malachite_q/arithmetic/
reciprocal.rs

1// Copyright © 2025 Mikhail Hogrefe
2//
3// This file is part of Malachite.
4//
5// Malachite is free software: you can redistribute it and/or modify it under the terms of the GNU
6// Lesser General Public License (LGPL) as published by the Free Software Foundation; either version
7// 3 of the License, or (at your option) any later version. See <https://www.gnu.org/licenses/>.
8
9use crate::Rational;
10use core::mem::swap;
11use malachite_base::num::arithmetic::traits::{Reciprocal, ReciprocalAssign};
12
13impl Reciprocal for Rational {
14    type Output = Self;
15
16    /// Reciprocates a [`Rational`], taking it by value.
17    ///
18    /// $$
19    /// f(x) = 1/x.
20    /// $$
21    ///
22    /// # Worst-case complexity
23    /// Constant time and additional memory.
24    ///
25    /// # Examples
26    /// ```
27    /// use malachite_base::num::arithmetic::traits::Reciprocal;
28    /// use malachite_q::Rational;
29    ///
30    /// assert_eq!(
31    ///     Rational::from_signeds(22, 7).reciprocal().to_string(),
32    ///     "7/22"
33    /// );
34    /// assert_eq!(
35    ///     Rational::from_signeds(7, 22).reciprocal().to_string(),
36    ///     "22/7"
37    /// );
38    /// ```
39    #[inline]
40    fn reciprocal(mut self) -> Self {
41        self.reciprocal_assign();
42        self
43    }
44}
45
46impl Reciprocal for &Rational {
47    type Output = Rational;
48
49    /// Reciprocates a [`Rational`], taking it by reference.
50    ///
51    /// $$
52    /// f(x) = 1/x.
53    /// $$
54    ///
55    /// # Worst-case complexity
56    /// $T(n) = O(n)$
57    ///
58    /// $M(n) = O(n)$
59    ///
60    /// where $T$ is time, $M$ is additional memory, and $n$ is `self.significant_bits()`.
61    ///
62    /// # Examples
63    /// ```
64    /// use malachite_base::num::arithmetic::traits::Reciprocal;
65    /// use malachite_q::Rational;
66    ///
67    /// assert_eq!(
68    ///     (&Rational::from_signeds(22, 7)).reciprocal().to_string(),
69    ///     "7/22"
70    /// );
71    /// assert_eq!(
72    ///     (&Rational::from_signeds(7, 22)).reciprocal().to_string(),
73    ///     "22/7"
74    /// );
75    /// ```
76    fn reciprocal(self) -> Rational {
77        assert_ne!(self.numerator, 0, "Cannot take reciprocal of zero");
78        Rational {
79            sign: self.sign,
80            numerator: self.denominator.clone(),
81            denominator: self.numerator.clone(),
82        }
83    }
84}
85
86impl ReciprocalAssign for Rational {
87    /// Reciprocates a [`Rational`] in place.
88    ///
89    /// $$
90    /// x \gets 1/x.
91    /// $$
92    ///
93    /// # Worst-case complexity
94    /// Constant time and additional memory.
95    ///
96    /// # Examples
97    /// ```
98    /// use malachite_base::num::arithmetic::traits::ReciprocalAssign;
99    /// use malachite_q::Rational;
100    ///
101    /// let mut x = Rational::from_signeds(22, 7);
102    /// x.reciprocal_assign();
103    /// assert_eq!(x.to_string(), "7/22");
104    ///
105    /// let mut x = Rational::from_signeds(7, 22);
106    /// x.reciprocal_assign();
107    /// assert_eq!(x.to_string(), "22/7");
108    /// ```
109    fn reciprocal_assign(&mut self) {
110        assert_ne!(self.numerator, 0, "Cannot take reciprocal of zero");
111        swap(&mut self.numerator, &mut self.denominator);
112    }
113}
malachite_q/arithmetic/reciprocal.rs

malachite_q/arithmetic/
reciprocal.rs
