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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::gaussian_integer::GaussianInteger;
use malachite_base::num::arithmetic::traits::{Conjugate, ConjugateAssign, NegAssign};
impl Conjugate for GaussianInteger {
type Output = Self;
/// Computes the complex conjugate of a [`GaussianInteger`], taking it by value. The sign of the
/// imaginary part is flipped.
///
/// $$
/// f(x) = \overline{x} = \Re(x) - \Im(x) i.
/// $$
///
/// # Worst-case complexity
/// Constant time and additional memory.
///
/// # Examples
/// ```
/// use malachite_base::num::arithmetic::traits::Conjugate;
/// use malachite_base::num::basic::traits::I;
/// use malachite_nz::gaussian_integer::GaussianInteger;
/// use std::str::FromStr;
///
/// assert_eq!(GaussianInteger::I.conjugate().to_string(), "-i");
/// assert_eq!(
/// GaussianInteger::from_str("2-3i")
/// .unwrap()
/// .conjugate()
/// .to_string(),
/// "2+3i"
/// );
/// assert_eq!(
/// GaussianInteger::from_str("-123")
/// .unwrap()
/// .conjugate()
/// .to_string(),
/// "-123"
/// );
/// ```
fn conjugate(mut self) -> Self {
self.conjugate_assign();
self
}
}
impl Conjugate for &GaussianInteger {
type Output = GaussianInteger;
/// Computes the complex conjugate of a [`GaussianInteger`], taking it by reference. The sign of
/// the imaginary part is flipped.
///
/// $$
/// f(x) = \overline{x} = \Re(x) - \Im(x) i.
/// $$
///
/// # Worst-case complexity
/// $T(n) = O(n)$
///
/// $M(n) = O(n)$
///
/// where $T$ is time, $M$ is additional memory, and $n$ is the maximum number of significant
/// bits of the real and imaginary parts.
///
/// # Examples
/// ```
/// use malachite_base::num::arithmetic::traits::Conjugate;
/// use malachite_nz::gaussian_integer::GaussianInteger;
/// use std::str::FromStr;
///
/// let x = GaussianInteger::from_str("2-3i").unwrap();
/// assert_eq!((&x).conjugate().to_string(), "2+3i");
/// ```
fn conjugate(self) -> GaussianInteger {
GaussianInteger {
real: self.real.clone(),
imaginary: -&self.imaginary,
}
}
}
impl ConjugateAssign for GaussianInteger {
/// Replaces a [`GaussianInteger`] with its complex conjugate. The sign of the imaginary part is
/// flipped.
///
/// $$
/// x \gets \overline{x} = \Re(x) - \Im(x) i.
/// $$
///
/// # Worst-case complexity
/// Constant time and additional memory.
///
/// # Examples
/// ```
/// use malachite_base::num::arithmetic::traits::ConjugateAssign;
/// use malachite_nz::gaussian_integer::GaussianInteger;
/// use std::str::FromStr;
///
/// let mut x = GaussianInteger::from_str("2-3i").unwrap();
/// x.conjugate_assign();
/// assert_eq!(x.to_string(), "2+3i");
/// ```
#[inline]
fn conjugate_assign(&mut self) {
self.imaginary.neg_assign();
}
}