1<html> 2<head> 3<meta http-equiv="Content-Type" content="text/html; charset=UTF-8"> 4<title>cbrt</title> 5<link rel="stylesheet" href="../../math.css" type="text/css"> 6<meta name="generator" content="DocBook XSL Stylesheets V1.79.1"> 7<link rel="home" href="../../index.html" title="Math Toolkit 2.12.0"> 8<link rel="up" href="../powers.html" title="Basic Functions"> 9<link rel="prev" href="expm1.html" title="expm1"> 10<link rel="next" href="sqrt1pm1.html" title="sqrt1pm1"> 11</head> 12<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF"> 13<table cellpadding="2" width="100%"><tr> 14<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../../boost.png"></td> 15<td align="center"><a href="../../../../../../index.html">Home</a></td> 16<td align="center"><a href="../../../../../../libs/libraries.htm">Libraries</a></td> 17<td align="center"><a href="http://www.boost.org/users/people.html">People</a></td> 18<td align="center"><a href="http://www.boost.org/users/faq.html">FAQ</a></td> 19<td align="center"><a href="../../../../../../more/index.htm">More</a></td> 20</tr></table> 21<hr> 22<div class="spirit-nav"> 23<a accesskey="p" href="expm1.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../powers.html"><img src="../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="sqrt1pm1.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a> 24</div> 25<div class="section"> 26<div class="titlepage"><div><div><h3 class="title"> 27<a name="math_toolkit.powers.cbrt"></a><a class="link" href="cbrt.html" title="cbrt">cbrt</a> 28</h3></div></div></div> 29<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">special_functions</span><span class="special">/</span><span class="identifier">cbrt</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span> 30</pre> 31<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span><span class="special">{</span> 32 33<span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">></span> 34<a class="link" href="../result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">cbrt</span><span class="special">(</span><span class="identifier">T</span> <span class="identifier">x</span><span class="special">);</span> 35 36<span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Chapter 21. Policies: Controlling Precision, Error Handling etc">Policy</a><span class="special">></span> 37<a class="link" href="../result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">cbrt</span><span class="special">(</span><span class="identifier">T</span> <span class="identifier">x</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Chapter 21. Policies: Controlling Precision, Error Handling etc">Policy</a><span class="special">&);</span> 38 39<span class="special">}}</span> <span class="comment">// namespaces</span> 40</pre> 41<p> 42 Returns the cubed root of x: x<sup>1/3</sup> or ∛x. 43 </p> 44<p> 45 The return type of this function is computed using the <a class="link" href="../result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>result 46 type calculation rules</em></span></a>: the return is <code class="computeroutput"><span class="keyword">double</span></code> 47 when <span class="emphasis"><em>x</em></span> is an integer type and T otherwise. 48 </p> 49<p> 50 The final <a class="link" href="../../policy.html" title="Chapter 21. Policies: Controlling Precision, Error Handling etc">Policy</a> argument is optional and can 51 be used to control the behaviour of the function: how it handles errors, 52 what level of precision to use etc. Refer to the <a class="link" href="../../policy.html" title="Chapter 21. Policies: Controlling Precision, Error Handling etc">policy 53 documentation for more details</a>. 54 </p> 55<p> 56 Implemented using Halley iteration. 57 </p> 58<p> 59 The following graph illustrates the behaviour of cbrt: 60 </p> 61<div class="blockquote"><blockquote class="blockquote"><p> 62 <span class="inlinemediaobject"><img src="../../../graphs/cbrt.svg" align="middle"></span> 63 64 </p></blockquote></div> 65<h5> 66<a name="math_toolkit.powers.cbrt.h0"></a> 67 <span class="phrase"><a name="math_toolkit.powers.cbrt.accuracy"></a></span><a class="link" href="cbrt.html#math_toolkit.powers.cbrt.accuracy">Accuracy</a> 68 </h5> 69<p> 70 For built in floating-point types <code class="computeroutput"><span class="identifier">cbrt</span></code> 71 should have approximately 2 epsilon accuracy. 72 </p> 73<div class="table"> 74<a name="math_toolkit.powers.cbrt.table_cbrt"></a><p class="title"><b>Table 8.83. Error rates for cbrt</b></p> 75<div class="table-contents"><table class="table" summary="Error rates for cbrt"> 76<colgroup> 77<col> 78<col> 79<col> 80<col> 81<col> 82</colgroup> 83<thead><tr> 84<th> 85 </th> 86<th> 87 <p> 88 GNU C++ version 7.1.0<br> linux<br> double 89 </p> 90 </th> 91<th> 92 <p> 93 GNU C++ version 7.1.0<br> linux<br> long double 94 </p> 95 </th> 96<th> 97 <p> 98 Sun compiler version 0x5150<br> Sun Solaris<br> long double 99 </p> 100 </th> 101<th> 102 <p> 103 Microsoft Visual C++ version 14.1<br> Win32<br> double 104 </p> 105 </th> 106</tr></thead> 107<tbody><tr> 108<td> 109 <p> 110 cbrt Function 111 </p> 112 </td> 113<td> 114 <p> 115 <span class="blue">Max = 0ε (Mean = 0ε)</span> 116 </p> 117 </td> 118<td> 119 <p> 120 <span class="blue">Max = 1.34ε (Mean = 0.471ε)</span><br> <br> 121 (<span class="emphasis"><em><cmath>:</em></span> Max = 1.34ε (Mean = 0.471ε))<br> 122 (<span class="emphasis"><em><math.h>:</em></span> Max = 1.34ε (Mean = 0.471ε)) 123 </p> 124 </td> 125<td> 126 <p> 127 <span class="blue">Max = 1.34ε (Mean = 0.471ε)</span><br> <br> 128 (<span class="emphasis"><em><math.h>:</em></span> Max = 1.34ε (Mean = 0.471ε)) 129 </p> 130 </td> 131<td> 132 <p> 133 <span class="blue">Max = 1.7ε (Mean = 0.565ε)</span><br> <br> 134 (<span class="emphasis"><em><math.h>:</em></span> Max = 1.7ε (Mean = 0.565ε)) 135 </p> 136 </td> 137</tr></tbody> 138</table></div> 139</div> 140<br class="table-break"><h5> 141<a name="math_toolkit.powers.cbrt.h1"></a> 142 <span class="phrase"><a name="math_toolkit.powers.cbrt.testing"></a></span><a class="link" href="cbrt.html#math_toolkit.powers.cbrt.testing">Testing</a> 143 </h5> 144<p> 145 A mixture of spot test sanity checks, and random high precision test values 146 calculated using NTL::RR at 1000-bit precision. 147 </p> 148</div> 149<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> 150<td align="left"></td> 151<td align="right"><div class="copyright-footer">Copyright © 2006-2019 Nikhar 152 Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, 153 Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan 154 Råde, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, 155 Daryle Walker and Xiaogang Zhang<p> 156 Distributed under the Boost Software License, Version 1.0. (See accompanying 157 file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) 158 </p> 159</div></td> 160</tr></table> 161<hr> 162<div class="spirit-nav"> 163<a accesskey="p" href="expm1.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../powers.html"><img src="../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="sqrt1pm1.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a> 164</div> 165</body> 166</html> 167