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<div class="section">
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
<a name="math_toolkit.examples"></a><a class="link" href="examples.html" title="Examples">Examples</a>
</h2></div></div></div>
<h4>
<a name="math_toolkit.examples.h0"></a>
      <span class="phrase"><a name="math_toolkit.examples.je_lambda"></a></span><a class="link" href="examples.html#math_toolkit.examples.je_lambda">Jahnke-Emden-Lambda
      function</a>
    </h4>
<p>
      The following code uses <code class="computeroutput"><span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">cstdfloat</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span></code>
      in combination with <code class="computeroutput"><span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">special_functions</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span></code> to
      compute a simplified version of the <a href="http://mathworld.wolfram.com/LambdaFunction.html" target="_top">Jahnke-Emden-Lambda
      function</a>. Here, we specify a floating-point type with <span class="bold"><strong>exactly
      64 bits</strong></span> (i.e., <code class="computeroutput"><span class="identifier">float64_t</span></code>).
      If we were to use, for instance, built-in <code class="computeroutput"><span class="keyword">double</span></code>,
      then there would be no guarantee that the code would behave identically on
      all platforms. With <code class="computeroutput"><span class="identifier">float64_t</span></code>
      from <code class="computeroutput"><span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">cstdfloat</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span></code>,
      however, it is very likely to be identical.
    </p>
<p>
      Using <code class="computeroutput"><span class="identifier">float64_t</span></code>, we know that
      this code is as portable as possible and uses a floating-point type with approximately
      15 decimal digits of precision, regardless of the compiler or version or operating
      system.
    </p>
<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">cstdfloat</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span> <span class="comment">// For float_64_t, float128_t. Must be first include!</span>
<span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">cmath</span><span class="special">&gt;</span>  <span class="comment">// for pow function.</span>
<span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">special_functions</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span> <span class="comment">// For gamma function.</span>
</pre>
<pre class="programlisting"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">float64_t</span> <span class="identifier">jahnke_emden_lambda</span><span class="special">(</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">float64_t</span> <span class="identifier">v</span><span class="special">,</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">float64_t</span> <span class="identifier">x</span><span class="special">)</span>
<span class="special">{</span>
  <span class="keyword">const</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">float64_t</span> <span class="identifier">gamma_v_plus_one</span> <span class="special">=</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">tgamma</span><span class="special">(</span><span class="identifier">v</span> <span class="special">+</span> <span class="number">1</span><span class="special">);</span>
  <span class="keyword">const</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">float64_t</span> <span class="identifier">x_half_pow_v</span>     <span class="special">=</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">pow</span><span class="special">(</span><span class="identifier">x</span> <span class="special">/</span><span class="number">2</span><span class="special">,</span> <span class="identifier">v</span><span class="special">);</span>

  <span class="keyword">return</span> <span class="identifier">gamma_v_plus_one</span> <span class="special">*</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">cyl_bessel_j</span><span class="special">(</span><span class="identifier">x</span><span class="special">,</span> <span class="identifier">v</span><span class="special">)</span> <span class="special">/</span> <span class="identifier">x_half_pow_v</span><span class="special">;</span>
<span class="special">}</span>
</pre>
<p>
      Ensure that all possibly significant digits (17) including trailing zeros are
      shown.
    </p>
<pre class="programlisting"><span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span><span class="special">.</span><span class="identifier">precision</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">boost</span><span class="special">::</span><span class="identifier">float64_t</span><span class="special">&gt;::</span><span class="identifier">max_digits10</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">setf</span><span class="special">(</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">ios</span><span class="special">::</span><span class="identifier">showpoint</span><span class="special">);</span> <span class="comment">// Show trailing zeros.</span>

<span class="keyword">try</span>
<span class="special">{</span> <span class="comment">// Always use try'n'catch blocks to ensure any error messages are displayed.</span>

<span class="comment">// Evaluate and display an evaluation of the Jahnke-Emden lambda function:</span>
<span class="identifier">boost</span><span class="special">::</span><span class="identifier">float64_t</span> <span class="identifier">v</span> <span class="special">=</span> <span class="number">1.</span><span class="special">;</span>
<span class="identifier">boost</span><span class="special">::</span><span class="identifier">float64_t</span> <span class="identifier">x</span> <span class="special">=</span> <span class="number">1.</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">jahnke_emden_lambda</span><span class="special">(</span><span class="identifier">v</span><span class="special">,</span> <span class="identifier">x</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="comment">// 0.88010117148986700</span>
</pre>
<p>
      For details, see <a href="../../../example/cstdfloat_example.cpp" target="_top">cstdfloat_example.cpp</a>
      - a extensive example program.
    </p>
<h4>
<a name="math_toolkit.examples.h1"></a>
      <span class="phrase"><a name="math_toolkit.examples.normal_table"></a></span><a class="link" href="examples.html#math_toolkit.examples.normal_table">Normal
      distribution table</a>
    </h4>
<p>
      This example shows printing tables of a normal distribution's PDF and CDF,
      using <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span></code> implementation of normal distribution.
    </p>
<p>
      A function templated on floating-point type prints a table for a range of standard
      variate z values.
    </p>
<p>
      The example shows use of the specified-width typedefs to either use a specific
      width, or to use the maximum available on the platform, perhaps a high as 128-bit.
    </p>
<p>
      The number of digits displayed is controlled by the precision of the type,
      so there are no spurious insignificant decimal digits:
    </p>
<pre class="programlisting"><span class="identifier">float_32_t</span>    <span class="number">0</span>    <span class="number">0.39894228</span>
<span class="identifier">float_128_t</span>  <span class="number">0</span>    <span class="number">0.398942280401432702863218082711682655</span>
</pre>
<p>
      Some sample output for two different platforms is appended to the code at
      <a href="../../../example/normal_tables.cpp" target="_top">normal_tables.cpp</a>.
    </p>
<pre class="programlisting"><span class="preprocessor">#ifdef</span> <span class="identifier">BOOST_FLOAT32_C</span>
    <span class="identifier">normal_table</span><span class="special">&lt;</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">float32_t</span><span class="special">&gt;();</span> <span class="comment">// Usually type float</span>
<span class="preprocessor">#endif</span>
    <span class="identifier">normal_table</span><span class="special">&lt;</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">float64_t</span><span class="special">&gt;();</span> <span class="comment">// Usually type double. Assume that float64_t is always available.</span>
<span class="preprocessor">#ifdef</span> <span class="identifier">BOOST_FLOAT80_C</span>
    <span class="identifier">normal_table</span><span class="special">&lt;</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">float80_t</span><span class="special">&gt;();</span> <span class="comment">// Type long double on some X86 platforms.</span>
<span class="preprocessor">#endif</span>
<span class="preprocessor">#ifdef</span> <span class="identifier">BOOST_FLOAT128_C</span>
    <span class="identifier">normal_table</span><span class="special">&lt;</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">float128_t</span><span class="special">&gt;();</span> <span class="comment">// Type _Quad on some Intel and __float128 on some GCC platforms.</span>
<span class="preprocessor">#endif</span>
    <span class="identifier">normal_table</span><span class="special">&lt;</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">floatmax_t</span><span class="special">&gt;();</span>
</pre>
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