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
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
// Copyright © 2026 Mikhail Hogrefe
//
// Uses code adopted from the FLINT Library.
//
// Copyright © 2011 Fredrik Johansson
//
// 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::Rational;
use core::cmp::max;
use malachite_base::num::arithmetic::traits::{Height, HeightRef};
use malachite_base::num::logic::traits::SignificantBits;
use malachite_nz::natural::Natural;
impl Height for Rational {
type Output = Natural;
/// Returns the height of a [`Rational`]: the larger of the absolute value of its numerator and
/// its denominator, taking the [`Rational`] by reference and cloning.
///
/// The height is the measure in which Diophantine approximation bounds are usually stated.
///
/// $$
/// f(p/q) = H(p/q) = \max(|p|, q).
/// $$
///
/// # 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 malachite_base::num::arithmetic::traits::Height;
/// use malachite_q::Rational;
/// use std::str::FromStr;
///
/// assert_eq!(Rational::from_str("22/7").unwrap().to_height(), 22);
/// assert_eq!(Rational::from_str("-1/101").unwrap().to_height(), 101);
/// assert_eq!(Rational::from_str("0").unwrap().to_height(), 1);
/// ```
///
/// This is fmpq_height from fmpq/height.c, FLINT 3.6.0, where the components are already
/// magnitudes, so no absolute values need to be taken.
#[inline]
fn to_height(&self) -> Natural {
self.height_ref().clone()
}
/// Returns the height of a [`Rational`]: the larger of the absolute value of its numerator and
/// its denominator, taking the [`Rational`] by value.
///
/// The height is the measure in which Diophantine approximation bounds are usually stated.
///
/// $$
/// f(p/q) = H(p/q) = \max(|p|, q).
/// $$
///
/// # Worst-case complexity
/// Constant time and additional memory.
///
/// # Examples
/// ```
/// use malachite_base::num::arithmetic::traits::Height;
/// use malachite_q::Rational;
/// use std::str::FromStr;
///
/// assert_eq!(Rational::from_str("22/7").unwrap().into_height(), 22);
/// assert_eq!(Rational::from_str("-1/101").unwrap().into_height(), 101);
/// assert_eq!(Rational::from_str("0").unwrap().into_height(), 1);
/// ```
///
/// This is fmpq_height from fmpq/height.c, FLINT 3.6.0, where the components are already
/// magnitudes, so no absolute values need to be taken.
#[inline]
fn into_height(self) -> Natural {
max(self.numerator, self.denominator)
}
/// Returns the number of significant bits of the height of a [`Rational`]: the larger of the
/// numbers of significant bits of its numerator and its denominator.
///
/// Since bit length is monotone, this is `self.to_height().significant_bits()`, without
/// materializing the height.
///
/// $$
/// f(p/q) = \lfloor \log_2 \max(|p|, q) \rfloor + 1.
/// $$
///
/// # Worst-case complexity
/// Constant time and additional memory.
///
/// # Examples
/// ```
/// use malachite_base::num::arithmetic::traits::Height;
/// use malachite_q::Rational;
/// use std::str::FromStr;
///
/// assert_eq!(
/// Rational::from_str("22/7")
/// .unwrap()
/// .height_significant_bits(),
/// 5
/// );
/// assert_eq!(
/// Rational::from_str("-1/101")
/// .unwrap()
/// .height_significant_bits(),
/// 7
/// );
/// assert_eq!(
/// Rational::from_str("0").unwrap().height_significant_bits(),
/// 1
/// );
/// ```
///
/// This is fmpq_height_bits from fmpq/height_bits.c, FLINT 3.6.0.
#[inline]
fn height_significant_bits(&self) -> u64 {
max(
self.numerator.significant_bits(),
self.denominator.significant_bits(),
)
}
}
impl HeightRef for Rational {
/// Returns a reference to the height of a [`Rational`]: the larger of the absolute value of its
/// numerator and its denominator.
///
/// A [`Rational`] holds its numerator's magnitude and its denominator as [`Natural`]s, so the
/// height is already there to be lent and nothing needs to be built.
///
/// $$
/// f(p/q) = H(p/q) = \max(|p|, q).
/// $$
///
/// # 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 malachite_base::num::arithmetic::traits::HeightRef;
/// use malachite_q::Rational;
/// use std::str::FromStr;
///
/// assert_eq!(*Rational::from_str("22/7").unwrap().height_ref(), 22);
/// assert_eq!(*Rational::from_str("-1/101").unwrap().height_ref(), 101);
/// assert_eq!(*Rational::from_str("0").unwrap().height_ref(), 1);
/// ```
///
/// This is fmpq_height from fmpq/height.c, FLINT 3.6.0, where the components are already
/// magnitudes, so no absolute values need to be taken and the larger can be lent.
#[inline]
fn height_ref(&self) -> &Natural {
max(&self.numerator, &self.denominator)
}
}