[WIP] Z/nZライブラリ

residue_ring.rs

use num::Num;
use std::ops;

#[derive(std::cmp::PartialEq, Clone, Copy)]
struct ResidueRing<T>
where T: std::fmt::Display + Copy + num::Num + num::Unsigned + PartialEq
{
    n: T,
    modulo: T,
}

impl<T> ResidueRing<T>
where T: std::fmt::Display + Copy + num::Num + num::Unsigned + PartialEq
{
    fn from(n: T, modulo: T) -> Self {
        Self {
            n: n % modulo, modulo
        }
    }
}

impl<T> std::ops::Add for ResidueRing<T>
where T: std::fmt::Display + Copy + num::Num + num::Unsigned + PartialEq
{
    type Output = Self;

    fn add(self, other: Self) -> Self {
        #[cfg(debug_assertions)]
        {
            if self.modulo != other.modulo {
                panic!("different modulo: {} (mod {}) + {} (mod {})", self.n, self.modulo, other.n, other.modulo);
            }
        }
        Self {
            n: (self.n + other.n) % self.modulo,
            modulo: self.modulo,
        }
    }
}

impl<T> std::ops::Add<T> for ResidueRing<T>
where T: std::fmt::Display + Copy + num::Num + num::Unsigned + PartialEq
{
    type Output = Self;

    fn add(self, other: T) -> Self {
        #[cfg(debug_assertions)]
        let other = Self::from(other, self.modulo);
        self + other
    }
}

impl<T> std::ops::Sub for ResidueRing<T>
where T: std::fmt::Display + Copy + num::Num + num::Unsigned + PartialEq
{
    type Output = Self;

    fn sub(self, other: Self) -> Self {
        #[cfg(debug_assertions)]
        {
            if self.modulo != other.modulo {
                panic!("different modulo: {} (mod {}) - {} (mod {})", self.n, self.modulo, other.n, other.modulo);
            }
        }
        Self {
            n: (self.modulo + self.n - other.n) % self.modulo,
            modulo: self.modulo,
        }
    }
}

impl<T> std::ops::Sub<T> for ResidueRing<T>
where T: std::fmt::Display + Copy + num::Num + num::Unsigned + PartialEq
{
    type Output = Self;

    fn sub(self, other: T) -> Self {
        #[cfg(debug_assertions)]
        let other = Self::from(other, self.modulo);
        self - other
    }
}

impl<T> std::ops::Index<ResidueRing<usize>> for Vec<T> {
    type Output = T;
    fn index(&self, index: ResidueRing<usize>) -> &T {
        &self[index.n]
    }
}

impl<T> std::ops::IndexMut<ResidueRing<usize>> for Vec<T> {
    fn index_mut(&mut self, index: ResidueRing<usize>) -> &mut T {
        &mut self[index.n]
    }
}