1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39

// 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::Rational;
use malachite_base::num::arithmetic::traits::IsPowerOf2;

impl IsPowerOf2 for Rational {
    /// Determines whether a [`Rational`] is an integer power of 2.
    ///
    /// $f(x) = (\exists n \in \Z : 2^n = x)$.
    ///
    /// # Worst-case complexity
    /// $T(n) = O(n)$
    ///
    /// $M(n) = O(1)$
    ///
    /// where $T$ is time, $M$ is additional memory, and $n$ is `self.significant_bits()`.
    ///
    /// # Examples
    /// ```
    /// use malachite_base::num::arithmetic::traits::IsPowerOf2;
    /// use malachite_q::Rational;
    ///
    /// assert_eq!(Rational::from(0x80).is_power_of_2(), true);
    /// assert_eq!(Rational::from_signeds(1, 8).is_power_of_2(), true);
    /// assert_eq!(Rational::from_signeds(-1, 8).is_power_of_2(), false);
    /// assert_eq!(Rational::from_signeds(22, 7).is_power_of_2(), false);
    /// ```
    fn is_power_of_2(&self) -> bool {
        self.sign
            && (self.denominator == 1u32 && self.numerator.is_power_of_2()
                || self.numerator == 1u32 && self.denominator.is_power_of_2())
    }
}