malachite_nz/integer/comparison/
cmp_abs.rs

1// Copyright © 2026 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::integer::Integer;
10use core::cmp::Ordering;
11use malachite_base::num::comparison::traits::{
12    OrdAbs, OrdAbsDouble, OrdDouble, PartialOrdAbs, PartialOrdAbsDouble,
13};
14
15impl PartialOrdAbs for Integer {
16    /// Compares the absolute values of two [`Integer`]s.
17    ///
18    /// See the documentation for the [`OrdAbs`] implementation.
19    #[inline]
20    fn partial_cmp_abs(&self, other: &Self) -> Option<Ordering> {
21        Some(self.cmp_abs(other))
22    }
23}
24
25impl OrdAbs for Integer {
26    /// Compares the absolute values of two [`Integer`]s.
27    ///
28    /// # Worst-case complexity
29    /// $T(n) = O(n)$
30    ///
31    /// $M(n) = O(1)$
32    ///
33    /// where $T$ is time, $M$ is additional memory, and $n$ is `min(self.significant_bits(),
34    /// other.significant_bits())`.
35    ///
36    /// # Examples
37    /// ```
38    /// use malachite_base::num::comparison::traits::PartialOrdAbs;
39    /// use malachite_nz::integer::Integer;
40    ///
41    /// assert!(Integer::from(-123).lt_abs(&Integer::from(-124)));
42    /// assert!(Integer::from(-123).le_abs(&Integer::from(-124)));
43    /// assert!(Integer::from(-124).gt_abs(&Integer::from(-123)));
44    /// assert!(Integer::from(-124).ge_abs(&Integer::from(-123)));
45    /// ```
46    #[inline]
47    fn cmp_abs(&self, other: &Self) -> Ordering {
48        self.abs.cmp(&other.abs)
49    }
50}
51
52impl OrdAbsDouble for Integer {
53    /// Compares the absolute value of an [`Integer`] with twice the absolute value of another
54    /// [`Integer`].
55    ///
56    /// The doubling is not actually performed, so no memory is allocated. This is the shape of a
57    /// round-to-nearest decision, where a remainder is weighed against half a divisor.
58    ///
59    /// $$
60    /// f(x, y) = \operatorname{cmp}(|x|, 2|y|).
61    /// $$
62    ///
63    /// # Worst-case complexity
64    /// $T(n) = O(n)$
65    ///
66    /// $M(n) = O(1)$
67    ///
68    /// where $T$ is time, $M$ is additional memory, and $n$ is `self.significant_bits()`.
69    ///
70    /// # Examples
71    /// ```
72    /// use malachite_base::num::basic::traits::Two;
73    /// use malachite_base::num::comparison::traits::OrdAbsDouble;
74    /// use malachite_nz::integer::Integer;
75    /// use std::cmp::Ordering::*;
76    ///
77    /// assert_eq!(Integer::from(4).cmp_abs_double(&Integer::TWO), Equal);
78    /// assert_eq!(Integer::from(-4).cmp_abs_double(&Integer::from(-2)), Equal);
79    /// assert_eq!(Integer::from(3).cmp_abs_double(&Integer::from(-2)), Less);
80    /// assert_eq!(Integer::from(-5).cmp_abs_double(&Integer::TWO), Greater);
81    /// ```
82    #[inline]
83    fn cmp_abs_double(&self, other: &Self) -> Ordering {
84        self.unsigned_abs_ref().cmp_double(other.unsigned_abs_ref())
85    }
86}
87
88impl PartialOrdAbsDouble for Integer {
89    /// Compares the absolute value of an [`Integer`] with twice the absolute value of another
90    /// [`Integer`].
91    ///
92    /// See the documentation for the [`OrdAbsDouble`] implementation.
93    #[inline]
94    fn partial_cmp_abs_double(&self, other: &Self) -> Option<Ordering> {
95        Some(self.cmp_abs_double(other))
96    }
97}
malachite_nz/integer/comparison/cmp_abs.rs

malachite_nz/integer/comparison/
cmp_abs.rs
