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// Copyright © 2026 Mikhail Hogrefe
//
// This file is part of Malachite.
//
// Malachite is free software: you can redistribute it and/or modify it under the terms of the GNU
// Lesser General Public License (LGPL) as published by the Free Software Foundation; either version
// 3 of the License, or (at your option) any later version. See <https://www.gnu.org/licenses/>.
use crate::natural::Natural;
use malachite_base::num::arithmetic::traits::{Mod, ModAssign, ModEuclidean, ModEuclideanAssign};
impl ModEuclidean<Self> for Natural {
type Output = Self;
/// Divides a [`Natural`] by another [`Natural`], taking both by value and returning just the
/// remainder.
///
/// If the quotient were computed, the quotient and remainder would satisfy $x = qy + r$ and $0
/// \leq r < y$. For [`Natural`]s, the Euclidean remainder coincides with
/// [`mod_op`](Mod::mod_op).
///
/// $$
/// f(x, y) = x - y\left \lfloor \frac{x}{y} \right \rfloor.
/// $$
///
/// # Worst-case complexity
/// $T(n) = O(n \log n \log \log n)$
///
/// $M(n) = O(n \log n)$
///
/// where $T$ is time, $M$ is additional memory, and $n$ is `self.significant_bits()`.
///
/// # Panics
/// Panics if `other` is zero.
///
/// # Examples
/// ```
/// use malachite_base::num::arithmetic::traits::ModEuclidean;
/// use malachite_nz::natural::Natural;
///
/// // 2 * 10 + 3 = 23
/// assert_eq!(Natural::from(23u32).mod_euclidean(Natural::from(10u32)), 3);
/// ```
#[inline]
fn mod_euclidean(self, other: Self) -> Self {
self.mod_op(other)
}
}
impl ModEuclidean<&Self> for Natural {
type Output = Self;
/// Divides a [`Natural`] by another [`Natural`], taking the first by value and the second by
/// reference and returning just the remainder.
///
/// If the quotient were computed, the quotient and remainder would satisfy $x = qy + r$ and $0
/// \leq r < y$. For [`Natural`]s, the Euclidean remainder coincides with
/// [`mod_op`](Mod::mod_op).
///
/// $$
/// f(x, y) = x - y\left \lfloor \frac{x}{y} \right \rfloor.
/// $$
///
/// # Worst-case complexity
/// $T(n) = O(n \log n \log \log n)$
///
/// $M(n) = O(n \log n)$
///
/// where $T$ is time, $M$ is additional memory, and $n$ is `self.significant_bits()`.
///
/// # Panics
/// Panics if `other` is zero.
///
/// # Examples
/// ```
/// use malachite_base::num::arithmetic::traits::ModEuclidean;
/// use malachite_nz::natural::Natural;
///
/// // 2 * 10 + 3 = 23
/// assert_eq!(Natural::from(23u32).mod_euclidean(&Natural::from(10u32)), 3);
/// ```
#[inline]
fn mod_euclidean(self, other: &Self) -> Self {
self.mod_op(other)
}
}
impl ModEuclidean<Natural> for &Natural {
type Output = Natural;
/// Divides a [`Natural`] by another [`Natural`], taking the first by reference and the second
/// by value and returning just the remainder.
///
/// If the quotient were computed, the quotient and remainder would satisfy $x = qy + r$ and $0
/// \leq r < y$. For [`Natural`]s, the Euclidean remainder coincides with
/// [`mod_op`](Mod::mod_op).
///
/// $$
/// f(x, y) = x - y\left \lfloor \frac{x}{y} \right \rfloor.
/// $$
///
/// # Worst-case complexity
/// $T(n) = O(n \log n \log \log n)$
///
/// $M(n) = O(n \log n)$
///
/// where $T$ is time, $M$ is additional memory, and $n$ is `self.significant_bits()`.
///
/// # Panics
/// Panics if `other` is zero.
///
/// # Examples
/// ```
/// use malachite_base::num::arithmetic::traits::ModEuclidean;
/// use malachite_nz::natural::Natural;
///
/// // 2 * 10 + 3 = 23
/// assert_eq!(
/// (&Natural::from(23u32)).mod_euclidean(Natural::from(10u32)),
/// 3
/// );
/// ```
#[inline]
fn mod_euclidean(self, other: Natural) -> Natural {
self.mod_op(other)
}
}
impl ModEuclidean<&Natural> for &Natural {
type Output = Natural;
/// Divides a [`Natural`] by another [`Natural`], taking both by reference and returning just
/// the remainder.
///
/// If the quotient were computed, the quotient and remainder would satisfy $x = qy + r$ and $0
/// \leq r < y$. For [`Natural`]s, the Euclidean remainder coincides with
/// [`mod_op`](Mod::mod_op).
///
/// $$
/// f(x, y) = x - y\left \lfloor \frac{x}{y} \right \rfloor.
/// $$
///
/// # Worst-case complexity
/// $T(n) = O(n \log n \log \log n)$
///
/// $M(n) = O(n \log n)$
///
/// where $T$ is time, $M$ is additional memory, and $n$ is `self.significant_bits()`.
///
/// # Panics
/// Panics if `other` is zero.
///
/// # Examples
/// ```
/// use malachite_base::num::arithmetic::traits::ModEuclidean;
/// use malachite_nz::natural::Natural;
///
/// // 2 * 10 + 3 = 23
/// assert_eq!(
/// (&Natural::from(23u32)).mod_euclidean(&Natural::from(10u32)),
/// 3
/// );
/// ```
#[inline]
fn mod_euclidean(self, other: &Natural) -> Natural {
self.mod_op(other)
}
}
impl ModEuclideanAssign<Self> for Natural {
/// Divides a [`Natural`] by another [`Natural`], taking the [`Natural`] on the right-hand side
/// by value and replacing the first [`Natural`] by the remainder.
///
/// If the quotient were computed, the quotient and remainder would satisfy $x = qy + r$ and $0
/// \leq r < y$. For [`Natural`]s, the Euclidean remainder coincides with
/// [`mod_op`](Mod::mod_op).
///
/// $$
/// x \gets x - y\left \lfloor \frac{x}{y} \right \rfloor.
/// $$
///
/// # Worst-case complexity
/// $T(n) = O(n \log n \log \log n)$
///
/// $M(n) = O(n \log n)$
///
/// where $T$ is time, $M$ is additional memory, and $n$ is `self.significant_bits()`.
///
/// # Panics
/// Panics if `other` is zero.
///
/// # Examples
/// ```
/// use malachite_base::num::arithmetic::traits::ModEuclideanAssign;
/// use malachite_nz::natural::Natural;
///
/// // 2 * 10 + 3 = 23
/// let mut x = Natural::from(23u32);
/// x.mod_euclidean_assign(Natural::from(10u32));
/// assert_eq!(x, 3);
/// ```
#[inline]
fn mod_euclidean_assign(&mut self, other: Self) {
self.mod_assign(other);
}
}
impl ModEuclideanAssign<&Self> for Natural {
/// Divides a [`Natural`] by another [`Natural`], taking the [`Natural`] on the right-hand side
/// by reference and replacing the first [`Natural`] by the remainder.
///
/// If the quotient were computed, the quotient and remainder would satisfy $x = qy + r$ and $0
/// \leq r < y$. For [`Natural`]s, the Euclidean remainder coincides with
/// [`mod_op`](Mod::mod_op).
///
/// $$
/// x \gets x - y\left \lfloor \frac{x}{y} \right \rfloor.
/// $$
///
/// # Worst-case complexity
/// $T(n) = O(n \log n \log \log n)$
///
/// $M(n) = O(n \log n)$
///
/// where $T$ is time, $M$ is additional memory, and $n$ is `self.significant_bits()`.
///
/// # Panics
/// Panics if `other` is zero.
///
/// # Examples
/// ```
/// use malachite_base::num::arithmetic::traits::ModEuclideanAssign;
/// use malachite_nz::natural::Natural;
///
/// // 2 * 10 + 3 = 23
/// let mut x = Natural::from(23u32);
/// x.mod_euclidean_assign(&Natural::from(10u32));
/// assert_eq!(x, 3);
/// ```
#[inline]
fn mod_euclidean_assign(&mut self, other: &Self) {
self.mod_assign(other);
}
}