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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::{
ModAbsSquared, ModAbsSquaredAssign, ModSquare, ModSquareAssign,
};
impl ModAbsSquared<Self> for Natural {
type Output = Self;
/// Computes the squared absolute value of a [`Natural`] modulo another [`Natural`] $m$, which
/// for a [`Natural`] is its square modulo $m$. The [`Natural`] must be already reduced modulo
/// $m$. The [`Natural`] is taken by value and the modulus by value.
///
/// $f(x, m) = y$, where $x, y < m$ and $|x|^2 = x^2 \equiv y \mod m$.
///
/// # 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 `m.significant_bits()`.
///
/// # Panics
/// Panics if `self` is greater than or equal to `m`.
///
/// # Examples
/// ```
/// use malachite_base::num::arithmetic::traits::ModAbsSquared;
/// use malachite_nz::natural::Natural;
///
/// assert_eq!(
/// Natural::from(100u32).mod_abs_squared(Natural::from(497u32)),
/// 60
/// );
/// ```
#[inline]
fn mod_abs_squared(self, m: Self) -> Self {
self.mod_square(m)
}
}
impl ModAbsSquared<&Self> for Natural {
type Output = Self;
/// Computes the squared absolute value of a [`Natural`] modulo another [`Natural`] $m$, which
/// for a [`Natural`] is its square modulo $m$. The [`Natural`] must be already reduced modulo
/// $m$. The [`Natural`] is taken by value and the modulus by reference.
///
/// $f(x, m) = y$, where $x, y < m$ and $|x|^2 = x^2 \equiv y \mod m$.
///
/// # 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 `m.significant_bits()`.
///
/// # Panics
/// Panics if `self` is greater than or equal to `m`.
///
/// # Examples
/// ```
/// use malachite_base::num::arithmetic::traits::ModAbsSquared;
/// use malachite_nz::natural::Natural;
///
/// assert_eq!(
/// Natural::from(100u32).mod_abs_squared(&Natural::from(497u32)),
/// 60
/// );
/// ```
#[inline]
fn mod_abs_squared(self, m: &Self) -> Self {
self.mod_square(m)
}
}
impl ModAbsSquared<Natural> for &Natural {
type Output = Natural;
/// Computes the squared absolute value of a [`Natural`] modulo another [`Natural`] $m$, which
/// for a [`Natural`] is its square modulo $m$. The [`Natural`] must be already reduced modulo
/// $m$. The [`Natural`] is taken by reference and the modulus by value.
///
/// $f(x, m) = y$, where $x, y < m$ and $|x|^2 = x^2 \equiv y \mod m$.
///
/// # 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 `m.significant_bits()`.
///
/// # Panics
/// Panics if `self` is greater than or equal to `m`.
///
/// # Examples
/// ```
/// use malachite_base::num::arithmetic::traits::ModAbsSquared;
/// use malachite_nz::natural::Natural;
///
/// assert_eq!(
/// (&Natural::from(100u32)).mod_abs_squared(Natural::from(497u32)),
/// 60
/// );
/// ```
#[inline]
fn mod_abs_squared(self, m: Natural) -> Natural {
self.mod_square(m)
}
}
impl ModAbsSquared<&Natural> for &Natural {
type Output = Natural;
/// Computes the squared absolute value of a [`Natural`] modulo another [`Natural`] $m$, which
/// for a [`Natural`] is its square modulo $m$. The [`Natural`] must be already reduced modulo
/// $m$. The [`Natural`] is taken by reference and the modulus by reference.
///
/// $f(x, m) = y$, where $x, y < m$ and $|x|^2 = x^2 \equiv y \mod m$.
///
/// # 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 `m.significant_bits()`.
///
/// # Panics
/// Panics if `self` is greater than or equal to `m`.
///
/// # Examples
/// ```
/// use malachite_base::num::arithmetic::traits::ModAbsSquared;
/// use malachite_nz::natural::Natural;
///
/// assert_eq!(
/// (&Natural::from(100u32)).mod_abs_squared(&Natural::from(497u32)),
/// 60
/// );
/// ```
#[inline]
fn mod_abs_squared(self, m: &Natural) -> Natural {
self.mod_square(m)
}
}
impl ModAbsSquaredAssign<Self> for Natural {
/// Replaces a [`Natural`] with its squared absolute value modulo another [`Natural`] $m$, which
/// for a [`Natural`] is its square modulo $m$. The [`Natural`] must be already reduced modulo
/// $m$. The modulus is taken by value.
///
/// $x \gets y$, where $x, y < m$ and $|x|^2 = x^2 \equiv y \mod m$.
///
/// # 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 `m.significant_bits()`.
///
/// # Panics
/// Panics if `self` is greater than or equal to `m`.
///
/// # Examples
/// ```
/// use malachite_base::num::arithmetic::traits::ModAbsSquaredAssign;
/// use malachite_nz::natural::Natural;
///
/// let mut n = Natural::from(100u32);
/// n.mod_abs_squared_assign(Natural::from(497u32));
/// assert_eq!(n, 60);
/// ```
#[inline]
fn mod_abs_squared_assign(&mut self, m: Self) {
self.mod_square_assign(m);
}
}
impl ModAbsSquaredAssign<&Self> for Natural {
/// Replaces a [`Natural`] with its squared absolute value modulo another [`Natural`] $m$, which
/// for a [`Natural`] is its square modulo $m$. The [`Natural`] must be already reduced modulo
/// $m$. The modulus is taken by reference.
///
/// $x \gets y$, where $x, y < m$ and $|x|^2 = x^2 \equiv y \mod m$.
///
/// # 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 `m.significant_bits()`.
///
/// # Panics
/// Panics if `self` is greater than or equal to `m`.
///
/// # Examples
/// ```
/// use malachite_base::num::arithmetic::traits::ModAbsSquaredAssign;
/// use malachite_nz::natural::Natural;
///
/// let mut n = Natural::from(100u32);
/// n.mod_abs_squared_assign(&Natural::from(497u32));
/// assert_eq!(n, 60);
/// ```
#[inline]
fn mod_abs_squared_assign(&mut self, m: &Self) {
self.mod_square_assign(m);
}
}