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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 malachite_base::num::arithmetic::traits::{Height, ModPowerOf2IsReduced};
impl ModPowerOf2IsReduced for NaturalPolynomial {
/// Returns whether a [`NaturalPolynomial`] is reduced modulo $2^k$; in other words, whether
/// every one of its coefficients has no more than $k$ significant bits.
///
/// Asking that of every coefficient is asking it of the largest, so this is the number of
/// significant bits of the polynomial's [`height`](Height::to_height) — which bit length
/// being monotone means is the largest of the coefficients' bit lengths, so the height itself
/// never has to be built or borrowed. The zero polynomial has no coefficients and is reduced
/// modulo every power of 2, including $2^0$.
///
/// $f(p, k) = (\max_i p_i < 2^k)$.
///
/// # Worst-case complexity
/// $T(n) = O(n)$
///
/// $M(n) = O(1)$
///
/// where $T$ is time, $M$ is additional memory, and $n$ is the number of coefficients.
///
/// # Examples
/// ```
/// use core::str::FromStr;
/// use malachite_base::num::arithmetic::traits::ModPowerOf2IsReduced;
/// use malachite_nz::natural_polynomial::NaturalPolynomial;
///
/// // The largest coefficient is 3, which needs two bits.
/// let p = NaturalPolynomial::from_str("x^2+3*x+2").unwrap();
/// assert_eq!(p.mod_power_of_2_is_reduced(2), true);
/// assert_eq!(p.mod_power_of_2_is_reduced(1), false);
///
/// // The zero polynomial is reduced modulo every power of 2.
/// assert_eq!(
/// NaturalPolynomial::from_str("0")
/// .unwrap()
/// .mod_power_of_2_is_reduced(0),
/// true
/// );
/// ```
#[inline]
fn mod_power_of_2_is_reduced(&self, pow: u64) -> bool {
self.height_significant_bits() <= pow
}
}