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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"><</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> | |
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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>) | |
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