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 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101
// 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 core::mem::swap;
use malachite_base::num::arithmetic::traits::{Reciprocal, ReciprocalAssign};
impl Reciprocal for Rational {
type Output = Rational;
/// Reciprocates a [`Rational`], taking it by value.
///
/// $$
/// f(x) = 1/x.
/// $$
///
/// # Worst-case complexity
/// Constant time and additional memory.
///
/// # Examples
/// ```
/// use malachite_base::num::arithmetic::traits::Reciprocal;
/// use malachite_q::Rational;
///
/// assert_eq!(Rational::from_signeds(22, 7).reciprocal().to_string(), "7/22");
/// assert_eq!(Rational::from_signeds(7, 22).reciprocal().to_string(), "22/7");
/// ```
#[inline]
fn reciprocal(mut self) -> Rational {
self.reciprocal_assign();
self
}
}
impl<'a> Reciprocal for &'a Rational {
type Output = Rational;
/// Reciprocates a [`Rational`], taking it by reference.
///
/// $$
/// f(x) = 1/x.
/// $$
///
/// # Worst-case complexity
/// $T(n) = O(n)$
///
/// $M(n) = O(n)$
///
/// where $T$ is time, $M$ is additional memory, and $n$ is `self.significant_bits()`.
///
/// # Examples
/// ```
/// use malachite_base::num::arithmetic::traits::Reciprocal;
/// use malachite_q::Rational;
///
/// assert_eq!((&Rational::from_signeds(22, 7)).reciprocal().to_string(), "7/22");
/// assert_eq!((&Rational::from_signeds(7, 22)).reciprocal().to_string(), "22/7");
/// ```
fn reciprocal(self) -> Rational {
assert_ne!(self.numerator, 0, "Cannot take reciprocal of zero");
Rational {
sign: self.sign,
numerator: self.denominator.clone(),
denominator: self.numerator.clone(),
}
}
}
impl ReciprocalAssign for Rational {
/// Reciprocates a [`Rational`] in place.
///
/// $$
/// x \gets 1/x.
/// $$
///
/// # Worst-case complexity
/// Constant time and additional memory.
///
/// # Examples
/// ```
/// use malachite_base::num::arithmetic::traits::ReciprocalAssign;
/// use malachite_q::Rational;
///
/// let mut x = Rational::from_signeds(22, 7);
/// x.reciprocal_assign();
/// assert_eq!(x.to_string(), "7/22");
///
/// let mut x = Rational::from_signeds(7, 22);
/// x.reciprocal_assign();
/// assert_eq!(x.to_string(), "22/7");
/// ```
fn reciprocal_assign(&mut self) {
assert_ne!(self.numerator, 0, "Cannot take reciprocal of zero");
swap(&mut self.numerator, &mut self.denominator);
}
}