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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::{AbsSquared, AbsSquaredAssign, Square, SquareAssign};
impl AbsSquared for Natural {
type Output = Self;
/// Computes the squared absolute value of a [`Natural`], taking it by value. For real types
/// this is the same as squaring.
///
/// $$
/// f(x) = |x|^2 = x^2.
/// $$
///
/// # 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 `self.significant_bits()`.
///
/// # Examples
/// ```
/// use malachite_base::num::arithmetic::traits::AbsSquared;
/// use malachite_base::num::basic::traits::Zero;
/// use malachite_nz::natural::Natural;
///
/// assert_eq!(Natural::ZERO.abs_squared(), 0);
/// assert_eq!(Natural::from(123u32).abs_squared(), 15129);
/// ```
#[inline]
fn abs_squared(self) -> Self {
self.square()
}
}
impl AbsSquared for &Natural {
type Output = Natural;
/// Computes the squared absolute value of a [`Natural`], taking it by reference. For real types
/// this is the same as squaring.
///
/// $$
/// f(x) = |x|^2 = x^2.
/// $$
///
/// # 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 `self.significant_bits()`.
///
/// # Examples
/// ```
/// use malachite_base::num::arithmetic::traits::AbsSquared;
/// use malachite_base::num::basic::traits::Zero;
/// use malachite_nz::natural::Natural;
///
/// assert_eq!((&Natural::ZERO).abs_squared(), 0);
/// assert_eq!((&Natural::from(123u32)).abs_squared(), 15129);
/// ```
#[inline]
fn abs_squared(self) -> Natural {
self.square()
}
}
impl AbsSquaredAssign for Natural {
/// Replaces a [`Natural`] with its squared absolute value. For real types this is the same as
/// squaring in place.
///
/// $$
/// x \gets |x|^2 = x^2.
/// $$
///
/// # 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 `self.significant_bits()`.
///
/// # Examples
/// ```
/// use malachite_base::num::arithmetic::traits::AbsSquaredAssign;
/// use malachite_nz::natural::Natural;
///
/// let mut x = Natural::from(123u32);
/// x.abs_squared_assign();
/// assert_eq!(x, 15129);
/// ```
#[inline]
fn abs_squared_assign(&mut self) {
self.square_assign();
}
}