1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
// Copyright © 2026 Mikhail Hogrefe
//
// This file is part of Malachite.
//
// Malachite is free software: you can redistribute it and/or modify it under the terms of the GNU
// Lesser General Public License (LGPL) as published by the Free Software Foundation; either version
// 3 of the License, or (at your option) any later version. See <https://www.gnu.org/licenses/>.
use crate::gaussian_rational::GaussianRational;
use core::cmp::max;
use malachite_base::num::arithmetic::traits::{Height, HeightRef};
use malachite_nz::natural::Natural;
impl Height for GaussianRational {
type Output = Natural;
/// Returns the height of a [`GaussianRational`]: the larger of the heights of its real and
/// imaginary parts, taking the [`GaussianRational`] by reference and cloning.
///
/// A [`Rational`](crate::Rational)'s height is the larger of the absolute value of its
/// numerator and its denominator, so this is the largest of four magnitudes. The height of zero
/// is 1, as it is for a [`Rational`](crate::Rational), since zero is $0/1$ and its denominator
/// is 1.
///
/// $$
/// f(a + bi) = H(a + bi) = \max(H(a), H(b)).
/// $$
///
/// # Worst-case complexity
/// $T(n) = O(n)$
///
/// $M(n) = O(n)$
///
/// where $T$ is time, $M$ is additional memory, and $n$ is `self.significant_bits()`.
///
/// # Examples
/// ```
/// use core::str::FromStr;
/// use malachite_base::num::arithmetic::traits::Height;
/// use malachite_q::gaussian_rational::GaussianRational;
///
/// assert_eq!(
/// GaussianRational::from_str("1/3+i/2").unwrap().to_height(),
/// 3
/// );
/// assert_eq!(GaussianRational::from_str("22/7").unwrap().to_height(), 22);
/// assert_eq!(GaussianRational::from_str("0").unwrap().to_height(), 1);
/// ```
#[inline]
fn to_height(&self) -> Natural {
self.height_ref().clone()
}
/// Returns the height of a [`GaussianRational`]: the larger of the heights of its real and
/// imaginary parts, taking the [`GaussianRational`] by value.
///
/// The largest of the four magnitudes is moved out rather than cloned.
///
/// # Worst-case complexity
/// Constant time and additional memory.
///
/// # Examples
/// ```
/// use core::str::FromStr;
/// use malachite_base::num::arithmetic::traits::Height;
/// use malachite_q::gaussian_rational::GaussianRational;
///
/// assert_eq!(
/// GaussianRational::from_str("1/3+i/2").unwrap().into_height(),
/// 3
/// );
/// assert_eq!(GaussianRational::from_str("0").unwrap().into_height(), 1);
/// ```
#[inline]
fn into_height(self) -> Natural {
max(self.real.into_height(), self.imaginary.into_height())
}
/// Returns the number of significant bits of the height of a [`GaussianRational`].
///
/// Since bit length is monotone, this is the larger of the two parts' height bit lengths,
/// without materializing the height.
///
/// # Worst-case complexity
/// Constant time and additional memory.
///
/// # Examples
/// ```
/// use core::str::FromStr;
/// use malachite_base::num::arithmetic::traits::Height;
/// use malachite_q::gaussian_rational::GaussianRational;
///
/// assert_eq!(
/// GaussianRational::from_str("1/3+i/2")
/// .unwrap()
/// .height_significant_bits(),
/// 2
/// );
/// assert_eq!(
/// GaussianRational::from_str("0")
/// .unwrap()
/// .height_significant_bits(),
/// 1
/// );
/// ```
#[inline]
fn height_significant_bits(&self) -> u64 {
max(
self.real.height_significant_bits(),
self.imaginary.height_significant_bits(),
)
}
}
impl HeightRef for GaussianRational {
/// Returns a reference to the height of a [`GaussianRational`]: the larger of the heights of
/// its real and imaginary parts.
///
/// Each part holds its numerator's magnitude and its denominator as [`Natural`]s, so the height
/// is one of those four and is already there to be lent.
///
/// # Worst-case complexity
/// $T(n) = O(n)$
///
/// $M(n) = O(1)$
///
/// where $T$ is time, $M$ is additional memory, and $n$ is `self.significant_bits()`.
///
/// # Examples
/// ```
/// use core::str::FromStr;
/// use malachite_base::num::arithmetic::traits::HeightRef;
/// use malachite_q::gaussian_rational::GaussianRational;
///
/// assert_eq!(
/// *GaussianRational::from_str("1/3+i/2").unwrap().height_ref(),
/// 3
/// );
/// assert_eq!(*GaussianRational::from_str("0").unwrap().height_ref(), 1);
/// ```
#[inline]
fn height_ref(&self) -> &Natural {
max(self.real.height_ref(), self.imaginary.height_ref())
}
}