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
// 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::num::arithmetic::traits::{OverflowingPow, OverflowingPowAssign, Parity, UnsignedAbs};
use crate::num::basic::signeds::PrimitiveSigned;
use crate::num::basic::unsigneds::PrimitiveUnsigned;
use crate::num::conversion::traits::OverflowingFrom;
use crate::num::logic::traits::BitIterable;
fn overflowing_pow_unsigned<T: PrimitiveUnsigned>(x: T, exp: u64) -> (T, bool) {
if exp == 0 {
(T::ONE, false)
} else if x < T::TWO {
(x, false)
} else {
let (mut power, mut overflow) = (x, false);
for bit in exp.bits().rev().skip(1) {
overflow |= power.overflowing_square_assign();
if bit {
overflow |= power.overflowing_mul_assign(x);
}
}
(power, overflow)
}
}
fn overflowing_unsigned_to_signed_neg<
U: PrimitiveUnsigned,
S: OverflowingFrom<U> + PrimitiveSigned,
>(
x: U,
) -> (S, bool) {
let (signed_x, overflow) = S::overflowing_from(x);
if signed_x == S::MIN {
(signed_x, false)
} else {
(signed_x.wrapping_neg(), overflow)
}
}
fn overflowing_pow_signed<
U: PrimitiveUnsigned,
S: OverflowingFrom<U> + PrimitiveSigned + UnsignedAbs<Output = U>,
>(
x: S,
exp: u64,
) -> (S, bool) {
let (p_abs, overflow) = OverflowingPow::overflowing_pow(x.unsigned_abs(), exp);
let (p, overflow_2) = if x >= S::ZERO || exp.even() {
S::overflowing_from(p_abs)
} else {
overflowing_unsigned_to_signed_neg(p_abs)
};
(p, overflow || overflow_2)
}
macro_rules! impl_overflowing_pow_unsigned {
($t:ident) => {
impl OverflowingPow<u64> for $t {
type Output = $t;
/// This is a wrapper over the `overflowing_pow` functions in the standard library, for
/// example [this one](u32::overflowing_pow).
#[inline]
fn overflowing_pow(self, exp: u64) -> ($t, bool) {
overflowing_pow_unsigned(self, exp)
}
}
};
}
apply_to_unsigneds!(impl_overflowing_pow_unsigned);
macro_rules! impl_overflowing_pow_signed {
($t:ident) => {
impl OverflowingPow<u64> for $t {
type Output = $t;
/// This is a wrapper over the `overflowing_pow` functions in the standard library, for
/// example [this one](i32::overflowing_pow).
#[inline]
fn overflowing_pow(self, exp: u64) -> ($t, bool) {
overflowing_pow_signed(self, exp)
}
}
};
}
apply_to_signeds!(impl_overflowing_pow_signed);
macro_rules! impl_overflowing_pow_primitive_int {
($t:ident) => {
impl OverflowingPowAssign<u64> for $t {
/// Raises a number to a power, in place.
///
/// Returns a boolean indicating whether an arithmetic overflow occurred. If an overflow
/// occurred, then the wrapped value is assigned.
///
/// # Worst-case complexity
/// $T(n) = O(n)$
///
/// $M(n) = O(1)$
///
/// where $T$ is time, $M$ is additional memory, and $n$ is `exp.significant_bits()`.
/// The square-and-multiply ladder performs one or two multiplications per exponent bit.
///
/// # Examples
/// See [here](super::overflowing_pow#overflowing_pow_assign).
#[inline]
fn overflowing_pow_assign(&mut self, exp: u64) -> bool {
let overflow;
(*self, overflow) = OverflowingPow::overflowing_pow(*self, exp);
overflow
}
}
};
}
apply_to_primitive_ints!(impl_overflowing_pow_primitive_int);