PrimeField.rs

use std::ops::{Add, Div, Mul, Neg, Rem, Sub};

use num_bigint::BigInt;
use num_traits::{One, Zero};

use crate::shared_math::traits::{ModPowU32, PrimeFieldElement};

pub trait PrimeFieldInnerElement {
    type Elem: Clone
        + Eq
        + Add<Output = Self::Elem>
        + Mul<Output = Self::Elem>
        + Rem<Output = Self::Elem>
        + Zero
        + One;

    const MODULUS: Self::Elem;
}

// pub trait PrimeFieldModulus<T: PrimeFieldInnerElement> {
//     const MODULUS: T::Elem;
// }

pub trait PrimeFieldElementGeneric<T: PrimeFieldInnerElement>
where
    Self: Sized,
{
    // Abstract
    fn new(value: T::Elem) -> Self;

    fn inner(&self) -> T::Elem;

    // Concrete
    fn zero() -> Self {
        Self::new(T::Elem::zero())
    }

    fn is_zero(&self) -> bool {
        self.inner() == T::Elem::zero()
    }

    fn one() -> Self {
        Self::new(T::Elem::one())
    }

    fn is_one(&self) -> bool {
        self.inner() == T::Elem::one()
    }

    fn add(&self, other: Self) -> Self {
        Self::new((self.inner() + other.inner()) % T::MODULUS)
    }

    fn mul(&self, other: Self) -> Self {
        Self::new((self.inner() * other.inner()) % T::MODULUS)
    }

    fn rem(&self, other: Self) -> Self {
        Self::new(self.inner() % other.inner())
    }
}

pub struct PrimeFieldElementBig17 {
    pub value: BigInt,
}

impl PrimeFieldInnerElement for PrimeFieldElementBig17 {
    type Elem = BigInt;

    const MODULUS: Self::Elem = 17.into();
}

// impl PrimeFieldModulus<PrimeFieldElementBig17> for PrimeFieldElementBig17 {
//     const MODULUS: PrimeFieldElementBig17::Elem = todo!();
// }

impl PrimeFieldElementGeneric<PrimeFieldElementBig17> for PrimeFieldElementBig17 {
    fn new(value: <PrimeFieldElementBig17 as PrimeFieldInnerElement>::Elem) -> Self {
        todo!()
    }

    fn inner(&self) -> <PrimeFieldElementBig17 as PrimeFieldInnerElement>::Elem {
        todo!()
    }
}