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use core::ops::{Add, Sub, Shr, Shl, Rem, Mul};

use crate::{BigUInt, property::IsBigInt};

pub mod impls;
pub mod slice;

/// perform arithmetic rhs % self, which is symmetic Rem
pub trait WrapAround<Rhs = Self> {
    fn wrap(self, rhs: Rhs) -> Self;
}

/// This trait requires bigint to implement methods for multiplication.
/// 
/// Due to restrictions on rust type system, it's difficult for us to express something like
/// 
/// ```text,ignore
/// Self: Mul<Output = impl BigUIntProperties<DIG_LEN == 2 * <Self as BigUIntProperties>::DIG_LEN> && Dig == <Self as BigUIntProperties>::Dig>
/// ```
/// 
/// So instead of implementing a multiplication that returns one biguint with twice of self's length, we return
/// two biguints representing the higher digs and lower digs seperatly.
/// 
/// This trait requires biguint to implement this kind of multiplication, and to use the return convinently, 
/// we should also implement a mod method to convert two biguints into one by modding one biguint, which is useful
/// when we are dealing with biguint mul-mod or exp-mod arithmetics.
pub trait BigIntOpsExt
where
    Self: 
        BigIntOps +
        Mul<Self, Output = [Self; 2]> + Mul<Self::Dig, Output = (Self, Self::Dig)> +
        WrapAround<[Self; 2]> + 
        PartialEq<[Self; 2]> + PartialOrd<[Self; 2]>
{ }

/// This trait requires bigint to at least implement add, sub, shl, shr, mod and order
pub trait BigIntOps
where
    Self:
        Sized + Copy +
        IsBigInt +
        Add<Output = (Self, Self::Dig)> + Add<Self::Dig, Output = (Self, Self::Dig)> +
        Sub<Output = (Self, Self::Dig)> + Sub<Self::Dig, Output = (Self, Self::Dig)> +
        Shr<usize, Output = Self> +
        Shl<usize, Output = Self> + 
        Rem<Output = Self> + 
        Ord + Eq
{ }

impl<T: Copy, const LEN: usize> BigIntOps for BigUInt<T, LEN> 
where
    Self: 
        IsBigInt +
        Add<Output = (Self, Self::Dig)> + Add<Self::Dig, Output = (Self, Self::Dig)> +
        Sub<Output = (Self, Self::Dig)> + Sub<Self::Dig, Output = (Self, Self::Dig)> +
        Shr<usize, Output = Self> +
        Shr<usize, Output = Self> +
        Shl<usize, Output = Self> + 
        Rem<Output = Self> +
        Ord + Eq,
{ }

impl<T: Copy, const LEN: usize> BigIntOpsExt for BigUInt<T, LEN> 
where
    Self: 
        BigIntOps + 
        Mul<Output = [Self; 2]> + Mul<Self::Dig, Output = (Self, Self::Dig)> +
        WrapAround<[Self; 2]> +
        PartialEq<[Self; 2]> + PartialOrd<[Self; 2]>
{ }