malachite_nz/integer/arithmetic/
balanced_mod_power_of_2.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 crate::natural::arithmetic::balanced_mod_power_of_2::balanced_from_mod_power_of_2;
11use core::mem::take;
12use malachite_base::num::arithmetic::traits::{
13    BalancedModPowerOf2, BalancedModPowerOf2Assign, ModPowerOf2,
14};
15
16impl BalancedModPowerOf2 for Integer {
17    type Output = Self;
18
19    /// Divides an [`Integer`] by $2^k$, returning the balanced remainder: the representative of
20    /// `self` modulo $2^k$ that is closest to zero. The [`Integer`] is taken by value.
21    ///
22    /// The remainder $r$ satisfies $-2^{k-1} < r \leq 2^{k-1}$ and $r \equiv x \bmod 2^k$, which
23    /// determine it uniquely; for $k = 0$ it is 0. A remainder of exactly $2^{k-1}$ is positive.
24    /// This is [`balanced_mod`](malachite_base::num::arithmetic::traits::BalancedMod::balanced_mod)
25    /// with modulus $2^k$.
26    ///
27    /// # Worst-case complexity
28    /// $T(n) = O(n)$
29    ///
30    /// $M(n) = O(n)$
31    ///
32    /// where $T$ is time, $M$ is additional memory, and $n$ is `pow`.
33    ///
34    /// # Examples
35    /// ```
36    /// use malachite_base::num::arithmetic::traits::BalancedModPowerOf2;
37    /// use malachite_nz::integer::Integer;
38    ///
39    /// assert_eq!(Integer::from(23).balanced_mod_power_of_2(3), -1);
40    /// // a negative value is reduced into the same range
41    /// assert_eq!(Integer::from(-19).balanced_mod_power_of_2(3), -3);
42    /// // exactly half the modulus stays positive
43    /// assert_eq!(Integer::from(-20).balanced_mod_power_of_2(3), 4);
44    /// ```
45    #[inline]
46    fn balanced_mod_power_of_2(self, pow: u64) -> Self {
47        balanced_from_mod_power_of_2(self.mod_power_of_2(pow), pow)
48    }
49}
50
51impl BalancedModPowerOf2 for &Integer {
52    type Output = Integer;
53
54    /// Divides an [`Integer`] by $2^k$, returning the balanced remainder: the representative of
55    /// `self` modulo $2^k$ that is closest to zero. The [`Integer`] is taken by reference.
56    ///
57    /// See the [`BalancedModPowerOf2`] documentation for details.
58    ///
59    /// # Worst-case complexity
60    /// $T(n) = O(n)$
61    ///
62    /// $M(n) = O(n)$
63    ///
64    /// where $T$ is time, $M$ is additional memory, and $n$ is `pow`.
65    ///
66    /// # Examples
67    /// ```
68    /// use malachite_base::num::arithmetic::traits::BalancedModPowerOf2;
69    /// use malachite_nz::integer::Integer;
70    ///
71    /// assert_eq!((&Integer::from(23)).balanced_mod_power_of_2(3), -1);
72    /// assert_eq!((&Integer::from(-19)).balanced_mod_power_of_2(3), -3);
73    /// assert_eq!((&Integer::from(-20)).balanced_mod_power_of_2(3), 4);
74    /// ```
75    #[inline]
76    fn balanced_mod_power_of_2(self, pow: u64) -> Integer {
77        balanced_from_mod_power_of_2(self.mod_power_of_2(pow), pow)
78    }
79}
80
81impl BalancedModPowerOf2Assign for Integer {
82    /// Divides an [`Integer`] by $2^k$, replacing it by the balanced remainder: the representative
83    /// of `self` modulo $2^k$ that is closest to zero.
84    ///
85    /// See the [`BalancedModPowerOf2`] documentation for details.
86    ///
87    /// # Worst-case complexity
88    /// $T(n) = O(n)$
89    ///
90    /// $M(n) = O(n)$
91    ///
92    /// where $T$ is time, $M$ is additional memory, and $n$ is `pow`.
93    ///
94    /// # Examples
95    /// ```
96    /// use malachite_base::num::arithmetic::traits::BalancedModPowerOf2Assign;
97    /// use malachite_nz::integer::Integer;
98    ///
99    /// let mut x = Integer::from(23);
100    /// x.balanced_mod_power_of_2_assign(3);
101    /// assert_eq!(x, -1);
102    /// ```
103    #[inline]
104    fn balanced_mod_power_of_2_assign(&mut self, pow: u64) {
105        *self = take(self).balanced_mod_power_of_2(pow);
106    }
107}
malachite_nz/integer/arithmetic/balanced_mod_power_of_2.rs

malachite_nz/integer/arithmetic/
balanced_mod_power_of_2.rs
