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1<?xml version="1.0" encoding="utf-8" ?>
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7<title>Random Access Traversal Concept</title>
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10<body>
11<h1 class="title">Random Access Traversal Concept</h1>
12<div class="document" id="random-access-traversal-concept">
13<p>A class or built-in type <tt class="literal"><span class="pre">X</span></tt> models the <em>Random Access Traversal</em>
14concept if the following expressions are valid and respect the stated
15semantics.  In the table below, <tt class="literal"><span class="pre">Distance</span></tt> is
16<tt class="literal"><span class="pre">iterator_traits&lt;X&gt;::difference_type</span></tt> and <tt class="literal"><span class="pre">n</span></tt> represents a
17constant object of type <tt class="literal"><span class="pre">Distance</span></tt>.</p>
18<table border="1" class="table">
19<colgroup>
20<col width="28%" />
21<col width="30%" />
22<col width="23%" />
23<col width="20%" />
24</colgroup>
25<thead valign="bottom">
26<tr><th colspan="4">Random Access Traversal Iterator Requirements (in addition to Bidirectional Traversal)</th>
27</tr>
28<tr><th>Expression</th>
29<th>Return Type</th>
30<th>Operational Semantics</th>
31<th>Assertion/
32Precondition</th>
33</tr>
34</thead>
35<tbody valign="top">
36<tr><td><tt class="literal"><span class="pre">r</span> <span class="pre">+=</span> <span class="pre">n</span></tt></td>
37<td><tt class="literal"><span class="pre">X&amp;</span></tt></td>
38<td><pre class="first last literal-block">
39{
40  Distance m = n;
41  if (m &gt;= 0)
42    while (m--)
43      ++r;
44  else
45    while (m++)
46      --r;
47  return r;
48}
49</pre>
50</td>
51<td>&nbsp;</td>
52</tr>
53<tr><td><tt class="literal"><span class="pre">a</span> <span class="pre">+</span> <span class="pre">n</span></tt>, <tt class="literal"><span class="pre">n</span> <span class="pre">+</span> <span class="pre">a</span></tt></td>
54<td><tt class="literal"><span class="pre">X</span></tt></td>
55<td><tt class="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>
56<span class="pre">+=</span> <span class="pre">n;</span> <span class="pre">}</span></tt></td>
57<td>&nbsp;</td>
58</tr>
59<tr><td><tt class="literal"><span class="pre">r</span> <span class="pre">-=</span> <span class="pre">n</span></tt></td>
60<td><tt class="literal"><span class="pre">X&amp;</span></tt></td>
61<td><tt class="literal"><span class="pre">return</span> <span class="pre">r</span> <span class="pre">+=</span> <span class="pre">-n</span></tt></td>
62<td>&nbsp;</td>
63</tr>
64<tr><td><tt class="literal"><span class="pre">a</span> <span class="pre">-</span> <span class="pre">n</span></tt></td>
65<td><tt class="literal"><span class="pre">X</span></tt></td>
66<td><tt class="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>
67<span class="pre">-=</span> <span class="pre">n;</span> <span class="pre">}</span></tt></td>
68<td>&nbsp;</td>
69</tr>
70<tr><td><tt class="literal"><span class="pre">b</span> <span class="pre">-</span> <span class="pre">a</span></tt></td>
71<td><tt class="literal"><span class="pre">Distance</span></tt></td>
72<td><tt class="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>
73<span class="pre">:</span> <span class="pre">-distance(b,a)</span></tt></td>
74<td>pre: there exists a
75value <tt class="literal"><span class="pre">n</span></tt> of
76<tt class="literal"><span class="pre">Distance</span></tt> such that
77<tt class="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="literal"><span class="pre">b</span>
78<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>
79</tr>
80<tr><td><tt class="literal"><span class="pre">a[n]</span></tt></td>
81<td>convertible to T</td>
82<td><tt class="literal"><span class="pre">*(a</span> <span class="pre">+</span> <span class="pre">n)</span></tt></td>
83<td>pre: a is a <em>Readable
84Iterator</em></td>
85</tr>
86<tr><td><tt class="literal"><span class="pre">a[n]</span> <span class="pre">=</span> <span class="pre">v</span></tt></td>
87<td>convertible to T</td>
88<td><tt class="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>
89<td>pre: a is a <em>Writable
90iterator</em></td>
91</tr>
92<tr><td><tt class="literal"><span class="pre">a</span> <span class="pre">&lt;</span> <span class="pre">b</span></tt></td>
93<td>convertible to <tt class="literal"><span class="pre">bool</span></tt></td>
94<td><tt class="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>
95<td><tt class="literal"><span class="pre">&lt;</span></tt> is a total
96ordering relation</td>
97</tr>
98<tr><td><tt class="literal"><span class="pre">a</span> <span class="pre">&gt;</span> <span class="pre">b</span></tt></td>
99<td>convertible to <tt class="literal"><span class="pre">bool</span></tt></td>
100<td><tt class="literal"><span class="pre">b</span> <span class="pre">&lt;</span> <span class="pre">a</span></tt></td>
101<td><tt class="literal"><span class="pre">&gt;</span></tt> is a total
102ordering relation</td>
103</tr>
104<tr><td><tt class="literal"><span class="pre">a</span> <span class="pre">&gt;=</span> <span class="pre">b</span></tt></td>
105<td>convertible to <tt class="literal"><span class="pre">bool</span></tt></td>
106<td><tt class="literal"><span class="pre">!(a</span> <span class="pre">&lt;</span> <span class="pre">b)</span></tt></td>
107<td>&nbsp;</td>
108</tr>
109<tr><td><tt class="literal"><span class="pre">a</span> <span class="pre">&lt;=</span> <span class="pre">b</span></tt></td>
110<td>convertible to <tt class="literal"><span class="pre">bool</span></tt></td>
111<td><tt class="literal"><span class="pre">!(a</span> <span class="pre">&gt;</span> <span class="pre">b)</span></tt></td>
112<td>&nbsp;</td>
113</tr>
114<tr><td><tt class="literal"><span class="pre">iterator_traversal&lt;X&gt;::type</span></tt></td>
115<td>Convertible to
116<tt class="literal"><span class="pre">random_access_traversal_tag</span></tt></td>
117<td>&nbsp;</td>
118<td>&nbsp;</td>
119</tr>
120</tbody>
121</table>
122</div>
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