<!DOCTYPE html><html lang="en"><head><meta charset="utf-8"><meta name="viewport" content="width=device-width, initial-scale=1.0"><meta name="generator" content="rustdoc"><meta name="description" content="Source of the Rust file `/Users/m018/.cargo/registry/src/github.com-1ecc6299db9ec823/num-traits-0.2.16/src/pow.rs`."><title>pow.rs - source</title><link rel="preload" as="font" type="font/woff2" crossorigin href="../../static.files/SourceSerif4-Regular-46f98efaafac5295.ttf.woff2"><link rel="preload" as="font" type="font/woff2" crossorigin href="../../static.files/FiraSans-Regular-018c141bf0843ffd.woff2"><link rel="preload" as="font" type="font/woff2" crossorigin href="../../static.files/FiraSans-Medium-8f9a781e4970d388.woff2"><link rel="preload" as="font" type="font/woff2" crossorigin href="../../static.files/SourceCodePro-Regular-562dcc5011b6de7d.ttf.woff2"><link rel="preload" as="font" type="font/woff2" crossorigin href="../../static.files/SourceSerif4-Bold-a2c9cd1067f8b328.ttf.woff2"><link rel="preload" as="font" type="font/woff2" crossorigin href="../../static.files/SourceCodePro-Semibold-d899c5a5c4aeb14a.ttf.woff2"><link rel="stylesheet" href="../../static.files/normalize-76eba96aa4d2e634.css"><link rel="stylesheet" href="../../static.files/rustdoc-c4dbdcde0fbd8430.css" id="mainThemeStyle"><link rel="stylesheet" id="themeStyle" href="../../static.files/light-db279b6232be9c13.css"><link rel="stylesheet" disabled href="../../static.files/dark-cf923f49f397b216.css"><link rel="stylesheet" disabled href="../../static.files/ayu-be46fdc453a55015.css"><script src="../../static.files/storage-3891ce972e3a2bf8.js"></script><script defer src="../../static.files/source-script-1b95b7cca98b26e5.js"></script><script defer src="../../source-files.js"></script><script defer src="../../static.files/main-98a684e84ae5b08b.js"></script><noscript><link rel="stylesheet" href="../../static.files/noscript-13285aec31fa243e.css"></noscript><link rel="alternate icon" type="image/png" href="../../static.files/favicon-16x16-8b506e7a72182f1c.png"><link rel="alternate icon" type="image/png" href="../../static.files/favicon-32x32-422f7d1d52889060.png"><link rel="icon" type="image/svg+xml" href="../../static.files/favicon-2c020d218678b618.svg"></head><body class="rustdoc source"><!--[if lte IE 11]><div class="warning">This old browser is unsupported and will most likely display funky things.</div><![endif]--><nav class="sidebar"></nav><main><nav class="sub"><a class="sub-logo-container" href="../../num_traits/index.html"><img class="rust-logo" src="../../static.files/rust-logo-151179464ae7ed46.svg" alt="logo"></a><form class="search-form"><span></span><input class="search-input" name="search" aria-label="Run search in the documentation" autocomplete="off" spellcheck="false" placeholder="Click or press ‘S’ to search, ‘?’ for more options…" type="search"><div id="help-button" title="help" tabindex="-1"><a href="../../help.html">?</a></div><div id="settings-menu" tabindex="-1"><a href="../../settings.html" title="settings"><img width="22" height="22" alt="Change settings" src="../../static.files/wheel-7b819b6101059cd0.svg"></a></div></form></nav><section id="main-content" class="content"><div class="example-wrap"><pre class="src-line-numbers"><a href="#1" id="1">1</a>
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</pre><pre class="rust"><code><span class="kw">use crate</span>::{CheckedMul, One};
<span class="kw">use </span>core::num::Wrapping;
<span class="kw">use </span>core::ops::Mul;
<span class="doccomment">/// Binary operator for raising a value to a power.
</span><span class="kw">pub trait </span>Pow<RHS> {
<span class="doccomment">/// The result after applying the operator.
</span><span class="kw">type </span>Output;
<span class="doccomment">/// Returns `self` to the power `rhs`.
///
/// # Examples
///
/// ```
/// use num_traits::Pow;
/// assert_eq!(Pow::pow(10u32, 2u32), 100);
/// ```
</span><span class="kw">fn </span>pow(<span class="self">self</span>, rhs: RHS) -> <span class="self">Self</span>::Output;
}
<span class="macro">macro_rules! </span>pow_impl {
(<span class="macro-nonterminal">$t</span>:ty) => {
<span class="macro">pow_impl!</span>(<span class="macro-nonterminal">$t</span>, u8);
<span class="macro">pow_impl!</span>(<span class="macro-nonterminal">$t</span>, usize);
<span class="comment">// FIXME: these should be possible
// pow_impl!($t, u16);
// pow_impl!($t, u32);
// pow_impl!($t, u64);
</span>};
(<span class="macro-nonterminal">$t</span>:ty, <span class="macro-nonterminal">$rhs</span>:ty) => {
<span class="macro">pow_impl!</span>(<span class="macro-nonterminal">$t</span>, <span class="macro-nonterminal">$rhs</span>, usize, pow);
};
(<span class="macro-nonterminal">$t</span>:ty, <span class="macro-nonterminal">$rhs</span>:ty, <span class="macro-nonterminal">$desired_rhs</span>:ty, <span class="macro-nonterminal">$method</span>:expr) => {
<span class="kw">impl </span>Pow<<span class="macro-nonterminal">$rhs</span>> <span class="kw">for </span><span class="macro-nonterminal">$t </span>{
<span class="kw">type </span>Output = <span class="macro-nonterminal">$t</span>;
<span class="attr">#[inline]
</span><span class="kw">fn </span>pow(<span class="self">self</span>, rhs: <span class="macro-nonterminal">$rhs</span>) -> <span class="macro-nonterminal">$t </span>{
(<span class="macro-nonterminal">$method</span>)(<span class="self">self</span>, <<span class="macro-nonterminal">$desired_rhs</span>>::from(rhs))
}
}
<span class="kw">impl</span><<span class="lifetime">'a</span>> Pow<<span class="kw-2">&</span><span class="lifetime">'a </span><span class="macro-nonterminal">$rhs</span>> <span class="kw">for </span><span class="macro-nonterminal">$t </span>{
<span class="kw">type </span>Output = <span class="macro-nonterminal">$t</span>;
<span class="attr">#[inline]
</span><span class="kw">fn </span>pow(<span class="self">self</span>, rhs: <span class="kw-2">&</span><span class="lifetime">'a </span><span class="macro-nonterminal">$rhs</span>) -> <span class="macro-nonterminal">$t </span>{
(<span class="macro-nonterminal">$method</span>)(<span class="self">self</span>, <<span class="macro-nonterminal">$desired_rhs</span>>::from(<span class="kw-2">*</span>rhs))
}
}
<span class="kw">impl</span><<span class="lifetime">'a</span>> Pow<<span class="macro-nonterminal">$rhs</span>> <span class="kw">for </span><span class="kw-2">&</span><span class="lifetime">'a </span><span class="macro-nonterminal">$t </span>{
<span class="kw">type </span>Output = <span class="macro-nonterminal">$t</span>;
<span class="attr">#[inline]
</span><span class="kw">fn </span>pow(<span class="self">self</span>, rhs: <span class="macro-nonterminal">$rhs</span>) -> <span class="macro-nonterminal">$t </span>{
(<span class="macro-nonterminal">$method</span>)(<span class="kw-2">*</span><span class="self">self</span>, <<span class="macro-nonterminal">$desired_rhs</span>>::from(rhs))
}
}
<span class="kw">impl</span><<span class="lifetime">'a</span>, <span class="lifetime">'b</span>> Pow<<span class="kw-2">&</span><span class="lifetime">'a </span><span class="macro-nonterminal">$rhs</span>> <span class="kw">for </span><span class="kw-2">&</span><span class="lifetime">'b </span><span class="macro-nonterminal">$t </span>{
<span class="kw">type </span>Output = <span class="macro-nonterminal">$t</span>;
<span class="attr">#[inline]
</span><span class="kw">fn </span>pow(<span class="self">self</span>, rhs: <span class="kw-2">&</span><span class="lifetime">'a </span><span class="macro-nonterminal">$rhs</span>) -> <span class="macro-nonterminal">$t </span>{
(<span class="macro-nonterminal">$method</span>)(<span class="kw-2">*</span><span class="self">self</span>, <<span class="macro-nonterminal">$desired_rhs</span>>::from(<span class="kw-2">*</span>rhs))
}
}
};
}
<span class="macro">pow_impl!</span>(u8, u8, u32, u8::pow);
<span class="macro">pow_impl!</span>(u8, u16, u32, u8::pow);
<span class="macro">pow_impl!</span>(u8, u32, u32, u8::pow);
<span class="macro">pow_impl!</span>(u8, usize);
<span class="macro">pow_impl!</span>(i8, u8, u32, i8::pow);
<span class="macro">pow_impl!</span>(i8, u16, u32, i8::pow);
<span class="macro">pow_impl!</span>(i8, u32, u32, i8::pow);
<span class="macro">pow_impl!</span>(i8, usize);
<span class="macro">pow_impl!</span>(u16, u8, u32, u16::pow);
<span class="macro">pow_impl!</span>(u16, u16, u32, u16::pow);
<span class="macro">pow_impl!</span>(u16, u32, u32, u16::pow);
<span class="macro">pow_impl!</span>(u16, usize);
<span class="macro">pow_impl!</span>(i16, u8, u32, i16::pow);
<span class="macro">pow_impl!</span>(i16, u16, u32, i16::pow);
<span class="macro">pow_impl!</span>(i16, u32, u32, i16::pow);
<span class="macro">pow_impl!</span>(i16, usize);
<span class="macro">pow_impl!</span>(u32, u8, u32, u32::pow);
<span class="macro">pow_impl!</span>(u32, u16, u32, u32::pow);
<span class="macro">pow_impl!</span>(u32, u32, u32, u32::pow);
<span class="macro">pow_impl!</span>(u32, usize);
<span class="macro">pow_impl!</span>(i32, u8, u32, i32::pow);
<span class="macro">pow_impl!</span>(i32, u16, u32, i32::pow);
<span class="macro">pow_impl!</span>(i32, u32, u32, i32::pow);
<span class="macro">pow_impl!</span>(i32, usize);
<span class="macro">pow_impl!</span>(u64, u8, u32, u64::pow);
<span class="macro">pow_impl!</span>(u64, u16, u32, u64::pow);
<span class="macro">pow_impl!</span>(u64, u32, u32, u64::pow);
<span class="macro">pow_impl!</span>(u64, usize);
<span class="macro">pow_impl!</span>(i64, u8, u32, i64::pow);
<span class="macro">pow_impl!</span>(i64, u16, u32, i64::pow);
<span class="macro">pow_impl!</span>(i64, u32, u32, i64::pow);
<span class="macro">pow_impl!</span>(i64, usize);
<span class="macro">pow_impl!</span>(u128, u8, u32, u128::pow);
<span class="macro">pow_impl!</span>(u128, u16, u32, u128::pow);
<span class="macro">pow_impl!</span>(u128, u32, u32, u128::pow);
<span class="macro">pow_impl!</span>(u128, usize);
<span class="macro">pow_impl!</span>(i128, u8, u32, i128::pow);
<span class="macro">pow_impl!</span>(i128, u16, u32, i128::pow);
<span class="macro">pow_impl!</span>(i128, u32, u32, i128::pow);
<span class="macro">pow_impl!</span>(i128, usize);
<span class="macro">pow_impl!</span>(usize, u8, u32, usize::pow);
<span class="macro">pow_impl!</span>(usize, u16, u32, usize::pow);
<span class="macro">pow_impl!</span>(usize, u32, u32, usize::pow);
<span class="macro">pow_impl!</span>(usize, usize);
<span class="macro">pow_impl!</span>(isize, u8, u32, isize::pow);
<span class="macro">pow_impl!</span>(isize, u16, u32, isize::pow);
<span class="macro">pow_impl!</span>(isize, u32, u32, isize::pow);
<span class="macro">pow_impl!</span>(isize, usize);
<span class="macro">pow_impl!</span>(Wrapping<u8>);
<span class="macro">pow_impl!</span>(Wrapping<i8>);
<span class="macro">pow_impl!</span>(Wrapping<u16>);
<span class="macro">pow_impl!</span>(Wrapping<i16>);
<span class="macro">pow_impl!</span>(Wrapping<u32>);
<span class="macro">pow_impl!</span>(Wrapping<i32>);
<span class="macro">pow_impl!</span>(Wrapping<u64>);
<span class="macro">pow_impl!</span>(Wrapping<i64>);
<span class="macro">pow_impl!</span>(Wrapping<u128>);
<span class="macro">pow_impl!</span>(Wrapping<i128>);
<span class="macro">pow_impl!</span>(Wrapping<usize>);
<span class="macro">pow_impl!</span>(Wrapping<isize>);
<span class="comment">// FIXME: these should be possible
// pow_impl!(u8, u64);
// pow_impl!(i16, u64);
// pow_impl!(i8, u64);
// pow_impl!(u16, u64);
// pow_impl!(u32, u64);
// pow_impl!(i32, u64);
// pow_impl!(u64, u64);
// pow_impl!(i64, u64);
// pow_impl!(usize, u64);
// pow_impl!(isize, u64);
</span><span class="attr">#[cfg(any(feature = <span class="string">"std"</span>, feature = <span class="string">"libm"</span>))]
</span><span class="kw">mod </span>float_impls {
<span class="kw">use </span><span class="kw">super</span>::Pow;
<span class="kw">use </span><span class="kw">crate</span>::Float;
<span class="macro">pow_impl!</span>(f32, i8, i32, <f32 <span class="kw">as </span>Float>::powi);
<span class="macro">pow_impl!</span>(f32, u8, i32, <f32 <span class="kw">as </span>Float>::powi);
<span class="macro">pow_impl!</span>(f32, i16, i32, <f32 <span class="kw">as </span>Float>::powi);
<span class="macro">pow_impl!</span>(f32, u16, i32, <f32 <span class="kw">as </span>Float>::powi);
<span class="macro">pow_impl!</span>(f32, i32, i32, <f32 <span class="kw">as </span>Float>::powi);
<span class="macro">pow_impl!</span>(f64, i8, i32, <f64 <span class="kw">as </span>Float>::powi);
<span class="macro">pow_impl!</span>(f64, u8, i32, <f64 <span class="kw">as </span>Float>::powi);
<span class="macro">pow_impl!</span>(f64, i16, i32, <f64 <span class="kw">as </span>Float>::powi);
<span class="macro">pow_impl!</span>(f64, u16, i32, <f64 <span class="kw">as </span>Float>::powi);
<span class="macro">pow_impl!</span>(f64, i32, i32, <f64 <span class="kw">as </span>Float>::powi);
<span class="macro">pow_impl!</span>(f32, f32, f32, <f32 <span class="kw">as </span>Float>::powf);
<span class="macro">pow_impl!</span>(f64, f32, f64, <f64 <span class="kw">as </span>Float>::powf);
<span class="macro">pow_impl!</span>(f64, f64, f64, <f64 <span class="kw">as </span>Float>::powf);
}
<span class="doccomment">/// Raises a value to the power of exp, using exponentiation by squaring.
///
/// Note that `0⁰` (`pow(0, 0)`) returns `1`. Mathematically this is undefined.
///
/// # Example
///
/// ```rust
/// use num_traits::pow;
///
/// assert_eq!(pow(2i8, 4), 16);
/// assert_eq!(pow(6u8, 3), 216);
/// assert_eq!(pow(0u8, 0), 1); // Be aware if this case affects you
/// ```
</span><span class="attr">#[inline]
</span><span class="kw">pub fn </span>pow<T: Clone + One + Mul<T, Output = T>>(<span class="kw-2">mut </span>base: T, <span class="kw-2">mut </span>exp: usize) -> T {
<span class="kw">if </span>exp == <span class="number">0 </span>{
<span class="kw">return </span>T::one();
}
<span class="kw">while </span>exp & <span class="number">1 </span>== <span class="number">0 </span>{
base = base.clone() * base;
exp >>= <span class="number">1</span>;
}
<span class="kw">if </span>exp == <span class="number">1 </span>{
<span class="kw">return </span>base;
}
<span class="kw">let </span><span class="kw-2">mut </span>acc = base.clone();
<span class="kw">while </span>exp > <span class="number">1 </span>{
exp >>= <span class="number">1</span>;
base = base.clone() * base;
<span class="kw">if </span>exp & <span class="number">1 </span>== <span class="number">1 </span>{
acc = acc * base.clone();
}
}
acc
}
<span class="doccomment">/// Raises a value to the power of exp, returning `None` if an overflow occurred.
///
/// Note that `0⁰` (`checked_pow(0, 0)`) returns `Some(1)`. Mathematically this is undefined.
///
/// Otherwise same as the `pow` function.
///
/// # Example
///
/// ```rust
/// use num_traits::checked_pow;
///
/// assert_eq!(checked_pow(2i8, 4), Some(16));
/// assert_eq!(checked_pow(7i8, 8), None);
/// assert_eq!(checked_pow(7u32, 8), Some(5_764_801));
/// assert_eq!(checked_pow(0u32, 0), Some(1)); // Be aware if this case affect you
/// ```
</span><span class="attr">#[inline]
</span><span class="kw">pub fn </span>checked_pow<T: Clone + One + CheckedMul>(<span class="kw-2">mut </span>base: T, <span class="kw-2">mut </span>exp: usize) -> <span class="prelude-ty">Option</span><T> {
<span class="kw">if </span>exp == <span class="number">0 </span>{
<span class="kw">return </span><span class="prelude-val">Some</span>(T::one());
}
<span class="kw">while </span>exp & <span class="number">1 </span>== <span class="number">0 </span>{
base = base.checked_mul(<span class="kw-2">&</span>base)<span class="question-mark">?</span>;
exp >>= <span class="number">1</span>;
}
<span class="kw">if </span>exp == <span class="number">1 </span>{
<span class="kw">return </span><span class="prelude-val">Some</span>(base);
}
<span class="kw">let </span><span class="kw-2">mut </span>acc = base.clone();
<span class="kw">while </span>exp > <span class="number">1 </span>{
exp >>= <span class="number">1</span>;
base = base.checked_mul(<span class="kw-2">&</span>base)<span class="question-mark">?</span>;
<span class="kw">if </span>exp & <span class="number">1 </span>== <span class="number">1 </span>{
acc = acc.checked_mul(<span class="kw-2">&</span>base)<span class="question-mark">?</span>;
}
}
<span class="prelude-val">Some</span>(acc)
}
</code></pre></div>
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