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use 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
    /// ```
    /// extern crate malachite_base;
    ///
    /// 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)
    }
}