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26 | <div class="titlepage"><div><div><h4 class="title"> | |
27 | <a name="boost_multiprecision.tut.floats.gmp_float"></a><a class="link" href="gmp_float.html" title="gmp_float">gmp_float</a> | |
28 | </h4></div></div></div> | |
29 | <p> | |
30 | <code class="computeroutput"><span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">multiprecision</span><span class="special">/</span><span class="identifier">gmp</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span></code> | |
31 | </p> | |
32 | <pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">multiprecision</span><span class="special">{</span> | |
33 | ||
34 | <span class="keyword">template</span> <span class="special"><</span><span class="keyword">unsigned</span> <span class="identifier">Digits10</span><span class="special">></span> | |
35 | <span class="keyword">class</span> <span class="identifier">gmp_float</span><span class="special">;</span> | |
36 | ||
37 | <span class="keyword">typedef</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">gmp_float</span><span class="special"><</span><span class="number">50</span><span class="special">></span> <span class="special">></span> <span class="identifier">mpf_float_50</span><span class="special">;</span> | |
38 | <span class="keyword">typedef</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">gmp_float</span><span class="special"><</span><span class="number">100</span><span class="special">></span> <span class="special">></span> <span class="identifier">mpf_float_100</span><span class="special">;</span> | |
39 | <span class="keyword">typedef</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">gmp_float</span><span class="special"><</span><span class="number">500</span><span class="special">></span> <span class="special">></span> <span class="identifier">mpf_float_500</span><span class="special">;</span> | |
40 | <span class="keyword">typedef</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">gmp_float</span><span class="special"><</span><span class="number">1000</span><span class="special">></span> <span class="special">></span> <span class="identifier">mpf_float_1000</span><span class="special">;</span> | |
41 | <span class="keyword">typedef</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">gmp_float</span><span class="special"><</span><span class="number">0</span><span class="special">></span> <span class="special">></span> <span class="identifier">mpf_float</span><span class="special">;</span> | |
42 | ||
43 | <span class="special">}}</span> <span class="comment">// namespaces</span> | |
44 | </pre> | |
45 | <p> | |
46 | The <code class="computeroutput"><span class="identifier">gmp_float</span></code> back-end | |
47 | is used in conjunction with <code class="computeroutput"><span class="identifier">number</span></code> | |
48 | : it acts as a thin wrapper around the <a href="http://gmplib.org" target="_top">GMP</a> | |
49 | <code class="computeroutput"><span class="identifier">mpf_t</span></code> to provide an real-number | |
50 | type that is a drop-in replacement for the native C++ floating-point types, | |
51 | but with much greater precision. | |
52 | </p> | |
53 | <p> | |
54 | Type <code class="computeroutput"><span class="identifier">gmp_float</span></code> can be used | |
55 | at fixed precision by specifying a non-zero <code class="computeroutput"><span class="identifier">Digits10</span></code> | |
56 | template parameter, or at variable precision by setting the template argument | |
57 | to zero. The typedefs mpf_float_50, mpf_float_100, mpf_float_500, mpf_float_1000 | |
58 | provide arithmetic types at 50, 100, 500 and 1000 decimal digits precision | |
59 | respectively. The typedef mpf_float provides a variable precision type | |
60 | whose precision can be controlled via the <code class="computeroutput"><span class="identifier">number</span></code>s | |
61 | member functions. | |
62 | </p> | |
63 | <div class="note"><table border="0" summary="Note"> | |
64 | <tr> | |
65 | <td rowspan="2" align="center" valign="top" width="25"><img alt="[Note]" src="../../../../../../../doc/src/images/note.png"></td> | |
66 | <th align="left">Note</th> | |
67 | </tr> | |
68 | <tr><td align="left" valign="top"><p> | |
69 | This type only provides standard library and <code class="computeroutput"><span class="identifier">numeric_limits</span></code> | |
70 | support when the precision is fixed at compile time. | |
71 | </p></td></tr> | |
72 | </table></div> | |
73 | <p> | |
74 | As well as the usual conversions from arithmetic and string types, instances | |
75 | of <code class="computeroutput"><span class="identifier">number</span><span class="special"><</span><span class="identifier">mpf_float</span><span class="special"><</span><span class="identifier">N</span><span class="special">></span> <span class="special">></span></code> are copy constructible and assignable | |
76 | from: | |
77 | </p> | |
78 | <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; "> | |
79 | <li class="listitem"> | |
80 | The <a href="http://gmplib.org" target="_top">GMP</a> native types <code class="computeroutput"><span class="identifier">mpf_t</span></code>, <code class="computeroutput"><span class="identifier">mpz_t</span></code>, | |
81 | <code class="computeroutput"><span class="identifier">mpq_t</span></code>. | |
82 | </li> | |
83 | <li class="listitem"> | |
84 | The <code class="computeroutput"><span class="identifier">number</span></code> wrappers | |
85 | around those types: <code class="computeroutput"><span class="identifier">number</span><span class="special"><</span><span class="identifier">mpf_float</span><span class="special"><</span><span class="identifier">M</span><span class="special">></span> <span class="special">></span></code>, | |
86 | <code class="computeroutput"><span class="identifier">number</span><span class="special"><</span><span class="identifier">gmp_int</span><span class="special">></span></code>, | |
87 | <code class="computeroutput"><span class="identifier">number</span><span class="special"><</span><span class="identifier">gmp_rational</span><span class="special">></span></code>. | |
88 | </li> | |
89 | </ul></div> | |
90 | <p> | |
91 | It's also possible to access the underlying <code class="computeroutput"><span class="identifier">mpf_t</span></code> | |
92 | via the <code class="computeroutput"><span class="identifier">data</span><span class="special">()</span></code> | |
93 | member function of <code class="computeroutput"><span class="identifier">gmp_float</span></code>. | |
94 | </p> | |
95 | <p> | |
96 | Things you should know when using this type: | |
97 | </p> | |
98 | <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; "> | |
99 | <li class="listitem"> | |
100 | Default constructed <code class="computeroutput"><span class="identifier">gmp_float</span></code>s | |
101 | have the value zero (this is the <a href="http://gmplib.org" target="_top">GMP</a> | |
102 | library's default behavior). | |
103 | </li> | |
104 | <li class="listitem"> | |
105 | No changes are made to the <a href="http://gmplib.org" target="_top">GMP</a> | |
106 | library's global settings, so this type can be safely mixed with existing | |
107 | <a href="http://gmplib.org" target="_top">GMP</a> code. | |
108 | </li> | |
109 | <li class="listitem"> | |
110 | This backend supports rvalue-references and is move-aware, making instantiations | |
111 | of <code class="computeroutput"><span class="identifier">number</span></code> on this backend | |
112 | move aware. | |
113 | </li> | |
114 | <li class="listitem"> | |
115 | It is not possible to round-trip objects of this type to and from a | |
116 | string and get back exactly the same value. This appears to be a limitation | |
117 | of <a href="http://gmplib.org" target="_top">GMP</a>. | |
118 | </li> | |
119 | <li class="listitem"> | |
120 | Since the underlying <a href="http://gmplib.org" target="_top">GMP</a> types | |
121 | have no notion of infinities or NaN's, care should be taken to avoid | |
122 | numeric overflow or division by zero. That latter will result in a | |
123 | std::overflow_error being thrown, while generating excessively large | |
124 | exponents may result in instability of the underlying <a href="http://gmplib.org" target="_top">GMP</a> | |
125 | library (in testing, converting a number with an excessively large | |
126 | or small exponent to a string caused <a href="http://gmplib.org" target="_top">GMP</a> | |
127 | to segfault). | |
128 | </li> | |
129 | <li class="listitem"> | |
130 | This type can equally be used with <a href="http://mpir.org/" target="_top">MPIR</a> | |
131 | as the underlying implementation - indeed that is the recommended option | |
132 | on Win32. | |
133 | </li> | |
134 | <li class="listitem"> | |
135 | Conversion from a string results in a <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">runtime_error</span></code> | |
136 | being thrown if the string can not be interpreted as a valid floating-point | |
137 | number. | |
138 | </li> | |
139 | <li class="listitem"> | |
140 | Division by zero results in a <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">overflow_error</span></code> | |
141 | being thrown. | |
142 | </li> | |
143 | </ul></div> | |
144 | <h6> | |
145 | <a name="boost_multiprecision.tut.floats.gmp_float.h0"></a> | |
146 | <span class="phrase"><a name="boost_multiprecision.tut.floats.gmp_float.gmp_example"></a></span><a class="link" href="gmp_float.html#boost_multiprecision.tut.floats.gmp_float.gmp_example"> GMP example:</a> | |
147 | </h6> | |
148 | <pre class="programlisting"><span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">multiprecision</span><span class="special">/</span><span class="identifier">gmp</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span> | |
149 | <span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">special_functions</span><span class="special">/</span><span class="identifier">gamma</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span> | |
150 | <span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">iostream</span><span class="special">></span> | |
151 | ||
152 | <span class="keyword">int</span> <span class="identifier">main</span><span class="special">()</span> | |
153 | <span class="special">{</span> | |
154 | <span class="keyword">using</span> <span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">multiprecision</span><span class="special">;</span> | |
155 | ||
156 | <span class="comment">// Operations at variable precision and limited standard library support:</span> | |
157 | <span class="identifier">mpf_float</span> <span class="identifier">a</span> <span class="special">=</span> <span class="number">2</span><span class="special">;</span> | |
158 | <span class="identifier">mpf_float</span><span class="special">::</span><span class="identifier">default_precision</span><span class="special">(</span><span class="number">1000</span><span class="special">);</span> | |
159 | <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="identifier">mpf_float</span><span class="special">::</span><span class="identifier">default_precision</span><span class="special">()</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span> | |
160 | <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="identifier">sqrt</span><span class="special">(</span><span class="identifier">a</span><span class="special">)</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span> <span class="comment">// print root-2</span> | |
161 | ||
162 | <span class="comment">// Operations at fixed precision and full standard library support:</span> | |
163 | <span class="identifier">mpf_float_100</span> <span class="identifier">b</span> <span class="special">=</span> <span class="number">2</span><span class="special">;</span> | |
164 | <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><</span><span class="identifier">mpf_float_100</span><span class="special">>::</span><span class="identifier">digits</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span> | |
165 | <span class="comment">// We can use any C++ std lib function:</span> | |
166 | <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="identifier">log</span><span class="special">(</span><span class="identifier">b</span><span class="special">)</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span> <span class="comment">// print log(2)</span> | |
167 | <span class="comment">// We can also use any function from Boost.Math:</span> | |
168 | <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">tgamma</span><span class="special">(</span><span class="identifier">b</span><span class="special">)</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span> | |
169 | <span class="comment">// These even work when the argument is an expression template:</span> | |
170 | <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">tgamma</span><span class="special">(</span><span class="identifier">b</span> <span class="special">*</span> <span class="identifier">b</span><span class="special">)</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span> | |
171 | ||
172 | <span class="comment">// Access the underlying representation:</span> | |
173 | <span class="identifier">mpf_t</span> <span class="identifier">f</span><span class="special">;</span> | |
174 | <span class="identifier">mpf_init</span><span class="special">(</span><span class="identifier">f</span><span class="special">);</span> | |
175 | <span class="identifier">mpf_set</span><span class="special">(</span><span class="identifier">f</span><span class="special">,</span> <span class="identifier">a</span><span class="special">.</span><span class="identifier">backend</span><span class="special">().</span><span class="identifier">data</span><span class="special">());</span> | |
176 | <span class="identifier">mpf_clear</span><span class="special">(</span><span class="identifier">f</span><span class="special">);</span> | |
177 | <span class="keyword">return</span> <span class="number">0</span><span class="special">;</span> | |
178 | <span class="special">}</span> | |
179 | </pre> | |
180 | </div> | |
181 | <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> | |
182 | <td align="left"></td> | |
183 | <td align="right"><div class="copyright-footer">Copyright © 2002-2013 John Maddock and Christopher Kormanyos<p> | |
184 | Distributed under the Boost Software License, Version 1.0. (See accompanying | |
185 | 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>) | |
186 | </p> | |
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