malachite_q/comparison/
partial_cmp_natural.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;
12use malachite_base::num::basic::traits::One;
13use malachite_base::num::conversion::traits::ExactFrom;
14use malachite_base::num::logic::traits::SignificantBits;
15use malachite_nz::natural::Natural;
16
17impl PartialOrd<Natural> for Rational {
18    /// Compares a [`Rational`] to a [`Natural`].
19    ///
20    /// # Worst-case complexity
21    /// $T(n) = O(n \log n \log\log n)$
22    ///
23    /// $M(n) = O(n \log n)$
24    ///
25    /// where $T$ is time, $M$ is additional memory, and $n$ is `max(self.significant_bits(),
26    /// other.significant_bits())`.
27    ///
28    /// # Examples
29    /// ```
30    /// use malachite_nz::natural::Natural;
31    /// use malachite_q::Rational;
32    ///
33    /// assert!(Rational::from_signeds(22, 7) > Natural::from(3u32));
34    /// assert!(Rational::from_signeds(22, 7) < Natural::from(4u32));
35    /// ```
36    fn partial_cmp(&self, other: &Natural) -> Option<Ordering> {
37        // First check signs
38        let self_sign = self.sign();
39        let other_sign = other.sign();
40        let sign_cmp = self_sign.cmp(&other_sign);
41        if sign_cmp != Equal || self_sign == Equal {
42            return Some(sign_cmp);
43        }
44        // Then check if one is < 1 and the other is > 1
45        let self_cmp_one = self.numerator.cmp(&self.denominator);
46        let other_cmp_one = other.cmp(&Natural::ONE);
47        let one_cmp = self_cmp_one.cmp(&other_cmp_one);
48        if one_cmp != Equal {
49            return Some(one_cmp);
50        }
51        // Then compare numerators and denominators
52        let n_cmp = self.numerator.cmp(other);
53        let d_cmp = self.denominator.cmp(&Natural::ONE);
54        if n_cmp == Equal && d_cmp == Equal {
55            return Some(Equal);
56        }
57        let nd_cmp = n_cmp.cmp(&d_cmp);
58        if nd_cmp != Equal {
59            return Some(nd_cmp);
60        }
61        let log_cmp = self
62            .floor_log_base_2_abs()
63            .cmp(&i64::exact_from(other.significant_bits() - 1));
64        if log_cmp != Equal {
65            return Some(if self.sign {
66                log_cmp
67            } else {
68                log_cmp.reverse()
69            });
70        }
71        // Finally, cross-multiply.
72        Some(self.numerator.cmp(&(&self.denominator * other)))
73    }
74}
75
76impl PartialOrd<Rational> for Natural {
77    /// Compares a [`Natural`] to a [`Rational`].
78    ///
79    /// # Worst-case complexity
80    /// $T(n) = O(n \log n \log\log n)$
81    ///
82    /// $M(n) = O(n \log n)$
83    ///
84    /// where $T$ is time, $M$ is additional memory, and $n$ is `max(self.significant_bits(),
85    /// other.significant_bits())`.
86    ///
87    /// # Examples
88    /// ```
89    /// use malachite_nz::natural::Natural;
90    /// use malachite_q::Rational;
91    ///
92    /// assert!(Natural::from(3u32) < Rational::from_signeds(22, 7));
93    /// assert!(Natural::from(4u32) > Rational::from_signeds(22, 7));
94    /// ```
95    #[inline]
96    fn partial_cmp(&self, other: &Rational) -> Option<Ordering> {
97        other.partial_cmp(self).map(Ordering::reverse)
98    }
99}
malachite_q/comparison/partial_cmp_natural.rs

malachite_q/comparison/
partial_cmp_natural.rs
