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| <div class="titlepage"><div><div><h3 class="title"> |
| <a name="boost_multiprecision.tut.random"></a><a class="link" href="random.html" title="Generating Random Numbers">Generating Random Numbers</a> |
| </h3></div></div></div> |
| <p> |
| Random numbers are generated in conjunction with Boost.Random. However, since |
| Boost.Random is unaware of <a href="http://en.wikipedia.org/wiki/Arbitrary-precision_arithmetic" target="_top">arbitrary |
| precision</a> numbers, it's necessary to include the header: |
| </p> |
| <pre class="programlisting"><span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">multiprecision</span><span class="special">/</span><span class="identifier">random</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span> |
| </pre> |
| <p> |
| In order to act as a bridge between the two libraries. |
| </p> |
| <p> |
| Integers with <span class="emphasis"><em>N</em></span> random bits are generated using <code class="computeroutput"><span class="identifier">independent_bits_engine</span></code>: |
| </p> |
| <pre class="programlisting"><span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">multiprecision</span><span class="special">/</span><span class="identifier">gmp</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span> |
| <span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">multiprecision</span><span class="special">/</span><span class="identifier">random</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span> |
| |
| <span class="keyword">int</span> <span class="identifier">main</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="identifier">multiprecision</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="identifier">random</span><span class="special">;</span> |
| |
| <span class="comment">//</span> |
| <span class="comment">// Declare our random number generator type, the underlying generator</span> |
| <span class="comment">// is the Mersenne twister mt19937 engine, and 256 bits are generated:</span> |
| <span class="comment">//</span> |
| <span class="keyword">typedef</span> <span class="identifier">independent_bits_engine</span><span class="special"><</span><span class="identifier">mt19937</span><span class="special">,</span> <span class="number">256</span><span class="special">,</span> <span class="identifier">mpz_int</span><span class="special">></span> <span class="identifier">generator_type</span><span class="special">;</span> |
| <span class="identifier">generator_type</span> <span class="identifier">gen</span><span class="special">;</span> |
| <span class="comment">//</span> |
| <span class="comment">// Generate some values:</span> |
| <span class="comment">//</span> |
| <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">hex</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">showbase</span><span class="special">;</span> |
| <span class="keyword">for</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">i</span> <span class="special">=</span> <span class="number">0</span><span class="special">;</span> <span class="identifier">i</span> <span class="special"><</span> <span class="number">10</span><span class="special">;</span> <span class="special">++</span><span class="identifier">i</span><span class="special">)</span> |
| <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="identifier">gen</span><span class="special">()</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span> |
| <span class="keyword">return</span> <span class="number">0</span><span class="special">;</span> |
| <span class="special">}</span> |
| </pre> |
| <p> |
| Alternatively we can generate integers in a given range using <code class="computeroutput"><span class="identifier">uniform_int_distribution</span></code>, this will invoke |
| the underlying engine multiple times to build up the required number of bits |
| in the result: |
| </p> |
| <pre class="programlisting"><span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">multiprecision</span><span class="special">/</span><span class="identifier">gmp</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span> |
| <span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">multiprecision</span><span class="special">/</span><span class="identifier">random</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span> |
| |
| <span class="keyword">int</span> <span class="identifier">main</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="identifier">multiprecision</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="identifier">random</span><span class="special">;</span> |
| |
| <span class="comment">//</span> |
| <span class="comment">// Generate integers in a given range using uniform_int,</span> |
| <span class="comment">// the underlying generator is invoked multiple times</span> |
| <span class="comment">// to generate enough bits:</span> |
| <span class="comment">//</span> |
| <span class="identifier">mt19937</span> <span class="identifier">mt</span><span class="special">;</span> |
| <span class="identifier">uniform_int_distribution</span><span class="special"><</span><span class="identifier">mpz_int</span><span class="special">></span> <span class="identifier">ui</span><span class="special">(</span><span class="number">0</span><span class="special">,</span> <span class="identifier">mpz_int</span><span class="special">(</span><span class="number">1</span><span class="special">)</span> <span class="special"><<</span> <span class="number">256</span><span class="special">);</span> |
| <span class="comment">//</span> |
| <span class="comment">// Generate the numbers:</span> |
| <span class="comment">//</span> |
| <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">hex</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">showbase</span><span class="special">;</span> |
| <span class="keyword">for</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">i</span> <span class="special">=</span> <span class="number">0</span><span class="special">;</span> <span class="identifier">i</span> <span class="special"><</span> <span class="number">10</span><span class="special">;</span> <span class="special">++</span><span class="identifier">i</span><span class="special">)</span> |
| <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="identifier">ui</span><span class="special">(</span><span class="identifier">mt</span><span class="special">)</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span> |
| |
| <span class="keyword">return</span> <span class="number">0</span><span class="special">;</span> |
| <span class="special">}</span> |
| </pre> |
| <p> |
| Floating point values in [0,1) are generated using <code class="computeroutput"><span class="identifier">uniform_01</span></code>, |
| the trick here is to ensure that the underlying generator produces as many |
| random bits as there are digits in the floating point type. As above <code class="computeroutput"><span class="identifier">independent_bits_engine</span></code> can be used for |
| this purpose, note that we also have to convert decimal digits (in the floating |
| point type) to bits (in the random number generator): |
| </p> |
| <pre class="programlisting"><span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">multiprecision</span><span class="special">/</span><span class="identifier">gmp</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span> |
| <span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">multiprecision</span><span class="special">/</span><span class="identifier">random</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span> |
| |
| <span class="keyword">int</span> <span class="identifier">main</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="identifier">multiprecision</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="identifier">random</span><span class="special">;</span> |
| <span class="comment">//</span> |
| <span class="comment">// We need an underlying generator with at least as many bits as the</span> |
| <span class="comment">// floating point type to generate numbers in [0, 1) with all the bits</span> |
| <span class="comment">// in the floating point type randomly filled:</span> |
| <span class="comment">//</span> |
| <span class="identifier">uniform_01</span><span class="special"><</span><span class="identifier">mpf_float_50</span><span class="special">></span> <span class="identifier">uf</span><span class="special">;</span> |
| <span class="identifier">independent_bits_engine</span><span class="special"><</span><span class="identifier">mt19937</span><span class="special">,</span> <span class="number">50L</span><span class="special">*</span><span class="number">1000L</span><span class="special">/</span><span class="number">301L</span><span class="special">,</span> <span class="identifier">mpz_int</span><span class="special">></span> <span class="identifier">gen</span><span class="special">;</span> |
| <span class="comment">//</span> |
| <span class="comment">// Generate the values:</span> |
| <span class="comment">//</span> |
| <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">setprecision</span><span class="special">(</span><span class="number">50</span><span class="special">);</span> |
| <span class="keyword">for</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">i</span> <span class="special">=</span> <span class="number">0</span><span class="special">;</span> <span class="identifier">i</span> <span class="special"><</span> <span class="number">20</span><span class="special">;</span> <span class="special">++</span><span class="identifier">i</span><span class="special">)</span> |
| <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="identifier">uf</span><span class="special">(</span><span class="identifier">gen</span><span class="special">)</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span> |
| <span class="keyword">return</span> <span class="number">0</span><span class="special">;</span> |
| <span class="special">}</span> |
| </pre> |
| <p> |
| Finally, we can modify the above example to produce numbers distributed according |
| to some distribution: |
| </p> |
| <pre class="programlisting"><span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">multiprecision</span><span class="special">/</span><span class="identifier">gmp</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span> |
| <span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">multiprecision</span><span class="special">/</span><span class="identifier">random</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span> |
| |
| <span class="keyword">int</span> <span class="identifier">main</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="identifier">multiprecision</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="identifier">random</span><span class="special">;</span> |
| <span class="comment">//</span> |
| <span class="comment">// We can repeat the above example, with other distributions:</span> |
| <span class="comment">//</span> |
| <span class="identifier">uniform_real_distribution</span><span class="special"><</span><span class="identifier">mpf_float_50</span><span class="special">></span> <span class="identifier">ur</span><span class="special">(-</span><span class="number">20</span><span class="special">,</span> <span class="number">20</span><span class="special">);</span> |
| <span class="identifier">gamma_distribution</span><span class="special"><</span><span class="identifier">mpf_float_50</span><span class="special">></span> <span class="identifier">gd</span><span class="special">(</span><span class="number">20</span><span class="special">);</span> |
| <span class="identifier">independent_bits_engine</span><span class="special"><</span><span class="identifier">mt19937</span><span class="special">,</span> <span class="number">50L</span><span class="special">*</span><span class="number">1000L</span><span class="special">/</span><span class="number">301L</span><span class="special">,</span> <span class="identifier">mpz_int</span><span class="special">></span> <span class="identifier">gen</span><span class="special">;</span> |
| <span class="comment">//</span> |
| <span class="comment">// Generate some values:</span> |
| <span class="comment">//</span> |
| <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">setprecision</span><span class="special">(</span><span class="number">50</span><span class="special">);</span> |
| <span class="keyword">for</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">i</span> <span class="special">=</span> <span class="number">0</span><span class="special">;</span> <span class="identifier">i</span> <span class="special"><</span> <span class="number">20</span><span class="special">;</span> <span class="special">++</span><span class="identifier">i</span><span class="special">)</span> |
| <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="identifier">ur</span><span class="special">(</span><span class="identifier">gen</span><span class="special">)</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span> |
| <span class="keyword">for</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">i</span> <span class="special">=</span> <span class="number">0</span><span class="special">;</span> <span class="identifier">i</span> <span class="special"><</span> <span class="number">20</span><span class="special">;</span> <span class="special">++</span><span class="identifier">i</span><span class="special">)</span> |
| <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="identifier">gd</span><span class="special">(</span><span class="identifier">gen</span><span class="special">)</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span> |
| <span class="keyword">return</span> <span class="number">0</span><span class="special">;</span> |
| <span class="special">}</span> |
| </pre> |
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| <td align="right"><div class="copyright-footer">Copyright © 2002-2013 John Maddock and Christopher Kormanyos<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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