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//! Implementation of modular arithmetic algorithms for all integer types in an
//! overflow-safe and const-compatible manner.

#![no_std]
#![warn(missing_docs)]

use core::ops::{Add, BitAnd, Neg, Rem, Shr, Sub};
use num_traits::{one, CheckedAdd, One};

/// Represents an integer with an associated modulus.
#[derive(Clone, Copy, PartialEq, Eq)]
pub struct Modular<T: Clone + Eq + Rem<Output = T>> {
    /// The integer.
    pub value: T,

    /// The modulus.
    pub modulus: T,
}

impl<T: CheckedAdd + Clone + Eq + Rem<Output = T> + Shr<Output = T> + BitAnd<Output = T> + One>
    Modular<T>
{
    fn try_add(self, rhs: Self) -> Option<Self> {
        if self.modulus != rhs.modulus {
            None
        } else {
            Some(match self.value.checked_add(&rhs.value) {
                Some(r) => Self {
                    value: r % self.modulus.clone(),
                    modulus: self.modulus,
                },
                None => Self {
                    value: (((self.value.clone() >> one()) + (rhs.value.clone() >> one()))
                        % self.modulus.clone()
                        + ((self.value & one()) + (rhs.value & one())) % self.modulus.clone())
                        % self.modulus.clone(),
                    modulus: self.modulus,
                },
            })
        }
    }

    fn try_sub(self, rhs: Self) -> Option<Self>
    where
        T: Sub<Output = T>,
    {
        self.try_add(-rhs)
    }
}

impl<T: Clone + Eq + Rem<Output = T> + Sub<Output = T> + One> Neg for Modular<T> {
    type Output = Self;

    fn neg(self) -> Self::Output {
        Self {
            value: self.modulus.clone() - self.value - one(),
            modulus: self.modulus,
        }
    }
}

impl<T: CheckedAdd + Clone + Eq + Rem<Output = T> + Shr<Output = T> + BitAnd<Output = T> + One> Add
    for Modular<T>
{
    type Output = Modular<<T as Add>::Output>;

    fn add(self, rhs: Self) -> Self::Output {
        self.try_add(rhs)
            .expect("operands do not have the same modulus!")
    }
}

impl<
        T: CheckedAdd
            + Clone
            + Eq
            + Rem<Output = T>
            + Sub<Output = T>
            + Shr<Output = T>
            + BitAnd<Output = T>
            + One,
    > Sub for Modular<T>
{
    type Output = Modular<<T as Add>::Output>;

    fn sub(self, rhs: Self) -> Self::Output {
        self.try_sub(rhs)
            .expect("operands do not have the same modulus!")
    }
}

/// Represents an integer with a statically specified modulus.
pub struct StaticModular<T: Clone + Eq + Rem<Output = T> + One + From<usize>, const M: usize>(T);

impl<
        T: CheckedAdd
            + Clone
            + Eq
            + Rem<Output = T>
            + Shr<Output = T>
            + BitAnd<Output = T>
            + One
            + From<usize>,
        const M: usize,
    > Add for StaticModular<T, M>
{
    type Output = StaticModular<<T as Add>::Output, M>;

    fn add(self, rhs: Self) -> Self::Output {
        Self(
            Modular {
                value: self.0,
                modulus: M.into(),
            }
            .try_add(Modular {
                value: rhs.0,
                modulus: M.into(),
            })
            .unwrap()
            .value,
        )
    }
}

impl<T: Clone + Eq + From<usize> + Rem<Output = T> + One, const M: usize> From<T>
    for StaticModular<T, M>
{
    fn from(value: T) -> Self {
        Self(value % M.into())
    }
}