1<html> 2<head> 3<meta http-equiv="Content-Type" content="text/html; charset=UTF-8"> 4<title>Introduction</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="../constants.html" title="Chapter 4. Mathematical Constants"> 9<link rel="prev" href="../constants.html" title="Chapter 4. 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<p class="simpara"> 87 Faster - can avoid (re-)calculation at runtime. 88 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: circle; "> 89<li class="listitem"> 90 If the value returned is a builtin type then it's returned by value 91 as a <code class="computeroutput"><span class="keyword">constexpr</span></code> (C++11 92 feature, if available). 93 </li> 94<li class="listitem"> 95 If the value is computed and cached (or constructed from a string 96 representation and cached), then it's returned by constant reference. 97 </li> 98</ul></div> 99 </p> 100<p class="simpara"> 101 This can be significant if: 102 </p> 103<p class="simpara"> 104 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: circle; "> 105<li class="listitem"> 106 Functions pow, trig or log are used. 107 </li> 108<li class="listitem"> 109 Inside an inner loop. 110 </li> 111<li class="listitem"> 112 Using a high-precision UDT like <a href="../../../../../libs/multiprecision/doc/html/index.html" target="_top">Boost.Multiprecision</a>. 113 </li> 114<li class="listitem"> 115 Compiler optimizations possible with built-in types, especially 116 <code class="computeroutput"><span class="keyword">double</span></code>, are not available. 117 </li> 118</ul></div> 119 </p> 120</li> 121</ul></div> 122</div> 123<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> 124<td align="left"></td> 125<td align="right"><div class="copyright-footer">Copyright © 2006-2019 Nikhar 126 Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, 127 Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan 128 Råde, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, 129 Daryle Walker and Xiaogang Zhang<p> 130 Distributed under the Boost Software License, Version 1.0. (See accompanying 131 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>) 132 </p> 133</div></td> 134</tr></table> 135<hr> 136<div class="spirit-nav"> 137<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> 138</div> 139</body> 140</html> 141
