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
// 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_integer::GaussianInteger;
use malachite_base::num::arithmetic::traits::{
CanonicalUnitIPow, CanonicalizeUnit, CanonicalizeUnitAssign, MulIPowAssign,
};
impl CanonicalizeUnit for GaussianInteger {
type Output = Self;
/// Brings a [`GaussianInteger`] into canonical unit form, taking it by value.
///
/// The result is the associate $x i^k$ whose argument lies in $(-\pi/4, \pi/4]$, where $k$ is
/// given by
/// [`canonical_unit_i_pow`](malachite_base::num::arithmetic::traits::CanonicalUnitIPow); zero
/// is its own canonical form.
///
/// # Worst-case complexity
/// $T(n) = O(n)$
///
/// $M(n) = O(1)$
///
/// where $T$ is time, $M$ is additional memory, and $n$ is the maximum number of significant
/// bits of the real and imaginary parts.
///
/// # Examples
/// ```
/// use malachite_base::num::arithmetic::traits::CanonicalizeUnit;
/// use malachite_nz::gaussian_integer::GaussianInteger;
/// use std::str::FromStr;
///
/// assert_eq!(
/// GaussianInteger::from_str("-1+2i")
/// .unwrap()
/// .canonicalize_unit()
/// .to_string(),
/// "2+i"
/// );
/// assert_eq!(
/// GaussianInteger::from_str("1-i")
/// .unwrap()
/// .canonicalize_unit()
/// .to_string(),
/// "1+i"
/// );
/// assert_eq!(
/// GaussianInteger::from_str("-3")
/// .unwrap()
/// .canonicalize_unit()
/// .to_string(),
/// "3"
/// );
/// ```
#[inline]
fn canonicalize_unit(mut self) -> Self {
self.canonicalize_unit_assign();
self
}
}
impl CanonicalizeUnit for &GaussianInteger {
type Output = GaussianInteger;
/// Brings a [`GaussianInteger`] into canonical unit form, taking it by reference.
///
/// The result is the associate $x i^k$ whose argument lies in $(-\pi/4, \pi/4]$, where $k$ is
/// given by
/// [`canonical_unit_i_pow`](malachite_base::num::arithmetic::traits::CanonicalUnitIPow); zero
/// is its own canonical form.
///
/// # Worst-case complexity
/// $T(n) = O(n)$
///
/// $M(n) = O(n)$
///
/// where $T$ is time, $M$ is additional memory, and $n$ is the maximum number of significant
/// bits of the real and imaginary parts.
///
/// # Examples
/// ```
/// use malachite_base::num::arithmetic::traits::CanonicalizeUnit;
/// use malachite_nz::gaussian_integer::GaussianInteger;
/// use std::str::FromStr;
///
/// let x = GaussianInteger::from_str("-1+2i").unwrap();
/// assert_eq!((&x).canonicalize_unit().to_string(), "2+i");
/// ```
#[inline]
fn canonicalize_unit(self) -> GaussianInteger {
self.clone().canonicalize_unit()
}
}
impl CanonicalizeUnitAssign for GaussianInteger {
/// Brings a [`GaussianInteger`] into canonical unit form in place.
///
/// The result is the associate $x i^k$ whose argument lies in $(-\pi/4, \pi/4]$, where $k$ is
/// given by
/// [`canonical_unit_i_pow`](malachite_base::num::arithmetic::traits::CanonicalUnitIPow); zero
/// is its own canonical form.
///
/// # Worst-case complexity
/// $T(n) = O(n)$
///
/// $M(n) = O(1)$
///
/// where $T$ is time, $M$ is additional memory, and $n$ is the maximum number of significant
/// bits of the real and imaginary parts.
///
/// # Examples
/// ```
/// use malachite_base::num::arithmetic::traits::CanonicalizeUnitAssign;
/// use malachite_nz::gaussian_integer::GaussianInteger;
/// use std::str::FromStr;
///
/// let mut x = GaussianInteger::from_str("-1+2i").unwrap();
/// x.canonicalize_unit_assign();
/// assert_eq!(x.to_string(), "2+i");
/// ```
fn canonicalize_unit_assign(&mut self) {
let k = self.canonical_unit_i_pow();
self.mul_i_pow_assign(k);
}
}