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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::gaussian_integer::GaussianInteger;
use malachite_base::num::arithmetic::traits::IsPowerOf2;
impl IsPowerOf2 for GaussianInteger {
/// Determines whether a [`GaussianInteger`] is an integer power of 2.
///
/// Only purely real, positive values qualify; in particular, $i$ and its multiples are not
/// powers of 2.
///
/// $f(x) = (\exists n \in \N : 2^n = x)$.
///
/// # Worst-case complexity
/// $T(n) = O(n)$
///
/// $M(n) = O(1)$
///
/// where $T$ is time, $M$ is additional memory, and $n$ is `self.real.significant_bits()`.
///
/// # Examples
/// ```
/// use malachite_base::num::arithmetic::traits::IsPowerOf2;
/// use malachite_nz::gaussian_integer::GaussianInteger;
/// use std::str::FromStr;
///
/// assert_eq!(GaussianInteger::from(0x80).is_power_of_2(), true);
/// assert_eq!(GaussianInteger::from(-0x80).is_power_of_2(), false);
/// assert_eq!(GaussianInteger::from(0x81).is_power_of_2(), false);
/// assert_eq!(
/// GaussianInteger::from_str("128i").unwrap().is_power_of_2(),
/// false
/// );
/// assert_eq!(
/// GaussianInteger::from_str("128+i").unwrap().is_power_of_2(),
/// false
/// );
/// ```
#[inline]
fn is_power_of_2(&self) -> bool {
self.imaginary == 0u32 && self.real.is_power_of_2()
}
}