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
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
// 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::Rational;
use malachite_base::num::arithmetic::traits::PowerOf2;
use malachite_base::num::basic::traits::One;
use malachite_nz::natural::Natural;
impl PowerOf2<u64> for Rational {
/// Raises 2 to an integer power.
///
/// $f(k) = 2^k$.
///
/// # Worst-case complexity
/// $T(n) = O(n)$
///
/// $M(n) = O(n)$
///
/// where $T$ is time, $M$ is additional memory, and $n$ is `pow`.
///
/// # Examples
/// ```
/// use malachite_base::num::arithmetic::traits::PowerOf2;
/// use malachite_q::Rational;
///
/// assert_eq!(Rational::power_of_2(0u64), 1);
/// assert_eq!(Rational::power_of_2(3u64), 8);
/// assert_eq!(
/// Rational::power_of_2(100u64).to_string(),
/// "1267650600228229401496703205376"
/// );
/// ```
fn power_of_2(pow: u64) -> Self {
Self::from(Natural::power_of_2(pow))
}
}
impl PowerOf2<i64> for Rational {
/// Raises 2 to an integer power.
///
/// $f(k) = 2^k$.
///
/// # Worst-case complexity
/// $T(n) = O(n)$
///
/// $M(n) = O(n)$
///
/// where $T$ is time, $M$ is additional memory, and $n$ is `pow.abs()`.
///
/// # Examples
/// ```
/// use malachite_base::num::arithmetic::traits::PowerOf2;
/// use malachite_q::Rational;
///
/// assert_eq!(Rational::power_of_2(0i64), 1);
/// assert_eq!(Rational::power_of_2(3i64), 8);
/// assert_eq!(
/// Rational::power_of_2(100i64).to_string(),
/// "1267650600228229401496703205376"
/// );
/// assert_eq!(Rational::power_of_2(-3i64).to_string(), "1/8");
/// assert_eq!(
/// Rational::power_of_2(-100i64).to_string(),
/// "1/1267650600228229401496703205376"
/// );
/// ```
fn power_of_2(pow: i64) -> Self {
let pow_abs = pow.unsigned_abs();
if pow >= 0 {
Self::from(Natural::power_of_2(pow_abs))
} else {
Self {
sign: true,
numerator: Natural::ONE,
denominator: Natural::power_of_2(pow_abs),
}
}
}
}