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<div class="section">
<div class="titlepage"><div><div><h3 class="title">
<a name="boost_icl.function_reference.subtraction"></a><a class="link" href="subtraction.html" title="Subtraction">Subtraction</a>
</h3></div></div></div>
<div class="toc"><dl class="toc">
<dt><span class="section"><a href="subtraction.html#boost_icl.function_reference.subtraction.synopsis">Synopsis</a></span></dt>
<dt><span class="section"><a href="subtraction.html#boost_icl.function_reference.subtraction.functions">Functions</a></span></dt>
<dt><span class="section"><a href="subtraction.html#boost_icl.function_reference.subtraction.inplace_operators">Inplace
        operators</a></span></dt>
<dt><span class="section"><a href="subtraction.html#boost_icl.function_reference.subtraction.infix_operators">Infix
        operators</a></span></dt>
<dt><span class="section"><a href="subtraction.html#boost_icl.function_reference.subtraction.subtraction_on_intervals">Subtraction
        on Intervals</a></span></dt>
</dl></div>
<div class="section">
<div class="titlepage"><div><div><h4 class="title">
<a name="boost_icl.function_reference.subtraction.synopsis"></a><a class="link" href="subtraction.html#boost_icl.function_reference.subtraction.synopsis" title="Synopsis">Synopsis</a>
</h4></div></div></div>
<div class="informaltable"><table class="table">
<colgroup>
<col>
<col>
<col>
<col>
<col>
<col>
</colgroup>
<thead><tr>
<th>
                  <p>
                    Subtraction
                  </p>
                </th>
<th>
                  <p>
                    intervals
                  </p>
                </th>
<th>
                  <p>
                    interval<br> sets
                  </p>
                </th>
<th>
                  <p>
                    interval<br> maps
                  </p>
                </th>
<th>
                  <p>
                    element<br> sets
                  </p>
                </th>
<th>
                  <p>
                    element<br> maps
                  </p>
                </th>
</tr></thead>
<tbody>
<tr>
<td>
                  <p>
                    <code class="computeroutput"><span class="identifier">T</span><span class="special">&amp;</span>
                    <span class="identifier">T</span><span class="special">::</span><span class="identifier">subtract</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">P</span><span class="special">&amp;)</span></code>
                  </p>
                </td>
<td>
                </td>
<td>
                  <p>
                    <a class="link" href="../interface/function_synopsis.html#element_type"><span class="bold"><strong>e</strong></span></a>
                    <a class="link" href="../interface/function_synopsis.html#interval_type"><span class="bold"><strong>i</strong></span></a>
                  </p>
                </td>
<td>
                  <p>
                    <a class="link" href="../interface/function_synopsis.html#element_mapping_type"><span class="bold"><strong>b</strong></span></a>
                    <a class="link" href="../interface/function_synopsis.html#interval_mapping_type"><span class="bold"><strong>p</strong></span></a>
                  </p>
                </td>
<td>
                </td>
<td>
                  <p>
                    <a class="link" href="../interface/function_synopsis.html#element_mapping_type"><span class="bold"><strong>b</strong></span></a>
                  </p>
                </td>
</tr>
<tr>
<td>
                  <p>
                    <code class="computeroutput"><span class="identifier">T</span><span class="special">&amp;</span>
                    <span class="identifier">subtract</span><span class="special">(</span><span class="identifier">T</span><span class="special">&amp;,</span>
                    <span class="keyword">const</span> <span class="identifier">P</span><span class="special">&amp;)</span></code>
                  </p>
                </td>
<td>
                </td>
<td>
                  <p>
                    <a class="link" href="../interface/function_synopsis.html#element_type"><span class="bold"><strong>e</strong></span></a>
                    <a class="link" href="../interface/function_synopsis.html#interval_type"><span class="bold"><strong>i</strong></span></a>
                  </p>
                </td>
<td>
                  <p>
                    <a class="link" href="../interface/function_synopsis.html#element_mapping_type"><span class="bold"><strong>b</strong></span></a>
                    <a class="link" href="../interface/function_synopsis.html#interval_mapping_type"><span class="bold"><strong>p</strong></span></a>
                  </p>
                </td>
<td>
                  <p>
                    <a class="link" href="../interface/function_synopsis.html#element_type"><span class="bold"><strong>e</strong></span></a>
                  </p>
                </td>
<td>
                  <p>
                    <a class="link" href="../interface/function_synopsis.html#element_mapping_type"><span class="bold"><strong>b</strong></span></a>
                  </p>
                </td>
</tr>
<tr>
<td>
                  <p>
                    <code class="computeroutput"><span class="identifier">T</span><span class="special">&amp;</span>
                    <span class="keyword">operator</span> <span class="special">-=(</span><span class="identifier">T</span><span class="special">&amp;,</span>
                    <span class="keyword">const</span> <span class="identifier">P</span><span class="special">&amp;)</span></code>
                  </p>
                </td>
<td>
                </td>
<td>
                  <p>
                    <a class="link" href="../interface/function_synopsis.html#element_type"><span class="bold"><strong>e</strong></span></a>
                    <a class="link" href="../interface/function_synopsis.html#interval_type"><span class="bold"><strong>i</strong></span></a>
                    <a class="link" href="../interface/function_synopsis.html#interval_set_types"><span class="bold"><strong>S</strong></span></a>
                  </p>
                </td>
<td>
                  <p>
                    <a class="link" href="../interface/function_synopsis.html#element_type"><span class="bold"><strong>e</strong></span></a>
                    <a class="link" href="../interface/function_synopsis.html#interval_type"><span class="bold"><strong>i</strong></span></a>
                    <a class="link" href="../interface/function_synopsis.html#interval_set_types"><span class="bold"><strong>S</strong></span></a>
                    <a class="link" href="../interface/function_synopsis.html#element_mapping_type"><span class="bold"><strong>b</strong></span></a>
                    <a class="link" href="../interface/function_synopsis.html#interval_mapping_type"><span class="bold"><strong>p</strong></span></a>
                    <a class="link" href="../interface/function_synopsis.html#interval_map_types"><span class="bold"><strong>M</strong></span></a>
                  </p>
                </td>
<td>
                  <p>
                    <a class="link" href="../interface/function_synopsis.html#element_type"><span class="bold"><strong>e</strong></span></a>
                    <a class="link" href="../interface/function_synopsis.html#itl_set_type"><span class="bold"><strong>s</strong></span></a>
                  </p>
                </td>
<td>
                  <p>
                    <a class="link" href="../interface/function_synopsis.html#element_mapping_type"><span class="bold"><strong>b</strong></span></a>
                    <a class="link" href="../interface/function_synopsis.html#itl_map_type"><span class="bold"><strong>m</strong></span></a>
                  </p>
                </td>
</tr>
<tr>
<td>
                  <p>
                    <code class="computeroutput"><span class="identifier">T</span> <span class="keyword">operator</span>
                    <span class="special">-</span> <span class="special">(</span><span class="identifier">T</span><span class="special">,</span>
                    <span class="keyword">const</span> <span class="identifier">P</span><span class="special">&amp;)</span></code>
                  </p>
                </td>
<td>
                </td>
<td>
                  <p>
                    <a class="link" href="../interface/function_synopsis.html#element_type"><span class="bold"><strong>e</strong></span></a>
                    <a class="link" href="../interface/function_synopsis.html#interval_type"><span class="bold"><strong>i</strong></span></a>
                    <a class="link" href="../interface/function_synopsis.html#interval_set_types"><span class="bold"><strong>S</strong></span></a>
                  </p>
                </td>
<td>
                  <p>
                    <a class="link" href="../interface/function_synopsis.html#element_type"><span class="bold"><strong>e</strong></span></a>
                    <a class="link" href="../interface/function_synopsis.html#interval_type"><span class="bold"><strong>i</strong></span></a>
                    <a class="link" href="../interface/function_synopsis.html#interval_set_types"><span class="bold"><strong>S</strong></span></a>
                    <a class="link" href="../interface/function_synopsis.html#element_mapping_type"><span class="bold"><strong>b</strong></span></a>
                    <a class="link" href="../interface/function_synopsis.html#interval_mapping_type"><span class="bold"><strong>p</strong></span></a>
                    <a class="link" href="../interface/function_synopsis.html#interval_map_types"><span class="bold"><strong>M</strong></span></a>
                  </p>
                </td>
<td>
                  <p>
                    <a class="link" href="../interface/function_synopsis.html#element_type"><span class="bold"><strong>e</strong></span></a>
                    <a class="link" href="../interface/function_synopsis.html#itl_set_type"><span class="bold"><strong>s</strong></span></a>
                  </p>
                </td>
<td>
                  <p>
                    <a class="link" href="../interface/function_synopsis.html#element_mapping_type"><span class="bold"><strong>b</strong></span></a>
                    <a class="link" href="../interface/function_synopsis.html#itl_map_type"><span class="bold"><strong>m</strong></span></a>
                  </p>
                </td>
</tr>
<tr>
<td>
                  <p>
                    <code class="computeroutput"><span class="identifier">T</span> <span class="identifier">left_subtract</span><span class="special">(</span><span class="identifier">T</span><span class="special">,</span> <span class="keyword">const</span>
                    <span class="identifier">T</span><span class="special">&amp;)</span></code>
                  </p>
                </td>
<td>
                  <p>
                    1
                  </p>
                </td>
<td>
                </td>
<td>
                </td>
<td>
                </td>
<td>
                </td>
</tr>
<tr>
<td>
                  <p>
                    <code class="computeroutput"><span class="identifier">T</span> <span class="identifier">right_subtract</span><span class="special">(</span><span class="identifier">T</span><span class="special">,</span> <span class="keyword">const</span>
                    <span class="identifier">T</span><span class="special">&amp;)</span></code>
                  </p>
                </td>
<td>
                  <p>
                    1
                  </p>
                </td>
<td>
                </td>
<td>
                </td>
<td>
                </td>
<td>
                </td>
</tr>
</tbody>
</table></div>
<p>
          Functions and operators that implement <span class="emphasis"><em><span class="bold"><strong>Subtraction</strong></span></em></span>
          on <span class="bold"><strong>icl</strong></span> objects are given in the table
          above.
        </p>
<div class="informaltable"><table class="table">
<colgroup>
<col>
<col>
</colgroup>
<thead><tr>
<th>
                </th>
<th>
                  <p>
                    Description of Subtraction
                  </p>
                </th>
</tr></thead>
<tbody>
<tr>
<td>
                  <p>
                    <code class="computeroutput"><span class="identifier">Sets</span></code>
                  </p>
                </td>
<td>
                  <p>
                    Subtraction on Sets implements <span class="emphasis"><em><span class="bold"><strong>set
                    difference</strong></span></em></span>
                  </p>
                </td>
</tr>
<tr>
<td>
                  <p>
                    <code class="computeroutput"><span class="identifier">Maps</span></code>
                  </p>
                </td>
<td>
                  <p>
                    Subtraction on Maps implements a <span class="emphasis"><em><span class="bold"><strong>map
                    difference</strong></span></em></span> function similar to <span class="emphasis"><em>set
                    difference</em></span>. If, on subtraction of an element value
                    pair <code class="computeroutput"><span class="special">(</span><span class="identifier">k</span><span class="special">,</span><span class="identifier">v</span><span class="special">)</span></code> it's key <code class="computeroutput"><span class="identifier">k</span></code>
                    is in the map already, the subtraction function is propagated
                    to the associated value. On the associated value an aggregation
                    is performed, that reverses the effect of the corresponding addition
                    function.
                  </p>
                  <p>
                    Find more on <a class="link" href="../concepts/aggrovering.html" title="Addability, Subtractability and Aggregate on Overlap"><span class="emphasis"><em>subtractability
                    of maps</em></span></a> and related <a class="link" href="../semantics/maps.html" title="Maps"><span class="emphasis"><em>semantic
                    issues</em></span></a> following the links.
                  </p>
                </td>
</tr>
</tbody>
</table></div>
</div>
<div class="section">
<div class="titlepage"><div><div><h4 class="title">
<a name="boost_icl.function_reference.subtraction.functions"></a><a class="link" href="subtraction.html#boost_icl.function_reference.subtraction.functions" title="Functions">Functions</a>
</h4></div></div></div>
<p>
          The admissible combinations of types for subtraction functions can be summarized
          in the <span class="emphasis"><em><span class="bold"><strong>overload table</strong></span></em></span>
          below:
        </p>
<p>
</p>
<pre class="programlisting"><span class="comment">// overload table for              T\P| e i b p  </span>
<span class="identifier">T</span><span class="special">&amp;</span> <span class="identifier">T</span><span class="special">::</span><span class="identifier">subtract</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">P</span><span class="special">&amp;)</span>           <span class="special">---+--------</span>
<span class="identifier">T</span><span class="special">&amp;</span> <span class="identifier">subtract</span><span class="special">(</span><span class="identifier">T</span><span class="special">&amp;,</span> <span class="keyword">const</span> <span class="identifier">P</span><span class="special">&amp;)</span>           <span class="identifier">s</span> <span class="special">|</span> <span class="identifier">s</span>
                                    <span class="identifier">m</span> <span class="special">|</span>     <span class="identifier">m</span>
                                    <span class="identifier">S</span> <span class="special">|</span> <span class="identifier">S</span> <span class="identifier">S</span>
                                    <span class="identifier">M</span> <span class="special">|</span>     <span class="identifier">M</span> <span class="identifier">M</span>
</pre>
<p>
        </p>
<p>
          The next table contains complexity characteristics for <code class="computeroutput"><span class="identifier">subtract</span></code>.
        </p>
<div class="table">
<a name="boost_icl.function_reference.subtraction.functions.t0"></a><p class="title"><b>Table&#160;1.24.&#160;Time Complexity for function subtract on icl containers</b></p>
<div class="table-contents"><table class="table" summary="Time Complexity for function subtract on icl containers">
<colgroup>
<col>
<col>
<col>
<col>
<col>
</colgroup>
<thead><tr>
<th>
                  <p>
                    <code class="computeroutput"><span class="identifier">T</span><span class="special">&amp;</span>
                    <span class="identifier">T</span><span class="special">::</span><span class="identifier">subtract</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">P</span><span class="special">&amp;)</span></code><br> <code class="computeroutput"><span class="identifier">T</span><span class="special">&amp;</span> <span class="identifier">subtract</span><span class="special">(</span><span class="identifier">T</span><span class="special">&amp;,</span> <span class="keyword">const</span>
                    <span class="identifier">P</span><span class="special">&amp;)</span></code>
                  </p>
                </th>
<th>
                  <p>
                    domain<br> type
                  </p>
                </th>
<th>
                  <p>
                    interval<br> type
                  </p>
                </th>
<th>
                  <p>
                    domain<br> mapping<br> type
                  </p>
                </th>
<th>
                  <p>
                    interval<br> mapping<br> type
                  </p>
                </th>
</tr></thead>
<tbody>
<tr>
<td>
                  <p>
                    <a href="http://www.cplusplus.com/reference/stl/set/" target="_top"><code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">set</span></code> </a>
                  </p>
                </td>
<td>
                  <p>
                    <span class="emphasis"><em>O(log n)</em></span>
                  </p>
                </td>
<td>
                </td>
<td>
                </td>
<td>
                </td>
</tr>
<tr>
<td>
                  <p>
                    <code class="computeroutput"><a class="link" href="../../boost/icl/map.html" title="Class template map">icl::map</a></code>
                  </p>
                </td>
<td>
                  <p>
                    <span class="emphasis"><em>O(log n)</em></span>
                  </p>
                </td>
<td>
                </td>
<td>
                  <p>
                    <span class="emphasis"><em>O(log n)</em></span>
                  </p>
                </td>
<td>
                </td>
</tr>
<tr>
<td>
                  <p>
                    <code class="computeroutput"><a class="link" href="../../boost/icl/interval_set.html" title="Class template interval_set">interval_sets</a></code>
                  </p>
                </td>
<td>
                  <p>
                    <span class="emphasis"><em>O(log n)</em></span>
                  </p>
                </td>
<td>
                  <p>
                    <span class="emphasis"><em>amortized<br> O(log n)</em></span>
                  </p>
                </td>
<td>
                </td>
<td>
                </td>
</tr>
<tr>
<td>
                  <p>
                    <code class="computeroutput"><a class="link" href="../../boost/icl/interval_map.html" title="Class template interval_map">interval_maps</a></code>
                  </p>
                </td>
<td>
                  <p>
                    <span class="emphasis"><em>O(log n)</em></span>
                  </p>
                </td>
<td>
                  <p>
                    <span class="emphasis"><em>O(n)</em></span>
                  </p>
                </td>
<td>
                  <p>
                    <span class="emphasis"><em>O(log n)</em></span>
                  </p>
                </td>
<td>
                  <p>
                    <span class="emphasis"><em>O(n)</em></span>
                  </p>
                </td>
</tr>
</tbody>
</table></div>
</div>
<br class="table-break">
</div>
<div class="section">
<div class="titlepage"><div><div><h4 class="title">
<a name="boost_icl.function_reference.subtraction.inplace_operators"></a><a class="link" href="subtraction.html#boost_icl.function_reference.subtraction.inplace_operators" title="Inplace operators">Inplace
        operators</a>
</h4></div></div></div>
<p>
          As presented in the overload tables for <code class="computeroutput"><span class="keyword">operator</span>
          <span class="special">-=</span></code> more type combinations are provided
          for subtraction than for addition.
        </p>
<p>
</p>
<pre class="programlisting"><span class="comment">// overload tables for             element containers:     interval containers:  </span>
<span class="identifier">T</span><span class="special">&amp;</span> <span class="keyword">operator</span> <span class="special">-=</span> <span class="special">(</span><span class="identifier">T</span><span class="special">&amp;,</span> <span class="keyword">const</span> <span class="identifier">P</span><span class="special">&amp;)</span>      <span class="special">-=</span> <span class="special">|</span> <span class="identifier">e</span> <span class="identifier">b</span> <span class="identifier">s</span> <span class="identifier">m</span>            <span class="special">-=</span> <span class="special">|</span> <span class="identifier">e</span> <span class="identifier">i</span> <span class="identifier">b</span> <span class="identifier">p</span> <span class="identifier">S</span> <span class="identifier">M</span>
                                   <span class="special">---+--------</span>            <span class="special">---+------------</span>
                                   <span class="identifier">s</span>  <span class="special">|</span> <span class="identifier">s</span>   <span class="identifier">s</span>              <span class="identifier">S</span>  <span class="special">|</span> <span class="identifier">S</span> <span class="identifier">S</span>     <span class="identifier">S</span>
                                   <span class="identifier">m</span>  <span class="special">|</span> <span class="identifier">m</span> <span class="identifier">m</span> <span class="identifier">m</span> <span class="identifier">m</span>            <span class="identifier">M</span>  <span class="special">|</span> <span class="identifier">M</span> <span class="identifier">M</span> <span class="identifier">M</span> <span class="identifier">M</span> <span class="identifier">M</span> <span class="identifier">M</span>
</pre>
<p>
        </p>
<p>
          Subtraction provides the <span class="emphasis"><em>reverse</em></span> operation of an addition
          for these overloads,
        </p>
<p>
</p>
<pre class="programlisting"><span class="comment">// Reverse addition                -= | e b s m            -= | e i b p S M </span>
                                   <span class="special">---+--------</span>            <span class="special">---+------------</span>
                                   <span class="identifier">s</span>  <span class="special">|</span> <span class="identifier">s</span>   <span class="identifier">s</span>              <span class="identifier">S</span>  <span class="special">|</span> <span class="identifier">S</span> <span class="identifier">S</span>     <span class="identifier">S</span>
                                   <span class="identifier">m</span>  <span class="special">|</span>   <span class="identifier">m</span>   <span class="identifier">m</span>            <span class="identifier">M</span>  <span class="special">|</span>     <span class="identifier">M</span> <span class="identifier">M</span>   <span class="identifier">M</span>
</pre>
<p>
        </p>
<p>
          <span class="bold"><strong>and</strong></span> you can erase parts of <code class="computeroutput"><a class="link" href="../../boost/icl/map.html" title="Class template map">icl::maps</a></code> or <code class="computeroutput"><a class="link" href="../../boost/icl/interval_map.html" title="Class template interval_map">interval_maps</a></code>
          using <span class="emphasis"><em>key values</em></span>, <span class="emphasis"><em>intervals</em></span> or
          <span class="emphasis"><em>element or interval sets</em></span> using these overloads:
        </p>
<p>
</p>
<pre class="programlisting"><span class="comment">// Erasure by key objects          -= | e b s m            -= | e i b p S M  </span>
                                   <span class="special">---+--------</span>            <span class="special">---+------------</span>
                                   <span class="identifier">s</span>  <span class="special">|</span> <span class="identifier">s</span>   <span class="identifier">s</span>              <span class="identifier">S</span>  <span class="special">|</span> <span class="identifier">S</span> <span class="identifier">S</span>     <span class="identifier">S</span>
                                   <span class="identifier">m</span>  <span class="special">|</span> <span class="identifier">m</span>   <span class="identifier">m</span>              <span class="identifier">M</span>  <span class="special">|</span> <span class="identifier">M</span> <span class="identifier">M</span>     <span class="identifier">M</span>
</pre>
<p>
        </p>
<p>
          On Sets both function groups fall together as <span class="emphasis"><em><span class="bold"><strong>set
          difference</strong></span></em></span>.
        </p>
<p>
          Complexity characteristics for inplace subtraction operations are given
          by the next tables where
</p>
<pre class="programlisting"><span class="identifier">n</span> <span class="special">=</span> <span class="identifier">iterative_size</span><span class="special">(</span><span class="identifier">y</span><span class="special">);</span>
<span class="identifier">m</span> <span class="special">=</span> <span class="identifier">iterative_size</span><span class="special">(</span><span class="identifier">x</span><span class="special">);</span> <span class="comment">//if P is a container type</span>
</pre>
<p>
        </p>
<div class="table">
<a name="boost_icl.function_reference.subtraction.inplace_operators.t0"></a><p class="title"><b>Table&#160;1.25.&#160;Time Complexity for inplace Subtraction on element containers</b></p>
<div class="table-contents"><table class="table" summary="Time Complexity for inplace Subtraction on element containers">
<colgroup>
<col>
<col>
<col>
<col>
<col>
</colgroup>
<thead><tr>
<th>
                  <p>
                    <code class="computeroutput"><span class="identifier">T</span><span class="special">&amp;</span>
                    <span class="keyword">operator</span> <span class="special">-=</span>
                    <span class="special">(</span><span class="identifier">T</span><span class="special">&amp;,</span> <span class="keyword">const</span>
                    <span class="identifier">P</span><span class="special">&amp;)</span></code>
                  </p>
                </th>
<th>
                  <p>
                    domain<br> type
                  </p>
                </th>
<th>
                  <p>
                    domain<br> mapping<br> type
                  </p>
                </th>
<th>
                  <p>
                    std::set
                  </p>
                </th>
<th>
                  <p>
                    icl::map
                  </p>
                </th>
</tr></thead>
<tbody>
<tr>
<td>
                  <p>
                    <a href="http://www.cplusplus.com/reference/stl/set/" target="_top"><code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">set</span></code> </a>
                  </p>
                </td>
<td>
                  <p>
                    <span class="emphasis"><em>O(log n)</em></span>
                  </p>
                </td>
<td>
                </td>
<td>
                  <p>
                    <span class="emphasis"><em>O(m log n)</em></span>
                  </p>
                </td>
<td>
                </td>
</tr>
<tr>
<td>
                  <p>
                    <code class="computeroutput"><a class="link" href="../../boost/icl/map.html" title="Class template map">icl::map</a></code>
                  </p>
                </td>
<td>
                  <p>
                    <span class="emphasis"><em>O(log n)</em></span>
                  </p>
                </td>
<td>
                  <p>
                    <span class="emphasis"><em>O(log n)</em></span>
                  </p>
                </td>
<td>
                  <p>
                    <span class="emphasis"><em>O(m log n)</em></span>
                  </p>
                </td>
<td>
                  <p>
                    <span class="emphasis"><em>O(m log n)</em></span>
                  </p>
                </td>
</tr>
</tbody>
</table></div>
</div>
<br class="table-break"><div class="table">
<a name="boost_icl.function_reference.subtraction.inplace_operators.t1"></a><p class="title"><b>Table&#160;1.26.&#160;Time Complexity for inplace Subtraction on interval containers</b></p>
<div class="table-contents"><table class="table" summary="Time Complexity for inplace Subtraction on interval containers">
<colgroup>
<col>
<col>
<col>
<col>
<col>
<col>
<col>
</colgroup>
<thead><tr>
<th>
                  <p>
                    <code class="computeroutput"><span class="identifier">T</span><span class="special">&amp;</span>
                    <span class="keyword">operator</span> <span class="special">-=</span>
                    <span class="special">(</span><span class="identifier">T</span><span class="special">&amp;,</span> <span class="keyword">const</span>
                    <span class="identifier">P</span><span class="special">&amp;)</span></code>
                  </p>
                </th>
<th>
                  <p>
                    domain<br> type
                  </p>
                </th>
<th>
                  <p>
                    interval<br> type
                  </p>
                </th>
<th>
                  <p>
                    domain<br> mapping<br> type
                  </p>
                </th>
<th>
                  <p>
                    interval<br> mapping<br> type
                  </p>
                </th>
<th>
                  <p>
                    interval<br> sets
                  </p>
                </th>
<th>
                  <p>
                    interval<br> maps
                  </p>
                </th>
</tr></thead>
<tbody>
<tr>
<td>
                  <p>
                    interval_sets
                  </p>
                </td>
<td>
                  <p>
                    <span class="emphasis"><em>O(log n)</em></span>
                  </p>
                </td>
<td>
                  <p>
                    <span class="emphasis"><em>amortized<br> O(log n)</em></span>
                  </p>
                </td>
<td>
                </td>
<td>
                </td>
<td>
                  <p>
                    <span class="emphasis"><em>O(m log(n+m))</em></span>
                  </p>
                </td>
<td>
                </td>
</tr>
<tr>
<td>
                  <p>
                    interval_maps
                  </p>
                </td>
<td>
                  <p>
                    <span class="emphasis"><em>O(log n)</em></span>
                  </p>
                </td>
<td>
                  <p>
                    <span class="emphasis"><em>amortized<br> O(log n)</em></span>
                  </p>
                </td>
<td>
                  <p>
                    <span class="emphasis"><em>O(log n)</em></span>
                  </p>
                </td>
<td>
                  <p>
                    <span class="emphasis"><em>O(n)</em></span>
                  </p>
                </td>
<td>
                  <p>
                    <span class="emphasis"><em>O(m log(n+m))</em></span>
                  </p>
                </td>
<td>
                  <p>
                    <span class="emphasis"><em>O(m log(n+m))</em></span>
                  </p>
                </td>
</tr>
</tbody>
</table></div>
</div>
<br class="table-break">
</div>
<div class="section">
<div class="titlepage"><div><div><h4 class="title">
<a name="boost_icl.function_reference.subtraction.infix_operators"></a><a class="link" href="subtraction.html#boost_icl.function_reference.subtraction.infix_operators" title="Infix operators">Infix
        operators</a>
</h4></div></div></div>
<p>
          The admissible overloads for the infix <span class="emphasis"><em>subtraction</em></span>
          <code class="computeroutput"><span class="keyword">operator</span> <span class="special">-</span></code>
          which is a non commutative operation is given by the next overload table.
        </p>
<p>
</p>
<pre class="programlisting"><span class="comment">// overload tables for         -  | e b s m      -  | e i b p S M   </span>
<span class="identifier">T</span> <span class="keyword">operator</span> <span class="special">-</span> <span class="special">(</span><span class="identifier">T</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">P</span><span class="special">&amp;)</span>     <span class="special">---+--------</span>      <span class="special">---+------------</span>
                               <span class="identifier">s</span>  <span class="special">|</span> <span class="identifier">s</span>   <span class="identifier">s</span>        <span class="identifier">S</span>  <span class="special">|</span> <span class="identifier">S</span> <span class="identifier">S</span>     <span class="identifier">S</span>
                               <span class="identifier">m</span>  <span class="special">|</span> <span class="identifier">m</span> <span class="identifier">m</span> <span class="identifier">m</span> <span class="identifier">m</span>      <span class="identifier">M</span>  <span class="special">|</span> <span class="identifier">M</span> <span class="identifier">M</span> <span class="identifier">M</span> <span class="identifier">M</span> <span class="identifier">M</span> <span class="identifier">M</span>
</pre>
<p>
        </p>
</div>
<div class="section">
<div class="titlepage"><div><div><h4 class="title">
<a name="boost_icl.function_reference.subtraction.subtraction_on_intervals"></a><a class="link" href="subtraction.html#boost_icl.function_reference.subtraction.subtraction_on_intervals" title="Subtraction on Intervals">Subtraction
        on Intervals</a>
</h4></div></div></div>
<div class="informaltable"><table class="table">
<colgroup>
<col>
<col>
<col>
</colgroup>
<thead><tr>
<th>
                  <p>
                    <span class="emphasis"><em><span class="bold"><strong>Subtraction</strong></span></em></span>
                  </p>
                </th>
<th>
                  <p>
                    Types
                  </p>
                </th>
<th>
                  <p>
                    Description
                  </p>
                </th>
</tr></thead>
<tbody>
<tr>
<td>
                  <p>
                    <code class="computeroutput"><span class="identifier">T</span> <span class="identifier">left_subtract</span><span class="special">(</span><span class="identifier">T</span>
                    <span class="identifier">right</span><span class="special">,</span>
                    <span class="keyword">const</span> <span class="identifier">T</span><span class="special">&amp;</span> <span class="identifier">left_minuend</span><span class="special">)</span></code>
                  </p>
                </td>
<td>
                  <p>
                    <a class="link" href="../interface/function_synopsis.html#interval_type"><span class="bold"><strong>i</strong></span></a>
                  </p>
                </td>
<td>
                  <p>
                    subtract <code class="computeroutput"><span class="identifier">left_minuend</span></code>
                    from the interval <code class="computeroutput"><span class="identifier">right</span></code>
                    on it's left side.
</p>
<pre xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" class="table-programlisting"><span class="identifier">right_over</span> <span class="special">=</span> <span class="identifier">left_subtract</span><span class="special">(</span><span class="identifier">right</span><span class="special">,</span> <span class="identifier">left_minuend</span><span class="special">);</span>
<span class="special">...</span>      <span class="identifier">d</span><span class="special">)</span> <span class="special">:</span> <span class="identifier">right</span>
<span class="special">...</span> <span class="identifier">c</span><span class="special">)</span>      <span class="special">:</span> <span class="identifier">left_minuend</span>
     <span class="special">[</span><span class="identifier">c</span>  <span class="identifier">d</span><span class="special">)</span> <span class="special">:</span> <span class="identifier">right_over</span>
</pre>
<p>
                  </p>
                </td>
</tr>
<tr>
<td>
                  <p>
                    <code class="computeroutput"><span class="identifier">T</span> <span class="identifier">right_subtract</span><span class="special">(</span><span class="identifier">T</span>
                    <span class="identifier">left</span><span class="special">,</span>
                    <span class="keyword">const</span> <span class="identifier">T</span><span class="special">&amp;</span> <span class="identifier">right_minuend</span><span class="special">)</span></code>
                  </p>
                </td>
<td>
                  <p>
                    <a class="link" href="../interface/function_synopsis.html#interval_type"><span class="bold"><strong>i</strong></span></a>
                  </p>
                </td>
<td>
                  <p>
                    subtract <code class="computeroutput"><span class="identifier">right_minuend</span></code>
                    from the interval <code class="computeroutput"><span class="identifier">left</span></code>
                    on it's right side.
</p>
<pre xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" class="table-programlisting"><span class="identifier">left_over</span> <span class="special">=</span> <span class="identifier">right_subtract</span><span class="special">(</span><span class="identifier">left</span><span class="special">,</span> <span class="identifier">right_minuend</span><span class="special">);</span>
<span class="special">[</span><span class="identifier">a</span>      <span class="special">...</span>  <span class="special">:</span> <span class="identifier">left</span>
     <span class="special">[</span><span class="identifier">b</span> <span class="special">...</span>  <span class="special">:</span> <span class="identifier">right_minuend</span>
<span class="special">[</span><span class="identifier">a</span>  <span class="identifier">b</span><span class="special">)</span>       <span class="special">:</span> <span class="identifier">left_over</span>
</pre>
<p>
                  </p>
                </td>
</tr>
</tbody>
</table></div>
</div>
<p>
        <span class="emphasis"><em><span class="bold"><strong>See also . . .</strong></span></em></span>
      </p>
<div class="informaltable"><table class="table">
<colgroup><col></colgroup>
<thead><tr></tr></thead>
<tbody>
<tr><td>
                <p>
                  <a class="link" href="addition.html" title="Addition"><span class="emphasis"><em><span class="bold"><strong>Addition</strong></span></em></span></a>
                </p>
              </td></tr>
<tr><td>
                <p>
                  <a class="link" href="erasure.html" title="Erasure"><span class="emphasis"><em><span class="bold"><strong>Erasure</strong></span></em></span></a>
                </p>
              </td></tr>
</tbody>
</table></div>
<p>
        <span class="emphasis"><em><span class="bold"><strong>Back to section . . .</strong></span></em></span>
      </p>
<div class="informaltable"><table class="table">
<colgroup><col></colgroup>
<thead><tr></tr></thead>
<tbody>
<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>
<tr><td>
                <p>
                  <a class="link" href="../interface.html" title="Interface"><span class="emphasis"><em><span class="bold"><strong>Interface</strong></span></em></span></a>
                </p>
              </td></tr>
</tbody>
</table></div>
</div>
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
<td align="left"></td>
<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>)
      </p>
</div></td>
</tr></table>
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