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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 malachite_base::num::arithmetic::traits::ModPowerOf2IsReduced;
use malachite_base::num::logic::traits::SignificantBits;
impl ModPowerOf2IsReduced for Natural {
/// Returns whether a [`Natural`] is reduced modulo 2^k$; in other words, whether it has no more
/// than $k$ significant bits.
///
/// $f(x, k) = (x < 2^k)$.
///
/// # Worst-case complexity
/// Constant time and additional memory.
///
/// # Examples
/// ```
/// use malachite_base::num::arithmetic::traits::{ModPowerOf2IsReduced, Pow};
/// use malachite_base::num::basic::traits::Zero;
/// use malachite_nz::natural::Natural;
///
/// assert_eq!(Natural::ZERO.mod_power_of_2_is_reduced(5), true);
/// assert_eq!(
/// Natural::from(10u32).pow(12).mod_power_of_2_is_reduced(39),
/// false
/// );
/// assert_eq!(
/// Natural::from(10u32).pow(12).mod_power_of_2_is_reduced(40),
/// true
/// );
/// ```
#[inline]
fn mod_power_of_2_is_reduced(&self, pow: u64) -> bool {
self.significant_bits() <= pow
}
}