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// Copyright © 2024 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::Integer;
use malachite_base::num::arithmetic::traits::DivisibleByPowerOf2;
impl<'a> DivisibleByPowerOf2 for &'a Integer {
/// Returns whether an [`Integer`] is divisible by $2^k$.
///
/// $f(x, k) = (2^k|x)$.
///
/// $f(x, k) = (\exists n \in \N : \ x = n2^k)$.
///
/// If `self` is 0, the result is always true; otherwise, it is equivalent to
/// `self.trailing_zeros().unwrap() <= pow`, but more efficient.
///
/// # Worst-case complexity
/// $T(n) = O(n)$
///
/// $M(n) = O(1)$
///
/// where $T$ is time, $M$ is additional memory, and $n$ is `min(pow, self.significant_bits())`.
///
/// # Examples
/// ```
/// use malachite_base::num::arithmetic::traits::{DivisibleByPowerOf2, Pow};
/// use malachite_base::num::basic::traits::Zero;
/// use malachite_nz::integer::Integer;
///
/// assert_eq!(Integer::ZERO.divisible_by_power_of_2(100), true);
/// assert_eq!(Integer::from(-100).divisible_by_power_of_2(2), true);
/// assert_eq!(Integer::from(100u32).divisible_by_power_of_2(3), false);
/// assert_eq!((-Integer::from(10u32).pow(12)).divisible_by_power_of_2(12), true);
/// assert_eq!((-Integer::from(10u32).pow(12)).divisible_by_power_of_2(13), false);
/// ```
fn divisible_by_power_of_2(self, pow: u64) -> bool {
self.abs.divisible_by_power_of_2(pow)
}
}