libs/multiprecision/doc/html/boost_multiprecision/tut/limits/how_to_tell.html


1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168

<html>
<head>
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>How to Determine the Kind of a Number From std::numeric_limits</title>
<link rel="stylesheet" href="../../../../../../../doc/src/boostbook.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets V1.78.1">
<link rel="home" href="../../../index.html" title="Chapter&#160;1.&#160;Boost.Multiprecision">
<link rel="up" href="../limits.html" title="Numeric Limits">
<link rel="prev" href="limits32.html" title="Numeric limits for 32-bit platform">
<link rel="next" href="../input_output.html" title="Input Output">
</head>
<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
<table cellpadding="2" width="100%"><tr>
<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../../../boost.png"></td>
<td align="center"><a href="../../../../../../../index.html">Home</a></td>
<td align="center"><a href="../../../../../../../libs/libraries.htm">Libraries</a></td>
<td align="center"><a href="http://www.boost.org/users/people.html">People</a></td>
<td align="center"><a href="http://www.boost.org/users/faq.html">FAQ</a></td>
<td align="center"><a href="../../../../../../../more/index.htm">More</a></td>
</tr></table>
<hr>
<div class="spirit-nav">
<a accesskey="p" href="limits32.html"><img src="../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../limits.html"><img src="../../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="../input_output.html"><img src="../../../../../../../doc/src/images/next.png" alt="Next"></a>
</div>
<div class="section">
<div class="titlepage"><div><div><h4 class="title">
<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
        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>
</h4></div></div></div>
<p>
          Based on the information above, one can see that different kinds of numbers
          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
          the traits class <a class="link" href="../../ref/number.html#boost_multiprecision.ref.number.traits_class_support">number_category</a>
          provided by this library.
        </p>
<h5>
<a name="boost_multiprecision.tut.limits.how_to_tell.h0"></a>
          <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
          Types</a>
        </h5>
<p>
          For an integer type T, all of the following conditions hold:
        </p>
<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>
<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>
<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>
<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>
<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>
<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>
<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>
</pre>
<p>
          In addition the type is <span class="emphasis"><em>signed</em></span> if:
        </p>
<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>
</pre>
<p>
          If the type is arbitrary precision then:
        </p>
<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>
</pre>
<p>
          Otherwise the type is bounded, and returns a non zero value from:
        </p>
<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>
</pre>
<p>
          and has:
        </p>
<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>
</pre>
<p>
          if the type implements modulo arithmetic on overflow.
        </p>
<h5>
<a name="boost_multiprecision.tut.limits.how_to_tell.h1"></a>
          <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
          Types</a>
        </h5>
<p>
          Rational types are just like integers except that:
        </p>
<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>
</pre>
<h5>
<a name="boost_multiprecision.tut.limits.how_to_tell.h2"></a>
          <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
          Precision Types</a>
        </h5>
<p>
          There appears to be no way to tell these apart from rational types, unless
          they set:
        </p>
<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>
</pre>
<p>
          This is because these types are in essence a rational type with a fixed
          denominator.
        </p>
<h5>
<a name="boost_multiprecision.tut.limits.how_to_tell.h3"></a>
          <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 Types</a>
        </h5>
<p>
          For a floating point type T, all of the following conditions hold:
        </p>
<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>
<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>
<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>
<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>
<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>
<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>
<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>
</pre>
<p>
          In addition the type is <span class="emphasis"><em>signed</em></span> if:
        </p>
<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>
</pre>
<p>
          And the type may be decimal or binary depending on the value of:
        </p>
<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>
</pre>
<p>
          In general, there are no arbitrary precision floating point types, and
          so:
        </p>
<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>
</pre>
<h5>
<a name="boost_multiprecision.tut.limits.how_to_tell.h4"></a>
          <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
          Floating Point Types</a>
        </h5>
<p>
          Exact floating point types are a <a href="http://en.wikipedia.org/wiki/Field_%28mathematics%29" target="_top">field</a>
          composed of an arbitrary precision integer scaled by an exponent. Such
          types have no division operator and are the same as floating point types
          except:
        </p>
<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>
</pre>
<h5>
<a name="boost_multiprecision.tut.limits.how_to_tell.h5"></a>
          <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
          Numbers</a>
        </h5>
<p>
          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
          <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="identifier">T</span><span class="special">::</span><span class="identifier">value_type</span><span class="special">&gt;</span></code>.
        </p>
</div>
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
<td align="left"></td>
<td align="right"><div class="copyright-footer">Copyright &#169; 2002-2013 John Maddock and Christopher Kormanyos<p>
        Distributed under the Boost Software License, Version 1.0. (See accompanying
        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>)
      </p>
</div></td>
</tr></table>
<hr>
<div class="spirit-nav">
<a accesskey="p" href="limits32.html"><img src="../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../limits.html"><img src="../../../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="../input_output.html"><img src="../../../../../../../doc/src/images/next.png" alt="Next"></a>
</div>
</body>
</html>