malachite_nz/integer_vector/arithmetic/
canonicalize_sign.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::integer_vector::IntegerVector;
10use malachite_base::num::arithmetic::traits::{
11    CanonicalizeSign, CanonicalizeSignAssign, NegAssign,
12};
13use malachite_base::vector::Vector;
14
15impl CanonicalizeSign for IntegerVector {
16    type Output = Self;
17
18    /// Brings an [`IntegerVector`] into canonical sign form, taking the vector by value: negates it
19    /// if its pivot, its first nonzero element, is negative.
20    ///
21    /// A vector and its negation are the same up to multiplication by $\pm 1$, the units of the
22    /// integers, and this picks the one whose pivot is positive to represent both. A vector of
23    /// zeros has no pivot and is left alone.
24    ///
25    /// # Worst-case complexity
26    /// $T(n) = O(n)$
27    ///
28    /// $M(n) = O(1)$
29    ///
30    /// where $T$ is time, $M$ is additional memory, and $n$ is `self.dimension()`.
31    ///
32    /// # Examples
33    /// ```
34    /// use core::str::FromStr;
35    /// use malachite_base::num::arithmetic::traits::CanonicalizeSign;
36    /// use malachite_nz::integer_vector::IntegerVector;
37    ///
38    /// let v = IntegerVector::from_str("(0, -2, 3)").unwrap();
39    /// assert_eq!(v.canonicalize_sign().to_string(), "(0, 2, -3)");
40    /// let v = IntegerVector::from_str("(0, 2, -3)").unwrap();
41    /// assert_eq!(v.canonicalize_sign().to_string(), "(0, 2, -3)");
42    /// ```
43    #[inline]
44    fn canonicalize_sign(mut self) -> Self {
45        self.canonicalize_sign_assign();
46        self
47    }
48}
49
50impl CanonicalizeSign for &IntegerVector {
51    type Output = IntegerVector;
52
53    /// Brings an [`IntegerVector`] into canonical sign form, taking the vector by reference:
54    /// negates it if its pivot, its first nonzero element, is negative.
55    ///
56    /// See the documentation for the [`CanonicalizeSign`] implementation on [`IntegerVector`].
57    ///
58    /// # Worst-case complexity
59    /// $T(n) = O(n)$
60    ///
61    /// $M(n) = O(n)$
62    ///
63    /// where $T$ is time, $M$ is additional memory, and $n$ is the total number of bits of the
64    /// elements.
65    ///
66    /// # Examples
67    /// ```
68    /// use core::str::FromStr;
69    /// use malachite_base::num::arithmetic::traits::CanonicalizeSign;
70    /// use malachite_nz::integer_vector::IntegerVector;
71    ///
72    /// let v = IntegerVector::from_str("(0, -2, 3)").unwrap();
73    /// assert_eq!((&v).canonicalize_sign().to_string(), "(0, 2, -3)");
74    /// ```
75    #[inline]
76    fn canonicalize_sign(self) -> IntegerVector {
77        if self.pivot().is_some_and(|x| *x < 0u32) {
78            -self
79        } else {
80            self.clone()
81        }
82    }
83}
84
85impl CanonicalizeSignAssign for IntegerVector {
86    /// Replaces an [`IntegerVector`] with its canonical sign form: negates it if its pivot, its
87    /// first nonzero element, is negative.
88    ///
89    /// See the documentation for the [`CanonicalizeSign`] implementation on [`IntegerVector`].
90    ///
91    /// # Worst-case complexity
92    /// $T(n) = O(n)$
93    ///
94    /// $M(n) = O(1)$
95    ///
96    /// where $T$ is time, $M$ is additional memory, and $n$ is `self.dimension()`.
97    ///
98    /// # Examples
99    /// ```
100    /// use core::str::FromStr;
101    /// use malachite_base::num::arithmetic::traits::CanonicalizeSignAssign;
102    /// use malachite_nz::integer_vector::IntegerVector;
103    ///
104    /// let mut v = IntegerVector::from_str("(0, -2, 3)").unwrap();
105    /// v.canonicalize_sign_assign();
106    /// assert_eq!(v.to_string(), "(0, 2, -3)");
107    /// ```
108    #[inline]
109    fn canonicalize_sign_assign(&mut self) {
110        if self.pivot().is_some_and(|x| *x < 0u32) {
111            self.neg_assign();
112        }
113    }
114}
malachite_nz/integer_vector/arithmetic/canonicalize_sign.rs

malachite_nz/integer_vector/arithmetic/
canonicalize_sign.rs
