malachite_nz/natural/arithmetic/
neg.rs

1// Copyright © 2026 Mikhail Hogrefe
2//
3// Uses code adopted from the GNU MP Library.
4//
5//      Copyright © 1991, 1993-1997, 1999-2016, 2020 Free Software Foundation, Inc.
6//
7// This file is part of Malachite.
8//
9// Malachite is free software: you can redistribute it and/or modify it under the terms of the GNU
10// Lesser General Public License (LGPL) as published by the Free Software Foundation; either version
11// 3 of the License, or (at your option) any later version. See <https://www.gnu.org/licenses/>.
12
13use crate::integer::Integer;
14use crate::natural::Natural;
15use crate::natural::logic::not::limbs_not_in_place;
16use crate::platform::Limb;
17use core::ops::Neg;
18use malachite_base::num::arithmetic::traits::WrappingNegAssign;
19use malachite_base::slices::slice_leading_zeros;
20
21// This is equivalent to `mpn_neg` from `gmp.h`, GMP 6.2.1, where rp == up.
22pub(crate) fn limbs_neg_in_place(xs: &mut [Limb]) -> bool {
23    let n = xs.len();
24    let zeros = slice_leading_zeros(xs);
25    if zeros == n {
26        return false;
27    }
28    xs[zeros].wrapping_neg_assign();
29    let offset = zeros + 1;
30    if offset != n {
31        limbs_not_in_place(&mut xs[offset..]);
32    }
33    true
34}
35
36impl Neg for Natural {
37    type Output = Integer;
38
39    /// Negates a [`Natural`], taking it by value and returning an [`Integer`].
40    ///
41    /// $$
42    /// f(x) = -x.
43    /// $$
44    ///
45    /// # Worst-case complexity
46    /// Constant time and additional memory.
47    ///
48    /// # Examples
49    /// ```
50    /// use malachite_base::num::basic::traits::Zero;
51    /// use malachite_nz::natural::Natural;
52    ///
53    /// assert_eq!(-Natural::ZERO, 0);
54    /// assert_eq!(-Natural::from(123u32), -123);
55    /// ```
56    fn neg(self) -> Integer {
57        Integer::from_sign_and_abs(self == 0, self)
58    }
59}
60
61impl Neg for &Natural {
62    type Output = Integer;
63
64    /// Negates a [`Natural`], taking it by reference and returning an [`Integer`].
65    ///
66    /// $$
67    /// f(x) = -x.
68    /// $$
69    ///
70    /// # Worst-case complexity
71    /// $T(n) = O(n)$
72    ///
73    /// $M(n) = O(n)$
74    ///
75    /// where $T$ is time, $M$ is additional memory, and $n$ is `self.significant_bits()`.
76    ///
77    /// # Examples
78    /// ```
79    /// use malachite_base::num::basic::traits::Zero;
80    /// use malachite_nz::natural::Natural;
81    ///
82    /// assert_eq!(-&Natural::ZERO, 0);
83    /// assert_eq!(-&Natural::from(123u32), -123);
84    /// ```
85    fn neg(self) -> Integer {
86        Integer::from_sign_and_abs_ref(*self == 0, self)
87    }
88}
malachite_nz/natural/arithmetic/neg.rs

malachite_nz/natural/arithmetic/
neg.rs
