> u32

Calculate 2*target mod m

fn neg(&self, target: u32) -> u32

Calculate -target mod m in reduced form

fn mul(&self, lhs: &u32, rhs: &u32) -> u32

Calculate (lhs * rhs) mod m in reduced form

fn inv(&self, target: u32) -> Option<u32>

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

fn sqr(&self, target: u32) -> u32

Calculate target^2 mod m in reduced form

fn pow(&self, base: u32, exp: &u32) -> u32

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)