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  26 <div class="titlepage"><div><div><h2 class="title" style="clear: both">
  27 <a name="math_toolkit.examples"></a><a class="link" href="examples.html" title="Examples">Examples</a>
  28 </h2></div></div></div>
  29 <h4>
  30 <a name="math_toolkit.examples.h0"></a>
  31       <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
  32       function</a>
  33     </h4>
  34 <p>
  35       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>
  36       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
  37       compute a simplified version of the <a href="http://mathworld.wolfram.com/LambdaFunction.html" target="_top">Jahnke-Emden-Lambda
  38       function</a>. Here, we specify a floating-point type with <span class="bold"><strong>exactly
  39       64 bits</strong></span> (i.e., <code class="computeroutput"><span class="identifier">float64_t</span></code>).
  40       If we were to use, for instance, built-in <code class="computeroutput"><span class="keyword">double</span></code>,
  41       then there would be no guarantee that the code would behave identically on
  42       all platforms. With <code class="computeroutput"><span class="identifier">float64_t</span></code>
  43       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>,
  44       however, it is very likely to be identical.
  45     </p>
  46 <p>
  47       Using <code class="computeroutput"><span class="identifier">float64_t</span></code>, we know that
  48       this code is as portable as possible and uses a floating-point type with approximately
  49       15 decimal digits of precision, regardless of the compiler or version or operating
  50       system.
  51     </p>
  52 <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>
  53 <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>
  54 <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>
  55 </pre>
  56 <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>
  57 <span class="special">{</span>
  58   <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>
  59   <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>
  60
  61   <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>
  62 <span class="special">}</span>
  63 </pre>
  64 <p>
  65       Ensure that all possibly significant digits (17) including trailing zeros are
  66       shown.
  67     </p>
  68 <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>
  69 <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>
  70
  71 <span class="keyword">try</span>
  72 <span class="special">{</span> <span class="comment">// Always use try'n'catch blocks to ensure any error messages are displayed.</span>
  73
  74 <span class="comment">// Evaluate and display an evaluation of the Jahnke-Emden lambda function:</span>
  75 <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>
  76 <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>
  77 <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>
  78 </pre>
  79 <p>
  80       For details, see <a href="../../../example/cstdfloat_example.cpp" target="_top">cstdfloat_example.cpp</a>
  81       - a extensive example program.
  82     </p>
  83 <h4>
  84 <a name="math_toolkit.examples.h1"></a>
  85       <span class="phrase"><a name="math_toolkit.examples.normal_table"></a></span><a class="link" href="examples.html#math_toolkit.examples.normal_table">Normal
  86       distribution table</a>
  87     </h4>
  88 <p>
  89       This example shows printing tables of a normal distribution's PDF and CDF,
  90       using <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span></code> implementation of normal distribution.
  91     </p>
  92 <p>
  93       A function templated on floating-point type prints a table for a range of standard
  94       variate z values.
  95     </p>
  96 <p>
  97       The example shows use of the specified-width typedefs to either use a specific
  98       width, or to use the maximum available on the platform, perhaps a high as 128-bit.
  99     </p>
 100 <p>
 101       The number of digits displayed is controlled by the precision of the type,
 102       so there are no spurious insignificant decimal digits:
 103     </p>
 104 <pre class="programlisting"><span class="identifier">float_32_t</span>    <span class="number">0</span>    <span class="number">0.39894228</span>
 105 <span class="identifier">float_128_t</span>  <span class="number">0</span>    <span class="number">0.398942280401432702863218082711682655</span>
 106 </pre>
 107 <p>
 108       Some sample output for two different platforms is appended to the code at
 109       <a href="../../../example/normal_tables.cpp" target="_top">normal_tables.cpp</a>.
 110     </p>
 111 <pre class="programlisting"><span class="preprocessor">#ifdef</span> <span class="identifier">BOOST_FLOAT32_C</span>
 112     <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>
 113 <span class="preprocessor">#endif</span>
 114     <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">// Uusually type double. Assume that float64_t is always available.</span>
 115 <span class="preprocessor">#ifdef</span> <span class="identifier">BOOST_FLOAT80_C</span>
 116     <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>
 117 <span class="preprocessor">#endif</span>
 118 <span class="preprocessor">#ifdef</span> <span class="identifier">BOOST_FLOAT128_C</span>
 119     <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>
 120 <span class="preprocessor">#endif</span>
 121     <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>
 122 </pre>
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 126 <td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014 Nikhar Agrawal,
 127       Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert
 128       Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam Sewani,
 129       Benjamin Sobotta, Thijs van den Berg, Daryle Walker and Xiaogang Zhang<p>
 130         Distributed under the Boost Software License, Version 1.0. (See accompanying
 131         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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