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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">&lt;</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">&gt;</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">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</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">&lt;</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">&gt;</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">&amp;);</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>
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156      Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
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158      Råde, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
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