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<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"><</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">></span></code>
in combination with <code class="computeroutput"><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">special_functions</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></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"><</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">></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"><</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">></span> <span class="comment">// For float_64_t. Must be first include!</span>
<span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">cmath</span><span class="special">></span> <span class="comment">// for pow function. </span>
<span class="preprocessor">#include</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">special_functions</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></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"><</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">float64_t</span><span class="special">>::</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"><<</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"><<</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> implmentation of normal.
</p>
<p>
A function templated on floating-point type prints a table for a range of 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"><</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">float32_t</span><span class="special">>();</span>
<span class="preprocessor">#endif</span>
<span class="identifier">normal_table</span><span class="special"><</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">float64_t</span><span class="special">>();</span> <span class="comment">// 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"><</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">float80_t</span><span class="special">>();</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"><</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">float128_t</span><span class="special">>();</span>
<span class="preprocessor">#endif</span>
<span class="identifier">normal_table</span><span class="special"><</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">floatmax_t</span><span class="special">>();</span>
</pre>
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<td align="right"><div class="copyright-footer">Copyright © 2006-2010, 2012-2014 Nikhar Agrawal,
Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert
Holin, Bruno Lalande, John Maddock, Johan Råde, Gautam Sewani, Benjamin Sobotta,
Thijs van den Berg, Daryle Walker and Xiaogang Zhang<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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