malachite_base/num/arithmetic/
saturating_pow.rs

1// Copyright © 2025 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::num::arithmetic::traits::{Parity, SaturatingPow, SaturatingPowAssign};
10use crate::num::basic::signeds::PrimitiveSigned;
11use crate::num::basic::unsigneds::PrimitiveUnsigned;
12
13fn saturating_pow_unsigned<T: PrimitiveUnsigned>(x: T, exp: u64) -> T {
14    if exp == 0 {
15        T::ONE
16    } else if x < T::TWO {
17        x
18    } else if let Some(p) = x.checked_pow(exp) {
19        p
20    } else {
21        T::MAX
22    }
23}
24
25fn saturating_pow_signed<T: PrimitiveSigned>(x: T, exp: u64) -> T {
26    if exp == 0 {
27        T::ONE
28    } else if x == T::ZERO || x == T::ONE {
29        x
30    } else if x == T::NEGATIVE_ONE {
31        if exp.even() { T::ONE } else { T::NEGATIVE_ONE }
32    } else if let Some(p) = x.checked_pow(exp) {
33        p
34    } else if x > T::ZERO || exp.even() {
35        T::MAX
36    } else {
37        T::MIN
38    }
39}
40
41macro_rules! impl_saturating_pow_unsigned {
42    ($t:ident) => {
43        impl SaturatingPow<u64> for $t {
44            type Output = $t;
45
46            /// This is a wrapper over the `saturating_pow` functions in the standard library, for
47            /// example [this one](u32::saturating_pow).
48            #[inline]
49            fn saturating_pow(self, exp: u64) -> $t {
50                saturating_pow_unsigned(self, exp)
51            }
52        }
53    };
54}
55apply_to_unsigneds!(impl_saturating_pow_unsigned);
56
57macro_rules! impl_saturating_pow_signed {
58    ($t:ident) => {
59        impl SaturatingPow<u64> for $t {
60            type Output = $t;
61
62            /// This is a wrapper over the `saturating_pow` functions in the standard library, for
63            /// example [this one](i32::saturating_pow).
64            #[inline]
65            fn saturating_pow(self, exp: u64) -> $t {
66                saturating_pow_signed(self, exp)
67            }
68        }
69    };
70}
71apply_to_signeds!(impl_saturating_pow_signed);
72
73macro_rules! impl_saturating_pow_primitive_int {
74    ($t:ident) => {
75        impl SaturatingPowAssign<u64> for $t {
76            /// Raises a number to a power, in place, saturating at the numeric bounds instead of
77            /// overflowing.
78            ///
79            /// $$
80            /// x \gets \\begin{cases}
81            ///     x^y & \text{if} \\quad m \leq x^y \leq M, \\\\
82            ///     M & \text{if} \\quad x^y > M, \\\\
83            ///     m & \text{if} \\quad x^y < m,
84            /// \\end{cases}
85            /// $$
86            /// where $m$ is `Self::MIN` and $M$ is `Self::MAX`.
87            ///
88            /// # Worst-case complexity
89            /// Constant time and additional memory.
90            ///
91            /// # Examples
92            /// See [here](super::saturating_pow#saturating_pow_assign).
93            #[inline]
94            fn saturating_pow_assign(&mut self, exp: u64) {
95                *self = SaturatingPow::saturating_pow(*self, exp);
96            }
97        }
98    };
99}
100apply_to_primitive_ints!(impl_saturating_pow_primitive_int);
malachite_base/num/arithmetic/saturating_pow.rs

malachite_base/num/arithmetic/
saturating_pow.rs
