malachite_q/comparison/
cmp.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::cmp::Ordering::{self, *};
11use malachite_base::num::arithmetic::traits::Sign;
12
13impl PartialOrd for Rational {
14    /// Compares two [`Rational`]s.
15    ///
16    /// See the documentation for the [`Ord`] implementation.
17    #[inline]
18    fn partial_cmp(&self, other: &Self) -> Option<Ordering> {
19        Some(self.cmp(other))
20    }
21}
22
23impl Ord for Rational {
24    /// Compares two [`Rational`]s.
25    ///
26    /// # Worst-case complexity
27    /// $T(n) = O(n \log n \log\log n)$
28    ///
29    /// $M(n) = O(n \log n)$
30    ///
31    /// where $T$ is time, $M$ is additional memory, and $n$ is `max(self.significant_bits(),
32    /// other.significant_bits())`.
33    ///
34    /// # Examples
35    /// ```
36    /// use malachite_base::num::basic::traits::OneHalf;
37    /// use malachite_q::Rational;
38    /// use std::str::FromStr;
39    ///
40    /// assert!(Rational::from_str("2/3").unwrap() > Rational::ONE_HALF);
41    /// assert!(Rational::from_str("-2/3").unwrap() < Rational::ONE_HALF);
42    /// ```
43    fn cmp(&self, other: &Self) -> Ordering {
44        if core::ptr::eq(self, other) {
45            return Equal;
46        }
47        // First check signs
48        let self_sign = self.sign();
49        let other_sign = other.sign();
50        let sign_cmp = self_sign.cmp(&other_sign);
51        if sign_cmp != Equal || self_sign == Equal {
52            return sign_cmp;
53        }
54        // Then check if one is < 1 and the other is > 1
55        let self_cmp_one = self.numerator.cmp(&self.denominator);
56        let other_cmp_one = other.numerator.cmp(&other.denominator);
57        let one_cmp = self_cmp_one.cmp(&other_cmp_one);
58        if one_cmp != Equal {
59            return if self.sign {
60                one_cmp
61            } else {
62                one_cmp.reverse()
63            };
64        }
65        // Then compare numerators and denominators
66        let n_cmp = self.numerator.cmp(&other.numerator);
67        let d_cmp = self.denominator.cmp(&other.denominator);
68        if n_cmp == Equal && d_cmp == Equal {
69            return Equal;
70        }
71        let nd_cmp = n_cmp.cmp(&d_cmp);
72        if nd_cmp != Equal {
73            return if self.sign { nd_cmp } else { nd_cmp.reverse() };
74        }
75        // Then compare floor ∘ log_2 ∘ abs
76        let log_cmp = self
77            .floor_log_base_2_abs()
78            .cmp(&other.floor_log_base_2_abs());
79        if log_cmp != Equal {
80            return if self.sign {
81                log_cmp
82            } else {
83                log_cmp.reverse()
84            };
85        }
86        // Finally, cross-multiply.
87        let prod_cmp =
88            (&self.numerator * &other.denominator).cmp(&(&self.denominator * &other.numerator));
89        if self.sign {
90            prod_cmp
91        } else {
92            prod_cmp.reverse()
93        }
94    }
95}
malachite_q/comparison/cmp.rs

malachite_q/comparison/
cmp.rs
