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| 4 | <title>How to Determine the Kind of a Number From std::numeric_limits</title> | |
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| 24 | </div> | |
| 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"><</span><span class="identifier">T</span><span class="special">>::</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"><</span><span class="identifier">T</span><span class="special">>::</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"><</span><span class="identifier">T</span><span class="special">>::</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"><</span><span class="identifier">T</span><span class="special">>::</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"><</span><span class="identifier">T</span><span class="special">>::</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"><</span><span class="identifier">T</span><span class="special">>::</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"><</span><span class="identifier">T</span><span class="special">>::</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"><</span><span class="identifier">T</span><span class="special">>::</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"><</span><span class="identifier">T</span><span class="special">>::</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"><</span><span class="identifier">T</span><span class="special">>::</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"><</span><span class="identifier">T</span><span class="special">>::</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"><</span><span class="identifier">T</span><span class="special">>::</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"><</span><span class="identifier">T</span><span class="special">>::</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"><</span><span class="identifier">T</span><span class="special">>::</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"><</span><span class="identifier">T</span><span class="special">>::</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"><</span><span class="identifier">T</span><span class="special">>::</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"><</span><span class="identifier">T</span><span class="special">>::</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"><</span><span class="identifier">T</span><span class="special">>::</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"><</span><span class="identifier">T</span><span class="special">>::</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"><</span><span class="identifier">T</span><span class="special">>::</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"><</span><span class="identifier">T</span><span class="special">>::</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"><</span><span class="identifier">T</span><span class="special">>::</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"><</span><span class="identifier">T</span><span class="special">>::</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"><</span><span class="identifier">T</span><span class="special">>::</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"><</span><span class="identifier">T</span><span class="special">::</span><span class="identifier">value_type</span><span class="special">></span></code>. | |
| 153 | </p> | |
| 154 | </div> | |
| 155 | <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> | |
| 156 | <td align="left"></td> | |
| 157 | <td align="right"><div class="copyright-footer">Copyright © 2002-2013 John Maddock and Christopher Kormanyos<p> | |
| 158 | Distributed under the Boost Software License, Version 1.0. (See accompanying | |
| 159 | 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>) | |
| 160 | </p> | |
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