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<title>Generating Random Numbers</title>
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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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