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<html> <head> <meta http-equiv="Content-Type" content="text/html; charset=US-ASCII"> <title>Introduction</title> <link rel="stylesheet" href="../math.css" type="text/css"> <meta name="generator" content="DocBook XSL Stylesheets V1.78.1"> <link rel="home" href="../index.html" title="Math Toolkit 2.1.0"> <link rel="up" href="../constants.html" title="Chapter 4. Mathematical Constants"> <link rel="prev" href="../constants.html" title="Chapter 4. Mathematical Constants"> <link rel="next" href="tutorial.html" title="Tutorial"> </head> <body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF"> <table cellpadding="2" width="100%"><tr> <td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../boost.png"></td> <td align="center"><a href="../../../../../index.html">Home</a></td> <td align="center"><a href="../../../../../libs/libraries.htm">Libraries</a></td> <td align="center"><a href="http://www.boost.org/users/people.html">People</a></td> <td align="center"><a href="http://www.boost.org/users/faq.html">FAQ</a></td> <td align="center"><a href="../../../../../more/index.htm">More</a></td> </tr></table> <hr> <div class="spirit-nav"> <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> </div> <div class="section"> <div class="titlepage"><div><div><h2 class="title" style="clear: both"> <a name="math_toolkit.constants_intro"></a><a class="link" href="constants_intro.html" title="Introduction">Introduction</a> </h2></div></div></div> <p> Boost.Math provides a collection of mathematical constants. </p> <h5> <a name="math_toolkit.constants_intro.h0"></a> <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 use Boost.Math mathematical constants?</a> </h5> <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; "> <li class="listitem"> <p class="simpara"> 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 </p> <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> <p class="simpara"> (If that's all you want, jump direct to <a class="link" href="tutorial/non_templ.html" title="Use in non-template code">use in non-template code</a>!) </p> </li> <li class="listitem"> Effortless - avoiding a search of reference sources. </li> <li class="listitem"> Usable with both builtin floating point types, and user-defined, possibly extended precision, types such as NTL, MPFR/GMP, mp_float: in the latter case the constants are computed to the necessary precision and then cached. </li> <li class="listitem"> Accurate - ensuring that the values are as accurate as possible for the chosen floating-point type <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: circle; "> <li class="listitem"> No loss of accuracy from repeated rounding of intermediate computations. </li> <li class="listitem"> Result is computed with higher precision and only rounded once. </li> <li class="listitem"> Less risk of inaccurate result from functions pow, trig and log at <a href="http://en.wikipedia.org/wiki/Corner_case" target="_top">corner cases</a>. </li> <li class="listitem"> Less risk of <a href="http://docs.oracle.com/cd/E19957-01/806-3568/ncg_goldberg.html" target="_top">cancellation error</a>. </li> </ul></div> </li> <li class="listitem"> Portable - as possible between different systems using different floating-point precisions: see <a class="link" href="tutorial/templ.html" title="Use in template code">use in template code</a>. </li> <li class="listitem"> Tested - by comparison with other published sources, or separately computed at long double precision. </li> <li class="listitem"> Faster - can avoid (re-)calculation at runtime. <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: circle; "> <li class="listitem"> If the value returned is a builtin type then it's returned by value as a <code class="computeroutput"><span class="keyword">constexpr</span></code> (C++11 feature, if available). </li> <li class="listitem"> If the value is computed and cached (or constructed from a string representation and cached), then it's returned by constant reference.<br> This can be significant if: </li> <li class="listitem"> Functions pow, trig or log are used. </li> <li class="listitem"> Inside an inner loop. </li> <li class="listitem"> Using a high-precision UDT like <a href="http://www.boost.org/doc/libs/1_53_0_beta1/libs/multiprecision/doc/html/index.html" target="_top">Boost.Multiprecision</a>. </li> <li class="listitem"> Compiler optimizations possible with built-in types, especially <code class="computeroutput"><span class="keyword">double</span></code>, are not available. </li> </ul></div> </li> </ul></div> </div> <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> <td align="left"></td> <td align="right"><div class="copyright-footer">Copyright © 2006-2010, 2012-2014 Nikhar Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert Holin, Bruno Lalande, John Maddock, Johan Råde, Gautam Sewani, Benjamin Sobotta, Thijs van den Berg, Daryle Walker and Xiaogang Zhang<p> Distributed under the Boost Software License, Version 1.0. (See accompanying 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>) </p> </div></td> </tr></table> <hr> <div class="spirit-nav"> <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> </div> </body> </html>