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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_polynomial::NaturalPolynomial;
use alloc::vec::Vec;
use malachite_base::num::arithmetic::traits::{ModPowerOf2, ModPowerOf2Assign};
use malachite_base::polynomial::Polynomial;
impl ModPowerOf2 for NaturalPolynomial {
type Output = Self;
/// Divides every coefficient of a [`NaturalPolynomial`] by $2^k$, keeping the remainders,
/// taking the polynomial by value.
///
/// The result 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.
///
/// Reducing can lower the degree, and can even give the zero polynomial: a leading coefficient
/// that is a multiple of $2^k$ becomes zero, and a polynomial does not hold trailing zero
/// coefficients. So $4x^2 + 3$ modulo $4$ is the constant $3$, not a quadratic with a zero
/// leading coefficient.
///
/// Unlike a [`UnsignedPolynomial`](malachite_base::unsigned_polynomial::UnsignedPolynomial),
/// there is no power wide enough to leave every polynomial alone: a
/// [`Natural`](crate::natural::Natural) coefficient can be larger than any $2^k$, so a large
/// $k$ is as meaningful as a small one.
///
/// $$
/// f(p, k) = q, \\quad \text{where} \\quad q_i = p_i - 2^k \left \lfloor \frac{p_i}{2^k}
/// \right \rfloor.
/// $$
///
/// # 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
/// coefficients.
///
/// # Examples
/// ```
/// use core::str::FromStr;
/// use malachite_base::num::arithmetic::traits::ModPowerOf2;
/// use malachite_nz::natural_polynomial::NaturalPolynomial;
///
/// // Every coefficient is taken modulo 2.
/// assert_eq!(
/// NaturalPolynomial::from_str("x^2+3*x+2")
/// .unwrap()
/// .mod_power_of_2(1)
/// .to_string(),
/// "x^2+x"
/// );
///
/// // Reducing the leading coefficient to zero lowers the degree.
/// assert_eq!(
/// NaturalPolynomial::from_str("4*x^2+3")
/// .unwrap()
/// .mod_power_of_2(2)
/// .to_string(),
/// "3"
/// );
///
/// // A power too wide for a `u64` still does something here.
/// assert_eq!(
/// NaturalPolynomial::from_str("340282366920938463463374607431768211457*x")
/// .unwrap()
/// .mod_power_of_2(64)
/// .to_string(),
/// "x"
/// );
/// ```
#[inline]
fn mod_power_of_2(mut self, pow: u64) -> Self {
self.mod_power_of_2_assign(pow);
self
}
}
impl ModPowerOf2 for &NaturalPolynomial {
type Output = NaturalPolynomial;
/// Divides every coefficient of a [`NaturalPolynomial`] by $2^k$, keeping the remainders,
/// taking the polynomial by reference.
///
/// See the documentation for the [`ModPowerOf2`] implementation on [`NaturalPolynomial`] for
/// details, including how reducing can lower the degree.
///
/// # 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
/// coefficients.
///
/// # Examples
/// ```
/// use core::str::FromStr;
/// use malachite_base::num::arithmetic::traits::ModPowerOf2;
/// use malachite_nz::natural_polynomial::NaturalPolynomial;
///
/// let p = NaturalPolynomial::from_str("4*x^2+3").unwrap();
/// assert_eq!((&p).mod_power_of_2(2).to_string(), "3");
/// // The polynomial is left alone.
/// assert_eq!(p.to_string(), "4*x^2+3");
/// ```
#[inline]
fn mod_power_of_2(self, pow: u64) -> NaturalPolynomial {
// `from_coefficients_asc` trims, which is what makes the degree fall when the leading
// coefficient reduces to zero.
NaturalPolynomial::from_coefficients_asc(
self.coefficients_asc()
.iter()
.map(|c| c.mod_power_of_2(pow))
.collect::<Vec<_>>(),
)
}
}
impl ModPowerOf2Assign for NaturalPolynomial {
/// Divides every coefficient of a [`NaturalPolynomial`] by $2^k$, replacing the polynomial by
/// the one whose coefficients are the remainders.
///
/// See the documentation for the [`ModPowerOf2`] implementation on [`NaturalPolynomial`] for
/// details, including how reducing can lower the degree.
///
/// # 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
/// coefficients.
///
/// # Examples
/// ```
/// use core::str::FromStr;
/// use malachite_base::num::arithmetic::traits::ModPowerOf2Assign;
/// use malachite_nz::natural_polynomial::NaturalPolynomial;
///
/// let mut p = NaturalPolynomial::from_str("x^2+3*x+2").unwrap();
/// p.mod_power_of_2_assign(1);
/// assert_eq!(p.to_string(), "x^2+x");
///
/// let mut p = NaturalPolynomial::from_str("4*x^2+3").unwrap();
/// p.mod_power_of_2_assign(2);
/// assert_eq!(p.to_string(), "3");
/// ```
fn mod_power_of_2_assign(&mut self, pow: u64) {
for c in &mut self.coefficients {
c.mod_power_of_2_assign(pow);
}
self.trim();
}
}