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  26 <div class="titlepage"><div><div><h2 class="title" style="clear: both">
  27 <a name="math_toolkit.constants_intro"></a><a class="link" href="constants_intro.html" title="Introduction">Introduction</a>
  28 </h2></div></div></div>
  29 <p>
  30       Boost.Math provides a collection of mathematical constants.
  31     </p>
  32 <h5>
  33 <a name="math_toolkit.constants_intro.h0"></a>
  34       <span class="phrase"><a name="math_toolkit.constants_intro.why_use_boost_math_mathematical_"></a></span><a class="link" href="constants_intro.html#math_toolkit.constants_intro.why_use_boost_math_mathematical_">Why
  35       use Boost.Math mathematical constants?</a>
  36     </h5>
  37 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
  38 <li class="listitem">
  39 <p class="simpara">
  40           Readable. For the very many jobs just using built-in like <code class="computeroutput"><span class="keyword">double</span></code>, you can just write expressions like
  41         </p>
  42 <pre class="programlisting"><span class="keyword">double</span> <span class="identifier">area</span> <span class="special">=</span> <span class="identifier">pi</span> <span class="special">*</span> <span class="identifier">r</span> <span class="special">*</span> <span class="identifier">r</span><span class="special">;</span></pre>
  43 <p class="simpara">
  44           (If that's all you want, jump direct to <a class="link" href="tutorial/non_templ.html" title="Use in non-template code">use
  45           in non-template code</a>!)
  46         </p>
  47 </li>
  48 <li class="listitem">
  49           Effortless - avoiding a search of reference sources.
  50         </li>
  51 <li class="listitem">
  52           Usable with both builtin floating point types, and user-defined, possibly
  53           extended precision, types such as NTL, MPFR/GMP, mp_float: in the latter
  54           case the constants are computed to the necessary precision and then cached.
  55         </li>
  56 <li class="listitem">
  57           Accurate - ensuring that the values are as accurate as possible for the
  58           chosen floating-point type
  59           <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: circle; ">
  60 <li class="listitem">
  61                 No loss of accuracy from repeated rounding of intermediate computations.
  62               </li>
  63 <li class="listitem">
  64                 Result is computed with higher precision and only rounded once.
  65               </li>
  66 <li class="listitem">
  67                 Less risk of inaccurate result from functions pow, trig and log at
  68                 <a href="http://en.wikipedia.org/wiki/Corner_case" target="_top">corner cases</a>.
  69               </li>
  70 <li class="listitem">
  71                 Less risk of <a href="http://docs.oracle.com/cd/E19957-01/806-3568/ncg_goldberg.html" target="_top">cancellation
  72                 error</a>.
  73               </li>
  74 </ul></div>
  75         </li>
  76 <li class="listitem">
  77           Portable - as possible between different systems using different floating-point
  78           precisions: see <a class="link" href="tutorial/templ.html" title="Use in template code">use in template
  79           code</a>.
  80         </li>
  81 <li class="listitem">
  82           Tested - by comparison with other published sources, or separately computed
  83           at long double precision.
  84         </li>
  85 <li class="listitem">
  86 <p class="simpara">
  87           Faster - can avoid (re-)calculation at runtime.
  88           <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: circle; ">
  89 <li class="listitem">
  90                 If the value returned is a builtin type then it's returned by value
  91                 as a <code class="computeroutput"><span class="keyword">constexpr</span></code> (C++11
  92                 feature, if available).
  93               </li>
  94 <li class="listitem">
  95                 If the value is computed and cached (or constructed from a string
  96                 representation and cached), then it's returned by constant reference.
  97               </li>
  98 </ul></div>
  99         </p>
 100 <p class="simpara">
 101           This can be significant if:
 102         </p>
 103 <p class="simpara">
 104           <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: circle; ">
 105 <li class="listitem">
 106                 Functions pow, trig or log are used.
 107               </li>
 108 <li class="listitem">
 109                 Inside an inner loop.
 110               </li>
 111 <li class="listitem">
 112                 Using a high-precision UDT like <a href="../../../../../libs/multiprecision/doc/html/index.html" target="_top">Boost.Multiprecision</a>.
 113               </li>
 114 <li class="listitem">
 115                 Compiler optimizations possible with built-in types, especially
 116                 <code class="computeroutput"><span class="keyword">double</span></code>, are not available.
 117               </li>
 118 </ul></div>
 119         </p>
 120 </li>
 121 </ul></div>
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