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  26 <div class="titlepage"><div><div><h3 class="title">
  27 <a name="math_toolkit.pol_ref.precision_pol"></a><a class="link" href="precision_pol.html" title="Precision Policies">Precision Policies</a>
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  29 <p>
  30         There are two equivalent policies that effect the <span class="emphasis"><em>working precision</em></span>
  31         used to calculate results, these policies both default to 0 - meaning calculate
  32         to the maximum precision available in the type being used - but can be set
  33         to other values to cause lower levels of precision to be used. One might
  34         want to trade precision for evaluation speed.
  35       </p>
  36 <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">policies</span><span class="special">{</span>
  37
  38 <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>
  39 <span class="identifier">digits10</span><span class="special">;</span>
  40
  41 <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>
  42 <span class="identifier">digits2</span><span class="special">;</span>
  43
  44 <span class="special">}}}</span> <span class="comment">// namespaces</span>
  45 </pre>
  46 <p>
  47         As you would expect, <span class="emphasis"><em>digits10</em></span> specifies the number of
  48         decimal digits to use, and <span class="emphasis"><em>digits2</em></span> the number of binary
  49         digits. Internally, whichever is used, the precision is always converted
  50         to <span class="emphasis"><em>binary digits</em></span>.
  51       </p>
  52 <p>
  53         These policies are specified at compile-time, because many of the special
  54         functions use compile-time-dispatch to select which approximation to use
  55         based on the precision requested and the numeric type being used.
  56       </p>
  57 <p>
  58         For example we could calculate <code class="computeroutput"><span class="identifier">tgamma</span></code>
  59         to approximately 5 decimal digits using:
  60       </p>
  61 <pre class="programlisting"><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">special_functions</span><span class="special">/</span><span class="identifier">gamma</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
  62 <span class="keyword">using</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>
  63 <span class="keyword">using</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">;</span>
  64 <span class="keyword">using</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">digits10</span><span class="special">;</span>
  65
  66 <span class="keyword">typedef</span> <span class="identifier">policy</span><span class="special">&lt;</span><span class="identifier">digits10</span><span class="special">&lt;</span><span class="number">5</span><span class="special">&gt;</span> <span class="special">&gt;</span> <span class="identifier">my_pol_5</span><span class="special">;</span> <span class="comment">// Define a new, non-default, policy</span>
  67 <span class="comment">// to calculate tgamma to accuracy of approximately 5 decimal digits.</span>
  68 </pre>
  69 <p>
  70         Or again using helper function <code class="computeroutput"><span class="identifier">make_policy</span></code>:
  71       </p>
  72 <pre class="programlisting"><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">special_functions</span><span class="special">/</span><span class="identifier">gamma</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
  73 <span class="keyword">using</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>
  74
  75 <span class="keyword">using</span> <span class="keyword">namespace</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>
  76
  77 <span class="keyword">double</span> <span class="identifier">t</span> <span class="special">=</span> <span class="identifier">tgamma</span><span class="special">(</span><span class="number">12</span><span class="special">,</span> <span class="identifier">policy</span><span class="special">&lt;</span><span class="identifier">digits10</span><span class="special">&lt;</span><span class="number">5</span><span class="special">&gt;</span> <span class="special">&gt;());</span>  <span class="comment">// Concise make_policy.</span>
  78 </pre>
  79 <p>
  80         And for a quantile of a distribution to approximately 25-bit precision:
  81       </p>
  82 <pre class="programlisting"><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">distributions</span><span class="special">/</span><span class="identifier">normal</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
  83 <span class="keyword">using</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">normal_distribution</span><span class="special">;</span>
  84
  85 <span class="keyword">using</span> <span class="keyword">namespace</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>
  86
  87 <span class="keyword">const</span> <span class="keyword">int</span> <span class="identifier">bits</span> <span class="special">=</span> <span class="number">25</span><span class="special">;</span> <span class="comment">// approximate precision.</span>
  88
  89 <span class="keyword">double</span> <span class="identifier">q</span> <span class="special">=</span> <span class="identifier">quantile</span><span class="special">(</span>
  90       <span class="identifier">normal_distribution</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">,</span> <span class="identifier">policy</span><span class="special">&lt;</span><span class="identifier">digits2</span><span class="special">&lt;</span><span class="identifier">bits</span><span class="special">&gt;</span> <span class="special">&gt;</span> <span class="special">&gt;(),</span>
  91       <span class="number">0.05</span><span class="special">);</span> <span class="comment">// 5% quantile.</span>
  92 </pre>
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  97       Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert
  98       Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam Sewani,
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 100         Distributed under the Boost Software License, Version 1.0. (See accompanying
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