Struct FixedTrinomialSolinas 

pub struct FixedTrinomialSolinas<const P1: u8, const P2: u8, const K: imax>();

A modular reducer for trinomial Solinas numbers 2^P1 - 2^P2 + K as modulus.

Supports P1 up to 127, P2 < P1, and odd signed K with |K| < 2^P2. All inputs and outputs are umax (currently u128).

The P1 is limited to 127 so that overflow checks aren’t necessary. This covers all trinomial Solinas primes within the range of umax (i.e. u128).

Example

use num_modular::{FixedTrinomialSolinas, Reducer};

const P1: u8 = 31;
const P2: u8 = 13;
const K: i128 = 1;
let modulus = (1u128 << P1) - (1u128 << P2) + (K as u128);
let reducer = FixedTrinomialSolinas::<P1, P2, 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 P1: u8, const P2: u8, const K: imax> FixedTrinomialSolinas<P1, P2, K>

pub const MODULUS: umax

Trait Implementations

impl<const P1: u8, const P2: u8, const K: imax> Clone for FixedTrinomialSolinas<P1, P2, K>

fn clone(&self) -> FixedTrinomialSolinas<P1, P2, K>

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl<const P1: u8, const P2: u8, const K: imax> Copy for FixedTrinomialSolinas<P1, P2, K>

impl<const P1: u8, const P2: u8, const K: imax> Debug for FixedTrinomialSolinas<P1, P2, K>

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

Formats the value using the given formatter.

impl<const P1: u8, const P2: u8, const K: imax> Reducer<u128> for FixedTrinomialSolinas<P1, P2, 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)