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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::{ModPowerOf2, RemPowerOf2, RemPowerOf2Assign};
impl ModPowerOf2 for IntegerVector {
type Output = NaturalVector;
/// Divides every element of an [`IntegerVector`] by $2^k$, keeping the remainders as a
/// [`NaturalVector`], taking the vector by value.
///
/// Each remainder is non-negative, as with [`ModPowerOf2`] for
/// [`Integer`](crate::integer::Integer): a negative element $x$ becomes $2^k - (-x \bmod 2^k)$
/// unless it is a multiple of $2^k$. So the result has natural elements, and is reduced modulo
/// $2^k$, which is to say that [`mod_power_of_2_is_reduced`](
/// malachite_base::num::arithmetic::traits::ModPowerOf2IsReduced::mod_power_of_2_is_reduced)
/// returns `true` for it. The dimension is unchanged: unlike a polynomial, a vector keeps the
/// elements that reduce to zero.
///
/// $$
/// f(v, k) = w, \quad \text{where} \quad w_i = v_i - 2^k \left \lfloor \frac{v_i}{2^k}
/// \right \rfloor.
/// $$
///
/// # Worst-case complexity
/// $T(n) = O(n)$
///
/// $M(n) = O(n)$
///
/// where $T$ is time, $M$ is additional memory, and $n$ is the total number of bits of the
/// elements.
///
/// # Examples
/// ```
/// use core::str::FromStr;
/// use malachite_base::num::arithmetic::traits::ModPowerOf2;
/// use malachite_nz::integer_vector::IntegerVector;
///
/// // Every element is taken modulo 4, and negative ones become non-negative.
/// let v = IntegerVector::from_str("(1, -3, -2)").unwrap();
/// assert_eq!(v.clone().mod_power_of_2(2).to_string(), "(1, 1, 2)");
///
/// // An element that reduces to zero stays, so the dimension is unchanged.
/// let v = IntegerVector::from_str("(-4, 3)").unwrap();
/// assert_eq!(v.clone().mod_power_of_2(2).to_string(), "(0, 3)");
/// ```
#[inline]
fn mod_power_of_2(self, pow: u64) -> NaturalVector {
NaturalVector {
elements: self
.elements
.into_iter()
.map(|x| x.mod_power_of_2(pow))
.collect(),
}
}
}
impl ModPowerOf2 for &IntegerVector {
type Output = NaturalVector;
/// Divides every element of an [`IntegerVector`] by $2^k$, keeping the remainders as a
/// [`NaturalVector`], taking the vector by reference.
///
/// See the documentation for the [`ModPowerOf2`] implementation on [`IntegerVector`] that takes
/// the vector by value for details.
///
/// # Worst-case complexity
/// $T(n) = O(n)$
///
/// $M(n) = O(n)$
///
/// where $T$ is time, $M$ is additional memory, and $n$ is the total number of bits of the
/// elements.
///
/// # Examples
/// ```
/// use core::str::FromStr;
/// use malachite_base::num::arithmetic::traits::ModPowerOf2;
/// use malachite_nz::integer_vector::IntegerVector;
///
/// // Every element is taken modulo 4, and negative ones become non-negative.
/// let v = IntegerVector::from_str("(1, -3, -2)").unwrap();
/// assert_eq!((&v).mod_power_of_2(2).to_string(), "(1, 1, 2)");
///
/// // An element that reduces to zero stays, so the dimension is unchanged.
/// let v = IntegerVector::from_str("(-4, 3)").unwrap();
/// assert_eq!((&v).mod_power_of_2(2).to_string(), "(0, 3)");
/// ```
#[inline]
fn mod_power_of_2(self, pow: u64) -> NaturalVector {
NaturalVector {
elements: self
.elements
.iter()
.map(|x| x.mod_power_of_2(pow))
.collect(),
}
}
}
impl RemPowerOf2 for IntegerVector {
type Output = Self;
/// Divides every element of an [`IntegerVector`] by $2^k$, keeping the remainders, taking the
/// vector by value.
///
/// Each remainder has the sign of its element and a smaller absolute value than $2^k$, as with
/// [`RemPowerOf2`] for [`Integer`](crate::integer::Integer)s. This is the remainder of
/// truncating division, and the result stays an [`IntegerVector`]; for a remainder that is
/// always non-negative, and a [`NaturalVector`] result, use [`ModPowerOf2`]. The dimension is
/// unchanged.
///
/// $$
/// f(v, k) = w, \quad \text{where} \quad w_i = v_i - 2^k \operatorname{sgn}(v_i)
/// \left \lfloor \frac{|v_i|}{2^k} \right \rfloor.
/// $$
///
/// # Worst-case complexity
/// $T(n) = O(n)$
///
/// $M(n) = O(1)$
///
/// where $T$ is time, $M$ is additional memory, and $n$ is the total number of bits of the
/// elements.
///
/// # Examples
/// ```
/// use core::str::FromStr;
/// use malachite_base::num::arithmetic::traits::RemPowerOf2;
/// use malachite_nz::integer_vector::IntegerVector;
///
/// // Every element is taken modulo 4, keeping its sign.
/// let v = IntegerVector::from_str("(1, -7, -2)").unwrap();
/// assert_eq!(v.clone().rem_power_of_2(2).to_string(), "(1, -3, -2)");
///
/// // An element that reduces to zero stays, so the dimension is unchanged.
/// let v = IntegerVector::from_str("(-4, -3)").unwrap();
/// assert_eq!(v.clone().rem_power_of_2(2).to_string(), "(0, -3)");
/// ```
#[inline]
fn rem_power_of_2(mut self, pow: u64) -> Self {
self.rem_power_of_2_assign(pow);
self
}
}
impl RemPowerOf2 for &IntegerVector {
type Output = IntegerVector;
/// Divides every element of an [`IntegerVector`] by $2^k$, keeping the remainders, taking the
/// vector by reference.
///
/// See the documentation for the [`RemPowerOf2`] implementation on [`IntegerVector`] that takes
/// the vector by value for details.
///
/// # Worst-case complexity
/// $T(n) = O(n)$
///
/// $M(n) = O(n)$
///
/// where $T$ is time, $M$ is additional memory, and $n$ is the total number of bits of the
/// elements.
///
/// # Examples
/// ```
/// use core::str::FromStr;
/// use malachite_base::num::arithmetic::traits::RemPowerOf2;
/// use malachite_nz::integer_vector::IntegerVector;
///
/// // Every element is taken modulo 4, keeping its sign.
/// let v = IntegerVector::from_str("(1, -7, -2)").unwrap();
/// assert_eq!((&v).rem_power_of_2(2).to_string(), "(1, -3, -2)");
///
/// // An element that reduces to zero stays, so the dimension is unchanged.
/// let v = IntegerVector::from_str("(-4, -3)").unwrap();
/// assert_eq!((&v).rem_power_of_2(2).to_string(), "(0, -3)");
/// ```
#[inline]
fn rem_power_of_2(self, pow: u64) -> IntegerVector {
IntegerVector {
elements: self
.elements
.iter()
.map(|x| x.rem_power_of_2(pow))
.collect(),
}
}
}
impl RemPowerOf2Assign for IntegerVector {
/// Divides every element of an [`IntegerVector`] by $2^k$, replacing each element by the
/// remainder.
///
/// See the documentation for the [`RemPowerOf2`] implementation on [`IntegerVector`] that takes
/// the vector by value for details.
///
/// # Worst-case complexity
/// $T(n) = O(n)$
///
/// $M(n) = O(1)$
///
/// where $T$ is time, $M$ is additional memory, and $n$ is the total number of bits of the
/// elements.
///
/// # Examples
/// ```
/// use core::str::FromStr;
/// use malachite_base::num::arithmetic::traits::RemPowerOf2Assign;
/// use malachite_nz::integer_vector::IntegerVector;
///
/// let mut v = IntegerVector::from_str("(1, -7, -2)").unwrap();
/// v.rem_power_of_2_assign(2);
/// assert_eq!(v.to_string(), "(1, -3, -2)");
/// ```
fn rem_power_of_2_assign(&mut self, pow: u64) {
for x in &mut self.elements {
x.rem_power_of_2_assign(pow);
}
}
}