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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::integer_vector::IntegerVector;
use crate::natural_vector::NaturalVector;
use malachite_base::num::arithmetic::traits::BalancedModPowerOf2;
impl BalancedModPowerOf2 for NaturalVector {
type Output = IntegerVector;
/// Reduces every element of a [`NaturalVector`] modulo $2^k$ to the representative closest to
/// zero, taking the vector by value.
///
/// Each element $r_i$ of the result satisfies $-2^{k-1} < r_i \leq 2^{k-1}$ and is congruent to
/// the original element modulo $2^k$, which determine it uniquely, as with
/// [`BalancedModPowerOf2`] for [`Natural`](crate::natural::Natural)s; for $k = 0$ every element
/// is 0. A remainder of exactly $2^{k-1}$ is positive. Remainders above $2^{k-1}$ become
/// negative, which is why the result is an [`IntegerVector`].
///
/// The dimension is unchanged: unlike a polynomial, a vector keeps the elements that reduce to
/// zero.
///
/// # Worst-case complexity
/// $T(n, m) = O(nm)$
///
/// $M(n, m) = O(nm)$
///
/// where $T$ is time, $M$ is additional memory, $n$ is the number of elements, and $m$ is
/// `pow`.
///
/// # Examples
/// ```
/// use core::str::FromStr;
/// use malachite_base::num::arithmetic::traits::BalancedModPowerOf2;
/// use malachite_nz::natural_vector::NaturalVector;
///
/// // Each element goes to its balanced remainder modulo 8, and half the modulus
/// // stays positive.
/// let v = NaturalVector::from_str("(19, 23, 20)").unwrap();
/// assert_eq!(
/// v.clone().balanced_mod_power_of_2(3).to_string(),
/// "(3, -1, 4)"
/// );
/// let v = NaturalVector::from_str("(8, 7)").unwrap();
/// assert_eq!(v.clone().balanced_mod_power_of_2(3).to_string(), "(0, -1)");
/// ```
fn balanced_mod_power_of_2(self, pow: u64) -> IntegerVector {
IntegerVector {
elements: self
.elements
.into_iter()
.map(|x| x.balanced_mod_power_of_2(pow))
.collect(),
}
}
}
impl BalancedModPowerOf2 for &NaturalVector {
type Output = IntegerVector;
/// Reduces every element of a [`NaturalVector`] modulo $2^k$ to the representative closest to
/// zero, taking the vector by reference.
///
/// See the documentation for the [`BalancedModPowerOf2`] implementation on [`NaturalVector`]
/// that takes the vector by value for details.
///
/// # Worst-case complexity
/// $T(n, m) = O(nm)$
///
/// $M(n, m) = O(nm)$
///
/// where $T$ is time, $M$ is additional memory, $n$ is the number of elements, and $m$ is
/// `pow`.
///
/// # Examples
/// ```
/// use core::str::FromStr;
/// use malachite_base::num::arithmetic::traits::BalancedModPowerOf2;
/// use malachite_nz::natural_vector::NaturalVector;
///
/// // Each element goes to its balanced remainder modulo 8, and half the modulus
/// // stays positive.
/// let v = NaturalVector::from_str("(19, 23, 20)").unwrap();
/// assert_eq!((&v).balanced_mod_power_of_2(3).to_string(), "(3, -1, 4)");
/// let v = NaturalVector::from_str("(8, 7)").unwrap();
/// assert_eq!((&v).balanced_mod_power_of_2(3).to_string(), "(0, -1)");
/// ```
fn balanced_mod_power_of_2(self, pow: u64) -> IntegerVector {
IntegerVector {
elements: self
.elements
.iter()
.map(|x| x.balanced_mod_power_of_2(pow))
.collect(),
}
}
}