<html> <head> <meta http-equiv="Content-Type" content="text/html; charset=US-ASCII"> <title>sqrt1pm1</title> <link rel="stylesheet" href="../../../../../../../../doc/src/boostbook.css" type="text/css"> <meta name="generator" content="DocBook XSL Stylesheets V1.74.0"> <link rel="home" href="../../../index.html" title="Math Toolkit"> <link rel="up" href="../powers.html" title="Logs, Powers, Roots and Exponentials"> <link rel="prev" href="cbrt.html" title="cbrt"> <link rel="next" href="powm1.html" title="powm1"> </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 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class="preprocessor">#include</span> <span class="special"><</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">sqrt1pm1</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span> </pre> <p> </p> <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> <span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">></span> <a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">sqrt1pm1</span><span class="special">(</span><span class="identifier">T</span> <span class="identifier">x</span><span class="special">);</span> <span class="keyword">template</span> <span class="special"><</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="Policies">Policy</a><span class="special">></span> <a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">sqrt1pm1</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="Policies">Policy</a><span class="special">&);</span> <span class="special">}}</span> <span class="comment">// namespaces </span></pre> <p> Returns <code class="computeroutput"><span class="identifier">sqrt</span><span class="special">(</span><span class="number">1</span><span class="special">+</span><span class="identifier">x</span><span class="special">)</span> <span class="special">-</span> <span class="number">1</span></code>. </p> <p> The return type of this function is computed using the <a class="link" href="../../main_overview/result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>result type calculation rules</em></span></a>: the return is <code class="computeroutput"><span class="keyword">double</span></code> when <span class="emphasis"><em>x</em></span> is an integer type and T otherwise. </p> <p> </p> <p> The final <a class="link" href="../../policy.html" title="Policies">Policy</a> argument is optional and can be used to control the behaviour of the function: how it handles errors, what level of precision to use etc. Refer to the <a class="link" href="../../policy.html" title="Policies">policy documentation for more details</a>. </p> <p> </p> <p> This function is useful when you need the difference between sqrt(x) and 1, when x is itself close to 1. </p> <p> Implemented in terms of <code class="computeroutput"><span class="identifier">log1p</span></code> and <code class="computeroutput"><span class="identifier">expm1</span></code>. </p> <p> The following graph illustrates the behaviour of sqrt1pm1: </p> <p> <span class="inlinemediaobject"><img src="../../../../graphs/sqrt1pm1.png" align="middle"></span> </p> <a name="math_toolkit.special.powers.sqrt1pm1.accuracy"></a><h5> <a name="id1151018"></a> <a class="link" href="sqrt1pm1.html#math_toolkit.special.powers.sqrt1pm1.accuracy">Accuracy</a> </h5> <p> For built in floating-point types <code class="computeroutput"><span class="identifier">sqrt1pm1</span></code> should have approximately 3 epsilon accuracy. </p> <a name="math_toolkit.special.powers.sqrt1pm1.testing"></a><h5> <a name="id1151042"></a> <a class="link" href="sqrt1pm1.html#math_toolkit.special.powers.sqrt1pm1.testing">Testing</a> </h5> <p> A selection of random high precision test values calculated using NTL::RR at 1000-bit precision. </p> </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 , 2007, 2008, 2009 John Maddock, Paul A. Bristow, Hubert Holin, Xiaogang Zhang, Bruno Lalande, Johan Råde, Gautam Sewani and Thijs van den Berg<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="cbrt.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="powm1.html"><img src="../../../../../../../../doc/src/images/next.png" alt="Next"></a> </div> </body> </html>