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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 crate::integer::Integer;
use malachite_base::num::arithmetic::traits::{AbsSquared, AbsSquaredAssign, Square, SquareAssign};
impl AbsSquared for GaussianInteger {
type Output = Integer;
/// Computes the squared absolute value of a [`GaussianInteger`], taking it by value. This is
/// the sum of the squares of the real and imaginary parts, also known as the norm. It is always
/// a non-negative [`Integer`].
///
/// $$
/// f(x) = |x|^2 = \Re(x)^2 + \Im(x)^2.
/// $$
///
/// # 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 the maximum number of significant
/// bits of the real and imaginary parts.
///
/// # Examples
/// ```
/// use malachite_base::num::arithmetic::traits::AbsSquared;
/// use malachite_base::num::basic::traits::{I, Zero};
/// use malachite_nz::gaussian_integer::GaussianInteger;
/// use std::str::FromStr;
///
/// assert_eq!(GaussianInteger::ZERO.abs_squared(), 0);
/// assert_eq!(GaussianInteger::I.abs_squared(), 1);
/// assert_eq!(GaussianInteger::from_str("2-3i").unwrap().abs_squared(), 13);
/// assert_eq!(GaussianInteger::from(-123).abs_squared(), 15129);
/// ```
#[inline]
fn abs_squared(self) -> Integer {
self.real.square() + self.imaginary.square()
}
}
impl AbsSquared for &GaussianInteger {
type Output = Integer;
/// Computes the squared absolute value of a [`GaussianInteger`], taking it by reference. This
/// is the sum of the squares of the real and imaginary parts, also known as the norm. It is
/// always a non-negative [`Integer`].
///
/// $$
/// f(x) = |x|^2 = \Re(x)^2 + \Im(x)^2.
/// $$
///
/// # 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 the maximum number of significant
/// bits of the real and imaginary parts.
///
/// # Examples
/// ```
/// use malachite_base::num::arithmetic::traits::AbsSquared;
/// use malachite_base::num::basic::traits::{I, Zero};
/// use malachite_nz::gaussian_integer::GaussianInteger;
/// use std::str::FromStr;
///
/// assert_eq!((&GaussianInteger::ZERO).abs_squared(), 0);
/// assert_eq!((&GaussianInteger::I).abs_squared(), 1);
/// let x = GaussianInteger::from_str("2-3i").unwrap();
/// assert_eq!((&x).abs_squared(), 13);
/// ```
#[inline]
fn abs_squared(self) -> Integer {
(&self.real).square() + (&self.imaginary).square()
}
}
impl AbsSquaredAssign for GaussianInteger {
/// Replaces a [`GaussianInteger`] with its squared absolute value: the purely real value
/// $|x|^2$, embedded in the same type. The real part becomes the sum of the squares of the real
/// and imaginary parts (the norm), and the imaginary part becomes zero.
///
/// $$
/// x \gets |x|^2 = \Re(x)^2 + \Im(x)^2.
/// $$
///
/// # 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 the maximum number of significant
/// bits of the real and imaginary parts.
///
/// # Examples
/// ```
/// use malachite_base::num::arithmetic::traits::AbsSquaredAssign;
/// use malachite_nz::gaussian_integer::GaussianInteger;
/// use std::str::FromStr;
///
/// let mut x = GaussianInteger::from_str("2-3i").unwrap();
/// x.abs_squared_assign();
/// assert_eq!(x.to_string(), "13");
/// ```
fn abs_squared_assign(&mut self) {
self.real.square_assign();
self.imaginary.square_assign();
self.real += core::mem::take(&mut self.imaginary);
}
}