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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>
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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
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.
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
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>
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>
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>
65 Ensure that all possibly significant digits (17) including trailing zeros are
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>
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>
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>
80 For details, see <a href="../../../example/cstdfloat_example.cpp" target="_top">cstdfloat_example.cpp</a>
81 - a extensive example program.
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>
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.
93 A function templated on floating-point type prints a table for a range of standard
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.
101 The number of digits displayed is controlled by the precision of the type,
102 so there are no spurious insignificant decimal digits:
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>
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>.
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">// 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"><</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>
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