libs/math/doc/html/math_toolkit/powers/cbrt.html

   1 <html>
   2 <head>
   3 <meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
   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 2.5.2">
   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">&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&#160;15.&#160;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&#160;15.&#160;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>.
  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&#160;15.&#160;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&#160;15.&#160;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&#160;6.80.&#160;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 = 1.7&#949; (Mean = 0.565&#949;)</span><br> <br>
 115                   (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 1.7&#949; (Mean = 0.565&#949;))
 116                 </p>
 117               </td>
 118 <td>
 119                 <p>
 120                   <span class="blue">Max = 0&#949; (Mean = 0&#949;)</span><br> <br> (<span class="emphasis"><em>Cephes:</em></span>
 121                   Max = 0&#949; (Mean = 0&#949;))
 122                 </p>
 123               </td>
 124 <td>
 125                 <p>
 126                   <span class="blue">Max = 1.34&#949; (Mean = 0.471&#949;)</span><br> <br>
 127                   (<span class="emphasis"><em>&lt;tr1/cmath&gt;:</em></span> Max = 1.34&#949; (Mean = 0.471&#949;))<br>
 128                   (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 1.34&#949; (Mean = 0.471&#949;))
 129                 </p>
 130               </td>
 131 <td>
 132                 <p>
 133                   <span class="blue">Max = 1.11&#949; (Mean = 0.424&#949;)</span><br> <br>
 134                   (<span class="emphasis"><em>&lt;math.h&gt;:</em></span> Max = 1.11&#949; (Mean = 0.424&#949;))
 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 &#169; 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 R&#229;de, 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>
 158 </div></td>
 159 </tr></table>
 160 <hr>
 161 <div class="spirit-nav">
 162 <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>
 163 </div>
 164 </body>
 165 </html>