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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 15. 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 15. 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>. | |
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 15. 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 15. 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 | <p> | |
62 | <span class="inlinemediaobject"><img src="../../../graphs/cbrt.svg" align="middle"></span> | |
63 | </p> | |
64 | <h5> | |
65 | <a name="math_toolkit.powers.cbrt.h0"></a> | |
66 | <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> | |
67 | </h5> | |
68 | <p> | |
69 | For built in floating-point types <code class="computeroutput"><span class="identifier">cbrt</span></code> | |
70 | should have approximately 2 epsilon accuracy. | |
71 | </p> | |
72 | <div class="table"> | |
73 | <a name="math_toolkit.powers.cbrt.table_cbrt"></a><p class="title"><b>Table 6.80. Error rates for cbrt</b></p> | |
74 | <div class="table-contents"><table class="table" summary="Error rates for cbrt"> | |
75 | <colgroup> | |
76 | <col> | |
77 | <col> | |
78 | <col> | |
79 | <col> | |
80 | <col> | |
81 | </colgroup> | |
82 | <thead><tr> | |
83 | <th> | |
84 | </th> | |
85 | <th> | |
86 | <p> | |
87 | Microsoft Visual C++ version 12.0<br> Win32<br> double | |
88 | </p> | |
89 | </th> | |
90 | <th> | |
91 | <p> | |
92 | GNU C++ version 5.1.0<br> linux<br> double | |
93 | </p> | |
94 | </th> | |
95 | <th> | |
96 | <p> | |
97 | GNU C++ version 5.1.0<br> linux<br> long double | |
98 | </p> | |
99 | </th> | |
100 | <th> | |
101 | <p> | |
102 | Sun compiler version 0x5130<br> Sun Solaris<br> long double | |
103 | </p> | |
104 | </th> | |
105 | </tr></thead> | |
106 | <tbody><tr> | |
107 | <td> | |
108 | <p> | |
109 | cbrt Function | |
110 | </p> | |
111 | </td> | |
112 | <td> | |
113 | <p> | |
114 | <span class="blue">Max = 1.7ε (Mean = 0.565ε)</span><br> <br> | |
115 | (<span class="emphasis"><em><math.h>:</em></span> Max = 1.7ε (Mean = 0.565ε)) | |
116 | </p> | |
117 | </td> | |
118 | <td> | |
119 | <p> | |
120 | <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>Cephes:</em></span> | |
121 | Max = 0ε (Mean = 0ε)) | |
122 | </p> | |
123 | </td> | |
124 | <td> | |
125 | <p> | |
126 | <span class="blue">Max = 1.34ε (Mean = 0.471ε)</span><br> <br> | |
127 | (<span class="emphasis"><em><tr1/cmath>:</em></span> Max = 1.34ε (Mean = 0.471ε))<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 = 1.11ε (Mean = 0.424ε)</span><br> <br> | |
134 | (<span class="emphasis"><em><math.h>:</em></span> Max = 1.11ε (Mean = 0.424ε)) | |
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 © 2006-2010, 2012-2014 Nikhar Agrawal, | |
152 | Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert | |
153 | Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan Råde, Gautam Sewani, | |
154 | Benjamin Sobotta, Thijs van den Berg, Daryle Walker and Xiaogang Zhang<p> | |
155 | Distributed under the Boost Software License, Version 1.0. (See accompanying | |
156 | 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>) | |
157 | </p> | |
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