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| <div class="titlepage"><div><div><h4 class="title"> |
| <a name="math_toolkit.special.powers.sqrt1pm1"></a><a class="link" href="sqrt1pm1.html" title="sqrt1pm1"> sqrt1pm1</a> |
| </h4></div></div></div> |
| <p> |
| |
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| <pre class="programlisting"><span 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="id1148225"></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="id1148249"></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> |
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| <td align="right"><div class="copyright-footer">Copyright © 2006 , 2007, 2008, 2009, 2010 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>) |
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