1<html> 2<head> 3<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII"> 4<title>interval<R></title> 5<link rel="stylesheet" href="boostbook.css" type="text/css"> 6<meta name="generator" content="DocBook XSL Stylesheets V1.79.1"> 7<link rel="home" href="index.html" title="Safe Numerics"> 8<link rel="up" href="library_implementation.html" title="Library Implementation"> 9<link rel="prev" href="checked_arithmetic.html" title="Checked Arithmetic"> 10<link rel="next" href="checked_integer_arithmetic.html" title="safe_compare<T, U>"> 11</head> 12<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF"> 13<table cellpadding="2" width="100%"><tr> 14<td valign="top"><img href="index.html" height="164px" src="pre-boost.jpg" alt="Library Documentation Index"></td> 15<td><h2>Safe Numerics</h2></td> 16</tr></table> 17<div class="spirit-nav"> 18<a accesskey="p" href="checked_arithmetic.html"><img src="images/prev.png" alt="Prev"></a><a accesskey="u" href="library_implementation.html"><img src="images/up.png" alt="Up"></a><a accesskey="h" href="index.html"><img src="images/home.png" alt="Home"></a><a accesskey="n" href="checked_integer_arithmetic.html"><img src="images/next.png" alt="Next"></a> 19</div> 20<div class="section"> 21<div class="titlepage"><div><div><h3 class="title"> 22<a name="safe_numerics.interval"></a>interval<R></h3></div></div></div> 23<div class="toc"><dl class="toc"> 24<dt><span class="section"><a href="interval.html#idm130202132352">Description</a></span></dt> 25<dt><span class="section"><a href="interval.html#idm130202129408">Template Parameters</a></span></dt> 26<dt><span class="section"><a href="interval.html#idm130202126048">Notation</a></span></dt> 27<dt><span class="section"><a href="interval.html#idm130202108592">Associated Types</a></span></dt> 28<dt><span class="section"><a href="interval.html#idm130202102752">Valid Expressions</a></span></dt> 29<dt><span class="section"><a href="interval.html#idm130202023104">Example of use</a></span></dt> 30<dt><span class="section"><a href="interval.html#idm130201930272">Header</a></span></dt> 31</dl></div> 32<div class="section"> 33<div class="titlepage"><div><div><h4 class="title"> 34<a name="idm130202132352"></a>Description</h4></div></div></div> 35<p>A closed arithmetic interval represented by a pair of elements of 36 type R. In principle, one should be able to use Boost.Interval library for 37 this. But the functions in this library are not <code class="computeroutput">constexpr</code>. 38 Also, this Boost.Interval is more complex and does not support certain 39 operations such bit operations. Perhaps some time in the future, 40 Boost.Interval will be used instead of this <code class="computeroutput">interval<R></code> 41 type.</p> 42</div> 43<div class="section"> 44<div class="titlepage"><div><div><h4 class="title"> 45<a name="idm130202129408"></a>Template Parameters</h4></div></div></div> 46<p>R must model the type requirements of <a class="link" href="numeric.html" title="Numeric<T>">Numeric</a>. Note this in principle 47 includes any numeric type including floating point numbers and instances 48 of <a class="link" href="checked_result.html" title="checked_result<R>"><code class="computeroutput">checked_result<R></code></a>.</p> 49</div> 50<div class="section"> 51<div class="titlepage"><div><div><h4 class="title"> 52<a name="idm130202126048"></a>Notation</h4></div></div></div> 53<div class="informaltable"><table class="table"> 54<colgroup> 55<col align="left"> 56<col align="left"> 57</colgroup> 58<thead><tr> 59<th align="left">Symbol</th> 60<th align="left">Description</th> 61</tr></thead> 62<tbody> 63<tr> 64<td align="left"><code class="computeroutput">I</code></td> 65<td align="left">An interval type</td> 66</tr> 67<tr> 68<td align="left"><code class="computeroutput">i, j</code></td> 69<td align="left">An instance of interval type</td> 70</tr> 71<tr> 72<td align="left"><code class="computeroutput">R</code></td> 73<td align="left">Numeric types which can be used to make an interval</td> 74</tr> 75<tr> 76<td align="left"><code class="computeroutput">r</code></td> 77<td align="left">An instance of type R</td> 78</tr> 79<tr> 80<td align="left"><code class="computeroutput">p</code></td> 81<td align="left">An instance of std::pair<R, R></td> 82</tr> 83<tr> 84<td align="left"><code class="computeroutput">l, u</code></td> 85<td align="left">Lowermost and uppermost values in an interval</td> 86</tr> 87<tr> 88<td align="left"><code class="computeroutput">os</code></td> 89<td align="left">std::basic_ostream<class CharT, class Traits = 90 std::char_traits<CharT>></td> 91</tr> 92</tbody> 93</table></div> 94</div> 95<div class="section"> 96<div class="titlepage"><div><div><h4 class="title"> 97<a name="idm130202108592"></a>Associated Types</h4></div></div></div> 98<div class="informaltable"><table class="table"> 99<colgroup> 100<col align="left"> 101<col align="left"> 102</colgroup> 103<tbody><tr> 104<td align="left"><a class="link" href="checked_result.html" title="checked_result<R>"><code class="computeroutput">checked_result</code></a></td> 105<td align="left">holds either the result of an operation or information as 106 to why it failed</td> 107</tr></tbody> 108</table></div> 109</div> 110<div class="section"> 111<div class="titlepage"><div><div><h4 class="title"> 112<a name="idm130202102752"></a>Valid Expressions</h4></div></div></div> 113<p>Note that all expressions are constexpr.</p> 114<div class="informaltable"><table class="table"> 115<colgroup> 116<col align="left"> 117<col align="left"> 118<col align="left"> 119</colgroup> 120<thead><tr> 121<th align="left">Expression</th> 122<th align="left">Return Type</th> 123<th align="left">Semantics</th> 124</tr></thead> 125<tbody> 126<tr> 127<td align="left"><code class="computeroutput">interval<R>(l, u)</code></td> 128<td align="left"><code class="computeroutput">interval<R></code></td> 129<td align="left">construct a new interval from a pair of limits</td> 130</tr> 131<tr> 132<td align="left"><code class="computeroutput">interval<R>(p)</code></td> 133<td align="left"><code class="computeroutput">interval<R></code></td> 134<td align="left">construct a new interval from a pair of limits</td> 135</tr> 136<tr> 137<td align="left"><code class="computeroutput">interval<R>(i)</code></td> 138<td align="left"><code class="computeroutput">interval<R></code></td> 139<td align="left">copy constructor</td> 140</tr> 141<tr> 142<td align="left"><code class="computeroutput">make_interval<R>()</code></td> 143<td align="left"><code class="computeroutput">interval<R></code></td> 144<td align="left">return new interval with 145 std::numric_limits<R>::min() and 146 std::numric_limits<R>::max()</td> 147</tr> 148<tr> 149<td align="left"><code class="computeroutput">make_interval<R>(const R 150 &r)</code></td> 151<td align="left"><code class="computeroutput">interval<R></code></td> 152<td align="left">return new interval with 153 std::numric_limits<R>::min() and 154 std::numric_limits<R>::max()</td> 155</tr> 156<tr> 157<td align="left"><code class="computeroutput">i.l</code></td> 158<td align="left"><code class="computeroutput">R</code></td> 159<td align="left">lowermost value in the interval i</td> 160</tr> 161<tr> 162<td align="left"><code class="computeroutput">i.u</code></td> 163<td align="left"><code class="computeroutput">R</code></td> 164<td align="left">uppermost value in the interval i</td> 165</tr> 166<tr> 167<td align="left"><code class="computeroutput">i.includes(j)</code></td> 168<td align="left"><code class="computeroutput">boost::logic::tribool</code></td> 169<td align="left">return true if interval i includes interval j</td> 170</tr> 171<tr> 172<td align="left"><code class="computeroutput">i.excludes(j)</code></td> 173<td align="left"><code class="computeroutput">boost::logic::tribool</code></td> 174<td align="left">return true if interval i includes interval j</td> 175</tr> 176<tr> 177<td align="left"><code class="computeroutput">i.includes(t)</code></td> 178<td align="left"><code class="computeroutput">bool</code></td> 179<td align="left">return true if interval i includes value t</td> 180</tr> 181<tr> 182<td align="left"><code class="computeroutput">i.excludes(t)</code></td> 183<td align="left"><code class="computeroutput">bool</code></td> 184<td align="left">return true if interval i includes value t</td> 185</tr> 186<tr> 187<td align="left"><code class="computeroutput">i + j</code></td> 188<td align="left"><code class="computeroutput">interval<R></code></td> 189<td align="left">add two intervals and return the result</td> 190</tr> 191<tr> 192<td align="left"><code class="computeroutput">i - j</code></td> 193<td align="left"><code class="computeroutput">interval<R></code></td> 194<td align="left">subtract two intervals and return the result</td> 195</tr> 196<tr> 197<td align="left"><code class="computeroutput">i * j</code></td> 198<td align="left"><code class="computeroutput">interval<R></code></td> 199<td align="left">multiply two intervals and return the result</td> 200</tr> 201<tr> 202<td align="left"><code class="computeroutput">i / j</code></td> 203<td align="left"><code class="computeroutput">interval<R></code></td> 204<td align="left">divide one interval by another and return the 205 result</td> 206</tr> 207<tr> 208<td align="left"><code class="computeroutput">i % j</code></td> 209<td align="left"><code class="computeroutput">interval<R></code></td> 210<td align="left">calculate modulus of one interval by another and return 211 the result</td> 212</tr> 213<tr> 214<td align="left"><code class="computeroutput">i << j</code></td> 215<td align="left"><code class="computeroutput">interval<R></code></td> 216<td align="left">calculate the range that would result from shifting one 217 interval by another</td> 218</tr> 219<tr> 220<td align="left"><code class="computeroutput">i >> j</code></td> 221<td align="left"><code class="computeroutput">interval<R></code></td> 222<td align="left">calculate the range that would result from shifting one 223 interval by another</td> 224</tr> 225<tr> 226<td align="left"><code class="computeroutput">i | j</code></td> 227<td align="left"><code class="computeroutput">interval<R></code></td> 228<td align="left">range of values which can result from applying | to any 229 pair of operands from I and j</td> 230</tr> 231<tr> 232<td align="left"><code class="computeroutput">i & j</code></td> 233<td align="left"><code class="computeroutput">interval<R></code></td> 234<td align="left">range of values which can result from applying & to 235 any pair of operands from I and j</td> 236</tr> 237<tr> 238<td align="left"><code class="computeroutput">i ^ j</code></td> 239<td align="left"><code class="computeroutput">interval<R></code></td> 240<td align="left">range of values which can result from applying ^ to any 241 pair of operands from I and j</td> 242</tr> 243<tr> 244<td align="left"><code class="computeroutput">t < u</code></td> 245<td align="left"><code class="computeroutput">boost::logic::tribool</code></td> 246<td align="left">true if every element in t is less than every element in 247 u</td> 248</tr> 249<tr> 250<td align="left"><code class="computeroutput">t > u</code></td> 251<td align="left"><code class="computeroutput">boost::logic::tribool</code></td> 252<td align="left">true if every element in t is greater than every element 253 in u</td> 254</tr> 255<tr> 256<td align="left"><code class="computeroutput">t <= u</code></td> 257<td align="left"><code class="computeroutput">boost::logic::tribool</code></td> 258<td align="left">true if every element in t is less than or equal to every 259 element in u</td> 260</tr> 261<tr> 262<td align="left"><code class="computeroutput">t >= u</code></td> 263<td align="left"><code class="computeroutput">boost::logic::tribool</code></td> 264<td align="left">true if every element in t is greater than or equal to 265 every element in u</td> 266</tr> 267<tr> 268<td align="left"><code class="computeroutput">t == u</code></td> 269<td align="left"><code class="computeroutput">bool</code></td> 270<td align="left">true if limits are equal</td> 271</tr> 272<tr> 273<td align="left"><code class="computeroutput">t != u</code></td> 274<td align="left"><code class="computeroutput">bool</code></td> 275<td align="left">true if limits are not equal</td> 276</tr> 277<tr> 278<td align="left"><code class="computeroutput">os << i</code></td> 279<td align="left"><code class="computeroutput">os &</code></td> 280<td align="left">print interval to output stream</td> 281</tr> 282</tbody> 283</table></div> 284</div> 285<div class="section"> 286<div class="titlepage"><div><div><h4 class="title"> 287<a name="idm130202023104"></a>Example of use</h4></div></div></div> 288<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">iostream</span><span class="special">></span> 289<span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">cstdint</span><span class="special">></span> 290<span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">cassert</span><span class="special">></span> 291<span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">numeric</span><span class="special">/</span><span class="identifier">safe_numerics</span><span class="special">/</span><span class="identifier">interval</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span> 292 293<span class="keyword">int</span> <span class="identifier">main</span><span class="special">(</span><span class="special">)</span><span class="special">{</span> 294 <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"test1"</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span> 295 <span class="identifier">interval</span><span class="special"><</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">int16_t</span><span class="special">></span> <span class="identifier">x</span> <span class="special">=</span> <span class="special">{</span><span class="special">-</span><span class="number">64</span><span class="special">,</span> <span class="number">63</span><span class="special">}</span><span class="special">;</span> 296 <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"x = "</span> <span class="special"><<</span> <span class="identifier">x</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span> 297 <span class="identifier">interval</span><span class="special"><</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">int16_t</span><span class="special">></span> <span class="identifier">y</span><span class="special">(</span><span class="special">-</span><span class="number">128</span><span class="special">,</span> <span class="number">126</span><span class="special">)</span><span class="special">;</span> 298 <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"y = "</span> <span class="special"><<</span> <span class="identifier">y</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span> 299 <span class="identifier">assert</span><span class="special">(</span><span class="keyword">static_cast</span><span class="special"><</span><span class="identifier">interval</span><span class="special"><</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">int16_t</span><span class="special">>></span><span class="special">(</span><span class="identifier">add</span><span class="special"><</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">int16_t</span><span class="special">></span><span class="special">(</span><span class="identifier">x</span><span class="special">,</span><span class="identifier">x</span><span class="special">)</span><span class="special">)</span> <span class="special">==</span> <span class="identifier">y</span><span class="special">)</span><span class="special">;</span> 300 <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"x + x ="</span> <span class="special"><<</span> <span class="identifier">add</span><span class="special"><</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">int16_t</span><span class="special">></span><span class="special">(</span><span class="identifier">x</span><span class="special">,</span> <span class="identifier">x</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> 301 <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"x - x = "</span> <span class="special"><<</span> <span class="identifier">subtract</span><span class="special"><</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">int16_t</span><span class="special">></span><span class="special">(</span><span class="identifier">x</span><span class="special">,</span> <span class="identifier">x</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> 302 <span class="keyword">return</span> <span class="number">0</span><span class="special">;</span> 303<span class="special">}</span></pre> 304</div> 305<div class="section"> 306<div class="titlepage"><div><div><h4 class="title"> 307<a name="idm130201930272"></a>Header</h4></div></div></div> 308<p><code class="computeroutput">#include 309 <boost/numeric/safe_numerics/interval.hpp></code></p> 310</div> 311</div> 312<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> 313<td align="left"></td> 314<td align="right"><div class="copyright-footer">Copyright © 2012-2018 Robert Ramey<p><a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">Subject to Boost 315 Software License</a></p> 316</div></td> 317</tr></table> 318<hr> 319<div class="spirit-nav"> 320<a accesskey="p" href="checked_arithmetic.html"><img src="images/prev.png" alt="Prev"></a><a accesskey="u" href="library_implementation.html"><img src="images/up.png" alt="Up"></a><a accesskey="h" href="index.html"><img src="images/home.png" alt="Home"></a><a accesskey="n" href="checked_integer_arithmetic.html"><img src="images/next.png" alt="Next"></a> 321</div> 322</body> 323</html> 324
