1use rand::{distr::Distribution, Rng};
 2use std::fmt::Debug;
 3use std::iter::Sum;
 4use std::ops::{Add, AddAssign, Mul, Neg, Sub, SubAssign};
 5
 6#[derive(Clone, Copy, Debug, PartialEq, Eq)]
 7pub struct RingParam {
 8    pub q: u64, // TODO think if really needed or it's fine with coeffs[0].q
 9    pub n: usize,
10}
11
12/// Represents a ring element. Currently implemented by ring_nq.rs#Rq and
13/// ring_torus.rs#Tn. Is not a 'pure algebraic ring', but more a custom trait
14/// definition which includes methods like `mod_switch`.
15// assumed to be mod (X^N +1)
16pub trait Ring:
17    Sized
18    + Add<Output = Self>
19    + AddAssign
20    + Sum
21    + Sub<Output = Self>
22    + SubAssign
23    + Mul<Output = Self> // internal product
24    + Mul<u64, Output = Self> // scalar mul, external product
25    + Mul<Self::C, Output = Self>
26    + Neg<Output = Self>
27    + PartialEq
28    + Debug
29    + Clone
30    // + Copy
31    + Sum<<Self as Add>::Output>
32    + Sum<<Self as Mul>::Output>
33{
34    /// C defines the coefficient type
35    type C: Debug + Clone;
36
37    fn param(&self) -> RingParam;
38    fn coeffs(&self) -> Vec<Self::C>;
39    fn zero(param: &RingParam) -> Self;
40    // note/wip/warning: dist (0,q) with f64, will output more '0=q' elements than other values
41    fn rand(rng: impl Rng, dist: impl Distribution<f64>, param: &RingParam) -> Self;
42
43    fn from_vec(param: &RingParam, coeffs: Vec<Self::C>) -> Self;
44
45    fn decompose(&self, beta: u32, l: u32) -> Vec<Self>;
46
47    fn remodule(&self, p:u64) -> impl Ring;
48    fn mod_switch(&self, p:u64) -> impl Ring;
49
50    /// returns [ [(num/den) * self].round() ] mod q
51    /// ie. performs the multiplication and division over f64, and then it
52    /// rounds the result, only applying the mod Q (if the ring is mod Q) at the
53    /// end.
54    fn mul_div_round(&self, num: u64, den: u64) -> Self;
55}