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  27 <a name="math_toolkit.new_const"></a><a class="link" href="new_const.html" title="Defining New Constants">Defining New Constants</a>
  28 </h2></div></div></div>
  29 <p>
  30       The library provides some helper code to assist in defining new constants;
  31       the process for defining a constant called <code class="computeroutput"><span class="identifier">my_constant</span></code>
  32       goes like this:
  33     </p>
  34 <p>
  35       1. <span class="bold"><strong>Define a function that calculates the value of the
  36       constant</strong></span>. This should be a template function, and be placed in
  37       <code class="computeroutput"><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">constants</span><span class="special">/</span><span class="identifier">calculate_constants</span><span class="special">.</span><span class="identifier">hpp</span></code> if the
  38       constant is to be added to this library, or else defined at the top of your
  39       source file if not.
  40     </p>
  41 <p>
  42       The function should look like this:
  43     </p>
  44 <pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">constants</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">detail</span><span class="special">{</span>
  45
  46 <span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">Real</span><span class="special">&gt;</span>
  47 <span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">int</span> <span class="identifier">N</span><span class="special">&gt;</span>
  48 <span class="identifier">Real</span> <span class="identifier">constant_my_constant</span><span class="special">&lt;</span><span class="identifier">Real</span><span class="special">&gt;::</span><span class="identifier">compute</span><span class="special">(</span><span class="identifier">BOOST_MATH_EXPLICIT_TEMPLATE_TYPE_SPEC</span><span class="special">(</span><span class="identifier">mpl</span><span class="special">::</span><span class="identifier">int_</span><span class="special">&lt;</span><span class="identifier">N</span><span class="special">&gt;))</span>
  49 <span class="special">{</span>
  50   <span class="keyword">int</span> <span class="identifier">required_precision</span> <span class="special">=</span> <span class="identifier">N</span> <span class="special">?</span> <span class="identifier">N</span> <span class="special">:</span> <span class="identifier">tools</span><span class="special">::</span><span class="identifier">digits</span><span class="special">&lt;</span><span class="identifier">Real</span><span class="special">&gt;();</span>
  51   <span class="identifier">Real</span> <span class="identifier">result</span> <span class="special">=</span> <span class="comment">/* value computed to required_precision bits */</span> <span class="special">;</span>
  52   <span class="keyword">return</span> <span class="identifier">result</span><span class="special">;</span>
  53 <span class="special">}</span>
  54
  55 <span class="special">}}}}</span> <span class="comment">// namespaces</span>
  56 </pre>
  57 <p>
  58       Then define a placeholder for the constant itself:
  59     </p>
  60 <pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">constants</span><span class="special">{</span>
  61
  62 <span class="identifier">BOOST_DEFINE_MATH_CONSTANT</span><span class="special">(</span><span class="identifier">my_constant</span><span class="special">,</span> <span class="number">0.0</span><span class="special">,</span> <span class="string">"0"</span><span class="special">);</span>
  63
  64 <span class="special">}}}</span>
  65 </pre>
  66 <p>
  67       For example, to calculate &#960;/2, add to <code class="computeroutput"><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">constants</span><span class="special">/</span><span class="identifier">calculate_constants</span><span class="special">.</span><span class="identifier">hpp</span></code>
  68     </p>
  69 <pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
  70 <span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">int</span> <span class="identifier">N</span><span class="special">&gt;</span>
  71 <span class="keyword">inline</span> <span class="identifier">T</span> <span class="identifier">constant_half_pi</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;::</span><span class="identifier">compute</span><span class="special">(</span><span class="identifier">BOOST_MATH_EXPLICIT_TEMPLATE_TYPE_SPEC</span><span class="special">(</span><span class="identifier">mpl</span><span class="special">::</span><span class="identifier">int_</span><span class="special">&lt;</span><span class="identifier">N</span><span class="special">&gt;))</span>
  72 <span class="special">{</span>
  73    <span class="identifier">BOOST_MATH_STD_USING</span>
  74    <span class="keyword">return</span> <span class="identifier">pi</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">,</span> <span class="identifier">policies</span><span class="special">::</span><span class="identifier">policy</span><span class="special">&lt;</span><span class="identifier">policies</span><span class="special">::</span><span class="identifier">digits2</span><span class="special">&lt;</span><span class="identifier">N</span><span class="special">&gt;</span> <span class="special">&gt;</span> <span class="special">&gt;()</span> <span class="special">/</span> <span class="keyword">static_cast</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;(</span><span class="number">2</span><span class="special">);</span>
  75 <span class="special">}</span>
  76 </pre>
  77 <p>
  78       Then to <code class="computeroutput"><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">constants</span><span class="special">/</span><span class="identifier">constants</span><span class="special">.</span><span class="identifier">hpp</span></code> add:
  79     </p>
  80 <pre class="programlisting"><span class="identifier">BOOST_DEFINE_MATH_CONSTANT</span><span class="special">(</span><span class="identifier">half_pi</span><span class="special">,</span> <span class="number">0.0</span><span class="special">,</span> <span class="string">"0"</span><span class="special">);</span>  <span class="comment">// Actual values are temporary, we'll replace them later.</span>
  81 </pre>
  82 <div class="note"><table border="0" summary="Note">
  83 <tr>
  84 <td rowspan="2" align="center" valign="top" width="25"><img alt="[Note]" src="../../../../../doc/src/images/note.png"></td>
  85 <th align="left">Note</th>
  86 </tr>
  87 <tr><td align="left" valign="top"><p>
  88         Previously defined constants like pi and e can be used, but by <span class="bold"><strong>not simply calling</strong></span> <code class="computeroutput"><span class="identifier">pi</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;()</span></code>;
  89         specifying the precision via the policy <code class="computeroutput"><span class="identifier">pi</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">,</span>
  90         <span class="identifier">policies</span><span class="special">::</span><span class="identifier">policy</span><span class="special">&lt;</span><span class="identifier">policies</span><span class="special">::</span><span class="identifier">digits2</span><span class="special">&lt;</span><span class="identifier">N</span><span class="special">&gt;</span> <span class="special">&gt;</span> <span class="special">&gt;()</span></code>
  91         is essential to ensure full accuracy.
  92       </p></td></tr>
  93 </table></div>
  94 <div class="warning"><table border="0" summary="Warning">
  95 <tr>
  96 <td rowspan="2" align="center" valign="top" width="25"><img alt="[Warning]" src="../../../../../doc/src/images/warning.png"></td>
  97 <th align="left">Warning</th>
  98 </tr>
  99 <tr><td align="left" valign="top">
 100 <p>
 101         Newly defined constants can only be used once they are included in <code class="computeroutput"><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">constants</span><span class="special">/</span><span class="identifier">constants</span><span class="special">.</span><span class="identifier">hpp</span></code>. So
 102         if you add <code class="computeroutput"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">N</span><span class="special">&gt;</span> <span class="identifier">T</span> <span class="identifier">constant_my_constant</span><span class="special">{...}</span></code>,
 103         then you cannot define <code class="computeroutput"><span class="identifier">constant_my_constant</span></code>
 104         until you add the temporary <code class="computeroutput"><span class="identifier">BOOST_DEFINE_MATH_CONSTANT</span><span class="special">(</span><span class="identifier">my_constant</span><span class="special">,</span> <span class="number">0.0</span><span class="special">,</span>
 105         <span class="string">"0"</span><span class="special">)</span></code>.
 106         Failing to do this will result in surprising compile errors:
 107       </p>
 108 <pre class="programlisting"><span class="identifier">error</span> <span class="identifier">C2143</span><span class="special">:</span> <span class="identifier">syntax</span> <span class="identifier">error</span> <span class="special">:</span> <span class="identifier">missing</span> <span class="char">';'</span> <span class="identifier">before</span> <span class="char">'&lt;'</span>
 109 <span class="identifier">error</span> <span class="identifier">C2433</span><span class="special">:</span> <span class="char">'constant_root_two_div_pi'</span> <span class="special">:</span> <span class="char">'inline'</span> <span class="keyword">not</span> <span class="identifier">permitted</span> <span class="identifier">on</span> <span class="identifier">data</span> <span class="identifier">declarations</span>
 110 <span class="identifier">error</span> <span class="identifier">C2888</span><span class="special">:</span> <span class="char">'T constant_root_two_div_pi'</span> <span class="special">:</span> <span class="identifier">symbol</span> <span class="identifier">cannot</span> <span class="identifier">be</span> <span class="identifier">defined</span> <span class="identifier">within</span> <span class="keyword">namespace</span> <span class="char">'detail'</span>
 111 <span class="identifier">error</span> <span class="identifier">C2988</span><span class="special">:</span> <span class="identifier">unrecognizable</span> <span class="keyword">template</span> <span class="identifier">declaration</span><span class="special">/</span><span class="identifier">definition</span>
 112 </pre>
 113 </td></tr>
 114 </table></div>
 115 <p>
 116       2. <span class="bold"><strong>You will need an arbitrary precision type to use to
 117       calculate the value</strong></span>. This library currently supports either <code class="computeroutput"><span class="identifier">cpp_float</span></code>, <code class="computeroutput"><span class="identifier">NTL</span><span class="special">::</span><span class="identifier">RR</span></code> or
 118       <code class="computeroutput"><span class="identifier">mpfr_class</span></code> used via the bindings
 119       in <code class="computeroutput"><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">bindings</span></code>.
 120       The default is to use <code class="computeroutput"><span class="identifier">NTL</span><span class="special">::</span><span class="identifier">RR</span></code> unless you define an alternate macro,
 121       for example, <code class="computeroutput"><span class="identifier">USE_MPFR</span></code> or <code class="computeroutput"><span class="identifier">USE_CPP_FLOAT</span></code> at the start of your program.
 122     </p>
 123 <p>
 124       3. It is necessary to link to the Boost.Regex library, and probably to your
 125       chosen arbitrary precision type library.
 126     </p>
 127 <p>
 128       4. You need to add <code class="computeroutput"><span class="identifier">libs</span><span class="special">\</span><span class="identifier">math</span><span class="special">\</span><span class="identifier">include_private</span></code>
 129       to your compiler's include path as the needed header is not installed in the
 130       usual places by default (this avoids a cyclic dependency between the Math and
 131       Multiprecision library's headers).
 132     </p>
 133 <p>
 134       5. The complete program to generate the constant <code class="computeroutput"><span class="identifier">half_pi</span></code>
 135       using function <code class="computeroutput"><span class="identifier">calculate_half_pi</span></code>
 136       is then:
 137     </p>
 138 <pre class="programlisting"><span class="preprocessor">#define</span> <span class="identifier">USE_CPP_FLOAT</span> <span class="comment">// If required.</span>
 139 <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">constants</span><span class="special">/</span><span class="identifier">generate</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
 140
 141 <span class="keyword">int</span> <span class="identifier">main</span><span class="special">()</span>
 142 <span class="special">{</span>
 143    <span class="identifier">BOOST_CONSTANTS_GENERATE</span><span class="special">(</span><span class="identifier">half_pi</span><span class="special">);</span>
 144 <span class="special">}</span>
 145 </pre>
 146 <p>
 147       The output from the program is a snippet of C++ code (actually a macro call)
 148       that can be cut and pasted into <code class="computeroutput"><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">constants</span><span class="special">/</span><span class="identifier">constants</span><span class="special">.</span><span class="identifier">hpp</span></code> or else into your own code, for example:
 149     </p>
 150 <pre class="programlisting">  BOOST_DEFINE_MATH_CONSTANT(half_pi, 1.570796326794896619231321691639751442e+00, "1.57079632679489661923132169163975144209858469968755291048747229615390820314310449931401741267105853399107404326e+00");
 151 </pre>
 152 <p>
 153       This macro BOOST_DEFINE_MATH_CONSTANT inserts a C++ struct code snippet that
 154       declares the <code class="computeroutput"><span class="keyword">float</span></code>, <code class="computeroutput"><span class="keyword">double</span></code> and <code class="computeroutput"><span class="keyword">long</span>
 155       <span class="keyword">double</span></code> versions of the constant, plus
 156       a decimal digit string representation correct to 100 decimal digits, and all
 157       the meta-programming machinery needed to select between them.
 158     </p>
 159 <p>
 160       The result of an expanded macro for Pi is shown below.
 161     </p>
 162 <pre class="programlisting"><span class="comment">// Preprocessed pi constant, annotated.</span>
 163
 164 <span class="keyword">namespace</span> <span class="identifier">boost</span>
 165 <span class="special">{</span>
 166   <span class="keyword">namespace</span> <span class="identifier">math</span>
 167   <span class="special">{</span>
 168     <span class="keyword">namespace</span> <span class="identifier">constants</span>
 169     <span class="special">{</span>
 170       <span class="keyword">namespace</span> <span class="identifier">detail</span>
 171       <span class="special">{</span>
 172         <span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">struct</span> <span class="identifier">constant_pi</span>
 173         <span class="special">{</span>
 174           <span class="keyword">private</span><span class="special">:</span>
 175             <span class="comment">// Default implementations from string of decimal digits:</span>
 176             <span class="keyword">static</span> <span class="keyword">inline</span> <span class="identifier">T</span> <span class="identifier">get_from_string</span><span class="special">()</span>
 177             <span class="special">{</span>
 178             <span class="keyword">static</span> <span class="keyword">const</span> <span class="identifier">T</span> <span class="identifier">result</span>
 179                <span class="special">=</span> <span class="identifier">detail</span><span class="special">::</span><span class="identifier">convert_from_string</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;(</span><span class="string">"3.14159265358979323846264338327950288419716939937510582097494459230781640628620899862803482534211706798214808651e+00"</span><span class="special">,</span>
 180                <span class="identifier">boost</span><span class="special">::</span><span class="identifier">is_convertible</span><span class="special">&lt;</span><span class="keyword">const</span> <span class="keyword">char</span><span class="special">*,</span> <span class="identifier">T</span><span class="special">&gt;());</span>
 181               <span class="keyword">return</span> <span class="identifier">result</span><span class="special">;</span>
 182             <span class="special">}</span>
 183             <span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">int</span> <span class="identifier">N</span><span class="special">&gt;</span> <span class="keyword">static</span> <span class="identifier">T</span> <span class="identifier">compute</span><span class="special">();</span>
 184
 185           <span class="keyword">public</span><span class="special">:</span>
 186             <span class="comment">// Default implementations from string of decimal digits:</span>
 187             <span class="keyword">static</span> <span class="keyword">inline</span> <span class="identifier">T</span> <span class="identifier">get</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">mpl</span><span class="special">::</span><span class="identifier">int_</span><span class="special">&lt;</span><span class="identifier">construct_from_string</span><span class="special">&gt;&amp;)</span>
 188             <span class="special">{</span>
 189               <span class="identifier">constant_initializer</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">,</span> <span class="special">&amp;</span> <span class="identifier">constant_pi</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;::</span><span class="identifier">get_from_string</span> <span class="special">&gt;::</span><span class="identifier">do_nothing</span><span class="special">();</span>
 190               <span class="keyword">return</span> <span class="identifier">get_from_string</span><span class="special">();</span>
 191             <span class="special">}</span>
 192             <span class="comment">// Float, double and long double versions:</span>
 193             <span class="keyword">static</span> <span class="keyword">inline</span> <span class="identifier">T</span> <span class="identifier">get</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">mpl</span><span class="special">::</span><span class="identifier">int_</span><span class="special">&lt;</span><span class="identifier">construct_from_float</span><span class="special">&gt;)</span>
 194             <span class="special">{</span>
 195               <span class="keyword">return</span> <span class="number">3.141592653589793238462643383279502884e+00F</span><span class="special">;</span>
 196             <span class="special">}</span>
 197             <span class="keyword">static</span> <span class="keyword">inline</span>  <span class="identifier">T</span> <span class="identifier">get</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">mpl</span><span class="special">::</span><span class="identifier">int_</span><span class="special">&lt;</span><span class="identifier">construct_from_double</span><span class="special">&gt;&amp;)</span>
 198             <span class="special">{</span>
 199               <span class="keyword">return</span> <span class="number">3.141592653589793238462643383279502884e+00</span><span class="special">;</span>
 200             <span class="special">}</span>
 201             <span class="keyword">static</span> <span class="keyword">inline</span>  <span class="identifier">T</span> <span class="identifier">get</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">mpl</span><span class="special">::</span><span class="identifier">int_</span><span class="special">&lt;</span><span class="identifier">construct_from_long_double</span><span class="special">&gt;&amp;)</span>
 202             <span class="special">{</span>
 203               <span class="keyword">return</span> <span class="number">3.141592653589793238462643383279502884e+00L</span><span class="special">;</span>
 204             <span class="special">}</span>
 205             <span class="comment">// For very high precision that is nonetheless can be calculated at compile time:</span>
 206             <span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">int</span> <span class="identifier">N</span><span class="special">&gt;</span> <span class="keyword">static</span> <span class="keyword">inline</span> <span class="identifier">T</span> <span class="identifier">get</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">mpl</span><span class="special">::</span><span class="identifier">int_</span><span class="special">&lt;</span><span class="identifier">N</span><span class="special">&gt;&amp;</span> <span class="identifier">n</span><span class="special">)</span>
 207             <span class="special">{</span>
 208               <span class="identifier">constant_initializer2</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">,</span> <span class="identifier">N</span><span class="special">,</span> <span class="special">&amp;</span> <span class="identifier">constant_pi</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;::</span><span class="keyword">template</span> <span class="identifier">compute</span><span class="special">&lt;</span><span class="identifier">N</span><span class="special">&gt;</span> <span class="special">&gt;::</span><span class="identifier">do_nothing</span><span class="special">();</span>
 209               <span class="keyword">return</span> <span class="identifier">compute</span><span class="special">&lt;</span><span class="identifier">N</span><span class="special">&gt;();</span>
 210             <span class="special">}</span>
 211             <span class="comment">//For true arbitrary precision, which may well vary at runtime.</span>
 212             <span class="keyword">static</span> <span class="keyword">inline</span> <span class="identifier">T</span> <span class="identifier">get</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">mpl</span><span class="special">::</span><span class="identifier">int_</span><span class="special">&lt;</span><span class="number">0</span><span class="special">&gt;&amp;)</span>
 213             <span class="special">{</span>
 214               <span class="keyword">return</span> <span class="identifier">tools</span><span class="special">::</span><span class="identifier">digits</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;()</span> <span class="special">&gt;</span> <span class="identifier">max_string_digits</span> <span class="special">?</span> <span class="identifier">compute</span><span class="special">&lt;</span><span class="number">0</span><span class="special">&gt;()</span> <span class="special">:</span> <span class="identifier">get</span><span class="special">(</span><span class="identifier">mpl</span><span class="special">::</span><span class="identifier">int_</span><span class="special">&lt;</span><span class="identifier">construct_from_string</span><span class="special">&gt;());</span>
 215             <span class="special">}</span>
 216          <span class="special">};</span> <span class="comment">// template &lt;class T&gt; struct constant_pi</span>
 217       <span class="special">}</span> <span class="comment">//  namespace detail</span>
 218
 219       <span class="comment">// The actual forwarding function (including policy to control precision).</span>
 220       <span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">Policy</span><span class="special">&gt;</span> <span class="keyword">inline</span> <span class="identifier">T</span> <span class="identifier">pi</span><span class="special">(</span> <span class="special">)</span>
 221       <span class="special">{</span>
 222         <span class="keyword">return</span> <span class="identifier">detail</span><span class="special">::</span> <span class="identifier">constant_pi</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;::</span><span class="identifier">get</span><span class="special">(</span><span class="keyword">typename</span> <span class="identifier">construction_traits</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">,</span> <span class="identifier">Policy</span><span class="special">&gt;::</span><span class="identifier">type</span><span class="special">());</span>
 223       <span class="special">}</span>
 224       <span class="comment">// The actual forwarding function (using default policy to control precision).</span>
 225       <span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">inline</span>  <span class="identifier">T</span> <span class="identifier">pi</span><span class="special">()</span>
 226       <span class="special">{</span>
 227         <span class="keyword">return</span> <span class="identifier">pi</span><span class="special">&lt;</span><span class="identifier">T</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">policies</span><span class="special">::</span><span class="identifier">policy</span><span class="special">&lt;&gt;</span> <span class="special">&gt;()</span>
 228       <span class="special">}</span>
 229     <span class="special">}</span> <span class="comment">//     namespace constants</span>
 230
 231     <span class="comment">// Namespace specific versions, for the three built-in floats:</span>
 232     <span class="keyword">namespace</span> <span class="identifier">float_constants</span>
 233     <span class="special">{</span>
 234       <span class="keyword">static</span> <span class="keyword">const</span> <span class="keyword">float</span> <span class="identifier">pi</span> <span class="special">=</span> <span class="number">3.141592653589793238462643383279502884e+00F</span><span class="special">;</span>
 235     <span class="special">}</span>
 236     <span class="keyword">namespace</span> <span class="identifier">double_constants</span>
 237     <span class="special">{</span>
 238       <span class="keyword">static</span> <span class="keyword">const</span> <span class="keyword">double</span> <span class="identifier">pi</span> <span class="special">=</span> <span class="number">3.141592653589793238462643383279502884e+00</span><span class="special">;</span>
 239     <span class="special">}</span>
 240     <span class="keyword">namespace</span> <span class="identifier">long_double_constants</span>
 241     <span class="special">{</span>
 242       <span class="keyword">static</span> <span class="keyword">const</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">pi</span> <span class="special">=</span> <span class="number">3.141592653589793238462643383279502884e+00L</span><span class="special">;</span>
 243     <span class="special">}</span>
 244     <span class="keyword">namespace</span> <span class="identifier">constants</span><span class="special">{;</span>
 245     <span class="special">}</span> <span class="comment">// namespace constants</span>
 246   <span class="special">}</span> <span class="comment">// namespace math</span>
 247 <span class="special">}</span> <span class="comment">// namespace boost</span>
 248 </pre>
 249 </div>
 250 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 251 <td align="left"></td>
 252 <td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
 253       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
 254       Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
 255       R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
 256       Daryle Walker and Xiaogang Zhang<p>
 257         Distributed under the Boost Software License, Version 1.0. (See accompanying
 258         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>)
 259       </p>
 260 </div></td>
 261 </tr></table>
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