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25 | <div class="section"> | |
26 | <div class="titlepage"><div><div><h4 class="title"> | |
27 | <a name="boost_multiprecision.tut.interval.mpfi"></a><a class="link" href="mpfi.html" title="mpfi_float">mpfi_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">mpfi</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">mpfi_float_backend</span><span class="special">;</span> | |
36 | ||
37 | <span class="keyword">typedef</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">mpfi_float_backend</span><span class="special"><</span><span class="number">50</span><span class="special">></span> <span class="special">></span> <span class="identifier">mpfi_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">mpfi_float_backend</span><span class="special"><</span><span class="number">100</span><span class="special">></span> <span class="special">></span> <span class="identifier">mpfifloat_100</span><span class="special">;</span> | |
39 | <span class="keyword">typedef</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">mpfi_float_backend</span><span class="special"><</span><span class="number">500</span><span class="special">></span> <span class="special">></span> <span class="identifier">mpfifloat_500</span><span class="special">;</span> | |
40 | <span class="keyword">typedef</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">mpfi_float_backend</span><span class="special"><</span><span class="number">1000</span><span class="special">></span> <span class="special">></span> <span class="identifier">mpfi_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">mpfi_float_backend</span><span class="special"><</span><span class="number">0</span><span class="special">></span> <span class="special">></span> <span class="identifier">mpfi_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">mpfi_float_backend</span></code> | |
47 | type 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://perso.ens-lyon.fr/nathalie.revol/software.html" target="_top">MPFI</a> | |
49 | <code class="computeroutput"><span class="identifier">mpfi_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 and implementing interval arithmetic. | |
52 | </p> | |
53 | <p> | |
54 | Type <code class="computeroutput"><span class="identifier">mpfi_float_backend</span></code> | |
55 | can be used 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 mpfi_float_50, mpfi_float_100, mpfi_float_500, mpfi_float_1000 | |
58 | provide arithmetic types at 50, 100, 500 and 1000 decimal digits precision | |
59 | respectively. The typedef mpfi_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 <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">mpfi_float_backend</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://perso.ens-lyon.fr/nathalie.revol/software.html" target="_top">MPFI</a> | |
81 | native type <code class="computeroutput"><span class="identifier">mpfi_t</span></code>. | |
82 | </li> | |
83 | <li class="listitem"> | |
84 | The <code class="computeroutput"><span class="identifier">number</span></code> wrappers | |
85 | around <a href="http://perso.ens-lyon.fr/nathalie.revol/software.html" target="_top">MPFI</a> | |
86 | or <a href="http://www.mpfr.org" target="_top">MPFR</a>: <code class="computeroutput"><span class="identifier">number</span><span class="special"><</span><span class="identifier">mpfi_float_backend</span><span class="special"><</span><span class="identifier">M</span><span class="special">></span> <span class="special">></span></code> | |
87 | and <code class="computeroutput"><span class="identifier">number</span><span class="special"><</span><span class="identifier">mpfr_float</span><span class="special"><</span><span class="identifier">M</span><span class="special">></span> <span class="special">></span></code>. | |
88 | </li> | |
89 | <li class="listitem"> | |
90 | There is a two argument constructor taking two <code class="computeroutput"><span class="identifier">number</span><span class="special"><</span><span class="identifier">mpfr_float</span><span class="special"><</span><span class="identifier">M</span><span class="special">></span> <span class="special">></span></code> | |
91 | arguments specifying the interval. | |
92 | </li> | |
93 | </ul></div> | |
94 | <p> | |
95 | It's also possible to access the underlying <code class="computeroutput"><span class="identifier">mpfi_t</span></code> | |
96 | via the data() member function of <code class="computeroutput"><span class="identifier">mpfi_float_backend</span></code>. | |
97 | </p> | |
98 | <p> | |
99 | Things you should know when using this type: | |
100 | </p> | |
101 | <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; "> | |
102 | <li class="listitem"> | |
103 | A default constructed <code class="computeroutput"><span class="identifier">mpfi_float_backend</span></code> | |
104 | is set to zero (<span class="emphasis"><em>Note that this is <span class="bold"><strong>not</strong></span> | |
105 | the default <a href="http://perso.ens-lyon.fr/nathalie.revol/software.html" target="_top">MPFI</a> | |
106 | behavior</em></span>). | |
107 | </li> | |
108 | <li class="listitem"> | |
109 | No changes are made to <a href="http://gmplib.org" target="_top">GMP</a> or | |
110 | <a href="http://www.mpfr.org" target="_top">MPFR</a> global settings, so this | |
111 | type can coexist with existing <a href="http://www.mpfr.org" target="_top">MPFR</a> | |
112 | or <a href="http://gmplib.org" target="_top">GMP</a> code. | |
113 | </li> | |
114 | <li class="listitem"> | |
115 | The code can equally use <a href="http://mpir.org/" target="_top">MPIR</a> | |
116 | in place of <a href="http://gmplib.org" target="_top">GMP</a> - indeed that | |
117 | is the preferred option on Win32. | |
118 | </li> | |
119 | <li class="listitem"> | |
120 | This backend supports rvalue-references and is move-aware, making instantiations | |
121 | of <code class="computeroutput"><span class="identifier">number</span></code> on this backend | |
122 | move aware. | |
123 | </li> | |
124 | <li class="listitem"> | |
125 | 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> | |
126 | being thrown if the string can not be interpreted as a valid floating-point | |
127 | number. | |
128 | </li> | |
129 | <li class="listitem"> | |
130 | Division by zero results in an infinity. | |
131 | </li> | |
132 | </ul></div> | |
133 | <p> | |
134 | There are some additional non member functions for working on intervals: | |
135 | </p> | |
136 | <pre class="programlisting"><span class="keyword">template</span> <span class="special"><</span><span class="keyword">unsigned</span> <span class="identifier">Digits10</span><span class="special">,</span> <span class="identifier">expression_template_option</span> <span class="identifier">ExpressionTemplates</span><span class="special">></span> | |
137 | <span class="identifier">number</span><span class="special"><</span><span class="identifier">mpfr_float_backend</span><span class="special"><</span><span class="identifier">Digits10</span><span class="special">>,</span> <span class="identifier">ExpressionTemplates</span><span class="special">></span> <span class="identifier">lower</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">mpfi_float_backend</span><span class="special"><</span><span class="identifier">Digits10</span><span class="special">>,</span> <span class="identifier">ExpressionTemplates</span><span class="special">>&</span> <span class="identifier">val</span><span class="special">);</span> | |
138 | </pre> | |
139 | <p> | |
140 | Returns the lower end of the interval. | |
141 | </p> | |
142 | <pre class="programlisting"><span class="keyword">template</span> <span class="special"><</span><span class="keyword">unsigned</span> <span class="identifier">Digits10</span><span class="special">,</span> <span class="identifier">expression_template_option</span> <span class="identifier">ExpressionTemplates</span><span class="special">></span> | |
143 | <span class="identifier">number</span><span class="special"><</span><span class="identifier">mpfr_float_backend</span><span class="special"><</span><span class="identifier">Digits10</span><span class="special">>,</span> <span class="identifier">ExpressionTemplates</span><span class="special">></span> <span class="identifier">upper</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">mpfi_float_backend</span><span class="special"><</span><span class="identifier">Digits10</span><span class="special">>,</span> <span class="identifier">ExpressionTemplates</span><span class="special">>&</span> <span class="identifier">val</span><span class="special">);</span> | |
144 | </pre> | |
145 | <p> | |
146 | Returns the upper end of the interval. | |
147 | </p> | |
148 | <pre class="programlisting"><span class="keyword">template</span> <span class="special"><</span><span class="keyword">unsigned</span> <span class="identifier">Digits10</span><span class="special">,</span> <span class="identifier">expression_template_option</span> <span class="identifier">ExpressionTemplates</span><span class="special">></span> | |
149 | <span class="identifier">number</span><span class="special"><</span><span class="identifier">mpfr_float_backend</span><span class="special"><</span><span class="identifier">Digits10</span><span class="special">>,</span> <span class="identifier">ExpressionTemplates</span><span class="special">></span> <span class="identifier">median</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">mpfi_float_backend</span><span class="special"><</span><span class="identifier">Digits10</span><span class="special">>,</span> <span class="identifier">ExpressionTemplates</span><span class="special">>&</span> <span class="identifier">val</span><span class="special">);</span> | |
150 | </pre> | |
151 | <p> | |
152 | Returns the mid point of the interval. | |
153 | </p> | |
154 | <pre class="programlisting"><span class="keyword">template</span> <span class="special"><</span><span class="keyword">unsigned</span> <span class="identifier">Digits10</span><span class="special">,</span> <span class="identifier">expression_template_option</span> <span class="identifier">ExpressionTemplates</span><span class="special">></span> | |
155 | <span class="identifier">number</span><span class="special"><</span><span class="identifier">mpfr_float_backend</span><span class="special"><</span><span class="identifier">Digits10</span><span class="special">>,</span> <span class="identifier">ExpressionTemplates</span><span class="special">></span> <span class="identifier">width</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">mpfi_float_backend</span><span class="special"><</span><span class="identifier">Digits10</span><span class="special">>,</span> <span class="identifier">ExpressionTemplates</span><span class="special">>&</span> <span class="identifier">val</span><span class="special">);</span> | |
156 | </pre> | |
157 | <p> | |
158 | Returns the absolute width of the interval. | |
159 | </p> | |
160 | <pre class="programlisting"><span class="keyword">template</span> <span class="special"><</span><span class="keyword">unsigned</span> <span class="identifier">Digits10</span><span class="special">,</span> <span class="identifier">expression_template_option</span> <span class="identifier">ExpressionTemplates</span><span class="special">></span> | |
161 | <span class="identifier">number</span><span class="special"><</span><span class="identifier">mpfi_float_backend</span><span class="special"><</span><span class="identifier">Digits10</span><span class="special">>,</span> <span class="identifier">ExpressionTemplates</span><span class="special">></span> <span class="identifier">intersect</span><span class="special">(</span> | |
162 | <span class="keyword">const</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">mpfi_float_backend</span><span class="special"><</span><span class="identifier">Digits10</span><span class="special">>,</span> <span class="identifier">ExpressionTemplates</span><span class="special">>&</span> <span class="identifier">a</span><span class="special">,</span> | |
163 | <span class="keyword">const</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">mpfi_float_backend</span><span class="special"><</span><span class="identifier">Digits10</span><span class="special">>,</span> <span class="identifier">ExpressionTemplates</span><span class="special">>&</span> <span class="identifier">b</span><span class="special">);</span> | |
164 | </pre> | |
165 | <p> | |
166 | Returns the interval which is the intersection of the <span class="emphasis"><em>a</em></span> | |
167 | and <span class="emphasis"><em>b</em></span>. Returns an unspecified empty interval if there | |
168 | is no such intersection. | |
169 | </p> | |
170 | <pre class="programlisting"><span class="keyword">template</span> <span class="special"><</span><span class="keyword">unsigned</span> <span class="identifier">Digits10</span><span class="special">,</span> <span class="identifier">expression_template_option</span> <span class="identifier">ExpressionTemplates</span><span class="special">></span> | |
171 | <span class="identifier">number</span><span class="special"><</span><span class="identifier">mpfi_float_backend</span><span class="special"><</span><span class="identifier">Digits10</span><span class="special">>,</span> <span class="identifier">ExpressionTemplates</span><span class="special">></span> <span class="identifier">hull</span><span class="special">(</span> | |
172 | <span class="keyword">const</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">mpfi_float_backend</span><span class="special"><</span><span class="identifier">Digits10</span><span class="special">>,</span> <span class="identifier">ExpressionTemplates</span><span class="special">>&</span> <span class="identifier">a</span><span class="special">,</span> | |
173 | <span class="keyword">const</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">mpfi_float_backend</span><span class="special"><</span><span class="identifier">Digits10</span><span class="special">>,</span> <span class="identifier">ExpressionTemplates</span><span class="special">>&</span> <span class="identifier">b</span><span class="special">);</span> | |
174 | </pre> | |
175 | <p> | |
176 | Returns the interval which is the union of <span class="emphasis"><em>a</em></span> and | |
177 | <span class="emphasis"><em>b</em></span>. | |
178 | </p> | |
179 | <pre class="programlisting"><span class="keyword">template</span> <span class="special"><</span><span class="keyword">unsigned</span> <span class="identifier">Digits10</span><span class="special">,</span> <span class="identifier">expression_template_option</span> <span class="identifier">ExpressionTemplates</span><span class="special">></span> | |
180 | <span class="keyword">bool</span> <span class="identifier">overlap</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">mpfi_float_backend</span><span class="special"><</span><span class="identifier">Digits10</span><span class="special">>,</span> <span class="identifier">ExpressionTemplates</span><span class="special">>&</span> <span class="identifier">a</span><span class="special">,</span> | |
181 | <span class="keyword">const</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">mpfi_float_backend</span><span class="special"><</span><span class="identifier">Digits10</span><span class="special">>,</span> <span class="identifier">ExpressionTemplates</span><span class="special">>&</span> <span class="identifier">b</span><span class="special">);</span> | |
182 | </pre> | |
183 | <p> | |
184 | Returns <code class="computeroutput"><span class="keyword">true</span></code> only if the intervals | |
185 | <span class="emphasis"><em>a</em></span> and <span class="emphasis"><em>b</em></span> overlap. | |
186 | </p> | |
187 | <pre class="programlisting"><span class="keyword">template</span> <span class="special"><</span><span class="keyword">unsigned</span> <span class="identifier">Digits10</span><span class="special">,</span> <span class="identifier">expression_template_option</span> <span class="identifier">ExpressionTemplates1</span><span class="special">,</span> <span class="identifier">expression_template_option</span> <span class="identifier">ExpressionTemplates2</span><span class="special">></span> | |
188 | <span class="keyword">bool</span> <span class="identifier">in</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">mpfr_float_backend</span><span class="special"><</span><span class="identifier">Digits10</span><span class="special">>,</span> <span class="identifier">ExpressionTemplates1</span><span class="special">>&</span> <span class="identifier">a</span><span class="special">,</span> | |
189 | <span class="keyword">const</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">mpfi_float_backend</span><span class="special"><</span><span class="identifier">Digits10</span><span class="special">>,</span> <span class="identifier">ExpressionTemplates2</span><span class="special">>&</span> <span class="identifier">b</span><span class="special">);</span> | |
190 | </pre> | |
191 | <p> | |
192 | Returns <code class="computeroutput"><span class="keyword">true</span></code> only if point | |
193 | <span class="emphasis"><em>a</em></span> is contained within the interval <span class="emphasis"><em>b</em></span>. | |
194 | </p> | |
195 | <pre class="programlisting"><span class="keyword">template</span> <span class="special"><</span><span class="keyword">unsigned</span> <span class="identifier">Digits10</span><span class="special">,</span> <span class="identifier">expression_template_option</span> <span class="identifier">ExpressionTemplates</span><span class="special">></span> | |
196 | <span class="keyword">bool</span> <span class="identifier">zero_in</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">mpfi_float_backend</span><span class="special"><</span><span class="identifier">Digits10</span><span class="special">>,</span> <span class="identifier">ExpressionTemplates</span><span class="special">>&</span> <span class="identifier">a</span><span class="special">);</span> | |
197 | </pre> | |
198 | <p> | |
199 | Returns <code class="computeroutput"><span class="keyword">true</span></code> only if the interval | |
200 | <span class="emphasis"><em>a</em></span> contains the value zero. | |
201 | </p> | |
202 | <pre class="programlisting"><span class="keyword">template</span> <span class="special"><</span><span class="keyword">unsigned</span> <span class="identifier">Digits10</span><span class="special">,</span> <span class="identifier">expression_template_option</span> <span class="identifier">ExpressionTemplates</span><span class="special">></span> | |
203 | <span class="keyword">bool</span> <span class="identifier">subset</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">mpfi_float_backend</span><span class="special"><</span><span class="identifier">Digits10</span><span class="special">>,</span> <span class="identifier">ExpressionTemplates</span><span class="special">>&</span> <span class="identifier">a</span><span class="special">,</span> | |
204 | <span class="keyword">const</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">mpfi_float_backend</span><span class="special"><</span><span class="identifier">Digits10</span><span class="special">>,</span> <span class="identifier">ExpressionTemplates</span><span class="special">>&</span> <span class="identifier">b</span><span class="special">);</span> | |
205 | </pre> | |
206 | <p> | |
207 | Returns <code class="computeroutput"><span class="keyword">true</span></code> only if <span class="emphasis"><em>a</em></span> | |
208 | is a subset of <span class="emphasis"><em>b</em></span>. | |
209 | </p> | |
210 | <pre class="programlisting"><span class="keyword">template</span> <span class="special"><</span><span class="keyword">unsigned</span> <span class="identifier">Digits10</span><span class="special">,</span> <span class="identifier">expression_template_option</span> <span class="identifier">ExpressionTemplates</span><span class="special">></span> | |
211 | <span class="keyword">bool</span> <span class="identifier">proper_subset</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">mpfi_float_backend</span><span class="special"><</span><span class="identifier">Digits10</span><span class="special">>,</span> <span class="identifier">ExpressionTemplates</span><span class="special">>&</span> <span class="identifier">a</span><span class="special">,</span> | |
212 | <span class="keyword">const</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">mpfi_float_backend</span><span class="special"><</span><span class="identifier">Digits10</span><span class="special">>,</span> <span class="identifier">ExpressionTemplates</span><span class="special">>&</span> <span class="identifier">b</span><span class="special">);</span> | |
213 | </pre> | |
214 | <p> | |
215 | Returns <code class="computeroutput"><span class="keyword">true</span></code> only if <span class="emphasis"><em>a</em></span> | |
216 | is a proper subset of <span class="emphasis"><em>b</em></span>. | |
217 | </p> | |
218 | <pre class="programlisting"><span class="keyword">template</span> <span class="special"><</span><span class="keyword">unsigned</span> <span class="identifier">Digits10</span><span class="special">,</span> <span class="identifier">expression_template_option</span> <span class="identifier">ExpressionTemplates</span><span class="special">></span> | |
219 | <span class="keyword">bool</span> <span class="identifier">empty</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">mpfi_float_backend</span><span class="special"><</span><span class="identifier">Digits10</span><span class="special">>,</span> <span class="identifier">ExpressionTemplates</span><span class="special">>&</span> <span class="identifier">a</span><span class="special">);</span> | |
220 | </pre> | |
221 | <p> | |
222 | Returns <code class="computeroutput"><span class="keyword">true</span></code> only if <span class="emphasis"><em>a</em></span> | |
223 | is an empty interval, equivalent to <code class="computeroutput"><span class="identifier">upper</span><span class="special">(</span><span class="identifier">a</span><span class="special">)</span> | |
224 | <span class="special"><</span> <span class="identifier">lower</span><span class="special">(</span><span class="identifier">a</span><span class="special">)</span></code>. | |
225 | </p> | |
226 | <pre class="programlisting"><span class="keyword">template</span> <span class="special"><</span><span class="keyword">unsigned</span> <span class="identifier">Digits10</span><span class="special">,</span> <span class="identifier">expression_template_option</span> <span class="identifier">ExpressionTemplates</span><span class="special">></span> | |
227 | <span class="keyword">bool</span> <span class="identifier">singleton</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">number</span><span class="special"><</span><span class="identifier">mpfi_float_backend</span><span class="special"><</span><span class="identifier">Digits10</span><span class="special">>,</span> <span class="identifier">ExpressionTemplates</span><span class="special">>&</span> <span class="identifier">a</span><span class="special">);</span> | |
228 | </pre> | |
229 | <p> | |
230 | Returns <code class="computeroutput"><span class="keyword">true</span></code> if <code class="computeroutput"><span class="identifier">lower</span><span class="special">(</span><span class="identifier">a</span><span class="special">)</span> <span class="special">==</span> | |
231 | <span class="identifier">upper</span><span class="special">(</span><span class="identifier">a</span><span class="special">)</span></code>. | |
232 | </p> | |
233 | <h6> | |
234 | <a name="boost_multiprecision.tut.interval.mpfi.h0"></a> | |
235 | <span class="phrase"><a name="boost_multiprecision.tut.interval.mpfi.mpfi_example"></a></span><a class="link" href="mpfi.html#boost_multiprecision.tut.interval.mpfi.mpfi_example"> MPFI | |
236 | example:</a> | |
237 | </h6> | |
238 | <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">mpfi</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span> | |
239 | <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> | |
240 | <span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">iostream</span><span class="special">></span> | |
241 | ||
242 | <span class="keyword">int</span> <span class="identifier">main</span><span class="special">()</span> | |
243 | <span class="special">{</span> | |
244 | <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> | |
245 | ||
246 | <span class="comment">// Operations at variable precision and no numeric_limits support:</span> | |
247 | <span class="identifier">mpfi_float</span> <span class="identifier">a</span> <span class="special">=</span> <span class="number">2</span><span class="special">;</span> | |
248 | <span class="identifier">mpfi_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> | |
249 | <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="identifier">mpfi_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> | |
250 | <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> | |
251 | ||
252 | <span class="comment">// Operations at fixed precision and full numeric_limits support:</span> | |
253 | <span class="identifier">mpfi_float_100</span> <span class="identifier">b</span> <span class="special">=</span> <span class="number">2</span><span class="special">;</span> | |
254 | <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">mpfi_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> | |
255 | <span class="comment">// We can use any C++ std lib function:</span> | |
256 | <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> | |
257 | ||
258 | <span class="comment">// Access the underlying data:</span> | |
259 | <span class="identifier">mpfi_t</span> <span class="identifier">r</span><span class="special">;</span> | |
260 | <span class="identifier">mpfi_init</span><span class="special">(</span><span class="identifier">r</span><span class="special">);</span> | |
261 | <span class="identifier">mpfi_set</span><span class="special">(</span><span class="identifier">r</span><span class="special">,</span> <span class="identifier">b</span><span class="special">.</span><span class="identifier">backend</span><span class="special">().</span><span class="identifier">data</span><span class="special">());</span> | |
262 | ||
263 | <span class="comment">// Construct some explicit intervals and perform set operations:</span> | |
264 | <span class="identifier">mpfi_float_50</span> <span class="identifier">i1</span><span class="special">(</span><span class="number">1</span><span class="special">,</span> <span class="number">2</span><span class="special">),</span> <span class="identifier">i2</span><span class="special">(</span><span class="number">1.5</span><span class="special">,</span> <span class="number">2.5</span><span class="special">);</span> | |
265 | <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="identifier">intersect</span><span class="special">(</span><span class="identifier">i1</span><span class="special">,</span> <span class="identifier">i2</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> | |
266 | <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="identifier">hull</span><span class="special">(</span><span class="identifier">i1</span><span class="special">,</span> <span class="identifier">i2</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> | |
267 | <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="identifier">overlap</span><span class="special">(</span><span class="identifier">i1</span><span class="special">,</span> <span class="identifier">i2</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> | |
268 | <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="identifier">subset</span><span class="special">(</span><span class="identifier">i1</span><span class="special">,</span> <span class="identifier">i2</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> | |
269 | <span class="identifier">mpfi_clear</span><span class="special">(</span><span class="identifier">r</span><span class="special">);</span> | |
270 | <span class="keyword">return</span> <span class="number">0</span><span class="special">;</span> | |
271 | <span class="special">}</span> | |
272 | </pre> | |
273 | </div> | |
274 | <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> | |
275 | <td align="left"></td> | |
276 | <td align="right"><div class="copyright-footer">Copyright © 2002-2013 John Maddock and Christopher Kormanyos<p> | |
277 | Distributed under the Boost Software License, Version 1.0. (See accompanying | |
278 | 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>) | |
279 | </p> | |
280 | </div></td> | |
281 | </tr></table> | |
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