malachite_nz/gaussian_integer/arithmetic/
height.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::gaussian_integer::GaussianInteger;
10use crate::natural::Natural;
11use core::cmp::max;
12use malachite_base::num::arithmetic::traits::{Height, HeightRef, UnsignedAbs};
13use malachite_base::num::logic::traits::SignificantBits;
14
15impl Height for GaussianInteger {
16    type Output = Natural;
17
18    /// Returns the height of a [`GaussianInteger`]: the larger of the absolute values of its real
19    /// and imaginary parts, taking the [`GaussianInteger`] by reference and cloning.
20    ///
21    /// $$
22    /// f(a + bi) = H(a + bi) = \max(|a|, |b|).
23    /// $$
24    ///
25    /// # Worst-case complexity
26    /// $T(n) = O(n)$
27    ///
28    /// $M(n) = O(n)$
29    ///
30    /// where $T$ is time, $M$ is additional memory, and $n$ is `self.significant_bits()`.
31    ///
32    /// # Examples
33    /// ```
34    /// use core::str::FromStr;
35    /// use malachite_base::num::arithmetic::traits::Height;
36    /// use malachite_nz::gaussian_integer::GaussianInteger;
37    ///
38    /// assert_eq!(GaussianInteger::from_str("3-5i").unwrap().to_height(), 5);
39    /// assert_eq!(GaussianInteger::from_str("-7").unwrap().to_height(), 7);
40    /// assert_eq!(GaussianInteger::from_str("0").unwrap().to_height(), 0);
41    /// ```
42    #[inline]
43    fn to_height(&self) -> Natural {
44        self.height_ref().clone()
45    }
46
47    /// Returns the height of a [`GaussianInteger`]: the larger of the absolute values of its real
48    /// and imaginary parts, taking the [`GaussianInteger`] by value.
49    ///
50    /// The larger part is moved out rather than cloned.
51    ///
52    /// # Worst-case complexity
53    /// $T(n) = O(n)$
54    ///
55    /// $M(n) = O(1)$
56    ///
57    /// where $T$ is time, $M$ is additional memory, and $n$ is `self.significant_bits()`.
58    ///
59    /// # Examples
60    /// ```
61    /// use core::str::FromStr;
62    /// use malachite_base::num::arithmetic::traits::Height;
63    /// use malachite_nz::gaussian_integer::GaussianInteger;
64    ///
65    /// assert_eq!(GaussianInteger::from_str("3-5i").unwrap().into_height(), 5);
66    /// assert_eq!(GaussianInteger::from_str("0").unwrap().into_height(), 0);
67    /// ```
68    #[inline]
69    fn into_height(self) -> Natural {
70        max(self.real.unsigned_abs(), self.imaginary.unsigned_abs())
71    }
72
73    /// Returns the number of significant bits of the height of a [`GaussianInteger`].
74    ///
75    /// Since bit length is monotone, this is the larger of the two parts' bit lengths, without
76    /// materializing the height.
77    ///
78    /// # Worst-case complexity
79    /// Constant time and additional memory.
80    ///
81    /// # Examples
82    /// ```
83    /// use core::str::FromStr;
84    /// use malachite_base::num::arithmetic::traits::Height;
85    /// use malachite_nz::gaussian_integer::GaussianInteger;
86    ///
87    /// assert_eq!(
88    ///     GaussianInteger::from_str("3-5i")
89    ///         .unwrap()
90    ///         .height_significant_bits(),
91    ///     3
92    /// );
93    /// assert_eq!(
94    ///     GaussianInteger::from_str("0")
95    ///         .unwrap()
96    ///         .height_significant_bits(),
97    ///     0
98    /// );
99    /// ```
100    #[inline]
101    fn height_significant_bits(&self) -> u64 {
102        max(
103            self.real.significant_bits(),
104            self.imaginary.significant_bits(),
105        )
106    }
107}
108
109impl HeightRef for GaussianInteger {
110    /// Returns a reference to the height of a [`GaussianInteger`]: the larger of the absolute
111    /// values of its real and imaginary parts.
112    ///
113    /// An [`Integer`](crate::integer::Integer) holds its magnitude as a [`Natural`], so the height
114    /// is already there to be lent and nothing needs to be built.
115    ///
116    /// # Worst-case complexity
117    /// $T(n) = O(n)$
118    ///
119    /// $M(n) = O(1)$
120    ///
121    /// where $T$ is time, $M$ is additional memory, and $n$ is `self.significant_bits()`.
122    ///
123    /// # Examples
124    /// ```
125    /// use core::str::FromStr;
126    /// use malachite_base::num::arithmetic::traits::HeightRef;
127    /// use malachite_nz::gaussian_integer::GaussianInteger;
128    ///
129    /// assert_eq!(*GaussianInteger::from_str("3-5i").unwrap().height_ref(), 5);
130    /// assert_eq!(*GaussianInteger::from_str("0").unwrap().height_ref(), 0);
131    /// ```
132    #[inline]
133    fn height_ref(&self) -> &Natural {
134        max(
135            self.real.unsigned_abs_ref(),
136            self.imaginary.unsigned_abs_ref(),
137        )
138    }
139}
malachite_nz/gaussian_integer/arithmetic/height.rs

malachite_nz/gaussian_integer/arithmetic/
height.rs
