malachite_nz/integer/arithmetic/
square.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::integer::Integer;
10use malachite_base::num::arithmetic::traits::{Square, SquareAssign};
11
12impl Square for Integer {
13    type Output = Self;
14
15    /// Squares an [`Integer`], taking it by value.
16    ///
17    /// $$
18    /// f(x) = x^2.
19    /// $$
20    ///
21    /// # Worst-case complexity
22    /// $T(n) = O(n \log n \log\log n)$
23    ///
24    /// $M(n) = O(n \log n)$
25    ///
26    /// where $T$ is time, $M$ is additional memory, and $n$ is `self.significant_bits()`.
27    ///
28    /// # Examples
29    /// ```
30    /// use malachite_base::num::arithmetic::traits::Square;
31    /// use malachite_base::num::basic::traits::Zero;
32    /// use malachite_nz::integer::Integer;
33    ///
34    /// assert_eq!(Integer::ZERO.square(), 0);
35    /// assert_eq!(Integer::from(123).square(), 15129);
36    /// assert_eq!(Integer::from(-123).square(), 15129);
37    /// ```
38    #[inline]
39    fn square(mut self) -> Self {
40        self.square_assign();
41        self
42    }
43}
44
45impl Square for &Integer {
46    type Output = Integer;
47
48    /// Squares an [`Integer`], taking it by reference.
49    ///
50    /// $$
51    /// f(x) = x^2.
52    /// $$
53    ///
54    /// # Worst-case complexity
55    /// $T(n) = O(n \log n \log\log n)$
56    ///
57    /// $M(n) = O(n \log n)$
58    ///
59    /// where $T$ is time, $M$ is additional memory, and $n$ is `self.significant_bits()`.
60    ///
61    /// # Examples
62    /// ```
63    /// use malachite_base::num::arithmetic::traits::Square;
64    /// use malachite_base::num::basic::traits::Zero;
65    /// use malachite_nz::integer::Integer;
66    ///
67    /// assert_eq!((&Integer::ZERO).square(), 0);
68    /// assert_eq!((&Integer::from(123)).square(), 15129);
69    /// assert_eq!((&Integer::from(-123)).square(), 15129);
70    /// ```
71    #[inline]
72    fn square(self) -> Integer {
73        Integer {
74            sign: true,
75            abs: (&self.abs).square(),
76        }
77    }
78}
79
80impl SquareAssign for Integer {
81    /// Squares an [`Integer`] in place.
82    ///
83    /// $$
84    /// x \gets x^2.
85    /// $$
86    ///
87    /// # Worst-case complexity
88    /// $T(n) = O(n \log n \log\log n)$
89    ///
90    /// $M(n) = O(n \log n)$
91    ///
92    /// where $T$ is time, $M$ is additional memory, and $n$ is `self.significant_bits()`.
93    ///
94    /// # Examples
95    /// ```
96    /// use malachite_base::num::arithmetic::traits::SquareAssign;
97    /// use malachite_base::num::basic::traits::Zero;
98    /// use malachite_nz::integer::Integer;
99    ///
100    /// let mut x = Integer::ZERO;
101    /// x.square_assign();
102    /// assert_eq!(x, 0);
103    ///
104    /// let mut x = Integer::from(123);
105    /// x.square_assign();
106    /// assert_eq!(x, 15129);
107    ///
108    /// let mut x = Integer::from(-123);
109    /// x.square_assign();
110    /// assert_eq!(x, 15129);
111    /// ```
112    fn square_assign(&mut self) {
113        self.sign = true;
114        self.abs.square_assign();
115    }
116}
malachite_nz/integer/arithmetic/square.rs

malachite_nz/integer/arithmetic/
square.rs
