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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">&lt;</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">&gt;</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">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</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">&lt;</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">&gt;</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">&amp;);</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>&lt;cmath&gt;:</em></span> Max = 1.34ε (Mean = 0.471ε))<br>
122                  (<span class="emphasis"><em>&lt;math.h&gt;:</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>&lt;math.h&gt;:</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>&lt;math.h&gt;:</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
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