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| <a name="boost.uniform_smallint"></a><div class="titlepage"></div> |
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| <h2><span class="refentrytitle">Class template uniform_smallint</span></h2> |
| <p>boost::uniform_smallint</p> |
| </div> |
| <h2 xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" class="refsynopsisdiv-title">Synopsis</h2> |
| <div xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" class="refsynopsisdiv"><pre class="synopsis"><span class="comment">// In header: <<a class="link" href="../boost_random/reference.html#header.boost.random.uniform_smallint_hpp" title="Header <boost/random/uniform_smallint.hpp>">boost/random/uniform_smallint.hpp</a>> |
| |
| </span><span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> IntType <span class="special">=</span> <span class="keyword">int</span><span class="special">></span> |
| <span class="keyword">class</span> <a class="link" href="uniform_smallint.html" title="Class template uniform_smallint">uniform_smallint</a> <span class="special">{</span> |
| <span class="keyword">public</span><span class="special">:</span> |
| <span class="comment">// types</span> |
| <span class="keyword">typedef</span> <span class="identifier">IntType</span> <a name="boost.uniform_smallint.input_type"></a><span class="identifier">input_type</span><span class="special">;</span> |
| <span class="keyword">typedef</span> <span class="identifier">IntType</span> <a name="boost.uniform_smallint.result_type"></a><span class="identifier">result_type</span><span class="special">;</span> |
| |
| <span class="comment">// <a class="link" href="uniform_smallint.html#boost.uniform_smallintconstruct-copy-destruct">construct/copy/destruct</a></span> |
| <a class="link" href="uniform_smallint.html#id1149808-bb"><span class="identifier">uniform_smallint</span></a><span class="special">(</span><span class="identifier">IntType</span> <span class="special">=</span> <span class="number">0</span><span class="special">,</span> <span class="identifier">IntType</span> <span class="special">=</span> <span class="number">9</span><span class="special">)</span><span class="special">;</span> |
| |
| <span class="comment">// <a class="link" href="uniform_smallint.html#id1149761-bb">public member functions</a></span> |
| <span class="identifier">result_type</span> <a class="link" href="uniform_smallint.html#id1149765-bb"><span class="identifier">min</span></a><span class="special">(</span><span class="special">)</span> <span class="keyword">const</span><span class="special">;</span> |
| <span class="identifier">result_type</span> <a class="link" href="uniform_smallint.html#id1149773-bb"><span class="identifier">max</span></a><span class="special">(</span><span class="special">)</span> <span class="keyword">const</span><span class="special">;</span> |
| <span class="keyword">void</span> <a class="link" href="uniform_smallint.html#id1149780-bb"><span class="identifier">reset</span></a><span class="special">(</span><span class="special">)</span><span class="special">;</span> |
| <span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> Engine<span class="special">></span> <span class="identifier">result_type</span> <a class="link" href="uniform_smallint.html#id1149788-bb"><span class="keyword">operator</span><span class="special">(</span><span class="special">)</span></a><span class="special">(</span><span class="identifier">Engine</span> <span class="special">&</span><span class="special">)</span><span class="special">;</span> |
| <span class="special">}</span><span class="special">;</span></pre></div> |
| <div class="refsect1"> |
| <a name="id2515052"></a><h2>Description</h2> |
| <p>The distribution function uniform_smallint models a <a class="link" href="../boost_random/reference.html#boost_random.reference.concepts.random_distribution" title="Random Distribution">random distribution</a> . On each invocation, it returns a random integer value uniformly distributed in the set of integer numbers {min, min+1, min+2, ..., max}. It assumes that the desired range (max-min+1) is small compared to the range of the underlying source of random numbers and thus makes no attempt to limit quantization errors.</p> |
| <p>Let r<sub>out</sub>=(max-min+1) the desired range of integer numbers, and let r<sub>base</sub> be the range of the underlying source of random numbers. Then, for the uniform distribution, the theoretical probability for any number i in the range r<sub>out</sub> will be p<sub>out</sub>(i) = 1/r<sub>out</sub>. Likewise, assume a uniform distribution on r<sub>base</sub> for the underlying source of random numbers, i.e. p<sub>base</sub>(i) = 1/r<sub>base</sub>. Let p<sub>out_s</sub>(i) denote the random distribution generated by <code class="computeroutput">uniform_smallint</code>. Then the sum over all i in r<sub>out</sub> of (p<sub>out_s</sub>(i)/p<sub>out</sub>(i) - 1)<sup>2</sup> shall not exceed r<sub>out</sub>/r<sub>base</sub><sup>2</sup> (r<sub>base</sub> mod r<sub>out</sub>)(r<sub>out</sub> - r<sub>base</sub> mod r<sub>out</sub>).</p> |
| <p>The template parameter IntType shall denote an integer-like value type.</p> |
| <p>Note: The property above is the square sum of the relative differences in probabilities between the desired uniform distribution p<sub>out</sub>(i) and the generated distribution p<sub>out_s</sub>(i). The property can be fulfilled with the calculation (base_rng mod r<sub>out</sub>), as follows: Let r = r<sub>base</sub> mod r<sub>out</sub>. The base distribution on r<sub>base</sub> is folded onto the range r<sub>out</sub>. The numbers i < r have assigned (r<sub>base</sub> div r<sub>out</sub>)+1 numbers of the base distribution, the rest has only (r<sub>base</sub> div r<sub>out</sub>). Therefore, p<sub>out_s</sub>(i) = ((r<sub>base</sub> div r<sub>out</sub>)+1) / r<sub>base</sub> for i < r and p<sub>out_s</sub>(i) = (r<sub>base</sub> div r<sub>out</sub>)/r<sub>base</sub> otherwise. Substituting this in the above sum formula leads to the desired result.</p> |
| <p>Note: The upper bound for (r<sub>base</sub> mod r<sub>out</sub>) (r<sub>out</sub> - r<sub>base</sub> mod r<sub>out</sub>) is r<sub>out</sub><sup>2</sup>/4. Regarding the upper bound for the square sum of the relative quantization error of r<sub>out</sub><sup>3</sup>/(4*r<sub>base</sub><sup>2</sup>), it seems wise to either choose r<sub>base</sub> so that r<sub>base</sub> > 10*r<sub>out</sub><sup>2</sup> or ensure that r<sub>base</sub> is divisible by r<sub>out</sub>. </p> |
| <div class="refsect2"> |
| <a name="id2515305"></a><h3> |
| <a name="boost.uniform_smallintconstruct-copy-destruct"></a><code class="computeroutput">uniform_smallint</code> |
| public |
| construct/copy/destruct</h3> |
| <div class="orderedlist"><ol class="orderedlist" type="1"><li class="listitem"> |
| <pre class="literallayout"><a name="id1149808-bb"></a><span class="identifier">uniform_smallint</span><span class="special">(</span><span class="identifier">IntType</span> min_arg <span class="special">=</span> <span class="number">0</span><span class="special">,</span> <span class="identifier">IntType</span> max_arg <span class="special">=</span> <span class="number">9</span><span class="special">)</span><span class="special">;</span></pre> |
| <p>Constructs a <code class="computeroutput">uniform_smallint</code>. <code class="computeroutput">min</code> and <code class="computeroutput">max</code> are the lower and upper bounds of the output range, respectively. </p> |
| </li></ol></div> |
| </div> |
| <div class="refsect2"> |
| <a name="id2515411"></a><h3> |
| <a name="id1149761-bb"></a><code class="computeroutput">uniform_smallint</code> public member functions</h3> |
| <div class="orderedlist"><ol class="orderedlist" type="1"> |
| <li class="listitem"><pre class="literallayout"><span class="identifier">result_type</span> <a name="id1149765-bb"></a><span class="identifier">min</span><span class="special">(</span><span class="special">)</span> <span class="keyword">const</span><span class="special">;</span></pre></li> |
| <li class="listitem"><pre class="literallayout"><span class="identifier">result_type</span> <a name="id1149773-bb"></a><span class="identifier">max</span><span class="special">(</span><span class="special">)</span> <span class="keyword">const</span><span class="special">;</span></pre></li> |
| <li class="listitem"><pre class="literallayout"><span class="keyword">void</span> <a name="id1149780-bb"></a><span class="identifier">reset</span><span class="special">(</span><span class="special">)</span><span class="special">;</span></pre></li> |
| <li class="listitem"><pre class="literallayout"><span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> Engine<span class="special">></span> <span class="identifier">result_type</span> <a name="id1149788-bb"></a><span class="keyword">operator</span><span class="special">(</span><span class="special">)</span><span class="special">(</span><span class="identifier">Engine</span> <span class="special">&</span> eng<span class="special">)</span><span class="special">;</span></pre></li> |
| </ol></div> |
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| <td align="right"><div class="copyright-footer">Copyright © 2000 -2005 Jens Maurer, 2009 Steven Watanabe<p> |
| Distributed under the Boost Software License, Version 1.0. (See accompanying |
| file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) |
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