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<h1 class="title">Random Access Traversal Concept</h1>

<!-- Copyright David Abrahams 2006. Distributed under the Boost -->
<!-- Software License, Version 1.0. (See accompanying -->
<!-- file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) -->
<p>A class or built-in type <tt class="docutils literal"><span class="pre">X</span></tt> models the <em>Random Access Traversal</em>
concept if the following expressions are valid and respect the stated
semantics.  In the table below, <tt class="docutils literal"><span class="pre">Distance</span></tt> is
<tt class="docutils literal"><span class="pre">iterator_traits&lt;X&gt;::difference_type</span></tt> and <tt class="docutils literal"><span class="pre">n</span></tt> represents a
constant object of type <tt class="docutils literal"><span class="pre">Distance</span></tt>.</p>
<table border="1" class="docutils">
<colgroup>
<col width="28%" />
<col width="30%" />
<col width="23%" />
<col width="20%" />
</colgroup>
<thead valign="bottom">
<tr><th class="head" colspan="4">Random Access Traversal Iterator Requirements (in addition to Bidirectional Traversal)</th>
</tr>
<tr><th class="head">Expression</th>
<th class="head">Return Type</th>
<th class="head">Operational Semantics</th>
<th class="head">Assertion/
Precondition</th>
</tr>
</thead>
<tbody valign="top">
<tr><td><tt class="docutils literal"><span class="pre">r</span> <span class="pre">+=</span> <span class="pre">n</span></tt></td>
<td><tt class="docutils literal"><span class="pre">X&amp;</span></tt></td>
<td><pre class="first last literal-block">
{
  Distance m = n;
  if (m &gt;= 0)
    while (m--)
      ++r;
  else
    while (m++)
      --r;
  return r;
}
</pre>
</td>
<td>&nbsp;</td>
</tr>
<tr><td><tt class="docutils literal"><span class="pre">a</span> <span class="pre">+</span> <span class="pre">n</span></tt>, <tt class="docutils literal"><span class="pre">n</span> <span class="pre">+</span> <span class="pre">a</span></tt></td>
<td><tt class="docutils literal"><span class="pre">X</span></tt></td>
<td><tt class="docutils literal"><span class="pre">{</span> <span class="pre">X</span> <span class="pre">tmp</span> <span class="pre">=</span> <span class="pre">a;</span> <span class="pre">return</span> <span class="pre">tmp</span>
<span class="pre">+=</span> <span class="pre">n;</span> <span class="pre">}</span></tt></td>
<td>&nbsp;</td>
</tr>
<tr><td><tt class="docutils literal"><span class="pre">r</span> <span class="pre">-=</span> <span class="pre">n</span></tt></td>
<td><tt class="docutils literal"><span class="pre">X&amp;</span></tt></td>
<td><tt class="docutils literal"><span class="pre">return</span> <span class="pre">r</span> <span class="pre">+=</span> <span class="pre">-n</span></tt></td>
<td>&nbsp;</td>
</tr>
<tr><td><tt class="docutils literal"><span class="pre">a</span> <span class="pre">-</span> <span class="pre">n</span></tt></td>
<td><tt class="docutils literal"><span class="pre">X</span></tt></td>
<td><tt class="docutils literal"><span class="pre">{</span> <span class="pre">X</span> <span class="pre">tmp</span> <span class="pre">=</span> <span class="pre">a;</span> <span class="pre">return</span> <span class="pre">tmp</span>
<span class="pre">-=</span> <span class="pre">n;</span> <span class="pre">}</span></tt></td>
<td>&nbsp;</td>
</tr>
<tr><td><tt class="docutils literal"><span class="pre">b</span> <span class="pre">-</span> <span class="pre">a</span></tt></td>
<td><tt class="docutils literal"><span class="pre">Distance</span></tt></td>
<td><tt class="docutils literal"><span class="pre">a</span> <span class="pre">&lt;</span> <span class="pre">b</span> <span class="pre">?</span>&nbsp; <span class="pre">distance(a,b)</span>
<span class="pre">:</span> <span class="pre">-distance(b,a)</span></tt></td>
<td>pre: there exists a
value <tt class="docutils literal"><span class="pre">n</span></tt> of
<tt class="docutils literal"><span class="pre">Distance</span></tt> such that
<tt class="docutils literal"><span class="pre">a</span> <span class="pre">+</span> <span class="pre">n</span> <span class="pre">==</span> <span class="pre">b</span></tt>.  <tt class="docutils literal"><span class="pre">b</span>
<span class="pre">==</span> <span class="pre">a</span> <span class="pre">+</span> <span class="pre">(b</span> <span class="pre">-</span> <span class="pre">a)</span></tt>.</td>
</tr>
<tr><td><tt class="docutils literal"><span class="pre">a[n]</span></tt></td>
<td>convertible to T</td>
<td><tt class="docutils literal"><span class="pre">*(a</span> <span class="pre">+</span> <span class="pre">n)</span></tt></td>
<td>pre: a is a <em>Readable
Iterator</em></td>
</tr>
<tr><td><tt class="docutils literal"><span class="pre">a[n]</span> <span class="pre">=</span> <span class="pre">v</span></tt></td>
<td>convertible to T</td>
<td><tt class="docutils literal"><span class="pre">*(a</span> <span class="pre">+</span> <span class="pre">n)</span> <span class="pre">=</span> <span class="pre">v</span></tt></td>
<td>pre: a is a <em>Writable
iterator</em></td>
</tr>
<tr><td><tt class="docutils literal"><span class="pre">a</span> <span class="pre">&lt;</span> <span class="pre">b</span></tt></td>
<td>convertible to <tt class="docutils literal"><span class="pre">bool</span></tt></td>
<td><tt class="docutils literal"><span class="pre">b</span> <span class="pre">-</span> <span class="pre">a</span> <span class="pre">&gt;</span> <span class="pre">0</span></tt></td>
<td><tt class="docutils literal"><span class="pre">&lt;</span></tt> is a total
ordering relation</td>
</tr>
<tr><td><tt class="docutils literal"><span class="pre">a</span> <span class="pre">&gt;</span> <span class="pre">b</span></tt></td>
<td>convertible to <tt class="docutils literal"><span class="pre">bool</span></tt></td>
<td><tt class="docutils literal"><span class="pre">b</span> <span class="pre">&lt;</span> <span class="pre">a</span></tt></td>
<td><tt class="docutils literal"><span class="pre">&gt;</span></tt> is a total
ordering relation</td>
</tr>
<tr><td><tt class="docutils literal"><span class="pre">a</span> <span class="pre">&gt;=</span> <span class="pre">b</span></tt></td>
<td>convertible to <tt class="docutils literal"><span class="pre">bool</span></tt></td>
<td><tt class="docutils literal"><span class="pre">!(a</span> <span class="pre">&lt;</span> <span class="pre">b)</span></tt></td>
<td>&nbsp;</td>
</tr>
<tr><td><tt class="docutils literal"><span class="pre">a</span> <span class="pre">&lt;=</span> <span class="pre">b</span></tt></td>
<td>convertible to <tt class="docutils literal"><span class="pre">bool</span></tt></td>
<td><tt class="docutils literal"><span class="pre">!(a</span> <span class="pre">&gt;</span> <span class="pre">b)</span></tt></td>
<td>&nbsp;</td>
</tr>
<tr><td><tt class="docutils literal"><span class="pre">iterator_traversal&lt;X&gt;::type</span></tt></td>
<td>Convertible to
<tt class="docutils literal"><span class="pre">random_access_traversal_tag</span></tt></td>
<td>&nbsp;</td>
<td>&nbsp;</td>
</tr>
</tbody>
</table>
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