ceph/src/boost/libs/math/doc/html/math_toolkit/constants_intro.html

   1 <html>
   2 <head>
   3 <meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
   4 <title>Introduction</title>
   5 <link rel="stylesheet" href="../math.css" type="text/css">
   6 <meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
   7 <link rel="home" href="../index.html" title="Math Toolkit 2.5.1">
   8 <link rel="up" href="../constants.html" title="Chapter&#160;4.&#160;Mathematical Constants">
   9 <link rel="prev" href="../constants.html" title="Chapter&#160;4.&#160;Mathematical Constants">
  10 <link rel="next" href="tutorial.html" title="Tutorial">
  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="../constants.html"><img src="../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../constants.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="tutorial.html"><img src="../../../../../doc/src/images/next.png" alt="Next"></a>
  24 </div>
  25 <div class="section">
  26 <div class="titlepage"><div><div><h2 class="title" style="clear: both">
  27 <a name="math_toolkit.constants_intro"></a><a class="link" href="constants_intro.html" title="Introduction">Introduction</a>
  28 </h2></div></div></div>
  29 <p>
  30       Boost.Math provides a collection of mathematical constants.
  31     </p>
  32 <h5>
  33 <a name="math_toolkit.constants_intro.h0"></a>
  34       <span class="phrase"><a name="math_toolkit.constants_intro.why_use_boost_math_mathematical_"></a></span><a class="link" href="constants_intro.html#math_toolkit.constants_intro.why_use_boost_math_mathematical_">Why
  35       use Boost.Math mathematical constants?</a>
  36     </h5>
  37 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
  38 <li class="listitem">
  39 <p class="simpara">
  40           Readable. For the very many jobs just using built-in like <code class="computeroutput"><span class="keyword">double</span></code>, you can just write expressions like
  41         </p>
  42 <pre class="programlisting"><span class="keyword">double</span> <span class="identifier">area</span> <span class="special">=</span> <span class="identifier">pi</span> <span class="special">*</span> <span class="identifier">r</span> <span class="special">*</span> <span class="identifier">r</span><span class="special">;</span></pre>
  43 <p class="simpara">
  44           (If that's all you want, jump direct to <a class="link" href="tutorial/non_templ.html" title="Use in non-template code">use
  45           in non-template code</a>!)
  46         </p>
  47 </li>
  48 <li class="listitem">
  49           Effortless - avoiding a search of reference sources.
  50         </li>
  51 <li class="listitem">
  52           Usable with both builtin floating point types, and user-defined, possibly
  53           extended precision, types such as NTL, MPFR/GMP, mp_float: in the latter
  54           case the constants are computed to the necessary precision and then cached.
  55         </li>
  56 <li class="listitem">
  57           Accurate - ensuring that the values are as accurate as possible for the
  58           chosen floating-point type
  59           <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: circle; ">
  60 <li class="listitem">
  61                 No loss of accuracy from repeated rounding of intermediate computations.
  62               </li>
  63 <li class="listitem">
  64                 Result is computed with higher precision and only rounded once.
  65               </li>
  66 <li class="listitem">
  67                 Less risk of inaccurate result from functions pow, trig and log at
  68                 <a href="http://en.wikipedia.org/wiki/Corner_case" target="_top">corner cases</a>.
  69               </li>
  70 <li class="listitem">
  71                 Less risk of <a href="http://docs.oracle.com/cd/E19957-01/806-3568/ncg_goldberg.html" target="_top">cancellation
  72                 error</a>.
  73               </li>
  74 </ul></div>
  75         </li>
  76 <li class="listitem">
  77           Portable - as possible between different systems using different floating-point
  78           precisions: see <a class="link" href="tutorial/templ.html" title="Use in template code">use in template
  79           code</a>.
  80         </li>
  81 <li class="listitem">
  82           Tested - by comparison with other published sources, or separately computed
  83           at long double precision.
  84         </li>
  85 <li class="listitem">
  86           Faster - can avoid (re-)calculation at runtime.
  87           <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: circle; ">
  88 <li class="listitem">
  89                 If the value returned is a builtin type then it's returned by value
  90                 as a <code class="computeroutput"><span class="keyword">constexpr</span></code> (C++11
  91                 feature, if available).
  92               </li>
  93 <li class="listitem">
  94                 If the value is computed and cached (or constructed from a string
  95                 representation and cached), then it's returned by constant reference.<br>
  96                 This can be significant if:
  97               </li>
  98 <li class="listitem">
  99                 Functions pow, trig or log are used.
 100               </li>
 101 <li class="listitem">
 102                 Inside an inner loop.
 103               </li>
 104 <li class="listitem">
 105                 Using a high-precision UDT like <a href="../../../../../libs/multiprecision/doc/html/index.html" target="_top">Boost.Multiprecision</a>.
 106               </li>
 107 <li class="listitem">
 108                 Compiler optimizations possible with built-in types, especially
 109                 <code class="computeroutput"><span class="keyword">double</span></code>, are not available.
 110               </li>
 111 </ul></div>
 112         </li>
 113 </ul></div>
 114 </div>
 115 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 116 <td align="left"></td>
 117 <td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014 Nikhar Agrawal,
 118       Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert
 119       Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam Sewani,
 120       Benjamin Sobotta, Thijs van den Berg, Daryle Walker and Xiaogang Zhang<p>
 121         Distributed under the Boost Software License, Version 1.0. (See accompanying
 122         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>)
 123       </p>
 124 </div></td>
 125 </tr></table>
 126 <hr>
 127 <div class="spirit-nav">
 128 <a accesskey="p" href="../constants.html"><img src="../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../constants.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="tutorial.html"><img src="../../../../../doc/src/images/next.png" alt="Next"></a>
 129 </div>
 130 </body>
 131 </html>