1<html> 2<head> 3<meta http-equiv="Content-Type" content="text/html; charset=UTF-8"> 4<title>sin_pi</title> 5<link rel="stylesheet" href="../../math.css" type="text/css"> 6<meta name="generator" content="DocBook XSL Stylesheets V1.79.1"> 7<link rel="home" href="../../index.html" title="Math Toolkit 2.12.0"> 8<link rel="up" href="../powers.html" title="Basic Functions"> 9<link rel="prev" href="../powers.html" title="Basic Functions"> 10<link rel="next" href="cos_pi.html" title="cos_pi"> 11</head> 12<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF"> 13<table cellpadding="2" width="100%"><tr> 14<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../../boost.png"></td> 15<td align="center"><a href="../../../../../../index.html">Home</a></td> 16<td align="center"><a href="../../../../../../libs/libraries.htm">Libraries</a></td> 17<td align="center"><a href="http://www.boost.org/users/people.html">People</a></td> 18<td align="center"><a href="http://www.boost.org/users/faq.html">FAQ</a></td> 19<td align="center"><a href="../../../../../../more/index.htm">More</a></td> 20</tr></table> 21<hr> 22<div class="spirit-nav"> 23<a accesskey="p" href="../powers.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="cos_pi.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a> 24</div> 25<div class="section"> 26<div class="titlepage"><div><div><h3 class="title"> 27<a name="math_toolkit.powers.sin_pi"></a><a class="link" href="sin_pi.html" title="sin_pi">sin_pi</a> 28</h3></div></div></div> 29<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">sin_pi</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span> 30</pre> 31<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> 32 33<span class="keyword">template</span> <span class="special"><</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">></span> 34<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">sin_pi</span><span class="special">(</span><span class="identifier">T</span> <span class="identifier">x</span><span class="special">);</span> 35 36<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="Chapter 21. Policies: Controlling Precision, Error Handling etc">Policy</a><span class="special">></span> 37<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">sin_pi</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="Chapter 21. Policies: Controlling Precision, Error Handling etc">Policy</a><span class="special">&);</span> 38 39<span class="special">}}</span> <span class="comment">// namespaces</span> 40</pre> 41<p> 42 Returns the sine of <span class="emphasis"><em>π x</em></span>. 43 </p> 44<p> 45 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 46 type calculation rules</em></span></a>: the return is <code class="computeroutput"><span class="keyword">double</span></code> 47 when <span class="emphasis"><em>x</em></span> is an integer type and T otherwise. 48 </p> 49<p> 50 The final <a class="link" href="../../policy.html" title="Chapter 21. Policies: Controlling Precision, Error Handling etc">Policy</a> argument is optional and can 51 be used to control the behaviour of the function: how it handles errors, 52 what level of precision to use etc. Refer to the <a class="link" href="../../policy.html" title="Chapter 21. Policies: Controlling Precision, Error Handling etc">policy 53 documentation for more details</a>. 54 </p> 55<p> 56 This function performs exact all-integer arithmetic argument reduction before 57 computing the sine of <span class="emphasis"><em>π⋅x</em></span>. 58 </p> 59<div class="table"> 60<a name="math_toolkit.powers.sin_pi.table_sin_pi"></a><p class="title"><b>Table 8.79. Error rates for sin_pi</b></p> 61<div class="table-contents"><table class="table" summary="Error rates for sin_pi"> 62<colgroup> 63<col> 64<col> 65<col> 66<col> 67<col> 68</colgroup> 69<thead><tr> 70<th> 71 </th> 72<th> 73 <p> 74 GNU C++ version 7.1.0<br> linux<br> double 75 </p> 76 </th> 77<th> 78 <p> 79 GNU C++ version 7.1.0<br> linux<br> long double 80 </p> 81 </th> 82<th> 83 <p> 84 Sun compiler version 0x5150<br> Sun Solaris<br> long double 85 </p> 86 </th> 87<th> 88 <p> 89 Microsoft Visual C++ version 14.1<br> Win32<br> double 90 </p> 91 </th> 92</tr></thead> 93<tbody> 94<tr> 95<td> 96 <p> 97 sin_pi and cos_pi 98 </p> 99 </td> 100<td> 101 <p> 102 <span class="blue">Max = 0ε (Mean = 0ε)</span> 103 </p> 104 </td> 105<td> 106 <p> 107 <span class="blue">Max = 0.996ε (Mean = 0.335ε)</span> 108 </p> 109 </td> 110<td> 111 <p> 112 <span class="blue">Max = 0.996ε (Mean = 0.336ε)</span> 113 </p> 114 </td> 115<td> 116 <p> 117 <span class="blue">Max = 0.99ε (Mean = 0.328ε)</span> 118 </p> 119 </td> 120</tr> 121<tr> 122<td> 123 <p> 124 sin_pi and cos_pi near integers and half integers 125 </p> 126 </td> 127<td> 128 <p> 129 <span class="blue">Max = 0ε (Mean = 0ε)</span> 130 </p> 131 </td> 132<td> 133 <p> 134 <span class="blue">Max = 0.976ε (Mean = 0.293ε)</span> 135 </p> 136 </td> 137<td> 138 <p> 139 <span class="blue">Max = 0.976ε (Mean = 0.293ε)</span> 140 </p> 141 </td> 142<td> 143 <p> 144 <span class="blue">Max = 0.996ε (Mean = 0.343ε)</span> 145 </p> 146 </td> 147</tr> 148</tbody> 149</table></div> 150</div> 151<br class="table-break"> 152</div> 153<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> 154<td align="left"></td> 155<td align="right"><div class="copyright-footer">Copyright © 2006-2019 Nikhar 156 Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, 157 Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan 158 Råde, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, 159 Daryle Walker and Xiaogang Zhang<p> 160 Distributed under the Boost Software License, Version 1.0. (See accompanying 161 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>) 162 </p> 163</div></td> 164</tr></table> 165<hr> 166<div class="spirit-nav"> 167<a accesskey="p" href="../powers.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="cos_pi.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a> 168</div> 169</body> 170</html> 171