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<html> <head> <meta http-equiv="Content-Type" content="text/html; charset=US-ASCII"> <title>sqrt1pm1</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="../powers.html" title="Basic Functions"> <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 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="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> <div class="section"> <div class="titlepage"><div><div><h3 class="title"> <a name="math_toolkit.powers.sqrt1pm1"></a><a class="link" href="sqrt1pm1.html" title="sqrt1pm1">sqrt1pm1</a> </h3></div></div></div> <pre class="programlisting">#include <boost/math/special_functions/sqrt1pm1.hpp> </pre> <pre class="programlisting">namespace boost{ namespace math{ template <class T> <a class="link" href="../result_type.html" title="Calculation of the Type of the Result">calculated-result-type</a> sqrt1pm1(T x); template <class T, class <a class="link" href="../../policy.html" title="Chapter 14. Policies: Controlling Precision, Error Handling etc">Policy</a>> <a class="link" href="../result_type.html" title="Calculation of the Type of the Result">calculated-result-type</a> sqrt1pm1(T x, const <a class="link" href="../../policy.html" title="Chapter 14. Policies: Controlling Precision, Error Handling etc">Policy</a>&); }} // namespaces </pre> Returns <code class="computeroutput">sqrt(1+x) - 1</code>. The return type of this function is computed using the <a class="link" href="../result_type.html" title="Calculation of the Type of the Result">result type calculation rules</a>: the return is <code class="computeroutput">double</code> when x is an integer type and T otherwise. The final <a class="link" href="../../policy.html" title="Chapter 14. Policies: Controlling Precision, Error Handling etc">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="Chapter 14. Policies: Controlling Precision, Error Handling etc">policy documentation for more details</a>. This function is useful when you need the difference between sqrt(x) and 1, when x is itself close to 1. Implemented in terms of <code class="computeroutput">log1p</code> and <code class="computeroutput">expm1</code>. The following graph illustrates the behaviour of sqrt1pm1: <img src="../../../graphs/sqrt1pm1.png" align="middle"> <h5> <a name="math_toolkit.powers.sqrt1pm1.h0"></a> <a name="math_toolkit.powers.sqrt1pm1.accuracy"></a><a class="link" href="sqrt1pm1.html#math_toolkit.powers.sqrt1pm1.accuracy">Accuracy</a> </h5> For built in floating-point types <code class="computeroutput">sqrt1pm1</code> should have approximately 3 epsilon accuracy. <h5> <a name="math_toolkit.powers.sqrt1pm1.h1"></a> <a name="math_toolkit.powers.sqrt1pm1.testing"></a><a class="link" href="sqrt1pm1.html#math_toolkit.powers.sqrt1pm1.testing">Testing</a> </h5> A selection of random high precision test values calculated using NTL::RR at 1000-bit precision. </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 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>) </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>