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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::{ModPow, ModPowAssign, ModSquare, ModSquareAssign};
use malachite_base::num::basic::traits::Two;
impl ModSquare<Self> for Natural {
type Output = Self;
/// Squares a [`Natural`] modulo another [`Natural`] $m$. The input must be already reduced
/// modulo $m$. Both [`Natural`]s are taken by value.
///
/// $f(x, m) = y$, where $x, y < m$ and $x^2 \equiv y \mod m$.
///
/// # 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::ModSquare;
/// use malachite_nz::natural::Natural;
///
/// assert_eq!(Natural::from(2u32).mod_square(Natural::from(10u32)), 4);
/// assert_eq!(Natural::from(100u32).mod_square(Natural::from(497u32)), 60);
/// ```
fn mod_square(self, m: Self) -> Self {
(&self).mod_pow(&Self::TWO, &m)
}
}
impl ModSquare<&Self> for Natural {
type Output = Self;
/// Squares a [`Natural`] modulo another [`Natural`] $m$. The input must be already reduced
/// modulo $m$. The first [`Natural`] is taken by value and the second by reference.
///
/// $f(x, m) = y$, where $x, y < m$ and $x^2 \equiv y \mod m$.
///
/// # 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::ModSquare;
/// use malachite_nz::natural::Natural;
///
/// assert_eq!(Natural::from(2u32).mod_square(&Natural::from(10u32)), 4);
/// assert_eq!(Natural::from(100u32).mod_square(&Natural::from(497u32)), 60);
/// ```
fn mod_square(self, m: &Self) -> Self {
(&self).mod_pow(&Self::TWO, m)
}
}
impl ModSquare<Natural> for &Natural {
type Output = Natural;
/// Squares a [`Natural`] modulo another [`Natural`] $m$. The input must be already reduced
/// modulo $m$. The first [`Natural`] is taken by reference and the second by value.
///
/// $f(x, m) = y$, where $x, y < m$ and $x^2 \equiv y \mod m$.
///
/// # 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::ModSquare;
/// use malachite_nz::natural::Natural;
///
/// assert_eq!((&Natural::from(2u32)).mod_square(Natural::from(10u32)), 4);
/// assert_eq!(
/// (&Natural::from(100u32)).mod_square(Natural::from(497u32)),
/// 60
/// );
/// ```
fn mod_square(self, m: Natural) -> Natural {
self.mod_pow(&Natural::TWO, &m)
}
}
impl ModSquare<&Natural> for &Natural {
type Output = Natural;
/// Squares a [`Natural`] modulo another [`Natural`] $m$. The input must be already reduced
/// modulo $m$. Both [`Natural`]s are taken by reference.
///
/// $f(x, m) = y$, where $x, y < m$ and $x^2 \equiv y \mod m$.
///
/// # 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::ModSquare;
/// use malachite_nz::natural::Natural;
///
/// assert_eq!((&Natural::from(2u32)).mod_square(&Natural::from(10u32)), 4);
/// assert_eq!(
/// (&Natural::from(100u32)).mod_square(&Natural::from(497u32)),
/// 60
/// );
/// ```
fn mod_square(self, m: &Natural) -> Natural {
self.mod_pow(&Natural::TWO, m)
}
}
impl ModSquareAssign<Self> for Natural {
/// Squares a [`Natural`] modulo another [`Natural`] $m$, in place. The input must be already
/// reduced modulo $m$. The [`Natural`] on the right-hand side is taken by value.
///
/// $x \gets y$, where $x, y < m$ and $x^2 \equiv y \mod m$.
///
/// # 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::ModSquareAssign;
/// use malachite_nz::natural::Natural;
///
/// let mut x = Natural::from(2u32);
/// x.mod_square_assign(Natural::from(10u32));
/// assert_eq!(x, 4);
///
/// let mut x = Natural::from(100u32);
/// x.mod_square_assign(Natural::from(497u32));
/// assert_eq!(x, 60);
/// ```
#[inline]
fn mod_square_assign(&mut self, m: Self) {
self.mod_pow_assign(&Self::TWO, &m);
}
}
impl ModSquareAssign<&Self> for Natural {
/// Squares a [`Natural`] modulo another [`Natural`] $m$, in place. The input must be already
/// reduced modulo $m$. The [`Natural`] on the right-hand side is taken by reference.
///
/// $x \gets y$, where $x, y < m$ and $x^2 \equiv y \mod m$.
///
/// # 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::ModSquareAssign;
/// use malachite_nz::natural::Natural;
///
/// let mut x = Natural::from(2u32);
/// x.mod_square_assign(&Natural::from(10u32));
/// assert_eq!(x, 4);
///
/// let mut x = Natural::from(100u32);
/// x.mod_square_assign(&Natural::from(497u32));
/// assert_eq!(x, 60);
/// ```
#[inline]
fn mod_square_assign(&mut self, m: &Self) {
self.mod_pow_assign(&Self::TWO, m);
}
}