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

use integer::Integer;
use malachite_base::num::arithmetic::traits::{Parity, Pow, PowAssign};

impl Pow<u64> for Integer {
    type Output = Integer;

    /// Raises an [`Integer`] to a power, taking the [`Integer`] by value.
    ///
    /// $f(x, n) = x^n$.
    ///
    /// # Worst-case complexity
    /// $T(n, m) = O(nm \log (nm) \log\log (nm))$
    ///
    /// $M(n, m) = O(nm \log (nm))$
    ///
    /// where $T$ is time, $M$ is additional memory, $n$ is `self.significant_bits()`, and $m$ is
    /// `exp`.
    ///
    /// # Examples
    /// ```
    /// extern crate malachite_base;
    ///
    /// use malachite_base::num::arithmetic::traits::Pow;
    /// use malachite_nz::integer::Integer;
    /// use std::str::FromStr;
    ///
    /// assert_eq!(
    ///     Integer::from(-3).pow(100).to_string(),
    ///     "515377520732011331036461129765621272702107522001"
    /// );
    /// assert_eq!(
    ///     Integer::from_str("-12345678987654321").unwrap().pow(3).to_string(),
    ///     "-1881676411868862234942354805142998028003108518161"
    /// );
    /// ```
    #[inline]
    fn pow(mut self, exp: u64) -> Integer {
        self.pow_assign(exp);
        self
    }
}

impl<'a> Pow<u64> for &'a Integer {
    type Output = Integer;

    /// Raises an [`Integer`] to a power, taking the [`Integer`] by reference.
    ///
    /// $f(x, n) = x^n$.
    ///
    /// # Worst-case complexity
    /// $T(n, m) = O(nm \log (nm) \log\log (nm))$
    ///
    /// $M(n, m) = O(nm \log (nm))$
    ///
    /// where $T$ is time, $M$ is additional memory, $n$ is `self.significant_bits()`, and $m$ is
    /// `exp`.
    ///
    /// # Examples
    /// ```
    /// extern crate malachite_base;
    ///
    /// use malachite_base::num::arithmetic::traits::Pow;
    /// use malachite_nz::integer::Integer;
    /// use std::str::FromStr;
    ///
    /// assert_eq!(
    ///     (&Integer::from(-3)).pow(100).to_string(),
    ///     "515377520732011331036461129765621272702107522001"
    /// );
    /// assert_eq!(
    ///     (&Integer::from_str("-12345678987654321").unwrap()).pow(3).to_string(),
    ///     "-1881676411868862234942354805142998028003108518161"
    /// );
    /// ```
    #[inline]
    fn pow(self, exp: u64) -> Integer {
        Integer {
            sign: exp.even() || self.sign,
            abs: (&self.abs).pow(exp),
        }
    }
}

impl PowAssign<u64> for Integer {
    /// Raises an [`Integer`] to a power in place.
    ///
    /// $x \gets x^n$.
    ///
    /// # Worst-case complexity
    /// $T(n, m) = O(nm \log (nm) \log\log (nm))$
    ///
    /// $M(n, m) = O(nm \log (nm))$
    ///
    /// where $T$ is time, $M$ is additional memory, $n$ is `self.significant_bits()`, and $m$ is
    /// `exp`.
    ///
    /// # Examples
    /// ```
    /// extern crate malachite_base;
    ///
    /// use malachite_base::num::arithmetic::traits::PowAssign;
    /// use malachite_nz::integer::Integer;
    /// use std::str::FromStr;
    ///
    /// let mut x = Integer::from(-3);
    /// x.pow_assign(100);
    /// assert_eq!(x.to_string(), "515377520732011331036461129765621272702107522001");
    ///
    /// let mut x = Integer::from_str("-12345678987654321").unwrap();
    /// x.pow_assign(3);
    /// assert_eq!(x.to_string(), "-1881676411868862234942354805142998028003108518161");
    /// ```
    fn pow_assign(&mut self, exp: u64) {
        self.sign = self.sign || exp.even();
        self.abs.pow_assign(exp);
    }
}