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7<title>The MPL Reference Manual: Numeric Metafunction</title>
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10<body class="docframe refmanual">
11<table class="header"><tr class="header"><td class="header-group navigation-bar"><span class="navigation-group"><a href="./tag-dispatched.html" class="navigation-link">Prev</a>&nbsp;<a href="./trivial-metafunction.html" class="navigation-link">Next</a></span><span class="navigation-group-separator">&nbsp;|&nbsp;</span><span class="navigation-group"><a href="./tag-dispatched.html" class="navigation-link">Back</a>&nbsp;<a href="./trivial-metafunction.html" class="navigation-link">Along</a></span><span class="navigation-group-separator">&nbsp;|&nbsp;</span><span class="navigation-group"><a href="./metafunctions-concepts.html" class="navigation-link">Up</a>&nbsp;<a href="../refmanual.html" class="navigation-link">Home</a></span><span class="navigation-group-separator">&nbsp;|&nbsp;</span><span class="navigation-group"><a href="./refmanual_toc.html" class="navigation-link">Full TOC</a></span></td>
12<td class="header-group page-location"><a href="../refmanual.html" class="navigation-link">Front Page</a> / <a href="./metafunctions.html" class="navigation-link">Metafunctions</a> / <a href="./metafunctions-concepts.html" class="navigation-link">Concepts</a> / <a href="./numeric-metafunction.html" class="navigation-link">Numeric Metafunction</a></td>
13</tr></table><div class="header-separator"></div>
14<div class="section" id="numeric-metafunction">
15<h1><a class="toc-backref" href="./metafunctions-concepts.html#id443" name="numeric-metafunction">Numeric Metafunction</a></h1>
16<div class="section" id="numeric-description">
17<h3><a class="subsection-title" href="#description" name="description">Description</a></h3>
18<p>A <a class="reference" href="./numeric-metafunction.html">Numeric Metafunction</a> is a <a class="reference" href="./tag-dispatched.html">Tag Dispatched Metafunction</a> that provides
19a built-in infrastructure for easy implementation of mixed-type operations.</p>
20</div>
21<div class="section" id="numeric-expression-requirements">
22<h3><a class="subsection-title" href="#expression-requirements" name="expression-requirements">Expression requirements</a></h3>
23<p>In the following table and subsequent specifications, <tt class="literal"><span class="pre">op</span></tt> is a placeholder token for the actual
24<a class="reference" href="./numeric-metafunction.html">Numeric Metafunction</a>'s name, and <tt class="literal"><span class="pre">x</span></tt>, <tt class="literal"><span class="pre">y</span></tt> and <em>x</em><sub>1</sub>,<em>x</em><sub>2</sub>,... <em>x</em><sub>n</sub> are
25arbitrary numeric types.</p>
26<table border="1" class="table">
27<colgroup>
28<col width="46%" />
29<col width="25%" />
30<col width="29%" />
31</colgroup>
32<thead valign="bottom">
33<tr><th>Expression</th>
34<th>Type</th>
35<th>Complexity</th>
36</tr>
37</thead>
38<tbody valign="top">
39<tr><td><tt class="literal"><span class="pre">op_tag&lt;x&gt;::type</span></tt></td>
40<td><a class="reference" href="./integral-constant.html">Integral Constant</a></td>
41<td>Amortized constant time.</td>
42</tr>
43<tr><td><pre class="first last literal-block">
44op_impl&lt;
45     op_tag&lt;x&gt;::type
46   , op_tag&lt;y&gt;::type
47   &gt;::<a href="./apply.html" class="identifier">apply</a>&lt;x,y&gt;::type
48</pre>
49</td>
50<td>Any type</td>
51<td>Unspecified.</td>
52</tr>
53<tr><td><tt class="literal"><span class="pre">op&lt;</span></tt><em>x</em><sub>1</sub>,<em>x</em><sub>2</sub>,... <em>x</em><sub>n</sub><tt class="literal"><span class="pre">&gt;::type</span></tt></td>
54<td>Any type</td>
55<td>Unspecified.</td>
56</tr>
57</tbody>
58</table>
59</div>
60<div class="section" id="numeric-expression-semantics">
61<h3><a class="subsection-title" href="#expression-semantics" name="expression-semantics">Expression semantics</a></h3>
62<pre class="literal-block">
63typedef op_tag&lt;x&gt;::type tag;
64</pre>
65<table class="field-list" frame="void" rules="none">
66<col class="field-name" />
67<col class="field-body" />
68<tbody valign="top">
69<tr class="field"><th class="field-name">Semantics:</th><td class="field-body"><tt class="literal"><span class="pre">tag</span></tt> is a tag type for <tt class="literal"><span class="pre">x</span></tt> for <tt class="literal"><span class="pre">op</span></tt>.
70<tt class="literal"><span class="pre">tag::value</span></tt> is <tt class="literal"><span class="pre">x</span></tt>'s <em>conversion rank</em>.</td>
71</tr>
72</tbody>
73</table>
74<!-- .......................................................................... -->
75<pre class="literal-block">
76typedef op_impl&lt;
77      op_tag&lt;x&gt;::type
78    , op_tag&lt;y&gt;::type
79    &gt;::<a href="./apply.html" class="identifier">apply</a>&lt;x,y&gt;::type r;
80</pre>
81<table class="field-list" frame="void" rules="none">
82<col class="field-name" />
83<col class="field-body" />
84<tbody valign="top">
85<tr class="field"><th class="field-name">Semantics:</th><td class="field-body"><tt class="literal"><span class="pre">r</span></tt> is the result of <tt class="literal"><span class="pre">op</span></tt> application on arguments <tt class="literal"><span class="pre">x</span></tt> 
86and <tt class="literal"><span class="pre">y</span></tt>.</td>
87</tr>
88</tbody>
89</table>
90<!-- .......................................................................... -->
91<pre class="literal-block">
92typedef op&lt;<em>x</em><sub>1</sub>,<em>x</em><sub>2</sub>,... <em>x</em><sub>n</sub>&gt;::type r;
93</pre>
94<table class="field-list" frame="void" rules="none">
95<col class="field-name" />
96<col class="field-body" />
97<tbody valign="top">
98<tr class="field"><th class="field-name">Semantics:</th><td class="field-body"><tt class="literal"><span class="pre">r</span></tt> is the result of <tt class="literal"><span class="pre">op</span></tt> application on arguments <em>x</em><sub>1</sub>,<em>x</em><sub>2</sub>,... <em>x</em><sub>n</sub>.</td>
99</tr>
100</tbody>
101</table>
102</div>
103<div class="section" id="numeric-example">
104<h3><a class="subsection-title" href="#example" name="example">Example</a></h3>
105<pre class="literal-block">
106struct complex_tag : <a href="./int.html" class="identifier">int_</a>&lt;10&gt; {};
107
108template&lt; typename Re, typename Im &gt; struct complex
109{
110    typedef complex_tag tag;
111    typedef complex type;
112    typedef Re real;
113    typedef Im imag;
114};
115
116template&lt; typename C &gt; struct real : C::real {};
117template&lt; typename C &gt; struct imag : C::imag {};
118
119namespace boost { namespace mpl {
120
121template&lt;&gt;
122struct plus_impl&lt; complex_tag,complex_tag &gt;
123{
124    template&lt; typename N1, typename N2 &gt; struct <a href="./apply.html" class="identifier">apply</a>
125        : complex&lt;
126              <a href="./plus.html" class="identifier">plus</a>&lt; typename N1::real, typename N2::real &gt;
127            , <a href="./plus.html" class="identifier">plus</a>&lt; typename N1::imag, typename N2::imag &gt;
128            &gt;
129    {
130    };
131};
132
133}}
134
135typedef complex&lt; <a href="./int.html" class="identifier">int_</a>&lt;5&gt;, <a href="./int.html" class="identifier">int_</a>&lt;-1&gt; &gt; c1;
136typedef complex&lt; <a href="./int.html" class="identifier">int_</a>&lt;-5&gt;, <a href="./int.html" class="identifier">int_</a>&lt;1&gt; &gt; c2;
137
138typedef <a href="./plus.html" class="identifier">plus</a>&lt;c1,c2&gt; r1;
139<a href="./assert-relation.html" class="identifier">BOOST_MPL_ASSERT_RELATION</a>( real&lt;r1&gt;::value, ==, 0 );
140<a href="./assert-relation.html" class="identifier">BOOST_MPL_ASSERT_RELATION</a>( imag&lt;r1&gt;::value, ==, 0 );
141
142typedef <a href="./plus.html" class="identifier">plus</a>&lt;c1,c1&gt; r2;
143<a href="./assert-relation.html" class="identifier">BOOST_MPL_ASSERT_RELATION</a>( real&lt;r2&gt;::value, ==, 10 );
144<a href="./assert-relation.html" class="identifier">BOOST_MPL_ASSERT_RELATION</a>( imag&lt;r2&gt;::value, ==, -2 );
145
146typedef <a href="./plus.html" class="identifier">plus</a>&lt;c2,c2&gt; r3;
147<a href="./assert-relation.html" class="identifier">BOOST_MPL_ASSERT_RELATION</a>( real&lt;r3&gt;::value, ==, -10 );
148<a href="./assert-relation.html" class="identifier">BOOST_MPL_ASSERT_RELATION</a>( imag&lt;r3&gt;::value, ==, 2 );
149</pre>
150</div>
151<div class="section" id="numeric-models">
152<h3><a class="subsection-title" href="#models" name="models">Models</a></h3>
153<ul class="simple">
154<li><a class="refentry reference" href="./plus.html"><tt class="refentry literal"><span class="pre">plus</span></tt></a></li>
155<li><a class="refentry reference" href="./minus.html"><tt class="refentry literal"><span class="pre">minus</span></tt></a></li>
156<li><a class="refentry reference" href="./times.html"><tt class="refentry literal"><span class="pre">times</span></tt></a></li>
157<li><a class="refentry reference" href="./divides.html"><tt class="refentry literal"><span class="pre">divides</span></tt></a></li>
158</ul>
159</div>
160<div class="section" id="numeric-see-also">
161<h3><a class="subsection-title" href="#see-also" name="see-also">See also</a></h3>
162<p><a class="reference" href="./tag-dispatched.html">Tag Dispatched Metafunction</a>, <a class="reference" href="./metafunctions.html">Metafunctions</a>, <a class="refentry reference" href="./numeric-cast.html"><tt class="refentry literal"><span class="pre">numeric_cast</span></tt></a></p>
163<!-- modtime: November 10, 2004 04:36:48 +0000 -->
164<!-- Metafunctions/Concepts//Trivial Metafunction |70 -->
165</div>
166</div>
167
168<div class="footer-separator"></div>
169<table class="footer"><tr class="footer"><td class="header-group navigation-bar"><span class="navigation-group"><a href="./tag-dispatched.html" class="navigation-link">Prev</a>&nbsp;<a href="./trivial-metafunction.html" class="navigation-link">Next</a></span><span class="navigation-group-separator">&nbsp;|&nbsp;</span><span class="navigation-group"><a href="./tag-dispatched.html" class="navigation-link">Back</a>&nbsp;<a href="./trivial-metafunction.html" class="navigation-link">Along</a></span><span class="navigation-group-separator">&nbsp;|&nbsp;</span><span class="navigation-group"><a href="./metafunctions-concepts.html" class="navigation-link">Up</a>&nbsp;<a href="../refmanual.html" class="navigation-link">Home</a></span><span class="navigation-group-separator">&nbsp;|&nbsp;</span><span class="navigation-group"><a href="./refmanual_toc.html" class="navigation-link">Full TOC</a></span></td>
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