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<!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="API documentation for the Rust `Roots` trait in crate `num_integer`."><meta name="keywords" content="rust, rustlang, rust-lang, Roots"><title>num_integer::Roots - Rust</title><link rel="stylesheet" type="text/css" href="../normalize.css"><link rel="stylesheet" type="text/css" href="../rustdoc.css" id="mainThemeStyle"><link rel="stylesheet" type="text/css" href="../dark.css"><link rel="stylesheet" type="text/css" href="../light.css" id="themeStyle"><script src="../storage.js"></script><noscript><link rel="stylesheet" href="../noscript.css"></noscript><link rel="shortcut icon" href="../favicon.ico"><style type="text/css">#crate-search{background-image:url("../down-arrow.svg");}</style></head><body class="rustdoc trait"><!--[if lte IE 8]><div class="warning">This old browser is unsupported and will most likely display funky things.</div><![endif]--><nav class="sidebar"><div class="sidebar-menu">&#9776;</div><a href='../num_integer/index.html'><div class='logo-container'><img src='../rust-logo.png' alt='logo'></div></a><p class='location'>Trait Roots</p><div class="sidebar-elems"><div class="block items"><a class="sidebar-title" href="#required-methods">Required Methods</a><div class="sidebar-links"><a href="#tymethod.nth_root">nth_root</a></div><a class="sidebar-title" href="#provided-methods">Provided Methods</a><div class="sidebar-links"><a href="#method.cbrt">cbrt</a><a href="#method.sqrt">sqrt</a></div><a class="sidebar-title" href="#foreign-impls">Implementations on Foreign Types</a><div class="sidebar-links"><a href="#impl-Roots-for-i128">i128</a><a href="#impl-Roots-for-i16">i16</a><a href="#impl-Roots-for-i32">i32</a><a href="#impl-Roots-for-i64">i64</a><a href="#impl-Roots-for-i8">i8</a><a href="#impl-Roots-for-isize">isize</a><a href="#impl-Roots-for-u128">u128</a><a href="#impl-Roots-for-u16">u16</a><a href="#impl-Roots-for-u32">u32</a><a href="#impl-Roots-for-u64">u64</a><a href="#impl-Roots-for-u8">u8</a><a href="#impl-Roots-for-usize">usize</a></div><a class="sidebar-title" href="#implementors">Implementors</a></div><p class='location'><a href='index.html'>num_integer</a></p><script>window.sidebarCurrent = {name: 'Roots', ty: 'trait', relpath: ''};</script><script defer src="sidebar-items.js"></script></div></nav><div class="theme-picker"><button id="theme-picker" aria-label="Pick another theme!"><img src="../brush.svg" width="18" alt="Pick another theme!"></button><div id="theme-choices"></div></div><script src="../theme.js"></script><nav class="sub"><form class="search-form js-only"><div class="search-container"><div><select id="crate-search"><option value="All crates">All crates</option></select><input class="search-input" name="search" autocomplete="off" spellcheck="false" placeholder="Click or press ‘S’ to search, ‘?’ for more options…" type="search"></div><a id="settings-menu" href="../settings.html"><img src="../wheel.svg" width="18" alt="Change settings"></a></div></form></nav><section id="main" class="content"><h1 class='fqn'><span class='out-of-band'><span id='render-detail'><a id="toggle-all-docs" href="javascript:void(0)" title="collapse all docs">[<span class='inner'>&#x2212;</span>]</a></span><a class='srclink' href='../src/num_integer/roots.rs.html#9-111' title='goto source code'>[src]</a></span><span class='in-band'>Trait <a href='index.html'>num_integer</a>::<wbr><a class="trait" href=''>Roots</a></span></h1><div class="docblock type-decl hidden-by-usual-hider"><pre class='rust trait'>pub trait Roots: <a class="trait" href="../num_integer/trait.Integer.html" title="trait num_integer::Integer">Integer</a> {
fn <a href='#tymethod.nth_root' class='fnname'>nth_root</a>(&amp;self, n: <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.u32.html">u32</a>) -&gt; Self;
fn <a href='#method.sqrt' class='fnname'>sqrt</a>(&amp;self) -&gt; Self { ... }
<div class='item-spacer'></div> fn <a href='#method.cbrt' class='fnname'>cbrt</a>(&amp;self) -&gt; Self { ... }
}</pre></div><div class='docblock'><p>Provides methods to compute an integer's square root, cube root,
and arbitrary <code>n</code>th root.</p>
</div>
<h2 id='required-methods' class='small-section-header'>Required methods<a href='#required-methods' class='anchor'></a></h2><div class='methods'><h3 id='tymethod.nth_root' class='method'><code id='nth_root.v'>fn <a href='#tymethod.nth_root' class='fnname'>nth_root</a>(&amp;self, n: <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.u32.html">u32</a>) -&gt; Self</code></h3><div class='docblock'><p>Returns the truncated principal <code>n</code>th root of an integer
-- <code>if x &gt;= 0 { ⌊ⁿ√x⌋ } else { ⌈ⁿ√x⌉ }</code></p>
<p>This is solving for <code>r</code> in <code>rⁿ = x</code>, rounding toward zero.
If <code>x</code> is positive, the result will satisfy <code>rⁿ ≤ x &lt; (r+1)ⁿ</code>.
If <code>x</code> is negative and <code>n</code> is odd, then <code>(r-1)ⁿ &lt; x ≤ rⁿ</code>.</p>
<h1 id="panics" class="section-header"><a href="#panics">Panics</a></h1>
<p>Panics if <code>n</code> is zero:</p>
<div class="example-wrap"><pre class="rust rust-example-rendered">
<span class="macro">println</span><span class="macro">!</span>(<span class="string">&quot;can&#39;t compute ⁰√x : {}&quot;</span>, <span class="number">123</span>.<span class="ident">nth_root</span>(<span class="number">0</span>));</pre></div>
<p>or if <code>n</code> is even and <code>self</code> is negative:</p>
<div class="example-wrap"><pre class="rust rust-example-rendered">
<span class="macro">println</span><span class="macro">!</span>(<span class="string">&quot;no imaginary numbers... {}&quot;</span>, (<span class="op">-</span><span class="number">1</span>).<span class="ident">nth_root</span>(<span class="number">10</span>));</pre></div>
<h1 id="examples" class="section-header"><a href="#examples">Examples</a></h1>
<div class="example-wrap"><pre class="rust rust-example-rendered">
<span class="kw">use</span> <span class="ident">num_integer</span>::<span class="ident">Roots</span>;
<span class="kw">let</span> <span class="ident">x</span>: <span class="ident">i32</span> <span class="op">=</span> <span class="number">12345</span>;
<span class="macro">assert_eq</span><span class="macro">!</span>(<span class="ident">x</span>.<span class="ident">nth_root</span>(<span class="number">1</span>), <span class="ident">x</span>);
<span class="macro">assert_eq</span><span class="macro">!</span>(<span class="ident">x</span>.<span class="ident">nth_root</span>(<span class="number">2</span>), <span class="ident">x</span>.<span class="ident">sqrt</span>());
<span class="macro">assert_eq</span><span class="macro">!</span>(<span class="ident">x</span>.<span class="ident">nth_root</span>(<span class="number">3</span>), <span class="ident">x</span>.<span class="ident">cbrt</span>());
<span class="macro">assert_eq</span><span class="macro">!</span>(<span class="ident">x</span>.<span class="ident">nth_root</span>(<span class="number">4</span>), <span class="number">10</span>);
<span class="macro">assert_eq</span><span class="macro">!</span>(<span class="ident">x</span>.<span class="ident">nth_root</span>(<span class="number">13</span>), <span class="number">2</span>);
<span class="macro">assert_eq</span><span class="macro">!</span>(<span class="ident">x</span>.<span class="ident">nth_root</span>(<span class="number">14</span>), <span class="number">1</span>);
<span class="macro">assert_eq</span><span class="macro">!</span>(<span class="ident">x</span>.<span class="ident">nth_root</span>(<span class="ident">std</span>::<span class="ident">u32</span>::<span class="ident">MAX</span>), <span class="number">1</span>);
<span class="macro">assert_eq</span><span class="macro">!</span>(<span class="ident">std</span>::<span class="ident">i32</span>::<span class="ident">MAX</span>.<span class="ident">nth_root</span>(<span class="number">30</span>), <span class="number">2</span>);
<span class="macro">assert_eq</span><span class="macro">!</span>(<span class="ident">std</span>::<span class="ident">i32</span>::<span class="ident">MAX</span>.<span class="ident">nth_root</span>(<span class="number">31</span>), <span class="number">1</span>);
<span class="macro">assert_eq</span><span class="macro">!</span>(<span class="ident">std</span>::<span class="ident">i32</span>::<span class="ident">MIN</span>.<span class="ident">nth_root</span>(<span class="number">31</span>), <span class="op">-</span><span class="number">2</span>);
<span class="macro">assert_eq</span><span class="macro">!</span>((<span class="ident">std</span>::<span class="ident">i32</span>::<span class="ident">MIN</span> <span class="op">+</span> <span class="number">1</span>).<span class="ident">nth_root</span>(<span class="number">31</span>), <span class="op">-</span><span class="number">1</span>);
<span class="macro">assert_eq</span><span class="macro">!</span>(<span class="ident">std</span>::<span class="ident">u32</span>::<span class="ident">MAX</span>.<span class="ident">nth_root</span>(<span class="number">31</span>), <span class="number">2</span>);
<span class="macro">assert_eq</span><span class="macro">!</span>(<span class="ident">std</span>::<span class="ident">u32</span>::<span class="ident">MAX</span>.<span class="ident">nth_root</span>(<span class="number">32</span>), <span class="number">1</span>);</pre></div>
</div></div><span class='loading-content'>Loading content...</span>
<h2 id='provided-methods' class='small-section-header'>Provided methods<a href='#provided-methods' class='anchor'></a></h2><div class='methods'><h3 id='method.sqrt' class='method'><code id='sqrt.v'>fn <a href='#method.sqrt' class='fnname'>sqrt</a>(&amp;self) -&gt; Self</code></h3><div class='docblock'><p>Returns the truncated principal square root of an integer -- <code>⌊√x⌋</code></p>
<p>This is solving for <code>r</code> in <code>r² = x</code>, rounding toward zero.
The result will satisfy <code>r² ≤ x &lt; (r+1)²</code>.</p>
<h1 id="panics-1" class="section-header"><a href="#panics-1">Panics</a></h1>
<p>Panics if <code>self</code> is less than zero:</p>
<div class="example-wrap"><pre class="rust rust-example-rendered">
<span class="macro">println</span><span class="macro">!</span>(<span class="string">&quot;no imaginary numbers... {}&quot;</span>, (<span class="op">-</span><span class="number">1</span>).<span class="ident">sqrt</span>());</pre></div>
<h1 id="examples-1" class="section-header"><a href="#examples-1">Examples</a></h1>
<div class="example-wrap"><pre class="rust rust-example-rendered">
<span class="kw">use</span> <span class="ident">num_integer</span>::<span class="ident">Roots</span>;
<span class="kw">let</span> <span class="ident">x</span>: <span class="ident">i32</span> <span class="op">=</span> <span class="number">12345</span>;
<span class="macro">assert_eq</span><span class="macro">!</span>((<span class="ident">x</span> <span class="op">*</span> <span class="ident">x</span>).<span class="ident">sqrt</span>(), <span class="ident">x</span>);
<span class="macro">assert_eq</span><span class="macro">!</span>((<span class="ident">x</span> <span class="op">*</span> <span class="ident">x</span> <span class="op">+</span> <span class="number">1</span>).<span class="ident">sqrt</span>(), <span class="ident">x</span>);
<span class="macro">assert_eq</span><span class="macro">!</span>((<span class="ident">x</span> <span class="op">*</span> <span class="ident">x</span> <span class="op">-</span> <span class="number">1</span>).<span class="ident">sqrt</span>(), <span class="ident">x</span> <span class="op">-</span> <span class="number">1</span>);</pre></div>
</div><h3 id='method.cbrt' class='method'><code id='cbrt.v'>fn <a href='#method.cbrt' class='fnname'>cbrt</a>(&amp;self) -&gt; Self</code></h3><div class='docblock'><p>Returns the truncated principal cube root of an integer --
<code>if x &gt;= 0 { ⌊∛x⌋ } else { ⌈∛x⌉ }</code></p>
<p>This is solving for <code>r</code> in <code>r³ = x</code>, rounding toward zero.
If <code>x</code> is positive, the result will satisfy <code>r³ ≤ x &lt; (r+1)³</code>.
If <code>x</code> is negative, then <code>(r-1)³ &lt; x ≤ r³</code>.</p>
<h1 id="examples-2" class="section-header"><a href="#examples-2">Examples</a></h1>
<div class="example-wrap"><pre class="rust rust-example-rendered">
<span class="kw">use</span> <span class="ident">num_integer</span>::<span class="ident">Roots</span>;
<span class="kw">let</span> <span class="ident">x</span>: <span class="ident">i32</span> <span class="op">=</span> <span class="number">1234</span>;
<span class="macro">assert_eq</span><span class="macro">!</span>((<span class="ident">x</span> <span class="op">*</span> <span class="ident">x</span> <span class="op">*</span> <span class="ident">x</span>).<span class="ident">cbrt</span>(), <span class="ident">x</span>);
<span class="macro">assert_eq</span><span class="macro">!</span>((<span class="ident">x</span> <span class="op">*</span> <span class="ident">x</span> <span class="op">*</span> <span class="ident">x</span> <span class="op">+</span> <span class="number">1</span>).<span class="ident">cbrt</span>(), <span class="ident">x</span>);
<span class="macro">assert_eq</span><span class="macro">!</span>((<span class="ident">x</span> <span class="op">*</span> <span class="ident">x</span> <span class="op">*</span> <span class="ident">x</span> <span class="op">-</span> <span class="number">1</span>).<span class="ident">cbrt</span>(), <span class="ident">x</span> <span class="op">-</span> <span class="number">1</span>);
<span class="macro">assert_eq</span><span class="macro">!</span>((<span class="op">-</span>(<span class="ident">x</span> <span class="op">*</span> <span class="ident">x</span> <span class="op">*</span> <span class="ident">x</span>)).<span class="ident">cbrt</span>(), <span class="op">-</span><span class="ident">x</span>);
<span class="macro">assert_eq</span><span class="macro">!</span>((<span class="op">-</span>(<span class="ident">x</span> <span class="op">*</span> <span class="ident">x</span> <span class="op">*</span> <span class="ident">x</span> <span class="op">+</span> <span class="number">1</span>)).<span class="ident">cbrt</span>(), <span class="op">-</span><span class="ident">x</span>);
<span class="macro">assert_eq</span><span class="macro">!</span>((<span class="op">-</span>(<span class="ident">x</span> <span class="op">*</span> <span class="ident">x</span> <span class="op">*</span> <span class="ident">x</span> <span class="op">-</span> <span class="number">1</span>)).<span class="ident">cbrt</span>(), <span class="op">-</span>(<span class="ident">x</span> <span class="op">-</span> <span class="number">1</span>));</pre></div>
</div></div><span class='loading-content'>Loading content...</span>
<h2 id='foreign-impls' class='small-section-header'>Implementations on Foreign Types<a href='#foreign-impls' class='anchor'></a></h2><h3 id='impl-Roots-for-i8' class='impl'><code class='in-band'>impl <a class="trait" href="../num_integer/trait.Roots.html" title="trait num_integer::Roots">Roots</a> for <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.i8.html">i8</a></code><a href='#impl-Roots-for-i8' class='anchor'></a><a class='srclink' href='../src/num_integer/roots.rs.html#136-161' title='goto source code'>[src]</a></h3><div class='impl-items'><h4 id='method.nth_root' class="method hidden"><code id='nth_root.v-1'>fn <a href='#method.nth_root' class='fnname'>nth_root</a>(&amp;self, n: <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.u32.html">u32</a>) -&gt; Self</code><a class='srclink' href='../src/num_integer/roots.rs.html#138-145' title='goto source code'>[src]</a></h4><h4 id='method.sqrt-1' class="method hidden"><code id='sqrt.v-1'>fn <a href='#method.sqrt' class='fnname'>sqrt</a>(&amp;self) -&gt; Self</code><a class='srclink' href='../src/num_integer/roots.rs.html#148-151' title='goto source code'>[src]</a></h4><h4 id='method.cbrt-1' class="method hidden"><code id='cbrt.v-1'>fn <a href='#method.cbrt' class='fnname'>cbrt</a>(&amp;self) -&gt; Self</code><a class='srclink' href='../src/num_integer/roots.rs.html#154-160' title='goto source code'>[src]</a></h4></div><h3 id='impl-Roots-for-i16' class='impl'><code class='in-band'>impl <a class="trait" href="../num_integer/trait.Roots.html" title="trait num_integer::Roots">Roots</a> for <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.i16.html">i16</a></code><a href='#impl-Roots-for-i16' class='anchor'></a><a class='srclink' href='../src/num_integer/roots.rs.html#136-161' title='goto source code'>[src]</a></h3><div class='impl-items'><h4 id='method.nth_root-1' class="method hidden"><code id='nth_root.v-2'>fn <a href='#method.nth_root' class='fnname'>nth_root</a>(&amp;self, n: <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.u32.html">u32</a>) -&gt; Self</code><a class='srclink' href='../src/num_integer/roots.rs.html#138-145' title='goto source code'>[src]</a></h4><h4 id='method.sqrt-2' class="method hidden"><code id='sqrt.v-2'>fn <a href='#method.sqrt' class='fnname'>sqrt</a>(&amp;self) -&gt; Self</code><a class='srclink' href='../src/num_integer/roots.rs.html#148-151' title='goto source code'>[src]</a></h4><h4 id='method.cbrt-2' class="method hidden"><code id='cbrt.v-2'>fn <a href='#method.cbrt' class='fnname'>cbrt</a>(&amp;self) -&gt; Self</code><a class='srclink' href='../src/num_integer/roots.rs.html#154-160' title='goto source code'>[src]</a></h4></div><h3 id='impl-Roots-for-i32' class='impl'><code class='in-band'>impl <a class="trait" href="../num_integer/trait.Roots.html" title="trait num_integer::Roots">Roots</a> for <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.i32.html">i32</a></code><a href='#impl-Roots-for-i32' class='anchor'></a><a class='srclink' href='../src/num_integer/roots.rs.html#136-161' title='goto source code'>[src]</a></h3><div class='impl-items'><h4 id='method.nth_root-2' class="method hidden"><code id='nth_root.v-3'>fn <a href='#method.nth_root' class='fnname'>nth_root</a>(&amp;self, n: <a class="primitive" href="https://doc.rust-lang.org/nightly/std/primitive.u32.html">u32</a>) -&gt; Self</code><a class='srclink' href='../src/num_integer/roots.rs.html#138-145' title='goto source code'>[src]</a></h4><h4 id='method.sqrt-3' class="method hidden"><code id='sqrt.v-3'>fn <a href='#method.sqrt' class='fnname'>sqrt</a>(&amp;self) -&gt; Self</code><a class='srclink' href='../src/num_integer/roots.rs.html#148-151' title='goto source code'>[src]</a></h4><h4 id='method.cbrt-3' class="method hidden"><code id='cbrt.v-3'>fn <a href='#method.cbrt' class='fnname'>cbrt</a>(&amp;self) -&gt; Self</code><a class='srclink' href='../src/num_integer/roots.rs.html#154-160' title='goto source code'>[src]</a></h4></div><h3 id='imp
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