Struct FixedProth 

pub struct FixedProth<const N: u8, const K: u8>;

A modular reducer for Proth primes K * 2^N + 1.

Supports N up to 127, K odd with K < 2^N. Montgomery form with R = 2¹²⁸.

Example

use num_modular::{FixedProth, Reducer};

const N: u8 = 16;
const K: u8 = 1;
let modulus = (K as u128) * (1u128 << N) + 1; // 2^16 + 1 = 65537
let reducer = FixedProth::<N, K>::new(&modulus);
let a = reducer.transform(1000);
let b = reducer.transform(2000);
assert_eq!(reducer.residue(reducer.mul(&a, &b)), (1000u128 * 2000) % modulus);

Implementations

impl<const N: u8, const K: u8> FixedProth<N, K>

pub const MODULUS: umax

pub fn reduce(&self, t: udouble) -> umax

Montgomery REDC with R = 2¹²⁸ and Proth-optimised m·p product.

Trait Implementations

impl<const N: u8, const K: u8> Clone for FixedProth<N, K>

fn clone(&self) -> FixedProth<N, K>

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl<const N: u8, const K: u8> Copy for FixedProth<N, K>

impl<const N: u8, const K: u8> Debug for FixedProth<N, K>

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

Formats the value using the given formatter.

impl<const N: u8, const K: u8> Reducer<u128> for FixedProth<N, 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 residue(&self, target: umax) -> umax

Transform a reduced form back to normal integer

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

Check whether target is a valid reduced form

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 -target mod m in reduced form

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

Calculate (lhs * rhs) mod m in reduced form

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

Calculate target^2 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 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)