malachite_base/num/comparison/
traits.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 core::cmp::Ordering::{self, *};
10
11/// Determines equality between the absolute values of two numbers.
12pub trait EqAbs<Rhs: ?Sized = Self> {
13    /// Compares the absolute values of two numbers for equality, taking both by reference.
14    fn eq_abs(&self, other: &Rhs) -> bool;
15
16    /// Compares the absolute values of two numbers for inequality, taking both by reference.
17    ///
18    /// # Worst-case complexity
19    /// Same as the time and additional memory complexity of [`eq_abs`](Self::eq_abs).
20    #[inline]
21    fn ne_abs(&self, other: &Rhs) -> bool {
22        !self.eq_abs(other)
23    }
24}
25
26/// Determines equality between the absolute values of two numbers, where some pairs of numbers may
27/// not be comparable.
28pub trait PartialOrdAbs<Rhs: ?Sized = Self> {
29    /// Compares the absolute values of two numbers, taking both by reference.
30    ///
31    /// If the two values are not comparable, `None` is returned.
32    fn partial_cmp_abs(&self, other: &Rhs) -> Option<Ordering>;
33
34    /// Determines whether the absolute value of one number is less than the absolute value of
35    /// another.
36    ///
37    /// # Worst-case complexity
38    /// Same as the time and additional memory complexity of
39    /// [`partial_cmp_abs`](Self::partial_cmp_abs).
40    #[inline]
41    fn lt_abs(&self, other: &Rhs) -> bool {
42        matches!(self.partial_cmp_abs(other), Some(Less))
43    }
44
45    /// Determines whether the absolute value of one number is less than or equal to the absolute
46    /// value of another.
47    ///
48    /// # Worst-case complexity
49    /// Same as the time and additional memory complexity of
50    /// [`partial_cmp_abs`](Self::partial_cmp_abs).
51    #[inline]
52    fn le_abs(&self, other: &Rhs) -> bool {
53        matches!(self.partial_cmp_abs(other), Some(Less | Equal))
54    }
55
56    /// Determines whether the absolute value of one number is greater than the absolute value of
57    /// another.
58    ///
59    /// # Worst-case complexity
60    /// Same as the time and additional memory complexity of
61    /// [`partial_cmp_abs`](Self::partial_cmp_abs).
62    #[inline]
63    fn gt_abs(&self, other: &Rhs) -> bool {
64        matches!(self.partial_cmp_abs(other), Some(Greater))
65    }
66
67    /// Determines whether the absolute value of one number is greater than or equal to the absolute
68    /// value of another.
69    ///
70    /// # Worst-case complexity
71    /// Same as the time and additional memory complexity of
72    /// [`partial_cmp_abs`](Self::partial_cmp_abs).
73    #[inline]
74    fn ge_abs(&self, other: &Rhs) -> bool {
75        matches!(self.partial_cmp_abs(other), Some(Greater | Equal))
76    }
77}
78
79/// Compares a number with twice another number, without computing the doubled value.
80///
81/// If the two values are not comparable, `None` is returned.
82pub trait PartialOrdDouble<Rhs: ?Sized = Self> {
83    /// Compares a number with twice another number, taking both by reference.
84    fn partial_cmp_double(&self, other: &Rhs) -> Option<Ordering>;
85}
86
87/// Compares the absolute value of a number with twice the absolute value of another number, without
88/// computing the doubled value.
89///
90/// If the two values are not comparable, `None` is returned.
91pub trait PartialOrdAbsDouble<Rhs: ?Sized = Self> {
92    /// Compares the absolute value of a number with twice the absolute value of another number,
93    /// taking both by reference.
94    fn partial_cmp_abs_double(&self, other: &Rhs) -> Option<Ordering>;
95}
96
97/// Compares a number with twice another number, without computing the doubled value.
98///
99/// This is the shape of a round-to-nearest decision, where a remainder is weighed against half a
100/// divisor, so it is worth doing without the allocation or the overflow that doubling would cost.
101pub trait OrdDouble<Rhs: ?Sized = Self>: PartialOrdDouble<Rhs> {
102    /// Compares a number with twice another number, taking both by reference.
103    fn cmp_double(&self, other: &Rhs) -> Ordering;
104}
105
106/// Compares the absolute value of a number with twice the absolute value of another number, without
107/// computing the doubled value.
108///
109/// This is the shape of a round-to-nearest decision, where a remainder is weighed against half a
110/// divisor, so it is worth doing without the allocation or the overflow that doubling would cost.
111pub trait OrdAbsDouble<Rhs: ?Sized = Self>: PartialOrdAbsDouble<Rhs> {
112    /// Compares the absolute value of a number with twice the absolute value of another number,
113    /// taking both by reference.
114    fn cmp_abs_double(&self, other: &Rhs) -> Ordering;
115}
116
117/// Compares the product of two numbers with a third number, without computing the product unless it
118/// is needed.
119///
120/// `T::cmp_product(&a, &b, &c)` compares $ab$ with $c$. Most comparisons are decided by cheap
121/// checks, such as comparing bit lengths, and the product is computed only when they cannot decide.
122pub trait OrdProduct {
123    fn cmp_product(a: &Self, b: &Self, c: &Self) -> Ordering;
124}
125
126/// Compares the product of two numbers with the negative of a third number, without computing the
127/// product unless it is needed and without computing the negative.
128///
129/// `T::cmp_product_neg(&a, &b, &c)` compares $ab$ with $-c$; equivalently, it gives the sign of $ab
130/// + c$.
131pub trait OrdProductNeg {
132    fn cmp_product_neg(a: &Self, b: &Self, c: &Self) -> Ordering;
133}
134
135/// Compares the products of two pairs of numbers, without computing the products unless they are
136/// needed.
137///
138/// `T::cmp_products(&a, &b, &c, &d)` compares $ab$ with $cd$. Most comparisons are decided by cheap
139/// checks, such as comparing the factors pairwise or comparing bit lengths, and the products are
140/// computed only when they cannot decide.
141pub trait OrdProducts {
142    fn cmp_products(a: &Self, b: &Self, c: &Self, d: &Self) -> Ordering;
143}
144
145/// Compares the product of two numbers with the negative of the product of two others, without
146/// computing the products unless they are needed and without computing the negative.
147///
148/// `T::cmp_products_neg(&a, &b, &c, &d)` compares $ab$ with $-cd$; equivalently, it gives the sign
149/// of $ab + cd$.
150pub trait OrdProductsNeg {
151    fn cmp_products_neg(a: &Self, b: &Self, c: &Self, d: &Self) -> Ordering;
152}
153
154/// Compares the absolute values of two numbers.
155pub trait OrdAbs: Eq + PartialOrdAbs<Self> {
156    fn cmp_abs(&self, other: &Self) -> Ordering;
157}
malachite_base/num/comparison/traits.rs

malachite_base/num/comparison/
traits.rs
