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
102
103
104
105
106
107
108
109
110
111
112
113
114
115
// 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 core::cmp::Ordering::{self, *};
use malachite_base::num::arithmetic::traits::Sign;
use malachite_base::num::basic::traits::One;
use malachite_base::num::conversion::traits::ExactFrom;
use malachite_base::num::logic::traits::SignificantBits;
use malachite_nz::integer::Integer;
use malachite_nz::natural::Natural;
impl PartialOrd<Integer> for Rational {
/// Compares a [`Rational`] to an [`Integer`].
///
/// # Worst-case complexity
/// $T(n) = O(n \log n \log\log n)$
///
/// $M(n) = O(n \log n)$
///
/// where $T$ is time, $M$ is additional memory, and $n$ is `max(self.significant_bits(),
/// other.significant_bits())`.
///
/// # Examples
/// ```
/// use malachite_nz::integer::Integer;
/// use malachite_q::Rational;
///
/// assert!(Rational::from_signeds(22, 7) > Integer::from(3));
/// assert!(Rational::from_signeds(22, 7) < Integer::from(4));
/// assert!(Rational::from_signeds(-22, 7) < Integer::from(-3));
/// assert!(Rational::from_signeds(-22, 7) > Integer::from(-4));
/// ```
fn partial_cmp(&self, other: &Integer) -> Option<Ordering> {
// First check signs
let self_sign = self.sign();
let other_sign = other.sign();
let sign_cmp = self_sign.cmp(&other_sign);
if sign_cmp != Equal || self_sign == Equal {
return Some(sign_cmp);
}
// Then check if one is < 1 and the other is > 1
let self_cmp_one = self.numerator.cmp(&self.denominator);
let other_cmp_one = other.unsigned_abs_ref().cmp(&Natural::ONE);
let one_cmp = self_cmp_one.cmp(&other_cmp_one);
if one_cmp != Equal {
return Some(if self.sign {
one_cmp
} else {
one_cmp.reverse()
});
}
// Then compare numerators and denominators
let n_cmp = self.numerator.cmp(other.unsigned_abs_ref());
let d_cmp = self.denominator.cmp(&Natural::ONE);
if n_cmp == Equal && d_cmp == Equal {
return Some(Equal);
}
let nd_cmp = n_cmp.cmp(&d_cmp);
if nd_cmp != Equal {
return Some(if self.sign { nd_cmp } else { nd_cmp.reverse() });
}
let log_cmp = self
.floor_log_base_2_abs()
.cmp(&i64::exact_from(other.significant_bits() - 1));
if log_cmp != Equal {
return Some(if self.sign {
log_cmp
} else {
log_cmp.reverse()
});
}
// Finally, cross-multiply.
let prod_cmp = self
.numerator
.cmp(&(&self.denominator * other.unsigned_abs_ref()));
Some(if self.sign {
prod_cmp
} else {
prod_cmp.reverse()
})
}
}
impl PartialOrd<Rational> for Integer {
/// Compares an [`Integer`] to a [`Rational`].
///
/// # Worst-case complexity
/// $T(n) = O(n \log n \log\log n)$
///
/// $M(n) = O(n \log n)$
///
/// where $T$ is time, $M$ is additional memory, and $n$ is `max(self.significant_bits(),
/// other.significant_bits())`.
///
/// # Examples
/// ```
/// use malachite_nz::integer::Integer;
/// use malachite_q::Rational;
///
/// assert!(Integer::from(3) < Rational::from_signeds(22, 7));
/// assert!(Integer::from(4) > Rational::from_signeds(22, 7));
/// assert!(Integer::from(-3) > Rational::from_signeds(-22, 7));
/// assert!(Integer::from(-4) < Rational::from_signeds(-22, 7));
/// ```
#[inline]
fn partial_cmp(&self, other: &Rational) -> Option<Ordering> {
other.partial_cmp(self).map(Ordering::reverse)
}
}