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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 crate::natural_vector::NaturalVector;
use malachite_base::num::arithmetic::traits::{ModAbsSquared, ModDot};
impl ModAbsSquared<Natural> for NaturalVector {
type Output = Natural;
/// Computes the squared norm of a [`NaturalVector`], the sum of the squares of its elements,
/// modulo $m$, taking the vector by value and the modulus by value. The elements must already
/// be reduced.
///
/// The squared norm of a 0-dimensional vector is 0.
///
/// $$
/// f(v, m) = \sum_{i=0}^{n-1} v_i^2 \bmod m,
/// $$
///
/// where $n$ is the dimension of $v$.
///
/// # Worst-case complexity
/// $T(n, m) = O(nm \log m \log\log m)$
///
/// $M(m) = O(m \log m)$
///
/// where $T$ is time, $M$ is additional memory, $n$ is the dimension of the vector, and $m$ is
/// `m.significant_bits()`.
///
/// # Panics
/// Panics if `m` is zero or if any element is greater than or equal to `m`.
///
/// # Examples
/// ```
/// use core::str::FromStr;
/// use malachite_base::num::arithmetic::traits::ModAbsSquared;
/// use malachite_nz::natural::Natural;
/// use malachite_nz::natural_vector::NaturalVector;
///
/// let v = NaturalVector::from_str("(1, 2, 3)").unwrap();
/// assert_eq!(v.clone().mod_abs_squared(Natural::from(10u32)), 4);
/// ```
#[inline]
fn mod_abs_squared(self, m: Natural) -> Natural {
(&self).mod_dot(&self, m)
}
}
impl ModAbsSquared<&Natural> for NaturalVector {
type Output = Natural;
/// Computes the squared norm of a [`NaturalVector`], the sum of the squares of its elements,
/// modulo $m$, taking the vector by value and the modulus by reference. The elements must
/// already be reduced.
///
/// The squared norm of a 0-dimensional vector is 0.
///
/// $$
/// f(v, m) = \sum_{i=0}^{n-1} v_i^2 \bmod m,
/// $$
///
/// where $n$ is the dimension of $v$.
///
/// # Worst-case complexity
/// $T(n, m) = O(nm \log m \log\log m)$
///
/// $M(m) = O(m \log m)$
///
/// where $T$ is time, $M$ is additional memory, $n$ is the dimension of the vector, and $m$ is
/// `m.significant_bits()`.
///
/// # Panics
/// Panics if `m` is zero or if any element is greater than or equal to `m`.
///
/// # Examples
/// ```
/// use core::str::FromStr;
/// use malachite_base::num::arithmetic::traits::ModAbsSquared;
/// use malachite_nz::natural::Natural;
/// use malachite_nz::natural_vector::NaturalVector;
///
/// let v = NaturalVector::from_str("(1, 2, 3)").unwrap();
/// assert_eq!(v.clone().mod_abs_squared(&Natural::from(10u32)), 4);
/// ```
#[inline]
fn mod_abs_squared(self, m: &Natural) -> Natural {
(&self).mod_dot(&self, m)
}
}
impl ModAbsSquared<Natural> for &NaturalVector {
type Output = Natural;
/// Computes the squared norm of a [`NaturalVector`], the sum of the squares of its elements,
/// modulo $m$, taking the vector by reference and the modulus by value. The elements must
/// already be reduced.
///
/// The squared norm of a 0-dimensional vector is 0.
///
/// $$
/// f(v, m) = \sum_{i=0}^{n-1} v_i^2 \bmod m,
/// $$
///
/// where $n$ is the dimension of $v$.
///
/// # Worst-case complexity
/// $T(n, m) = O(nm \log m \log\log m)$
///
/// $M(m) = O(m \log m)$
///
/// where $T$ is time, $M$ is additional memory, $n$ is the dimension of the vector, and $m$ is
/// `m.significant_bits()`.
///
/// # Panics
/// Panics if `m` is zero or if any element is greater than or equal to `m`.
///
/// # Examples
/// ```
/// use core::str::FromStr;
/// use malachite_base::num::arithmetic::traits::ModAbsSquared;
/// use malachite_nz::natural::Natural;
/// use malachite_nz::natural_vector::NaturalVector;
///
/// let v = NaturalVector::from_str("(1, 2, 3)").unwrap();
/// assert_eq!((&v).mod_abs_squared(Natural::from(10u32)), 4);
/// ```
#[inline]
fn mod_abs_squared(self, m: Natural) -> Natural {
self.mod_dot(self, m)
}
}
impl ModAbsSquared<&Natural> for &NaturalVector {
type Output = Natural;
/// Computes the squared norm of a [`NaturalVector`], the sum of the squares of its elements,
/// modulo $m$, taking the vector by reference and the modulus by reference. The elements must
/// already be reduced.
///
/// The squared norm of a 0-dimensional vector is 0.
///
/// $$
/// f(v, m) = \sum_{i=0}^{n-1} v_i^2 \bmod m,
/// $$
///
/// where $n$ is the dimension of $v$.
///
/// # Worst-case complexity
/// $T(n, m) = O(nm \log m \log\log m)$
///
/// $M(m) = O(m \log m)$
///
/// where $T$ is time, $M$ is additional memory, $n$ is the dimension of the vector, and $m$ is
/// `m.significant_bits()`.
///
/// # Panics
/// Panics if `m` is zero or if any element is greater than or equal to `m`.
///
/// # Examples
/// ```
/// use core::str::FromStr;
/// use malachite_base::num::arithmetic::traits::ModAbsSquared;
/// use malachite_nz::natural::Natural;
/// use malachite_nz::natural_vector::NaturalVector;
///
/// let v = NaturalVector::from_str("(1, 2, 3)").unwrap();
/// assert_eq!((&v).mod_abs_squared(&Natural::from(10u32)), 4);
/// ```
#[inline]
fn mod_abs_squared(self, m: &Natural) -> Natural {
self.mod_dot(self, m)
}
}