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<html>
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<head>
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<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
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<title>Introduction</title>
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<link rel="stylesheet" href="../math.css" type="text/css">
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<link rel="home" href="../index.html" title="Math Toolkit 2.5.1">
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<link rel="up" href="../constants.html" title="Chapter 4. Mathematical Constants">
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<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
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<table cellpadding="2" width="100%"><tr>
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<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../boost.png"></td>
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<td align="center"><a href="../../../../../index.html">Home</a></td>
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<td align="center"><a href="../../../../../libs/libraries.htm">Libraries</a></td>
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<td align="center"><a href="http://www.boost.org/users/people.html">People</a></td>
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<td align="center"><a href="http://www.boost.org/users/faq.html">FAQ</a></td>
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<td align="center"><a href="../../../../../more/index.htm">More</a></td>
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<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>
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</div>
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<div class="section">
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<div class="titlepage"><div><div><h2 class="title" style="clear: both">
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<a name="math_toolkit.constants_intro"></a><a class="link" href="constants_intro.html" title="Introduction">Introduction</a>
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</h2></div></div></div>
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<p>
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Boost.Math provides a collection of mathematical constants.
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</p>
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<h5>
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<a name="math_toolkit.constants_intro.h0"></a>
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<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
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use Boost.Math mathematical constants?</a>
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</h5>
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<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
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<li class="listitem">
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<p class="simpara">
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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
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</p>
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<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>
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<p class="simpara">
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(If that's all you want, jump direct to <a class="link" href="tutorial/non_templ.html" title="Use in non-template code">use
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in non-template code</a>!)
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</p>
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</li>
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<li class="listitem">
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Effortless - avoiding a search of reference sources.
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</li>
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<li class="listitem">
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Usable with both builtin floating point types, and user-defined, possibly
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extended precision, types such as NTL, MPFR/GMP, mp_float: in the latter
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case the constants are computed to the necessary precision and then cached.
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</li>
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<li class="listitem">
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Accurate - ensuring that the values are as accurate as possible for the
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chosen floating-point type
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<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: circle; ">
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<li class="listitem">
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No loss of accuracy from repeated rounding of intermediate computations.
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</li>
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<li class="listitem">
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Result is computed with higher precision and only rounded once.
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</li>
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<li class="listitem">
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Less risk of inaccurate result from functions pow, trig and log at
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<a href="http://en.wikipedia.org/wiki/Corner_case" target="_top">corner cases</a>.
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</li>
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<li class="listitem">
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Less risk of <a href="http://docs.oracle.com/cd/E19957-01/806-3568/ncg_goldberg.html" target="_top">cancellation
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error</a>.
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</li>
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</ul></div>
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</li>
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<li class="listitem">
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Portable - as possible between different systems using different floating-point
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precisions: see <a class="link" href="tutorial/templ.html" title="Use in template code">use in template
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code</a>.
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</li>
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<li class="listitem">
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Tested - by comparison with other published sources, or separately computed
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at long double precision.
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</li>
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<li class="listitem">
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Faster - can avoid (re-)calculation at runtime.
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<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: circle; ">
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<li class="listitem">
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If the value returned is a builtin type then it's returned by value
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as a <code class="computeroutput"><span class="keyword">constexpr</span></code> (C++11
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feature, if available).
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</li>
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<li class="listitem">
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If the value is computed and cached (or constructed from a string
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representation and cached), then it's returned by constant reference.<br>
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This can be significant if:
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</li>
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<li class="listitem">
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Functions pow, trig or log are used.
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</li>
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<li class="listitem">
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Inside an inner loop.
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</li>
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<li class="listitem">
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Using a high-precision UDT like <a href="../../../../../libs/multiprecision/doc/html/index.html" target="_top">Boost.Multiprecision</a>.
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</li>
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<li class="listitem">
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Compiler optimizations possible with built-in types, especially
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<code class="computeroutput"><span class="keyword">double</span></code>, are not available.
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</li>
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</ul></div>
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</li>
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</ul></div>
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</div>
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<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
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<td align="left"></td>
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<td align="right"><div class="copyright-footer">Copyright © 2006-2010, 2012-2014 Nikhar Agrawal,
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Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert
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Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan Råde, Gautam Sewani,
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Benjamin Sobotta, Thijs van den Berg, Daryle Walker and Xiaogang Zhang<p>
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Distributed under the Boost Software License, Version 1.0. (See accompanying
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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>)
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</p>
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</div></td>
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</tr></table>
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<hr>
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<div class="spirit-nav">
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<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>
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