libs/multiprecision/doc/html/boost_multiprecision/tut/rational.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
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261

<html>
<head>
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Rational Number Types</title>
<link rel="stylesheet" href="../../../../../../doc/src/boostbook.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
<link rel="home" href="../../index.html" title="Chapter&#160;1.&#160;Boost.Multiprecision">
<link rel="up" href="../tut.html" title="Tutorial">
<link rel="prev" href="interval/mpfi.html" title="mpfi_float">
<link rel="next" href="rational/cpp_rational.html" title="cpp_rational">
</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="interval/mpfi.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../tut.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="rational/cpp_rational.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a>
</div>
<div class="section">
<div class="titlepage"><div><div><h3 class="title">
<a name="boost_multiprecision.tut.rational"></a><a class="link" href="rational.html" title="Rational Number Types">Rational Number Types</a>
</h3></div></div></div>
<div class="toc"><dl>
<dt><span class="section"><a href="rational/cpp_rational.html">cpp_rational</a></span></dt>
<dt><span class="section"><a href="rational/gmp_rational.html">gmp_rational</a></span></dt>
<dt><span class="section"><a href="rational/tommath_rational.html">tommath_rational</a></span></dt>
<dt><span class="section"><a href="rational/br.html">Use With Boost.Rational</a></span></dt>
<dt><span class="section"><a href="rational/rational_adaptor.html">rational_adaptor</a></span></dt>
</dl></div>
<p>
        The following back-ends provide rational number arithmetic:
      </p>
<div class="informaltable"><table class="table">
<colgroup>
<col>
<col>
<col>
<col>
<col>
<col>
</colgroup>
<thead><tr>
<th>
                <p>
                  Backend Type
                </p>
              </th>
<th>
                <p>
                  Header
                </p>
              </th>
<th>
                <p>
                  Radix
                </p>
              </th>
<th>
                <p>
                  Dependencies
                </p>
              </th>
<th>
                <p>
                  Pros
                </p>
              </th>
<th>
                <p>
                  Cons
                </p>
              </th>
</tr></thead>
<tbody>
<tr>
<td>
                <p>
                  <code class="computeroutput"><span class="identifier">cpp_rational</span></code>
                </p>
              </td>
<td>
                <p>
                  boost/multiprecision/cpp_int.hpp
                </p>
              </td>
<td>
                <p>
                  2
                </p>
              </td>
<td>
                <p>
                  None
                </p>
              </td>
<td>
                <p>
                  An all C++ Boost-licensed implementation.
                </p>
              </td>
<td>
                <p>
                  Slower than <a href="http://gmplib.org" target="_top">GMP</a>.
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  <code class="computeroutput"><span class="identifier">gmp_rational</span></code>
                </p>
              </td>
<td>
                <p>
                  boost/multiprecision/gmp.hpp
                </p>
              </td>
<td>
                <p>
                  2
                </p>
              </td>
<td>
                <p>
                  <a href="http://gmplib.org" target="_top">GMP</a>
                </p>
              </td>
<td>
                <p>
                  Very fast and efficient back-end.
                </p>
              </td>
<td>
                <p>
                  Dependency on GNU licensed <a href="http://gmplib.org" target="_top">GMP</a>
                  library.
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  <code class="computeroutput"><span class="identifier">tommath_rational</span></code>
                </p>
              </td>
<td>
                <p>
                  boost/multiprecision/tommath.hpp
                </p>
              </td>
<td>
                <p>
                  2
                </p>
              </td>
<td>
                <p>
                  <a href="http://libtom.org/?page=features&amp;newsitems=5&amp;whatfile=ltm" target="_top">libtommath</a>
                </p>
              </td>
<td>
                <p>
                  All C/C++ implementation that's Boost Software Licence compatible.
                </p>
              </td>
<td>
                <p>
                  Slower than <a href="http://gmplib.org" target="_top">GMP</a>.
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  <code class="computeroutput"><span class="identifier">rational_adaptor</span></code>
                </p>
              </td>
<td>
                <p>
                  boost/multiprecision/rational_adaptor.hpp
                </p>
              </td>
<td>
                <p>
                  N/A
                </p>
              </td>
<td>
                <p>
                  none
                </p>
              </td>
<td>
                <p>
                  All C++ adaptor that allows any integer back-end type to be used
                  as a rational type.
                </p>
              </td>
<td>
                <p>
                  Requires an underlying integer back-end type.
                </p>
              </td>
</tr>
<tr>
<td>
                <p>
                  <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">rational</span></code>
                </p>
              </td>
<td>
                <p>
                  boost/rational.hpp
                </p>
              </td>
<td>
                <p>
                  N/A
                </p>
              </td>
<td>
                <p>
                  None
                </p>
              </td>
<td>
                <p>
                  A C++ rational number type that can used with any <code class="computeroutput"><span class="identifier">number</span></code> integer type.
                </p>
              </td>
<td>
                <p>
                  The expression templates used by <code class="computeroutput"><span class="identifier">number</span></code>
                  end up being "hidden" inside <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">rational</span></code>:
                  performance may well suffer as a result.
                </p>
              </td>
</tr>
</tbody>
</table></div>
</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="interval/mpfi.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../tut.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="rational/cpp_rational.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a>
</div>
</body>
</html>