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<div class="titlepage"><div><div><h2 class="title" style="clear: both">
<a name="boost_icl.projects"></a><a class="link" href="projects.html" title="Projects">Projects</a>
</h2></div></div></div>
<div class="toc"><dl class="toc"><dt><span class="section"><a href="projects.html#boost_icl.projects.large_bitset">Large Bitset</a></span></dt></dl></div>
<p>
      <span class="emphasis"><em><span class="bold"><strong>Projects</strong></span></em></span> are examples
      on the usage of interval containers that go beyond small toy snippets of code.
      The code presented here addresses more serious applications that approach the
      quality of real world programming. At the same time it aims to guide the reader
      more deeply into various aspects of the library. In order not to overburden
      the reader with implementation details, the code in <span class="emphasis"><em><span class="bold"><strong>projects</strong></span></em></span>
      tries to be <span class="emphasis"><em><span class="bold"><strong>minimal</strong></span></em></span>.
      It has a focus on the main aspects of the projects and is not intended to be
      complete and mature like the library code itself. Cause it's minimal, project
      code lives in <code class="computeroutput"><span class="keyword">namespace</span> <span class="identifier">mini</span></code>.
    </p>
<div class="section">
<div class="titlepage"><div><div><h3 class="title">
<a name="boost_icl.projects.large_bitset"></a><a class="link" href="projects.html#boost_icl.projects.large_bitset" title="Large Bitset">Large Bitset</a>
</h3></div></div></div>
<div class="toc"><dl class="toc">
<dt><span class="section"><a href="projects.html#boost_icl.projects.large_bitset.using_large_bitset">Using
        large_bitset</a></span></dt>
<dt><span class="section"><a href="projects.html#boost_icl.projects.large_bitset.the_interval_bitmap">The
        interval_bitmap</a></span></dt>
<dt><span class="section"><a href="projects.html#boost_icl.projects.large_bitset.a_class_implementation_for_the_bitset_type">A
        class implementation for the bitset type</a></span></dt>
<dt><span class="section"><a href="projects.html#boost_icl.projects.large_bitset.implementation_of_a_large_bitset">Implementation
        of a large bitset</a></span></dt>
</dl></div>
<p>
        Bitsets are just sets. Sets of unsigned integrals, to be more precise. The
        prefix <span class="emphasis"><em><span class="bold"><strong>bit</strong></span></em></span> usually
        only indicates, that the representation of those sets is organized in a compressed
        form that exploits the fact, that we can switch on an off single bits in
        machine words. Bitsets are therefore known to be very small and thus efficient.
        The efficiency of bitsets is usually coupled to the precondition that the
        range of values of elements is relatively small, like [0..32) or [0..64),
        values that can be typically represented in single or a small number of machine
        words. If we wanted to represent a set containing two values {1, 1000000},
        we would be much better off using other sets like e.g. an <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">set</span></code>.
      </p>
<p>
        Bitsets compress well, if elements spread over narrow ranges only. Interval
        sets compress well, if many elements are clustered over intervals. They can
        span large sets very efficiently then. In project <span class="emphasis"><em><span class="bold"><strong>Large
        Bitset</strong></span></em></span> we want to <span class="emphasis"><em><span class="bold"><strong>combine
        the bit compression and the interval compression</strong></span></em></span> to
        achieve a set implementation, that is capable of spanning large chunks of
        contiguous elements using intervals and also to represent more narrow <span class="emphasis"><em>nests</em></span>
        of varying bit sequences using bitset compression. As we will see, this can
        be achieved using only a small amount of code because most of the properties
        we need are provided by an <code class="computeroutput"><a class="link" href="../boost/icl/interval_map.html" title="Class template interval_map">interval_map</a></code>
        of <code class="computeroutput"><span class="identifier">bitsets</span></code>:
      </p>
<p>
</p>
<pre class="programlisting"><span class="keyword">typedef</span> <span class="identifier">interval_map</span><span class="special">&lt;</span><span class="identifier">IntegralT</span><span class="special">,</span> <span class="identifier">SomeBitSet</span><span class="special">&lt;</span><span class="identifier">N</span><span class="special">&gt;,</span> <span class="identifier">partial_absorber</span><span class="special">,</span>
                     <span class="identifier">std</span><span class="special">::</span><span class="identifier">less</span><span class="special">,</span> <span class="identifier">inplace_bit_add</span><span class="special">,</span> <span class="identifier">inplace_bit_and</span><span class="special">&gt;</span> <span class="identifier">IntervalBitmap</span><span class="special">;</span>
</pre>
<p>
      </p>
<p>
        Such an <code class="computeroutput"><span class="identifier">IntervalBitmap</span></code> represents
        <code class="computeroutput"><span class="identifier">k</span><span class="special">*</span><span class="identifier">N</span></code> bits for every segment.
</p>
<pre class="programlisting"><span class="special">[</span><span class="identifier">a</span><span class="special">,</span> <span class="identifier">a</span><span class="special">+</span><span class="identifier">k</span><span class="special">)-&gt;</span><span class="char">'1111....1111'</span> <span class="comment">// N bits associated: Represents a total of k*N bits.  </span>
</pre>
<p>
      </p>
<p>
        For the interval <code class="computeroutput"><span class="special">[</span><span class="identifier">a</span><span class="special">,</span> <span class="identifier">a</span><span class="special">+</span><span class="identifier">k</span><span class="special">)</span></code> above
        all bits are set. But we can also have individual <span class="emphasis"><em>nests</em></span>
        or <span class="emphasis"><em>clusters</em></span> of bitsequences.
      </p>
<p>
</p>
<pre class="programlisting"><span class="special">[</span><span class="identifier">b</span><span class="special">,</span>  <span class="identifier">b</span><span class="special">+</span><span class="number">1</span><span class="special">)-&gt;</span><span class="char">'01001011...1'</span>
<span class="special">[</span><span class="identifier">b</span><span class="special">+</span><span class="number">1</span><span class="special">,</span><span class="identifier">b</span><span class="special">+</span><span class="number">2</span><span class="special">)-&gt;</span><span class="char">'11010001...0'</span>
<span class="special">.</span> <span class="special">.</span> <span class="special">.</span>
</pre>
<p>
      </p>
<p>
        and we can span intervals of equal bit sequences that represent periodic
        patterns.
      </p>
<p>
</p>
<pre class="programlisting"><span class="special">[</span><span class="identifier">c</span><span class="special">,</span><span class="identifier">d</span><span class="special">)-&gt;</span><span class="char">'010101....01'</span>  <span class="comment">// Every second bit is set              in range [c,d)</span>
<span class="special">[</span><span class="identifier">d</span><span class="special">,</span><span class="identifier">e</span><span class="special">)-&gt;</span><span class="char">'001100..0011'</span>  <span class="comment">// Every two bits alterate              in range [d,e)</span>
<span class="special">[</span><span class="identifier">e</span><span class="special">,</span><span class="identifier">f</span><span class="special">)-&gt;</span><span class="char">'bit-sequence'</span>  <span class="comment">// 'bit-sequence' reoccurs every N bits in range [e,f)</span>
</pre>
<p>
      </p>
<p>
        An <code class="computeroutput"><span class="identifier">IntervalBitmap</span></code> can represent
        <code class="computeroutput"><span class="identifier">N</span><span class="special">*(</span><span class="number">2</span><span class="special">^</span><span class="identifier">M</span><span class="special">)</span></code> elements, if <code class="computeroutput"><span class="identifier">M</span></code>
        is the number of bits of the integral type <code class="computeroutput"><span class="identifier">IntegralT</span></code>.
        Unlike bitsets, that usually represent <span class="emphasis"><em><span class="bold"><strong>unsigned</strong></span></em></span>
        integral numbers, large_bitset may range over negative numbers as well. There
        are fields where such large bitsets implementations are needed. E.g. for
        the compact representation of large file allocation tables. What remains
        to be done for project <span class="bold"><strong>Large Bitset</strong></span> is to
        code a wrapper <code class="computeroutput"><span class="keyword">class</span> <span class="identifier">large_bitset</span></code>
        around <code class="computeroutput"><span class="identifier">IntervalBitmap</span></code> so
        that <code class="computeroutput"><span class="identifier">large_bitset</span></code> looks and
        feels like a usual set class.
      </p>
<div class="section">
<div class="titlepage"><div><div><h4 class="title">
<a name="boost_icl.projects.large_bitset.using_large_bitset"></a><a class="link" href="projects.html#boost_icl.projects.large_bitset.using_large_bitset" title="Using large_bitset">Using
        large_bitset</a>
</h4></div></div></div>
<p>
          To quicken your appetite for a look at the implementation here are a few
          use cases first. Within the examples that follow, we will use <code class="computeroutput"><span class="identifier">nat</span></code><code class="literal"><span class="emphasis"><em>k</em></span></code>
          for unsigned integrals and <code class="computeroutput"><span class="identifier">bits</span></code><code class="literal"><span class="emphasis"><em>k</em></span></code>
          for bitsets containing <code class="literal"><span class="emphasis"><em>k</em></span></code> bits.
        </p>
<p>
          Let's start large. In the first example . . .
        </p>
<p>
</p>
<pre class="programlisting"><span class="keyword">void</span> <span class="identifier">test_large</span><span class="special">()</span>
<span class="special">{</span>
    <span class="keyword">const</span> <span class="identifier">nat64</span> <span class="identifier">much</span> <span class="special">=</span> <span class="number">0</span><span class="identifier">xffffffffffffffffull</span><span class="special">;</span>
    <span class="identifier">large_bitset</span><span class="special">&lt;&gt;</span> <span class="identifier">venti</span><span class="special">;</span> <span class="comment">// ... the largest, I can think of ;)</span>
    <span class="identifier">venti</span> <span class="special">+=</span> <span class="identifier">discrete_interval</span><span class="special">&lt;</span><span class="identifier">nat64</span><span class="special">&gt;(</span><span class="number">0</span><span class="special">,</span> <span class="identifier">much</span><span class="special">);</span>

    <span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"----- Test function test_large() -----------------------------------------------\n"</span><span class="special">;</span>
    <span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"We have just turned on the awesome amount of 18,446,744,073,709,551,616 bits ;-)\n"</span><span class="special">;</span>
    <span class="identifier">venti</span><span class="special">.</span><span class="identifier">show_segments</span><span class="special">();</span>
</pre>
<p>
        </p>
<p>
          . . . we are testing the limits. First we set all bits and then we switch
          off the very last bit.
        </p>
<p>
</p>
<pre class="programlisting">    <span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"---- Let's swich off the very last bit -----------------------------------------\n"</span><span class="special">;</span>
    <span class="identifier">venti</span> <span class="special">-=</span> <span class="identifier">much</span><span class="special">;</span>
    <span class="identifier">venti</span><span class="special">.</span><span class="identifier">show_segments</span><span class="special">();</span>

    <span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"---- Venti is plenty ... let's do something small: A tall ----------------------\n\n"</span><span class="special">;</span>
<span class="special">}</span>
</pre>
<p>
        </p>
<p>
          Program output (<span class="emphasis"><em>a little beautified</em></span>):
</p>
<pre class="programlisting"><span class="special">-----</span> <span class="identifier">Test</span> <span class="identifier">function</span> <span class="identifier">test_large</span><span class="special">()</span> <span class="special">-----------------------------------------------</span>
<span class="identifier">We</span> <span class="identifier">have</span> <span class="identifier">just</span> <span class="identifier">turned</span> <span class="identifier">on</span> <span class="identifier">the</span> <span class="identifier">awesome</span> <span class="identifier">amount</span> <span class="identifier">of</span> <span class="number">18</span><span class="special">,</span><span class="number">446</span><span class="special">,</span><span class="number">744</span><span class="special">,</span><span class="number">073</span><span class="special">,</span><span class="number">709</span><span class="special">,</span><span class="number">551</span><span class="special">,</span><span class="number">616</span> <span class="identifier">bits</span> <span class="special">;-)</span>
<span class="special">[</span>                 <span class="number">0</span><span class="special">,</span> <span class="number">288230376151711744</span><span class="special">)</span> <span class="special">-&gt;</span> <span class="number">1111111111111111111111111111111111111111111111111111111111111111</span>
<span class="special">----</span> <span class="identifier">Let</span><span class="char">'s swich off the very last bit -----------------------------------------
[                 0, 288230376151711743) -&gt; 1111111111111111111111111111111111111111111111111111111111111111
[288230376151711743, 288230376151711744) -&gt; 1111111111111111111111111111111111111111111111111111111111111110
---- Venti is plenty ... let'</span><span class="identifier">s</span> <span class="keyword">do</span> <span class="identifier">something</span> <span class="identifier">small</span><span class="special">:</span> <span class="identifier">A</span> <span class="identifier">tall</span> <span class="special">----------------------</span>
</pre>
<p>
        </p>
<p>
          More readable is a smaller version of <code class="computeroutput"><span class="identifier">large_bitset</span></code>.
          In function <code class="computeroutput"><span class="identifier">test_small</span><span class="special">()</span></code> we apply a few more operations . . .
        </p>
<p>
</p>
<pre class="programlisting"><span class="keyword">void</span> <span class="identifier">test_small</span><span class="special">()</span>
<span class="special">{</span>
    <span class="identifier">large_bitset</span><span class="special">&lt;</span><span class="identifier">nat32</span><span class="special">,</span> <span class="identifier">bits8</span><span class="special">&gt;</span> <span class="identifier">tall</span><span class="special">;</span> <span class="comment">// small is tall ...</span>
        <span class="comment">// ... because even this 'small' large_bitset </span>
        <span class="comment">// can represent up to 2^32 == 4,294,967,296 bits.</span>

    <span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"----- Test function test_small() -----------\n"</span><span class="special">;</span>
    <span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"-- Switch on all bits in range [0,64] ------\n"</span><span class="special">;</span>
    <span class="identifier">tall</span> <span class="special">+=</span> <span class="identifier">discrete_interval</span><span class="special">&lt;</span><span class="identifier">nat</span><span class="special">&gt;(</span><span class="number">0</span><span class="special">,</span> <span class="number">64</span><span class="special">);</span>
    <span class="identifier">tall</span><span class="special">.</span><span class="identifier">show_segments</span><span class="special">();</span>
    <span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"--------------------------------------------\n"</span><span class="special">;</span>

    <span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"-- Turn off bits: 25,27,28 -----------------\n"</span><span class="special">;</span>

    <span class="special">(((</span><span class="identifier">tall</span> <span class="special">-=</span> <span class="number">25</span><span class="special">)</span> <span class="special">-=</span> <span class="number">27</span><span class="special">)</span> <span class="special">-=</span> <span class="number">28</span><span class="special">)</span> <span class="special">;</span>
    <span class="identifier">tall</span><span class="special">.</span><span class="identifier">show_segments</span><span class="special">();</span>
    <span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"--------------------------------------------\n"</span><span class="special">;</span>

    <span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"-- Flip bits in range [24,30) --------------\n"</span><span class="special">;</span>
    <span class="identifier">tall</span> <span class="special">^=</span> <span class="identifier">discrete_interval</span><span class="special">&lt;</span><span class="identifier">nat</span><span class="special">&gt;::</span><span class="identifier">right_open</span><span class="special">(</span><span class="number">24</span><span class="special">,</span><span class="number">30</span><span class="special">);</span>
    <span class="identifier">tall</span><span class="special">.</span><span class="identifier">show_segments</span><span class="special">();</span>
    <span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"--------------------------------------------\n"</span><span class="special">;</span>

    <span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"-- Remove the first 10 bits ----------------\n"</span><span class="special">;</span>
    <span class="identifier">tall</span> <span class="special">-=</span> <span class="identifier">discrete_interval</span><span class="special">&lt;</span><span class="identifier">nat</span><span class="special">&gt;::</span><span class="identifier">right_open</span><span class="special">(</span><span class="number">0</span><span class="special">,</span><span class="number">10</span><span class="special">);</span>
    <span class="identifier">tall</span><span class="special">.</span><span class="identifier">show_segments</span><span class="special">();</span>

    <span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"-- Remove even bits in range [0,72) --------\n"</span><span class="special">;</span>
    <span class="keyword">int</span> <span class="identifier">bit</span><span class="special">;</span>
    <span class="keyword">for</span><span class="special">(</span><span class="identifier">bit</span><span class="special">=</span><span class="number">0</span><span class="special">;</span> <span class="identifier">bit</span><span class="special">&lt;</span><span class="number">72</span><span class="special">;</span> <span class="identifier">bit</span><span class="special">++)</span> <span class="keyword">if</span><span class="special">(!(</span><span class="identifier">bit</span><span class="special">%</span><span class="number">2</span><span class="special">))</span> <span class="identifier">tall</span> <span class="special">-=</span> <span class="identifier">bit</span><span class="special">;</span>
    <span class="identifier">tall</span><span class="special">.</span><span class="identifier">show_segments</span><span class="special">();</span>

    <span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"--    Set odd  bits in range [0,72) --------\n"</span><span class="special">;</span>
    <span class="keyword">for</span><span class="special">(</span><span class="identifier">bit</span><span class="special">=</span><span class="number">0</span><span class="special">;</span> <span class="identifier">bit</span><span class="special">&lt;</span><span class="number">72</span><span class="special">;</span> <span class="identifier">bit</span><span class="special">++)</span> <span class="keyword">if</span><span class="special">(</span><span class="identifier">bit</span><span class="special">%</span><span class="number">2</span><span class="special">)</span> <span class="identifier">tall</span> <span class="special">+=</span> <span class="identifier">bit</span><span class="special">;</span>
    <span class="identifier">tall</span><span class="special">.</span><span class="identifier">show_segments</span><span class="special">();</span>

    <span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"--------------------------------------------\n\n"</span><span class="special">;</span>

<span class="special">}</span>
</pre>
<p>
        </p>
<p>
          . . . producing this output:
</p>
<pre class="programlisting"><span class="special">-----</span> <span class="identifier">Test</span> <span class="identifier">function</span> <span class="identifier">test_small</span><span class="special">()</span> <span class="special">-----------</span>
<span class="special">--</span> <span class="identifier">Switch</span> <span class="identifier">on</span> <span class="identifier">all</span> <span class="identifier">bits</span> <span class="identifier">in</span> <span class="identifier">range</span> <span class="special">[</span><span class="number">0</span><span class="special">,</span><span class="number">64</span><span class="special">]</span> <span class="special">------</span>
<span class="special">[</span><span class="number">0</span><span class="special">,</span><span class="number">8</span><span class="special">)-&gt;</span><span class="number">11111111</span>
<span class="special">[</span><span class="number">8</span><span class="special">,</span><span class="number">9</span><span class="special">)-&gt;</span><span class="number">10000000</span>
<span class="special">--------------------------------------------</span>
<span class="special">--</span> <span class="identifier">Turn</span> <span class="identifier">off</span> <span class="identifier">bits</span><span class="special">:</span> <span class="number">25</span><span class="special">,</span><span class="number">27</span><span class="special">,</span><span class="number">28</span> <span class="special">-----------------</span>
<span class="special">[</span><span class="number">0</span><span class="special">,</span><span class="number">3</span><span class="special">)-&gt;</span><span class="number">11111111</span>
<span class="special">[</span><span class="number">3</span><span class="special">,</span><span class="number">4</span><span class="special">)-&gt;</span><span class="number">10100111</span>
<span class="special">[</span><span class="number">4</span><span class="special">,</span><span class="number">8</span><span class="special">)-&gt;</span><span class="number">11111111</span>
<span class="special">[</span><span class="number">8</span><span class="special">,</span><span class="number">9</span><span class="special">)-&gt;</span><span class="number">10000000</span>
<span class="special">--------------------------------------------</span>
<span class="special">--</span> <span class="identifier">Flip</span> <span class="identifier">bits</span> <span class="identifier">in</span> <span class="identifier">range</span> <span class="special">[</span><span class="number">24</span><span class="special">,</span><span class="number">30</span><span class="special">)</span> <span class="special">--------------</span>
<span class="special">[</span><span class="number">0</span><span class="special">,</span><span class="number">3</span><span class="special">)-&gt;</span><span class="number">11111111</span>
<span class="special">[</span><span class="number">3</span><span class="special">,</span><span class="number">4</span><span class="special">)-&gt;</span><span class="number">01011011</span>
<span class="special">[</span><span class="number">4</span><span class="special">,</span><span class="number">8</span><span class="special">)-&gt;</span><span class="number">11111111</span>
<span class="special">[</span><span class="number">8</span><span class="special">,</span><span class="number">9</span><span class="special">)-&gt;</span><span class="number">10000000</span>
<span class="special">--------------------------------------------</span>
<span class="special">--</span> <span class="identifier">Remove</span> <span class="identifier">the</span> <span class="identifier">first</span> <span class="number">10</span> <span class="identifier">bits</span> <span class="special">----------------</span>
<span class="special">[</span><span class="number">1</span><span class="special">,</span><span class="number">2</span><span class="special">)-&gt;</span><span class="number">00111111</span>
<span class="special">[</span><span class="number">2</span><span class="special">,</span><span class="number">3</span><span class="special">)-&gt;</span><span class="number">11111111</span>
<span class="special">[</span><span class="number">3</span><span class="special">,</span><span class="number">4</span><span class="special">)-&gt;</span><span class="number">01011011</span>
<span class="special">[</span><span class="number">4</span><span class="special">,</span><span class="number">8</span><span class="special">)-&gt;</span><span class="number">11111111</span>
<span class="special">[</span><span class="number">8</span><span class="special">,</span><span class="number">9</span><span class="special">)-&gt;</span><span class="number">10000000</span>
<span class="special">--</span> <span class="identifier">Remove</span> <span class="identifier">even</span> <span class="identifier">bits</span> <span class="identifier">in</span> <span class="identifier">range</span> <span class="special">[</span><span class="number">0</span><span class="special">,</span><span class="number">72</span><span class="special">)</span> <span class="special">--------</span>
<span class="special">[</span><span class="number">1</span><span class="special">,</span><span class="number">2</span><span class="special">)-&gt;</span><span class="number">00010101</span>
<span class="special">[</span><span class="number">2</span><span class="special">,</span><span class="number">3</span><span class="special">)-&gt;</span><span class="number">01010101</span>
<span class="special">[</span><span class="number">3</span><span class="special">,</span><span class="number">4</span><span class="special">)-&gt;</span><span class="number">01010001</span>
<span class="special">[</span><span class="number">4</span><span class="special">,</span><span class="number">8</span><span class="special">)-&gt;</span><span class="number">01010101</span>
<span class="special">--</span>    <span class="identifier">Set</span> <span class="identifier">odd</span>  <span class="identifier">bits</span> <span class="identifier">in</span> <span class="identifier">range</span> <span class="special">[</span><span class="number">0</span><span class="special">,</span><span class="number">72</span><span class="special">)</span> <span class="special">--------</span>
<span class="special">[</span><span class="number">0</span><span class="special">,</span><span class="number">9</span><span class="special">)-&gt;</span><span class="number">01010101</span>
<span class="special">--------------------------------------------</span>
</pre>
<p>
        </p>
<p>
          Finally, we present a little <span class="emphasis"><em>picturesque</em></span> example,
          that demonstrates that <code class="computeroutput"><span class="identifier">large_bitset</span></code>
          can also serve as a self compressing bitmap, that we can 'paint' with.
        </p>
<p>
</p>
<pre class="programlisting"><span class="keyword">void</span> <span class="identifier">test_picturesque</span><span class="special">()</span>
<span class="special">{</span>
    <span class="keyword">typedef</span> <span class="identifier">large_bitset</span><span class="special">&lt;</span><span class="identifier">nat</span><span class="special">,</span> <span class="identifier">bits8</span><span class="special">&gt;</span> <span class="identifier">Bit8Set</span><span class="special">;</span>

    <span class="identifier">Bit8Set</span> <span class="identifier">square</span><span class="special">,</span> <span class="identifier">stare</span><span class="special">;</span>
    <span class="identifier">square</span> <span class="special">+=</span> <span class="identifier">discrete_interval</span><span class="special">&lt;</span><span class="identifier">nat</span><span class="special">&gt;(</span><span class="number">0</span><span class="special">,</span><span class="number">8</span><span class="special">);</span>
    <span class="keyword">for</span><span class="special">(</span><span class="keyword">int</span> <span class="identifier">i</span><span class="special">=</span><span class="number">1</span><span class="special">;</span> <span class="identifier">i</span><span class="special">&lt;</span><span class="number">5</span><span class="special">;</span> <span class="identifier">i</span><span class="special">++)</span>
    <span class="special">{</span>
        <span class="identifier">square</span> <span class="special">+=</span> <span class="number">8</span><span class="special">*</span><span class="identifier">i</span><span class="special">;</span>
        <span class="identifier">square</span> <span class="special">+=</span> <span class="number">8</span><span class="special">*</span><span class="identifier">i</span><span class="special">+</span><span class="number">7</span><span class="special">;</span>
    <span class="special">}</span>

    <span class="identifier">square</span> <span class="special">+=</span> <span class="identifier">discrete_interval</span><span class="special">&lt;</span><span class="identifier">nat</span><span class="special">&gt;(</span><span class="number">41</span><span class="special">,</span><span class="number">47</span><span class="special">);</span>

    <span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"----- Test function test_picturesque() -----\n"</span><span class="special">;</span>
    <span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"-------- empty face:       "</span>
         <span class="special">&lt;&lt;</span> <span class="identifier">square</span><span class="special">.</span><span class="identifier">interval_count</span><span class="special">()</span>           <span class="special">&lt;&lt;</span> <span class="string">" intervals -----\n"</span><span class="special">;</span>
    <span class="identifier">square</span><span class="special">.</span><span class="identifier">show_matrix</span><span class="special">(</span><span class="string">" *"</span><span class="special">);</span>

    <span class="identifier">stare</span> <span class="special">+=</span> <span class="number">18</span><span class="special">;</span> <span class="identifier">stare</span> <span class="special">+=</span> <span class="number">21</span><span class="special">;</span>
    <span class="identifier">stare</span> <span class="special">+=</span> <span class="identifier">discrete_interval</span><span class="special">&lt;</span><span class="identifier">nat</span><span class="special">&gt;(</span><span class="number">34</span><span class="special">,</span><span class="number">38</span><span class="special">);</span>

    <span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"-------- compressed smile: "</span>
         <span class="special">&lt;&lt;</span> <span class="identifier">stare</span><span class="special">.</span><span class="identifier">interval_count</span><span class="special">()</span>            <span class="special">&lt;&lt;</span> <span class="string">" intervals -----\n"</span><span class="special">;</span>
    <span class="identifier">stare</span><span class="special">.</span><span class="identifier">show_matrix</span><span class="special">(</span><span class="string">" *"</span><span class="special">);</span>

    <span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"-------- staring bitset:   "</span>
         <span class="special">&lt;&lt;</span> <span class="special">(</span><span class="identifier">square</span> <span class="special">+</span> <span class="identifier">stare</span><span class="special">).</span><span class="identifier">interval_count</span><span class="special">()</span> <span class="special">&lt;&lt;</span> <span class="string">" intervals -----\n"</span><span class="special">;</span>
    <span class="special">(</span><span class="identifier">square</span> <span class="special">+</span> <span class="identifier">stare</span><span class="special">).</span><span class="identifier">show_matrix</span><span class="special">(</span><span class="string">" *"</span><span class="special">);</span>

    <span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"--------------------------------------------\n"</span><span class="special">;</span>
<span class="special">}</span>
</pre>
<p>
        </p>
<p>
          Note that we have two <code class="computeroutput"><span class="identifier">large_bitsets</span></code>
          for the <span class="emphasis"><em>outline</em></span> and the <span class="emphasis"><em>interior</em></span>.
          Both parts are compressed but we can compose both by <code class="computeroutput"><span class="keyword">operator</span>
          <span class="special">+</span></code>, because the right <span class="emphasis"><em>positions</em></span>
          are provided. This is the program output:
        </p>
<p>
</p>
<pre class="programlisting"><span class="special">-----</span> <span class="identifier">Test</span> <span class="identifier">function</span> <span class="identifier">test_picturesque</span><span class="special">()</span> <span class="special">-----</span>
<span class="special">--------</span> <span class="identifier">empty</span> <span class="identifier">face</span><span class="special">:</span>       <span class="number">3</span> <span class="identifier">intervals</span> <span class="special">-----</span>
<span class="special">********</span>
<span class="special">*</span>      <span class="special">*</span>
<span class="special">*</span>      <span class="special">*</span>
<span class="special">*</span>      <span class="special">*</span>
<span class="special">*</span>      <span class="special">*</span>
 <span class="special">******</span>
<span class="special">--------</span> <span class="identifier">compressed</span> <span class="identifier">smile</span><span class="special">:</span> <span class="number">2</span> <span class="identifier">intervals</span> <span class="special">-----</span>
  <span class="special">*</span>  <span class="special">*</span>
  <span class="special">****</span>
<span class="special">--------</span> <span class="identifier">staring</span> <span class="identifier">bitset</span><span class="special">:</span>   <span class="number">6</span> <span class="identifier">intervals</span> <span class="special">-----</span>
<span class="special">********</span>
<span class="special">*</span>      <span class="special">*</span>
<span class="special">*</span> <span class="special">*</span>  <span class="special">*</span> <span class="special">*</span>
<span class="special">*</span>      <span class="special">*</span>
<span class="special">*</span> <span class="special">****</span> <span class="special">*</span>
 <span class="special">******</span>
<span class="special">--------------------------------------------</span>
</pre>
<p>
        </p>
<p>
          So, may be you are curious how this class template is coded on top of
          <code class="computeroutput"><a class="link" href="../boost/icl/interval_map.html" title="Class template interval_map">interval_map</a></code> using
          only about 250 lines of code. This is shown in the sections that follow.
        </p>
</div>
<div class="section">
<div class="titlepage"><div><div><h4 class="title">
<a name="boost_icl.projects.large_bitset.the_interval_bitmap"></a><a class="link" href="projects.html#boost_icl.projects.large_bitset.the_interval_bitmap" title="The interval_bitmap">The
        interval_bitmap</a>
</h4></div></div></div>
<p>
          To begin, let's look at the basic data type again, that will be providing
          the major functionality:
        </p>
<p>
</p>
<pre class="programlisting"><span class="keyword">typedef</span> <span class="identifier">interval_map</span><span class="special">&lt;</span><span class="identifier">DomainT</span><span class="special">,</span> <span class="identifier">BitSetT</span><span class="special">,</span> <span class="identifier">partial_absorber</span><span class="special">,</span>
                     <span class="identifier">std</span><span class="special">::</span><span class="identifier">less</span><span class="special">,</span> <span class="identifier">inplace_bit_add</span><span class="special">,</span> <span class="identifier">inplace_bit_and</span><span class="special">&gt;</span> <span class="identifier">IntervalBitmap</span><span class="special">;</span>
</pre>
<p>
        </p>
<p>
          <code class="computeroutput"><span class="identifier">DomainT</span></code> is supposed to
          be an integral type, the bitset type <code class="computeroutput"><span class="identifier">BitSetT</span></code>
          will be a wrapper class around an unsigned integral type. <code class="computeroutput"><span class="identifier">BitSetT</span></code> has to implement bitwise operators
          that will be called by the functors <code class="computeroutput"><span class="identifier">inplace_bit_add</span><span class="special">&lt;</span><span class="identifier">BitSetT</span><span class="special">&gt;</span></code> and <code class="computeroutput"><span class="identifier">inplace_bit_and</span><span class="special">&lt;</span><span class="identifier">BitSetT</span><span class="special">&gt;</span></code>. The type trait of interval_map is
          <code class="computeroutput"><span class="identifier">partial_absorber</span></code>, which
          means that it is <span class="emphasis"><em>partial</em></span> and that empty <code class="computeroutput"><span class="identifier">BitSetTs</span></code> are not stored in the map. This
          is desired and keeps the <code class="computeroutput"><span class="identifier">interval_map</span></code>
          minimal, storing only bitsets, that contain at least one bit switched on.
          Functor template <code class="computeroutput"><span class="identifier">inplace_bit_add</span></code>
          for parameter <code class="computeroutput"><span class="identifier">Combine</span></code> indicates
          that we do not expect <code class="computeroutput"><span class="keyword">operator</span> <span class="special">+=</span></code> as addition but the bitwise operator
          <code class="computeroutput"><span class="special">|=</span></code>. For template parameter
          <code class="computeroutput"><span class="identifier">Section</span></code> which is instaniated
          by <code class="computeroutput"><span class="identifier">inplace_bit_and</span></code> we expect
          the bitwise <code class="computeroutput"><span class="special">&amp;=</span></code> operator.
        </p>
</div>
<div class="section">
<div class="titlepage"><div><div><h4 class="title">
<a name="boost_icl.projects.large_bitset.a_class_implementation_for_the_bitset_type"></a><a class="link" href="projects.html#boost_icl.projects.large_bitset.a_class_implementation_for_the_bitset_type" title="A class implementation for the bitset type">A
        class implementation for the bitset type</a>
</h4></div></div></div>
<p>
          The code of the project is enclosed in a <code class="computeroutput"><span class="keyword">namespace</span>
          <span class="identifier">mini</span></code>. The name indicates, that
          the implementation is a <span class="emphasis"><em>minimal</em></span> example implementation.
          The name of the bitset class will be <code class="computeroutput"><span class="identifier">bits</span></code>
          or <code class="computeroutput"><span class="identifier">mini</span><span class="special">::</span><span class="identifier">bits</span></code> if qualified.
        </p>
<p>
          To be used as a codomain parameter of class template <code class="computeroutput"><a class="link" href="../boost/icl/interval_map.html" title="Class template interval_map">interval_map</a></code>,
          <code class="computeroutput"><span class="identifier">mini</span><span class="special">::</span><span class="identifier">bits</span></code> has to implement all the functions
          that are required for a codomain_type in general, which are the default
          constructor <code class="computeroutput"><span class="identifier">bits</span><span class="special">()</span></code>
          and an equality <code class="computeroutput"><span class="keyword">operator</span><span class="special">==</span></code>.
          Moreover <code class="computeroutput"><span class="identifier">mini</span><span class="special">::</span><span class="identifier">bits</span></code> has to implement operators required
          by the instantiations for parameter <code class="computeroutput"><span class="identifier">Combine</span></code>
          and <code class="computeroutput"><span class="identifier">Section</span></code> which are
          <code class="computeroutput"><span class="identifier">inplace_bit_add</span></code> and <code class="computeroutput"><span class="identifier">inplace_bit_and</span></code>. From functors <code class="computeroutput"><span class="identifier">inplace_bit_add</span></code> and <code class="computeroutput"><span class="identifier">inplace_bit_and</span></code>
          there are inverse functors <code class="computeroutput"><span class="identifier">inplace_bit_subtract</span></code>
          and <code class="computeroutput"><span class="identifier">inplace_bit_xor</span></code>. Those
          functors use operators <code class="computeroutput"><span class="special">|=</span> <span class="special">&amp;=</span> <span class="special">^=</span></code>
          and <code class="computeroutput"><span class="special">~</span></code>. Finally if we want
          to apply lexicographical and subset comparison on large_bitset, we also
          need an <code class="computeroutput"><span class="keyword">operator</span> <span class="special">&lt;</span></code>.
          All the operators that we need can be implemented for <code class="computeroutput"><span class="identifier">mini</span><span class="special">::</span><span class="identifier">bits</span></code>
          on a few lines:
        </p>
<p>
</p>
<pre class="programlisting"><span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">NaturalT</span><span class="special">&gt;</span> <span class="keyword">class</span> <span class="identifier">bits</span>
<span class="special">{</span>
<span class="keyword">public</span><span class="special">:</span>
    <span class="keyword">typedef</span> <span class="identifier">NaturalT</span> <span class="identifier">word_type</span><span class="special">;</span>
    <span class="keyword">static</span> <span class="keyword">const</span> <span class="keyword">int</span>       <span class="identifier">digits</span> <span class="special">=</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special">&lt;</span><span class="identifier">NaturalT</span><span class="special">&gt;::</span><span class="identifier">digits</span><span class="special">;</span>
    <span class="keyword">static</span> <span class="keyword">const</span> <span class="identifier">word_type</span> <span class="identifier">w1</span>     <span class="special">=</span> <span class="keyword">static_cast</span><span class="special">&lt;</span><span class="identifier">NaturalT</span><span class="special">&gt;(</span><span class="number">1</span><span class="special">)</span> <span class="special">;</span>

    <span class="identifier">bits</span><span class="special">():</span><span class="identifier">_bits</span><span class="special">(){}</span>
    <span class="keyword">explicit</span> <span class="identifier">bits</span><span class="special">(</span><span class="identifier">word_type</span> <span class="identifier">value</span><span class="special">):</span><span class="identifier">_bits</span><span class="special">(</span><span class="identifier">value</span><span class="special">){}</span>

    <span class="identifier">word_type</span> <span class="identifier">word</span><span class="special">()</span><span class="keyword">const</span><span class="special">{</span> <span class="keyword">return</span> <span class="identifier">_bits</span><span class="special">;</span> <span class="special">}</span>
    <span class="identifier">bits</span><span class="special">&amp;</span> <span class="keyword">operator</span> <span class="special">|=</span> <span class="special">(</span><span class="keyword">const</span> <span class="identifier">bits</span><span class="special">&amp;</span> <span class="identifier">value</span><span class="special">){</span><span class="identifier">_bits</span> <span class="special">|=</span> <span class="identifier">value</span><span class="special">.</span><span class="identifier">_bits</span><span class="special">;</span> <span class="keyword">return</span> <span class="special">*</span><span class="keyword">this</span><span class="special">;}</span>
    <span class="identifier">bits</span><span class="special">&amp;</span> <span class="keyword">operator</span> <span class="special">&amp;=</span> <span class="special">(</span><span class="keyword">const</span> <span class="identifier">bits</span><span class="special">&amp;</span> <span class="identifier">value</span><span class="special">){</span><span class="identifier">_bits</span> <span class="special">&amp;=</span> <span class="identifier">value</span><span class="special">.</span><span class="identifier">_bits</span><span class="special">;</span> <span class="keyword">return</span> <span class="special">*</span><span class="keyword">this</span><span class="special">;}</span>
    <span class="identifier">bits</span><span class="special">&amp;</span> <span class="keyword">operator</span> <span class="special">^=</span> <span class="special">(</span><span class="keyword">const</span> <span class="identifier">bits</span><span class="special">&amp;</span> <span class="identifier">value</span><span class="special">){</span><span class="identifier">_bits</span> <span class="special">^=</span> <span class="identifier">value</span><span class="special">.</span><span class="identifier">_bits</span><span class="special">;</span> <span class="keyword">return</span> <span class="special">*</span><span class="keyword">this</span><span class="special">;}</span>
    <span class="identifier">bits</span>  <span class="keyword">operator</span> <span class="special">~</span>  <span class="special">()</span><span class="keyword">const</span> <span class="special">{</span> <span class="keyword">return</span> <span class="identifier">bits</span><span class="special">(~</span><span class="identifier">_bits</span><span class="special">);</span> <span class="special">}</span>
    <span class="keyword">bool</span> <span class="keyword">operator</span>  <span class="special">&lt;</span>  <span class="special">(</span><span class="keyword">const</span> <span class="identifier">bits</span><span class="special">&amp;</span> <span class="identifier">value</span><span class="special">)</span><span class="keyword">const</span><span class="special">{</span><span class="keyword">return</span> <span class="identifier">_bits</span> <span class="special">&lt;</span> <span class="identifier">value</span><span class="special">.</span><span class="identifier">_bits</span><span class="special">;}</span>
    <span class="keyword">bool</span> <span class="keyword">operator</span>  <span class="special">==</span> <span class="special">(</span><span class="keyword">const</span> <span class="identifier">bits</span><span class="special">&amp;</span> <span class="identifier">value</span><span class="special">)</span><span class="keyword">const</span><span class="special">{</span><span class="keyword">return</span> <span class="identifier">_bits</span> <span class="special">==</span> <span class="identifier">value</span><span class="special">.</span><span class="identifier">_bits</span><span class="special">;}</span>

    <span class="keyword">bool</span> <span class="identifier">contains</span><span class="special">(</span><span class="identifier">word_type</span> <span class="identifier">element</span><span class="special">)</span><span class="keyword">const</span><span class="special">{</span> <span class="keyword">return</span> <span class="special">((</span><span class="identifier">w1</span> <span class="special">&lt;&lt;</span> <span class="identifier">element</span><span class="special">)</span> <span class="special">&amp;</span> <span class="identifier">_bits</span><span class="special">)</span> <span class="special">!=</span> <span class="number">0</span><span class="special">;</span> <span class="special">}</span>
    <span class="identifier">std</span><span class="special">::</span><span class="identifier">string</span> <span class="identifier">as_string</span><span class="special">(</span><span class="keyword">const</span> <span class="keyword">char</span> <span class="identifier">off_on</span><span class="special">[</span><span class="number">2</span><span class="special">]</span> <span class="special">=</span> <span class="string">" 1"</span><span class="special">)</span><span class="keyword">const</span><span class="special">;</span>

<span class="keyword">private</span><span class="special">:</span>
    <span class="identifier">word_type</span> <span class="identifier">_bits</span><span class="special">;</span>
<span class="special">};</span>
</pre>
<p>
        </p>
<p>
          Finally there is one important piece of meta information, we have to provide:
          <code class="computeroutput"><span class="identifier">mini</span><span class="special">::</span><span class="identifier">bits</span></code> has to be recognized as a <code class="computeroutput"><span class="identifier">Set</span></code> by the icl code. Otherwise we can
          not exploit the fact that a map of sets is model of <code class="computeroutput"><span class="identifier">Set</span></code>
          and the resulting large_bitset would not behave like a set. So we have
          to say that <code class="computeroutput"><span class="identifier">mini</span><span class="special">::</span><span class="identifier">bits</span></code> shall be sets:
        </p>
<p>
</p>
<pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span> <span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">icl</span>
<span class="special">{</span>
    <span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">NaturalT</span><span class="special">&gt;</span>
    <span class="keyword">struct</span> <span class="identifier">is_set</span><span class="special">&lt;</span><span class="identifier">mini</span><span class="special">::</span><span class="identifier">bits</span><span class="special">&lt;</span><span class="identifier">NaturalT</span><span class="special">&gt;</span> <span class="special">&gt;</span>
    <span class="special">{</span>
        <span class="keyword">typedef</span> <span class="identifier">is_set</span><span class="special">&lt;</span><span class="identifier">mini</span><span class="special">::</span><span class="identifier">bits</span><span class="special">&lt;</span><span class="identifier">NaturalT</span><span class="special">&gt;</span> <span class="special">&gt;</span> <span class="identifier">type</span><span class="special">;</span>
        <span class="identifier">BOOST_STATIC_CONSTANT</span><span class="special">(</span><span class="keyword">bool</span><span class="special">,</span> <span class="identifier">value</span> <span class="special">=</span> <span class="keyword">true</span><span class="special">);</span>
    <span class="special">};</span>

    <span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">NaturalT</span><span class="special">&gt;</span>
    <span class="keyword">struct</span> <span class="identifier">has_set_semantics</span><span class="special">&lt;</span><span class="identifier">mini</span><span class="special">::</span><span class="identifier">bits</span><span class="special">&lt;</span><span class="identifier">NaturalT</span><span class="special">&gt;</span> <span class="special">&gt;</span>
    <span class="special">{</span>
        <span class="keyword">typedef</span> <span class="identifier">has_set_semantics</span><span class="special">&lt;</span><span class="identifier">mini</span><span class="special">::</span><span class="identifier">bits</span><span class="special">&lt;</span><span class="identifier">NaturalT</span><span class="special">&gt;</span> <span class="special">&gt;</span> <span class="identifier">type</span><span class="special">;</span>
        <span class="identifier">BOOST_STATIC_CONSTANT</span><span class="special">(</span><span class="keyword">bool</span><span class="special">,</span> <span class="identifier">value</span> <span class="special">=</span> <span class="keyword">true</span><span class="special">);</span>
    <span class="special">};</span>
<span class="special">}}</span>
</pre>
<p>
        </p>
<p>
          This is done by adding a partial template specialization to the type trait
          template <code class="computeroutput"><span class="identifier">icl</span><span class="special">::</span><span class="identifier">is_set</span></code>. For the extension of this type
          trait template and the result values of inclusion_compare we need these
          <code class="computeroutput"><span class="preprocessor">#includes</span></code> for the implementation
          of <code class="computeroutput"><span class="identifier">mini</span><span class="special">::</span><span class="identifier">bits</span></code>:
        </p>
<p>
</p>
<pre class="programlisting">                                               <span class="comment">// These includes are needed ...</span>
<span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">string</span><span class="special">&gt;</span>                              <span class="comment">// for conversion to output and to</span>
<span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">icl</span><span class="special">/</span><span class="identifier">type_traits</span><span class="special">/</span><span class="identifier">has_set_semantics</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;//</span><span class="identifier">declare</span> <span class="identifier">that</span> <span class="identifier">bits</span> <span class="identifier">has</span> <span class="identifier">the</span>
                                               <span class="comment">// behavior of a set.</span>
</pre>
<p>
        </p>
</div>
<div class="section">
<div class="titlepage"><div><div><h4 class="title">
<a name="boost_icl.projects.large_bitset.implementation_of_a_large_bitset"></a><a class="link" href="projects.html#boost_icl.projects.large_bitset.implementation_of_a_large_bitset" title="Implementation of a large bitset">Implementation
        of a large bitset</a>
</h4></div></div></div>
<div class="toc"><dl class="toc">
<dt><span class="section"><a href="projects.html#boost_icl.projects.large_bitset.implementation_of_a_large_bitset.large_bitset__public_interface">large_bitset:
          Public interface</a></span></dt>
<dt><span class="section"><a href="projects.html#boost_icl.projects.large_bitset.implementation_of_a_large_bitset.large_bitset__private_implementation">large_bitset:
          Private implementation</a></span></dt>
</dl></div>
<p>
          Having finished our <code class="computeroutput"><span class="identifier">mini</span><span class="special">::</span><span class="identifier">bits</span></code>
          implementation, we can start to code the wrapper class that hides the efficient
          interval map of mini::bits and exposes a simple and convenient set behavior
          to the world of users.
        </p>
<p>
          Let's start with the required <code class="computeroutput"><span class="preprocessor">#include</span></code>s
          this time:
        </p>
<p>
</p>
<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">iostream</span><span class="special">&gt;</span>                   <span class="comment">// to organize output</span>
<span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">limits</span><span class="special">&gt;</span>                     <span class="comment">// limits and associated constants</span>
<span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">operators</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>        <span class="comment">// to define operators with minimal effort</span>
<span class="preprocessor">#include</span> <span class="string">"meta_log.hpp"</span>               <span class="comment">// a meta logarithm</span>
<span class="preprocessor">#include</span> <span class="string">"bits.hpp"</span>                   <span class="comment">// a minimal bitset implementation</span>
<span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">icl</span><span class="special">/</span><span class="identifier">interval_map</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span> <span class="comment">// base of large bitsets</span>

<span class="keyword">namespace</span> <span class="identifier">mini</span> <span class="comment">// minimal implementations for example projects</span>
<span class="special">{</span>
</pre>
<p>
        </p>
<p>
          Besides <code class="computeroutput"><span class="identifier">boost</span><span class="special">/</span><span class="identifier">icl</span><span class="special">/</span><span class="identifier">interval_map</span><span class="special">.</span><span class="identifier">hpp</span></code> and <code class="computeroutput"><span class="identifier">bits</span><span class="special">.</span><span class="identifier">hpp</span></code>
          the most important include here is <code class="computeroutput"><span class="identifier">boost</span><span class="special">/</span><span class="identifier">operators</span><span class="special">.</span><span class="identifier">hpp</span></code>.
          We use this library in order to further minimize the code and to provide
          pretty extensive operator functionality using very little code.
        </p>
<p>
          For a short and concise naming of the most important unsigned integer types
          and the corresponding <code class="computeroutput"><span class="identifier">mini</span><span class="special">::</span><span class="identifier">bits</span></code>
          we define this:
        </p>
<p>
</p>
<pre class="programlisting"><span class="keyword">typedef</span> <span class="keyword">unsigned</span> <span class="keyword">char</span>      <span class="identifier">nat8</span><span class="special">;</span> <span class="comment">// nati i: number bits</span>
<span class="keyword">typedef</span> <span class="keyword">unsigned</span> <span class="keyword">short</span>     <span class="identifier">nat16</span><span class="special">;</span>
<span class="keyword">typedef</span> <span class="keyword">unsigned</span> <span class="keyword">long</span>      <span class="identifier">nat32</span><span class="special">;</span>
<span class="keyword">typedef</span> <span class="keyword">unsigned</span> <span class="keyword">long</span> <span class="keyword">long</span> <span class="identifier">nat64</span><span class="special">;</span>
<span class="keyword">typedef</span> <span class="keyword">unsigned</span> <span class="keyword">long</span>      <span class="identifier">nat</span><span class="special">;</span>

<span class="keyword">typedef</span> <span class="identifier">bits</span><span class="special">&lt;</span><span class="identifier">nat8</span><span class="special">&gt;</span>  <span class="identifier">bits8</span><span class="special">;</span>
<span class="keyword">typedef</span> <span class="identifier">bits</span><span class="special">&lt;</span><span class="identifier">nat16</span><span class="special">&gt;</span> <span class="identifier">bits16</span><span class="special">;</span>
<span class="keyword">typedef</span> <span class="identifier">bits</span><span class="special">&lt;</span><span class="identifier">nat32</span><span class="special">&gt;</span> <span class="identifier">bits32</span><span class="special">;</span>
<span class="keyword">typedef</span> <span class="identifier">bits</span><span class="special">&lt;</span><span class="identifier">nat64</span><span class="special">&gt;</span> <span class="identifier">bits64</span><span class="special">;</span>
</pre>
<p>
        </p>
<div class="section">
<div class="titlepage"><div><div><h5 class="title">
<a name="boost_icl.projects.large_bitset.implementation_of_a_large_bitset.large_bitset__public_interface"></a><a class="link" href="projects.html#boost_icl.projects.large_bitset.implementation_of_a_large_bitset.large_bitset__public_interface" title="large_bitset: Public interface">large_bitset:
          Public interface</a>
</h5></div></div></div>
<p>
            And now let's code <code class="computeroutput"><span class="identifier">large_bitset</span></code>.
          </p>
<p>
</p>
<pre class="programlisting"><span class="keyword">template</span>
<span class="special">&lt;</span>
    <span class="keyword">typename</span>    <span class="identifier">DomainT</span> <span class="special">=</span> <span class="identifier">nat64</span><span class="special">,</span>
    <span class="keyword">typename</span>    <span class="identifier">BitSetT</span> <span class="special">=</span> <span class="identifier">bits64</span><span class="special">,</span>
    <span class="identifier">ICL_COMPARE</span> <span class="identifier">Compare</span> <span class="special">=</span> <span class="identifier">ICL_COMPARE_INSTANCE</span><span class="special">(</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">less</span><span class="special">,</span> <span class="identifier">DomainT</span><span class="special">),</span>
    <span class="identifier">ICL_INTERVAL</span><span class="special">(</span><span class="identifier">ICL_COMPARE</span><span class="special">)</span> <span class="identifier">Interval</span> <span class="special">=</span> <span class="identifier">ICL_INTERVAL_INSTANCE</span><span class="special">(</span><span class="identifier">ICL_INTERVAL_DEFAULT</span><span class="special">,</span> <span class="identifier">DomainT</span><span class="special">,</span> <span class="identifier">Compare</span><span class="special">),</span>
    <span class="identifier">ICL_ALLOC</span>   <span class="identifier">Alloc</span>   <span class="special">=</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">allocator</span>
<span class="special">&gt;</span>
<span class="keyword">class</span> <span class="identifier">large_bitset</span>
    <span class="special">:</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">equality_comparable</span> <span class="special">&lt;</span> <span class="identifier">large_bitset</span><span class="special">&lt;</span><span class="identifier">DomainT</span><span class="special">,</span><span class="identifier">BitSetT</span><span class="special">,</span><span class="identifier">Compare</span><span class="special">,</span><span class="identifier">Interval</span><span class="special">,</span><span class="identifier">Alloc</span><span class="special">&gt;</span>
    <span class="special">,</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">less_than_comparable</span><span class="special">&lt;</span> <span class="identifier">large_bitset</span><span class="special">&lt;</span><span class="identifier">DomainT</span><span class="special">,</span><span class="identifier">BitSetT</span><span class="special">,</span><span class="identifier">Compare</span><span class="special">,</span><span class="identifier">Interval</span><span class="special">,</span><span class="identifier">Alloc</span><span class="special">&gt;</span>

    <span class="special">,</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">addable</span>       <span class="special">&lt;</span> <span class="identifier">large_bitset</span><span class="special">&lt;</span><span class="identifier">DomainT</span><span class="special">,</span><span class="identifier">BitSetT</span><span class="special">,</span><span class="identifier">Compare</span><span class="special">,</span><span class="identifier">Interval</span><span class="special">,</span><span class="identifier">Alloc</span><span class="special">&gt;</span>
    <span class="special">,</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">orable</span>        <span class="special">&lt;</span> <span class="identifier">large_bitset</span><span class="special">&lt;</span><span class="identifier">DomainT</span><span class="special">,</span><span class="identifier">BitSetT</span><span class="special">,</span><span class="identifier">Compare</span><span class="special">,</span><span class="identifier">Interval</span><span class="special">,</span><span class="identifier">Alloc</span><span class="special">&gt;</span>
    <span class="special">,</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">subtractable</span>  <span class="special">&lt;</span> <span class="identifier">large_bitset</span><span class="special">&lt;</span><span class="identifier">DomainT</span><span class="special">,</span><span class="identifier">BitSetT</span><span class="special">,</span><span class="identifier">Compare</span><span class="special">,</span><span class="identifier">Interval</span><span class="special">,</span><span class="identifier">Alloc</span><span class="special">&gt;</span>
    <span class="special">,</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">andable</span>       <span class="special">&lt;</span> <span class="identifier">large_bitset</span><span class="special">&lt;</span><span class="identifier">DomainT</span><span class="special">,</span><span class="identifier">BitSetT</span><span class="special">,</span><span class="identifier">Compare</span><span class="special">,</span><span class="identifier">Interval</span><span class="special">,</span><span class="identifier">Alloc</span><span class="special">&gt;</span>
    <span class="special">,</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">xorable</span>       <span class="special">&lt;</span> <span class="identifier">large_bitset</span><span class="special">&lt;</span><span class="identifier">DomainT</span><span class="special">,</span><span class="identifier">BitSetT</span><span class="special">,</span><span class="identifier">Compare</span><span class="special">,</span><span class="identifier">Interval</span><span class="special">,</span><span class="identifier">Alloc</span><span class="special">&gt;</span>

    <span class="special">,</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">addable2</span>      <span class="special">&lt;</span> <span class="identifier">large_bitset</span><span class="special">&lt;</span><span class="identifier">DomainT</span><span class="special">,</span><span class="identifier">BitSetT</span><span class="special">,</span><span class="identifier">Compare</span><span class="special">,</span><span class="identifier">Interval</span><span class="special">,</span><span class="identifier">Alloc</span><span class="special">&gt;,</span> <span class="identifier">DomainT</span>
    <span class="special">,</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">orable2</span>       <span class="special">&lt;</span> <span class="identifier">large_bitset</span><span class="special">&lt;</span><span class="identifier">DomainT</span><span class="special">,</span><span class="identifier">BitSetT</span><span class="special">,</span><span class="identifier">Compare</span><span class="special">,</span><span class="identifier">Interval</span><span class="special">,</span><span class="identifier">Alloc</span><span class="special">&gt;,</span> <span class="identifier">DomainT</span>
    <span class="special">,</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">subtractable2</span> <span class="special">&lt;</span> <span class="identifier">large_bitset</span><span class="special">&lt;</span><span class="identifier">DomainT</span><span class="special">,</span><span class="identifier">BitSetT</span><span class="special">,</span><span class="identifier">Compare</span><span class="special">,</span><span class="identifier">Interval</span><span class="special">,</span><span class="identifier">Alloc</span><span class="special">&gt;,</span> <span class="identifier">DomainT</span>
    <span class="special">,</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">andable2</span>      <span class="special">&lt;</span> <span class="identifier">large_bitset</span><span class="special">&lt;</span><span class="identifier">DomainT</span><span class="special">,</span><span class="identifier">BitSetT</span><span class="special">,</span><span class="identifier">Compare</span><span class="special">,</span><span class="identifier">Interval</span><span class="special">,</span><span class="identifier">Alloc</span><span class="special">&gt;,</span> <span class="identifier">DomainT</span>
    <span class="special">,</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">xorable2</span>      <span class="special">&lt;</span> <span class="identifier">large_bitset</span><span class="special">&lt;</span><span class="identifier">DomainT</span><span class="special">,</span><span class="identifier">BitSetT</span><span class="special">,</span><span class="identifier">Compare</span><span class="special">,</span><span class="identifier">Interval</span><span class="special">,</span><span class="identifier">Alloc</span><span class="special">&gt;,</span> <span class="identifier">DomainT</span>

    <span class="special">,</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">addable2</span>      <span class="special">&lt;</span> <span class="identifier">large_bitset</span><span class="special">&lt;</span><span class="identifier">DomainT</span><span class="special">,</span><span class="identifier">BitSetT</span><span class="special">,</span><span class="identifier">Compare</span><span class="special">,</span><span class="identifier">Interval</span><span class="special">,</span><span class="identifier">Alloc</span><span class="special">&gt;,</span> <span class="identifier">ICL_INTERVAL_TYPE</span><span class="special">(</span><span class="identifier">Interval</span><span class="special">,</span><span class="identifier">DomainT</span><span class="special">,</span><span class="identifier">Compare</span><span class="special">)</span>
    <span class="special">,</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">orable2</span>       <span class="special">&lt;</span> <span class="identifier">large_bitset</span><span class="special">&lt;</span><span class="identifier">DomainT</span><span class="special">,</span><span class="identifier">BitSetT</span><span class="special">,</span><span class="identifier">Compare</span><span class="special">,</span><span class="identifier">Interval</span><span class="special">,</span><span class="identifier">Alloc</span><span class="special">&gt;,</span> <span class="identifier">ICL_INTERVAL_TYPE</span><span class="special">(</span><span class="identifier">Interval</span><span class="special">,</span><span class="identifier">DomainT</span><span class="special">,</span><span class="identifier">Compare</span><span class="special">)</span>
    <span class="special">,</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">subtractable2</span> <span class="special">&lt;</span> <span class="identifier">large_bitset</span><span class="special">&lt;</span><span class="identifier">DomainT</span><span class="special">,</span><span class="identifier">BitSetT</span><span class="special">,</span><span class="identifier">Compare</span><span class="special">,</span><span class="identifier">Interval</span><span class="special">,</span><span class="identifier">Alloc</span><span class="special">&gt;,</span> <span class="identifier">ICL_INTERVAL_TYPE</span><span class="special">(</span><span class="identifier">Interval</span><span class="special">,</span><span class="identifier">DomainT</span><span class="special">,</span><span class="identifier">Compare</span><span class="special">)</span>
    <span class="special">,</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">andable2</span>      <span class="special">&lt;</span> <span class="identifier">large_bitset</span><span class="special">&lt;</span><span class="identifier">DomainT</span><span class="special">,</span><span class="identifier">BitSetT</span><span class="special">,</span><span class="identifier">Compare</span><span class="special">,</span><span class="identifier">Interval</span><span class="special">,</span><span class="identifier">Alloc</span><span class="special">&gt;,</span> <span class="identifier">ICL_INTERVAL_TYPE</span><span class="special">(</span><span class="identifier">Interval</span><span class="special">,</span><span class="identifier">DomainT</span><span class="special">,</span><span class="identifier">Compare</span><span class="special">)</span>
    <span class="special">,</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">xorable2</span>      <span class="special">&lt;</span> <span class="identifier">large_bitset</span><span class="special">&lt;</span><span class="identifier">DomainT</span><span class="special">,</span><span class="identifier">BitSetT</span><span class="special">,</span><span class="identifier">Compare</span><span class="special">,</span><span class="identifier">Interval</span><span class="special">,</span><span class="identifier">Alloc</span><span class="special">&gt;,</span> <span class="identifier">ICL_INTERVAL_TYPE</span><span class="special">(</span><span class="identifier">Interval</span><span class="special">,</span><span class="identifier">DomainT</span><span class="special">,</span><span class="identifier">Compare</span><span class="special">)</span>
      <span class="special">&gt;</span> <span class="special">&gt;</span> <span class="special">&gt;</span> <span class="special">&gt;</span> <span class="special">&gt;</span> <span class="special">&gt;</span> <span class="special">&gt;</span> <span class="special">&gt;</span> <span class="special">&gt;</span> <span class="special">&gt;</span> <span class="special">&gt;</span> <span class="special">&gt;</span> <span class="special">&gt;</span> <span class="special">&gt;</span> <span class="special">&gt;</span> <span class="special">&gt;</span> <span class="special">&gt;</span>
    <span class="comment">//^ &amp; - | + ^ &amp; - | + ^ &amp; - | + &lt; == </span>
    <span class="comment">//segment   element   container</span>
</pre>
<p>
          </p>
<p>
            The first template parameter <code class="computeroutput"><span class="identifier">DomainT</span></code>
            will be instantiated with an integral type that defines the kind of numbers
            that can be elements of the set. Since we want to go for a large set
            we use <code class="computeroutput"><span class="identifier">nat64</span></code> as default
            which is a 64 bit unsigned integer ranging from <code class="computeroutput"><span class="number">0</span></code>
            to <code class="computeroutput"><span class="number">2</span><span class="special">^</span><span class="number">64</span><span class="special">-</span><span class="number">1</span></code>.
            As bitset parameter we also choose a 64-bit default. Parameters <code class="computeroutput"><span class="identifier">Combine</span></code> and <code class="computeroutput"><span class="identifier">Interval</span></code>
            are necessary to be passed to dependent type expressions. An allocator
            can be chosen, if desired.
          </p>
<p>
            The nested list of private inheritance contains groups of template instantiations
            from <a href="http://www.boost.org/doc/libs/1_39_0/libs/utility/operators.htm" target="_top">Boost.Operator</a>,
            that provides derivable operators from more fundamental once. Implementing
            the fundamental operators, we get the derivable ones <span class="emphasis"><em>for free</em></span>.
            Below is a short overview of what we get using Boost.Operator, where
            <a class="link" href="interface/function_synopsis.html#interval_set_types"><span class="bold"><strong>S</strong></span></a>
            stands for <code class="computeroutput"><span class="identifier">large_bitset</span></code>,
            <a class="link" href="interface/function_synopsis.html#interval_type"><span class="bold"><strong>i</strong></span></a>
            for it's <code class="computeroutput"><span class="identifier">interval_type</span></code>
            and <a class="link" href="interface/function_synopsis.html#element_type"><span class="bold"><strong>e</strong></span></a>
            for it's <code class="computeroutput"><span class="identifier">domain_type</span></code>
            or <code class="computeroutput"><span class="identifier">element_type</span></code>.
          </p>
<div class="informaltable"><table class="table">
<colgroup>
<col>
<col>
<col>
</colgroup>
<thead><tr>
<th>
                    <p>
                      Group
                    </p>
                  </th>
<th>
                    <p>
                      fundamental
                    </p>
                  </th>
<th>
                    <p>
                      derivable
                    </p>
                  </th>
</tr></thead>
<tbody>
<tr>
<td>
                    <p>
                      Equality, ordering
                    </p>
                  </td>
<td>
                    <p>
                      <code class="computeroutput"><span class="special">==</span></code>
                    </p>
                  </td>
<td>
                    <p>
                      <code class="computeroutput"><span class="special">!=</span></code>
                    </p>
                  </td>
</tr>
<tr>
<td>
                  </td>
<td>
                    <p>
                      <code class="computeroutput"><span class="special">&lt;</span></code>
                    </p>
                  </td>
<td>
                    <p>
                      <code class="computeroutput"><span class="special">&gt;</span> <span class="special">&lt;=</span>
                      <span class="special">&gt;=</span></code>
                    </p>
                  </td>
</tr>
<tr>
<td>
                    <p>
                      Set operators (<a class="link" href="interface/function_synopsis.html#interval_set_types"><span class="bold"><strong>S</strong></span></a> x <a class="link" href="interface/function_synopsis.html#interval_set_types"><span class="bold"><strong>S</strong></span></a>)
                    </p>
                  </td>
<td>
                    <p>
                      <code class="computeroutput"><span class="special">+=</span> <span class="special">|=</span>
                      <span class="special">-=</span> <span class="special">&amp;=</span>
                      <span class="special">^=</span></code>
                    </p>
                  </td>
<td>
                    <p>
                      <code class="computeroutput"><span class="special">+</span> <span class="special">|</span>
                      <span class="special">-</span> <span class="special">&amp;</span>
                      <span class="special">^</span></code>
                    </p>
                  </td>
</tr>
<tr>
<td>
                    <p>
                      Set operators (<a class="link" href="interface/function_synopsis.html#interval_set_types"><span class="bold"><strong>S</strong></span></a> x <a class="link" href="interface/function_synopsis.html#element_type"><span class="bold"><strong>e</strong></span></a>)
                    </p>
                  </td>
<td>
                    <p>
                      <code class="computeroutput"><span class="special">+=</span> <span class="special">|=</span>
                      <span class="special">-=</span> <span class="special">&amp;=</span>
                      <span class="special">^=</span></code>
                    </p>
                  </td>
<td>
                    <p>
                      <code class="computeroutput"><span class="special">+</span> <span class="special">|</span>
                      <span class="special">-</span> <span class="special">&amp;</span>
                      <span class="special">^</span></code>
                    </p>
                  </td>
</tr>
<tr>
<td>
                    <p>
                      Set operators (<a class="link" href="interface/function_synopsis.html#interval_set_types"><span class="bold"><strong>S</strong></span></a> x <a class="link" href="interface/function_synopsis.html#interval_type"><span class="bold"><strong>i</strong></span></a>)
                    </p>
                  </td>
<td>
                    <p>
                      <code class="computeroutput"><span class="special">+=</span> <span class="special">|=</span>
                      <span class="special">-=</span> <span class="special">&amp;=</span>
                      <span class="special">^=</span></code>
                    </p>
                  </td>
<td>
                    <p>
                      <code class="computeroutput"><span class="special">+</span> <span class="special">|</span>
                      <span class="special">-</span> <span class="special">&amp;</span>
                      <span class="special">^</span></code>
                    </p>
                  </td>
</tr>
</tbody>
</table></div>
<p>
            There is a number of associated types
          </p>
<p>
</p>
<pre class="programlisting"><span class="keyword">typedef</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">icl</span><span class="special">::</span><span class="identifier">interval_map</span>
    <span class="special">&lt;</span><span class="identifier">DomainT</span><span class="special">,</span> <span class="identifier">BitSetT</span><span class="special">,</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">icl</span><span class="special">::</span><span class="identifier">partial_absorber</span><span class="special">,</span>
     <span class="identifier">std</span><span class="special">::</span><span class="identifier">less</span><span class="special">,</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">icl</span><span class="special">::</span><span class="identifier">inplace_bit_add</span><span class="special">,</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">icl</span><span class="special">::</span><span class="identifier">inplace_bit_and</span><span class="special">&gt;</span> <span class="identifier">interval_bitmap_type</span><span class="special">;</span>

<span class="keyword">typedef</span> <span class="identifier">DomainT</span>                                      <span class="identifier">domain_type</span><span class="special">;</span>
<span class="keyword">typedef</span> <span class="identifier">DomainT</span>                                      <span class="identifier">element_type</span><span class="special">;</span>
<span class="keyword">typedef</span> <span class="identifier">BitSetT</span>                                      <span class="identifier">bitset_type</span><span class="special">;</span>
<span class="keyword">typedef</span> <span class="keyword">typename</span> <span class="identifier">BitSetT</span><span class="special">::</span><span class="identifier">word_type</span>                  <span class="identifier">word_type</span><span class="special">;</span>
<span class="keyword">typedef</span> <span class="keyword">typename</span> <span class="identifier">interval_bitmap_type</span><span class="special">::</span><span class="identifier">interval_type</span> <span class="identifier">interval_type</span><span class="special">;</span>
<span class="keyword">typedef</span> <span class="keyword">typename</span> <span class="identifier">interval_bitmap_type</span><span class="special">::</span><span class="identifier">value_type</span>    <span class="identifier">value_type</span><span class="special">;</span>
</pre>
<p>
          </p>
<p>
            most importantly the implementing <code class="computeroutput"><span class="identifier">interval_bitmap_type</span></code>
            that is used for the implementing container.
          </p>
<p>
</p>
<pre class="programlisting"><span class="keyword">private</span><span class="special">:</span>
    <span class="identifier">interval_bitmap_type</span> <span class="identifier">_map</span><span class="special">;</span>
</pre>
<p>
          </p>
<p>
            In order to use <a href="http://www.boost.org/doc/libs/1_39_0/libs/utility/operators.htm" target="_top">Boost.Operator</a>
            we have to implement the fundamental operators as class members. This
            can be done quite schematically.
          </p>
<p>
</p>
<pre class="programlisting"><span class="keyword">public</span><span class="special">:</span>
    <span class="keyword">bool</span>     <span class="keyword">operator</span> <span class="special">==(</span><span class="keyword">const</span> <span class="identifier">large_bitset</span><span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">)</span><span class="keyword">const</span> <span class="special">{</span> <span class="keyword">return</span> <span class="identifier">_map</span> <span class="special">==</span> <span class="identifier">rhs</span><span class="special">.</span><span class="identifier">_map</span><span class="special">;</span> <span class="special">}</span>
    <span class="keyword">bool</span>     <span class="keyword">operator</span> <span class="special">&lt;</span> <span class="special">(</span><span class="keyword">const</span> <span class="identifier">large_bitset</span><span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">)</span><span class="keyword">const</span> <span class="special">{</span> <span class="keyword">return</span> <span class="identifier">_map</span> <span class="special">&lt;</span>  <span class="identifier">rhs</span><span class="special">.</span><span class="identifier">_map</span><span class="special">;</span> <span class="special">}</span>

    <span class="identifier">large_bitset</span><span class="special">&amp;</span> <span class="keyword">operator</span> <span class="special">+=(</span><span class="keyword">const</span> <span class="identifier">large_bitset</span><span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">)</span> <span class="special">{</span><span class="identifier">_map</span> <span class="special">+=</span> <span class="identifier">rhs</span><span class="special">.</span><span class="identifier">_map</span><span class="special">;</span> <span class="keyword">return</span> <span class="special">*</span><span class="keyword">this</span><span class="special">;}</span>
    <span class="identifier">large_bitset</span><span class="special">&amp;</span> <span class="keyword">operator</span> <span class="special">|=(</span><span class="keyword">const</span> <span class="identifier">large_bitset</span><span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">)</span> <span class="special">{</span><span class="identifier">_map</span> <span class="special">|=</span> <span class="identifier">rhs</span><span class="special">.</span><span class="identifier">_map</span><span class="special">;</span> <span class="keyword">return</span> <span class="special">*</span><span class="keyword">this</span><span class="special">;}</span>
    <span class="identifier">large_bitset</span><span class="special">&amp;</span> <span class="keyword">operator</span> <span class="special">-=(</span><span class="keyword">const</span> <span class="identifier">large_bitset</span><span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">)</span> <span class="special">{</span><span class="identifier">_map</span> <span class="special">-=</span> <span class="identifier">rhs</span><span class="special">.</span><span class="identifier">_map</span><span class="special">;</span> <span class="keyword">return</span> <span class="special">*</span><span class="keyword">this</span><span class="special">;}</span>
    <span class="identifier">large_bitset</span><span class="special">&amp;</span> <span class="keyword">operator</span> <span class="special">&amp;=(</span><span class="keyword">const</span> <span class="identifier">large_bitset</span><span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">)</span> <span class="special">{</span><span class="identifier">_map</span> <span class="special">&amp;=</span> <span class="identifier">rhs</span><span class="special">.</span><span class="identifier">_map</span><span class="special">;</span> <span class="keyword">return</span> <span class="special">*</span><span class="keyword">this</span><span class="special">;}</span>
    <span class="identifier">large_bitset</span><span class="special">&amp;</span> <span class="keyword">operator</span> <span class="special">^=(</span><span class="keyword">const</span> <span class="identifier">large_bitset</span><span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">)</span> <span class="special">{</span><span class="identifier">_map</span> <span class="special">^=</span> <span class="identifier">rhs</span><span class="special">.</span><span class="identifier">_map</span><span class="special">;</span> <span class="keyword">return</span> <span class="special">*</span><span class="keyword">this</span><span class="special">;}</span>

    <span class="identifier">large_bitset</span><span class="special">&amp;</span> <span class="keyword">operator</span> <span class="special">+=(</span><span class="keyword">const</span> <span class="identifier">element_type</span><span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">)</span> <span class="special">{</span><span class="keyword">return</span> <span class="identifier">add</span><span class="special">(</span><span class="identifier">interval_type</span><span class="special">(</span><span class="identifier">rhs</span><span class="special">));</span>      <span class="special">}</span>
    <span class="identifier">large_bitset</span><span class="special">&amp;</span> <span class="keyword">operator</span> <span class="special">|=(</span><span class="keyword">const</span> <span class="identifier">element_type</span><span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">)</span> <span class="special">{</span><span class="keyword">return</span> <span class="identifier">add</span><span class="special">(</span><span class="identifier">interval_type</span><span class="special">(</span><span class="identifier">rhs</span><span class="special">));</span>      <span class="special">}</span>
    <span class="identifier">large_bitset</span><span class="special">&amp;</span> <span class="keyword">operator</span> <span class="special">-=(</span><span class="keyword">const</span> <span class="identifier">element_type</span><span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">)</span> <span class="special">{</span><span class="keyword">return</span> <span class="identifier">subtract</span><span class="special">(</span><span class="identifier">interval_type</span><span class="special">(</span><span class="identifier">rhs</span><span class="special">));</span> <span class="special">}</span>
    <span class="identifier">large_bitset</span><span class="special">&amp;</span> <span class="keyword">operator</span> <span class="special">&amp;=(</span><span class="keyword">const</span> <span class="identifier">element_type</span><span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">)</span> <span class="special">{</span><span class="keyword">return</span> <span class="identifier">intersect</span><span class="special">(</span><span class="identifier">interval_type</span><span class="special">(</span><span class="identifier">rhs</span><span class="special">));}</span>
    <span class="identifier">large_bitset</span><span class="special">&amp;</span> <span class="keyword">operator</span> <span class="special">^=(</span><span class="keyword">const</span> <span class="identifier">element_type</span><span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">)</span> <span class="special">{</span><span class="keyword">return</span> <span class="identifier">flip</span><span class="special">(</span><span class="identifier">interval_type</span><span class="special">(</span><span class="identifier">rhs</span><span class="special">));</span>     <span class="special">}</span>

    <span class="identifier">large_bitset</span><span class="special">&amp;</span> <span class="keyword">operator</span> <span class="special">+=(</span><span class="keyword">const</span> <span class="identifier">interval_type</span><span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">){</span><span class="keyword">return</span> <span class="identifier">add</span><span class="special">(</span><span class="identifier">rhs</span><span class="special">);</span>      <span class="special">}</span>
    <span class="identifier">large_bitset</span><span class="special">&amp;</span> <span class="keyword">operator</span> <span class="special">|=(</span><span class="keyword">const</span> <span class="identifier">interval_type</span><span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">){</span><span class="keyword">return</span> <span class="identifier">add</span><span class="special">(</span><span class="identifier">rhs</span><span class="special">);</span>      <span class="special">}</span>
    <span class="identifier">large_bitset</span><span class="special">&amp;</span> <span class="keyword">operator</span> <span class="special">-=(</span><span class="keyword">const</span> <span class="identifier">interval_type</span><span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">){</span><span class="keyword">return</span> <span class="identifier">subtract</span><span class="special">(</span><span class="identifier">rhs</span><span class="special">);</span> <span class="special">}</span>
    <span class="identifier">large_bitset</span><span class="special">&amp;</span> <span class="keyword">operator</span> <span class="special">&amp;=(</span><span class="keyword">const</span> <span class="identifier">interval_type</span><span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">){</span><span class="keyword">return</span> <span class="identifier">intersect</span><span class="special">(</span><span class="identifier">rhs</span><span class="special">);}</span>
    <span class="identifier">large_bitset</span><span class="special">&amp;</span> <span class="keyword">operator</span> <span class="special">^=(</span><span class="keyword">const</span> <span class="identifier">interval_type</span><span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">){</span><span class="keyword">return</span> <span class="identifier">flip</span><span class="special">(</span><span class="identifier">rhs</span><span class="special">);</span>     <span class="special">}</span>
</pre>
<p>
          </p>
<p>
            As we can see, the seven most important operators that work on the class
            type <code class="computeroutput"><span class="identifier">large_bitset</span></code> can
            be directly implemented by propagating the operation to the implementing
            <code class="computeroutput"><span class="identifier">_map</span></code> of type <code class="computeroutput"><span class="identifier">interval_bitmap_type</span></code>. For the operators
            that work on segment and element types, we use member functions <code class="computeroutput"><span class="identifier">add</span></code>, <code class="computeroutput"><span class="identifier">subtract</span></code>,
            <code class="computeroutput"><span class="identifier">intersect</span></code> and <code class="computeroutput"><span class="identifier">flip</span></code>. As we will see only a small amount
            of adaper code is needed to couple those functions with the functionality
            of the implementing container.
          </p>
<p>
            Member functions <code class="computeroutput"><span class="identifier">add</span></code>,
            <code class="computeroutput"><span class="identifier">subtract</span></code>, <code class="computeroutput"><span class="identifier">intersect</span></code> and <code class="computeroutput"><span class="identifier">flip</span></code>,
            that allow to combine <span class="emphasis"><em><span class="bold"><strong>intervals</strong></span></em></span>
            to <code class="computeroutput"><span class="identifier">large_bitsets</span></code> can
            be uniformly implemented using a private function <code class="computeroutput"><span class="identifier">segment_apply</span></code>
            that applies <span class="emphasis"><em>addition</em></span>, <span class="emphasis"><em>subtraction</em></span>,
            <span class="emphasis"><em>intersection</em></span> or <span class="emphasis"><em>symmetric difference</em></span>,
            after having translated the interval's borders into the right bitset
            positions.
          </p>
<p>
</p>
<pre class="programlisting"><span class="identifier">large_bitset</span><span class="special">&amp;</span> <span class="identifier">add</span>      <span class="special">(</span><span class="keyword">const</span> <span class="identifier">interval_type</span><span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">){</span><span class="keyword">return</span> <span class="identifier">segment_apply</span><span class="special">(&amp;</span><span class="identifier">large_bitset</span><span class="special">::</span><span class="identifier">add_</span><span class="special">,</span>      <span class="identifier">rhs</span><span class="special">);}</span>
<span class="identifier">large_bitset</span><span class="special">&amp;</span> <span class="identifier">subtract</span> <span class="special">(</span><span class="keyword">const</span> <span class="identifier">interval_type</span><span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">){</span><span class="keyword">return</span> <span class="identifier">segment_apply</span><span class="special">(&amp;</span><span class="identifier">large_bitset</span><span class="special">::</span><span class="identifier">subtract_</span><span class="special">,</span> <span class="identifier">rhs</span><span class="special">);}</span>
<span class="identifier">large_bitset</span><span class="special">&amp;</span> <span class="identifier">intersect</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">interval_type</span><span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">){</span><span class="keyword">return</span> <span class="identifier">segment_apply</span><span class="special">(&amp;</span><span class="identifier">large_bitset</span><span class="special">::</span><span class="identifier">intersect_</span><span class="special">,</span><span class="identifier">rhs</span><span class="special">);}</span>
<span class="identifier">large_bitset</span><span class="special">&amp;</span> <span class="identifier">flip</span>     <span class="special">(</span><span class="keyword">const</span> <span class="identifier">interval_type</span><span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">){</span><span class="keyword">return</span> <span class="identifier">segment_apply</span><span class="special">(&amp;</span><span class="identifier">large_bitset</span><span class="special">::</span><span class="identifier">flip_</span><span class="special">,</span>     <span class="identifier">rhs</span><span class="special">);}</span>
</pre>
<p>
          </p>
<p>
            In the sample programs, that we will present to demonstrate the capabilities
            of <code class="computeroutput"><span class="identifier">large_bitset</span></code> we will
            need a few additional functions specifically output functions in two
            different flavors.
          </p>
<p>
</p>
<pre class="programlisting"><span class="identifier">size_t</span> <span class="identifier">interval_count</span><span class="special">()</span><span class="keyword">const</span> <span class="special">{</span> <span class="keyword">return</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">icl</span><span class="special">::</span><span class="identifier">interval_count</span><span class="special">(</span><span class="identifier">_map</span><span class="special">);</span> <span class="special">}</span>

<span class="keyword">void</span> <span class="identifier">show_segments</span><span class="special">()</span><span class="keyword">const</span>
<span class="special">{</span>
    <span class="keyword">for</span><span class="special">(</span><span class="keyword">typename</span> <span class="identifier">interval_bitmap_type</span><span class="special">::</span><span class="identifier">const_iterator</span> <span class="identifier">it_</span> <span class="special">=</span> <span class="identifier">_map</span><span class="special">.</span><span class="identifier">begin</span><span class="special">();</span>
        <span class="identifier">it_</span> <span class="special">!=</span> <span class="identifier">_map</span><span class="special">.</span><span class="identifier">end</span><span class="special">();</span> <span class="special">++</span><span class="identifier">it_</span><span class="special">)</span>
    <span class="special">{</span>
        <span class="identifier">interval_type</span>   <span class="identifier">itv</span>  <span class="special">=</span> <span class="identifier">it_</span><span class="special">-&gt;</span><span class="identifier">first</span><span class="special">;</span>
        <span class="identifier">bitset_type</span>     <span class="identifier">bits</span> <span class="special">=</span> <span class="identifier">it_</span><span class="special">-&gt;</span><span class="identifier">second</span><span class="special">;</span>
        <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">itv</span> <span class="special">&lt;&lt;</span> <span class="string">"-&gt;"</span> <span class="special">&lt;&lt;</span> <span class="identifier">bits</span><span class="special">.</span><span class="identifier">as_string</span><span class="special">(</span><span class="string">"01"</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
    <span class="special">}</span>
<span class="special">}</span>

<span class="keyword">void</span> <span class="identifier">show_matrix</span><span class="special">(</span><span class="keyword">const</span> <span class="keyword">char</span> <span class="identifier">off_on</span><span class="special">[</span><span class="number">2</span><span class="special">]</span> <span class="special">=</span> <span class="string">" 1"</span><span class="special">)</span><span class="keyword">const</span>
<span class="special">{</span>
    <span class="keyword">using</span> <span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">;</span>
    <span class="keyword">typename</span> <span class="identifier">interval_bitmap_type</span><span class="special">::</span><span class="identifier">const_iterator</span> <span class="identifier">iter</span> <span class="special">=</span> <span class="identifier">_map</span><span class="special">.</span><span class="identifier">begin</span><span class="special">();</span>
    <span class="keyword">while</span><span class="special">(</span><span class="identifier">iter</span> <span class="special">!=</span> <span class="identifier">_map</span><span class="special">.</span><span class="identifier">end</span><span class="special">())</span>
    <span class="special">{</span>
        <span class="identifier">element_type</span> <span class="identifier">fst</span> <span class="special">=</span> <span class="identifier">icl</span><span class="special">::</span><span class="identifier">first</span><span class="special">(</span><span class="identifier">iter</span><span class="special">-&gt;</span><span class="identifier">first</span><span class="special">),</span> <span class="identifier">lst</span> <span class="special">=</span> <span class="identifier">icl</span><span class="special">::</span><span class="identifier">last</span><span class="special">(</span><span class="identifier">iter</span><span class="special">-&gt;</span><span class="identifier">first</span><span class="special">);</span>
        <span class="keyword">for</span><span class="special">(</span><span class="identifier">element_type</span> <span class="identifier">chunk</span> <span class="special">=</span> <span class="identifier">fst</span><span class="special">;</span> <span class="identifier">chunk</span> <span class="special">&lt;=</span> <span class="identifier">lst</span><span class="special">;</span> <span class="identifier">chunk</span><span class="special">++)</span>
            <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">iter</span><span class="special">-&gt;</span><span class="identifier">second</span><span class="special">.</span><span class="identifier">as_string</span><span class="special">(</span><span class="identifier">off_on</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
        <span class="special">++</span><span class="identifier">iter</span><span class="special">;</span>
    <span class="special">}</span>
<span class="special">}</span>
</pre>
<p>
          </p>
<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
<li class="listitem">
                The first one, <code class="computeroutput"><span class="identifier">show_segments</span><span class="special">()</span></code> shows the container content as
                it is implemented, in the compressed form.
              </li>
<li class="listitem">
                The second function <code class="computeroutput"><span class="identifier">show_matrix</span></code>
                shows the complete matrix of bits that is represented by the container.
              </li>
</ul></div>
</div>
<div class="section">
<div class="titlepage"><div><div><h5 class="title">
<a name="boost_icl.projects.large_bitset.implementation_of_a_large_bitset.large_bitset__private_implementation"></a><a class="link" href="projects.html#boost_icl.projects.large_bitset.implementation_of_a_large_bitset.large_bitset__private_implementation" title="large_bitset: Private implementation">large_bitset:
          Private implementation</a>
</h5></div></div></div>
<p>
            In order to implement operations like the addition of an element say
            <code class="computeroutput"><span class="number">42</span></code> to the large bitset, we
            need to translate the <span class="emphasis"><em>value</em></span> to the <span class="emphasis"><em>position</em></span>
            of the associated <span class="bold"><strong>bit</strong></span> representing
            <code class="computeroutput"><span class="number">42</span></code> in the interval container
            of bitsets. As an example, suppose we use a
</p>
<pre class="programlisting"><span class="identifier">large_bitset</span><span class="special">&lt;</span><span class="identifier">nat</span><span class="special">,</span> <span class="identifier">mini</span><span class="special">::</span><span class="identifier">bits8</span><span class="special">&gt;</span> <span class="identifier">lbs</span><span class="special">;</span>
</pre>
<p>
            that carries small bitsets of 8 bits only. The first four interval of
            <code class="computeroutput"><span class="identifier">lbs</span></code> are assumed to be
            associated with some bitsets. Now we want to add the interval <code class="computeroutput"><span class="special">[</span><span class="identifier">a</span><span class="special">,</span><span class="identifier">b</span><span class="special">]==[</span><span class="number">5</span><span class="special">,</span><span class="number">27</span><span class="special">]</span></code>. This
            will result in the following situation:
</p>
<pre class="programlisting">   <span class="special">[</span><span class="number">0</span><span class="special">,</span><span class="number">1</span><span class="special">)-&gt;</span>   <span class="special">[</span><span class="number">1</span><span class="special">,</span><span class="number">2</span><span class="special">)-&gt;</span>   <span class="special">[</span><span class="number">2</span><span class="special">,</span><span class="number">3</span><span class="special">)-&gt;</span>   <span class="special">[</span><span class="number">3</span><span class="special">,</span><span class="number">4</span><span class="special">)-&gt;</span>
   <span class="special">[</span><span class="number">00101100</span><span class="special">][</span><span class="number">11001011</span><span class="special">][</span><span class="number">11101001</span><span class="special">][</span><span class="number">11100000</span><span class="special">]</span>
<span class="special">+</span>       <span class="special">[</span><span class="number">111</span>  <span class="number">11111111</span>  <span class="number">11111111</span>  <span class="number">1111</span><span class="special">]</span>      <span class="special">[</span><span class="number">5</span><span class="special">,</span><span class="number">27</span><span class="special">]</span> <span class="identifier">as</span> <span class="identifier">bitset</span>
         <span class="identifier">a</span>                           <span class="identifier">b</span>

<span class="special">=&gt;</span> <span class="special">[</span><span class="number">0</span><span class="special">,</span><span class="number">1</span><span class="special">)-&gt;</span>   <span class="special">[</span><span class="number">1</span><span class="special">,</span><span class="number">3</span><span class="special">)-&gt;</span>   <span class="special">[</span><span class="number">3</span><span class="special">,</span><span class="number">4</span><span class="special">)-&gt;</span>
   <span class="special">[</span><span class="number">00101111</span><span class="special">][</span><span class="number">11111111</span><span class="special">][</span><span class="number">11110000</span><span class="special">]</span>
</pre>
<p>
            So we have to convert values 5 and 27 into a part that points to the
            interval and a part that refers to the position within the interval,
            which is done by a <span class="emphasis"><em>division</em></span> and a <span class="emphasis"><em>modulo</em></span>
            computation. (In order to have a consistent representation of the bitsequences
            across the containers, within this project, bitsets are denoted with
            the <span class="emphasis"><em><span class="bold"><strong>least significant bit on the left!</strong></span></em></span>)
          </p>
<p>
</p>
<pre class="programlisting"><span class="identifier">A</span> <span class="special">=</span> <span class="identifier">a</span><span class="special">/</span><span class="number">8</span> <span class="special">=</span>  <span class="number">5</span><span class="special">/</span><span class="number">8</span> <span class="special">=</span> <span class="number">0</span> <span class="comment">// refers to interval </span>
<span class="identifier">B</span> <span class="special">=</span> <span class="identifier">b</span><span class="special">/</span><span class="number">8</span> <span class="special">=</span> <span class="number">27</span><span class="special">/</span><span class="number">8</span> <span class="special">=</span> <span class="number">3</span>
<span class="identifier">R</span> <span class="special">=</span> <span class="identifier">a</span><span class="special">%</span><span class="number">8</span> <span class="special">=</span>  <span class="number">5</span><span class="special">%</span><span class="number">8</span> <span class="special">=</span> <span class="number">5</span> <span class="comment">// refers to the position in the associated bitset.</span>
<span class="identifier">S</span> <span class="special">=</span> <span class="identifier">b</span><span class="special">%</span><span class="number">8</span> <span class="special">=</span> <span class="number">27</span><span class="special">%</span><span class="number">8</span> <span class="special">=</span> <span class="number">3</span>
</pre>
<p>
          </p>
<p>
            All <span class="emphasis"><em>division</em></span> and <span class="emphasis"><em>modulo operations</em></span>
            needed here are always done using a divisor <code class="computeroutput"><span class="identifier">d</span></code>
            that is a power of <code class="computeroutput"><span class="number">2</span></code>: <code class="computeroutput"><span class="identifier">d</span> <span class="special">=</span> <span class="number">2</span><span class="special">^</span><span class="identifier">x</span></code>.
            Therefore division and modulo can be expressed by bitset operations.
            The constants needed for those bitset computations are defined here:
          </p>
<p>
</p>
<pre class="programlisting"><span class="keyword">private</span><span class="special">:</span>                                      <span class="comment">// Example value</span>
    <span class="keyword">static</span> <span class="keyword">const</span> <span class="identifier">word_type</span>                    <span class="comment">//   8-bit case  </span>
        <span class="identifier">digits</span>  <span class="special">=</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span>         <span class="comment">// --------------------------------------------------------------</span>
                  <span class="special">&lt;</span><span class="identifier">word_type</span><span class="special">&gt;::</span><span class="identifier">digits</span>       <span class="special">,</span> <span class="comment">//   8           Size of the associated bitsets </span>
        <span class="identifier">divisor</span> <span class="special">=</span> <span class="identifier">digits</span>                    <span class="special">,</span> <span class="comment">//   8           Divisor to find intervals for values</span>
        <span class="identifier">last</span>    <span class="special">=</span> <span class="identifier">digits</span><span class="special">-</span><span class="number">1</span>                  <span class="special">,</span> <span class="comment">//   7           Last bit (0 based)</span>
        <span class="identifier">shift</span>   <span class="special">=</span> <span class="identifier">log2_</span><span class="special">&lt;</span><span class="identifier">divisor</span><span class="special">&gt;::</span><span class="identifier">value</span>     <span class="special">,</span> <span class="comment">//   3           To express the division as bit shift</span>
        <span class="identifier">w1</span>      <span class="special">=</span> <span class="keyword">static_cast</span><span class="special">&lt;</span><span class="identifier">word_type</span><span class="special">&gt;(</span><span class="number">1</span><span class="special">)</span> <span class="special">,</span> <span class="comment">//               Helps to avoid static_casts for long long</span>
        <span class="identifier">mask</span>    <span class="special">=</span> <span class="identifier">divisor</span> <span class="special">-</span> <span class="identifier">w1</span>              <span class="special">,</span> <span class="comment">//   7=11100000  Helps to express the modulo operation as bit_and</span>
        <span class="identifier">all</span>     <span class="special">=</span> <span class="special">~</span><span class="keyword">static_cast</span><span class="special">&lt;</span><span class="identifier">word_type</span><span class="special">&gt;(</span><span class="number">0</span><span class="special">),</span> <span class="comment">// 255=11111111  Helps to express a complete associated bitset</span>
        <span class="identifier">top</span>     <span class="special">=</span> <span class="identifier">w1</span> <span class="special">&lt;&lt;</span> <span class="special">(</span><span class="identifier">digits</span><span class="special">-</span><span class="identifier">w1</span><span class="special">)</span>      <span class="special">;</span>    <span class="comment">// 128=00000001  Value of the most significant bit of associated bitsets</span>
                                              <span class="comment">//            !&gt; Note: Most signigicant bit on the right.</span>
</pre>
<p>
          </p>
<p>
            Looking at the example again, we can see that we have to identify the
            positions of the beginning and ending of the interval [5,27] that is
            to insert, and then <span class="emphasis"><em><span class="bold"><strong>subdivide</strong></span></em></span>
            that range of bitsets into three partitions.
          </p>
<div class="orderedlist"><ol class="orderedlist" type="1">
<li class="listitem">
                The bitset where the interval starts.
              </li>
<li class="listitem">
                the bitset where the interval ends
              </li>
<li class="listitem">
                The bitsets that are completely overlapped by the interval
              </li>
</ol></div>
<p>
</p>
<pre class="programlisting"><span class="identifier">combine</span> <span class="identifier">interval</span> <span class="special">[</span><span class="number">5</span><span class="special">,</span><span class="number">27</span><span class="special">]</span> <span class="identifier">to</span> <span class="identifier">large_bitset</span> <span class="identifier">lbs</span> <span class="identifier">w</span><span class="special">.</span><span class="identifier">r</span><span class="special">.</span><span class="identifier">t</span><span class="special">.</span> <span class="identifier">some</span> <span class="identifier">operation</span> <span class="identifier">o</span>

   <span class="special">[</span><span class="number">0</span><span class="special">,</span><span class="number">1</span><span class="special">)-&gt;</span>   <span class="special">[</span><span class="number">1</span><span class="special">,</span><span class="number">2</span><span class="special">)-&gt;</span>   <span class="special">[</span><span class="number">2</span><span class="special">,</span><span class="number">3</span><span class="special">)-&gt;</span>   <span class="special">[</span><span class="number">3</span><span class="special">,</span><span class="number">4</span><span class="special">)-&gt;</span>
   <span class="special">[</span><span class="number">00101100</span><span class="special">][</span><span class="number">11001011</span><span class="special">][</span><span class="number">11101001</span><span class="special">][</span><span class="number">11100000</span><span class="special">]</span>
<span class="identifier">o</span>       <span class="special">[</span><span class="number">111</span>  <span class="number">11111111</span>  <span class="number">11111111</span>  <span class="number">1111</span><span class="special">]</span>
         <span class="identifier">a</span>                           <span class="identifier">b</span>
<span class="identifier">subdivide</span><span class="special">:</span>
   <span class="special">[</span><span class="identifier">first</span><span class="special">!</span>  <span class="special">][</span><span class="identifier">mid_1</span><span class="special">]</span> <span class="special">.</span> <span class="special">.</span> <span class="special">.[</span><span class="identifier">mid_n</span><span class="special">][</span>   <span class="special">!</span><span class="identifier">last</span><span class="special">]</span>
   <span class="special">[</span><span class="number">00000111</span><span class="special">][</span><span class="number">1.</span><span class="special">..</span><span class="number">1</span><span class="special">]</span> <span class="special">.</span> <span class="special">.</span> <span class="special">.[</span><span class="number">1.</span><span class="special">..</span><span class="number">1</span><span class="special">][</span><span class="number">11110000</span><span class="special">]</span>
</pre>
<p>
          </p>
<p>
            After subdividing, we perform the operation <code class="computeroutput"><span class="identifier">o</span></code>
            as follows:
          </p>
<div class="orderedlist"><ol class="orderedlist" type="1">
<li class="listitem">
                For the first bitset: Set all bits from ther starting bit (<code class="computeroutput"><span class="special">!</span></code>) to the end of the bitset to <code class="computeroutput"><span class="number">1</span></code>. All other bits are <code class="computeroutput"><span class="number">0</span></code>. Then perform operation <code class="computeroutput"><span class="identifier">o</span></code>: <code class="computeroutput"><span class="identifier">_map</span>
                <span class="identifier">o</span><span class="special">=</span>
                <span class="special">([</span><span class="number">0</span><span class="special">,</span><span class="number">1</span><span class="special">)-&gt;</span><span class="number">00000111</span><span class="special">)</span></code>
              </li>
<li class="listitem">
                For the last bitset: Set all bits from the beginning of the bitset
                to the ending bit (<code class="computeroutput"><span class="special">!</span></code>)
                to <code class="computeroutput"><span class="number">1</span></code>. All other bits
                are <code class="computeroutput"><span class="number">0</span></code>. Then perform operation
                <code class="computeroutput"><span class="identifier">o</span></code>: <code class="computeroutput"><span class="identifier">_map</span> <span class="identifier">o</span><span class="special">=</span> <span class="special">([</span><span class="number">3</span><span class="special">,</span><span class="number">4</span><span class="special">)-&gt;</span><span class="number">11110000</span><span class="special">)</span></code>
              </li>
<li class="listitem">
                For the range of bitsets in between the staring and ending one, perform
                operation <code class="computeroutput"><span class="identifier">o</span></code>: <code class="computeroutput"><span class="identifier">_map</span> <span class="identifier">o</span><span class="special">=</span> <span class="special">([</span><span class="number">1</span><span class="special">,</span><span class="number">3</span><span class="special">)-&gt;</span><span class="number">11111111</span><span class="special">)</span></code>
              </li>
</ol></div>
<p>
            The algorithm, that has been outlined and illustrated by the example,
            is implemented by the private member function <code class="computeroutput"><span class="identifier">segment_apply</span></code>.
            To make the combiner operation a variable in this algorithm, we use a
            <span class="emphasis"><em>pointer to member function type</em></span>
          </p>
<p>
</p>
<pre class="programlisting"><span class="keyword">typedef</span> <span class="keyword">void</span> <span class="special">(</span><span class="identifier">large_bitset</span><span class="special">::*</span><span class="identifier">segment_combiner</span><span class="special">)(</span><span class="identifier">element_type</span><span class="special">,</span> <span class="identifier">element_type</span><span class="special">,</span> <span class="identifier">bitset_type</span><span class="special">);</span>
</pre>
<p>
          </p>
<p>
            as first function argument. We will pass member functions <code class="computeroutput"><span class="identifier">combine_</span></code> here,
</p>
<pre class="programlisting"><span class="identifier">combine_</span><span class="special">(</span><span class="identifier">first_of_interval</span><span class="special">,</span> <span class="identifier">end_of_interval</span><span class="special">,</span> <span class="identifier">some_bitset</span><span class="special">);</span>
</pre>
<p>
            that take the beginning and ending of an interval and a bitset and combine
            them to the implementing <code class="computeroutput"><span class="identifier">interval_bitmap_type</span>
            <span class="identifier">_map</span></code>. Here are these functions:
          </p>
<p>
</p>
<pre class="programlisting"><span class="keyword">void</span>       <span class="identifier">add_</span><span class="special">(</span><span class="identifier">DomainT</span> <span class="identifier">lo</span><span class="special">,</span> <span class="identifier">DomainT</span> <span class="identifier">up</span><span class="special">,</span> <span class="identifier">BitSetT</span> <span class="identifier">bits</span><span class="special">){</span><span class="identifier">_map</span> <span class="special">+=</span> <span class="identifier">value_type</span><span class="special">(</span><span class="identifier">interval_type</span><span class="special">::</span><span class="identifier">right_open</span><span class="special">(</span><span class="identifier">lo</span><span class="special">,</span><span class="identifier">up</span><span class="special">),</span> <span class="identifier">bits</span><span class="special">);}</span>
<span class="keyword">void</span>  <span class="identifier">subtract_</span><span class="special">(</span><span class="identifier">DomainT</span> <span class="identifier">lo</span><span class="special">,</span> <span class="identifier">DomainT</span> <span class="identifier">up</span><span class="special">,</span> <span class="identifier">BitSetT</span> <span class="identifier">bits</span><span class="special">){</span><span class="identifier">_map</span> <span class="special">-=</span> <span class="identifier">value_type</span><span class="special">(</span><span class="identifier">interval_type</span><span class="special">::</span><span class="identifier">right_open</span><span class="special">(</span><span class="identifier">lo</span><span class="special">,</span><span class="identifier">up</span><span class="special">),</span> <span class="identifier">bits</span><span class="special">);}</span>
<span class="keyword">void</span> <span class="identifier">intersect_</span><span class="special">(</span><span class="identifier">DomainT</span> <span class="identifier">lo</span><span class="special">,</span> <span class="identifier">DomainT</span> <span class="identifier">up</span><span class="special">,</span> <span class="identifier">BitSetT</span> <span class="identifier">bits</span><span class="special">){</span><span class="identifier">_map</span> <span class="special">&amp;=</span> <span class="identifier">value_type</span><span class="special">(</span><span class="identifier">interval_type</span><span class="special">::</span><span class="identifier">right_open</span><span class="special">(</span><span class="identifier">lo</span><span class="special">,</span><span class="identifier">up</span><span class="special">),</span> <span class="identifier">bits</span><span class="special">);}</span>
<span class="keyword">void</span>      <span class="identifier">flip_</span><span class="special">(</span><span class="identifier">DomainT</span> <span class="identifier">lo</span><span class="special">,</span> <span class="identifier">DomainT</span> <span class="identifier">up</span><span class="special">,</span> <span class="identifier">BitSetT</span> <span class="identifier">bits</span><span class="special">){</span><span class="identifier">_map</span> <span class="special">^=</span> <span class="identifier">value_type</span><span class="special">(</span><span class="identifier">interval_type</span><span class="special">::</span><span class="identifier">right_open</span><span class="special">(</span><span class="identifier">lo</span><span class="special">,</span><span class="identifier">up</span><span class="special">),</span> <span class="identifier">bits</span><span class="special">);}</span>
</pre>
<p>
          </p>
<p>
            Finally we can code function <code class="computeroutput"><span class="identifier">segment_apply</span></code>,
            that does the partitioning and subsequent combining:
          </p>
<p>
</p>
<pre class="programlisting"><span class="identifier">large_bitset</span><span class="special">&amp;</span> <span class="identifier">segment_apply</span><span class="special">(</span><span class="identifier">segment_combiner</span> <span class="identifier">combine</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">interval_type</span><span class="special">&amp;</span> <span class="identifier">operand</span><span class="special">)</span>
<span class="special">{</span>
    <span class="keyword">using</span> <span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">;</span>
    <span class="keyword">if</span><span class="special">(</span><span class="identifier">icl</span><span class="special">::</span><span class="identifier">is_empty</span><span class="special">(</span><span class="identifier">operand</span><span class="special">))</span>
        <span class="keyword">return</span> <span class="special">*</span><span class="keyword">this</span><span class="special">;</span>
                                                        <span class="comment">// same as</span>
    <span class="identifier">element_type</span>   <span class="identifier">base</span> <span class="special">=</span> <span class="identifier">icl</span><span class="special">::</span><span class="identifier">first</span><span class="special">(</span><span class="identifier">operand</span><span class="special">)</span> <span class="special">&gt;&gt;</span> <span class="identifier">shift</span><span class="special">,</span> <span class="comment">// icl::first(operand) / divisor</span>
                   <span class="identifier">ceil</span> <span class="special">=</span> <span class="identifier">icl</span><span class="special">::</span><span class="identifier">last</span> <span class="special">(</span><span class="identifier">operand</span><span class="special">)</span> <span class="special">&gt;&gt;</span> <span class="identifier">shift</span><span class="special">;</span> <span class="comment">// icl::last (operand) / divisor</span>
    <span class="identifier">word_type</span> <span class="identifier">base_rest</span> <span class="special">=</span> <span class="identifier">icl</span><span class="special">::</span><span class="identifier">first</span><span class="special">(</span><span class="identifier">operand</span><span class="special">)</span> <span class="special">&amp;</span>  <span class="identifier">mask</span> <span class="special">,</span> <span class="comment">// icl::first(operand) % divisor</span>
              <span class="identifier">ceil_rest</span> <span class="special">=</span> <span class="identifier">icl</span><span class="special">::</span><span class="identifier">last</span> <span class="special">(</span><span class="identifier">operand</span><span class="special">)</span> <span class="special">&amp;</span>  <span class="identifier">mask</span> <span class="special">;</span> <span class="comment">// icl::last (operand) % divisor  </span>

    <span class="keyword">if</span><span class="special">(</span><span class="identifier">base</span> <span class="special">==</span> <span class="identifier">ceil</span><span class="special">)</span> <span class="comment">// [first, last] are within one bitset (chunk)</span>
        <span class="special">(</span><span class="keyword">this</span><span class="special">-&gt;*</span><span class="identifier">combine</span><span class="special">)(</span><span class="identifier">base</span><span class="special">,</span> <span class="identifier">base</span><span class="special">+</span><span class="number">1</span><span class="special">,</span> <span class="identifier">bitset_type</span><span class="special">(</span>  <span class="identifier">to_upper_from</span><span class="special">(</span><span class="identifier">base_rest</span><span class="special">)</span>
                                                   <span class="special">&amp;</span> <span class="identifier">from_lower_to</span><span class="special">(</span><span class="identifier">ceil_rest</span><span class="special">)));</span>
    <span class="keyword">else</span> <span class="comment">// [first, last] spread over more than one bitset (chunk)</span>
    <span class="special">{</span>
        <span class="identifier">element_type</span> <span class="identifier">mid_low</span> <span class="special">=</span> <span class="identifier">base_rest</span> <span class="special">==</span> <span class="number">0</span>   <span class="special">?</span> <span class="identifier">base</span>   <span class="special">:</span> <span class="identifier">base</span><span class="special">+</span><span class="number">1</span><span class="special">,</span> <span class="comment">// first element of mid part </span>
                     <span class="identifier">mid_up</span>  <span class="special">=</span> <span class="identifier">ceil_rest</span> <span class="special">==</span> <span class="identifier">all</span> <span class="special">?</span> <span class="identifier">ceil</span><span class="special">+</span><span class="number">1</span> <span class="special">:</span> <span class="identifier">ceil</span>  <span class="special">;</span> <span class="comment">// last  element of mid part</span>

        <span class="keyword">if</span><span class="special">(</span><span class="identifier">base_rest</span> <span class="special">&gt;</span> <span class="number">0</span><span class="special">)</span>    <span class="comment">// Bitset of base interval has to be filled from base_rest to last</span>
            <span class="special">(</span><span class="keyword">this</span><span class="special">-&gt;*</span><span class="identifier">combine</span><span class="special">)(</span><span class="identifier">base</span><span class="special">,</span> <span class="identifier">base</span><span class="special">+</span><span class="number">1</span><span class="special">,</span> <span class="identifier">bitset_type</span><span class="special">(</span><span class="identifier">to_upper_from</span><span class="special">(</span><span class="identifier">base_rest</span><span class="special">)));</span>
        <span class="keyword">if</span><span class="special">(</span><span class="identifier">ceil_rest</span> <span class="special">&lt;</span> <span class="identifier">all</span><span class="special">)</span>  <span class="comment">// Bitset of ceil interval has to be filled from first to ceil_rest</span>
            <span class="special">(</span><span class="keyword">this</span><span class="special">-&gt;*</span><span class="identifier">combine</span><span class="special">)(</span><span class="identifier">ceil</span><span class="special">,</span> <span class="identifier">ceil</span><span class="special">+</span><span class="number">1</span><span class="special">,</span> <span class="identifier">bitset_type</span><span class="special">(</span><span class="identifier">from_lower_to</span><span class="special">(</span><span class="identifier">ceil_rest</span><span class="special">)));</span>
        <span class="keyword">if</span><span class="special">(</span><span class="identifier">mid_low</span> <span class="special">&lt;</span> <span class="identifier">mid_up</span><span class="special">)</span> <span class="comment">// For the middle part all bits have to set.</span>
            <span class="special">(</span><span class="keyword">this</span><span class="special">-&gt;*</span><span class="identifier">combine</span><span class="special">)(</span><span class="identifier">mid_low</span><span class="special">,</span> <span class="identifier">mid_up</span><span class="special">,</span> <span class="identifier">bitset_type</span><span class="special">(</span><span class="identifier">all</span><span class="special">));</span>
    <span class="special">}</span>
    <span class="keyword">return</span> <span class="special">*</span><span class="keyword">this</span><span class="special">;</span>
<span class="special">}</span>
</pre>
<p>
          </p>
<p>
            The functions that help filling bitsets to and from a given bit are implemented
            here:
          </p>
<p>
</p>
<pre class="programlisting"><span class="keyword">static</span> <span class="identifier">word_type</span> <span class="identifier">from_lower_to</span><span class="special">(</span><span class="identifier">word_type</span> <span class="identifier">bit</span><span class="special">){</span><span class="keyword">return</span> <span class="identifier">bit</span><span class="special">==</span><span class="identifier">last</span> <span class="special">?</span> <span class="identifier">all</span> <span class="special">:</span> <span class="special">(</span><span class="identifier">w1</span><span class="special">&lt;&lt;(</span><span class="identifier">bit</span><span class="special">+</span><span class="identifier">w1</span><span class="special">))-</span><span class="identifier">w1</span><span class="special">;}</span>
<span class="keyword">static</span> <span class="identifier">word_type</span> <span class="identifier">to_upper_from</span><span class="special">(</span><span class="identifier">word_type</span> <span class="identifier">bit</span><span class="special">){</span><span class="keyword">return</span> <span class="identifier">bit</span><span class="special">==</span><span class="identifier">last</span> <span class="special">?</span> <span class="identifier">top</span> <span class="special">:</span> <span class="special">~((</span><span class="identifier">w1</span><span class="special">&lt;&lt;</span><span class="identifier">bit</span><span class="special">)-</span><span class="identifier">w1</span><span class="special">);</span> <span class="special">}</span>
</pre>
<p>
          </p>
<p>
            This completes the implementation of class template <code class="computeroutput"><span class="identifier">large_bitset</span></code>.
            Using only a small amount of mostly schematic code, we have been able
            to provide a pretty powerful, self compressing and generally usable set
            type for all integral domain types.
          </p>
</div>
</div>
</div>
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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>)
      </p>
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