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<title>Additional Interval Orderings</title>
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<div class="titlepage"><div><div><h3 class="title">
<a name="boost_icl.function_reference.additional_interval_orderings"></a><a class="link" href="additional_interval_orderings.html" title="Additional Interval Orderings">Additional
      Interval Orderings</a>
</h3></div></div></div>
<p>
        In addition to the standard orderings <code class="computeroutput"><span class="keyword">operator</span>
        <span class="special">&lt;</span></code> and rleated <code class="computeroutput"><span class="special">&gt;</span>
        <span class="special">&lt;=</span> <span class="special">&gt;=</span></code>
        that you will find in the <a class="link" href="../interface/function_synopsis.html#function_synopsis_table"><span class="emphasis"><em><span class="bold"><strong>librarie's function synopsis</strong></span></em></span></a>, intervals
        implement some additional orderings that can be useful.
      </p>
<div class="informaltable"><table class="table">
<colgroup>
<col>
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<th>
                <p>
                  T
                </p>
              </th>
<th>
                <p>
                  discrete<br> _interval
                </p>
              </th>
<th>
                <p>
                  continuous<br> _interval
                </p>
              </th>
<th>
                <p>
                  right_open<br> _interval
                </p>
              </th>
<th>
                <p>
                  left_open<br> _interval
                </p>
              </th>
<th>
                <p>
                  closed<br> _interval
                </p>
              </th>
<th>
                <p>
                  open<br> _interval
                </p>
              </th>
</tr></thead>
<tbody>
<tr>
<td>
                <p>
                  Interval bounds
                </p>
              </td>
<td>
                <p>
                  dynamic
                </p>
              </td>
<td>
                <p>
                  dynamic
                </p>
              </td>
<td>
                <p>
                  static
                </p>
              </td>
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                <p>
                  static
                </p>
              </td>
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                <p>
                  static
                </p>
              </td>
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                <p>
                  static
                </p>
              </td>
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<td>
                <p>
                  Form
                </p>
              </td>
<td>
              </td>
<td>
              </td>
<td>
                <p>
                  asymmetric
                </p>
              </td>
<td>
                <p>
                  asymmetric
                </p>
              </td>
<td>
                <p>
                  symmetric
                </p>
              </td>
<td>
                <p>
                  symmetric
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  <span class="emphasis"><em><span class="bold"><strong>Orderings</strong></span></em></span>
                </p>
              </td>
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              </td>
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              </td>
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              </td>
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              </td>
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              </td>
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              </td>
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<td>
                <p>
                  <code class="computeroutput"><span class="keyword">bool</span> <span class="identifier">exclusive_less</span><span class="special">(</span><span class="keyword">const</span>
                  <span class="identifier">T</span><span class="special">&amp;,</span>
                  <span class="keyword">const</span> <span class="identifier">T</span><span class="special">&amp;)</span></code>
                </p>
              </td>
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                <p>
                  1
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                <p>
                  1
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                  1
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                  1
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                  1
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                <p>
</p>
<pre xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" class="table-programlisting"><span class="keyword">bool</span> <span class="identifier">lower_less</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">T</span><span class="special">&amp;,</span> <span class="keyword">const</span> <span class="identifier">T</span><span class="special">&amp;)</span>
<span class="keyword">bool</span> <span class="identifier">lower_equal</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">T</span><span class="special">&amp;,</span> <span class="keyword">const</span> <span class="identifier">T</span><span class="special">&amp;)</span>
<span class="keyword">bool</span> <span class="identifier">lower_less_equal</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">T</span><span class="special">&amp;,</span> <span class="keyword">const</span> <span class="identifier">T</span><span class="special">&amp;)</span>
</pre>
<p>
                </p>
              </td>
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                <p>
                  1
                </p>
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                <p>
                  1
                </p>
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                <p>
                  1
                </p>
              </td>
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                <p>
                  1
                </p>
              </td>
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                  1
                </p>
              </td>
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                <p>
                  1
                </p>
              </td>
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                <p>
</p>
<pre xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" class="table-programlisting"><span class="keyword">bool</span> <span class="identifier">upper_less</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">T</span><span class="special">&amp;,</span> <span class="keyword">const</span> <span class="identifier">T</span><span class="special">&amp;)</span>
<span class="keyword">bool</span> <span class="identifier">upper_equal</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">T</span><span class="special">&amp;,</span> <span class="keyword">const</span> <span class="identifier">T</span><span class="special">&amp;)</span>
<span class="keyword">bool</span> <span class="identifier">upper_less_equal</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">T</span><span class="special">&amp;,</span> <span class="keyword">const</span> <span class="identifier">T</span><span class="special">&amp;)</span>
</pre>
<p>
                </p>
              </td>
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                  1
                </p>
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                <p>
                  1
                </p>
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                  1
                </p>
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                  1
                </p>
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<p>
        A central role for the <span class="bold"><strong>icl</strong></span> plays the <code class="computeroutput"><span class="identifier">exclusive_less</span></code> ordering, which is used
        in all interval containers. The other orderings can be useful to simplify
        comparison of intervals specifically for dynamically bounded ones.
      </p>
<div class="informaltable"><table class="table">
<colgroup>
<col>
<col>
</colgroup>
<thead><tr>
<th>
                <p>
                  <span class="emphasis"><em><span class="bold"><strong>Orderings</strong></span></em></span>
                </p>
              </th>
<th>
                <p>
                  Description
                </p>
              </th>
</tr></thead>
<tbody>
<tr>
<td>
                <p>
                  <code class="computeroutput"><span class="keyword">bool</span> <span class="identifier">exclusive_less</span><span class="special">(</span><span class="keyword">const</span>
                  <span class="identifier">T</span><span class="special">&amp;,</span>
                  <span class="keyword">const</span> <span class="identifier">T</span><span class="special">&amp;)</span></code>
                </p>
              </td>
<td>
                <p>
                  <code class="computeroutput"><span class="identifier">exclusive_less</span><span class="special">(</span><span class="identifier">x1</span><span class="special">,</span> <span class="identifier">x2</span><span class="special">)</span></code> is true if every element of interval
                  <code class="computeroutput"><span class="identifier">x1</span></code> is less than
                  every element of interval <code class="computeroutput"><span class="identifier">x2</span></code>
                  w.r.t. the the intervals <code class="computeroutput"><span class="identifier">Compare</span></code>
                  ordering
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
</p>
<pre xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" class="table-programlisting"><span class="keyword">bool</span> <span class="identifier">lower_less</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">T</span><span class="special">&amp;,</span> <span class="keyword">const</span> <span class="identifier">T</span><span class="special">&amp;)</span>
<span class="keyword">bool</span> <span class="identifier">lower_equal</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">T</span><span class="special">&amp;,</span> <span class="keyword">const</span> <span class="identifier">T</span><span class="special">&amp;)</span>
<span class="keyword">bool</span> <span class="identifier">lower_less_equal</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">T</span><span class="special">&amp;,</span> <span class="keyword">const</span> <span class="identifier">T</span><span class="special">&amp;)</span>
</pre>
<p>
                </p>
              </td>
<td>
                <p>
                  Compares the beginnings of intervals.
</p>
<pre xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" class="table-programlisting"><span class="identifier">lower_less</span><span class="special">(</span><span class="identifier">x</span><span class="special">,</span><span class="identifier">y</span><span class="special">)</span>  <span class="special">==</span> <span class="keyword">true</span><span class="special">;</span> <span class="comment">// x begins before y</span>
<span class="identifier">lower_equal</span><span class="special">(</span><span class="identifier">x</span><span class="special">,</span><span class="identifier">y</span><span class="special">)</span> <span class="special">==</span> <span class="keyword">true</span><span class="special">;</span> <span class="comment">// x and y begin at the same element</span>
<span class="identifier">lower_less_equal</span><span class="special">(</span><span class="identifier">x</span><span class="special">,</span><span class="identifier">y</span><span class="special">)</span> <span class="special">==</span> <span class="identifier">lower_less</span><span class="special">(</span><span class="identifier">x</span><span class="special">,</span><span class="identifier">y</span><span class="special">)</span> <span class="special">||</span> <span class="identifier">lower_equal</span><span class="special">(</span><span class="identifier">x</span><span class="special">,</span><span class="identifier">y</span><span class="special">);</span>
</pre>
<p>
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
</p>
<pre xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" class="table-programlisting"><span class="keyword">bool</span> <span class="identifier">upper_less</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">T</span><span class="special">&amp;,</span> <span class="keyword">const</span> <span class="identifier">T</span><span class="special">&amp;)</span>
<span class="keyword">bool</span> <span class="identifier">upper_equal</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">T</span><span class="special">&amp;,</span> <span class="keyword">const</span> <span class="identifier">T</span><span class="special">&amp;)</span>
<span class="keyword">bool</span> <span class="identifier">upper_less_equal</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">T</span><span class="special">&amp;,</span> <span class="keyword">const</span> <span class="identifier">T</span><span class="special">&amp;)</span>
</pre>
<p>
                </p>
              </td>
<td>
                <p>
                  Compares the endings of intervals.
</p>
<pre xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" class="table-programlisting"><span class="identifier">upper_less</span><span class="special">(</span><span class="identifier">x</span><span class="special">,</span><span class="identifier">y</span><span class="special">)</span>  <span class="special">==</span> <span class="keyword">true</span><span class="special">;</span> <span class="comment">// x ends before y</span>
<span class="identifier">upper_equal</span><span class="special">(</span><span class="identifier">x</span><span class="special">,</span><span class="identifier">y</span><span class="special">)</span> <span class="special">==</span> <span class="keyword">true</span><span class="special">;</span> <span class="comment">// x and y end at the same element</span>
<span class="identifier">upper_less_equal</span><span class="special">(</span><span class="identifier">x</span><span class="special">,</span><span class="identifier">y</span><span class="special">)</span> <span class="special">==</span> <span class="identifier">upper_less</span><span class="special">(</span><span class="identifier">x</span><span class="special">,</span><span class="identifier">y</span><span class="special">)</span> <span class="special">||</span> <span class="identifier">upper_equal</span><span class="special">(</span><span class="identifier">x</span><span class="special">,</span><span class="identifier">y</span><span class="special">);</span>
</pre>
<p>
                </p>
              </td>
</tr>
</tbody>
</table></div>
<p>
        <span class="emphasis"><em><span class="bold"><strong>See also . . .</strong></span></em></span>
      </p>
<div class="informaltable"><table class="table">
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<thead><tr></tr></thead>
<tbody><tr><td>
                <p>
                  <a class="link" href="equivalences_and_orderings.html" title="Equivalences and Orderings"><span class="emphasis"><em><span class="bold"><strong>Equivalences and Orderings</strong></span></em></span></a>
                </p>
              </td></tr></tbody>
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<p>
        <span class="emphasis"><em><span class="bold"><strong>Back to section . . .</strong></span></em></span>
      </p>
<div class="informaltable"><table class="table">
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<thead><tr></tr></thead>
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                <p>
                  <a class="link" href="../interface/function_synopsis.html#additional_interval_functions"><span class="emphasis"><em><span class="bold"><strong>Additional interval functions</strong></span></em></span></a>
                </p>
              </td></tr>
<tr><td>
                <p>
                  <a class="link" href="../interface/function_synopsis.html#function_synopsis_table"><span class="emphasis"><em><span class="bold"><strong>Function
                  Synopsis</strong></span></em></span></a>
                </p>
              </td></tr>
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                <p>
                  <a class="link" href="../interface.html" title="Interface"><span class="emphasis"><em><span class="bold"><strong>Interface</strong></span></em></span></a>
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<td align="right"><div class="copyright-footer">Copyright &#169; 2007-2010 Joachim
      Faulhaber<br>Copyright &#169; 1999-2006 Cortex Software
      GmbH<p>
        Distributed under the Boost Software License, Version 1.0. (See accompanying
        file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
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