72e469da0a
[CI SKIP]
166 lines
8.9 KiB
HTML
166 lines
8.9 KiB
HTML
<html>
|
|
<head>
|
|
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
|
|
<title>powm1</title>
|
|
<link rel="stylesheet" href="../../math.css" type="text/css">
|
|
<meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
|
|
<link rel="home" href="../../index.html" title="Math Toolkit 2.11.0">
|
|
<link rel="up" href="../powers.html" title="Basic Functions">
|
|
<link rel="prev" href="sqrt1pm1.html" title="sqrt1pm1">
|
|
<link rel="next" href="hypot.html" title="hypot">
|
|
</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="sqrt1pm1.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="hypot.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.powm1"></a><a class="link" href="powm1.html" title="powm1">powm1</a>
|
|
</h3></div></div></div>
|
|
<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">powm1</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span>
|
|
</pre>
|
|
<p>
|
|
namespace boost{ namespace math{
|
|
</p>
|
|
<pre class="programlisting"><span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">></span>
|
|
<a class="link" href="../result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">powm1</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">x</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">y</span><span class="special">);</span>
|
|
|
|
<span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">T1</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T2</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Chapter 20. Policies: Controlling Precision, Error Handling etc">Policy</a><span class="special">></span>
|
|
<a class="link" href="../result_type.html" title="Calculation of the Type of the Result"><span class="emphasis"><em>calculated-result-type</em></span></a> <span class="identifier">powm1</span><span class="special">(</span><span class="identifier">T1</span> <span class="identifier">x</span><span class="special">,</span> <span class="identifier">T2</span> <span class="identifier">y</span><span class="special">,</span> <span class="keyword">const</span> <a class="link" href="../../policy.html" title="Chapter 20. Policies: Controlling Precision, Error Handling etc">Policy</a><span class="special">&);</span>
|
|
|
|
<span class="special">}}</span> <span class="comment">// namespaces</span>
|
|
</pre>
|
|
<p>
|
|
Returns x<sup>y </sup> - 1.
|
|
</p>
|
|
<p>
|
|
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"><span class="emphasis"><em>result
|
|
type calculation rules</em></span></a> when T1 and T2 are different types.
|
|
</p>
|
|
<p>
|
|
The final <a class="link" href="../../policy.html" title="Chapter 20. 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 20. Policies: Controlling Precision, Error Handling etc">policy
|
|
documentation for more details</a>.
|
|
</p>
|
|
<p>
|
|
There are two domains where this is useful: when <span class="emphasis"><em>y</em></span> is
|
|
very small, or when <span class="emphasis"><em>x</em></span> is close to 1.
|
|
</p>
|
|
<p>
|
|
Implemented in terms of <code class="computeroutput"><span class="identifier">expm1</span></code>.
|
|
</p>
|
|
<p>
|
|
The following graph illustrates the behaviour of powm1:
|
|
</p>
|
|
<div class="blockquote"><blockquote class="blockquote"><p>
|
|
<span class="inlinemediaobject"><img src="../../../graphs/powm1.svg" align="middle"></span>
|
|
|
|
</p></blockquote></div>
|
|
<h5>
|
|
<a name="math_toolkit.powers.powm1.h0"></a>
|
|
<span class="phrase"><a name="math_toolkit.powers.powm1.accuracy"></a></span><a class="link" href="powm1.html#math_toolkit.powers.powm1.accuracy">Accuracy</a>
|
|
</h5>
|
|
<p>
|
|
Should have approximately 2-3 epsilon accuracy.
|
|
</p>
|
|
<div class="table">
|
|
<a name="math_toolkit.powers.powm1.table_powm1"></a><p class="title"><b>Table 8.85. Error rates for powm1</b></p>
|
|
<div class="table-contents"><table class="table" summary="Error rates for powm1">
|
|
<colgroup>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
<col>
|
|
</colgroup>
|
|
<thead><tr>
|
|
<th>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
GNU C++ version 7.1.0<br> linux<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Sun compiler version 0x5150<br> Sun Solaris<br> long double
|
|
</p>
|
|
</th>
|
|
<th>
|
|
<p>
|
|
Microsoft Visual C++ version 14.1<br> Win32<br> double
|
|
</p>
|
|
</th>
|
|
</tr></thead>
|
|
<tbody><tr>
|
|
<td>
|
|
<p>
|
|
powm1
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.06ε (Mean = 0.425ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 2.04ε (Mean = 0.493ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.88ε (Mean = 0.49ε)</span>
|
|
</p>
|
|
</td>
|
|
<td>
|
|
<p>
|
|
<span class="blue">Max = 1.84ε (Mean = 0.486ε)</span>
|
|
</p>
|
|
</td>
|
|
</tr></tbody>
|
|
</table></div>
|
|
</div>
|
|
<br class="table-break"><h5>
|
|
<a name="math_toolkit.powers.powm1.h1"></a>
|
|
<span class="phrase"><a name="math_toolkit.powers.powm1.testing"></a></span><a class="link" href="powm1.html#math_toolkit.powers.powm1.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 © 2006-2019 Nikhar
|
|
Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
|
|
Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
|
|
Råde, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, 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="sqrt1pm1.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="hypot.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a>
|
|
</div>
|
|
</body>
|
|
</html>
|