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Specified-width floating-point typedefs"> 9<link rel="prev" href="macros.html" title="Floating-Point Constant Macros"> 10<link rel="next" href="float128_hints.html" title="Hints on using float128 (and __float128)"> 11</head> 12<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF"> 13<table cellpadding="2" width="100%"><tr> 14<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../boost.png"></td> 15<td align="center"><a href="../../../../../index.html">Home</a></td> 16<td align="center"><a href="../../../../../libs/libraries.htm">Libraries</a></td> 17<td align="center"><a href="http://www.boost.org/users/people.html">People</a></td> 18<td align="center"><a href="http://www.boost.org/users/faq.html">FAQ</a></td> 19<td align="center"><a href="../../../../../more/index.htm">More</a></td> 20</tr></table> 21<hr> 22<div class="spirit-nav"> 23<a accesskey="p" href="macros.html"><img src="../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../cstdfloat.html"><img src="../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../index.html"><img src="../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="float128_hints.html"><img src="../../../../../doc/src/images/next.png" alt="Next"></a> 24</div> 25<div class="section"> 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"><</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> 36 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 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"><</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>, 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"><</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, float128_t. Must be first include!</span> 53<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> 54<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> 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"><</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> 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"><<</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> 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"><</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">float32_t</span><span class="special">>();</span> <span class="comment">// Usually type float</span> 113<span class="preprocessor">#endif</span> 114 <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">// Usually 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"><</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">float80_t</span><span class="special">>();</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"><</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">float128_t</span><span class="special">>();</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"><</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">floatmax_t</span><span class="special">>();</span> 122</pre> 123</div> 124<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> 125<td align="left"></td> 126<td align="right"><div class="copyright-footer">Copyright © 2006-2019 Nikhar 127 Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, 128 Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan 129 Råde, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, 130 Daryle Walker and Xiaogang Zhang<p> 131 Distributed under the Boost Software License, Version 1.0. (See accompanying 132 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>) 133 </p> 134</div></td> 135</tr></table> 136<hr> 137<div class="spirit-nav"> 138<a accesskey="p" href="macros.html"><img src="../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../cstdfloat.html"><img src="../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../index.html"><img src="../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="float128_hints.html"><img src="../../../../../doc/src/images/next.png" alt="Next"></a> 139</div> 140</body> 141</html> 142
