ceph/src/boost/libs/icl/doc/html/boost_icl/function_reference/addition.html

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  24 </div>
  25 <div class="section boost_icl_function_reference_addition" lang="en">
  26 <div class="titlepage"><div><div><h3 class="title">
  27 <a name="boost_icl.function_reference.addition"></a><a class="link" href="addition.html" title="Addition">Addition</a>
  28 </h3></div></div></div>
  29 <div class="toc"><dl>
  30 <dt><span class="section"><a href="addition.html#boost_icl.function_reference.addition.synopsis">Synopsis</a></span></dt>
  31 <dt><span class="section"><a href="addition.html#boost_icl.function_reference.addition.functions">Functions</a></span></dt>
  32 <dt><span class="section"><a href="addition.html#boost_icl.function_reference.addition.inplace_operators">Inplace
  33         operators</a></span></dt>
  34 <dt><span class="section"><a href="addition.html#boost_icl.function_reference.addition.infix_operators">Infix
  35         operators</a></span></dt>
  36 </dl></div>
  37 <div class="section boost_icl_function_reference_addition_synopsis" lang="en">
  38 <div class="titlepage"><div><div><h4 class="title">
  39 <a name="boost_icl.function_reference.addition.synopsis"></a><a class="link" href="addition.html#boost_icl.function_reference.addition.synopsis" title="Synopsis">Synopsis</a>
  40 </h4></div></div></div>
  41 <div class="informaltable"><table class="table">
  42 <colgroup>
  43 <col>
  44 <col>
  45 <col>
  46 <col>
  47 <col>
  48 </colgroup>
  49 <thead><tr>
  50 <th>
  51                 <p>
  52                   Addition
  53                 </p>
  54                 </th>
  55 <th>
  56                 <p>
  57                   interval<br> sets
  58                 </p>
  59                 </th>
  60 <th>
  61                 <p>
  62                   interval<br> maps
  63                 </p>
  64                 </th>
  65 <th>
  66                 <p>
  67                   element<br> sets
  68                 </p>
  69                 </th>
  70 <th>
  71                 <p>
  72                   element<br> maps
  73                 </p>
  74                 </th>
  75 </tr></thead>
  76 <tbody>
  77 <tr>
  78 <td>
  79                 <p>
  80                   <code class="computeroutput"><span class="identifier">T</span><span class="special">&amp;</span>
  81                   <span class="identifier">T</span><span class="special">::</span><span class="identifier">add</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">P</span><span class="special">&amp;)</span></code>
  82                 </p>
  83                 </td>
  84 <td>
  85                 <p>
  86                   <a class="link" href="../interface/function_synopsis.html#element_type"><span class="bold"><strong>e</strong></span></a>
  87                   <a class="link" href="../interface/function_synopsis.html#interval_type"><span class="bold"><strong>i</strong></span></a>
  88                 </p>
  89                 </td>
  90 <td>
  91                 <p>
  92                   <a class="link" href="../interface/function_synopsis.html#element_mapping_type"><span class="bold"><strong>b</strong></span></a>
  93                   <a class="link" href="../interface/function_synopsis.html#interval_mapping_type"><span class="bold"><strong>p</strong></span></a>
  94                 </p>
  95                 </td>
  96 <td>
  97                 <p>
  98                 </p>
  99                 </td>
 100 <td>
 101                 <p>
 102                   <a class="link" href="../interface/function_synopsis.html#element_mapping_type"><span class="bold"><strong>b</strong></span></a>
 103                 </p>
 104                 </td>
 105 </tr>
 106 <tr>
 107 <td>
 108                 <p>
 109                   <code class="computeroutput"><span class="identifier">T</span><span class="special">&amp;</span>
 110                   <span class="identifier">add</span><span class="special">(</span><span class="identifier">T</span><span class="special">&amp;,</span>
 111                   <span class="keyword">const</span> <span class="identifier">P</span><span class="special">&amp;)</span></code>
 112                 </p>
 113                 </td>
 114 <td>
 115                 <p>
 116                   <a class="link" href="../interface/function_synopsis.html#element_type"><span class="bold"><strong>e</strong></span></a>
 117                   <a class="link" href="../interface/function_synopsis.html#interval_type"><span class="bold"><strong>i</strong></span></a>
 118                 </p>
 119                 </td>
 120 <td>
 121                 <p>
 122                   <a class="link" href="../interface/function_synopsis.html#element_mapping_type"><span class="bold"><strong>b</strong></span></a>
 123                   <a class="link" href="../interface/function_synopsis.html#interval_mapping_type"><span class="bold"><strong>p</strong></span></a>
 124                 </p>
 125                 </td>
 126 <td>
 127                 <p>
 128                   <a class="link" href="../interface/function_synopsis.html#element_type"><span class="bold"><strong>e</strong></span></a>
 129                 </p>
 130                 </td>
 131 <td>
 132                 <p>
 133                   <a class="link" href="../interface/function_synopsis.html#element_mapping_type"><span class="bold"><strong>b</strong></span></a>
 134                 </p>
 135                 </td>
 136 </tr>
 137 <tr>
 138 <td>
 139                 <p>
 140                   <code class="computeroutput"><span class="identifier">J</span> <span class="identifier">T</span><span class="special">::</span><span class="identifier">add</span><span class="special">(</span><span class="identifier">J</span>
 141                   <span class="identifier">pos</span><span class="special">,</span>
 142                   <span class="keyword">const</span> <span class="identifier">P</span><span class="special">&amp;)</span></code>
 143                 </p>
 144                 </td>
 145 <td>
 146                 <p>
 147                   <a class="link" href="../interface/function_synopsis.html#interval_type"><span class="bold"><strong>i</strong></span></a>
 148                 </p>
 149                 </td>
 150 <td>
 151                 <p>
 152                   <a class="link" href="../interface/function_synopsis.html#interval_mapping_type"><span class="bold"><strong>p</strong></span></a>
 153                 </p>
 154                 </td>
 155 <td>
 156                 <p>
 157                 </p>
 158                 </td>
 159 <td>
 160                 <p>
 161                   <a class="link" href="../interface/function_synopsis.html#element_mapping_type"><span class="bold"><strong>b</strong></span></a>
 162                 </p>
 163                 </td>
 164 </tr>
 165 <tr>
 166 <td>
 167                 <p>
 168                   <code class="computeroutput"><span class="identifier">J</span> <span class="identifier">add</span><span class="special">(</span><span class="identifier">T</span><span class="special">&amp;,</span> <span class="identifier">J</span>
 169                   <span class="identifier">pos</span><span class="special">,</span>
 170                   <span class="keyword">const</span> <span class="identifier">P</span><span class="special">&amp;)</span></code>
 171                 </p>
 172                 </td>
 173 <td>
 174                 <p>
 175                   <a class="link" href="../interface/function_synopsis.html#interval_type"><span class="bold"><strong>i</strong></span></a>
 176                 </p>
 177                 </td>
 178 <td>
 179                 <p>
 180                   <a class="link" href="../interface/function_synopsis.html#interval_mapping_type"><span class="bold"><strong>p</strong></span></a>
 181                 </p>
 182                 </td>
 183 <td>
 184                 <p>
 185                   <a class="link" href="../interface/function_synopsis.html#element_type"><span class="bold"><strong>e</strong></span></a>
 186                 </p>
 187                 </td>
 188 <td>
 189                 <p>
 190                   <a class="link" href="../interface/function_synopsis.html#element_mapping_type"><span class="bold"><strong>b</strong></span></a>
 191                 </p>
 192                 </td>
 193 </tr>
 194 <tr>
 195 <td>
 196                 <p>
 197                   <code class="computeroutput"><span class="identifier">T</span><span class="special">&amp;</span>
 198                   <span class="keyword">operator</span> <span class="special">+=(</span><span class="identifier">T</span><span class="special">&amp;,</span>
 199                   <span class="keyword">const</span> <span class="identifier">P</span><span class="special">&amp;)</span></code>
 200                 </p>
 201                 </td>
 202 <td>
 203                 <p>
 204                   <a class="link" href="../interface/function_synopsis.html#element_type"><span class="bold"><strong>e</strong></span></a>
 205                   <a class="link" href="../interface/function_synopsis.html#interval_type"><span class="bold"><strong>i</strong></span></a>
 206                   <a class="link" href="../interface/function_synopsis.html#interval_set_types"><span class="bold"><strong>S</strong></span></a>
 207                 </p>
 208                 </td>
 209 <td>
 210                 <p>
 211                   <a class="link" href="../interface/function_synopsis.html#element_mapping_type"><span class="bold"><strong>b</strong></span></a>
 212                   <a class="link" href="../interface/function_synopsis.html#interval_mapping_type"><span class="bold"><strong>p</strong></span></a>
 213                   <a class="link" href="../interface/function_synopsis.html#interval_map_types"><span class="bold"><strong>M</strong></span></a>
 214                 </p>
 215                 </td>
 216 <td>
 217                 <p>
 218                   <a class="link" href="../interface/function_synopsis.html#element_type"><span class="bold"><strong>e</strong></span></a>
 219                   <a class="link" href="../interface/function_synopsis.html#itl_set_type"><span class="bold"><strong>s</strong></span></a>
 220                 </p>
 221                 </td>
 222 <td>
 223                 <p>
 224                   <a class="link" href="../interface/function_synopsis.html#element_mapping_type"><span class="bold"><strong>b</strong></span></a>
 225                   <a class="link" href="../interface/function_synopsis.html#itl_map_type"><span class="bold"><strong>m</strong></span></a>
 226                 </p>
 227                 </td>
 228 </tr>
 229 <tr>
 230 <td>
 231                 <p>
 232                   <code class="computeroutput"><span class="identifier">T</span> <span class="keyword">operator</span>
 233                   <span class="special">+</span> <span class="special">(</span><span class="identifier">T</span><span class="special">,</span>
 234                   <span class="keyword">const</span> <span class="identifier">P</span><span class="special">&amp;)</span></code><br> <code class="computeroutput"><span class="identifier">T</span>
 235                   <span class="keyword">operator</span> <span class="special">+</span>
 236                   <span class="special">(</span><span class="keyword">const</span>
 237                   <span class="identifier">P</span><span class="special">&amp;,</span>
 238                   <span class="identifier">T</span><span class="special">)</span></code>
 239                 </p>
 240                 </td>
 241 <td>
 242                 <p>
 243                   <a class="link" href="../interface/function_synopsis.html#element_type"><span class="bold"><strong>e</strong></span></a>
 244                   <a class="link" href="../interface/function_synopsis.html#interval_type"><span class="bold"><strong>i</strong></span></a>
 245                   <a class="link" href="../interface/function_synopsis.html#interval_set_types"><span class="bold"><strong>S</strong></span></a>
 246                 </p>
 247                 </td>
 248 <td>
 249                 <p>
 250                   <a class="link" href="../interface/function_synopsis.html#element_mapping_type"><span class="bold"><strong>b</strong></span></a>
 251                   <a class="link" href="../interface/function_synopsis.html#interval_mapping_type"><span class="bold"><strong>p</strong></span></a>
 252                   <a class="link" href="../interface/function_synopsis.html#interval_map_types"><span class="bold"><strong>M</strong></span></a>
 253                 </p>
 254                 </td>
 255 <td>
 256                 <p>
 257                   <a class="link" href="../interface/function_synopsis.html#element_type"><span class="bold"><strong>e</strong></span></a>
 258                   <a class="link" href="../interface/function_synopsis.html#itl_set_type"><span class="bold"><strong>s</strong></span></a>
 259                 </p>
 260                 </td>
 261 <td>
 262                 <p>
 263                   <a class="link" href="../interface/function_synopsis.html#element_mapping_type"><span class="bold"><strong>b</strong></span></a>
 264                   <a class="link" href="../interface/function_synopsis.html#itl_map_type"><span class="bold"><strong>m</strong></span></a>
 265                 </p>
 266                 </td>
 267 </tr>
 268 <tr>
 269 <td>
 270                 <p>
 271                   <code class="computeroutput"><span class="identifier">T</span><span class="special">&amp;</span>
 272                   <span class="keyword">operator</span> <span class="special">|=(</span>
 273                   <span class="identifier">T</span><span class="special">&amp;,</span>
 274                   <span class="keyword">const</span> <span class="identifier">P</span><span class="special">&amp;)</span></code>
 275                 </p>
 276                 </td>
 277 <td>
 278                 <p>
 279                   <a class="link" href="../interface/function_synopsis.html#element_type"><span class="bold"><strong>e</strong></span></a>
 280                   <a class="link" href="../interface/function_synopsis.html#interval_type"><span class="bold"><strong>i</strong></span></a>
 281                   <a class="link" href="../interface/function_synopsis.html#interval_set_types"><span class="bold"><strong>S</strong></span></a>
 282                 </p>
 283                 </td>
 284 <td>
 285                 <p>
 286                   <a class="link" href="../interface/function_synopsis.html#element_mapping_type"><span class="bold"><strong>b</strong></span></a>
 287                   <a class="link" href="../interface/function_synopsis.html#interval_mapping_type"><span class="bold"><strong>p</strong></span></a>
 288                   <a class="link" href="../interface/function_synopsis.html#interval_map_types"><span class="bold"><strong>M</strong></span></a>
 289                 </p>
 290                 </td>
 291 <td>
 292                 <p>
 293                   <a class="link" href="../interface/function_synopsis.html#element_type"><span class="bold"><strong>e</strong></span></a>
 294                   <a class="link" href="../interface/function_synopsis.html#itl_set_type"><span class="bold"><strong>s</strong></span></a>
 295                 </p>
 296                 </td>
 297 <td>
 298                 <p>
 299                   <a class="link" href="../interface/function_synopsis.html#element_mapping_type"><span class="bold"><strong>b</strong></span></a>
 300                   <a class="link" href="../interface/function_synopsis.html#itl_map_type"><span class="bold"><strong>m</strong></span></a>
 301                 </p>
 302                 </td>
 303 </tr>
 304 <tr>
 305 <td>
 306                 <p>
 307                   <code class="computeroutput"><span class="identifier">T</span> <span class="keyword">operator</span>
 308                   <span class="special">|</span> <span class="special">(</span><span class="identifier">T</span><span class="special">,</span>
 309                   <span class="keyword">const</span> <span class="identifier">P</span><span class="special">&amp;)</span></code><br> <code class="computeroutput"><span class="identifier">T</span>
 310                   <span class="keyword">operator</span> <span class="special">|</span>
 311                   <span class="special">(</span><span class="keyword">const</span>
 312                   <span class="identifier">P</span><span class="special">&amp;,</span>
 313                   <span class="identifier">T</span><span class="special">)</span></code>
 314                 </p>
 315                 </td>
 316 <td>
 317                 <p>
 318                   <a class="link" href="../interface/function_synopsis.html#element_type"><span class="bold"><strong>e</strong></span></a>
 319                   <a class="link" href="../interface/function_synopsis.html#interval_type"><span class="bold"><strong>i</strong></span></a>
 320                   <a class="link" href="../interface/function_synopsis.html#interval_set_types"><span class="bold"><strong>S</strong></span></a>
 321                 </p>
 322                 </td>
 323 <td>
 324                 <p>
 325                   <a class="link" href="../interface/function_synopsis.html#element_mapping_type"><span class="bold"><strong>b</strong></span></a>
 326                   <a class="link" href="../interface/function_synopsis.html#interval_mapping_type"><span class="bold"><strong>p</strong></span></a>
 327                   <a class="link" href="../interface/function_synopsis.html#interval_map_types"><span class="bold"><strong>M</strong></span></a>
 328                 </p>
 329                 </td>
 330 <td>
 331                 <p>
 332                   <a class="link" href="../interface/function_synopsis.html#element_type"><span class="bold"><strong>e</strong></span></a>
 333                   <a class="link" href="../interface/function_synopsis.html#itl_set_type"><span class="bold"><strong>s</strong></span></a>
 334                 </p>
 335                 </td>
 336 <td>
 337                 <p>
 338                   <a class="link" href="../interface/function_synopsis.html#element_mapping_type"><span class="bold"><strong>b</strong></span></a>
 339                   <a class="link" href="../interface/function_synopsis.html#itl_map_type"><span class="bold"><strong>m</strong></span></a>
 340                 </p>
 341                 </td>
 342 </tr>
 343 </tbody>
 344 </table></div>
 345 <p>
 346           Functions and operators that implement <span class="emphasis"><em><span class="bold"><strong>Addition</strong></span></em></span>
 347           on <span class="bold"><strong>icl</strong></span> objects are given in the table
 348           above. <code class="computeroutput"><span class="keyword">operator</span> <span class="special">|=</span></code>
 349           and <code class="computeroutput"><span class="keyword">operator</span> <span class="special">|</span></code>
 350           are behavioral identical to <code class="computeroutput"><span class="keyword">operator</span>
 351           <span class="special">+=</span></code> and <code class="computeroutput"><span class="keyword">operator</span>
 352           <span class="special">+</span></code>. This is a redundancy that has
 353           been introduced deliberately, because a <span class="emphasis"><em>set union</em></span>
 354           semantics is often attached <code class="computeroutput"><span class="identifier">operators</span>
 355           <span class="special">|=</span></code> and <code class="computeroutput"><span class="special">|</span></code>.
 356         </p>
 357 <div class="informaltable"><table class="table">
 358 <colgroup>
 359 <col>
 360 <col>
 361 </colgroup>
 362 <thead><tr>
 363 <th>
 364                 <p>
 365                 </p>
 366                 </th>
 367 <th>
 368                 <p>
 369                   Description of Addition
 370                 </p>
 371                 </th>
 372 </tr></thead>
 373 <tbody>
 374 <tr>
 375 <td>
 376                 <p>
 377                   <code class="computeroutput"><span class="identifier">Sets</span></code>
 378                 </p>
 379                 </td>
 380 <td>
 381                 <p>
 382                   Addition on Sets implements <span class="emphasis"><em><span class="bold"><strong>set
 383                   union</strong></span></em></span>
 384                 </p>
 385                 </td>
 386 </tr>
 387 <tr>
 388 <td>
 389                 <p>
 390                   <code class="computeroutput"><span class="identifier">Maps</span></code>
 391                 </p>
 392                 </td>
 393 <td>
 394                 <p>
 395                   Addition on Maps implements a <span class="emphasis"><em><span class="bold"><strong>map
 396                   union</strong></span></em></span> function similar to <span class="emphasis"><em>set union</em></span>.
 397                   If, on insertion of an element value pair <code class="computeroutput"><span class="special">(</span><span class="identifier">k</span><span class="special">,</span><span class="identifier">v</span><span class="special">)</span></code>
 398                   it's key <code class="computeroutput"><span class="identifier">k</span></code> is in
 399                   the map already, the addition function is propagated to the associated
 400                   value. This functionality has been introduced as <span class="emphasis"><em>aggregate
 401                   on collision</em></span> for element maps and <span class="emphasis"><em>aggregate
 402                   on overlap</em></span> for interval maps.
 403                 </p>
 404                 <p>
 405                   Find more on <a class="link" href="../concepts/aggrovering.html" title="Addability, Subtractability and Aggregate on Overlap"><span class="emphasis"><em>addability
 406                   of maps</em></span></a> and related <a class="link" href="../semantics/maps.html" title="Maps"><span class="emphasis"><em>semantic
 407                   issues</em></span></a> following the links.
 408                 </p>
 409                 <p>
 410                   Examples, demonstrating Addition on interval containers are <a class="link" href="../examples/overlap_counter.html" title="Overlap counter"><span class="emphasis"><em>overlap
 411                   counter</em></span></a>, <a class="link" href="../examples/party.html" title="Party"><span class="emphasis"><em>party</em></span></a>
 412                   and <a class="link" href="../examples/partys_height_average.html" title="Party's height average"><span class="emphasis"><em>party's
 413                   height average.</em></span></a>
 414                 </p>
 415                 </td>
 416 </tr>
 417 </tbody>
 418 </table></div>
 419 <p>
 420           For <code class="computeroutput"><span class="identifier">Sets</span></code> <span class="emphasis"><em><span class="bold"><strong>addition</strong></span></em></span> and <span class="emphasis"><em><span class="bold"><strong>insertion</strong></span></em></span>
 421           are implemented identically. Functions <code class="computeroutput"><span class="identifier">add</span></code>
 422           and <code class="computeroutput"><span class="identifier">insert</span></code> collapse to
 423           the same function. For <code class="computeroutput"><span class="identifier">Maps</span></code>
 424           <span class="emphasis"><em><span class="bold"><strong>addition</strong></span></em></span> and <span class="emphasis"><em><span class="bold"><strong>insertion</strong></span></em></span> work differently. Function
 425           <code class="computeroutput"><span class="identifier">add</span></code> performs aggregations
 426           on collision or overlap, while function <code class="computeroutput"><span class="identifier">insert</span></code>
 427           only inserts values that do not yet have key values.
 428         </p>
 429 </div>
 430 <div class="section boost_icl_function_reference_addition_functions" lang="en">
 431 <div class="titlepage"><div><div><h4 class="title">
 432 <a name="boost_icl.function_reference.addition.functions"></a><a class="link" href="addition.html#boost_icl.function_reference.addition.functions" title="Functions">Functions</a>
 433 </h4></div></div></div>
 434 <p>
 435           The admissible combinations of types for member function <code class="computeroutput"><span class="identifier">T</span><span class="special">&amp;</span> <span class="identifier">T</span><span class="special">::</span><span class="identifier">add</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">P</span><span class="special">&amp;)</span></code>
 436           can be summarized in the <span class="emphasis"><em><span class="bold"><strong>overload table</strong></span></em></span>
 437           below:
 438         </p>
 439 <p>
 440
 441 </p>
 442 <pre class="programlisting"><span class="comment">// overload table for    T\P| e i b p
 443 </span><span class="identifier">T</span><span class="special">&amp;</span> <span class="identifier">T</span><span class="special">::</span><span class="identifier">add</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">P</span><span class="special">&amp;)</span>      <span class="special">---+--------</span>
 444 <span class="identifier">T</span><span class="special">&amp;</span> <span class="identifier">add</span><span class="special">(</span><span class="identifier">T</span><span class="special">&amp;,</span> <span class="keyword">const</span> <span class="identifier">P</span><span class="special">&amp;)</span>      <span class="identifier">s</span> <span class="special">|</span> <span class="identifier">s</span>
 445                           <span class="identifier">m</span> <span class="special">|</span>     <span class="identifier">m</span>
 446                           <span class="identifier">S</span> <span class="special">|</span> <span class="identifier">S</span> <span class="identifier">S</span>
 447                           <span class="identifier">M</span> <span class="special">|</span>     <span class="identifier">M</span> <span class="identifier">M</span>
 448 </pre>
 449 <p>
 450         </p>
 451 <p>
 452           The next table contains complexity characteristics for <code class="computeroutput"><span class="identifier">add</span></code>.
 453         </p>
 454 <div class="table">
 455 <a name="id1155216"></a><p class="title"><b>Table&#160;1.21.&#160;Time Complexity for member function add on icl
 456         containers</b></p>
 457 <div class="table-contents"><table class="table" summary="Time Complexity for member function add on icl
 458         containers">
 459 <colgroup>
 460 <col>
 461 <col>
 462 <col>
 463 <col>
 464 <col>
 465 </colgroup>
 466 <thead><tr>
 467 <th>
 468               <p>
 469                 <code class="computeroutput"><span class="identifier">T</span><span class="special">&amp;</span>
 470                 <span class="identifier">T</span><span class="special">::</span><span class="identifier">add</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">P</span><span class="special">&amp;)</span></code><br> <code class="computeroutput"><span class="identifier">T</span><span class="special">&amp;</span> <span class="identifier">add</span><span class="special">(</span><span class="identifier">T</span><span class="special">&amp;,</span> <span class="keyword">const</span>
 471                 <span class="identifier">P</span><span class="special">&amp;)</span></code>
 472               </p>
 473               </th>
 474 <th>
 475               <p>
 476                 domain<br> type
 477               </p>
 478               </th>
 479 <th>
 480               <p>
 481                 interval<br> type
 482               </p>
 483               </th>
 484 <th>
 485               <p>
 486                 domain<br> mapping<br> type
 487               </p>
 488               </th>
 489 <th>
 490               <p>
 491                 interval<br> mapping<br> type
 492               </p>
 493               </th>
 494 </tr></thead>
 495 <tbody>
 496 <tr>
 497 <td>
 498               <p>
 499                 <a href="http://www.cplusplus.com/reference/stl/set/" target="_top"><code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">set</span></code> </a>
 500               </p>
 501               </td>
 502 <td>
 503               <p>
 504                 <span class="emphasis"><em>O(log n)</em></span>
 505               </p>
 506               </td>
 507 <td>
 508               <p>
 509               </p>
 510               </td>
 511 <td>
 512               <p>
 513               </p>
 514               </td>
 515 <td>
 516               <p>
 517               </p>
 518               </td>
 519 </tr>
 520 <tr>
 521 <td>
 522               <p>
 523                 <code class="computeroutput"><a class="link" href="../../boost/icl/map.html" title="Class template map">icl::map</a></code>
 524               </p>
 525               </td>
 526 <td>
 527               <p>
 528               </p>
 529               </td>
 530 <td>
 531               <p>
 532               </p>
 533               </td>
 534 <td>
 535               <p>
 536                 <span class="emphasis"><em>O(log n)</em></span>
 537               </p>
 538               </td>
 539 <td>
 540               <p>
 541               </p>
 542               </td>
 543 </tr>
 544 <tr>
 545 <td>
 546               <p>
 547                 <code class="computeroutput"><a class="link" href="../../boost/icl/interval_set.html" title="Class template interval_set">interval_set</a></code><br>
 548                 <code class="computeroutput"><a class="link" href="../../boost/icl/separate_interval_set.html" title="Class template separate_interval_set">separate_interval_set</a></code>
 549               </p>
 550               </td>
 551 <td>
 552               <p>
 553                 <span class="emphasis"><em>O(log n)</em></span>
 554               </p>
 555               </td>
 556 <td>
 557               <p>
 558                 <span class="emphasis"><em>amortized<br> O(log n)</em></span>
 559               </p>
 560               </td>
 561 <td>
 562               <p>
 563               </p>
 564               </td>
 565 <td>
 566               <p>
 567               </p>
 568               </td>
 569 </tr>
 570 <tr>
 571 <td>
 572               <p>
 573                 <code class="computeroutput"><a class="link" href="../../boost/icl/split_interval_set.html" title="Class template split_interval_set">split_interval_set</a></code>
 574               </p>
 575               </td>
 576 <td>
 577               <p>
 578                 <span class="emphasis"><em>O(log n)</em></span>
 579               </p>
 580               </td>
 581 <td>
 582               <p>
 583                 <span class="emphasis"><em>O(n)</em></span>
 584               </p>
 585               </td>
 586 <td>
 587               <p>
 588               </p>
 589               </td>
 590 <td>
 591               <p>
 592               </p>
 593               </td>
 594 </tr>
 595 <tr>
 596 <td>
 597               <p>
 598                 <code class="computeroutput"><a class="link" href="../../boost/icl/interval_map.html" title="Class template interval_map">interval_map</a></code><br>
 599                 <code class="computeroutput"><a class="link" href="../../boost/icl/split_interval_map.html" title="Class template split_interval_map">split_interval_map</a></code>
 600               </p>
 601               </td>
 602 <td>
 603               <p>
 604               </p>
 605               </td>
 606 <td>
 607               <p>
 608               </p>
 609               </td>
 610 <td>
 611               <p>
 612                 <span class="emphasis"><em>O(log n)</em></span>
 613               </p>
 614               </td>
 615 <td>
 616               <p>
 617                 <span class="emphasis"><em>O(n)</em></span>
 618               </p>
 619               </td>
 620 </tr>
 621 </tbody>
 622 </table></div>
 623 </div>
 624 <br class="table-break"><a name="boost_icl.function_reference.addition.functions.hinted_addition"></a><h6>
 625 <a name="id1155640"></a>
 626           <a class="link" href="addition.html#boost_icl.function_reference.addition.functions.hinted_addition">Hinted
 627           addition</a>
 628         </h6>
 629 <p>
 630           Function <code class="computeroutput"><span class="identifier">J</span> <span class="identifier">T</span><span class="special">::</span><span class="identifier">add</span><span class="special">(</span><span class="identifier">J</span> <span class="identifier">prior</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">P</span><span class="special">&amp;</span> <span class="identifier">addend</span><span class="special">)</span></code>
 631           allows for an addition in <span class="emphasis"><em><span class="bold"><strong>constant time</strong></span></em></span>,
 632           if <code class="computeroutput"><span class="identifier">addend</span></code> can be inserted
 633           right after iterator <code class="computeroutput"><span class="identifier">prior</span></code>
 634           without collision. If this is not possible the complexity characteristics
 635           are as stated for the non hinted addition above. Hinted addition is available
 636           for these combinations of types:
 637 </p>
 638 <pre class="programlisting"><span class="comment">// overload table for addition with hint        T\P| e i b p
 639 </span><span class="identifier">J</span> <span class="identifier">T</span><span class="special">::</span><span class="identifier">add</span><span class="special">(</span><span class="identifier">J</span> <span class="identifier">prior</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">P</span><span class="special">&amp;)</span>                     <span class="special">---+--------</span>
 640 <span class="identifier">J</span> <span class="identifier">add</span><span class="special">(</span><span class="identifier">T</span><span class="special">&amp;,</span> <span class="identifier">J</span> <span class="identifier">prior</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">P</span><span class="special">&amp;)</span>                     <span class="identifier">s</span> <span class="special">|</span> <span class="identifier">s</span>
 641                                                  <span class="identifier">m</span> <span class="special">|</span>     <span class="identifier">m</span>
 642                                                  <span class="identifier">S</span> <span class="special">|</span>   <span class="identifier">S</span>
 643                                                  <span class="identifier">M</span> <span class="special">|</span>       <span class="identifier">M</span>
 644 </pre>
 645 <p>
 646         </p>
 647 </div>
 648 <div class="section boost_icl_function_reference_addition_inplace_operators" lang="en">
 649 <div class="titlepage"><div><div><h4 class="title">
 650 <a name="boost_icl.function_reference.addition.inplace_operators"></a><a class="link" href="addition.html#boost_icl.function_reference.addition.inplace_operators" title="Inplace operators">Inplace
 651         operators</a>
 652 </h4></div></div></div>
 653 <p>
 654           The possible overloads of inplace <code class="computeroutput"><span class="identifier">T</span><span class="special">&amp;</span> <span class="keyword">operator</span>
 655           <span class="special">+=</span> <span class="special">(</span><span class="identifier">T</span><span class="special">&amp;,</span> <span class="keyword">const</span> <span class="identifier">P</span><span class="special">&amp;)</span></code> are given by two tables, that show
 656           admissible combinations of types. Row types show instantiations of argument
 657           type <code class="computeroutput"><span class="identifier">T</span></code>. Columns types show
 658           show instantiations of argument type <code class="computeroutput"><span class="identifier">P</span></code>.
 659           If a combination of argument types is possible, the related table cell
 660           contains the result type of the operation. <a class="link" href="../interface/function_synopsis.html#element_type">Placeholders</a>
 661           <a class="link" href="../interface/function_synopsis.html#element_type"><span class="bold"><strong>e</strong></span></a>
 662           <a class="link" href="../interface/function_synopsis.html#interval_type"><span class="bold"><strong>i</strong></span></a>
 663           <a class="link" href="../interface/function_synopsis.html#element_mapping_type"><span class="bold"><strong>b</strong></span></a>
 664           <a class="link" href="../interface/function_synopsis.html#interval_mapping_type"><span class="bold"><strong>p</strong></span></a>
 665           <a class="link" href="../interface/function_synopsis.html#itl_set_type"><span class="bold"><strong>s</strong></span></a>
 666           <a class="link" href="../interface/function_synopsis.html#interval_set_types"><span class="bold"><strong>S</strong></span></a>
 667           <a class="link" href="../interface/function_synopsis.html#itl_map_type"><span class="bold"><strong>m</strong></span></a>
 668           <a class="link" href="../interface/function_synopsis.html#interval_map_types"><span class="bold"><strong>M</strong></span></a>
 669           will be used to denote <span class="emphasis"><em>elements, intervals, element value pairs,
 670           interval value pairs, element sets, interval sets, element maps</em></span>
 671           and <span class="emphasis"><em>interval maps</em></span>. The first table shows the overloads
 672           of <code class="computeroutput"><span class="special">+=</span></code> for <span class="emphasis"><em>element
 673           containers</em></span> the second table refers to <span class="emphasis"><em>interval containers</em></span>.
 674         </p>
 675 <p>
 676
 677 </p>
 678 <pre class="programlisting"><span class="comment">// overload tables for             element containers:     interval containers:
 679 </span><span class="identifier">T</span><span class="special">&amp;</span> <span class="keyword">operator</span> <span class="special">+=</span> <span class="special">(</span><span class="identifier">T</span><span class="special">&amp;,</span> <span class="keyword">const</span> <span class="identifier">P</span><span class="special">&amp;)</span>      <span class="special">+=</span> <span class="special">|</span> <span class="identifier">e</span> <span class="identifier">b</span> <span class="identifier">s</span> <span class="identifier">m</span>            <span class="special">+=</span> <span class="special">|</span> <span class="identifier">e</span> <span class="identifier">i</span> <span class="identifier">b</span> <span class="identifier">p</span> <span class="identifier">S</span> <span class="identifier">M</span>
 680                                    <span class="special">---+--------</span>            <span class="special">---+------------</span>
 681                                    <span class="identifier">s</span>  <span class="special">|</span> <span class="identifier">s</span>   <span class="identifier">s</span>              <span class="identifier">S</span>  <span class="special">|</span> <span class="identifier">S</span> <span class="identifier">S</span>     <span class="identifier">S</span>
 682                                    <span class="identifier">m</span>  <span class="special">|</span>   <span class="identifier">m</span>   <span class="identifier">m</span>            <span class="identifier">M</span>  <span class="special">|</span>     <span class="identifier">M</span> <span class="identifier">M</span>   <span class="identifier">M</span>
 683 </pre>
 684 <p>
 685         </p>
 686 <p>
 687           For the definition of admissible overloads we separate <span class="emphasis"><em>element
 688           containers</em></span> from <span class="emphasis"><em>interval containers</em></span>. Within
 689           each group all combinations of types are supported for an operation, that
 690           are in line with the <span class="bold"><strong>icl's</strong></span> design and
 691           the sets of laws, that establish the <span class="bold"><strong>icl's</strong></span>
 692           <a class="link" href="../semantics.html" title="Semantics">semantics</a>.
 693         </p>
 694 <p>
 695           Overloads between <span class="emphasis"><em>element containers</em></span> and <span class="emphasis"><em>interval
 696           containers</em></span> could also be defined. But this has not been done
 697           for pragmatical reasons: Each additional combination of types for an operation
 698           enlarges the space of possible overloads. This makes the overload resolution
 699           by compilers more complex, error prone and slows down compilation speed.
 700           Error messages for unresolvable or ambiguous overloads are difficult to
 701           read and understand. Therefore overloading of namespace global functions
 702           in the <span class="bold"><strong>icl</strong></span> are limited to a reasonable
 703           field of combinations, that are described here.
 704         </p>
 705 </div>
 706 <a name="boost_icl.function_reference.addition.complexity"></a><h5>
 707 <a name="id1156317"></a>
 708         <a class="link" href="addition.html#boost_icl.function_reference.addition.complexity">Complexity</a>
 709       </h5>
 710 <p>
 711         For different combinations of argument types <code class="computeroutput"><span class="identifier">T</span></code>
 712         and <code class="computeroutput"><span class="identifier">P</span></code> different implementations
 713         of the <code class="computeroutput"><span class="keyword">operator</span> <span class="special">+=</span></code>
 714         are selected. These implementations show different complexity characteristics.
 715         If <code class="computeroutput"><span class="identifier">T</span></code> is a container type,
 716         the combination of domain elements (<a class="link" href="../interface/function_synopsis.html#element_type"><span class="bold"><strong>e</strong></span></a>) or element value pairs (<a class="link" href="../interface/function_synopsis.html#element_mapping_type"><span class="bold"><strong>b</strong></span></a>) is faster than a combination of intervals
 717         (<a class="link" href="../interface/function_synopsis.html#interval_type"><span class="bold"><strong>i</strong></span></a>)
 718         or interval value pairs (<a class="link" href="../interface/function_synopsis.html#interval_mapping_type"><span class="bold"><strong>p</strong></span></a>) which in turn is faster than the combination
 719         of element or interval containers. The next table shows <span class="emphasis"><em>time complexities</em></span>
 720         of addition for <span class="bold"><strong>icl's</strong></span> element containers.
 721       </p>
 722 <p>
 723         Sizes <code class="computeroutput"><span class="identifier">n</span></code> and <code class="computeroutput"><span class="identifier">m</span></code> are in the complexity statements are
 724         sizes of objects <code class="computeroutput"><span class="identifier">T</span> <span class="identifier">y</span></code>
 725         and <code class="computeroutput"><span class="identifier">P</span> <span class="identifier">x</span></code>:
 726
 727 </p>
 728 <pre class="programlisting"><span class="identifier">n</span> <span class="special">=</span> <span class="identifier">iterative_size</span><span class="special">(</span><span class="identifier">y</span><span class="special">);</span>
 729 <span class="identifier">m</span> <span class="special">=</span> <span class="identifier">iterative_size</span><span class="special">(</span><span class="identifier">x</span><span class="special">);</span> <span class="comment">//if P is a container type
 730 </span></pre>
 731 <p>
 732         Note, that for an interval container the number of elements <code class="computeroutput"><span class="identifier">T</span><span class="special">::</span><span class="identifier">size</span></code>
 733         is different from the number of intervals that you can iterate over. Therefore
 734         a function <code class="computeroutput"><span class="identifier">T</span><span class="special">::</span><span class="identifier">iterative_size</span><span class="special">()</span></code>
 735         is used that provides the desired kind of size.
 736       </p>
 737 <div class="table">
 738 <a name="id1157636"></a><p class="title"><b>Table&#160;1.22.&#160;Time Complexity for inplace Addition on element
 739       containers</b></p>
 740 <div class="table-contents"><table class="table" summary="Time Complexity for inplace Addition on element
 741       containers">
 742 <colgroup>
 743 <col>
 744 <col>
 745 <col>
 746 <col>
 747 <col>
 748 </colgroup>
 749 <thead><tr>
 750 <th>
 751             <p>
 752               <code class="computeroutput"><span class="identifier">T</span><span class="special">&amp;</span>
 753               <span class="keyword">operator</span> <span class="special">+=</span>
 754               <span class="special">(</span><span class="identifier">T</span><span class="special">&amp;</span> <span class="identifier">y</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">P</span><span class="special">&amp;</span>
 755               <span class="identifier">x</span><span class="special">)</span></code>
 756             </p>
 757             </th>
 758 <th>
 759             <p>
 760               domain<br> type
 761             </p>
 762             </th>
 763 <th>
 764             <p>
 765               domain<br> mapping<br> type
 766             </p>
 767             </th>
 768 <th>
 769             <p>
 770               __ch_icl<span class="underline">sets</span><span class="underline">][</span>_ch_icl<span class="underline">maps</span>_
 771             </p>
 772             </th>
 773 <td class="auto-generated">&#160;</td>
 774 </tr></thead>
 775 <tbody>
 776 <tr>
 777 <td>
 778             <p>
 779               <a href="http://www.cplusplus.com/reference/stl/set/" target="_top"><code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">set</span></code> </a>
 780             </p>
 781             </td>
 782 <td>
 783             <p>
 784               <span class="emphasis"><em>O(log n)</em></span>
 785             </p>
 786             </td>
 787 <td>
 788             <p>
 789             </p>
 790             </td>
 791 <td>
 792             <p>
 793               <span class="emphasis"><em>O(m)</em></span>
 794             </p>
 795             </td>
 796 <td>
 797             <p>
 798             </p>
 799             </td>
 800 </tr>
 801 <tr>
 802 <td>
 803             <p>
 804               <code class="computeroutput"><a class="link" href="../../boost/icl/map.html" title="Class template map">icl::map</a></code>
 805             </p>
 806             </td>
 807 <td>
 808             <p>
 809             </p>
 810             </td>
 811 <td>
 812             <p>
 813               <span class="emphasis"><em>O(log n)</em></span>
 814             </p>
 815             </td>
 816 <td>
 817             <p>
 818             </p>
 819             </td>
 820 <td>
 821             <p>
 822               <span class="emphasis"><em>O(m)</em></span>
 823             </p>
 824             </td>
 825 </tr>
 826 </tbody>
 827 </table></div>
 828 </div>
 829 <br class="table-break"><p>
 830         Time complexity characteristics of inplace addition for interval containers
 831         is given by this table.
 832       </p>
 833 <div class="table">
 834 <a name="id1157881"></a><p class="title"><b>Table&#160;1.23.&#160;Time Complexity for inplace Addition on interval
 835       containers</b></p>
 836 <div class="table-contents"><table class="table" summary="Time Complexity for inplace Addition on interval
 837       containers">
 838 <colgroup>
 839 <col>
 840 <col>
 841 <col>
 842 <col>
 843 <col>
 844 <col>
 845 <col>
 846 <col>
 847 </colgroup>
 848 <thead><tr>
 849 <th>
 850             <p>
 851               <code class="computeroutput"><span class="identifier">T</span><span class="special">&amp;</span>
 852               <span class="keyword">operator</span> <span class="special">+=</span>
 853               <span class="special">(</span><span class="identifier">T</span><span class="special">&amp;</span> <span class="identifier">y</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">P</span><span class="special">&amp;</span>
 854               <span class="identifier">x</span><span class="special">)</span></code>
 855             </p>
 856             </th>
 857 <th>
 858             <p>
 859             </p>
 860             </th>
 861 <th>
 862             <p>
 863               domain<br> type
 864             </p>
 865             </th>
 866 <th>
 867             <p>
 868               interval<br> type
 869             </p>
 870             </th>
 871 <th>
 872             <p>
 873               domain<br> mapping<br> type
 874             </p>
 875             </th>
 876 <th>
 877             <p>
 878               interval<br> mapping<br> type
 879             </p>
 880             </th>
 881 <th>
 882             <p>
 883               interval<br> sets
 884             </p>
 885             </th>
 886 <th>
 887             <p>
 888               interval<br> maps
 889             </p>
 890             </th>
 891 </tr></thead>
 892 <tbody>
 893 <tr>
 894 <td>
 895             <p>
 896               interval_sets
 897             </p>
 898             </td>
 899 <td>
 900             <p>
 901               <code class="computeroutput"><a class="link" href="../../boost/icl/interval_set.html" title="Class template interval_set">interval_set</a></code><br>
 902               <code class="computeroutput"><a class="link" href="../../boost/icl/separate_interval_set.html" title="Class template separate_interval_set">separate_interval_set</a></code>
 903             </p>
 904             </td>
 905 <td>
 906             <p>
 907               <span class="emphasis"><em>O(log n)</em></span>
 908             </p>
 909             </td>
 910 <td>
 911             <p>
 912               <span class="emphasis"><em>amortized<br> O(log n)</em></span>
 913             </p>
 914             </td>
 915 <td>
 916             <p>
 917             </p>
 918             </td>
 919 <td>
 920             <p>
 921             </p>
 922             </td>
 923 <td>
 924             <p>
 925               <span class="emphasis"><em>O(m log(n+m))</em></span>
 926             </p>
 927             </td>
 928 <td>
 929             <p>
 930             </p>
 931             </td>
 932 </tr>
 933 <tr>
 934 <td>
 935             <p>
 936             </p>
 937             </td>
 938 <td>
 939             <p>
 940               <code class="computeroutput"><a class="link" href="../../boost/icl/split_interval_set.html" title="Class template split_interval_set">split_interval_set</a></code>
 941             </p>
 942             </td>
 943 <td>
 944             <p>
 945               <span class="emphasis"><em>O(log n)</em></span>
 946             </p>
 947             </td>
 948 <td>
 949             <p>
 950               <span class="emphasis"><em>O(n)</em></span>
 951             </p>
 952             </td>
 953 <td>
 954             <p>
 955             </p>
 956             </td>
 957 <td>
 958             <p>
 959             </p>
 960             </td>
 961 <td>
 962             <p>
 963               <span class="emphasis"><em>O(m log(n+m))</em></span>
 964             </p>
 965             </td>
 966 <td>
 967             <p>
 968             </p>
 969             </td>
 970 </tr>
 971 <tr>
 972 <td>
 973             <p>
 974               interval_maps
 975             </p>
 976             </td>
 977 <td>
 978             <p>
 979             </p>
 980             </td>
 981 <td>
 982             <p>
 983             </p>
 984             </td>
 985 <td>
 986             <p>
 987             </p>
 988             </td>
 989 <td>
 990             <p>
 991               <span class="emphasis"><em>O(log n)</em></span>
 992             </p>
 993             </td>
 994 <td>
 995             <p>
 996               <span class="emphasis"><em>O(n)</em></span>
 997             </p>
 998             </td>
 999 <td>
1000             <p>
1001             </p>
1002             </td>
1003 <td>
1004             <p>
1005               <span class="emphasis"><em>O(m log(n+m))</em></span>
1006             </p>
1007             </td>
1008 </tr>
1009 </tbody>
1010 </table></div>
1011 </div>
1012 <br class="table-break"><p>
1013         Since the implementation of element and interval containers is based on the
1014         <a class="link" href="../implementation.html" title="Implementation">link red-black tree implementation</a>
1015         of std::AssociativeContainers, we have a logarithmic complexity for addition
1016         of elements. Addition of intervals or interval value pairs is amortized logarithmic
1017         for <code class="computeroutput"><a class="link" href="../../boost/icl/interval_set.html" title="Class template interval_set">interval_sets</a></code> and
1018         <code class="computeroutput"><a class="link" href="../../boost/icl/separate_interval_set.html" title="Class template separate_interval_set">separate_interval_sets</a></code>
1019         and linear for <code class="computeroutput"><a class="link" href="../../boost/icl/split_interval_set.html" title="Class template split_interval_set">split_interval_sets</a></code>
1020         and <code class="computeroutput"><a class="link" href="../../boost/icl/interval_map.html" title="Class template interval_map">interval_maps</a></code>.
1021         Addition is linear for element containers and loglinear for interval containers.
1022       </p>
1023 <div class="section boost_icl_function_reference_addition_infix_operators" lang="en">
1024 <div class="titlepage"><div><div><h4 class="title">
1025 <a name="boost_icl.function_reference.addition.infix_operators"></a><a class="link" href="addition.html#boost_icl.function_reference.addition.infix_operators" title="Infix operators">Infix
1026         operators</a>
1027 </h4></div></div></div>
1028 <p>
1029           The admissible type combinations for infix <code class="computeroutput"><span class="keyword">operator</span>
1030           <span class="special">+</span></code> are defined by the overload tables
1031           below.
1032         </p>
1033 <p>
1034
1035 </p>
1036 <pre class="programlisting"><span class="comment">// overload tables for          element containers:     interval containers:
1037 </span><span class="identifier">T</span> <span class="keyword">operator</span> <span class="special">+</span> <span class="special">(</span><span class="identifier">T</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">P</span><span class="special">&amp;)</span>      <span class="special">+</span>  <span class="special">|</span> <span class="identifier">e</span> <span class="identifier">b</span> <span class="identifier">s</span> <span class="identifier">m</span>            <span class="special">+</span>  <span class="special">|</span> <span class="identifier">e</span>  <span class="identifier">i</span>  <span class="identifier">b</span>  <span class="identifier">p</span>  <span class="identifier">S1</span> <span class="identifier">S2</span> <span class="identifier">S3</span> <span class="identifier">M1</span> <span class="identifier">M3</span>
1038 <span class="identifier">T</span> <span class="keyword">operator</span> <span class="special">+</span> <span class="special">(</span><span class="keyword">const</span> <span class="identifier">P</span><span class="special">&amp;,</span> <span class="identifier">T</span><span class="special">)</span>      <span class="special">---+--------</span>            <span class="special">---+---------------------------</span>
1039                                 <span class="identifier">e</span>  <span class="special">|</span>     <span class="identifier">s</span>              <span class="identifier">e</span>  <span class="special">|</span>             <span class="identifier">S1</span> <span class="identifier">S2</span> <span class="identifier">S3</span>
1040                                 <span class="identifier">b</span>  <span class="special">|</span>       <span class="identifier">m</span>            <span class="identifier">i</span>  <span class="special">|</span>             <span class="identifier">S1</span> <span class="identifier">S2</span> <span class="identifier">S3</span>
1041                                 <span class="identifier">s</span>  <span class="special">|</span> <span class="identifier">s</span>   <span class="identifier">s</span>              <span class="identifier">b</span>  <span class="special">|</span>                      <span class="identifier">M1</span> <span class="identifier">M3</span>
1042                                 <span class="identifier">m</span>  <span class="special">|</span>   <span class="identifier">m</span>   <span class="identifier">m</span>            <span class="identifier">p</span>  <span class="special">|</span>                      <span class="identifier">M1</span> <span class="identifier">M3</span>
1043                                                         <span class="identifier">S1</span> <span class="special">|</span> <span class="identifier">S1</span> <span class="identifier">S1</span>       <span class="identifier">S1</span> <span class="identifier">S2</span> <span class="identifier">S3</span>
1044                                                         <span class="identifier">S2</span> <span class="special">|</span> <span class="identifier">S2</span> <span class="identifier">S2</span>       <span class="identifier">S2</span> <span class="identifier">S2</span> <span class="identifier">S3</span>
1045                                                         <span class="identifier">S3</span> <span class="special">|</span> <span class="identifier">S3</span> <span class="identifier">S3</span>       <span class="identifier">S3</span> <span class="identifier">S3</span> <span class="identifier">S3</span>
1046                                                         <span class="identifier">M1</span> <span class="special">|</span>       <span class="identifier">M1</span> <span class="identifier">M1</span>          <span class="identifier">M1</span> <span class="identifier">M3</span>
1047                                                         <span class="identifier">M3</span> <span class="special">|</span>       <span class="identifier">M3</span> <span class="identifier">M3</span>          <span class="identifier">M3</span> <span class="identifier">M3</span>
1048 </pre>
1049 <p>
1050         </p>
1051 </div>
1052 <p>
1053         <span class="emphasis"><em><span class="bold"><strong>See also . . .</strong></span></em></span>
1054       </p>
1055 <div class="informaltable"><table class="table">
1056 <colgroup><col></colgroup>
1057 <thead><tr></tr></thead>
1058 <tbody>
1059 <tr><td>
1060               <p>
1061                 <a class="link" href="subtraction.html" title="Subtraction"><span class="emphasis"><em><span class="bold"><strong>Subtraction</strong></span></em></span></a>
1062               </p>
1063               </td></tr>
1064 <tr><td>
1065               <p>
1066                 <a class="link" href="insertion.html" title="Insertion"><span class="emphasis"><em><span class="bold"><strong>Insertion</strong></span></em></span></a>
1067               </p>
1068               </td></tr>
1069 </tbody>
1070 </table></div>
1071 <p>
1072         <span class="emphasis"><em><span class="bold"><strong>Back to section . . .</strong></span></em></span>
1073       </p>
1074 <div class="informaltable"><table class="table">
1075 <colgroup><col></colgroup>
1076 <thead><tr></tr></thead>
1077 <tbody>
1078 <tr><td>
1079               <p>
1080                 <a class="link" href="../interface/function_synopsis.html#function_synopsis_table"><span class="emphasis"><em><span class="bold"><strong>Function
1081                 Synopsis</strong></span></em></span></a>
1082               </p>
1083               </td></tr>
1084 <tr><td>
1085               <p>
1086                 <a class="link" href="../interface.html" title="Interface"><span class="emphasis"><em><span class="bold"><strong>Interface</strong></span></em></span></a>
1087               </p>
1088               </td></tr>
1089 </tbody>
1090 </table></div>
1091 </div>
1092 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
1093 <td align="left"></td>
1094 <td align="right"><div class="copyright-footer">Copyright &#169; 2007 -2010 Joachim Faulhaber<br>Copyright &#169; 1999 -2006 Cortex Software GmbH<p>
1095         Distributed under the Boost Software License, Version 1.0. (See accompanying
1096         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>)
1097       </p>
1098 </div></td>
1099 </tr></table>
1100 <hr>
1101 <div class="spirit-nav">
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