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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::{Conjugate, ConjugateAssign};
impl Conjugate for Natural {
type Output = Self;
/// Computes the complex conjugate of a [`Natural`], taking it by value. A real number is its
/// own conjugate, so this is the identity.
///
/// $$
/// f(x) = \overline{x} = x.
/// $$
///
/// # Worst-case complexity
/// Constant time and additional memory.
///
/// # Examples
/// ```
/// use malachite_base::num::arithmetic::traits::Conjugate;
/// use malachite_nz::natural::Natural;
///
/// assert_eq!(Natural::from(123u32).conjugate(), Natural::from(123u32));
/// ```
#[inline]
fn conjugate(self) -> Self {
self
}
}
impl Conjugate for &Natural {
type Output = Natural;
/// Computes the complex conjugate of a [`Natural`], taking it by reference. A real number is
/// its own conjugate, so this just clones.
///
/// $$
/// f(x) = \overline{x} = x.
/// $$
///
/// # Worst-case complexity
/// $T(n) = O(n)$
///
/// $M(n) = O(n)$
///
/// where $T$ is time, $M$ is additional memory, and $n$ is `self.significant_bits()`.
///
/// # Examples
/// ```
/// use malachite_base::num::arithmetic::traits::Conjugate;
/// use malachite_nz::natural::Natural;
///
/// assert_eq!((&Natural::from(123u32)).conjugate(), Natural::from(123u32));
/// ```
#[inline]
fn conjugate(self) -> Natural {
self.clone()
}
}
impl ConjugateAssign for Natural {
/// Replaces a [`Natural`] with its complex conjugate. A real number is its own conjugate, so
/// this does nothing.
///
/// $$
/// x \gets \overline{x} = x.
/// $$
///
/// # Worst-case complexity
/// Constant time and additional memory.
///
/// # Examples
/// ```
/// use malachite_base::num::arithmetic::traits::ConjugateAssign;
/// use malachite_nz::natural::Natural;
///
/// let mut x = Natural::from(123u32);
/// x.conjugate_assign();
/// assert_eq!(x, Natural::from(123u32));
/// ```
#[inline]
fn conjugate_assign(&mut self) {}
}