Struct FixedProth64 

pub struct FixedProth64<const N: u8, const K: u8>;

A modular reducer for Proth primes K * 2^N + 1 with 64-bit operands.

Supports N up to 63, K odd with K < 2^N. Montgomery form with R = 2⁶⁴.

Example

use num_modular::{FixedProth64, Reducer};

const N: u8 = 5;
const K: u8 = 3;
let modulus = (K as u64) * (1u64 << N) + 1; // 3*2^5 + 1 = 97
let reducer = FixedProth64::<N, K>::new(&modulus);
let a = reducer.transform(10);
let b = reducer.transform(20);
assert_eq!(reducer.residue(reducer.mul(&a, &b)), (10u64 * 20) % 97);

Implementations

impl<const N: u8, const K: u8> FixedProth64<N, K>

pub const MODULUS: u64

pub fn reduce(&self, t: u128) -> u64

Trait Implementations

impl<const N: u8, const K: u8> Clone for FixedProth64<N, K>

fn clone(&self) -> FixedProth64<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 FixedProth64<N, K>

impl<const N: u8, const K: u8> Debug for FixedProth64<N, K>

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

Formats the value using the given formatter.

impl<const N: u8, const K: u8> Reducer<u64> for FixedProth64<N, 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 residue(&self, target: u64) -> u64

Transform a reduced form back to normal integer

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

Check whether target is a valid reduced form

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 -target mod m in reduced form

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

Calculate (lhs * rhs) mod m in reduced form

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

Calculate target^2 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 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)