| <!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 `/root/.cargo/registry/src/github.com-1ecc6299db9ec823/num-integer-0.1.45/src/roots.rs`."><meta name="keywords" content="rust, rustlang, rust-lang"><title>roots.rs - source</title><link rel="preload" as="font" type="font/woff2" crossorigin href="../../SourceSerif4-Regular.ttf.woff2"><link rel="preload" as="font" type="font/woff2" crossorigin href="../../FiraSans-Regular.woff2"><link rel="preload" as="font" type="font/woff2" crossorigin href="../../FiraSans-Medium.woff2"><link rel="preload" as="font" type="font/woff2" crossorigin href="../../SourceCodePro-Regular.ttf.woff2"><link rel="preload" as="font" type="font/woff2" crossorigin href="../../SourceSerif4-Bold.ttf.woff2"><link rel="preload" as="font" type="font/woff2" crossorigin href="../../SourceCodePro-Semibold.ttf.woff2"><link rel="stylesheet" href="../../normalize.css"><link rel="stylesheet" href="../../rustdoc.css" id="mainThemeStyle"><link rel="stylesheet" href="../../ayu.css" disabled><link rel="stylesheet" href="../../dark.css" disabled><link rel="stylesheet" href="../../light.css" id="themeStyle"><script id="default-settings" ></script><script src="../../storage.js"></script><script defer src="../../source-script.js"></script><script defer src="../../source-files.js"></script><script defer src="../../main.js"></script><noscript><link rel="stylesheet" href="../../noscript.css"></noscript><link rel="alternate icon" type="image/png" href="../../favicon-16x16.png"><link rel="alternate icon" type="image/png" href="../../favicon-32x32.png"><link rel="icon" type="image/svg+xml" href="../../favicon.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"><a class="sidebar-logo" href="../../num_integer/index.html"><div class="logo-container"><img class="rust-logo" src="../../rust-logo.svg" alt="logo"></div></a></nav><main><div class="width-limiter"><nav class="sub"><a class="sub-logo-container" href="../../num_integer/index.html"><img class="rust-logo" src="../../rust-logo.svg" alt="logo"></a><form class="search-form"><div class="search-container"><span></span><input class="search-input" name="search" 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="../../wheel.svg"></a></div></div></form></nav><section id="main-content" class="content"><div class="example-wrap"><pre class="src-line-numbers"><span id="1">1</span> |
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| </pre><pre class="rust"><code><span class="kw">use </span>core; |
| <span class="kw">use </span>core::mem; |
| <span class="kw">use </span>traits::checked_pow; |
| <span class="kw">use </span>traits::PrimInt; |
| <span class="kw">use </span>Integer; |
| |
| <span class="doccomment">/// Provides methods to compute an integer's square root, cube root, |
| /// and arbitrary `n`th root. |
| </span><span class="kw">pub trait </span>Roots: Integer { |
| <span class="doccomment">/// Returns the truncated principal `n`th root of an integer |
| /// -- `if x >= 0 { ⌊ⁿ√x⌋ } else { ⌈ⁿ√x⌉ }` |
| /// |
| /// This is solving for `r` in `rⁿ = x`, rounding toward zero. |
| /// If `x` is positive, the result will satisfy `rⁿ ≤ x < (r+1)ⁿ`. |
| /// If `x` is negative and `n` is odd, then `(r-1)ⁿ < x ≤ rⁿ`. |
| /// |
| /// # Panics |
| /// |
| /// Panics if `n` is zero: |
| /// |
| /// ```should_panic |
| /// # use num_integer::Roots; |
| /// println!("can't compute ⁰√x : {}", 123.nth_root(0)); |
| /// ``` |
| /// |
| /// or if `n` is even and `self` is negative: |
| /// |
| /// ```should_panic |
| /// # use num_integer::Roots; |
| /// println!("no imaginary numbers... {}", (-1).nth_root(10)); |
| /// ``` |
| /// |
| /// # Examples |
| /// |
| /// ``` |
| /// use num_integer::Roots; |
| /// |
| /// let x: i32 = 12345; |
| /// assert_eq!(x.nth_root(1), x); |
| /// assert_eq!(x.nth_root(2), x.sqrt()); |
| /// assert_eq!(x.nth_root(3), x.cbrt()); |
| /// assert_eq!(x.nth_root(4), 10); |
| /// assert_eq!(x.nth_root(13), 2); |
| /// assert_eq!(x.nth_root(14), 1); |
| /// assert_eq!(x.nth_root(std::u32::MAX), 1); |
| /// |
| /// assert_eq!(std::i32::MAX.nth_root(30), 2); |
| /// assert_eq!(std::i32::MAX.nth_root(31), 1); |
| /// assert_eq!(std::i32::MIN.nth_root(31), -2); |
| /// assert_eq!((std::i32::MIN + 1).nth_root(31), -1); |
| /// |
| /// assert_eq!(std::u32::MAX.nth_root(31), 2); |
| /// assert_eq!(std::u32::MAX.nth_root(32), 1); |
| /// ``` |
| </span><span class="kw">fn </span>nth_root(<span class="kw-2">&</span><span class="self">self</span>, n: u32) -> <span class="self">Self</span>; |
| |
| <span class="doccomment">/// Returns the truncated principal square root of an integer -- `⌊√x⌋` |
| /// |
| /// This is solving for `r` in `r² = x`, rounding toward zero. |
| /// The result will satisfy `r² ≤ x < (r+1)²`. |
| /// |
| /// # Panics |
| /// |
| /// Panics if `self` is less than zero: |
| /// |
| /// ```should_panic |
| /// # use num_integer::Roots; |
| /// println!("no imaginary numbers... {}", (-1).sqrt()); |
| /// ``` |
| /// |
| /// # Examples |
| /// |
| /// ``` |
| /// use num_integer::Roots; |
| /// |
| /// let x: i32 = 12345; |
| /// assert_eq!((x * x).sqrt(), x); |
| /// assert_eq!((x * x + 1).sqrt(), x); |
| /// assert_eq!((x * x - 1).sqrt(), x - 1); |
| /// ``` |
| </span><span class="attribute">#[inline] |
| </span><span class="kw">fn </span>sqrt(<span class="kw-2">&</span><span class="self">self</span>) -> <span class="self">Self </span>{ |
| <span class="self">self</span>.nth_root(<span class="number">2</span>) |
| } |
| |
| <span class="doccomment">/// Returns the truncated principal cube root of an integer -- |
| /// `if x >= 0 { ⌊∛x⌋ } else { ⌈∛x⌉ }` |
| /// |
| /// This is solving for `r` in `r³ = x`, rounding toward zero. |
| /// If `x` is positive, the result will satisfy `r³ ≤ x < (r+1)³`. |
| /// If `x` is negative, then `(r-1)³ < x ≤ r³`. |
| /// |
| /// # Examples |
| /// |
| /// ``` |
| /// use num_integer::Roots; |
| /// |
| /// let x: i32 = 1234; |
| /// assert_eq!((x * x * x).cbrt(), x); |
| /// assert_eq!((x * x * x + 1).cbrt(), x); |
| /// assert_eq!((x * x * x - 1).cbrt(), x - 1); |
| /// |
| /// assert_eq!((-(x * x * x)).cbrt(), -x); |
| /// assert_eq!((-(x * x * x + 1)).cbrt(), -x); |
| /// assert_eq!((-(x * x * x - 1)).cbrt(), -(x - 1)); |
| /// ``` |
| </span><span class="attribute">#[inline] |
| </span><span class="kw">fn </span>cbrt(<span class="kw-2">&</span><span class="self">self</span>) -> <span class="self">Self </span>{ |
| <span class="self">self</span>.nth_root(<span class="number">3</span>) |
| } |
| } |
| |
| <span class="doccomment">/// Returns the truncated principal square root of an integer -- |
| /// see [Roots::sqrt](trait.Roots.html#method.sqrt). |
| </span><span class="attribute">#[inline] |
| </span><span class="kw">pub fn </span>sqrt<T: Roots>(x: T) -> T { |
| x.sqrt() |
| } |
| |
| <span class="doccomment">/// Returns the truncated principal cube root of an integer -- |
| /// see [Roots::cbrt](trait.Roots.html#method.cbrt). |
| </span><span class="attribute">#[inline] |
| </span><span class="kw">pub fn </span>cbrt<T: Roots>(x: T) -> T { |
| x.cbrt() |
| } |
| |
| <span class="doccomment">/// Returns the truncated principal `n`th root of an integer -- |
| /// see [Roots::nth_root](trait.Roots.html#tymethod.nth_root). |
| </span><span class="attribute">#[inline] |
| </span><span class="kw">pub fn </span>nth_root<T: Roots>(x: T, n: u32) -> T { |
| x.nth_root(n) |
| } |
| |
| <span class="macro">macro_rules! </span>signed_roots { |
| (<span class="macro-nonterminal">$T</span>:ty, <span class="macro-nonterminal">$U</span>:ty) => { |
| <span class="kw">impl </span>Roots <span class="kw">for </span><span class="macro-nonterminal">$T </span>{ |
| <span class="attribute">#[inline] |
| </span><span class="kw">fn </span>nth_root(<span class="kw-2">&</span><span class="self">self</span>, n: u32) -> <span class="self">Self </span>{ |
| <span class="kw">if </span><span class="kw-2">*</span><span class="self">self </span>>= <span class="number">0 </span>{ |
| (<span class="kw-2">*</span><span class="self">self </span><span class="kw">as </span><span class="macro-nonterminal">$U</span>).nth_root(n) <span class="kw">as </span><span class="self">Self |
| </span>} <span class="kw">else </span>{ |
| <span class="macro">assert!</span>(n.is_odd(), <span class="string">"even roots of a negative are imaginary"</span>); |
| -((<span class="self">self</span>.wrapping_neg() <span class="kw">as </span><span class="macro-nonterminal">$U</span>).nth_root(n) <span class="kw">as </span><span class="self">Self</span>) |
| } |
| } |
| |
| <span class="attribute">#[inline] |
| </span><span class="kw">fn </span>sqrt(<span class="kw-2">&</span><span class="self">self</span>) -> <span class="self">Self </span>{ |
| <span class="macro">assert!</span>(<span class="kw-2">*</span><span class="self">self </span>>= <span class="number">0</span>, <span class="string">"the square root of a negative is imaginary"</span>); |
| (<span class="kw-2">*</span><span class="self">self </span><span class="kw">as </span><span class="macro-nonterminal">$U</span>).sqrt() <span class="kw">as </span><span class="self">Self |
| </span>} |
| |
| <span class="attribute">#[inline] |
| </span><span class="kw">fn </span>cbrt(<span class="kw-2">&</span><span class="self">self</span>) -> <span class="self">Self </span>{ |
| <span class="kw">if </span><span class="kw-2">*</span><span class="self">self </span>>= <span class="number">0 </span>{ |
| (<span class="kw-2">*</span><span class="self">self </span><span class="kw">as </span><span class="macro-nonterminal">$U</span>).cbrt() <span class="kw">as </span><span class="self">Self |
| </span>} <span class="kw">else </span>{ |
| -((<span class="self">self</span>.wrapping_neg() <span class="kw">as </span><span class="macro-nonterminal">$U</span>).cbrt() <span class="kw">as </span><span class="self">Self</span>) |
| } |
| } |
| } |
| }; |
| } |
| |
| <span class="macro">signed_roots!</span>(i8, u8); |
| <span class="macro">signed_roots!</span>(i16, u16); |
| <span class="macro">signed_roots!</span>(i32, u32); |
| <span class="macro">signed_roots!</span>(i64, u64); |
| <span class="attribute">#[cfg(has_i128)] |
| </span><span class="macro">signed_roots!</span>(i128, u128); |
| <span class="macro">signed_roots!</span>(isize, usize); |
| |
| <span class="attribute">#[inline] |
| </span><span class="kw">fn </span>fixpoint<T, F>(<span class="kw-2">mut </span>x: T, f: F) -> T |
| <span class="kw">where |
| </span>T: Integer + Copy, |
| F: Fn(T) -> T, |
| { |
| <span class="kw">let </span><span class="kw-2">mut </span>xn = f(x); |
| <span class="kw">while </span>x < xn { |
| x = xn; |
| xn = f(x); |
| } |
| <span class="kw">while </span>x > xn { |
| x = xn; |
| xn = f(x); |
| } |
| x |
| } |
| |
| <span class="attribute">#[inline] |
| </span><span class="kw">fn </span>bits<T>() -> u32 { |
| <span class="number">8 </span>* mem::size_of::<T>() <span class="kw">as </span>u32 |
| } |
| |
| <span class="attribute">#[inline] |
| </span><span class="kw">fn </span>log2<T: PrimInt>(x: T) -> u32 { |
| <span class="macro">debug_assert!</span>(x > T::zero()); |
| bits::<T>() - <span class="number">1 </span>- x.leading_zeros() |
| } |
| |
| <span class="macro">macro_rules! </span>unsigned_roots { |
| (<span class="macro-nonterminal">$T</span>:ident) => { |
| <span class="kw">impl </span>Roots <span class="kw">for </span><span class="macro-nonterminal">$T </span>{ |
| <span class="attribute">#[inline] |
| </span><span class="kw">fn </span>nth_root(<span class="kw-2">&</span><span class="self">self</span>, n: u32) -> <span class="self">Self </span>{ |
| <span class="kw">fn </span>go(a: <span class="macro-nonterminal">$T</span>, n: u32) -> <span class="macro-nonterminal">$T </span>{ |
| <span class="comment">// Specialize small roots |
| </span><span class="kw">match </span>n { |
| <span class="number">0 </span>=> <span class="macro">panic!</span>(<span class="string">"can't find a root of degree 0!"</span>), |
| <span class="number">1 </span>=> <span class="kw">return </span>a, |
| <span class="number">2 </span>=> <span class="kw">return </span>a.sqrt(), |
| <span class="number">3 </span>=> <span class="kw">return </span>a.cbrt(), |
| <span class="kw">_ </span>=> (), |
| } |
| |
| <span class="comment">// The root of values less than 2ⁿ can only be 0 or 1. |
| </span><span class="kw">if </span>bits::<<span class="macro-nonterminal">$T</span>>() <= n || a < (<span class="number">1 </span><< n) { |
| <span class="kw">return </span>(a > <span class="number">0</span>) <span class="kw">as </span><span class="macro-nonterminal">$T</span>; |
| } |
| |
| <span class="kw">if </span>bits::<<span class="macro-nonterminal">$T</span>>() > <span class="number">64 </span>{ |
| <span class="comment">// 128-bit division is slow, so do a bitwise `nth_root` until it's small enough. |
| </span><span class="kw">return if </span>a <= core::u64::MAX <span class="kw">as </span><span class="macro-nonterminal">$T </span>{ |
| (a <span class="kw">as </span>u64).nth_root(n) <span class="kw">as </span><span class="macro-nonterminal">$T |
| </span>} <span class="kw">else </span>{ |
| <span class="kw">let </span>lo = (a >> n).nth_root(n) << <span class="number">1</span>; |
| <span class="kw">let </span>hi = lo + <span class="number">1</span>; |
| <span class="comment">// 128-bit `checked_mul` also involves division, but we can't always |
| // compute `hiⁿ` without risking overflow. Try to avoid it though... |
| </span><span class="kw">if </span>hi.next_power_of_two().trailing_zeros() * n >= bits::<<span class="macro-nonterminal">$T</span>>() { |
| <span class="kw">match </span>checked_pow(hi, n <span class="kw">as </span>usize) { |
| <span class="prelude-val">Some</span>(x) <span class="kw">if </span>x <= a => hi, |
| <span class="kw">_ </span>=> lo, |
| } |
| } <span class="kw">else </span>{ |
| <span class="kw">if </span>hi.pow(n) <= a { |
| hi |
| } <span class="kw">else </span>{ |
| lo |
| } |
| } |
| }; |
| } |
| |
| <span class="attribute">#[cfg(feature = <span class="string">"std"</span>)] |
| #[inline] |
| </span><span class="kw">fn </span>guess(x: <span class="macro-nonterminal">$T</span>, n: u32) -> <span class="macro-nonterminal">$T </span>{ |
| <span class="comment">// for smaller inputs, `f64` doesn't justify its cost. |
| </span><span class="kw">if </span>bits::<<span class="macro-nonterminal">$T</span>>() <= <span class="number">32 </span>|| x <= core::u32::MAX <span class="kw">as </span><span class="macro-nonterminal">$T </span>{ |
| <span class="number">1 </span><< ((log2(x) + n - <span class="number">1</span>) / n) |
| } <span class="kw">else </span>{ |
| ((x <span class="kw">as </span>f64).ln() / f64::from(n)).exp() <span class="kw">as </span><span class="macro-nonterminal">$T |
| </span>} |
| } |
| |
| <span class="attribute">#[cfg(not(feature = <span class="string">"std"</span>))] |
| #[inline] |
| </span><span class="kw">fn </span>guess(x: <span class="macro-nonterminal">$T</span>, n: u32) -> <span class="macro-nonterminal">$T </span>{ |
| <span class="number">1 </span><< ((log2(x) + n - <span class="number">1</span>) / n) |
| } |
| |
| <span class="comment">// https://en.wikipedia.org/wiki/Nth_root_algorithm |
| </span><span class="kw">let </span>n1 = n - <span class="number">1</span>; |
| <span class="kw">let </span>next = |x: <span class="macro-nonterminal">$T</span>| { |
| <span class="kw">let </span>y = <span class="kw">match </span>checked_pow(x, n1 <span class="kw">as </span>usize) { |
| <span class="prelude-val">Some</span>(ax) => a / ax, |
| <span class="prelude-val">None </span>=> <span class="number">0</span>, |
| }; |
| (y + x * n1 <span class="kw">as </span><span class="macro-nonterminal">$T</span>) / n <span class="kw">as </span><span class="macro-nonterminal">$T |
| </span>}; |
| fixpoint(guess(a, n), next) |
| } |
| go(<span class="kw-2">*</span><span class="self">self</span>, n) |
| } |
| |
| <span class="attribute">#[inline] |
| </span><span class="kw">fn </span>sqrt(<span class="kw-2">&</span><span class="self">self</span>) -> <span class="self">Self </span>{ |
| <span class="kw">fn </span>go(a: <span class="macro-nonterminal">$T</span>) -> <span class="macro-nonterminal">$T </span>{ |
| <span class="kw">if </span>bits::<<span class="macro-nonterminal">$T</span>>() > <span class="number">64 </span>{ |
| <span class="comment">// 128-bit division is slow, so do a bitwise `sqrt` until it's small enough. |
| </span><span class="kw">return if </span>a <= core::u64::MAX <span class="kw">as </span><span class="macro-nonterminal">$T </span>{ |
| (a <span class="kw">as </span>u64).sqrt() <span class="kw">as </span><span class="macro-nonterminal">$T |
| </span>} <span class="kw">else </span>{ |
| <span class="kw">let </span>lo = (a >> <span class="number">2u32</span>).sqrt() << <span class="number">1</span>; |
| <span class="kw">let </span>hi = lo + <span class="number">1</span>; |
| <span class="kw">if </span>hi * hi <= a { |
| hi |
| } <span class="kw">else </span>{ |
| lo |
| } |
| }; |
| } |
| |
| <span class="kw">if </span>a < <span class="number">4 </span>{ |
| <span class="kw">return </span>(a > <span class="number">0</span>) <span class="kw">as </span><span class="macro-nonterminal">$T</span>; |
| } |
| |
| <span class="attribute">#[cfg(feature = <span class="string">"std"</span>)] |
| #[inline] |
| </span><span class="kw">fn </span>guess(x: <span class="macro-nonterminal">$T</span>) -> <span class="macro-nonterminal">$T </span>{ |
| (x <span class="kw">as </span>f64).sqrt() <span class="kw">as </span><span class="macro-nonterminal">$T |
| </span>} |
| |
| <span class="attribute">#[cfg(not(feature = <span class="string">"std"</span>))] |
| #[inline] |
| </span><span class="kw">fn </span>guess(x: <span class="macro-nonterminal">$T</span>) -> <span class="macro-nonterminal">$T </span>{ |
| <span class="number">1 </span><< ((log2(x) + <span class="number">1</span>) / <span class="number">2</span>) |
| } |
| |
| <span class="comment">// https://en.wikipedia.org/wiki/Methods_of_computing_square_roots#Babylonian_method |
| </span><span class="kw">let </span>next = |x: <span class="macro-nonterminal">$T</span>| (a / x + x) >> <span class="number">1</span>; |
| fixpoint(guess(a), next) |
| } |
| go(<span class="kw-2">*</span><span class="self">self</span>) |
| } |
| |
| <span class="attribute">#[inline] |
| </span><span class="kw">fn </span>cbrt(<span class="kw-2">&</span><span class="self">self</span>) -> <span class="self">Self </span>{ |
| <span class="kw">fn </span>go(a: <span class="macro-nonterminal">$T</span>) -> <span class="macro-nonterminal">$T </span>{ |
| <span class="kw">if </span>bits::<<span class="macro-nonterminal">$T</span>>() > <span class="number">64 </span>{ |
| <span class="comment">// 128-bit division is slow, so do a bitwise `cbrt` until it's small enough. |
| </span><span class="kw">return if </span>a <= core::u64::MAX <span class="kw">as </span><span class="macro-nonterminal">$T </span>{ |
| (a <span class="kw">as </span>u64).cbrt() <span class="kw">as </span><span class="macro-nonterminal">$T |
| </span>} <span class="kw">else </span>{ |
| <span class="kw">let </span>lo = (a >> <span class="number">3u32</span>).cbrt() << <span class="number">1</span>; |
| <span class="kw">let </span>hi = lo + <span class="number">1</span>; |
| <span class="kw">if </span>hi * hi * hi <= a { |
| hi |
| } <span class="kw">else </span>{ |
| lo |
| } |
| }; |
| } |
| |
| <span class="kw">if </span>bits::<<span class="macro-nonterminal">$T</span>>() <= <span class="number">32 </span>{ |
| <span class="comment">// Implementation based on Hacker's Delight `icbrt2` |
| </span><span class="kw">let </span><span class="kw-2">mut </span>x = a; |
| <span class="kw">let </span><span class="kw-2">mut </span>y2 = <span class="number">0</span>; |
| <span class="kw">let </span><span class="kw-2">mut </span>y = <span class="number">0</span>; |
| <span class="kw">let </span>smax = bits::<<span class="macro-nonterminal">$T</span>>() / <span class="number">3</span>; |
| <span class="kw">for </span>s <span class="kw">in </span>(<span class="number">0</span>..smax + <span class="number">1</span>).rev() { |
| <span class="kw">let </span>s = s * <span class="number">3</span>; |
| y2 <span class="kw-2">*</span>= <span class="number">4</span>; |
| y <span class="kw-2">*</span>= <span class="number">2</span>; |
| <span class="kw">let </span>b = <span class="number">3 </span>* (y2 + y) + <span class="number">1</span>; |
| <span class="kw">if </span>x >> s >= b { |
| x -= b << s; |
| y2 += <span class="number">2 </span>* y + <span class="number">1</span>; |
| y += <span class="number">1</span>; |
| } |
| } |
| <span class="kw">return </span>y; |
| } |
| |
| <span class="kw">if </span>a < <span class="number">8 </span>{ |
| <span class="kw">return </span>(a > <span class="number">0</span>) <span class="kw">as </span><span class="macro-nonterminal">$T</span>; |
| } |
| <span class="kw">if </span>a <= core::u32::MAX <span class="kw">as </span><span class="macro-nonterminal">$T </span>{ |
| <span class="kw">return </span>(a <span class="kw">as </span>u32).cbrt() <span class="kw">as </span><span class="macro-nonterminal">$T</span>; |
| } |
| |
| <span class="attribute">#[cfg(feature = <span class="string">"std"</span>)] |
| #[inline] |
| </span><span class="kw">fn </span>guess(x: <span class="macro-nonterminal">$T</span>) -> <span class="macro-nonterminal">$T </span>{ |
| (x <span class="kw">as </span>f64).cbrt() <span class="kw">as </span><span class="macro-nonterminal">$T |
| </span>} |
| |
| <span class="attribute">#[cfg(not(feature = <span class="string">"std"</span>))] |
| #[inline] |
| </span><span class="kw">fn </span>guess(x: <span class="macro-nonterminal">$T</span>) -> <span class="macro-nonterminal">$T </span>{ |
| <span class="number">1 </span><< ((log2(x) + <span class="number">2</span>) / <span class="number">3</span>) |
| } |
| |
| <span class="comment">// https://en.wikipedia.org/wiki/Cube_root#Numerical_methods |
| </span><span class="kw">let </span>next = |x: <span class="macro-nonterminal">$T</span>| (a / (x * x) + x * <span class="number">2</span>) / <span class="number">3</span>; |
| fixpoint(guess(a), next) |
| } |
| go(<span class="kw-2">*</span><span class="self">self</span>) |
| } |
| } |
| }; |
| } |
| |
| <span class="macro">unsigned_roots!</span>(u8); |
| <span class="macro">unsigned_roots!</span>(u16); |
| <span class="macro">unsigned_roots!</span>(u32); |
| <span class="macro">unsigned_roots!</span>(u64); |
| <span class="attribute">#[cfg(has_i128)] |
| </span><span class="macro">unsigned_roots!</span>(u128); |
| <span class="macro">unsigned_roots!</span>(usize); |
| </code></pre></div> |
| </section></div></main><div id="rustdoc-vars" data-root-path="../../" data-current-crate="num_integer" data-themes="ayu,dark,light" data-resource-suffix="" data-rustdoc-version="1.66.0-nightly (5c8bff74b 2022-10-21)" ></div></body></html> |
