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 <h1><img src="../../../../boost.png" alt="boost.png (6897 bytes)" align=
 "middle" width="277" height="86">Boost.MultiIndex Key extraction reference</h1>

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 <h2>Contents</h2>

 <ul>
   <li><a href="#key_extractors">Key Extractors</a>
     <ul>
       <li><a href="#chained_pointers">Chained pointers</a></li>
     </ul>
   </li>
   <li><a href="#synopsis">Header
     <code>"boost/multi_index/key_extractors.hpp"</code> synopsis</a>
   </li>
   <li><a href="#identity_synopsis">Header
     <code>"boost/multi_index/identity.hpp"</code> synopsis</a>
     <ul>
       <li><a href="#identity">Class template <code>identity</code></a></li>
     </ul>
   </li>
   <li><a href="#member_synopsis">Header
     <code>"boost/multi_index/member.hpp"</code> synopsis</a>
     <ul>
       <li><a href="#member">Class template <code>member</code></a></li>
       <li><a href="#member_offset">Class template <code>member_offset</code></a></li>
       <li><a href="#boost_multi_index_member">Macro <code>BOOST_MULTI_INDEX_MEMBER</code></a></li>
     </ul>
   </li>
   <li><a href="#mem_fun_synopsis">Header
     <code>"boost/multi_index/mem_fun.hpp"</code> synopsis</a>
     <ul>
       <li><a href="#const_mem_fun">Class template <code>const_mem_fun</code></a></li>
       <li><a href="#mem_fun">Class template <code>mem_fun</code></a></li>
       <li><a href="#const_mem_fun_explicit">Class template <code>const_mem_fun_explicit</code></a></li>
       <li><a href="#mem_fun_explicit">Class template <code>mem_fun_explicit</code></a></li>
       <li><a href="#boost_multi_index_const_mem_fun">Macro <code>BOOST_MULTI_INDEX_CONST_MEM_FUN</code></a></li>
       <li><a href="#boost_multi_index_mem_fun">Macro <code>BOOST_MULTI_INDEX_MEM_FUN</code></a></li>
     </ul>
   </li>
   <li><a href="#global_fun_synopsis">Header
     <code>"boost/multi_index/global_fun.hpp"</code> synopsis</a>
     <ul>
       <li><a href="#global_fun">Class template <code>global_fun</code></a></li>
     </ul>
   </li>
   <li><a href="#composite_key_synopsis">Header
     <code>"boost/multi_index/composite_key.hpp"</code> synopsis</a>
     <ul>
       <li><a href="#composite_key">Class template <code>composite_key</code></a></li>
       <li><a href="#composite_key_result">Class template <code>composite_key_result</code></a></li>
       <li><a href="#ckey_result_equality">Equality</a>
         <ul>
           <li><a href="#composite_key_equal_to">Class template <code>composite_key_equal_to</code></a></li>
           <li><a href="#composite_key_result_equal_to">Class template <code>composite_key_result_equal_to</code></a></li>
           <li><a href="#equal_to_composite_key_result">Specialization of <code>std::equal_to</code> for <code>composite_key</code> results</a></li>
         </ul>
       </li>
       <li><a href="#ckey_result_comparison">Comparison</a>
         <ul>
           <li><a href="#composite_key_compare">Class template <code>composite_key_compare</code></a></li>
           <li><a href="#composite_key_result_less">Class template <code>composite_key_result_less</code></a></li>
           <li><a href="#composite_key_result_greater">Class template <code>composite_key_result_greater</code></a></li>
           <li><a href="#less_composite_key_result">Specialization of <code>std::less</code> for <code>composite_key</code> results</a></li>
           <li><a href="#greater_composite_key_result">Specialization of <code>std::greater</code> for <code>composite_key</code> results</a></li>
         </ul>
       </li>
       <li><a href="#ckey_result_hashing">Hashing</a>
         <ul>
           <li><a href="#composite_key_hash">Class template <code>composite_key_hash</code></a></li>
           <li><a href="#composite_key_result_hash">Class template <code>composite_key_result_hash</code></a></li>
           <li><a href="#hash_composite_key_result">Specialization of <code>boost::hash</code> for <code>composite_key</code> results</a></li>
         </ul>
       </li>
       <li><a href="#ckey_result_semantics">Semantics of <code>composite_key_result</code></a></li>
     </ul>
   </li>
 </ul>

 <h2><a name="key_extractors">Key Extractors</a></h2>

 <p>
 Key extraction classes are used by
 <a href="indices.html#key_based_indices">key-based indices</a> to
 obtain the indexing keys from the elements of a <code>multi_index_container</code>.
 An <a href="http://www.sgi.com/tech/stl/Assignable.html"><code>Assignable</code></a>
 class <code>KeyFromValue</code> is said to be a key extractor from a
 type <code>Type</code> if
 <ol>
   <li>the type <code>KeyFromValue::result_type</code> is defined,</li>
   <li><code>k1(ca)</code> is defined and returns a value convertible
     to <code>const KeyFromValue::result_type&amp;</code>,</li>
   <li>if <code>k2</code> is a copy of <code>k1</code>, <code>k1(ca)</code> is the
     same value as <code>k2(ca)</code>,</li>
 </ol>
 for every <code>k1</code>, <code>k2</code> of type <code>const KeyFromValue</code>,
 and <code>ca</code> of type <code>const Type&amp;</code>.
 </p>

 <p>
 Additionally, <code>KeyFromValue</code> is a <i>read/write</i> key extractor
 if the following extra conditions are met:
 <ol>
   <li><code>k1(a)</code> is defined and returns a value convertible
     to <code>KeyFromValue::result_type&amp;</code>,</li>
   <li><code>const_cast&lt;const KeyFromValue::result_type&amp;>(k1(a))</code>
     is the same  value as
     <code>k1(const_cast&lt;const Type&amp;>(a))</code>,</li>
 </ol>
 for every <code>k1</code> of type <code>const KeyFromValue</code> and
 <code>a</code> of type <code>Type&amp;</code>.
 </p>

 <p>
 Boost.MultiIndex provides six general-purpose key extractors:
 <ul>
   <li><a href="#identity"><code>identity</code></a>,</li>
   <li><a href="#member"><code>member</code></a>,</li>
   <li><a href="#const_mem_fun"><code>const_mem_fun</code></a>,</li>
   <li><a href="#mem_fun"><code>mem_fun</code></a>,</li>
   <li><a href="#global_fun"><code>global_fun</code></a> and</li>
   <li><a href="#composite_key"><code>composite_key</code></a>,</li>
 </ul>
 plus replacements for some of them:
 <ul>
   <li><a href="#member_offset"><code>member_offset</code></a>,</li>
   <li><a href="#const_mem_fun_explicit"><code>const_mem_fun_explicit</code></a> and</li>
   <li><a href="#mem_fun_explicit"><code>mem_fun_explicit</code></a>,</li>
 </ul>
 that workaround some deficiencies in the support for non-type template parameters
 by certain compilers.
 </p>

 <h3><a name="chained_pointers">Chained pointers</a></h3>

 <p>
 The key extractors provided by Boost.MultiIndex are templatized according
 to the type <code>Type</code> and serve to extract keys not only from objects
 of type <code>Type</code>, but also from reference wrappers provided by
 <a href="../../../../doc/html/ref.html">Boost.Ref</a> and from <i>chained pointers</i>
 to <code>Type</code> (or to reference wrappers of <code>Type</code>): a chained pointer
 is any type <code>P</code> such that, for an object <code>p</code> of type
 <code>const P</code>
 <ul>
   <li><code>*p</code> yields an object of type <code>Type&amp;</code> or
     <code>boost::reference_wrapper&lt;Type></code>, OR</li>
   <li><code>*p</code> yields a chained pointer to <code>Type</code>,</li>
 </ul>
 that is, chained pointers are arbitrary compositions of pointer-like objects
 ultimately dereferencing to values of <code>Type&amp;</code> or
 <code>boost::reference_wrapper&lt;Type></code>.
 <p>

 <h2><a name="synopsis">Header
 <a href="../../../../boost/multi_index/key_extractors.hpp">
 <code>"boost/multi_index/key_extractors.hpp"</code></a> synopsis</a>
 </h2>

 <blockquote><pre>
 <span class=preprocessor>#include</span> <span class=special>&lt;</span><span class=identifier>boost</span><span class=special>/</span><span class=identifier>multi_index</span><span class=special>/</span><span class=identifier>identity</span><span class=special>.</span><span class=identifier>hpp</span><span class=special>&gt;</span>
 <span class=preprocessor>#include</span> <span class=special>&lt;</span><span class=identifier>boost</span><span class=special>/</span><span class=identifier>multi_index</span><span class=special>/</span><span class=identifier>member</span><span class=special>.</span><span class=identifier>hpp</span><span class=special>&gt;</span>
 <span class=preprocessor>#include</span> <span class=special>&lt;</span><span class=identifier>boost</span><span class=special>/</span><span class=identifier>multi_index</span><span class=special>/</span><span class=identifier>mem_fun</span><span class=special>.</span><span class=identifier>hpp</span><span class=special>&gt;</span>
 <span class=preprocessor>#include</span> <span class=special>&lt;</span><span class=identifier>boost</span><span class=special>/</span><span class=identifier>multi_index</span><span class=special>/</span><span class=identifier>global_fun</span><span class=special>.</span><span class=identifier>hpp</span><span class=special>&gt;</span>
 <span class=preprocessor>#include</span> <span class=special>&lt;</span><span class=identifier>boost</span><span class=special>/</span><span class=identifier>multi_index</span><span class=special>/</span><span class=identifier>composite_key</span><span class=special>.</span><span class=identifier>hpp</span><span class=special>&gt;</span>
 </pre></blockquote>

 <p>
 This header includes all the key extractors provided by Boost.MultiIndex.
 </p>

 <h2>
 <a name="identity_synopsis">Header
 <a href="../../../../boost/multi_index/identity.hpp">
 <code>"boost/multi_index/identity.hpp"</code></a> synopsis</a></h2>

 <blockquote><pre>
 <span class=keyword>namespace</span> <span class=identifier>boost</span><span class=special>{</span>

 <span class=keyword>namespace</span> <span class=identifier>multi_index</span><span class=special>{</span>

 <span class=keyword>template</span><span class=special>&lt;</span><span class=keyword>typename</span> <span class=identifier>T</span><span class=special>&gt;</span> <span class=keyword>struct</span> <span class=identifier>identity</span><span class=special>;</span>

 <span class=special>}</span> <span class=comment>// namespace boost::multi_index</span>

 <span class=special>}</span> <span class=comment>// namespace boost</span>
 </pre></blockquote>

 <h3><a name="identity">Class template <code>identity</code></a></h3>

 <p>
 <code>identity</code> is a <a href="#key_extractors"><code>Key Extractor</code></a>
 that acts as a do-nothing identity functor.
 </p>

 <blockquote><pre>
 <span class=keyword>template</span><span class=special>&lt;</span><span class=keyword>typename</span> <span class=identifier>Type</span><span class=special>&gt;</span>
 <span class=keyword>struct</span> <span class=identifier>identity</span>
 <span class=special>{</span>
   <span class=keyword>typedef</span> <span class=identifier>Type</span> <span class=identifier>result_type</span><span class=special>;</span>

   <span class=comment>// only provided if const ChainedPtr&amp; is not convertible to const Type&amp;</span>
   <span class=keyword>template</span><span class=special>&lt;</span><span class=keyword>typename</span> <span class=identifier>ChainedPtr</span><span class=special>&gt;</span> <span class=identifier>Type</span><span class=special>&amp;</span> <span class=keyword>operator</span><span class=special>()(</span><span class=keyword>const</span> <span class=identifier>ChainedPtr</span><span class=special>&amp;</span> <span class=identifier>x</span><span class=special>)</span><span class=keyword>const</span><span class=special>;</span>

   <span class=keyword>const</span> <span class=identifier>Type</span><span class=special>&amp;</span> <span class=keyword>operator</span><span class=special>()(</span><span class=keyword>const</span> <span class=identifier>Type</span><span class=special>&amp;</span> <span class=identifier>x</span><span class=special>)</span><span class=keyword>const</span><span class=special>;</span>
   <span class=identifier>Type</span><span class=special>&amp;</span>       <span class=keyword>operator</span><span class=special>()(</span><span class=identifier>Type</span><span class=special>&amp;</span> <span class=identifier>x</span><span class=special>)</span><span class=keyword>const</span><span class=special>;</span> <span class=comment>// only provided if Type is non-const

   // only provided if Type is non-const</span>
   <span class=keyword>const</span> <span class=identifier>Type</span><span class=special>&amp;</span> <span class=keyword>operator</span><span class=special>()(</span><span class=keyword>const</span> <span class=identifier>reference_wrapper</span><span class=special>&lt;</span><span class=keyword>const</span> <span class=identifier>Type</span><span class=special>&gt;&amp;</span> <span class=identifier>x</span><span class=special>)</span><span class=keyword>const</span><span class=special>;</span>

   <span class=comment>// only provided if Type is const</span>
   <span class=identifier>Type</span><span class=special>&amp;</span> <span class=keyword>operator</span><span class=special>()(</span>
     <span class=keyword>const</span> <span class=identifier>reference_wrapper</span><span class=special>&lt;</span><span class=keyword>typename</span> <span class=identifier>remove_const</span><span class=special>&lt;</span><span class=identifier>Type</span><span class=special>&gt;::</span><span class=identifier>type</span><span class=special>&gt;&amp;</span> <span class=identifier>x</span><span class=special>)</span><span class=keyword>const</span><span class=special>;</span>

   <span class=identifier>Type</span><span class=special>&amp;</span> <span class=keyword>operator</span><span class=special>()(</span><span class=keyword>const</span> <span class=identifier>reference_wrapper</span><span class=special>&lt;</span><span class=identifier>Type</span><span class=special>&gt;&amp;</span> <span class=identifier>x</span><span class=special>)</span><span class=keyword>const</span><span class=special>;</span>
 <span class=special>};</span>
 </pre></blockquote>

 <p>
 <code>identity&lt;Type></code> is a model of:
 <ul>
   <li>read/write <a href="#key_extractors"><code>Key Extractor</code></a>
     from <code>Type</code>,</li>
   <li><a href="#key_extractors"><code>Key Extractor</code></a>
     from <code>reference_wrapper&lt;const Type></code>,</li>
   <li>read/write <a href="#key_extractors"><code>Key Extractor</code></a>
     from <code>reference_wrapper&lt;Type></code>,</li>
   <li><a href="#key_extractors"><code>Key Extractor</code></a>
     from any <a href="#chained_pointers">chained pointer</a> to
     <code>const Type</code>,</li>
   <li>read/write <a href="#key_extractors"><code>Key Extractor</code></a>
     from any <a href="#chained_pointers">chained pointer</a>
     to <code>Type</code>.</li>
 </ul>
 </p>

 <h4><code>identity</code> members</h4>

 <code>template&lt;typename ChainedPtr> Type&amp; operator()(const ChainedPtr&amp; x)const;</code>

 <blockquote>
 <b>Requires:</b> <code>ChainedPtr</code> is a <a href="#chained_pointers">chained pointer</a>
 type to <code>Type</code>.<br>
 <b>Returns:</b> a reference to the object chained-pointed to by <code>x</code>.
 </blockquote>

 <code>const Type&amp; operator()(const Type&amp; x)const;</code>

 <blockquote>
 <b>Returns:</b> <code>x</code>.
 </blockquote>

 <code>Type&amp; operator()(Type&amp; x)const;</code>

 <blockquote>
 <b>Returns:</b> <code>x</code>.
 </blockquote>

 <code>const Type&amp; operator()(const reference_wrapper&lt;const Type>&amp; x)const;</code>
 <blockquote>
 <b>Returns:</b> <code>x.get()</code>.
 </blockquote>

 <code>Type&amp; operator()(const reference_wrapper&lt;typename remove_const&lt;Type>::type>&amp; x)const;</code>
 <blockquote>
 <b>Returns:</b> <code>x.get()</code>.
 </blockquote>

 <code>Type&amp; operator()(const reference_wrapper&lt;Type>&amp; x)const;</code>
 <blockquote>
 <b>Returns:</b> <code>x.get()</code>.
 </blockquote>


 <h2>
 <a name="member_synopsis">Header
 <a href="../../../../boost/multi_index/member.hpp">
 <code>"boost/multi_index/member.hpp"</code></a> synopsis</a></h2>

 <blockquote><pre>
 <span class=keyword>namespace</span> <span class=identifier>boost</span><span class=special>{</span>

 <span class=keyword>namespace</span> <span class=identifier>multi_index</span><span class=special>{</span>

 <span class=keyword>template</span><span class=special>&lt;</span><span class=keyword>class</span> <span class=identifier>Class</span><span class=special>,</span><span class=keyword>typename</span> <span class=identifier>Type</span><span class=special>,</span><span class=identifier>Type</span> <span class=identifier>Class</span><span class=special>::*</span><span class=identifier>PtrToMember</span><span class=special>&gt;</span>
 <span class=keyword>struct</span> <span class=identifier>member</span><span class=special>;</span>

 <span class=keyword>template</span><span class=special>&lt;</span><span class=keyword>class</span> <span class=identifier>Class</span><span class=special>,</span><span class=keyword>typename</span> <span class=identifier>Type</span><span class=special>,</span><span class=identifier>std</span><span class=special>::</span><span class=identifier>size_t</span> <span class=identifier>OffsetOfMember</span><span class=special>&gt;</span>
 <span class=keyword>struct</span> <span class=identifier>member_offset</span><span class=special>;</span>

 <span class=preprocessor>#define</span> <span class=identifier>BOOST_MULTI_INDEX_MEMBER</span><span class=special>(</span><span class=identifier>Class</span><span class=special>,</span><span class=identifier>Type</span><span class=special>,</span><span class=identifier>MemberName</span><span class=special>)</span> <b>implementation defined</b>

 <span class=special>}</span> <span class=comment>// namespace boost::multi_index</span>

 <span class=special>}</span> <span class=comment>// namespace boost</span>
 </pre></blockquote>

 <h3><a name="member">Class template <code>member</code></a></h3>

 <p>
 <code>member</code> is a <a href="#key_extractors"><code>Key Extractor</code></a>
 aimed at accessing a given member of a class.
 </p>

 <blockquote><pre>
 <span class=keyword>template</span><span class=special>&lt;</span><span class=keyword>class</span> <span class=identifier>Class</span><span class=special>,</span><span class=keyword>typename</span> <span class=identifier>Type</span><span class=special>,</span><span class=identifier>Type</span> <span class=identifier>Class</span><span class=special>::*</span><span class=identifier>PtrToMember</span><span class=special>&gt;</span>
 <span class=keyword>struct</span> <span class=identifier>member</span>
 <span class=special>{</span>
   <span class=keyword>typedef</span> <span class=identifier>Type</span> <span class=identifier>result_type</span><span class=special>;</span>

   <span class=comment>// only provided if const ChainedPtr&amp; is not convertible to const Class&amp;</span>
   <span class=keyword>template</span><span class=special>&lt;</span><span class=keyword>typename</span> <span class=identifier>ChainedPtr</span><span class=special>&gt;</span> <span class=identifier>Type</span><span class=special>&amp;</span> <span class=keyword>operator</span><span class=special>()(</span><span class=keyword>const</span> <span class=identifier>ChainedPtr</span><span class=special>&amp;</span> <span class=identifier>x</span><span class=special>)</span><span class=keyword>const</span><span class=special>;</span>

   <span class=keyword>const</span> <span class=identifier>Type</span><span class=special>&amp;</span> <span class=keyword>operator</span><span class=special>()(</span><span class=keyword>const</span> <span class=identifier>Class</span><span class=special>&amp;</span> <span class=identifier>x</span><span class=special>)</span><span class=keyword>const</span><span class=special>;</span>
   <span class=identifier>Type</span><span class=special>&amp;</span>       <span class=keyword>operator</span><span class=special>()(</span><span class=identifier>Class</span><span class=special>&amp;</span> <span class=identifier>x</span><span class=special>)</span><span class=keyword>const</span><span class=special>;</span> <span class=comment>// only provided if Type is non-const</span>
   <span class=keyword>const</span> <span class=identifier>Type</span><span class=special>&amp;</span> <span class=keyword>operator</span><span class=special>()(</span><span class=keyword>const</span> <span class=identifier>reference_wrapper</span><span class=special>&lt;</span><span class=keyword>const</span> <span class=identifier>Class</span><span class=special>&gt;&amp;</span> <span class=identifier>x</span><span class=special>)</span><span class=keyword>const</span><span class=special>;</span>
   <span class=identifier>Type</span><span class=special>&amp;</span>       <span class=keyword>operator</span><span class=special>()(</span><span class=keyword>const</span> <span class=identifier>reference_wrapper</span><span class=special>&lt;</span><span class=identifier>Class</span><span class=special>&gt;&amp;</span> <span class=identifier>x</span><span class=special>)</span><span class=keyword>const</span><span class=special>;</span>
 <span class=special>};</span>
 </pre></blockquote>

 <p>
 The <code>PtrToMember</code> template argument specifies the particular
 <code>Type Class::*</code> pointer to the member to be extracted.
 <code>member&lt;Class,Type,PtrToMember></code> is a model of:
 <ul>
   <li>read/write <a href="#key_extractors"><code>Key Extractor</code></a>
     from <code>Class</code>,</li>
   <li><a href="#key_extractors"><code>Key Extractor</code></a>
     from <code>reference_wrapper&lt;const Class></code>,</li>
   <li>read/write <a href="#key_extractors"><code>Key Extractor</code></a>
     from <code>reference_wrapper&lt;Class></code>,</li>
   <li><a href="#key_extractors"><code>Key Extractor</code></a>
     from any <a href="#chained_pointers">chained pointer</a>
     to <code>const Class</code>,</li>
   <li>read/write <a href="#key_extractors"><code>Key Extractor</code></a>
     from any <a href="#chained_pointers">chained pointer</a>
     to <code>Class</code>.</li>
 </ul>
 </p>

 <h4><code>member</code> members</h4>

 <code>template&lt;typename ChainedPtr> Type&amp; operator()(const ChainedPtr&amp; x)const;</code>

 <blockquote>
 <b>Requires:</b> <code>ChainedPtr</code> is a <a href="#chained_pointers">chained pointer</a>
 type to <code>Type</code>.<br>
 <b>Returns:</b> a reference to the object chained-pointed to by <code>x</code>.
 </blockquote>

 <code>const Type&amp; operator()(const Class&amp; x)const;</code>

 <blockquote>
 <b>Returns:</b> <code>x.*PtrToMember</code>.
 </blockquote>

 <code>Type&amp; operator()(Class&amp; x)const;</code>

 <blockquote>
 <b>Returns:</b> <code>x.*PtrToMember</code>.
 </blockquote>

 <code>const Type&amp; operator()(const reference_wrapper&lt;const Class>&amp; x)const;</code>

 <blockquote>
 <b>Returns:</b> <code>x.get().*PtrToMember</code>.
 </blockquote>

 <code>Type&amp; operator()(const reference_wrapper&lt;Class>&amp; x)const;</code>

 <blockquote>
 <b>Returns:</b> <code>x.get().*PtrToMember</code>.
 </blockquote>

 <h3><a name="member_offset">Class template <code>member_offset</code></a></h3>

 <p>
 Some compilers do not properly support pointers to members as non-type
 template arguments. The following have been confirmed to have bugs in
 this respect:
 <ul>
   <li>MSVC++ 6.0 (see
     <a href="http://support.microsoft.com/default.aspx?scid=kb;EN-US;249045">Microsoft
     Knowledge Base article #249045</a>),</li>
   <li>MSVC++ 7.0 (not officially confirmed by Microsoft),</li>
   <li>Intel C++ 7.0/7.1 for Windows (support issue #207321),</li>
   <li>VisualAge 6.0 for AIX (internal defect #288539.)</li>
 </ul>
 In this situation, <code>member_offset</code> provides an
 alternative to <a href="#member"><code>member</code></a> accepting offsets
 instead of pointers to members. Please note that the use of
 <code>offsetof</code> on non-POD types is forbidden by the standard;
 luckily enough, most compilers accept it nevertheless, so
 <code>member_offset</code> serves as a workaround for most practical purposes.
 </p>

 <blockquote><pre>
 <span class=keyword>template</span><span class=special>&lt;</span><span class=keyword>class</span> <span class=identifier>Class</span><span class=special>,</span><span class=keyword>typename</span> <span class=identifier>Type</span><span class=special>,</span><span class=identifier>std</span><span class=special>::</span><span class=identifier>size_t</span> <span class=identifier>OffsetOfMember</span><span class=special>&gt;</span>
 <span class=keyword>struct</span> <span class=identifier>member_offset</span>
 <span class=special>{</span>
   <span class=keyword>typedef</span> <span class=identifier>Type</span> <span class=identifier>result_type</span><span class=special>;</span>

   <span class=comment>// only provided if const ChainedPtr&amp; is not convertible to const Class&amp;</span>
   <span class=keyword>template</span><span class=special>&lt;</span><span class=keyword>typename</span> <span class=identifier>ChainedPtr</span><span class=special>&gt;</span> <span class=identifier>Type</span><span class=special>&amp;</span> <span class=keyword>operator</span><span class=special>()(</span><span class=keyword>const</span> <span class=identifier>ChainedPtr</span><span class=special>&amp;</span> <span class=identifier>x</span><span class=special>)</span><span class=keyword>const</span><span class=special>;</span>

   <span class=keyword>const</span> <span class=identifier>Type</span><span class=special>&amp;</span> <span class=keyword>operator</span><span class=special>()(</span><span class=keyword>const</span> <span class=identifier>Class</span><span class=special>&amp;</span> <span class=identifier>x</span><span class=special>)</span><span class=keyword>const</span><span class=special>;</span>
   <span class=identifier>Type</span><span class=special>&amp;</span>       <span class=keyword>operator</span><span class=special>()(</span><span class=identifier>Class</span><span class=special>&amp;</span> <span class=identifier>x</span><span class=special>)</span><span class=keyword>const</span><span class=special>;</span> <span class=comment>// only provided if Type is non-const</span>
   <span class=keyword>const</span> <span class=identifier>Type</span><span class=special>&amp;</span> <span class=keyword>operator</span><span class=special>()(</span><span class=keyword>const</span> <span class=identifier>reference_wrapper</span><span class=special>&lt;</span><span class=keyword>const</span> <span class=identifier>Class</span><span class=special>&gt;&amp;</span> <span class=identifier>x</span><span class=special>)</span><span class=keyword>const</span><span class=special>;</span>
   <span class=identifier>Type</span><span class=special>&amp;</span>       <span class=keyword>operator</span><span class=special>()(</span><span class=keyword>const</span> <span class=identifier>reference_wrapper</span><span class=special>&lt;</span><span class=identifier>Class</span><span class=special>&gt;&amp;</span> <span class=identifier>x</span><span class=special>)</span><span class=keyword>const</span><span class=special>;</span>
 <span class=special>};</span>
 </pre></blockquote>

 <p>As an example of use, given the class</p>

 <blockquote><pre>
 <span class=keyword>class</span> <span class=identifier>A</span>
 <span class=special>{</span>
   <span class=keyword>int</span> <span class=identifier>x</span><span class=special>;</span>
 <span class=special>}</span>
 </pre></blockquote>

 <p>
 the instantiation <code>member&lt;A,int,&amp;A::x></code> can be simulated then
 as <code>member_offset&lt;A,int,offsetof(A,x)></code>.
 </p>

 <h3><a name="boost_multi_index_member">Macro <code>BOOST_MULTI_INDEX_MEMBER</code></a></h3>

 <blockquote><pre>
 <span class=identifier>BOOST_MULTI_INDEX_MEMBER</span><span class=special>(</span><span class=identifier>Class</span><span class=special>,</span><span class=identifier>Type</span><span class=special>,</span><span class=identifier>MemberName</span><span class=special>)</span>
 </pre></blockquote>

 <p>
 This macro is provided as an aid for using <code>member</code> and
 <code>member_offset</code> when writing cross-platform code. In the usual cases,
 it expands to
 </p>

 <blockquote><pre>
 <span class=special>::</span><span class=identifier>boost</span><span class=special>::</span><span class=identifier>multi_index</span><span class=special>::</span><span class=identifier>member</span><span class=special>&lt;</span><span class=identifier>Class</span><span class=special>,</span><span class=identifier>Type</span><span class=special>,&amp;</span><span class=identifier>Class</span><span class=special>::</span><span class=identifier>MemberName</span><span class=special>&gt;</span>
 </pre></blockquote>

 <p>
 but it resolves to
 </p>

 <blockquote><pre>
 <span class=special>::</span><span class=identifier>boost</span><span class=special>::</span><span class=identifier>multi_index</span><span class=special>::</span><span class=identifier>member_offset</span><span class=special>&lt;</span><span class=identifier>Class</span><span class=special>,</span><span class=identifier>Type</span><span class=special>,</span><span class=identifier>offsetof</span><span class=special>(</span><span class=identifier>Class</span><span class=special>,</span><span class=identifier>MemberName</span><span class=special>)&gt;</span>
 </pre></blockquote>

 <p>
 if the <a href="../../../../libs/config/config.htm">Boost Configuration Library</a>
 defect macro <code>BOOST_NO_POINTER_TO_MEMBER_TEMPLATE_PARAMETERS</code>
 is defined.
 </p>

 <h2>
 <a name="mem_fun_synopsis">Header
 <a href="../../../../boost/multi_index/mem_fun.hpp">
 <code>"boost/multi_index/mem_fun.hpp"</code></a> synopsis</a></h2>

 <blockquote><pre>
 <span class=keyword>namespace</span> <span class=identifier>boost</span><span class=special>{</span>

 <span class=keyword>namespace</span> <span class=identifier>multi_index</span><span class=special>{</span>

 <span class=keyword>template</span><span class=special>&lt;</span><span class=keyword>class</span> <span class=identifier>Class</span><span class=special>,</span><span class=keyword>typename</span> <span class=identifier>Type</span><span class=special>,</span><span class=identifier>Type</span> <span class=special>(</span><span class=identifier>Class</span><span class=special>::*</span><span class=identifier>PtrToMemberFunction</span><span class=special>)()</span><span class=keyword>const</span><span class=special>&gt;</span>
 <span class=keyword>struct</span> <span class=identifier>const_mem_fun</span><span class=special>;</span>

 <span class=keyword>template</span><span class=special>&lt;</span><span class=keyword>class</span> <span class=identifier>Class</span><span class=special>,</span><span class=keyword>typename</span> <span class=identifier>Type</span><span class=special>,</span><span class=identifier>Type</span> <span class=special>(</span><span class=identifier>Class</span><span class=special>::*</span><span class=identifier>PtrToMemberFunction</span><span class=special>)()&gt;</span>
 <span class=keyword>struct</span> <span class=identifier>mem_fun</span><span class=special>;</span>

 <span class=keyword>template</span><span class=special>&lt;</span>
   <span class=keyword>class</span> <span class=identifier>Class</span><span class=special>,</span><span class=keyword>typename</span> <span class=identifier>Type</span><span class=special>,</span>
   <span class=keyword>typename</span> <span class=identifier>PtrToMemberFunctionType</span><span class=special>,</span><span class=identifier>PtrToMemberFunctionType</span> <span class=identifier>PtrToMemberFunction</span>
 <span class=special>&gt;</span>
 <span class=keyword>struct</span> <span class=identifier>const_mem_fun_explicit</span><span class=special>;</span>

 <span class=keyword>template</span><span class=special>&lt;</span>
   <span class=keyword>class</span> <span class=identifier>Class</span><span class=special>,</span><span class=keyword>typename</span> <span class=identifier>Type</span><span class=special>,</span>
   <span class=keyword>typename</span> <span class=identifier>PtrToMemberFunctionType</span><span class=special>,</span><span class=identifier>PtrToMemberFunctionType</span> <span class=identifier>PtrToMemberFunction</span>
 <span class=special>&gt;</span>
 <span class=keyword>struct</span> <span class=identifier>mem_fun_explicit</span><span class=special>;</span>

 <span class=preprocessor>#define</span> <span class=identifier>BOOST_MULTI_INDEX_CONST_MEM_FUN</span><span class=special>(</span><span class=identifier>Class</span><span class=special>,</span><span class=identifier>Type</span><span class=special>,</span><span class=identifier>MemberFunName</span><span class=special>)</span> <span class=special>\</span>
 <b>implementation defined</b>
 <span class=preprocessor>#define</span> <span class=identifier>BOOST_MULTI_INDEX_MEM_FUN</span><span class=special>(</span><span class=identifier>Class</span><span class=special>,</span><span class=identifier>Type</span><span class=special>,</span><span class=identifier>MemberFunName</span><span class=special>)</span> <span class=special>\</span>
 <b>implementation defined</b>

 <span class=special>}</span> <span class=comment>// namespace boost::multi_index</span>

 <span class=special>}</span> <span class=comment>// namespace boost</span>
 </pre></blockquote>

 <h3><a name="const_mem_fun">Class template <code>const_mem_fun</code></a></h3>

 <p>
 <code>const_mem_fun</code> is a <a href="#key_extractors"><code>Key Extractor</code></a>
 returning as key the result of invoking a given constant member function of a class.
 </p>

 <blockquote><pre>
 <span class=keyword>template</span><span class=special>&lt;</span><span class=keyword>class</span> <span class=identifier>Class</span><span class=special>,</span><span class=keyword>typename</span> <span class=identifier>Type</span><span class=special>,</span><span class=identifier>Type</span> <span class=special>(</span><span class=identifier>Class</span><span class=special>::*</span><span class=identifier>PtrToMemberFunction</span><span class=special>)()</span><span class=keyword>const</span><span class=special>&gt;</span>
 <span class=keyword>struct</span> <span class=identifier>const_mem_fun</span>
 <span class=special>{</span>
   <span class=keyword>typedef</span> <span class=keyword>typename</span> <span class=identifier>remove_reference</span><span class=special>&lt;</span><span class=identifier>Type</span><span class=special>&gt;::</span><span class=identifier>type</span> <span class=identifier>result_type</span><span class=special>;</span>

   <span class=comment>// only provided if const ChainedPtr&amp; is not convertible to const Class&amp;</span>
   <span class=keyword>template</span><span class=special>&lt;</span><span class=keyword>typename</span> <span class=identifier>ChainedPtr</span><span class=special>&gt;</span> <span class=identifier>Type</span> <span class=keyword>operator</span><span class=special>()(</span><span class=keyword>const</span> <span class=identifier>ChainedPtr</span><span class=special>&amp;</span> <span class=identifier>x</span><span class=special>)</span><span class=keyword>const</span><span class=special>;</span>

   <span class=identifier>Type</span> <span class=keyword>operator</span><span class=special>()(</span><span class=keyword>const</span> <span class=identifier>Class</span><span class=special>&amp;</span> <span class=identifier>x</span><span class=special>)</span><span class=keyword>const</span><span class=special>;</span>
   <span class=identifier>Type</span> <span class=keyword>operator</span><span class=special>()(</span><span class=keyword>const</span> <span class=identifier>reference_wrapper</span><span class=special>&lt;</span><span class=keyword>const</span> <span class=identifier>Class</span><span class=special>&gt;&amp;</span> <span class=identifier>x</span><span class=special>)</span><span class=keyword>const</span><span class=special>;</span>
   <span class=identifier>Type</span> <span class=keyword>operator</span><span class=special>()(</span><span class=keyword>const</span> <span class=identifier>reference_wrapper</span><span class=special>&lt;</span><span class=identifier>Class</span><span class=special>&gt;&amp;</span> <span class=identifier>x</span><span class=special>)</span><span class=keyword>const</span><span class=special>;</span>
 <span class=special>};</span>
 </pre></blockquote>

 <p>
 The <code>PtrToMemberFunction</code> template argument specifies the particular
 <code>Type (Class::*PtrToMemberFunction)()const</code> pointer to the the constant
 member function used in the extraction.
 <code>const_mem_fun&lt;Class,Type,PtrToMemberFunction></code> is a model of:
 <ul>
   <li><a href="#key_extractors"><code>Key Extractor</code></a>
     from <code>Class</code>,</li>
   <li><a href="#key_extractors"><code>Key Extractor</code></a>
     from <code>reference_wrapper&lt;const Class></code>,</li>
   <li><a href="#key_extractors"><code>Key Extractor</code></a>
     from <code>reference_wrapper&lt;Class></code>,</li>
   <li><a href="#key_extractors"><code>Key Extractor</code></a>
     from any <a href="#chained_pointers">chained pointer</a>
     to <code>const Class</code>,</li>
   <li><a href="#key_extractors"><code>Key Extractor</code></a>
     from any <a href="#chained_pointers">chained pointer</a>
     to <code>Class</code>.</li>
 </ul>
 </p>

 <h4><code>const_mem_fun</code> members</h4>

 <code>template&lt;typename ChainedPtr> Type operator()(const ChainedPtr&amp; x)const;</code>

 <blockquote>
 <b>Requires:</b> <code>ChainedPtr</code> is a <a href="#chained_pointers">chained pointer</a>
 type to <code>Type</code>.<br>
 <b>Returns:</b> <code>(y.*PtrToMemberFunction)()</code>, where <code>y</code> is the
 object chained-pointed to by <code>x</code>.
 </blockquote>

 <code>Type operator()(const Class&amp; x)const;</code>

 <blockquote>
 <b>Returns:</b> <code>(x.*PtrToMemberFunction)()</code>.
 </blockquote>

 <code>Type operator()(const reference_wrapper&lt;const Class>&amp; x)const;</code>

 <blockquote>
 <b>Returns:</b> <code>(x.get().*PtrToMemberFunction)()</code>.
 </blockquote>

 <code>Type operator()(const reference_wrapper&lt;Class>&amp; x)const;</code>

 <blockquote>
 <b>Returns:</b> <code>(x.get().*PtrToMemberFunction)()</code>.
 </blockquote>

 <h3><a name="mem_fun">Class template <code>mem_fun</code></a></h3>

 <p>
 <code>mem_fun</code> is a <a href="#key_extractors"><code>Key Extractor</code></a>
 returning as key the result of invoking a given member function of a class.
 </p>

 <blockquote><pre>
 <span class=keyword>template</span><span class=special>&lt;</span><span class=keyword>class</span> <span class=identifier>Class</span><span class=special>,</span><span class=keyword>typename</span> <span class=identifier>Type</span><span class=special>,</span><span class=identifier>Type</span> <span class=special>(</span><span class=identifier>Class</span><span class=special>::*</span><span class=identifier>PtrToMemberFunction</span><span class=special>)()&gt;</span>
 <span class=keyword>struct</span> <span class=identifier>mem_fun</span>
 <span class=special>{</span>
   <span class=keyword>typedef</span> <span class=keyword>typename</span> <span class=identifier>remove_reference</span><span class=special>&lt;</span><span class=identifier>Type</span><span class=special>&gt;::</span><span class=identifier>type</span> <span class=identifier>result_type</span><span class=special>;</span>

   <span class=comment>// only provided if ChainedPtr&amp; is not convertible to Class&amp;</span>
   <span class=keyword>template</span><span class=special>&lt;</span><span class=keyword>typename</span> <span class=identifier>ChainedPtr</span><span class=special>&gt;</span> <span class=identifier>Type</span> <span class=keyword>operator</span><span class=special>()(</span><span class=keyword>const</span> <span class=identifier>ChainedPtr</span><span class=special>&amp;</span> <span class=identifier>x</span><span class=special>)</span><span class=keyword>const</span><span class=special>;</span>

   <span class=identifier>Type</span> <span class=keyword>operator</span><span class=special>()(</span><span class=identifier>Class</span><span class=special>&amp;</span> <span class=identifier>x</span><span class=special>)</span><span class=keyword>const</span><span class=special>;</span>
   <span class=identifier>Type</span> <span class=keyword>operator</span><span class=special>()(</span><span class=keyword>const</span> <span class=identifier>reference_wrapper</span><span class=special>&lt;</span><span class=identifier>Class</span><span class=special>&gt;&amp;</span> <span class=identifier>x</span><span class=special>)</span><span class=keyword>const</span><span class=special>;</span>
 <span class=special>};</span>
 </pre></blockquote>

 <p>
 The <code>PtrToMemberFunction</code> template argument specifies the particular
 <code>Type (Class::*PtrToMemberFunction)()</code> pointer to the the member
 function used in the extraction.
 <code>mem_fun&lt;Class,Type,PtrToMemberFunction></code> is a model of:
 <ul>
   <li><a href="#key_extractors"><code>Key Extractor</code></a>
     from <code>reference_wrapper&lt;Class></code>,</li>
   <li><a href="#key_extractors"><code>Key Extractor</code></a>
     from any <a href="#chained_pointers">chained pointer</a>
     to <code>Class</code>.</li>
 </ul>
 </p>

 <h4><code>mem_fun</code> members</h4>

 <code>template&lt;typename ChainedPtr> Type operator()(const ChainedPtr&amp; x)const;</code>

 <blockquote>
 <b>Requires:</b> <code>ChainedPtr</code> is a <a href="#chained_pointers">chained pointer</a>
 type to <code>Type</code>.<br>
 <b>Returns:</b> <code>(y.*PtrToMemberFunction)()</code>, where <code>y</code> is the
 object chained-pointed to by <code>x</code>.
 </blockquote>

 <code>Type operator()(Class&amp; x)const;</code>

 <blockquote>
 <b>Returns:</b> <code>(x.*PtrToMemberFunction)()</code>.
 </blockquote>

 <code>Type operator()(const reference_wrapper&lt;Class>&amp; x)const;</code>

 <blockquote>
 <b>Returns:</b> <code>(x.get().*PtrToMemberFunction)()</code>.
 </blockquote>

 <h3><a name="const_mem_fun_explicit">Class template <code>const_mem_fun_explicit</code></a></h3>

 <p>
 MSVC++ 6.0 do not properly support pointers to constant member functions as non-type
 template parameters, thus <a href="#const_mem_fun"><code>const_mem_fun</code></a> cannot be
 used in this compiler. A simple workaround consists in specifying the <i>type</i> of
 these pointers as an additional template parameter.
 </p>

 <blockquote><pre>
 <span class=keyword>template</span><span class=special>&lt;</span>
   <span class=keyword>class</span> <span class=identifier>Class</span><span class=special>,</span><span class=keyword>typename</span> <span class=identifier>Type</span><span class=special>,</span>
   <span class=keyword>typename</span> <span class=identifier>PtrToMemberFunctionType</span><span class=special>,</span><span class=identifier>PtrToMemberFunctionType</span> <span class=identifier>PtrToMemberFunction</span>
 <span class=special>&gt;</span>
 <span class=keyword>struct</span> <span class=identifier>const_mem_fun_explicit</span>
 <span class=special>{</span>
   <span class=keyword>typedef</span> <span class=keyword>typename</span> <span class=identifier>remove_reference</span><span class=special>&lt;</span><span class=identifier>Type</span><span class=special>&gt;::</span><span class=identifier>type</span> <span class=identifier>result_type</span><span class=special>;</span>

   <span class=comment>// only provided if const ChainedPtr&amp; is not convertible to const Class&amp;</span>
   <span class=keyword>template</span><span class=special>&lt;</span><span class=keyword>typename</span> <span class=identifier>ChainedPtr</span><span class=special>&gt;</span> <span class=identifier>Type</span> <span class=keyword>operator</span><span class=special>()(</span><span class=keyword>const</span> <span class=identifier>ChainedPtr</span><span class=special>&amp;</span> <span class=identifier>x</span><span class=special>)</span><span class=keyword>const</span><span class=special>;</span>

   <span class=identifier>Type</span> <span class=keyword>operator</span><span class=special>()(</span><span class=keyword>const</span> <span class=identifier>Class</span><span class=special>&amp;</span> <span class=identifier>x</span><span class=special>)</span><span class=keyword>const</span><span class=special>;</span>
   <span class=identifier>Type</span> <span class=keyword>operator</span><span class=special>()(</span><span class=keyword>const</span> <span class=identifier>reference_wrapper</span><span class=special>&lt;</span><span class=keyword>const</span> <span class=identifier>Class</span><span class=special>&gt;&amp;</span> <span class=identifier>x</span><span class=special>)</span><span class=keyword>const</span><span class=special>;</span>
   <span class=identifier>Type</span> <span class=keyword>operator</span><span class=special>()(</span><span class=keyword>const</span> <span class=identifier>reference_wrapper</span><span class=special>&lt;</span><span class=identifier>Class</span><span class=special>&gt;&amp;</span> <span class=identifier>x</span><span class=special>)</span><span class=keyword>const</span><span class=special>;</span>
 <span class=special>};</span>
 </pre></blockquote>

 <p>
 <code>const_mem_fun_explicit</code> provides the very same functionality as
 its <code>const_mem_fun</code> analogous instantiation. For example, given the type
 </p>

 <blockquote><pre>
 <span class=keyword>struct</span> <span class=identifier>A</span>
 <span class=special>{</span>
   <span class=keyword>int</span> <span class=identifier>f</span><span class=special>()</span><span class=keyword>const</span><span class=special>;</span>
 <span class=special>};</span>
 </pre></blockquote>

 <p>
 the extractor <code>const_mem_fun&lt;A,int,&amp;A::f></code> can be replaced by
 <code>const_mem_fun_explicit&lt;A,int,int (A::*)()const,&amp;A::f></code>.
 </p>

 <h3><a name="mem_fun_explicit">Class template <code>mem_fun_explicit</code></a></h3>

 <p>
 For analogy with <a href="#const_mem_fun_explicit"><code>const_mem_fun_explicit</code></a>,
 a variation of <a href="#mem_fun"><code>mem_fun</code></a> is provided accepting
 an additional parameter with the type of the pointer to non-constant member function
 used for extraction.
 </p>

 <blockquote><pre>
 <span class=keyword>template</span><span class=special>&lt;</span>
   <span class=keyword>class</span> <span class=identifier>Class</span><span class=special>,</span><span class=keyword>typename</span> <span class=identifier>Type</span><span class=special>,</span>
   <span class=keyword>typename</span> <span class=identifier>PtrToMemberFunctionType</span><span class=special>,</span><span class=identifier>PtrToMemberFunctionType</span> <span class=identifier>PtrToMemberFunction</span>
 <span class=special>&gt;</span>
 <span class=keyword>struct</span> <span class=identifier>mem_fun_explicit</span>
 <span class=special>{</span>
   <span class=keyword>typedef</span> <span class=keyword>typename</span> <span class=identifier>remove_reference</span><span class=special>&lt;</span><span class=identifier>Type</span><span class=special>&gt;::</span><span class=identifier>type</span> <span class=identifier>result_type</span><span class=special>;</span>

   <span class=comment>// only provided if ChainedPtr&amp; is not convertible to Class&amp;</span>
   <span class=keyword>template</span><span class=special>&lt;</span><span class=keyword>typename</span> <span class=identifier>ChainedPtr</span><span class=special>&gt;</span> <span class=identifier>Type</span> <span class=keyword>operator</span><span class=special>()(</span><span class=keyword>const</span> <span class=identifier>ChainedPtr</span><span class=special>&amp;</span> <span class=identifier>x</span><span class=special>)</span><span class=keyword>const</span><span class=special>;</span>

   <span class=identifier>Type</span> <span class=keyword>operator</span><span class=special>()(</span><span class=identifier>Class</span><span class=special>&amp;</span> <span class=identifier>x</span><span class=special>)</span><span class=keyword>const</span><span class=special>;</span>
   <span class=identifier>Type</span> <span class=keyword>operator</span><span class=special>()(</span><span class=keyword>const</span> <span class=identifier>reference_wrapper</span><span class=special>&lt;</span><span class=identifier>Class</span><span class=special>&gt;&amp;</span> <span class=identifier>x</span><span class=special>)</span><span class=keyword>const</span><span class=special>;</span>
 <span class=special>};</span>
 </pre></blockquote>

 <h3><a name="boost_multi_index_const_mem_fun">Macro
 <code>BOOST_MULTI_INDEX_CONST_MEM_FUN</code></a></h3>

 <blockquote><pre>
 <span class=identifier>BOOST_MULTI_INDEX_CONST_MEM_FUN</span><span class=special>(</span><span class=identifier>Class</span><span class=special>,</span><span class=identifier>Type</span><span class=special>,</span><span class=identifier>MemberFunName</span><span class=special>)</span>
 </pre></blockquote>

 <p>
 Use this macro when writing cross-platform code selectively using
 <code>const_mem_fun_explicit</code> in place of <code>const_mem_fun</code> for
 compilers not supporting the latter. In the usual cases, the macro expands to
 </p>

 <blockquote><pre>
 <span class=special>::</span><span class=identifier>boost</span><span class=special>::</span><span class=identifier>multi_index</span><span class=special>::</span><span class=identifier>const_mem_fun</span><span class=special>&lt;</span><span class=identifier>Class</span><span class=special>,</span><span class=identifier>Type</span><span class=special>,&amp;</span><span class=identifier>Class</span><span class=special>::</span><span class=identifier>MemberFunName</span><span class=special>&gt;</span>
 </pre></blockquote>

 <p>
 but it resolves to
 </p>

 <blockquote><pre>
 <span class=special>::</span><span class=identifier>boost</span><span class=special>::</span><span class=identifier>multi_index</span><span class=special>::</span><span class=identifier>const_mem_fun_explicit</span><span class=special>&lt;</span>
   <span class=identifier>Class</span><span class=special>,</span><span class=identifier>Type</span><span class=special>,</span><span class=identifier>Type</span> <span class=special>(</span><span class=identifier>Class</span><span class=special>::*)()</span><span class=keyword>const</span><span class=special>,&amp;</span><span class=identifier>Class</span><span class=special>::</span><span class=identifier>MemberFunName</span>
 <span class=special>&gt;</span>
 </pre></blockquote>

 <p>
 for MSVC++ 6.0 or lower.
 </p>


 <h3><a name="boost_multi_index_mem_fun">Macro
 <code>BOOST_MULTI_INDEX_MEM_FUN</code></a></h3>

 <blockquote><pre>
 <span class=identifier>BOOST_MULTI_INDEX_MEM_FUN</span><span class=special>(</span><span class=identifier>Class</span><span class=special>,</span><span class=identifier>Type</span><span class=special>,</span><span class=identifier>MemberFunName</span><span class=special>)</span>
 </pre></blockquote>

 <p>
 By default, the macro expands to
 </p>

 <blockquote><pre>
 <span class=special>::</span><span class=identifier>boost</span><span class=special>::</span><span class=identifier>multi_index</span><span class=special>::</span><span class=identifier>mem_fun</span><span class=special>&lt;</span><span class=identifier>Class</span><span class=special>,</span><span class=identifier>Type</span><span class=special>,&amp;</span><span class=identifier>Class</span><span class=special>::</span><span class=identifier>MemberFunName</span><span class=special>&gt;</span>
 </pre></blockquote>

 <p>
 but it resolves to
 </p>

 <blockquote><pre>
 <span class=special>::</span><span class=identifier>boost</span><span class=special>::</span><span class=identifier>multi_index</span><span class=special>::</span><span class=identifier>mem_fun_explicit</span><span class=special>&lt;</span>
   <span class=identifier>Class</span><span class=special>,</span><span class=identifier>Type</span><span class=special>,</span><span class=identifier>Type</span> <span class=special>(</span><span class=identifier>Class</span><span class=special>::*)()</span><span class=special>,&amp;</span><span class=identifier>Class</span><span class=special>::</span><span class=identifier>MemberFunName</span>
 <span class=special>&gt;</span>
 </pre></blockquote>

 <p>
 for MSVC++ 6.0 or lower.
 </p>

 <h2>
 <a name="global_fun_synopsis">Header
 <a href="../../../../boost/multi_index/global_fun.hpp">
 <code>"boost/multi_index/global_fun.hpp"</code></a> synopsis</a></h2>

 <blockquote><pre>
 <span class=keyword>namespace</span> <span class=identifier>boost</span><span class=special>{</span>

 <span class=keyword>namespace</span> <span class=identifier>multi_index</span><span class=special>{</span>

 <span class=keyword>template</span><span class=special>&lt;</span><span class=keyword>class</span> <span class=identifier>Value</span><span class=special>,</span><span class=keyword>typename</span> <span class=identifier>Type</span><span class=special>,</span><span class=identifier>Type</span> <span class=special>(*</span><span class=identifier>PtrToFunction</span><span class=special>)(</span><span class=identifier>Value</span><span class=special>)&gt;</span>
 <span class=keyword>struct</span> <span class=identifier>global_fun</span><span class=special>;</span>

 <span class=special>}</span> <span class=comment>// namespace boost::multi_index</span>

 <span class=special>}</span> <span class=comment>// namespace boost</span>
 </pre></blockquote>

 <h3><a name="global_fun">Class template <code>global_fun</code></a></h3>

 <p>
 <code>global_fun</code> is a <a href="#key_extractors"><code>Key Extractor</code></a>
 based on a given global or static member function accepting the base type as argument
 and returning the associated key.
 </p>

 <blockquote><pre>
 <span class=keyword>template</span><span class=special>&lt;</span><span class=keyword>class</span> <span class=identifier>Value</span><span class=special>,</span><span class=keyword>typename</span> <span class=identifier>Type</span><span class=special>,</span><span class=identifier>Type</span> <span class=special>(*</span><span class=identifier>PtrToFunction</span><span class=special>)(</span><span class=identifier>Value</span><span class=special>)&gt;</span>
 <span class=keyword>struct</span> <span class=identifier>global_fun</span>
 <span class=special>{</span>
   <span class=keyword>typedef</span> <span class=keyword>typename</span> <span class=identifier>remove_reference</span><span class=special>&lt;</span><span class=identifier>Type</span><span class=special>&gt;::</span><span class=identifier>type</span> <span class=identifier>result_type</span><span class=special>;</span>

   <span class=comment>// Only provided under the following circumstances:
   //   - If Value is a reference to a constant type, only provided
   //     when const ChainedPtr&amp; is not convertible to Value;
   //   - if Value is a reference to a non-const type, only provided
   //     when ChainedPtr&amp; is not convertible to Value;
   //   - else, only provided when const ChainedPtr&amp; is not
   //     convertible to const Value&amp;.</span>
   <span class=identifier>Type</span> <span class=keyword>operator</span><span class=special>()(</span><span class=keyword>const</span> <span class=identifier>ChainedPtr</span><span class=special>&amp;</span> <span class=identifier>x</span><span class=special>)</span><span class=keyword>const</span><span class=special>;</span>

   <span class=comment>// only provided if Value is a reference type</span>
   <span class=identifier>Type</span> <span class=keyword>operator</span><span class=special>()(</span><span class=identifier>Value</span> <span class=identifier>x</span><span class=special>)</span><span class=keyword>const</span><span class=special>;</span>

   <span class=comment>// only provided if Value is not a reference type</span>
   <span class=identifier>Type</span> <span class=keyword>operator</span><span class=special>()(</span><span class=keyword>const</span> <span class=identifier>Value</span><span class=special>&amp;</span> <span class=identifier>x</span><span class=special>)</span><span class=keyword>const</span><span class=special>;</span>

   <span class=comment>// only provided if Value is not a reference type</span>
   <span class=identifier>Type</span> <span class=keyword>operator</span><span class=special>()(</span><span class=keyword>const</span> <span class=identifier>reference_wrapper</span><span class=special>&lt;</span><span class=keyword>const</span> <span class=identifier>Value</span><span class=special>&gt;&amp;</span> <span class=identifier>x</span><span class=special>)</span><span class=keyword>const</span><span class=special>;</span>

   <span class=comment>// only provided if Value is a reference type</span>
   <span class=identifier>Type</span> <span class=keyword>operator</span><span class=special>()(</span>
     <span class=keyword>const</span> <span class=identifier>reference_wrapper</span><span class=special>&lt;</span>
       <span class=identifier>remove_reference</span><span class=special>&lt;</span><span class=identifier>Value</span><span class=special>&gt;::</span><span class=identifier>type</span><span class=special>&gt;&amp;</span> <span class=identifier>x</span><span class=special>)</span><span class=keyword>const</span><span class=special>;</span>

   <span class=comment>// only provided if Value is not a reference type or is
   // a reference to a constant type</span>
   <span class=identifier>Type</span> <span class=keyword>operator</span><span class=special>()(</span>
     <span class=keyword>const</span> <span class=identifier>reference_wrapper</span><span class=special>&lt;</span>
       <span class=keyword>typename</span> <span class=identifier>remove_const</span><span class=special>&lt;</span>
         <span class=keyword>typename</span> <span class=identifier>remove_reference</span><span class=special>&lt;</span><span class=identifier>Value</span><span class=special>&gt;::</span><span class=identifier>type</span><span class=special>&gt;::</span><span class=identifier>type</span><span class=special>&gt;&amp;</span> <span class=identifier>x</span><span class=special>)</span><span class=keyword>const</span><span class=special>;</span>
 <span class=special>};</span>
 </pre></blockquote>

 <p>
 <code>PtrToFunction</code> specifies the particular function used to extract
 the key of type <code>Type</code> from some <code>BaseType</code>.
 <code>global_fun</code> supports the following function signatures:
 <ul>
   <li><code>Type f(BaseType)</code> (<code>Value</code> is <code>BaseType</code>),</li>
   <li><code>Type f(const BaseType&amp;)</code> (<code>Value</code> is <code>const BaseType&amp;</code>),</li>
   <li><code>Type f(BaseType&amp;)</code> (<code>Value</code> is <code>BaseType&amp;</code>).</li>
 </ul>
 <code>global_fun&lt;Type,Value,PtrToFunction&gt;</code> is a model of:
 <ul>
   <li><a href="#key_extractors"><code>Key Extractor</code></a>
     from <code>reference_wrapper&lt;BaseType></code>,</li>
   <li><a href="#key_extractors"><code>Key Extractor</code></a>
     from any <a href="#chained_pointers">chained pointer</a>
     to <code>BaseType</code>.</li>
 </ul>
 When <code>Value</code> is <code>BaseType</code> or
 <code>const BaseType&amp;</code>,
 <code>global_fun&lt;Type,Value,PtrToFunction&gt;</code> is also a model of:
 <ul>
   <li><a href="#key_extractors"><code>Key Extractor</code></a>
     from <code>BaseType</code>,</li>
   <li><a href="#key_extractors"><code>Key Extractor</code></a>
     from <code>reference_wrapper&lt;const BaseType></code>,</li>
   <li><a href="#key_extractors"><code>Key Extractor</code></a>
     from any <a href="#chained_pointers">chained pointer</a>
     to <code>const BaseType</code>.</li>
 </ul>
 </p>

 <h4><code>global_fun</code> members</h4>

 <code>template&lt;typename ChainedPtr> Type operator()(const ChainedPtr&amp; x)const;</code>

 <blockquote>
 <b>Requires:</b> <code>ChainedPtr</code> is a <a href="#chained_pointers">chained pointer</a>
 type to <code>Value</code>.<br>
 <b>Returns:</b> <code>PtrToFunction)(y)</code>, where <code>y</code> is the
 object chained-pointed to by <code>x</code>.
 </blockquote>

 <code>Type operator()(Value x)const;</code>

 <blockquote>
 <b>Returns:</b> <code>PtrToFunction(x)</code>.
 </blockquote>

 <code>Type operator()(const Value&amp; x)const;</code>

 <blockquote>
 <b>Returns:</b> <code>PtrToFunction(x)</code>.
 </blockquote>

 <code>Type operator()(const reference_wrapper&lt;const Value&gt;&amp; x)const;</code>

 <blockquote>
 <b>Returns:</b> <code>PtrToFunction(x.get())</code>.
 </blockquote>

 <code>
 Type operator()(<br>
 &nbsp;&nbsp;const reference_wrapper&lt;remove_reference&lt;Value&gt;::type&gt;&amp; x)const;</code>

 <blockquote>
 <b>Returns:</b> <code>PtrToFunction(x.get())</code>.
 </blockquote>

 <code>Type operator()(<br>
 &nbsp;&nbsp;const reference_wrapper&lt;<br>
 &nbsp;&nbsp;&nbsp;&nbsp;typename remove_const&lt;<br>
 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;typename remove_reference&lt;Value&gt;::type&gt;::type&gt;&amp; x)const;</code>

 <blockquote>
 <b>Returns:</b> <code>PtrToFunction(x.get())</code>.
 </blockquote>

 <h2>
 <a name="composite_key_synopsis">Header
 <a href="../../../../boost/multi_index/composite_key.hpp">
 <code>"boost/multi_index/composite_key.hpp"</code></a> synopsis</a></h2>

 <blockquote><pre>
 <span class=keyword>namespace</span> <span class=identifier>boost</span><span class=special>{</span>

 <span class=keyword>namespace</span> <span class=identifier>multi_index</span><span class=special>{</span>

 <span class=keyword>template</span><span class=special>&lt;</span><span class=keyword>typename</span> <span class=identifier>Value</span><span class=special>,</span><span class=keyword>typename</span> <span class=identifier>KeyFromValue0</span><span class=special>,...,</span><span class=keyword>typename</span> <span class=identifier>KeyFromValuen</span><span class=special>&gt;</span>
 <span class=keyword>struct</span> <span class=identifier>composite_key</span><span class=special>;</span>

 <span class=keyword>template</span><span class=special>&lt;</span><span class=keyword>typename</span> <span class=identifier>CompositeKey</span><span class=special>&gt;</span>
 <span class=keyword>struct</span> <span class=identifier>composite_key_result</span><span class=special>;</span>

 <span class=comment>// comparison operators for composite_key_result:</span>

 <span class=comment>// <b>OP</b> is any of ==,&lt;,!=,&gt;,&gt;=,&lt;=</span>

 <span class=keyword>template</span><span class=special>&lt;</span><span class=keyword>typename</span> <span class=identifier>CompositeKey1</span><span class=special>,</span><span class=keyword>typename</span> <span class=identifier>CompositeKey2</span><span class=special>&gt;</span>
 <span class=keyword>bool</span> <span class=keyword>operator</span> <b><i>OP</i></b><span class=special>(</span>
   <span class=keyword>const</span> <span class=identifier>composite_key_result</span><span class=special>&lt;</span><span class=identifier>CompositeKey1</span><span class=special>&gt;&amp;</span> <span class=identifier>x</span><span class=special>,</span>
   <span class=keyword>const</span> <span class=identifier>composite_key_result</span><span class=special>&lt;</span><span class=identifier>CompositeKey2</span><span class=special>&gt;&amp;</span> <span class=identifier>y</span><span class=special>);</span>

 <span class=keyword>template</span><span class=special>&lt;</span><span class=keyword>typename</span> <span class=identifier>CompositeKey</span><span class=special>,</span><span class=keyword>typename</span> <span class=identifier>Value0</span><span class=special>,...,</span><span class=keyword>typename</span> <span class=identifier>Valuen</span><span class=special>&gt;</span>
 <span class=keyword>bool</span> <span class=keyword>operator</span> <b><i>OP</i></b><span class=special>(</span>
   <span class=keyword>const</span> <span class=identifier>composite_key_result</span><span class=special>&lt;</span><span class=identifier>CompositeKey</span><span class=special>&gt;&amp;</span> <span class=identifier>x</span><span class=special>,</span>
   <span class=keyword>const</span> <span class=identifier>tuple</span><span class=special>&lt;</span><span class=identifier>Value0</span><span class=special>,...,</span><span class=identifier>Valuen</span><span class=special>&gt;&amp;</span> <span class=identifier>y</span><span class=special>);</span>

 <span class=keyword>template</span><span class=special>&lt;</span><span class=keyword>typename</span> <span class=identifier>Value0</span><span class=special>,...,</span><span class=keyword>typename</span> <span class=identifier>Valuen</span><span class=special>,</span><span class=keyword>typename</span> <span class=identifier>CompositeKey</span><span class=special>&gt;</span>
 <span class=keyword>bool</span> <span class=keyword>operator</span> <b><i>OP</i></b><span class=special>(</span>
   <span class=keyword>const</span> <span class=identifier>tuple</span><span class=special>&lt;</span><span class=identifier>Value0</span><span class=special>,...,</span><span class=identifier>Valuen</span><span class=special>&gt;&amp;</span> <span class=identifier>x</span><span class=special>,</span>
   <span class=keyword>const</span> <span class=identifier>composite_key_result</span><span class=special>&lt;</span><span class=identifier>CompositeKey</span><span class=special>&gt;&amp;</span> <span class=identifier>y</span><span class=special>);</span>

 <span class=comment>// equality functors:</span>

 <span class=keyword>template</span><span class=special>&lt;</span><span class=keyword>typename</span> <span class=identifier>Pred0</span><span class=special>,...,</span><span class=keyword>typename</span> <span class=identifier>Predn</span><span class=special>&gt;</span>
 <span class=keyword>struct</span> <span class=identifier>composite_key_equal_to</span><span class=special>;</span>

 <span class=keyword>template</span><span class=special>&lt;</span><span class=keyword>typename</span> <span class=identifier>CompositeKeyResult</span><span class=special>&gt;</span>
 <span class=keyword>struct</span> <span class=identifier>composite_key_result_equal_to</span><span class=special>;</span>

 <span class=comment>// comparison functors:</span>

 <span class=keyword>template</span><span class=special>&lt;</span><span class=keyword>typename</span> <span class=identifier>Compare0</span><span class=special>,...,</span><span class=keyword>typename</span> <span class=identifier>Comparen</span><span class=special>&gt;</span>
 <span class=keyword>struct</span> <span class=identifier>composite_key_compare</span><span class=special>;</span>

 <span class=keyword>template</span><span class=special>&lt;</span><span class=keyword>typename</span> <span class=identifier>CompositeKeyResult</span><span class=special>&gt;</span>
 <span class=keyword>struct</span> <span class=identifier>composite_key_result_less</span><span class=special>;</span>

 <span class=keyword>template</span><span class=special>&lt;</span><span class=keyword>typename</span> <span class=identifier>CompositeKeyResult</span><span class=special>&gt;</span>
 <span class=keyword>struct</span> <span class=identifier>composite_key_result_greater</span><span class=special>;</span>

 <span class=comment>// hash functors:</span>

 <span class=keyword>template</span><span class=special>&lt;</span><span class=keyword>typename</span> <span class=identifier>Hash0</span><span class=special>,...,</span><span class=keyword>typename</span> <span class=identifier>Hashn</span><span class=special>&gt;</span>
 <span class=keyword>struct</span> <span class=identifier>composite_key_hash</span><span class=special>;</span>

 <span class=keyword>template</span><span class=special>&lt;</span><span class=keyword>typename</span> <span class=identifier>CompositeKeyResult</span><span class=special>&gt;</span>
 <span class=keyword>struct</span> <span class=identifier>composite_key_result_hash</span><span class=special>;</span>

 <span class=special>}</span> <span class=comment>// namespace boost::multi_index</span>

 <span class=special>}</span> <span class=comment>// namespace boost</span>

 <span class=comment>// specializations of external functors for composite_key_result:</span>

 <span class=keyword>namespace</span> <span class=identifier>std</span><span class=special>{</span>

 <span class=keyword>template</span><span class=special>&lt;</span><span class=keyword>typename</span> <span class=identifier>CompositeKey</span><span class=special>&gt;</span>
 <span class=keyword>struct</span> <span class=identifier>equal_to</span><span class=special>&lt;</span><span class=identifier>boost</span><span class=special>::</span><span class=identifier>multi_index</span><span class=special>::</span><span class=identifier>composite_key_result</span><span class=special>&lt;</span><span class=identifier>CompositeKey</span><span class=special>&gt;</span> <span class=special>&gt;;</span>

 <span class=keyword>template</span><span class=special>&lt;</span><span class=keyword>typename</span> <span class=identifier>CompositeKey</span><span class=special>&gt;</span>
 <span class=keyword>struct</span> <span class=identifier>less</span><span class=special>&lt;</span><span class=identifier>boost</span><span class=special>::</span><span class=identifier>multi_index</span><span class=special>::</span><span class=identifier>composite_key_result</span><span class=special>&lt;</span><span class=identifier>CompositeKey</span><span class=special>&gt;</span> <span class=special>&gt;;</span>

 <span class=keyword>template</span><span class=special>&lt;</span><span class=keyword>typename</span> <span class=identifier>CompositeKey</span><span class=special>&gt;</span>
 <span class=keyword>struct</span> <span class=identifier>greater</span><span class=special>&lt;</span><span class=identifier>boost</span><span class=special>::</span><span class=identifier>multi_index</span><span class=special>::</span><span class=identifier>composite_key_result</span><span class=special>&lt;</span><span class=identifier>CompositeKey</span><span class=special>&gt;</span> <span class=special>&gt;;</span>

 <span class=special>}</span> <span class=comment>// namespace std</span>

 <span class=keyword>namespace</span> <span class=identifier>boost</span><span class=special>{</span>

 <span class=keyword>template</span><span class=special>&lt;</span><span class=keyword>typename</span> <span class=identifier>CompositeKey</span><span class=special>&gt;</span>
 <span class=keyword>struct</span> <span class=identifier>hash</span><span class=special>&lt;</span><span class=identifier>boost</span><span class=special>::</span><span class=identifier>multi_index</span><span class=special>::</span><span class=identifier>composite_key_result</span><span class=special>&lt;</span><span class=identifier>CompositeKey</span><span class=special>&gt;</span> <span class=special>&gt;;</span>

 <span class=special>}</span> <span class=comment>// namespace boost</span>
 </pre></blockquote>

 <h3><a name="composite_key">Class template <code>composite_key</code></a></h3>

 <p>
 <code>composite_key</code> is a <a href="#key_extractors"><code>Key Extractor</code></a>
 returning the combined value of several key extractors whose type is specified
 at compile time. The returned object is of type
 <a href="#composite_key_result">
 <code>composite_key_result</code></a><code>&lt;composite_key></code>.
 </p>

 <blockquote><pre>
 <span class=keyword>template</span><span class=special>&lt;</span><span class=keyword>typename</span> <span class=identifier>Value</span><span class=special>,</span><span class=keyword>typename</span> <span class=identifier>KeyFromValue0</span><span class=special>,...,</span><span class=keyword>typename</span> <span class=identifier>KeyFromValuen</span><span class=special>&gt;</span>
 <span class=keyword>struct</span> <span class=identifier>composite_key</span>
 <span class=special>{</span>
   <span class=keyword>typedef</span> <span class=identifier>tuple</span><span class=special>&lt;</span><span class=identifier>KeyFromValue0</span><span class=special>,...,</span><span class=identifier>KeyFromValuen</span><span class=special>&gt;</span> <span class=identifier>key_extractor_tuple</span><span class=special>;</span>
   <span class=keyword>typedef</span> <span class=identifier>Value</span>                                  <span class=identifier>value_type</span><span class=special>;</span>
   <span class=keyword>typedef</span> <span class=identifier>composite_key_result</span><span class=special>&lt;</span><span class=identifier>composite_key</span><span class=special>&gt;</span>    <span class=identifier>result_type</span><span class=special>;</span>

   <span class=identifier>composite_key</span><span class=special>(</span>
     <span class=keyword>const</span> <span class=identifier>KeyFromValue0</span><span class=special>&amp;</span> <span class=identifier>k0</span><span class=special>=</span><span class=identifier>KeyFromValue0</span><span class=special>(),</span>
     <span class=special>...</span>
     <span class=keyword>const</span> <span class=identifier>KeyFromValuen</span><span class=special>&amp;</span> <span class=identifier>kn</span><span class=special>=</span><span class=identifier>KeyFromValuen</span><span class=special>());</span>

   <span class=identifier>composite_key</span><span class=special>(</span><span class=keyword>const</span> <span class=identifier>key_extractor_tuple</span><span class=special>&amp;</span> <span class=identifier>x</span><span class=special>);</span>

   <span class=keyword>const</span> <span class=identifier>key_extractor_tuple</span><span class=special>&amp;</span> <span class=identifier>key_extractors</span><span class=special>()</span><span class=keyword>const</span><span class=special>;</span>
   <span class=identifier>key_extractor_tuple</span><span class=special>&amp;</span>       <span class=identifier>key_extractors</span><span class=special>()</span>

   <span class=comment>// only provided if const ChainedPtr&amp; is not convertible to const value_type&amp;</span>
   <span class=keyword>template</span><span class=special>&lt;</span><span class=keyword>typename</span> <span class=identifier>ChainedPtr</span><span class=special>&gt;</span>
   <span class=identifier>result_type</span> <span class=keyword>operator</span><span class=special>()(</span><span class=keyword>const</span> <span class=identifier>ChainedPtr</span><span class=special>&amp;</span> <span class=identifier>x</span><span class=special>)</span><span class=keyword>const</span><span class=special>;</span>

   <span class=identifier>result_type</span> <span class=keyword>operator</span><span class=special>()(</span><span class=keyword>const</span> <span class=identifier>value_type</span><span class=special>&amp;</span> <span class=identifier>x</span><span class=special>)</span><span class=keyword>const</span><span class=special>;</span>
   <span class=identifier>result_type</span> <span class=keyword>operator</span><span class=special>()(</span><span class=keyword>const</span> <span class=identifier>reference_wrapper</span><span class=special>&lt;</span><span class=keyword>const</span> <span class=identifier>value_type</span><span class=special>&gt;&amp;</span> <span class=identifier>x</span><span class=special>)</span><span class=keyword>const</span><span class=special>;</span>
   <span class=identifier>result_type</span> <span class=keyword>operator</span><span class=special>()(</span><span class=keyword>const</span> <span class=identifier>reference_wrapper</span><span class=special>&lt;</span><span class=identifier>value_type</span><span class=special>&gt;&amp;</span> <span class=identifier>x</span><span class=special>)</span><span class=keyword>const</span><span class=special>;</span>
 <span class=special>};</span>
 </pre></blockquote>

 <p>
 <code>KeyFromValue0</code>, ... , <code>KeyFromValuen</code> are the types of
 the key extractors combined into the composite key. Each of these types
 must be a <a href="#key_extractors"><code>Key Extractor</code></a> from
 <code>Value</code>. At least a key extractor must be provided. The maximum
 number of key extractors of a <code>composite_key</code> instantiation is
 implementation defined. <code>composite_key</code> internally stores an
 object of every constituent key extractor type.
 <code>composite_key&lt;Value,KeyFromValue0,...,KeyFromValuen></code> is a model
 of:
 <ul>
   <li><a href="#key_extractors"><code>Key Extractor</code></a>
     from <code>Value</code>,</li>
   <li><a href="#key_extractors"><code>Key Extractor</code></a>
     from <code>reference_wrapper&lt;const Value></code>,</li>
   <li><a href="#key_extractors"><code>Key Extractor</code></a>
     from <code>reference_wrapper&lt;Value></code>,</li>
   <li><a href="#key_extractors"><code>Key Extractor</code></a>
     from any <a href="#chained_pointers">chained pointer</a>
     to <code>const Value</code>,</li>
   <li><a href="#key_extractors"><code>Key Extractor</code></a>
     from any <a href="#chained_pointers">chained pointer</a>
     to <code>Value</code>.</li>
 </ul>
 </p>

 <h4><code>composite_key</code> members</h4>

 <code>composite_key(<br>
 &nbsp;&nbsp;const KeyFromValue0&amp; k0=KeyFromValue0(),<br>
 &nbsp;&nbsp;...<br>
 &nbsp;&nbsp;const KeyFromValuen&amp; kn=KeyFromValuen());
 </code>

 <blockquote>
 <b>Effects:</b> Constructs a <code>composite_key</code> that stores
 copies of the key extractor objects supplied.
 </blockquote>

 <code>composite_key(const key_extractor_tuple&amp; x);</code>

 <blockquote>
 <b>Effects:</b> Constructs a <code>composite_key</code> that stores
 copies of the key extractor objects supplied in <code>x</code>.
 </blockquote>

 <code>const key_extractor_tuple&amp; key_extractors()const;</code>

 <blockquote>
 <b>Returns:</b> a constant reference to a tuple holding the
 key extractors internally stored by the <code>composite_key</code>.
 </blockquote>

 <code>key_extractor_tuple&amp; key_extractors();</code>

 <blockquote>
 <b>Returns:</b> a reference to a tuple holding the
 key extractors internally stored by the <code>composite_key</code>.
 </blockquote>

 <code>template&lt;typename ChainedPtr><br>
 result_type operator()(const ChainedPtr&amp; x)const;</code>

 <blockquote>
 <b>Requires:</b> <code>ChainedPtr</code> is a <a href="#chained_pointers">chained pointer</a>
 type to <code>result_type</code>.<br>
 <b>Returns:</b> a <code>result_type</code> object dependent on
 <code>*this</code> and <code>y</code>, where <code>y</code> is the
 object chained-pointed to by <code>x</code>.
 </blockquote>

 <code>result_type operator()(const value_type&amp; x)const;</code>

 <blockquote>
 <b>Returns:</b> a <code>result_type</code> object dependent on
 <code>*this</code> and <code>x</code>.
 </blockquote>

 <code>result_type operator()(const reference_wrapper&lt;const value_type>&amp; x)const;</code>

 <blockquote>
 <b>Returns:</b> a <code>result_type</code> object dependent on
 <code>*this</code> and <code>x.get()</code>.
 </blockquote>

 <code>result_type operator()(const reference_wrapper&lt;value_type>&amp; x)const;</code>

 <blockquote>
 <b>Returns:</b> a <code>result_type</code> object dependent on
 <code>*this</code> and <code>x.get()</code>.
 </blockquote>

 <h3><a name="composite_key_result">Class template
 <code>composite_key_result</code></a></h3>

 <p>
 This is an opaque type returned by <code>composite_key</code>
 instantiations as their extracted key.
 </p>

 <blockquote><pre>
 <span class=keyword>template</span><span class=special>&lt;</span><span class=keyword>typename</span> <span class=identifier>CompositeKey</span><span class=special>&gt;</span>
 <span class=keyword>struct</span> <span class=identifier>composite_key_result</span>
 <span class=special>{</span>
   <b>no public interface available</b>
 <span class=special>};</span>

 <span class=comment>// comparison:</span>

 <span class=comment>// <b>OP</b> is any of ==,&lt;,!=,&gt;,&gt;=,&lt;=</span>

 <span class=keyword>template</span><span class=special>&lt;</span><span class=keyword>typename</span> <span class=identifier>CompositeKey1</span><span class=special>,</span><span class=keyword>typename</span> <span class=identifier>CompositeKey2</span><span class=special>&gt;</span>
 <span class=keyword>bool</span> <span class=keyword>operator</span> <b><i>OP</i></b><span class=special>(</span>
   <span class=keyword>const</span> <span class=identifier>composite_key_result</span><span class=special>&lt;</span><span class=identifier>CompositeKey1</span><span class=special>&gt;&amp;</span> <span class=identifier>x</span><span class=special>,</span>
   <span class=keyword>const</span> <span class=identifier>composite_key_result</span><span class=special>&lt;</span><span class=identifier>CompositeKey2</span><span class=special>&gt;&amp;</span> <span class=identifier>y</span><span class=special>);</span>

 <span class=keyword>template</span><span class=special>&lt;</span><span class=keyword>typename</span> <span class=identifier>CompositeKey</span><span class=special>,</span><span class=keyword>typename</span> <span class=identifier>Value0</span><span class=special>,...,</span><span class=keyword>typename</span> <span class=identifier>Valuen</span><span class=special>&gt;</span>
 <span class=keyword>bool</span> <span class=keyword>operator</span> <b><i>OP</i></b><span class=special>(</span>
   <span class=keyword>const</span> <span class=identifier>composite_key_result</span><span class=special>&lt;</span><span class=identifier>CompositeKey</span><span class=special>&gt;&amp;</span> <span class=identifier>x</span><span class=special>,</span>
   <span class=keyword>const</span> <span class=identifier>tuple</span><span class=special>&lt;</span><span class=identifier>Value0</span><span class=special>,...,</span><span class=identifier>Valuen</span><span class=special>&gt;&amp;</span> <span class=identifier>y</span><span class=special>);</span>

 <span class=keyword>template</span><span class=special>&lt;</span><span class=keyword>typename</span> <span class=identifier>Value0</span><span class=special>,...,</span><span class=keyword>typename</span> <span class=identifier>Valuen</span><span class=special>,</span><span class=keyword>typename</span> <span class=identifier>CompositeKey</span><span class=special>&gt;</span>
 <span class=keyword>bool</span> <span class=keyword>operator</span> <b><i>OP</i></b><span class=special>(</span>
   <span class=keyword>const</span> <span class=identifier>tuple</span><span class=special>&lt;</span><span class=identifier>Value0</span><span class=special>,...,</span><span class=identifier>Valuen</span><span class=special>&gt;&amp;</span> <span class=identifier>x</span><span class=special>,</span>
   <span class=keyword>const</span> <span class=identifier>composite_key_result</span><span class=special>&lt;</span><span class=identifier>CompositeKey</span><span class=special>&gt;&amp;</span> <span class=identifier>y</span><span class=special>);</span>
 </pre></blockquote>

 <code>CompositeKey</code> is the <code>composite_key</code> instantiation to
 which the <code>composite_key_result</code> type is associated. Objects of type
 <code>composite_key_result</code> returned by a composite key must be always treated
 as <i>temporary</i>, i.e. they should not be stored or copied.
 <code>composite_key_result</code> is <i>not</i> guaranteed to be a model of
 <a href="http://www.sgi.com/tech/stl/DefaultConstructible.html">
 <code>Default Constructible</code></a> or
 <a href="http://www.sgi.com/tech/stl/Assignable.html"><code>Assignable</code></a>.
 Every object of type <code>composite_key_result&lt;CompositeKey></code> is
 internally associated to the <code>CompositeKey</code> from which it is returned
 and the object of type <code>CompositeKey::value_type</code> to which the
 composite key was applied.
 </p>

 <h4><a name="ckey_result_notation">Notation</a></h4>

 <p>
 Given an <code>x</code> of type <code>composite_key_result&lt;CompositeKey></code>,
 we use the following notation:
 <ul>
   <li><code>ck(x)</code> is the <code>CompositeKey</code> object associated to
     <code>x</code>,</li>
   <li><code>v(x)</code> is the object of type <code>CompositeKey::value_type</code>
     associated to <code>x</code>,</li>
   <li><code>k<sub>i</sub>(x) = ck(x).key_extractors().get&lt;i>()</code>,
     that is, is the <code>i</code>-th key extractor of <code>ck(x)</code>,</li>
   <li><code>x<sub>i</sub> = k<sub>i</sub>(x)(v(x))</code>, that is, the
     key extracted from <code>v(x)</code> by the <code>i</code>-th key extractor,</li>
   <li><code>length(x)</code> is the number of key extractors of <code>ck(x)</code>.</li>
 </ul>
 Also, if <code>y</code> is a tuple of values, we define:
 <ul>
   <li><code>y<sub>i</sub>=y.get&lt;i>()</code>,</li>
   <li><code>length(y)</code> is the number of elements of <code>y</code>.</li>
 </ul>
 </p>

 <h4>Comparison operators</h4>

 <code>template&lt;typename CompositeKey1,typename CompositeKey2><br>
 bool operator==(<br>
 &nbsp;&nbsp;const composite_key_result&lt;CompositeKey1>&amp; x,<br>
 &nbsp;&nbsp;const composite_key_result&lt;CompositeKey2>&amp; y);<br>
 template&lt;typename CompositeKey,typename Value0,...,typename Valuen><br>
 bool operator==(<br>
 &nbsp;&nbsp;const composite_key_result&lt;CompositeKey>&amp; x,<br>
 &nbsp;&nbsp;const tuple&lt;Value0,...,Valuen>&amp; y);<br>
 template&lt;typename Value0,...,typename Valuen,typename CompositeKey><br>
 bool operator==(<br>
 &nbsp;&nbsp;const tuple&lt;Value0,...,Valuen>&amp; x,<br>
 &nbsp;&nbsp;const composite_key_result&lt;CompositeKey>&amp; y);
 </code>

 <blockquote>
 <b>Requires:</b> <code>length(x)==length(y)</code>. The expression
 <code>x<sub>i</sub>==y<sub>i</sub></code> is valid for all <code>i</code>
 in <code>[0,length(x))</code>.<br>
 <b>Returns:</b> <code>true</code> if and only if
 <blockquote>
 <code>x<sub>i</sub>==y<sub>i</sub></code> for all <code>i</code>
 in <code>[0,length(x))</code>.
 </blockquote>
 <b>Complexity:</b> No more key extraction operations and comparisons
 are performed than those necessary for the evaluation of the expression above,
 starting at <code>i==0</code>. The evaluation is short-circuited as soon as
 the result is determined to be <code>false</code>.
 </blockquote>

 <code>template&lt;typename CompositeKey1,typename CompositeKey2><br>
 bool operator<(<br>
 &nbsp;&nbsp;const composite_key_result&lt;CompositeKey1>&amp; x,<br>
 &nbsp;&nbsp;const composite_key_result&lt;CompositeKey2>&amp; y);<br>
 template&lt;typename CompositeKey,typename Value0,...,typename Valuen><br>
 bool operator<(<br>
 &nbsp;&nbsp;const composite_key_result&lt;CompositeKey>&amp; x,<br>
 &nbsp;&nbsp;const tuple&lt;Value0,...,Valuen>&amp; y);<br>
 template&lt;typename Value0,...,typename Valuen,typename CompositeKey><br>
 bool operator<(<br>
 &nbsp;&nbsp;const tuple&lt;Value0,...,Valuen>&amp; x,<br>
 &nbsp;&nbsp;const composite_key_result&lt;CompositeKey>&amp; y);
 </code>

 <blockquote>
 <b>Requires:</b> The expressions
 <code>x<sub>i</sub>&lt;y<sub>i</sub></code> and
 <code>y<sub>i</sub>&lt;x<sub>i</sub></code> are valid for all <code>i</code>
 in <code>[0,min(length(x),length(y)))</code>.<br>
 <b>Returns:</b> <code>true</code> if and only if there exists some
 <code>j</code> in the range <code>[0,min(length(x),length(y)))</code>
 such that
 <blockquote>
 <code>!(x<sub>i</sub>&lt;y<sub>i</sub>) &amp;&amp; !(y<sub>i</sub>&lt;x<sub>i</sub>)</code>
 for all <code>i</code> in <code>[0,j)</code>,<br>
 <code>&nbsp;&nbsp;x<sub>j</sub>&lt;y<sub>j</sub></code>.
 </blockquote>
 <b>Complexity:</b> No more key extraction operations and comparisons
 are performed than those necessary for the evaluation of the expression above,
 starting at <code>i==0</code>. The evaluation is short-circuited as soon as
 the result is determined to be <code>false</code>.
 </blockquote>

 <code>template&lt;typename CompositeKey1,typename CompositeKey2><br>
 bool operator <b><i>OP</i></b>(<br>
 &nbsp;&nbsp;const composite_key_result&lt;CompositeKey1>&amp; x,<br>
 &nbsp;&nbsp;const composite_key_result&lt;CompositeKey2>&amp; y);<br>
 template&lt;typename CompositeKey,typename Value0,...,typename Valuen><br>
 bool operator <b><i>OP</i></b>(<br>
 &nbsp;&nbsp;const composite_key_result&lt;CompositeKey>&amp; x,<br>
 &nbsp;&nbsp;const tuple&lt;Value0,...,Valuen>&amp; y);<br>
 template&lt;typename Value0,...,typename Valuen,typename CompositeKey><br>
 bool operator <b><i>OP</i></b>(<br>
 &nbsp;&nbsp;const tuple&lt;Value0,...,Valuen>&amp; x,<br>
 &nbsp;&nbsp;const composite_key_result&lt;CompositeKey>&amp; y);
 </code>

 <p>
 (<code><b><i>OP</i></b></code> is any of <code>!=</code>, <code>></code>,
 <code>>=</code>, <code>&lt;=</code>.)
 </p>

 <blockquote>
 <b>Requires:</b> The expressions given below are valid (for the particular
 <code><b><i>OP</i></b></code> considered.)<br>
 <b>Returns:</b> <code>true</code> if and only if
 <blockquote>
 <code>!(x==y)</code> (<code><b><i>OP</i></b></code> is <code>!=</code>),<br>
 <code>&nbsp;&nbsp;y&lt;&nbsp;x&nbsp;</code> (<code><b><i>OP</i></b></code> is <code>>&nbsp;</code>),<br>
 <code>!(x&lt;&nbsp;y)</code> (<code><b><i>OP</i></b></code> is <code>>=</code>),<br>
 <code>!(y&lt;&nbsp;x)</code> (<code><b><i>OP</i></b></code> is <code>&lt;=</code>).
 </blockquote>
 </blockquote>

 <h3><a name="ckey_result_equality">Equality</a></h3>

 <h4><a name="composite_key_equal_to">Class template
 <code>composite_key_equal_to</code></a></h4>

 <p>
 <code>composite_key_equal_to</code> tests for equality between
 <code>composite_key_result</code> instantiations and between
 these and tuples of values, using an internally stored
 collection of elementary equality predicates.
 </p>

 <blockquote><pre>
 <span class=keyword>template</span><span class=special>&lt;</span><span class=keyword>typename</span> <span class=identifier>Pred0</span><span class=special>,...,</span><span class=keyword>typename</span> <span class=identifier>Predn</span><span class=special>&gt;</span>
 <span class=keyword>struct</span> <span class=identifier>composite_key_equal_to</span>
 <span class=special>{</span>
   <span class=keyword>typedef</span> <span class=identifier>tuple</span><span class=special>&lt;</span><span class=identifier>Pred0</span><span class=special>,...,</span><span class=identifier>Predn</span><span class=special>&gt;</span> <span class=identifier>key_eq_tuple</span><span class=special>;</span>

   <span class=identifier>composite_key_equal_to</span><span class=special>(</span>
     <span class=keyword>const</span> <span class=identifier>Pred0</span><span class=special>&amp;</span> <span class=identifier>p0</span><span class=special>=</span><span class=identifier>Pred0</span><span class=special>(),</span>
     <span class=special>...</span>
     <span class=keyword>const</span> <span class=identifier>Predn</span><span class=special>&amp;</span> <span class=identifier>pn</span><span class=special>=</span><span class=identifier>Predn</span><span class=special>());</span>

   <span class=identifier>composite_key_equal_to</span><span class=special>(</span><span class=keyword>const</span> <span class=identifier>key_eq_tuple</span><span class=special>&amp;</span> <span class=identifier>x</span><span class=special>);</span>

   <span class=keyword>const</span> <span class=identifier>key_eq_tuple</span><span class=special>&amp;</span> <span class=identifier>key_eqs</span><span class=special>()</span><span class=keyword>const</span><span class=special>;</span>
   <span class=identifier>key_eq_tuple</span><span class=special>&amp;</span>       <span class=identifier>key_eqs</span><span class=special>()</span><span class=special>;</span>

   <span class=keyword>template</span><span class=special>&lt;</span><span class=keyword>typename</span> <span class=identifier>CompositeKey1</span><span class=special>,</span><span class=keyword>typename</span> <span class=identifier>CompositeKey2</span><span class=special>&gt;</span>
   <span class=keyword>bool</span> <span class=keyword>operator</span><span class=special>()(</span>
     <span class=keyword>const</span> <span class=identifier>composite_key_result</span><span class=special>&lt;</span><span class=identifier>CompositeKey1</span><span class=special>&gt;</span> <span class=special>&amp;</span> <span class=identifier>x</span><span class=special>,</span>
     <span class=keyword>const</span> <span class=identifier>composite_key_result</span><span class=special>&lt;</span><span class=identifier>CompositeKey2</span><span class=special>&gt;</span> <span class=special>&amp;</span> <span class=identifier>y</span><span class=special>)</span><span class=keyword>const</span><span class=special>;</span>

   <span class=keyword>template</span><span class=special>&lt;</span><span class=keyword>typename</span> <span class=identifier>CompositeKey</span><span class=special>,</span><span class=keyword>typename</span> <span class=identifier>Value0</span><span class=special>,...,</span><span class=keyword>typename</span> <span class=identifier>Valuen</span><span class=special>&gt;</span>
   <span class=keyword>bool</span> <span class=keyword>operator</span><span class=special>()(</span>
     <span class=keyword>const</span> <span class=identifier>composite_key_result</span><span class=special>&lt;</span><span class=identifier>CompositeKey</span><span class=special>&gt;&amp;</span> <span class=identifier>x</span><span class=special>,</span>
     <span class=keyword>const</span> <span class=identifier>tuple</span><span class=special>&lt;</span><span class=identifier>Value0</span><span class=special>,...,</span><span class=identifier>Valuen</span><span class=special>&gt;&amp;</span> <span class=identifier>y</span><span class=special>)</span><span class=keyword>const</span><span class=special>;</span>

   <span class=keyword>template</span><span class=special>&lt;</span><span class=keyword>typename</span> <span class=identifier>Value0</span><span class=special>,...,</span><span class=keyword>typename</span> <span class=identifier>Valuen</span><span class=special>,</span><span class=keyword>typename</span> <span class=identifier>CompositeKey</span><span class=special>&gt;</span>
   <span class=keyword>bool</span> <span class=keyword>operator</span><span class=special>()(</span>
     <span class=keyword>const</span> <span class=identifier>tuple</span><span class=special>&lt;</span><span class=identifier>Value0</span><span class=special>,...,</span><span class=identifier>Valuen</span><span class=special>&gt;&amp;</span> <span class=identifier>x</span><span class=special>,</span>
     <span class=keyword>const</span> <span class=identifier>composite_key_result</span><span class=special>&lt;</span><span class=identifier>CompositeKey</span><span class=special>&gt;&amp;</span> <span class=identifier>y</span><span class=special>)</span><span class=keyword>const</span><span class=special>;</span>
 <span class=special>};</span>
 </pre></blockquote>

 <p>
 <code>Pred0</code>, ... , <code>Predn</code> are the types of the equality
 predicates stored by <code>composite_key_equal_to</code>. Each of these types
 must be a <a href="http://www.sgi.com/tech/stl/BinaryPredicate.html">
 <code>Binary Predicate</code></a>. At least an
 equality predicate must be provided. The maximum number of equality predicates of
 a <code>composite_key_equal_to</code> instantiation is implementation defined.
 <code>composite_key_equal_to</code> is
 <a href="http://www.sgi.com/tech/stl/Assignable.html"><code>Assignable</code></a>.
 It is also
 <a href="http://www.sgi.com/tech/stl/DefaultConstructible.html">
 <code>Default Constructible</code></a>
 if each <code>Predi</code> is
 <a href="http://www.sgi.com/tech/stl/DefaultConstructible.html">
 <code>Default Constructible</code></a>.
 </p>

 <p>
 Note that formally it is not required that the <code>Predi</code> types
 behave as equality predicates in any definite way. However, the
 semantics of <code>composite_key_equal_to</code> is well defined if this
 is the case, as explained in the section on the
 <a href="#ckey_result_semantics">semantics of <code>composite_key_result</code></a>.
 </p>

 <h4>Notation</h4>

 <p>
 In what follows we use the same <a href="#ckey_result_notation">notation</a>
 introduced for <code>composite_key_result</code>.

 <h4><code>composite_key_equal_to</code> members</h4>

 <code>composite_key_equal_to(<br>
 &nbsp;&nbsp;const Pred0&amp; p0=Pred0(),<br>
 &nbsp;&nbsp;...<br>
 &nbsp;&nbsp;const Predn&amp; pn=Predn());
 </code>

 <blockquote>
 <b>Effects:</b> Constructs a <code>composite_key_equal_to</code> that stores
 copies of the equality predicates supplied.
 </blockquote>

 <code>composite_key_equal_to(const key_eq_tuple&amp; x);</code>

 <blockquote>
 <b>Effects:</b> Constructs a <code>composite_key_equal_to</code> that stores
 copies of the equality predicate objects supplied in <code>x</code>.
 </blockquote>

 <code>const key_eq_tuple&amp; key_eqs()const;</code>

 <blockquote>
 <b>Returns:</b> a constant reference to a tuple holding the
 equality predicate objects internally stored by the
 <code>composite_key_equal_to</code>.
 </blockquote>

 <code>key_eq_tuple&amp; key_eqs();</code>

 <blockquote>
 <b>Returns:</b> a reference to a tuple holding the
 equality predicate objects internally stored by the
 <code>composite_key_equal_to</code>.
 </blockquote>

 <code>
 template&lt;typename CompositeKey1,typename CompositeKey2><br>
 bool operator()(<br>
 &nbsp;&nbsp;const composite_key_result&lt;CompositeKey1> &amp; x,<br>
 &nbsp;&nbsp;const composite_key_result&lt;CompositeKey2> &amp; y)const;<br>
 template&lt;typename CompositeKey,typename Value0,...,typename Valuen><br>
 bool operator()(<br>
 &nbsp;&nbsp;const composite_key_result&lt;CompositeKey>&amp; x,<br>
 &nbsp;&nbsp;const tuple&lt;Value0,...,Valuen>&amp; y)const;<br>
 template&lt;typename Value0,...,typename Valuen,typename CompositeKey><br>
 bool operator()(<br>
 &nbsp;&nbsp;const tuple&lt;Value0,...,Valuen>&amp; x,<br>
 &nbsp;&nbsp;const composite_key_result&lt;CompositeKey>&amp; y)const;<br>
 </code>

 <blockquote>
 <b>Requires:</b> <code>length(x)==length(y)</code>. The expressions
 <code>key_eqs().get&lt;i>()(x<sub>i</sub>,y<sub>i</sub>)</code> and
 <code>key_eqs().get&lt;i>()(y<sub>i</sub>,x<sub>i</sub>)</code>
 are valid for all <code>i</code> in <code>[0,length(x))</code>.<br>
 <b>Returns:</b> <code>true</code> if and only
 <blockquote>
 <code>key_eqs().get&lt;i>()(x<sub>i</sub>,y<sub>i</sub>)</code>
 for all <code>i</code> in <code>[0,length(x))</code>.<br>
 </blockquote>
 <b>Complexity:</b> No more key extraction operations and comparisons
 are performed than those necessary for the evaluation of the expression above,
 starting at <code>i==0</code>. The evaluation is short-circuited as soon as
 the result is determined to be <code>false</code>.
 </blockquote>

 <h4><a name="composite_key_result_equal_to">Class template
 <code>composite_key_result_equal_to</code></a></h4>

 <p>
 <code>composite_key_result_equal_to</code> acts as a particularization of
 <code>composite_key_equal_to</code> where all the comparison predicates supplied
 are instantiations of <code>std::equal_to</code>.
 </p>

 <blockquote><pre>
 <span class=keyword>template</span><span class=special>&lt;</span><span class=keyword>typename</span> <span class=identifier>CompositeKeyResult</span><span class=special>&gt;</span>
 <span class=keyword>struct</span> <span class=identifier>composite_key_result_equal_to</span>
 <span class=special>{</span>
   <span class=keyword>typedef</span> <span class=identifier>CompositeKeyResult</span>  <span class=identifier>first_argument_type</span><span class=special>;</span>
   <span class=keyword>typedef</span> <span class=identifier>first_argument_type</span> <span class=identifier>second_argument_type</span><span class=special>;</span>
   <span class=keyword>typedef</span> <span class=keyword>bool</span>                <span class=identifier>result_type</span><span class=special>;</span>

   <span class=keyword>template</span><span class=special>&lt;</span><span class=keyword>typename</span> <span class=identifier>CompositeKey1</span><span class=special>,</span><span class=keyword>typename</span> <span class=identifier>CompositeKey2</span><span class=special>&gt;</span>
   <span class=keyword>bool</span> <span class=keyword>operator</span><span class=special>()(</span>
     <span class=keyword>const</span> <span class=identifier>composite_key_result</span><span class=special>&lt;</span><span class=identifier>CompositeKey1</span><span class=special>&gt;</span> <span class=special>&amp;</span> <span class=identifier>x</span><span class=special>,</span>
     <span class=keyword>const</span> <span class=identifier>composite_key_result</span><span class=special>&lt;</span><span class=identifier>CompositeKey2</span><span class=special>&gt;</span> <span class=special>&amp;</span> <span class=identifier>y</span><span class=special>)</span><span class=keyword>const</span><span class=special>;</span>

   <span class=keyword>template</span><span class=special>&lt;</span><span class=keyword>typename</span> <span class=identifier>CompositeKey</span><span class=special>,</span><span class=keyword>typename</span> <span class=identifier>Value0</span><span class=special>,...,</span><span class=keyword>typename</span> <span class=identifier>Valuen</span><span class=special>&gt;</span>
   <span class=keyword>bool</span> <span class=keyword>operator</span><span class=special>()(</span>
     <span class=keyword>const</span> <span class=identifier>composite_key_result</span><span class=special>&lt;</span><span class=identifier>CompositeKey</span><span class=special>&gt;&amp;</span> <span class=identifier>x</span><span class=special>,</span>
     <span class=keyword>const</span> <span class=identifier>tuple</span><span class=special>&lt;</span><span class=identifier>Value0</span><span class=special>,...,</span><span class=identifier>Valuen</span><span class=special>&gt;&amp;</span> <span class=identifier>y</span><span class=special>)</span><span class=keyword>const</span><span class=special>;</span>

   <span class=keyword>template</span><span class=special>&lt;</span><span class=keyword>typename</span> <span class=identifier>Value0</span><span class=special>,...,</span><span class=keyword>typename</span> <span class=identifier>Valuen</span><span class=special>,</span><span class=keyword>typename</span> <span class=identifier>CompositeKey</span><span class=special>&gt;</span>
   <span class=keyword>bool</span> <span class=keyword>operator</span><span class=special>()(</span>
     <span class=keyword>const</span> <span class=identifier>tuple</span><span class=special>&lt;</span><span class=identifier>Value0</span><span class=special>,...,</span><span class=identifier>Valuen</span><span class=special>&gt;&amp;</span> <span class=identifier>x</span><span class=special>,</span>
     <span class=keyword>const</span> <span class=identifier>composite_key_result</span><span class=special>&lt;</span><span class=identifier>CompositeKey</span><span class=special>&gt;&amp;</span> <span class=identifier>y</span><span class=special>)</span><span class=keyword>const</span><span class=special>;</span>
 <span class=special>};</span>
 </pre></blockquote>

 <p>
 <code>CompositeKeyResult</code> must be an instantiation of
 <code>composite_key_result</code> for some type
 <code>composite_key&lt;KeyFromValue0,...,KeyFromValuen></code>.
 <code>composite_key_result_equal_to&lt;CompositeKeyResult>::operator()</code> is
 then equivalent to
 <code>composite_key_equal_to&lt;Pred0,...,Predn>::operator()</code>, taking
 <blockquote>
 <code>Predi = std::equal_to&lt;KeyFromValuei::result_type></code> for all
 <code>i = 0,...,n</code>.
 </blockquote>
 </p>

 <p>
 In addition to the requirements on <code>Predi</code> imposed by
 <code>composite_key_equal_to</code>, each of these types must be
 <a href="http://www.sgi.com/tech/stl/DefaultConstructible.html">
 <code>Default Constructible</code></a>. <code>composite_key_result_equal_to</code>
 is <a href="http://www.sgi.com/tech/stl/DefaultConstructible.html">
 <code>Default Constructible</code></a> and
 <a href="http://www.sgi.com/tech/stl/Assignable.html"><code>Assignable</code></a>.
 </p>

 <h4><a name="equal_to_composite_key_result">Specialization of
 <code>std::equal_to</code> for <code>composite_key</code> results</a></h4>

 <p>
 <code>std::equal_to&lt;CompositeKeyResult></code>, for <code>CompositeKeyResult</code>
 being an instantiation of <code>composite_key_result</code>, has the same interface
 and functionality as <code>composite_key_result_equal_to&lt;CompositeKeyResult></code>.
 </p>

 <blockquote><pre>
 <span class=keyword>namespace</span> <span class=identifier>std</span><span class=special>{</span>

 <span class=keyword>template</span><span class=special>&lt;</span><span class=keyword>typename</span> <span class=identifier>CompositeKey</span><span class=special>&gt;</span>
 <span class=keyword>struct</span> <span class=identifier>equal_to</span><span class=special>&lt;</span><span class=identifier>boost</span><span class=special>::</span><span class=identifier>multi_index</span><span class=special>::</span><span class=identifier>composite_key_result</span><span class=special>&lt;</span><span class=identifier>CompositeKey</span><span class=special>&gt;</span> <span class=special>&gt;</span>
 <span class=special>{</span>
   <span class=keyword>typedef</span>
     <span class=identifier>boost</span><span class=special>::</span><span class=identifier>multi_index</span><span class=special>::</span><span class=identifier>composite_key_result</span><span class=special>&lt;</span>
       <span class=identifier>CompositeKey</span><span class=special>&gt;</span>                           <span class=identifier>first_argument_type</span><span class=special>;</span>
   <span class=keyword>typedef</span> <span class=identifier>first_argument_type</span>                 <span class=identifier>second_argument_type</span><span class=special>;</span>
   <span class=keyword>typedef</span> <span class=keyword>bool</span>                                <span class=identifier>result_type</span><span class=special>;</span>

   <span class=keyword>template</span><span class=special>&lt;</span><span class=keyword>typename</span> <span class=identifier>CompositeKey1</span><span class=special>,</span><span class=keyword>typename</span> <span class=identifier>CompositeKey2</span><span class=special>&gt;</span>
   <span class=keyword>bool</span> <span class=keyword>operator</span><span class=special>()(</span>
     <span class=keyword>const</span> <span class=identifier>boost</span><span class=special>::</span><span class=identifier>multi_index</span><span class=special>::</span><span class=identifier>composite_key_result</span><span class=special>&lt;</span><span class=identifier>CompositeKey1</span><span class=special>&gt;</span> <span class=special>&amp;</span> <span class=identifier>x</span><span class=special>,</span>
     <span class=keyword>const</span> <span class=identifier>boost</span><span class=special>::</span><span class=identifier>multi_index</span><span class=special>::</span><span class=identifier>composite_key_result</span><span class=special>&lt;</span><span class=identifier>CompositeKey2</span><span class=special>&gt;</span> <span class=special>&amp;</span> <span class=identifier>y</span><span class=special>)</span><span class=keyword>const</span><span class=special>;</span>

   <span class=keyword>template</span><span class=special>&lt;</span><span class=keyword>typename</span> <span class=identifier>CompositeKey</span><span class=special>,</span><span class=keyword>typename</span> <span class=identifier>Value0</span><span class=special>,...,</span><span class=keyword>typename</span> <span class=identifier>Valuen</span><span class=special>&gt;</span>
   <span class=keyword>bool</span> <span class=keyword>operator</span><span class=special>()(</span>
     <span class=keyword>const</span> <span class=identifier>boost</span><span class=special>::</span><span class=identifier>multi_index</span><span class=special>::</span><span class=identifier>composite_key_result</span><span class=special>&lt;</span><span class=identifier>CompositeKey</span><span class=special>&gt;&amp;</span> <span class=identifier>x</span><span class=special>,</span>
     <span class=keyword>const</span> <span class=identifier>boost</span><span class=special>::</span><span class=identifier>tuple</span><span class=special>&lt;</span><span class=identifier>Value0</span><span class=special>,...,</span><span class=identifier>Valuen</span><span class=special>&gt;&amp;</span> <span class=identifier>y</span><span class=special>)</span><span class=keyword>const</span><span class=special>;</span>

   <span class=keyword>template</span><span class=special>&lt;</span><span class=keyword>typename</span> <span class=identifier>Value0</span><span class=special>,...,</span><span class=keyword>typename</span> <span class=identifier>Valuen</span><span class=special>,</span><span class=keyword>typename</span> <span class=identifier>CompositeKey</span><span class=special>&gt;</span>
   <span class=keyword>bool</span> <span class=keyword>operator</span><span class=special>()(</span>
     <span class=keyword>const</span> <span class=identifier>boost</span><span class=special>::</span><span class=identifier>tuple</span><span class=special>&lt;</span><span class=identifier>Value0</span><span class=special>,...,</span><span class=identifier>Valuen</span><span class=special>&gt;&amp;</span> <span class=identifier>x</span><span class=special>,</span>
     <span class=keyword>const</span> <span class=identifier>boost</span><span class=special>::</span><span class=identifier>multi_index</span><span class=special>::</span><span class=identifier>composite_key_result</span><span class=special>&lt;</span><span class=identifier>CompositeKey</span><span class=special>&gt;&amp;</span> <span class=identifier>y</span><span class=special>)</span><span class=keyword>const</span><span class=special>;</span>
 <span class=special>};</span>

 <span class=special>}</span> <span class=comment>// namespace std</span>
 </pre></blockquote>

 <h3><a name="ckey_result_comparison">Comparison</a></h3>

 <h4><a name="composite_key_compare">Class template
 <code>composite_key_compare</code></a></h4>

 <p>
 <code>composite_key_compare</code> compares <code>composite_key_result</code>
 instantiations between them and with tuples of values using an internally stored
 collection of elementary comparison predicates.
 </p>

 <blockquote><pre>
 <span class=keyword>template</span><span class=special>&lt;</span><span class=keyword>typename</span> <span class=identifier>Compare0</span><span class=special>,...,</span><span class=keyword>typename</span> <span class=identifier>Comparen</span><span class=special>&gt;</span>
 <span class=keyword>struct</span> <span class=identifier>composite_key_compare</span>
 <span class=special>{</span>
   <span class=keyword>typedef</span> <span class=identifier>tuple</span><span class=special>&lt;</span><span class=identifier>Compare0</span><span class=special>,...,</span><span class=identifier>Comparen</span><span class=special>&gt;</span> <span class=identifier>key_comp_tuple</span><span class=special>;</span>

   <span class=identifier>composite_key_compare</span><span class=special>(</span>
     <span class=keyword>const</span> <span class=identifier>Compare0</span><span class=special>&amp;</span> <span class=identifier>c0</span><span class=special>=</span><span class=identifier>Compare0</span><span class=special>(),</span>
     <span class=special>...</span>
     <span class=keyword>const</span> <span class=identifier>Comparen</span><span class=special>&amp;</span> <span class=identifier>cn</span><span class=special>=</span><span class=identifier>Comparen</span><span class=special>());</span>

   <span class=identifier>composite_key_compare</span><span class=special>(</span><span class=keyword>const</span> <span class=identifier>key_comp_tuple</span><span class=special>&amp;</span> <span class=identifier>x</span><span class=special>);</span>

   <span class=keyword>const</span> <span class=identifier>key_comp_tuple</span><span class=special>&amp;</span> <span class=identifier>key_comps</span><span class=special>()</span><span class=keyword>const</span><span class=special>;</span>
   <span class=identifier>key_comp_tuple</span><span class=special>&amp;</span>       <span class=identifier>key_comps</span><span class=special>()</span><span class=special>;</span>

   <span class=keyword>template</span><span class=special>&lt;</span><span class=keyword>typename</span> <span class=identifier>CompositeKey1</span><span class=special>,</span><span class=keyword>typename</span> <span class=identifier>CompositeKey2</span><span class=special>&gt;</span>
   <span class=keyword>bool</span> <span class=keyword>operator</span><span class=special>()(</span>
     <span class=keyword>const</span> <span class=identifier>composite_key_result</span><span class=special>&lt;</span><span class=identifier>CompositeKey1</span><span class=special>&gt;</span> <span class=special>&amp;</span> <span class=identifier>x</span><span class=special>,</span>
     <span class=keyword>const</span> <span class=identifier>composite_key_result</span><span class=special>&lt;</span><span class=identifier>CompositeKey2</span><span class=special>&gt;</span> <span class=special>&amp;</span> <span class=identifier>y</span><span class=special>)</span><span class=keyword>const</span><span class=special>;</span>

   <span class=keyword>template</span><span class=special>&lt;</span><span class=keyword>typename</span> <span class=identifier>CompositeKey</span><span class=special>,</span><span class=keyword>typename</span> <span class=identifier>Value0</span><span class=special>,...,</span><span class=keyword>typename</span> <span class=identifier>Valuen</span><span class=special>&gt;</span>
   <span class=keyword>bool</span> <span class=keyword>operator</span><span class=special>()(</span>
     <span class=keyword>const</span> <span class=identifier>composite_key_result</span><span class=special>&lt;</span><span class=identifier>CompositeKey</span><span class=special>&gt;&amp;</span> <span class=identifier>x</span><span class=special>,</span>
     <span class=keyword>const</span> <span class=identifier>tuple</span><span class=special>&lt;</span><span class=identifier>Value0</span><span class=special>,...,</span><span class=identifier>Valuen</span><span class=special>&gt;&amp;</span> <span class=identifier>y</span><span class=special>)</span><span class=keyword>const</span><span class=special>;</span>

   <span class=keyword>template</span><span class=special>&lt;</span><span class=keyword>typename</span> <span class=identifier>Value0</span><span class=special>,...,</span><span class=keyword>typename</span> <span class=identifier>Valuen</span><span class=special>,</span><span class=keyword>typename</span> <span class=identifier>CompositeKey</span><span class=special>&gt;</span>
   <span class=keyword>bool</span> <span class=keyword>operator</span><span class=special>()(</span>
     <span class=keyword>const</span> <span class=identifier>tuple</span><span class=special>&lt;</span><span class=identifier>Value0</span><span class=special>,...,</span><span class=identifier>Valuen</span><span class=special>&gt;&amp;</span> <span class=identifier>x</span><span class=special>,</span>
     <span class=keyword>const</span> <span class=identifier>composite_key_result</span><span class=special>&lt;</span><span class=identifier>CompositeKey</span><span class=special>&gt;&amp;</span> <span class=identifier>y</span><span class=special>)</span><span class=keyword>const</span><span class=special>;</span>

   <span class=keyword>template</span><span class=special>&lt;</span><span class=keyword>typename</span> <span class=identifier>CompositeKey</span><span class=special>,</span><span class=keyword>typename</span> <span class=identifier>Value</span><span class=special>&gt;</span>
   <span class=keyword>bool</span> <span class=keyword>operator</span><span class=special>()(</span>
     <span class=keyword>const</span> <span class=identifier>composite_key_result</span><span class=special>&lt;</span><span class=identifier>CompositeKey</span><span class=special>&gt;&amp;</span> <span class=identifier>x</span><span class=special>,</span><span class=keyword>const</span> <span class=identifier>Value</span><span class=special>&amp;</span> <span class=identifier>y</span><span class=special>)</span><span class=keyword>const</span><span class=special>;</span>

   <span class=keyword>template</span><span class=special>&lt;</span><span class=keyword>typename</span> <span class=identifier>Value</span><span class=special>,</span><span class=keyword>typename</span> <span class=identifier>CompositeKey</span><span class=special>&gt;</span>
   <span class=keyword>bool</span> <span class=keyword>operator</span><span class=special>()(</span>
     <span class=keyword>const</span> <span class=identifier>Value</span><span class=special>&amp;</span> <span class=identifier>x</span><span class=special>,</span><span class=keyword>const</span> <span class=identifier>composite_key_result</span><span class=special>&lt;</span><span class=identifier>CompositeKey</span><span class=special>&gt;&amp;</span> <span class=identifier>y</span><span class=special>)</span><span class=keyword>const</span><span class=special>;</span>
 <span class=special>};</span>
 </pre></blockquote>

 <p>
 <code>Compare0</code>, ... , <code>Comparen</code> are the types of the comparison
 predicates stored by <code>composite_key_compare</code>. Each of these types
 must be a <a href="http://www.sgi.com/tech/stl/BinaryPredicate.html">
 <code>Binary Predicate</code></a>. At least a
 comparison predicate must be provided. The maximum number of comparison predicates of
 a <code>composite_key_compare</code> instantiation is implementation defined.
 <code>composite_key_compare</code> is
 <a href="http://www.sgi.com/tech/stl/Assignable.html"><code>Assignable</code></a>.
 It is also
 <a href="http://www.sgi.com/tech/stl/DefaultConstructible.html">
 <code>Default Constructible</code></a>
 if each <code>Comparei</code> is
 <a href="http://www.sgi.com/tech/stl/DefaultConstructible.html">
 <code>Default Constructible</code></a>.
 </p>

 <p>
 Note that formally it is not required that the <code>Comparei</code> types
 behave as comparison predicates in any definite way. However, the
 semantics of <code>composite_key_compare</code> is well defined if this
 is the case, as explained in the section on the
 <a href="#ckey_result_semantics">semantics of <code>composite_key_result</code></a>.
 </p>

 <h4>Notation</h4>

 <p>
 In what follows we use the same <a href="#ckey_result_notation">notation</a>
 introduced for <code>composite_key_result</code>.

 <h4><code>composite_key_compare</code> members</h4>

 <code>composite_key_compare(<br>
 &nbsp;&nbsp;const Compare0&amp; c0=Compare0(),<br>
 &nbsp;&nbsp;...<br>
 &nbsp;&nbsp;const Comparen&amp; cn=Comparen());
 </code>

 <blockquote>
 <b>Effects:</b> Constructs a <code>composite_key_compare</code> that stores
 copies of the comparison predicates supplied.
 </blockquote>

 <code>composite_key_compare(const key_comp_tuple&amp; x);</code>

 <blockquote>
 <b>Effects:</b> Constructs a <code>composite_key_compare</code> that stores
 copies of the comparison predicate objects supplied in <code>x</code>.
 </blockquote>

 <code>const key_comp_tuple&amp; key_comps()const;</code>

 <blockquote>
 <b>Returns:</b> a constant reference to a tuple holding the
 comparison predicate objects internally stored by the
 <code>composite_key_compare</code>.
 </blockquote>

 <code>key_comp_tuple&amp; key_comps();</code>

 <blockquote>
 <b>Returns:</b> a reference to a tuple holding the
 comparison predicate objects internally stored by the
 <code>composite_key_compare</code>.
 </blockquote>

 <code>
 template&lt;typename CompositeKey1,typename CompositeKey2><br>
 bool operator()(<br>
 &nbsp;&nbsp;const composite_key_result&lt;CompositeKey1> &amp; x,<br>
 &nbsp;&nbsp;const composite_key_result&lt;CompositeKey2> &amp; y)const;<br>
 template&lt;typename CompositeKey,typename Value0,...,typename Valuen><br>
 bool operator()(<br>
 &nbsp;&nbsp;const composite_key_result&lt;CompositeKey>&amp; x,<br>
 &nbsp;&nbsp;const tuple&lt;Value0,...,Valuen>&amp; y)const;<br>
 template&lt;typename Value0,...,typename Valuen,typename CompositeKey><br>
 bool operator()(<br>
 &nbsp;&nbsp;const tuple&lt;Value0,...,Valuen>&amp; x,<br>
 &nbsp;&nbsp;const composite_key_result&lt;CompositeKey>&amp; y)const;<br>
 </code>

 <blockquote>
 <b>Requires:</b> The expressions
 <code>key_comps().get&lt;i>()(x<sub>i</sub>,y<sub>i</sub>)</code> and
 <code>key_comps().get&lt;i>()(y<sub>i</sub>,x<sub>i</sub>)</code>
 are valid for all <code>i</code>
 in <code>[0,min(length(x),length(y)))</code>.<br>
 <b>Returns:</b> <code>true</code> if and only if there exists some
 <code>j</code> in the range <code>[0,min(length(x),length(y)))</code>
 such that
 <blockquote>
 <code>!key_comps().get&lt;i>()(x<sub>i</sub>,y<sub>i</sub>) &amp;&amp; !key_comps().get&lt;i>()(y<sub>i</sub>,x<sub>i</sub>)</code>
 for all <code>i</code> in <code>[0,j)</code>,<br>
 <code>&nbsp;key_comps().get&lt;j>()(x<sub>j</sub>,y<sub>j</sub>)</code>.
 </blockquote>
 <b>Complexity:</b> No more key extraction operations and comparisons
 are performed than those necessary for the evaluation of the expression above,
 starting at <code>i==0</code>. The evaluation is short-circuited as soon as
 the result is determined to be <code>false</code>.
 </blockquote>

 <code>
 template&lt;typename CompositeKey,typename Value&gt;<br>
 bool operator()(<br>
 &nbsp;&nbsp;const composite_key_result&lt;CompositeKey&gt;&amp; x,const Value&amp; y)const;
 </code>

 <blockquote>
 <b>Effects:</b>
 <blockquote><pre>
 <span class=keyword>return</span> <span class=keyword>operator</span><span class=special>()(</span><span class=identifier>x</span><span class=special>,</span><span class=identifier>make_tuple</span><span class=special>(</span><span class=identifier>cref</span><span class=special>(</span><span class=identifier>y</span><span class=special>)));</span>
 </pre></blockquote><br>
 </blockquote>

 <code>
 template&lt;typename Value,typename CompositeKey&gt;<br>
 bool operator()(<br>
 &nbsp;&nbsp;const Value&amp; x,const composite_key_result&lt;CompositeKey&gt;&amp; y)const;
 </code>

 <blockquote>
 <b>Effects:</b>
 <blockquote><pre>
 <span class=keyword>return</span> <span class=keyword>operator</span><span class=special>()(</span><span class=identifier>make_tuple</span><span class=special>(</span><span class=identifier>cref</span><span class=special>(</span><span class=identifier>x</span><span class=special>)),</span><span class=identifier>y</span><span class=special>);</span>
 </pre></blockquote><br>
 </blockquote>

 <h4><a name="composite_key_result_less">Class template
 <code>composite_key_result_less</code></a></h4>

 <p>
 <code>composite_key_result_less</code> acts as a particularization of
 <code>composite_key_compare</code> where all the comparison predicates supplied
 are instantiations of <code>std::less</code>.
 </p>

 <blockquote><pre>
 <span class=keyword>template</span><span class=special>&lt;</span><span class=keyword>typename</span> <span class=identifier>CompositeKeyResult</span><span class=special>&gt;</span>
 <span class=keyword>struct</span> <span class=identifier>composite_key_result_less</span>
 <span class=special>{</span>
   <span class=keyword>typedef</span> <span class=identifier>CompositeKeyResult</span>  <span class=identifier>first_argument_type</span><span class=special>;</span>
   <span class=keyword>typedef</span> <span class=identifier>first_argument_type</span> <span class=identifier>second_argument_type</span><span class=special>;</span>
   <span class=keyword>typedef</span> <span class=keyword>bool</span>                <span class=identifier>result_type</span><span class=special>;</span>

   <span class=keyword>template</span><span class=special>&lt;</span><span class=keyword>typename</span> <span class=identifier>CompositeKey1</span><span class=special>,</span><span class=keyword>typename</span> <span class=identifier>CompositeKey2</span><span class=special>&gt;</span>
   <span class=keyword>bool</span> <span class=keyword>operator</span><span class=special>()(</span>
     <span class=keyword>const</span> <span class=identifier>composite_key_result</span><span class=special>&lt;</span><span class=identifier>CompositeKey1</span><span class=special>&gt;</span> <span class=special>&amp;</span> <span class=identifier>x</span><span class=special>,</span>
     <span class=keyword>const</span> <span class=identifier>composite_key_result</span><span class=special>&lt;</span><span class=identifier>CompositeKey2</span><span class=special>&gt;</span> <span class=special>&amp;</span> <span class=identifier>y</span><span class=special>)</span><span class=keyword>const</span><span class=special>;</span>

   <span class=keyword>template</span><span class=special>&lt;</span><span class=keyword>typename</span> <span class=identifier>CompositeKey</span><span class=special>,</span><span class=keyword>typename</span> <span class=identifier>Value0</span><span class=special>,...,</span><span class=keyword>typename</span> <span class=identifier>Valuen</span><span class=special>&gt;</span>
   <span class=keyword>bool</span> <span class=keyword>operator</span><span class=special>()(</span>
     <span class=keyword>const</span> <span class=identifier>composite_key_result</span><span class=special>&lt;</span><span class=identifier>CompositeKey</span><span class=special>&gt;&amp;</span> <span class=identifier>x</span><span class=special>,</span>
     <span class=keyword>const</span> <span class=identifier>tuple</span><span class=special>&lt;</span><span class=identifier>Value0</span><span class=special>,...,</span><span class=identifier>Valuen</span><span class=special>&gt;&amp;</span> <span class=identifier>y</span><span class=special>)</span><span class=keyword>const</span><span class=special>;</span>

   <span class=keyword>template</span><span class=special>&lt;</span><span class=keyword>typename</span> <span class=identifier>Value0</span><span class=special>,...,</span><span class=keyword>typename</span> <span class=identifier>Valuen</span><span class=special>,</span><span class=keyword>typename</span> <span class=identifier>CompositeKey</span><span class=special>&gt;</span>
   <span class=keyword>bool</span> <span class=keyword>operator</span><span class=special>()(</span>
     <span class=keyword>const</span> <span class=identifier>tuple</span><span class=special>&lt;</span><span class=identifier>Value0</span><span class=special>,...,</span><span class=identifier>Valuen</span><span class=special>&gt;&amp;</span> <span class=identifier>x</span><span class=special>,</span>
     <span class=keyword>const</span> <span class=identifier>composite_key_result</span><span class=special>&lt;</span><span class=identifier>CompositeKey</span><span class=special>&gt;&amp;</span> <span class=identifier>y</span><span class=special>)</span><span class=keyword>const</span><span class=special>;</span>

   <span class=keyword>template</span><span class=special>&lt;</span><span class=keyword>typename</span> <span class=identifier>CompositeKey</span><span class=special>,</span><span class=keyword>typename</span> <span class=identifier>Value</span><span class=special>&gt;</span>
   <span class=keyword>bool</span> <span class=keyword>operator</span><span class=special>()(</span>
     <span class=keyword>const</span> <span class=identifier>composite_key_result</span><span class=special>&lt;</span><span class=identifier>CompositeKey</span><span class=special>&gt;&amp;</span> <span class=identifier>x</span><span class=special>,</span><span class=keyword>const</span> <span class=identifier>Value</span><span class=special>&amp;</span> <span class=identifier>y</span><span class=special>)</span><span class=keyword>const</span><span class=special>;</span>

   <span class=keyword>template</span><span class=special>&lt;</span><span class=keyword>typename</span> <span class=identifier>Value</span><span class=special>,</span><span class=keyword>typename</span> <span class=identifier>CompositeKey</span><span class=special>&gt;</span>
   <span class=keyword>bool</span> <span class=keyword>operator</span><span class=special>()(</span>
     <span class=keyword>const</span> <span class=identifier>Value</span><span class=special>&amp;</span> <span class=identifier>x</span><span class=special>,</span><span class=keyword>const</span> <span class=identifier>composite_key_result</span><span class=special>&lt;</span><span class=identifier>CompositeKey</span><span class=special>&gt;&amp;</span> <span class=identifier>y</span><span class=special>)</span><span class=keyword>const</span><span class=special>;</span>
 <span class=special>};</span>
 </pre></blockquote>

 <p>
 <code>CompositeKeyResult</code> must be an instantiation of
 <code>composite_key_result</code> for some type
 <code>composite_key&lt;KeyFromValue0,...,KeyFromValuen></code>.
 <code>composite_key_result_less&lt;CompositeKeyResult>::operator()</code> is
 then equivalent to
 <code>composite_key_compare&lt;Compare0,...,Comparen>::operator()</code>, taking
 <blockquote>
 <code>Comparei = std::less&lt;KeyFromValuei::result_type></code> for all
 <code>i = 0,...,n</code>.
 </blockquote>
 </p>

 <p>
 In addition to the requirements on <code>Comparei</code> imposed by
 <code>composite_key_compare</code>, each of these types must be
 <a href="http://www.sgi.com/tech/stl/DefaultConstructible.html">
 <code>Default Constructible</code></a>. <code>composite_key_result_less</code>
 is <a href="http://www.sgi.com/tech/stl/DefaultConstructible.html">
 <code>Default Constructible</code></a> and
 <a href="http://www.sgi.com/tech/stl/Assignable.html"><code>Assignable</code></a>.
 </p>

 <h4><a name="composite_key_result_greater">Class template
 <code>composite_key_result_greater</code></a></h4>

 <p>
 <code>composite_key_result</code> acts as a particularization of
 <code>composite_key_compare</code> where all the comparison predicates supplied
 are instantiations of <code>std::greater</code>.
 </p>

 <blockquote><pre>
 <span class=keyword>template</span><span class=special>&lt;</span><span class=keyword>typename</span> <span class=identifier>CompositeKeyResult</span><span class=special>&gt;</span>
 <span class=keyword>struct</span> <span class=identifier>composite_key_result_greater</span>
 <span class=special>{</span>
   <span class=keyword>typedef</span> <span class=identifier>CompositeKeyResult</span>  <span class=identifier>first_argument_type</span><span class=special>;</span>
   <span class=keyword>typedef</span> <span class=identifier>first_argument_type</span> <span class=identifier>second_argument_type</span><span class=special>;</span>
   <span class=keyword>typedef</span> <span class=keyword>bool</span>                <span class=identifier>result_type</span><span class=special>;</span>

   <span class=keyword>template</span><span class=special>&lt;</span><span class=keyword>typename</span> <span class=identifier>CompositeKey1</span><span class=special>,</span><span class=keyword>typename</span> <span class=identifier>CompositeKey2</span><span class=special>&gt;</span>
   <span class=keyword>bool</span> <span class=keyword>operator</span><span class=special>()(</span>
     <span class=keyword>const</span> <span class=identifier>composite_key_result</span><span class=special>&lt;</span><span class=identifier>CompositeKey1</span><span class=special>&gt;</span> <span class=special>&amp;</span> <span class=identifier>x</span><span class=special>,</span>
     <span class=keyword>const</span> <span class=identifier>composite_key_result</span><span class=special>&lt;</span><span class=identifier>CompositeKey2</span><span class=special>&gt;</span> <span class=special>&amp;</span> <span class=identifier>y</span><span class=special>)</span><span class=keyword>const</span><span class=special>;</span>

   <span class=keyword>template</span><span class=special>&lt;</span><span class=keyword>typename</span> <span class=identifier>CompositeKey</span><span class=special>,</span><span class=keyword>typename</span> <span class=identifier>Value0</span><span class=special>,...,</span><span class=keyword>typename</span> <span class=identifier>Valuen</span><span class=special>&gt;</span>
   <span class=keyword>bool</span> <span class=keyword>operator</span><span class=special>()(</span>
     <span class=keyword>const</span> <span class=identifier>composite_key_result</span><span class=special>&lt;</span><span class=identifier>CompositeKey</span><span class=special>&gt;&amp;</span> <span class=identifier>x</span><span class=special>,</span>
     <span class=keyword>const</span> <span class=identifier>tuple</span><span class=special>&lt;</span><span class=identifier>Value0</span><span class=special>,...,</span><span class=identifier>Valuen</span><span class=special>&gt;&amp;</span> <span class=identifier>y</span><span class=special>)</span><span class=keyword>const</span><span class=special>;</span>

   <span class=keyword>template</span><span class=special>&lt;</span><span class=keyword>typename</span> <span class=identifier>Value0</span><span class=special>,...,</span><span class=keyword>typename</span> <span class=identifier>Valuen</span><span class=special>,</span><span class=keyword>typename</span> <span class=identifier>CompositeKey</span><span class=special>&gt;</span>
   <span class=keyword>bool</span> <span class=keyword>operator</span><span class=special>()(</span>
     <span class=keyword>const</span> <span class=identifier>tuple</span><span class=special>&lt;</span><span class=identifier>Value0</span><span class=special>,...,</span><span class=identifier>Valuen</span><span class=special>&gt;&amp;</span> <span class=identifier>x</span><span class=special>,</span>
     <span class=keyword>const</span> <span class=identifier>composite_key_result</span><span class=special>&lt;</span><span class=identifier>CompositeKey</span><span class=special>&gt;&amp;</span> <span class=identifier>y</span><span class=special>)</span><span class=keyword>const</span><span class=special>;</span>

   <span class=keyword>template</span><span class=special>&lt;</span><span class=keyword>typename</span> <span class=identifier>CompositeKey</span><span class=special>,</span><span class=keyword>typename</span> <span class=identifier>Value</span><span class=special>&gt;</span>
   <span class=keyword>bool</span> <span class=keyword>operator</span><span class=special>()(</span>
     <span class=keyword>const</span> <span class=identifier>composite_key_result</span><span class=special>&lt;</span><span class=identifier>CompositeKey</span><span class=special>&gt;&amp;</span> <span class=identifier>x</span><span class=special>,</span><span class=keyword>const</span> <span class=identifier>Value</span><span class=special>&amp;</span> <span class=identifier>y</span><span class=special>)</span><span class=keyword>const</span><span class=special>;</span>

   <span class=keyword>template</span><span class=special>&lt;</span><span class=keyword>typename</span> <span class=identifier>Value</span><span class=special>,</span><span class=keyword>typename</span> <span class=identifier>CompositeKey</span><span class=special>&gt;</span>
   <span class=keyword>bool</span> <span class=keyword>operator</span><span class=special>()(</span>
     <span class=keyword>const</span> <span class=identifier>Value</span><span class=special>&amp;</span> <span class=identifier>x</span><span class=special>,</span><span class=keyword>const</span> <span class=identifier>composite_key_result</span><span class=special>&lt;</span><span class=identifier>CompositeKey</span><span class=special>&gt;&amp;</span> <span class=identifier>y</span><span class=special>)</span><span class=keyword>const</span><span class=special>;</span>
 <span class=special>};</span>
 </pre></blockquote>

 <p>
 <code>CompositeKeyResult</code> must be an instantiation of
 <code>composite_key_result</code> for some type
 <code>composite_key&lt;KeyFromValue0,...,KeyFromValuen></code>.
 <code>composite_key_result_greater&lt;CompositeKeyResult>::operator()</code> is
 then equivalent to
 <code>composite_key_compare&lt;Compare0,...,Comparen>::operator()</code>, taking
 <blockquote>
 <code>Comparei = std::greater&lt;KeyFromValuei::result_type></code> for all
 <code>i = 0,...,n</code>.
 </blockquote>
 </p>

 <p>
 In addition to the requirements on <code>Comparei</code> imposed by
 <code>composite_key_compare</code>, each of these types must be
 <a href="http://www.sgi.com/tech/stl/DefaultConstructible.html">
 <code>Default Constructible</code></a>. <code>composite_key_result_greater</code>
 is <a href="http://www.sgi.com/tech/stl/DefaultConstructible.html">
 <code>Default Constructible</code></a> and
 <a href="http://www.sgi.com/tech/stl/Assignable.html"><code>Assignable</code></a>.
 </p>

 <h4><a name="less_composite_key_result">Specialization of <code>std::less</code> for
 <code>composite_key</code> results</a></h4>

 <p>
 <code>std::less&lt;CompositeKeyResult></code>, for <code>CompositeKeyResult</code>
 being an instantiation of <code>composite_key_result</code>, has the same interface
 and functionality as <code>composite_key_result_less&lt;CompositeKeyResult></code>.
 </p>

 <blockquote><pre>
 <span class=keyword>namespace</span> <span class=identifier>std</span><span class=special>{</span>

 <span class=keyword>template</span><span class=special>&lt;</span><span class=keyword>typename</span> <span class=identifier>CompositeKey</span><span class=special>&gt;</span>
 <span class=keyword>struct</span> <span class=identifier>less</span><span class=special>&lt;</span><span class=identifier>boost</span><span class=special>::</span><span class=identifier>multi_index</span><span class=special>::</span><span class=identifier>composite_key_result</span><span class=special>&lt;</span><span class=identifier>CompositeKey</span><span class=special>&gt;</span> <span class=special>&gt;</span>
 <span class=special>{</span>
   <span class=keyword>typedef</span>
     <span class=identifier>boost</span><span class=special>::</span><span class=identifier>multi_index</span><span class=special>::</span><span class=identifier>composite_key_result</span><span class=special>&lt;</span>
       <span class=identifier>CompositeKey</span><span class=special>&gt;</span>                           <span class=identifier>first_argument_type</span><span class=special>;</span>
   <span class=keyword>typedef</span> <span class=identifier>first_argument_type</span>                 <span class=identifier>second_argument_type</span><span class=special>;</span>
   <span class=keyword>typedef</span> <span class=keyword>bool</span>                                <span class=identifier>result_type</span><span class=special>;</span>

   <span class=keyword>template</span><span class=special>&lt;</span><span class=keyword>typename</span> <span class=identifier>CompositeKey1</span><span class=special>,</span><span class=keyword>typename</span> <span class=identifier>CompositeKey2</span><span class=special>&gt;</span>
   <span class=keyword>bool</span> <span class=keyword>operator</span><span class=special>()(</span>
     <span class=keyword>const</span> <span class=identifier>boost</span><span class=special>::</span><span class=identifier>multi_index</span><span class=special>::</span><span class=identifier>composite_key_result</span><span class=special>&lt;</span><span class=identifier>CompositeKey1</span><span class=special>&gt;</span> <span class=special>&amp;</span> <span class=identifier>x</span><span class=special>,</span>
     <span class=keyword>const</span> <span class=identifier>boost</span><span class=special>::</span><span class=identifier>multi_index</span><span class=special>::</span><span class=identifier>composite_key_result</span><span class=special>&lt;</span><span class=identifier>CompositeKey2</span><span class=special>&gt;</span> <span class=special>&amp;</span> <span class=identifier>y</span><span class=special>)</span><span class=keyword>const</span><span class=special>;</span>

   <span class=keyword>template</span><span class=special>&lt;</span><span class=keyword>typename</span> <span class=identifier>CompositeKey</span><span class=special>,</span><span class=keyword>typename</span> <span class=identifier>Value0</span><span class=special>,...,</span><span class=keyword>typename</span> <span class=identifier>Valuen</span><span class=special>&gt;</span>
   <span class=keyword>bool</span> <span class=keyword>operator</span><span class=special>()(</span>
     <span class=keyword>const</span> <span class=identifier>boost</span><span class=special>::</span><span class=identifier>multi_index</span><span class=special>::</span><span class=identifier>composite_key_result</span><span class=special>&lt;</span><span class=identifier>CompositeKey</span><span class=special>&gt;&amp;</span> <span class=identifier>x</span><span class=special>,</span>
     <span class=keyword>const</span> <span class=identifier>boost</span><span class=special>::</span><span class=identifier>tuple</span><span class=special>&lt;</span><span class=identifier>Value0</span><span class=special>,...,</span><span class=identifier>Valuen</span><span class=special>&gt;&amp;</span> <span class=identifier>y</span><span class=special>)</span><span class=keyword>const</span><span class=special>;</span>

   <span class=keyword>template</span><span class=special>&lt;</span><span class=keyword>typename</span> <span class=identifier>Value0</span><span class=special>,...,</span><span class=keyword>typename</span> <span class=identifier>Valuen</span><span class=special>,</span><span class=keyword>typename</span> <span class=identifier>CompositeKey</span><span class=special>&gt;</span>
   <span class=keyword>bool</span> <span class=keyword>operator</span><span class=special>()(</span>
     <span class=keyword>const</span> <span class=identifier>boost</span><span class=special>::</span><span class=identifier>tuple</span><span class=special>&lt;</span><span class=identifier>Value0</span><span class=special>,...,</span><span class=identifier>Valuen</span><span class=special>&gt;&amp;</span> <span class=identifier>x</span><span class=special>,</span>
     <span class=keyword>const</span> <span class=identifier>boost</span><span class=special>::</span><span class=identifier>multi_index</span><span class=special>::</span><span class=identifier>composite_key_result</span><span class=special>&lt;</span><span class=identifier>CompositeKey</span><span class=special>&gt;&amp;</span> <span class=identifier>y</span><span class=special>)</span><span class=keyword>const</span><span class=special>;</span>

   <span class=keyword>template</span><span class=special>&lt;</span><span class=keyword>typename</span> <span class=identifier>CompositeKey</span><span class=special>,</span><span class=keyword>typename</span> <span class=identifier>Value</span><span class=special>&gt;</span>
   <span class=keyword>bool</span> <span class=keyword>operator</span><span class=special>()(</span>
     <span class=keyword>const</span> <span class=identifier>boost</span><span class=special>::</span><span class=identifier>multi_index</span><span class=special>::</span><span class=identifier>composite_key_result</span><span class=special>&lt;</span><span class=identifier>CompositeKey</span><span class=special>&gt;&amp;</span> <span class=identifier>x</span><span class=special>,</span>
     <span class=keyword>const</span> <span class=identifier>Value</span><span class=special>&amp;</span> <span class=identifier>y</span><span class=special>)</span><span class=keyword>const</span><span class=special>;</span>

   <span class=keyword>template</span><span class=special>&lt;</span><span class=keyword>typename</span> <span class=identifier>Value</span><span class=special>,</span><span class=keyword>typename</span> <span class=identifier>CompositeKey</span><span class=special>&gt;</span>
   <span class=keyword>bool</span> <span class=keyword>operator</span><span class=special>()(</span>
     <span class=keyword>const</span> <span class=identifier>Value</span><span class=special>&amp;</span> <span class=identifier>x</span><span class=special>,</span>
     <span class=keyword>const</span> <span class=identifier>boost</span><span class=special>::</span><span class=identifier>multi_index</span><span class=special>::</span><span class=identifier>composite_key_result</span><span class=special>&lt;</span><span class=identifier>CompositeKey</span><span class=special>&gt;&amp;</span> <span class=identifier>y</span><span class=special>)</span><span class=keyword>const</span><span class=special>;</span>
 <span class=special>};</span>

 <span class=special>}</span> <span class=comment>// namespace std</span>
 </pre></blockquote>

 <h4><a name="greater_composite_key_result">Specialization of <code>std::greater</code> for
 <code>composite_key</code> results</a></h4>

 <p>
 <code>std::greater&lt;CompositeKeyResult></code>, for <code>CompositeKeyResult</code>
 being an instantiation of <code>composite_key_result</code>, has the same interface
 and functionality as <code>composite_key_result_greater&lt;CompositeKeyResult></code>.
 </p>

 <blockquote><pre>
 <span class=keyword>namespace</span> <span class=identifier>std</span><span class=special>{</span>

 <span class=keyword>template</span><span class=special>&lt;</span><span class=keyword>typename</span> <span class=identifier>CompositeKey</span><span class=special>&gt;</span>
 <span class=keyword>struct</span> <span class=identifier>greater</span><span class=special>&lt;</span><span class=identifier>boost</span><span class=special>::</span><span class=identifier>multi_index</span><span class=special>::</span><span class=identifier>composite_key_result</span><span class=special>&lt;</span><span class=identifier>CompositeKey</span><span class=special>&gt;</span> <span class=special>&gt;</span>
 <span class=special>{</span>
   <span class=keyword>typedef</span>
     <span class=identifier>boost</span><span class=special>::</span><span class=identifier>multi_index</span><span class=special>::</span><span class=identifier>composite_key_result</span><span class=special>&lt;</span>
       <span class=identifier>CompositeKey</span><span class=special>&gt;</span>                           <span class=identifier>first_argument_type</span><span class=special>;</span>
   <span class=keyword>typedef</span> <span class=identifier>first_argument_type</span>                 <span class=identifier>second_argument_type</span><span class=special>;</span>
   <span class=keyword>typedef</span> <span class=keyword>bool</span>                                <span class=identifier>result_type</span><span class=special>;</span>

   <span class=keyword>template</span><span class=special>&lt;</span><span class=keyword>typename</span> <span class=identifier>CompositeKey1</span><span class=special>,</span><span class=keyword>typename</span> <span class=identifier>CompositeKey2</span><span class=special>&gt;</span>
   <span class=keyword>bool</span> <span class=keyword>operator</span><span class=special>()(</span>
     <span class=keyword>const</span> <span class=identifier>boost</span><span class=special>::</span><span class=identifier>multi_index</span><span class=special>::</span><span class=identifier>composite_key_result</span><span class=special>&lt;</span><span class=identifier>CompositeKey1</span><span class=special>&gt;</span> <span class=special>&amp;</span> <span class=identifier>x</span><span class=special>,</span>
     <span class=keyword>const</span> <span class=identifier>boost</span><span class=special>::</span><span class=identifier>multi_index</span><span class=special>::</span><span class=identifier>composite_key_result</span><span class=special>&lt;</span><span class=identifier>CompositeKey2</span><span class=special>&gt;</span> <span class=special>&amp;</span> <span class=identifier>y</span><span class=special>)</span><span class=keyword>const</span><span class=special>;</span>

   <span class=keyword>template</span><span class=special>&lt;</span><span class=keyword>typename</span> <span class=identifier>CompositeKey</span><span class=special>,</span><span class=keyword>typename</span> <span class=identifier>Value0</span><span class=special>,...,</span><span class=keyword>typename</span> <span class=identifier>Valuen</span><span class=special>&gt;</span>
   <span class=keyword>bool</span> <span class=keyword>operator</span><span class=special>()(</span>
     <span class=keyword>const</span> <span class=identifier>boost</span><span class=special>::</span><span class=identifier>multi_index</span><span class=special>::</span><span class=identifier>composite_key_result</span><span class=special>&lt;</span><span class=identifier>CompositeKey</span><span class=special>&gt;&amp;</span> <span class=identifier>x</span><span class=special>,</span>
     <span class=keyword>const</span> <span class=identifier>boost</span><span class=special>::</span><span class=identifier>tuple</span><span class=special>&lt;</span><span class=identifier>Value0</span><span class=special>,...,</span><span class=identifier>Valuen</span><span class=special>&gt;&amp;</span> <span class=identifier>y</span><span class=special>)</span><span class=keyword>const</span><span class=special>;</span>

   <span class=keyword>template</span><span class=special>&lt;</span><span class=keyword>typename</span> <span class=identifier>Value0</span><span class=special>,...,</span><span class=keyword>typename</span> <span class=identifier>Valuen</span><span class=special>,</span><span class=keyword>typename</span> <span class=identifier>CompositeKey</span><span class=special>&gt;</span>
   <span class=keyword>bool</span> <span class=keyword>operator</span><span class=special>()(</span>
     <span class=keyword>const</span> <span class=identifier>boost</span><span class=special>::</span><span class=identifier>tuple</span><span class=special>&lt;</span><span class=identifier>Value0</span><span class=special>,...,</span><span class=identifier>Valuen</span><span class=special>&gt;&amp;</span> <span class=identifier>x</span><span class=special>,</span>
     <span class=keyword>const</span> <span class=identifier>boost</span><span class=special>::</span><span class=identifier>multi_index</span><span class=special>::</span><span class=identifier>composite_key_result</span><span class=special>&lt;</span><span class=identifier>CompositeKey</span><span class=special>&gt;&amp;</span> <span class=identifier>y</span><span class=special>)</span><span class=keyword>const</span><span class=special>;</span>

   <span class=keyword>template</span><span class=special>&lt;</span><span class=keyword>typename</span> <span class=identifier>CompositeKey</span><span class=special>,</span><span class=keyword>typename</span> <span class=identifier>Value</span><span class=special>&gt;</span>
   <span class=keyword>bool</span> <span class=keyword>operator</span><span class=special>()(</span>
     <span class=keyword>const</span> <span class=identifier>boost</span><span class=special>::</span><span class=identifier>multi_index</span><span class=special>::</span><span class=identifier>composite_key_result</span><span class=special>&lt;</span><span class=identifier>CompositeKey</span><span class=special>&gt;&amp;</span> <span class=identifier>x</span><span class=special>,</span>
     <span class=keyword>const</span> <span class=identifier>Value</span><span class=special>&amp;</span> <span class=identifier>y</span><span class=special>)</span><span class=keyword>const</span><span class=special>;</span>

   <span class=keyword>template</span><span class=special>&lt;</span><span class=keyword>typename</span> <span class=identifier>Value</span><span class=special>,</span><span class=keyword>typename</span> <span class=identifier>CompositeKey</span><span class=special>&gt;</span>
   <span class=keyword>bool</span> <span class=keyword>operator</span><span class=special>()(</span>
     <span class=keyword>const</span> <span class=identifier>Value</span><span class=special>&amp;</span> <span class=identifier>x</span><span class=special>,</span>
     <span class=keyword>const</span> <span class=identifier>boost</span><span class=special>::</span><span class=identifier>multi_index</span><span class=special>::</span><span class=identifier>composite_key_result</span><span class=special>&lt;</span><span class=identifier>CompositeKey</span><span class=special>&gt;&amp;</span> <span class=identifier>y</span><span class=special>)</span><span class=keyword>const</span><span class=special>;</span>
 <span class=special>};</span>

 <span class=special>}</span> <span class=comment>// namespace std</span>
 </pre></blockquote>

 <h3><a name="ckey_result_hashing">Hashing</a></h3>

 <h4><a name="composite_key_hash">Class template
 <code>composite_key_hash</code></a></h4>

 <p>
 <code>composite_key_hash</code> produces hash values for <code>composite_key_result</code>
 instantiations based on a collection of elementary hash functors.
 </p>

 <blockquote><pre>
 <span class=keyword>template</span><span class=special>&lt;</span><span class=keyword>typename</span> <span class=identifier>Hash0</span><span class=special>,...,</span><span class=keyword>typename</span> <span class=identifier>Hashn</span><span class=special>&gt;</span>
 <span class=keyword>struct</span> <span class=identifier>composite_key_hash</span>
 <span class=special>{</span>
   <span class=keyword>typedef</span> <span class=identifier>tuple</span><span class=special>&lt;</span><span class=identifier>Hash0</span><span class=special>,...,</span><span class=identifier>Hashn</span><span class=special>&gt;</span> <span class=identifier>key_hasher_tuple</span><span class=special>;</span>

   <span class=identifier>composite_key_hash</span><span class=special>(</span>
     <span class=keyword>const</span> <span class=identifier>Hash0</span><span class=special>&amp;</span> <span class=identifier>h0</span><span class=special>=</span><span class=identifier>Hash0</span><span class=special>(),</span>
     <span class=special>...</span>
     <span class=keyword>const</span> <span class=identifier>Hashn</span><span class=special>&amp;</span> <span class=identifier>hn</span><span class=special>=</span><span class=identifier>Hashn</span><span class=special>());</span>

   <span class=identifier>composite_key_hash</span><span class=special>(</span><span class=keyword>const</span> <span class=identifier>key_hasher_tuple</span><span class=special>&amp;</span> <span class=identifier>x</span><span class=special>);</span>

   <span class=keyword>const</span> <span class=identifier>key_hasher_tuple</span><span class=special>&amp;</span> <span class=identifier>key_hash_functions</span><span class=special>()</span><span class=keyword>const</span><span class=special>;</span>
   <span class=identifier>key_hasher_tuple</span><span class=special>&amp;</span>       <span class=identifier>key_hash_functions</span><span class=special>()</span><span class=special>;</span>

   <span class=keyword>template</span><span class=special>&lt;</span><span class=keyword>typename</span> <span class=identifier>CompositeKey</span><span class=special>&gt;</span>
   <span class=identifier>std</span><span class=special>::</span><span class=identifier>size_t</span> <span class=keyword>operator</span><span class=special>()(</span>
     <span class=keyword>const</span> <span class=identifier>composite_key_result</span><span class=special>&lt;</span><span class=identifier>CompositeKey</span><span class=special>&gt;&amp;</span> <span class=identifier>x</span><span class=special>)</span><span class=keyword>const</span><span class=special>;</span>

   <span class=keyword>template</span><span class=special>&lt;</span><span class=keyword>typename</span> <span class=identifier>Value0</span><span class=special>,...,</span><span class=keyword>typename</span> <span class=identifier>Valuen</span><span class=special>&gt;</span>
   <span class=identifier>std</span><span class=special>::</span><span class=identifier>size_t</span> <span class=keyword>operator</span><span class=special>()(</span>
     <span class=keyword>const</span> <span class=identifier>tuple</span><span class=special>&lt;</span><span class=identifier>Value0</span><span class=special>,...,</span><span class=identifier>Valuen</span><span class=special>&gt;&amp;</span> <span class=identifier>x</span><span class=special>)</span><span class=keyword>const</span><span class=special>;</span>
 <span class=special>};</span>
 </pre></blockquote>

 <p>
 <code>Hash0</code>, ... , <code>Hashn</code> are the types of the hash functors
 stored by <code>composite_key_hash</code>. Each of these types
 must be a
 <a href="http://www.sgi.com/tech/stl/UnaryFunction.html"><code>Unary Function</code></a>
 returning a value of type <code>std::size_t</code> in the range
 <code>[0, std::numeric_limits&lt;std::size_t&gt;::max())</code>.
 At least a
 hash functor must be provided. The maximum number of hash functors of
 a <code>composite_key_hash</code> instantiation is implementation defined.
 <code>composite_key_hash</code> is
 <a href="http://www.sgi.com/tech/stl/Assignable.html"><code>Assignable</code></a>.
 It is also
 <a href="http://www.sgi.com/tech/stl/DefaultConstructible.html">
 <code>Default Constructible</code></a>
 if each <code>Hashi</code> is
 <a href="http://www.sgi.com/tech/stl/DefaultConstructible.html">
 <code>Default Constructible</code></a>.
 </p>

 <h4>Notation</h4>

 <p>
 In what follows we use the same <a href="#ckey_result_notation">notation</a>
 introduced for <code>composite_key_result</code>.

 <h4><code>composite_key_hash</code> members</h4>

 <code>composite_key_hash(<br>
 &nbsp;&nbsp;const Hash0&amp; h0=Hash0(),<br>
 &nbsp;&nbsp;...<br>
 &nbsp;&nbsp;const Hashn&amp; hn=Hashn());
 </code>

 <blockquote>
 <b>Effects:</b> Constructs a <code>composite_key_hash</code> that stores
 copies of the hash functors supplied.
 </blockquote>

 <code>composite_key_hash(const key_hasher_tuple&amp; x);</code>

 <blockquote>
 <b>Effects:</b> Constructs a <code>composite_key_hash</code> that stores
 copies of the hash functors supplied in <code>x</code>.
 </blockquote>

 <code>const key_hasher_tuple&amp; key_hash_functions()const;</code>

 <blockquote>
 <b>Returns:</b> a constant reference to a tuple holding the
 hash functors internally stored by the
 <code>composite_key_hash</code>.
 </blockquote>

 <code>key_hasher_tuple&amp; key_hash_functions();</code>

 <blockquote>
 <b>Returns:</b> a reference to a tuple holding the
 hash functors internally stored by the
 <code>composite_key_hash</code>.
 </blockquote>

 <code>
 template&lt;typename CompositeKey><br>
 bool operator()(<br>
 &nbsp;&nbsp;const composite_key_result&lt;CompositeKey>&amp; x)const;<br>
 template&lt;typename Value0,...,typename Valuen><br>
 bool operator()(<br>
 &nbsp;&nbsp;const tuple&lt;Value0,...,Valuen>&amp; x)const;
 </code>

 <blockquote>
 <b>Requires:</b> <code>length(x)==length(key_hash_functions())</code>.
 The expression
 <code>key_hash_functions().get&lt;i>()(x<sub>i</sub>)</code>
 is valid for all <code>i</code> in <code>[0,length(x))</code>.
 <br>
 <b>Returns:</b> A value in the range
 <code>[0, std::numeric_limits&lt;std::size_t&gt;::max())</code> that
 solely depends on the numerical tuple
 <blockquote>
 (<code>key_hash_functions().get&lt;0>()(x<sub>0</sub>)</code>, ... ,
 <code>key_hash_functions().get&lt;N>()(x<sub>N</sub>)</code>),
 with <code>N=length(x)-1</code>.
 </blockquote>
 </blockquote>

 <h4><a name="composite_key_result_hash">Class template
 <code>composite_key_result_hash</code></a></h4>

 <p>
 <code>composite_key_result_hash</code> acts as a particularization of
 <code>composite_key_hash</code> where all the hash functors supplied
 are instantiations of
 <a href="../../../functional/hash/index.html"><code>boost::hash</code></a>.
 </p>

 <blockquote><pre>
 <span class=keyword>template</span><span class=special>&lt;</span><span class=keyword>typename</span> <span class=identifier>CompositeKeyResult</span><span class=special>&gt;</span>
 <span class=keyword>struct</span> <span class=identifier>composite_key_result_hash</span>
 <span class=special>{</span>
   <span class=keyword>typedef</span> <span class=identifier>CompositeKeyResult</span> <span class=identifier>argument_type</span><span class=special>;</span>
   <span class=keyword>typedef</span> <span class=identifier>std</span><span class=special>::</span><span class=identifier>size_t</span>        <span class=identifier>result_type</span><span class=special>;</span>

   <span class=keyword>template</span><span class=special>&lt;</span><span class=keyword>typename</span> <span class=identifier>CompositeKey</span><span class=special>&gt;</span>
   <span class=identifier>std</span><span class=special>::</span><span class=identifier>size_t</span> <span class=keyword>operator</span><span class=special>()(</span>
     <span class=keyword>const</span> <span class=identifier>composite_key_result</span><span class=special>&lt;</span><span class=identifier>CompositeKey</span><span class=special>&gt;</span><span class=special>&amp;</span> <span class=identifier>x</span><span class=special>)</span><span class=keyword>const</span><span class=special>;</span>

   <span class=keyword>template</span><span class=special>&lt;</span><span class=keyword>typename</span> <span class=identifier>Value0</span><span class=special>,...,</span><span class=keyword>typename</span> <span class=identifier>Valuen</span><span class=special>&gt;</span>
   <span class=identifier>std</span><span class=special>::</span><span class=identifier>size_t</span> <span class=keyword>operator</span><span class=special>()(</span>
      <span class=keyword>const</span> <span class=identifier>tuple</span><span class=special>&lt;</span><span class=identifier>Value0</span><span class=special>,...,</span><span class=identifier>Valuen</span><span class=special>&gt;&amp;</span> <span class=identifier>x</span><span class=special>)</span><span class=keyword>const</span><span class=special>;</span>
 <span class=special>};</span>
 </pre></blockquote>

 <p>
 <code>CompositeKeyResult</code> must be an instantiation of
 <code>composite_key_result</code> for some type
 <code>composite_key&lt;KeyFromValue0,...,KeyFromValuen></code>.
 <code>composite_key_result_hash&lt;CompositeKeyResult>::operator()</code> is
 then equivalent to
 <code>composite_key_hash&lt;Hash0,...,Hashn>::operator()</code>, taking
 <blockquote>
 <code>Hashi = boost::hash&lt;KeyFromValuei::result_type></code> for all
 <code>i = 0,...,n</code>.
 </blockquote>
 </p>

 <p>
 In addition to the requirements on <code>Hashi</code> imposed by
 <code>composite_key_hash</code>, each of these types must be
 <a href="http://www.sgi.com/tech/stl/DefaultConstructible.html">
 <code>Default Constructible</code></a>. <code>composite_key_result_hash</code>
 is <a href="http://www.sgi.com/tech/stl/DefaultConstructible.html">
 <code>Default Constructible</code></a> and
 <a href="http://www.sgi.com/tech/stl/Assignable.html"><code>Assignable</code></a>.
 </p>

 <h4><a name="hash_composite_key_result">Specialization of
 <a href="../../../functional/hash/index.html"><code>boost::hash</code></a>
 for <code>composite_key</code> results</a></h4>

 <p>
 <code>boost::hash&lt;CompositeKeyResult></code>, for <code>CompositeKeyResult</code>
 being an instantiation of <code>composite_key_result</code>, has the same interface
 and functionality as <code>composite_key_result_hash&lt;CompositeKeyResult></code>.
 </p>

 <blockquote><pre>
 <span class=keyword>namespace</span> <span class=identifier>boost</span><span class=special>{</span>

 <span class=keyword>template</span><span class=special>&lt;</span><span class=keyword>typename</span> <span class=identifier>CompositeKey</span><span class=special>&gt;</span>
 <span class=keyword>struct</span> <span class=identifier>hash</span><span class=special>&lt;</span><span class=identifier>multi_index</span><span class=special>::</span><span class=identifier>composite_key_result</span><span class=special>&lt;</span><span class=identifier>CompositeKey</span><span class=special>&gt;</span> <span class=special>&gt;</span>
 <span class=special>{</span>
   <span class=keyword>typedef</span> <span class=identifier>multi_index</span><span class=special>::</span><span class=identifier>composite_key_result</span><span class=special>&lt;</span><span class=identifier>CompositeKey</span><span class=special>&gt;</span> <span class=identifier>argument_type</span><span class=special>;</span>
   <span class=keyword>typedef</span> <span class=identifier>std</span><span class=special>::</span><span class=identifier>size_t</span>                                     <span class=identifier>result_type</span><span class=special>;</span>

   <span class=keyword>template</span><span class=special>&lt;</span><span class=keyword>typename</span> <span class=identifier>CompositeKey</span><span class=special>&gt;</span>
   <span class=identifier>std</span><span class=special>::</span><span class=identifier>size_t</span> <span class=keyword>operator</span><span class=special>()(</span>
     <span class=keyword>const</span> <span class=identifier>multi_index</span><span class=special>::</span><span class=identifier>composite_key_result</span><span class=special>&lt;</span><span class=identifier>CompositeKey</span><span class=special>&gt;&amp;</span> <span class=identifier>x</span><span class=special>)</span><span class=keyword>const</span><span class=special>;</span>

   <span class=keyword>template</span><span class=special>&lt;</span><span class=keyword>typename</span> <span class=identifier>Value0</span><span class=special>,...,</span><span class=keyword>typename</span> <span class=identifier>Valuen</span><span class=special>&gt;</span>
   <span class=identifier>std</span><span class=special>::</span><span class=identifier>size_t</span> <span class=keyword>operator</span><span class=special>()(</span>
     <span class=keyword>const</span> <span class=identifier>tuple</span><span class=special>&lt;</span><span class=identifier>Value0</span><span class=special>,...,</span><span class=identifier>Valuen</span><span class=special>&gt;&amp;</span> <span class=identifier>x</span><span class=special>)</span><span class=keyword>const</span><span class=special>;</span>
 <span class=special>};</span>

 <span class=special>}</span> <span class=comment>// namespace boost</span>
 </pre></blockquote>

 <h3><a name="ckey_result_semantics">Semantics of
 <code>composite_key_result</code></a></h3>

 <p>
 The design of equality, comparison and hash operations for
 <code>composite_key_result</code> objects is based on the following rationale:
 a <code>composite_key_result</code> is regarded as a "virtual" tuple, each
 of its elements being the result of the corresponding elementary
 key extractor. Accordingly, any given operation resolves to a
 combination of the corresponding elementwise operations.
 This mapping preserves the fundamental properties of the elementary operations
 involved; for instance, it defines a true equivalence relation if the
 basic predicates induce equivalence relations themselves.
 We can state these facts in a formal way as follows.
 </p>

 <p>
 Consider an instantiation of <code>composite_key_equal_to</code>
 with types <code>Pred0</code>, ... , <code>Predn</code> such that each
 <code>Predi</code> induces an equivalence relation on a certain type <code>Ti</code>,
 and let <code>CompositeKey</code> be a type of the form
 <code>composite_key&lt;Value,KeyFromValue0,...,KeyFromValuej></code>,
 with <code>j &lt;= n</code>, such that
 <blockquote>
 <code>KeyFromValuei::result_type = Ti</code>, for all <code>i = 0,...,j</code>.
 </blockquote>
 Then, <code>composite_key_equal_to</code> induces an equivalence relation
 on elements of type <code>composite_key_result&lt;CompositeKey></code>;
 such two objects are equivalent if all its elementary key extractor values
 are also equivalent. Additionally, given an instantiation
 <code>composite_key_hash&lt;Hash0,...,Hashj></code>, the following types are
 <a href="hash_indices.html#lookup"><code>Compatible Keys</code></a> of
 (<code>composite_key_hash</code>, <code>composite_key_equal_to</code>)
 with respect to <code>composite_key_result&lt;CompositeKey></code>:
 <blockquote>
 <code>tuple&lt;Q0,...,Qj></code>,<br>
 <code>composite_key_result&lt;composite_key&lt;K0,...,Kj> ></code>, with
 <code>Ki::result_type = Qi</code> for all <code>i = 0,...,j</code>.
 </blockquote>
 provided that each <code>Qi</code> is either <code>Ti</code> or a
 <a href="hash_indices.html#lookup"><code>Compatible Key</code></a>
 of (<code>Hashi</code>, <code>Predi</code>).</p>

 <p>
 As for comparison, consider an instantiation of <code>composite_key_compare</code>
 with types <code>Compare0</code>, ... , <code>Comparen</code> such that each
 <code>Comparei</code> is a
 <a href="http://www.sgi.com/tech/stl/StrictWeakOrdering.html"><code>Strict
 Weak Ordering</code></a> on the type <code>Ti</code>. Then, for a
 <code>CompositeKey</code> type defined in the same manner as above,
 <code>composite_key_compare</code> is a
 <a href="http://www.sgi.com/tech/stl/StrictWeakOrdering.html"><code>Strict
 Weak Ordering</code></a> on elements of type
 <code>composite_key_result&lt;CompositeKey></code>, and the order induced
 is lexicographical. Also, the following types are
 <a href="ord_indices.html#set_operations"><code>Compatible Keys</code></a> of
 <code>composite_key_compare</code> with respect to
 <code>composite_key_result&lt;CompositeKey></code>:
 <blockquote>
 <code>tuple&lt;Q0,...,Qk></code>, <code>k &lt;= n</code><br>
 <code>composite_key_result&lt;composite_key&lt;K0,...,Kk> ></code>, with
 <code>Ki::result_type = Qi</code> for all <code>i = 0,...,k</code>.
 </blockquote>
 provided that
 <ul>
   <li>for <code>i = 0,...,min(j,k)-1</code>, <code>Qi</code> is either <code>Ti</code>
     or <i>not coarser</i> than <code>Ti</code> (<code>Qi</code> is a
     <a href="ord_indices.html#set_operations"><code>Compatible Key</code></a>
     of <code>Comparei</code> and there are no two distinct elements of
     <code>Ti</code> equivalent to one single element of <code>Qi</code>);
   </li>
   <li>
     <code>Qm</code> (with <code>m = min(j,k)</code>) is either <code>Tm</code> or a
     <a href="ord_indices.html#set_operations"><code>Compatible Key</code></a>
     of <code>Comparem</code>.
   </li>
 </ul>

 In this case, the comparison is done
 lexicographically only on the first <code>1+min(j,k)</code> elements.
 </p>

 <p>
 Analogous properties hold for the equality and comparison operators
 of <code>composite_key_result</code>. Note, however,
 that equality is only defined for objects of the same length, whilst
 comparison takes the minimum length of the operands considered.
 Therefore, the equivalence classes induced by <code>x==y</code> are
 subsets of those associated to <code>!(x&lt;y)&amp;&amp;!(y&lt;x)</code>.
 </p>

 <hr>

 <div class="prev_link"><a href="rnd_indices.html"><img src="../prev.gif" alt="random access indices" border="0"><br>
 Random access indices
 </a></div>
 <div class="up_link"><a href="index.html"><img src="../up.gif" alt="Boost.MultiIndex reference" border="0"><br>
 Boost.MultiIndex reference
 </a></div>
 <div class="next_link"><a href="../compiler_specifics.html"><img src="../next.gif" alt="compiler specifics" border="0"><br>
 Compiler specifics
 </a></div><br clear="all" style="clear: all;">

 <br>

 <p>Revised June 25th 2008</p>

 <p>&copy; Copyright 2003-2008 Joaqu&iacute;n M L&oacute;pez Mu&ntilde;oz.
 Distributed under the Boost Software
 License, Version 1.0. (See accompanying file <a href="../../../../LICENSE_1_0.txt">
 LICENSE_1_0.txt</a> or copy at <a href="http://www.boost.org/LICENSE_1_0.txt">
 http://www.boost.org/LICENSE_1_0.txt</a>)
 </p>

 </body>
 </html>