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14<div class="section" id="metafunctions">
15<h1><a class="toc-backref" href="../refmanual.html#id1510">Metafunctions</a></h1>
16<p id="label-metafunctions">The MPL includes a number of predefined metafunctions that can be roughly
17classified in two categories: <cite>general purpose metafunctions</cite>, dealing with
18conditional <a class="reference internal" href="./type-selection.html">type selection</a> and higher-order metafunction <a class="reference internal" href="./invocation.html">invocation</a>,
19<a class="reference internal" href="./composition-and-argument-binding.html">composition</a>, and <a class="reference internal" href="./composition-and-argument-binding.html">argument binding</a>, and <cite>numeric metafunctions</cite>,
20incapsulating built-in and user-defined <a class="reference internal" href="./arithmetic-operations.html">arithmetic</a>, <a class="reference internal" href="./comparisons.html">comparison</a>,
21<a class="reference internal" href="./logical-operations.html">logical</a>, and <a class="reference internal" href="./bitwise-operations.html">bitwise</a> operations.</p>
22<p>Given that it is possible to perform integer numeric computations at
23compile time using the conventional operators notation, the need for the
24second category might be not obvious, but it in fact plays a cental role in
25making programming with MPL seemingly effortless. In
26particular, there are at least two contexts where built-in language
27facilities fall short <a class="footnote-reference" href="#portability" id="id820">[3]</a>:</p>
28<ol class="arabic simple">
29<li>Passing a computation to an algorithm.</li>
30<li>Performing a computation on non-integer data.</li>
31</ol>
32<p>The second use case deserves special attention. In contrast to the built-in,
33strictly integer compile-time arithmetics, the MPL numeric metafunctions are
34<em>polymorphic</em>, with support for <em>mixed-type arithmetics</em>. This means that they
35can operate on a variety of numeric types — for instance, rational,
36fixed-point or complex numbers, — and that, in general, you are allowed to
37freely intermix these types within a single expression. See <a class="reference internal" href="./numeric-metafunction.html">Numeric Metafunction</a> concept for more details on the MPL numeric infrastructure.</p>
38<!-- The provided `infrastructure`__ allows easy plugging of user-defined numeric
39types
40Naturally, they also , meaning that you can perform a computation on the
41arguments of different types, and the result will yeild the largest/most general
42of them. For user-defined numeric types, they provide an `infrastructure`__ that
43allows easy plugging and seemless integration with predefined library
44types. details.
45
46__ `Numeric Metafunction`_ -->
47<p>To reduce a negative syntactical impact of the metafunctions notation
48over the infix operator notation, all numeric metafunctions
49allow to pass up to N arguments, where N is defined by the value of
50<a class="reference internal" href="./limit-metafunction-arity.html">BOOST_MPL_LIMIT_METAFUNCTION_ARITY</a> configuration macro.</p>
51<table class="docutils footnote" frame="void" id="portability" rules="none">
52<colgroup><col class="label" /><col /></colgroup>
53<tbody valign="top">
54<tr><td class="label"><a class="fn-backref" href="#id820">[3]</a></td><td>All other considerations aside, as of the time of this writing
55(early 2004), using built-in operators on integral constants still often
56present a portability problem — many compilers cannot handle particular
57forms of expressions, forcing us to use conditional compilation. Because MPL
58numeric metafunctions work on types and encapsulate these kind of workarounds
59internally, they elude these problems, so if you aim for portability, it is
60generally adviced to use them in the place of the conventional operators, even
61at the price of slightly decreased readability.</td></tr>
62</tbody>
63</table>
64<ul class="toc simple" id="outline">
65<li><a class="reference internal" href="./metafunctions-concepts.html" id="id1511">Concepts</a></li>
66<li><a class="reference internal" href="./type-selection.html" id="id1519">Type Selection</a></li>
67<li><a class="reference internal" href="./invocation.html" id="id1524">Invocation</a></li>
68<li><a class="reference internal" href="./composition-and-argument-binding.html" id="id1528">Composition and Argument Binding</a></li>
69<li><a class="reference internal" href="./arithmetic-operations.html" id="id1535">Arithmetic Operations</a></li>
70<li><a class="reference internal" href="./comparisons.html" id="id1542">Comparisons</a></li>
71<li><a class="reference internal" href="./logical-operations.html" id="id1549">Logical Operations</a></li>
72<li><a class="reference internal" href="./bitwise-operations.html" id="id1553">Bitwise Operations</a></li>
73<li><a class="reference internal" href="./trivial.html" id="id1559">Trivial</a></li>
74<li><a class="reference internal" href="./string-operations.html" id="id1561">String Operations</a></li>
75<li><a class="reference internal" href="./miscellaneous.html" id="id1563">Miscellaneous</a></li>
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81<td><div class="copyright-footer"><div class="copyright">Copyright © 2001-2009 Aleksey Gurtovoy and David Abrahams</div>
82Distributed under the Boost Software License, Version 1.0. (See accompanying
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