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   4 <title>How to Determine the Kind of a Number From std::numeric_limits</title>
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  25 <div class="section">
  26 <div class="titlepage"><div><div><h4 class="title">
  27 <a name="boost_multiprecision.tut.limits.how_to_tell"></a><a class="link" href="how_to_tell.html" title="How to Determine the Kind of a Number From std::numeric_limits">How to
  28         Determine the Kind of a Number From <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span></code></a>
  29 </h4></div></div></div>
  30 <p>
  31           Based on the information above, one can see that different kinds of numbers
  32           can be differentiated based on the information stored in <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span></code>. This is in addition to
  33           the traits class <a class="link" href="../../ref/number.html#boost_multiprecision.ref.number.traits_class_support">number_category</a>
  34           provided by this library.
  35         </p>
  36 <h5>
  37 <a name="boost_multiprecision.tut.limits.how_to_tell.h0"></a>
  38           <span class="phrase"><a name="boost_multiprecision.tut.limits.how_to_tell.integer_types"></a></span><a class="link" href="how_to_tell.html#boost_multiprecision.tut.limits.how_to_tell.integer_types">Integer
  39           Types</a>
  40         </h5>
  41 <p>
  42           For an integer type T, all of the following conditions hold:
  43         </p>
  44 <pre class="programlisting"><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;::</span><span class="identifier">is_specialized</span> <span class="special">==</span> <span class="keyword">true</span>
  45 <span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;::</span><span class="identifier">is_integer</span> <span class="special">==</span> <span class="keyword">true</span>
  46 <span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;::</span><span class="identifier">is_exact</span> <span class="special">==</span> <span class="keyword">true</span>
  47 <span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;::</span><span class="identifier">min_exponent</span> <span class="special">==</span> <span class="number">0</span>
  48 <span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;::</span><span class="identifier">max_exponent</span> <span class="special">==</span> <span class="number">0</span>
  49 <span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;::</span><span class="identifier">min_exponent10</span> <span class="special">==</span> <span class="number">0</span>
  50 <span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;::</span><span class="identifier">max_exponent10</span> <span class="special">==</span> <span class="number">0</span>
  51 </pre>
  52 <p>
  53           In addition the type is <span class="emphasis"><em>signed</em></span> if:
  54         </p>
  55 <pre class="programlisting"><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;::</span><span class="identifier">is_signed</span> <span class="special">==</span> <span class="keyword">true</span>
  56 </pre>
  57 <p>
  58           If the type is arbitrary precision then:
  59         </p>
  60 <pre class="programlisting"><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;::</span><span class="identifier">is_bounded</span> <span class="special">==</span> <span class="keyword">false</span>
  61 </pre>
  62 <p>
  63           Otherwise the type is bounded, and returns a non zero value from:
  64         </p>
  65 <pre class="programlisting"><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;::</span><span class="identifier">max</span><span class="special">()</span>
  66 </pre>
  67 <p>
  68           and has:
  69         </p>
  70 <pre class="programlisting"><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;::</span><span class="identifier">is_modulo</span> <span class="special">==</span> <span class="keyword">true</span>
  71 </pre>
  72 <p>
  73           if the type implements modulo arithmetic on overflow.
  74         </p>
  75 <h5>
  76 <a name="boost_multiprecision.tut.limits.how_to_tell.h1"></a>
  77           <span class="phrase"><a name="boost_multiprecision.tut.limits.how_to_tell.rational_types"></a></span><a class="link" href="how_to_tell.html#boost_multiprecision.tut.limits.how_to_tell.rational_types">Rational
  78           Types</a>
  79         </h5>
  80 <p>
  81           Rational types are just like integers except that:
  82         </p>
  83 <pre class="programlisting"><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;::</span><span class="identifier">is_integer</span> <span class="special">==</span> <span class="keyword">false</span>
  84 </pre>
  85 <h5>
  86 <a name="boost_multiprecision.tut.limits.how_to_tell.h2"></a>
  87           <span class="phrase"><a name="boost_multiprecision.tut.limits.how_to_tell.fixed_precision_types"></a></span><a class="link" href="how_to_tell.html#boost_multiprecision.tut.limits.how_to_tell.fixed_precision_types">Fixed
  88           Precision Types</a>
  89         </h5>
  90 <p>
  91           There appears to be no way to tell these apart from rational types, unless
  92           they set:
  93         </p>
  94 <pre class="programlisting"><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;::</span><span class="identifier">is_exact</span> <span class="special">==</span> <span class="keyword">false</span>
  95 </pre>
  96 <p>
  97           This is because these types are in essence a rational type with a fixed
  98           denominator.
  99         </p>
 100 <h5>
 101 <a name="boost_multiprecision.tut.limits.how_to_tell.h3"></a>
 102           <span class="phrase"><a name="boost_multiprecision.tut.limits.how_to_tell.floating_point_types"></a></span><a class="link" href="how_to_tell.html#boost_multiprecision.tut.limits.how_to_tell.floating_point_types">floating-point
 103           Types</a>
 104         </h5>
 105 <p>
 106           For a floating-point type T, all of the following conditions hold:
 107         </p>
 108 <pre class="programlisting"><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;::</span><span class="identifier">is_specialized</span> <span class="special">==</span> <span class="keyword">true</span>
 109 <span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;::</span><span class="identifier">is_integer</span> <span class="special">==</span> <span class="keyword">false</span>
 110 <span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;::</span><span class="identifier">is_exact</span> <span class="special">==</span> <span class="keyword">false</span>
 111 <span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;::</span><span class="identifier">min_exponent</span> <span class="special">!=</span> <span class="number">0</span>
 112 <span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;::</span><span class="identifier">max_exponent</span> <span class="special">!=</span> <span class="number">0</span>
 113 <span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;::</span><span class="identifier">min_exponent10</span> <span class="special">!=</span> <span class="number">0</span>
 114 <span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;::</span><span class="identifier">max_exponent10</span> <span class="special">!=</span> <span class="number">0</span>
 115 </pre>
 116 <p>
 117           In addition the type is <span class="emphasis"><em>signed</em></span> if:
 118         </p>
 119 <pre class="programlisting"><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;::</span><span class="identifier">is_signed</span> <span class="special">==</span> <span class="keyword">true</span>
 120 </pre>
 121 <p>
 122           And the type may be decimal or binary depending on the value of:
 123         </p>
 124 <pre class="programlisting"><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;::</span><span class="identifier">radix</span>
 125 </pre>
 126 <p>
 127           In general, there are no arbitrary precision floating-point types, and
 128           so:
 129         </p>
 130 <pre class="programlisting"><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;::</span><span class="identifier">is_bounded</span> <span class="special">==</span> <span class="keyword">false</span>
 131 </pre>
 132 <h5>
 133 <a name="boost_multiprecision.tut.limits.how_to_tell.h4"></a>
 134           <span class="phrase"><a name="boost_multiprecision.tut.limits.how_to_tell.exact_floating_point_types"></a></span><a class="link" href="how_to_tell.html#boost_multiprecision.tut.limits.how_to_tell.exact_floating_point_types">Exact
 135           floating-point Types</a>
 136         </h5>
 137 <p>
 138           Exact floating-point types are a <a href="http://en.wikipedia.org/wiki/Field_%28mathematics%29" target="_top">field</a>
 139           composed of an arbitrary precision integer scaled by an exponent. Such
 140           types have no division operator and are the same as floating-point types
 141           except:
 142         </p>
 143 <pre class="programlisting"><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;::</span><span class="identifier">is_exact</span> <span class="special">==</span> <span class="keyword">true</span>
 144 </pre>
 145 <h5>
 146 <a name="boost_multiprecision.tut.limits.how_to_tell.h5"></a>
 147           <span class="phrase"><a name="boost_multiprecision.tut.limits.how_to_tell.complex_numbers"></a></span><a class="link" href="how_to_tell.html#boost_multiprecision.tut.limits.how_to_tell.complex_numbers">Complex
 148           Numbers</a>
 149         </h5>
 150 <p>
 151           For historical reasons, complex numbers do not specialize <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span></code>, instead you must inspect
 152           <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">::</span><span class="identifier">value_type</span><span class="special">&gt;</span></code>.
 153         </p>
 154 </div>
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 156 <td align="left"></td>
 157 <td align="right"><div class="copyright-footer">Copyright &#169; 2002-2019 John Maddock
 158       and Christopher Kormanyos<p>
 159         Distributed under the Boost Software License, Version 1.0. (See accompanying
 160         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>)
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