3 <meta http-equiv=
"Content-Type" content=
"text/html; charset=US-ASCII">
4 <title>How to Determine the Kind of a Number From std::numeric_limits
</title>
5 <link rel=
"stylesheet" href=
"../../../../../../../doc/src/boostbook.css" type=
"text/css">
6 <meta name=
"generator" content=
"DocBook XSL Stylesheets V1.77.1">
7 <link rel=
"home" href=
"../../../index.html" title=
"Chapter 1. Boost.Multiprecision">
8 <link rel=
"up" href=
"../limits.html" title=
"Numeric Limits">
9 <link rel=
"prev" href=
"limits32.html" title=
"Numeric limits for 32-bit platform">
10 <link rel=
"next" href=
"../input_output.html" title=
"Input Output">
12 <body bgcolor=
"white" text=
"black" link=
"#0000FF" vlink=
"#840084" alink=
"#0000FF">
13 <table cellpadding=
"2" width=
"100%"><tr>
14 <td valign=
"top"><img alt=
"Boost C++ Libraries" width=
"277" height=
"86" src=
"../../../../../../../boost.png"></td>
15 <td align=
"center"><a href=
"../../../../../../../index.html">Home
</a></td>
16 <td align=
"center"><a href=
"../../../../../../../libs/libraries.htm">Libraries
</a></td>
17 <td align=
"center"><a href=
"http://www.boost.org/users/people.html">People
</a></td>
18 <td align=
"center"><a href=
"http://www.boost.org/users/faq.html">FAQ
</a></td>
19 <td align=
"center"><a href=
"../../../../../../../more/index.htm">More
</a></td>
22 <div class=
"spirit-nav">
23 <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>
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>
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.
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
42 For an integer type T, all of the following conditions hold:
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>
53 In addition the type is
<span class=
"emphasis"><em>signed
</em></span> if:
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>
58 If the type is arbitrary precision then:
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>
63 Otherwise the type is bounded, and returns a non zero value from:
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>
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>
73 if the type implements modulo arithmetic on overflow.
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
81 Rational types are just like integers except that:
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>
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
91 There appears to be no way to tell these apart from rational types, unless
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>
97 This is because these types are in essence a rational type with a fixed
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
106 For a floating-point type T, all of the following conditions hold:
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>
117 In addition the type is
<span class=
"emphasis"><em>signed
</em></span> if:
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>
122 And the type may be decimal or binary depending on the value of:
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>
127 In general, there are no arbitrary precision floating-point types, and
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>
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>
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
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>
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
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>.
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>)
164 <div class=
"spirit-nav">
165 <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>