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  26 <div class="titlepage"><div><div><h3 class="title">
  27 <a name="boost_multiprecision.ref.backendconc"></a><a class="link" href="backendconc.html" title="Backend Requirements">Backend Requirements</a>
  28 </h3></div></div></div>
  29 <p>
  30         The requirements on the <code class="computeroutput"><span class="identifier">Backend</span></code>
  31         template argument to <code class="computeroutput"><span class="identifier">number</span></code>
  32         are split up into sections: compulsory and optional.
  33       </p>
  34 <p>
  35         Compulsory requirements have no default implementation in the library, therefore
  36         if the feature they implement is to be supported at all, then they must be
  37         implemented by the backend.
  38       </p>
  39 <p>
  40         Optional requirements have default implementations that are called if the
  41         backend doesn't provide it's own. Typically the backend will implement these
  42         to improve performance.
  43       </p>
  44 <p>
  45         In the following tables, type B is the <code class="computeroutput"><span class="identifier">Backend</span></code>
  46         template argument to <code class="computeroutput"><span class="identifier">number</span></code>,
  47         <code class="computeroutput"><span class="identifier">b</span></code> and <code class="computeroutput"><span class="identifier">b2</span></code>
  48         are a variables of type B, <code class="computeroutput"><span class="identifier">pb</span></code>
  49         is a variable of type B*, <code class="computeroutput"><span class="identifier">cb</span></code>,
  50         <code class="computeroutput"><span class="identifier">cb2</span></code> and <code class="computeroutput"><span class="identifier">cb3</span></code>
  51         are constant variables of type <code class="computeroutput"><span class="keyword">const</span>
  52         <span class="identifier">B</span></code>, <code class="computeroutput"><span class="identifier">rb</span></code>
  53         is a variable of type <code class="computeroutput"><span class="identifier">B</span><span class="special">&amp;&amp;</span></code>,
  54         <code class="computeroutput"><span class="identifier">a</span></code> and <code class="computeroutput"><span class="identifier">a2</span></code>
  55         are variables of Arithmetic type, <code class="computeroutput"><span class="identifier">s</span></code>
  56         is a variable of type <code class="computeroutput"><span class="keyword">const</span> <span class="keyword">char</span><span class="special">*</span></code>, <code class="computeroutput"><span class="identifier">ui</span></code> is a variable of type <code class="computeroutput"><span class="keyword">unsigned</span></code>, <code class="computeroutput"><span class="identifier">bb</span></code>
  57         is a variable of type <code class="computeroutput"><span class="keyword">bool</span></code>,
  58         <code class="computeroutput"><span class="identifier">pa</span></code> is a variable of type
  59         pointer-to-arithmetic-type, <code class="computeroutput"><span class="identifier">exp</span></code>
  60         is a variable of type <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">exp_type</span></code>, <code class="computeroutput"><span class="identifier">pexp</span></code>
  61         is a variable of type <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">exp_type</span><span class="special">*</span></code>,
  62         <code class="computeroutput"><span class="identifier">i</span></code> is a variable of type
  63         <code class="computeroutput"><span class="keyword">int</span></code>, <code class="computeroutput"><span class="identifier">pi</span></code>
  64         pointer to a variable of type <code class="computeroutput"><span class="keyword">int</span></code>,
  65         B2 is another type that meets these requirements, b2 is a variable of type
  66         B2, <code class="computeroutput"><span class="identifier">ss</span></code> is variable of type
  67         <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">streamsize</span></code> and <code class="computeroutput"><span class="identifier">ff</span></code>
  68         is a variable of type <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">ios_base</span><span class="special">::</span><span class="identifier">fmtflags</span></code>.
  69       </p>
  70 <div class="table">
  71 <a name="boost_multiprecision.ref.backendconc.compulsory_requirements_on_the_b"></a><p class="title"><b>Table&#160;1.8.&#160;Compulsory Requirements on the Backend type.</b></p>
  72 <div class="table-contents"><table class="table" summary="Compulsory Requirements on the Backend type.">
  73 <colgroup>
  74 <col>
  75 <col>
  76 <col>
  77 <col>
  78 </colgroup>
  79 <thead><tr>
  80 <th>
  81                 <p>
  82                   Expression
  83                 </p>
  84               </th>
  85 <th>
  86                 <p>
  87                   Return Type
  88                 </p>
  89               </th>
  90 <th>
  91                 <p>
  92                   Comments
  93                 </p>
  94               </th>
  95 <th>
  96                 <p>
  97                   Throws
  98                 </p>
  99               </th>
 100 </tr></thead>
 101 <tbody>
 102 <tr>
 103 <td>
 104                 <p>
 105                   <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">signed_types</span></code>
 106                 </p>
 107               </td>
 108 <td>
 109                 <p>
 110                   <code class="computeroutput"><span class="identifier">mpl</span><span class="special">::</span><span class="identifier">list</span><span class="special">&lt;</span><span class="identifier">type</span><span class="special">-</span><span class="identifier">list</span><span class="special">&gt;</span></code>
 111                 </p>
 112               </td>
 113 <td>
 114                 <p>
 115                   A list of signed integral types that can be assigned to type B.
 116                   The types shall be listed in order of size, smallest first, and
 117                   shall terminate in the type that is <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">intmax_t</span></code>.
 118                 </p>
 119               </td>
 120 <td>
 121                 <p>
 122                   &#160;
 123                 </p>
 124               </td>
 125 </tr>
 126 <tr>
 127 <td>
 128                 <p>
 129                   <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">unsigned_types</span></code>
 130                 </p>
 131               </td>
 132 <td>
 133                 <p>
 134                   <code class="computeroutput"><span class="identifier">mpl</span><span class="special">::</span><span class="identifier">list</span><span class="special">&lt;</span><span class="identifier">type</span><span class="special">-</span><span class="identifier">list</span><span class="special">&gt;</span></code>
 135                 </p>
 136               </td>
 137 <td>
 138                 <p>
 139                   A list of unsigned integral types that can be assigned to type
 140                   B. The types shall be listed in order of size, smallest first,
 141                   and shall terminate in the type that is <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">uintmax_t</span></code>.
 142                 </p>
 143               </td>
 144 <td>
 145                 <p>
 146                   &#160;
 147                 </p>
 148               </td>
 149 </tr>
 150 <tr>
 151 <td>
 152                 <p>
 153                   <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">float_types</span></code>
 154                 </p>
 155               </td>
 156 <td>
 157                 <p>
 158                   <code class="computeroutput"><span class="identifier">mpl</span><span class="special">::</span><span class="identifier">list</span><span class="special">&lt;</span><span class="identifier">type</span><span class="special">-</span><span class="identifier">list</span><span class="special">&gt;</span></code>
 159                 </p>
 160               </td>
 161 <td>
 162                 <p>
 163                   A list of floating-point types that can be assigned to type B.The
 164                   types shall be listed in order of size, smallest first, and shall
 165                   terminate in type <code class="computeroutput"><span class="keyword">long</span> <span class="keyword">double</span></code>.
 166                 </p>
 167               </td>
 168 <td>
 169                 <p>
 170                   &#160;
 171                 </p>
 172               </td>
 173 </tr>
 174 <tr>
 175 <td>
 176                 <p>
 177                   <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">exponent_type</span></code>
 178                 </p>
 179               </td>
 180 <td>
 181                 <p>
 182                   A signed integral type.
 183                 </p>
 184               </td>
 185 <td>
 186                 <p>
 187                   The type of the exponent of type B. This type is required only
 188                   for floating-point types.
 189                 </p>
 190               </td>
 191 <td>
 192                 <p>
 193                   &#160;
 194                 </p>
 195               </td>
 196 </tr>
 197 <tr>
 198 <td>
 199                 <p>
 200                   <code class="computeroutput"><span class="identifier">B</span><span class="special">()</span></code>
 201                 </p>
 202               </td>
 203 <td>
 204               </td>
 205 <td>
 206                 <p>
 207                   Default constructor.
 208                 </p>
 209               </td>
 210 <td>
 211                 <p>
 212                   &#160;
 213                 </p>
 214               </td>
 215 </tr>
 216 <tr>
 217 <td>
 218                 <p>
 219                   <code class="computeroutput"><span class="identifier">B</span><span class="special">(</span><span class="identifier">cb</span><span class="special">)</span></code>
 220                 </p>
 221               </td>
 222 <td>
 223               </td>
 224 <td>
 225                 <p>
 226                   Copy Constructor.
 227                 </p>
 228               </td>
 229 <td>
 230                 <p>
 231                   &#160;
 232                 </p>
 233               </td>
 234 </tr>
 235 <tr>
 236 <td>
 237                 <p>
 238                   <code class="computeroutput"><span class="identifier">b</span> <span class="special">=</span>
 239                   <span class="identifier">b</span></code>
 240                 </p>
 241               </td>
 242 <td>
 243                 <p>
 244                   <code class="computeroutput"><span class="identifier">B</span><span class="special">&amp;</span></code>
 245                 </p>
 246               </td>
 247 <td>
 248                 <p>
 249                   Assignment operator.
 250                 </p>
 251               </td>
 252 <td>
 253                 <p>
 254                   &#160;
 255                 </p>
 256               </td>
 257 </tr>
 258 <tr>
 259 <td>
 260                 <p>
 261                   <code class="computeroutput"><span class="identifier">b</span> <span class="special">=</span>
 262                   <span class="identifier">a</span></code>
 263                 </p>
 264               </td>
 265 <td>
 266                 <p>
 267                   <code class="computeroutput"><span class="identifier">B</span><span class="special">&amp;</span></code>
 268                 </p>
 269               </td>
 270 <td>
 271                 <p>
 272                   Assignment from an Arithmetic type. The type of <code class="computeroutput"><span class="identifier">a</span></code>
 273                   shall be listed in one of the type lists <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">signed_types</span></code>,
 274                   <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">unsigned_types</span></code> or <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">float_types</span></code>.
 275                 </p>
 276               </td>
 277 <td>
 278                 <p>
 279                   &#160;
 280                 </p>
 281               </td>
 282 </tr>
 283 <tr>
 284 <td>
 285                 <p>
 286                   <code class="computeroutput"><span class="identifier">b</span> <span class="special">=</span>
 287                   <span class="identifier">s</span></code>
 288                 </p>
 289               </td>
 290 <td>
 291                 <p>
 292                   <code class="computeroutput"><span class="identifier">B</span><span class="special">&amp;</span></code>
 293                 </p>
 294               </td>
 295 <td>
 296                 <p>
 297                   Assignment from a string.
 298                 </p>
 299               </td>
 300 <td>
 301                 <p>
 302                   Throws a <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">runtime_error</span></code> if the string could
 303                   not be interpreted as a valid number.
 304                 </p>
 305               </td>
 306 </tr>
 307 <tr>
 308 <td>
 309                 <p>
 310                   <code class="computeroutput"><span class="identifier">b</span><span class="special">.</span><span class="identifier">swap</span><span class="special">(</span><span class="identifier">b</span><span class="special">)</span></code>
 311                 </p>
 312               </td>
 313 <td>
 314                 <p>
 315                   <code class="computeroutput"><span class="keyword">void</span></code>
 316                 </p>
 317               </td>
 318 <td>
 319                 <p>
 320                   Swaps the contents of its arguments.
 321                 </p>
 322               </td>
 323 <td>
 324                 <p>
 325                   <code class="computeroutput"><span class="keyword">noexcept</span></code>
 326                 </p>
 327               </td>
 328 </tr>
 329 <tr>
 330 <td>
 331                 <p>
 332                   <code class="computeroutput"><span class="identifier">cb</span><span class="special">.</span><span class="identifier">str</span><span class="special">(</span><span class="identifier">ss</span><span class="special">,</span>
 333                   <span class="identifier">ff</span><span class="special">)</span></code>
 334                 </p>
 335               </td>
 336 <td>
 337                 <p>
 338                   <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">string</span></code>
 339                 </p>
 340               </td>
 341 <td>
 342                 <p>
 343                   Returns the string representation of <code class="computeroutput"><span class="identifier">b</span></code>
 344                   with <code class="computeroutput"><span class="identifier">ss</span></code> digits
 345                   and formatted according to the flags set in <code class="computeroutput"><span class="identifier">ff</span></code>.
 346                   If <code class="computeroutput"><span class="identifier">ss</span></code> is zero,
 347                   then returns as many digits as are required to reconstruct the
 348                   original value.
 349                 </p>
 350               </td>
 351 <td>
 352                 <p>
 353                   &#160;
 354                 </p>
 355               </td>
 356 </tr>
 357 <tr>
 358 <td>
 359                 <p>
 360                   <code class="computeroutput"><span class="identifier">b</span><span class="special">.</span><span class="identifier">negate</span><span class="special">()</span></code>
 361                 </p>
 362               </td>
 363 <td>
 364                 <p>
 365                   <code class="computeroutput"><span class="keyword">void</span></code>
 366                 </p>
 367               </td>
 368 <td>
 369                 <p>
 370                   Negates <code class="computeroutput"><span class="identifier">b</span></code>.
 371                 </p>
 372               </td>
 373 <td>
 374                 <p>
 375                   &#160;
 376                 </p>
 377               </td>
 378 </tr>
 379 <tr>
 380 <td>
 381                 <p>
 382                   <code class="computeroutput"><span class="identifier">cb</span><span class="special">.</span><span class="identifier">compare</span><span class="special">(</span><span class="identifier">cb2</span><span class="special">)</span></code>
 383                 </p>
 384               </td>
 385 <td>
 386                 <p>
 387                   <code class="computeroutput"><span class="keyword">int</span></code>
 388                 </p>
 389               </td>
 390 <td>
 391                 <p>
 392                   Compares <code class="computeroutput"><span class="identifier">cb</span></code> and
 393                   <code class="computeroutput"><span class="identifier">cb2</span></code>, returns a
 394                   value less than zero if <code class="computeroutput"><span class="identifier">cb</span>
 395                   <span class="special">&lt;</span> <span class="identifier">cb2</span></code>,
 396                   a value greater than zero if <code class="computeroutput"><span class="identifier">cb</span>
 397                   <span class="special">&gt;</span> <span class="identifier">cb2</span></code>
 398                   and zero if <code class="computeroutput"><span class="identifier">cb</span> <span class="special">==</span> <span class="identifier">cb2</span></code>.
 399                 </p>
 400               </td>
 401 <td>
 402                 <p>
 403                   <code class="computeroutput"><span class="keyword">noexcept</span></code>
 404                 </p>
 405               </td>
 406 </tr>
 407 <tr>
 408 <td>
 409                 <p>
 410                   <code class="computeroutput"><span class="identifier">cb</span><span class="special">.</span><span class="identifier">compare</span><span class="special">(</span><span class="identifier">a</span><span class="special">)</span></code>
 411                 </p>
 412               </td>
 413 <td>
 414                 <p>
 415                   <code class="computeroutput"><span class="keyword">int</span></code>
 416                 </p>
 417               </td>
 418 <td>
 419                 <p>
 420                   Compares <code class="computeroutput"><span class="identifier">cb</span></code> and
 421                   <code class="computeroutput"><span class="identifier">a</span></code>, returns a value
 422                   less than zero if <code class="computeroutput"><span class="identifier">cb</span>
 423                   <span class="special">&lt;</span> <span class="identifier">a</span></code>,
 424                   a value greater than zero if <code class="computeroutput"><span class="identifier">cb</span>
 425                   <span class="special">&gt;</span> <span class="identifier">a</span></code>
 426                   and zero if <code class="computeroutput"><span class="identifier">cb</span> <span class="special">==</span> <span class="identifier">a</span></code>.
 427                   The type of <code class="computeroutput"><span class="identifier">a</span></code> shall
 428                   be listed in one of the type lists <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">signed_types</span></code>,
 429                   <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">unsigned_types</span></code> or <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">float_types</span></code>.
 430                 </p>
 431               </td>
 432 <td>
 433                 <p>
 434                   &#160;
 435                 </p>
 436               </td>
 437 </tr>
 438 <tr>
 439 <td>
 440                 <p>
 441                   <code class="computeroutput"><span class="identifier">eval_add</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span>
 442                   <span class="identifier">cb</span><span class="special">)</span></code>
 443                 </p>
 444               </td>
 445 <td>
 446                 <p>
 447                   <code class="computeroutput"><span class="keyword">void</span></code>
 448                 </p>
 449               </td>
 450 <td>
 451                 <p>
 452                   Adds <code class="computeroutput"><span class="identifier">cb</span></code> to <code class="computeroutput"><span class="identifier">b</span></code>.
 453                 </p>
 454               </td>
 455 <td>
 456                 <p>
 457                   &#160;
 458                 </p>
 459               </td>
 460 </tr>
 461 <tr>
 462 <td>
 463                 <p>
 464                   <code class="computeroutput"><span class="identifier">eval_subtract</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span>
 465                   <span class="identifier">cb</span><span class="special">)</span></code>
 466                 </p>
 467               </td>
 468 <td>
 469                 <p>
 470                   <code class="computeroutput"><span class="keyword">void</span></code>
 471                 </p>
 472               </td>
 473 <td>
 474                 <p>
 475                   Subtracts <code class="computeroutput"><span class="identifier">cb</span></code> from
 476                   <code class="computeroutput"><span class="identifier">b</span></code>.
 477                 </p>
 478               </td>
 479 <td>
 480                 <p>
 481                   &#160;
 482                 </p>
 483               </td>
 484 </tr>
 485 <tr>
 486 <td>
 487                 <p>
 488                   <code class="computeroutput"><span class="identifier">eval_multiply</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span>
 489                   <span class="identifier">cb</span><span class="special">)</span></code>
 490                 </p>
 491               </td>
 492 <td>
 493                 <p>
 494                   <code class="computeroutput"><span class="keyword">void</span></code>
 495                 </p>
 496               </td>
 497 <td>
 498                 <p>
 499                   Multiplies <code class="computeroutput"><span class="identifier">b</span></code> by
 500                   <code class="computeroutput"><span class="identifier">cb</span></code>.
 501                 </p>
 502               </td>
 503 <td>
 504                 <p>
 505                   &#160;
 506                 </p>
 507               </td>
 508 </tr>
 509 <tr>
 510 <td>
 511                 <p>
 512                   <code class="computeroutput"><span class="identifier">eval_divide</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span>
 513                   <span class="identifier">cb</span><span class="special">)</span></code>
 514                 </p>
 515               </td>
 516 <td>
 517                 <p>
 518                   <code class="computeroutput"><span class="keyword">void</span></code>
 519                 </p>
 520               </td>
 521 <td>
 522                 <p>
 523                   Divides <code class="computeroutput"><span class="identifier">b</span></code> by <code class="computeroutput"><span class="identifier">cb</span></code>.
 524                 </p>
 525               </td>
 526 <td>
 527                 <p>
 528                   <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">overflow_error</span></code> if cb has the
 529                   value zero, and <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special">&lt;</span><span class="identifier">number</span><span class="special">&lt;</span><span class="identifier">B</span><span class="special">&gt;</span> <span class="special">&gt;::</span><span class="identifier">has_infinity</span> <span class="special">==</span>
 530                   <span class="keyword">false</span></code>
 531                 </p>
 532               </td>
 533 </tr>
 534 <tr>
 535 <td>
 536                 <p>
 537                   <code class="computeroutput"><span class="identifier">eval_modulus</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span>
 538                   <span class="identifier">cb</span><span class="special">)</span></code>
 539                 </p>
 540               </td>
 541 <td>
 542                 <p>
 543                   <code class="computeroutput"><span class="keyword">void</span></code>
 544                 </p>
 545               </td>
 546 <td>
 547                 <p>
 548                   Computes <code class="computeroutput"><span class="identifier">b</span> <span class="special">%=</span>
 549                   <span class="identifier">cb</span></code>, only required when
 550                   <code class="computeroutput"><span class="identifier">B</span></code> is an integer
 551                   type.
 552                 </p>
 553               </td>
 554 <td>
 555                 <p>
 556                   <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">overflow_error</span></code> if cb has the
 557                   value zero.
 558                 </p>
 559               </td>
 560 </tr>
 561 <tr>
 562 <td>
 563                 <p>
 564                   <code class="computeroutput"><span class="identifier">eval_bitwise_and</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> <span class="identifier">cb</span><span class="special">)</span></code>
 565                 </p>
 566               </td>
 567 <td>
 568                 <p>
 569                   <code class="computeroutput"><span class="keyword">void</span></code>
 570                 </p>
 571               </td>
 572 <td>
 573                 <p>
 574                   Computes <code class="computeroutput"><span class="identifier">b</span> <span class="special">&amp;=</span>
 575                   <span class="identifier">cb</span></code>, only required when
 576                   <code class="computeroutput"><span class="identifier">B</span></code> is an integer
 577                   type.
 578                 </p>
 579               </td>
 580 <td>
 581                 <p>
 582                   &#160;
 583                 </p>
 584               </td>
 585 </tr>
 586 <tr>
 587 <td>
 588                 <p>
 589                   <code class="computeroutput"><span class="identifier">eval_bitwise_or</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> <span class="identifier">cb</span><span class="special">)</span></code>
 590                 </p>
 591               </td>
 592 <td>
 593                 <p>
 594                   <code class="computeroutput"><span class="keyword">void</span></code>
 595                 </p>
 596               </td>
 597 <td>
 598                 <p>
 599                   Computes <code class="computeroutput"><span class="identifier">b</span> <span class="special">|=</span>
 600                   <span class="identifier">cb</span></code>, only required when
 601                   <code class="computeroutput"><span class="identifier">B</span></code> is an integer
 602                   type.
 603                 </p>
 604               </td>
 605 <td>
 606                 <p>
 607                   &#160;
 608                 </p>
 609               </td>
 610 </tr>
 611 <tr>
 612 <td>
 613                 <p>
 614                   <code class="computeroutput"><span class="identifier">eval_bitwise_xor</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> <span class="identifier">cb</span><span class="special">)</span></code>
 615                 </p>
 616               </td>
 617 <td>
 618                 <p>
 619                   <code class="computeroutput"><span class="keyword">void</span></code>
 620                 </p>
 621               </td>
 622 <td>
 623                 <p>
 624                   Computes <code class="computeroutput"><span class="identifier">b</span> <span class="special">^=</span>
 625                   <span class="identifier">cb</span></code>, only required when
 626                   <code class="computeroutput"><span class="identifier">B</span></code> is an integer
 627                   type.
 628                 </p>
 629               </td>
 630 <td>
 631                 <p>
 632                   &#160;
 633                 </p>
 634               </td>
 635 </tr>
 636 <tr>
 637 <td>
 638                 <p>
 639                   <code class="computeroutput"><span class="identifier">eval_complement</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> <span class="identifier">cb</span><span class="special">)</span></code>
 640                 </p>
 641               </td>
 642 <td>
 643                 <p>
 644                   <code class="computeroutput"><span class="keyword">void</span></code>
 645                 </p>
 646               </td>
 647 <td>
 648                 <p>
 649                   Computes the ones-complement of <code class="computeroutput"><span class="identifier">cb</span></code>
 650                   and stores the result in <code class="computeroutput"><span class="identifier">b</span></code>,
 651                   only required when <code class="computeroutput"><span class="identifier">B</span></code>
 652                   is an integer type.
 653                 </p>
 654               </td>
 655 <td>
 656                 <p>
 657                   &#160;
 658                 </p>
 659               </td>
 660 </tr>
 661 <tr>
 662 <td>
 663                 <p>
 664                   <code class="computeroutput"><span class="identifier">eval_left_shift</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> <span class="identifier">ui</span><span class="special">)</span></code>
 665                 </p>
 666               </td>
 667 <td>
 668                 <p>
 669                   <code class="computeroutput"><span class="keyword">void</span></code>
 670                 </p>
 671               </td>
 672 <td>
 673                 <p>
 674                   Computes <code class="computeroutput"><span class="identifier">b</span> <span class="special">&lt;&lt;=</span>
 675                   <span class="identifier">ui</span></code>, only required when
 676                   <code class="computeroutput"><span class="identifier">B</span></code> is an integer
 677                   type.
 678                 </p>
 679               </td>
 680 <td>
 681                 <p>
 682                   &#160;
 683                 </p>
 684               </td>
 685 </tr>
 686 <tr>
 687 <td>
 688                 <p>
 689                   <code class="computeroutput"><span class="identifier">eval_right_shift</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> <span class="identifier">ui</span><span class="special">)</span></code>
 690                 </p>
 691               </td>
 692 <td>
 693                 <p>
 694                   <code class="computeroutput"><span class="keyword">void</span></code>
 695                 </p>
 696               </td>
 697 <td>
 698                 <p>
 699                   Computes <code class="computeroutput"><span class="identifier">b</span> <span class="special">&gt;&gt;=</span>
 700                   <span class="identifier">ui</span></code>, only required when
 701                   <code class="computeroutput"><span class="identifier">B</span></code> is an integer
 702                   type.
 703                 </p>
 704               </td>
 705 <td>
 706                 <p>
 707                   &#160;
 708                 </p>
 709               </td>
 710 </tr>
 711 <tr>
 712 <td>
 713                 <p>
 714                   <code class="computeroutput"><span class="identifier">eval_convert_to</span><span class="special">(</span><span class="identifier">pa</span><span class="special">,</span> <span class="identifier">cb</span><span class="special">)</span></code>
 715                 </p>
 716               </td>
 717 <td>
 718                 <p>
 719                   <code class="computeroutput"><span class="keyword">void</span></code>
 720                 </p>
 721               </td>
 722 <td>
 723                 <p>
 724                   Converts <code class="computeroutput"><span class="identifier">cb</span></code> to
 725                   the type of <code class="computeroutput"><span class="special">*</span><span class="identifier">pa</span></code>
 726                   and store the result in <code class="computeroutput"><span class="special">*</span><span class="identifier">pa</span></code>. Type <code class="computeroutput"><span class="identifier">B</span></code>
 727                   shall support conversion to at least types <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">intmax_t</span></code>,
 728                   <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">uintmax_t</span></code> and <code class="computeroutput"><span class="keyword">long</span>
 729                   <span class="keyword">long</span></code>. Conversion to other
 730                   arithmetic types can then be synthesised using other operations.
 731                   Conversions to other types are entirely optional.
 732                 </p>
 733               </td>
 734 <td>
 735                 <p>
 736                   &#160;
 737                 </p>
 738               </td>
 739 </tr>
 740 <tr>
 741 <td>
 742                 <p>
 743                   <code class="computeroutput"><span class="identifier">eval_frexp</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span>
 744                   <span class="identifier">cb</span><span class="special">,</span>
 745                   <span class="identifier">pexp</span><span class="special">)</span></code>
 746                 </p>
 747               </td>
 748 <td>
 749                 <p>
 750                   <code class="computeroutput"><span class="keyword">void</span></code>
 751                 </p>
 752               </td>
 753 <td>
 754                 <p>
 755                   Stores values in <code class="computeroutput"><span class="identifier">b</span></code>
 756                   and <code class="computeroutput"><span class="special">*</span><span class="identifier">pexp</span></code>
 757                   such that the value of <code class="computeroutput"><span class="identifier">cb</span></code>
 758                   is b * 2<sup>*pexp</sup>, only required when <code class="computeroutput"><span class="identifier">B</span></code>
 759                   is a floating-point type.
 760                 </p>
 761               </td>
 762 <td>
 763                 <p>
 764                   &#160;
 765                 </p>
 766               </td>
 767 </tr>
 768 <tr>
 769 <td>
 770                 <p>
 771                   <code class="computeroutput"><span class="identifier">eval_ldexp</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span>
 772                   <span class="identifier">cb</span><span class="special">,</span>
 773                   <span class="identifier">exp</span><span class="special">)</span></code>
 774                 </p>
 775               </td>
 776 <td>
 777                 <p>
 778                   <code class="computeroutput"><span class="keyword">void</span></code>
 779                 </p>
 780               </td>
 781 <td>
 782                 <p>
 783                   Stores a value in <code class="computeroutput"><span class="identifier">b</span></code>
 784                   that is cb * 2<sup>exp</sup>, only required when <code class="computeroutput"><span class="identifier">B</span></code>
 785                   is a floating-point type.
 786                 </p>
 787               </td>
 788 <td>
 789                 <p>
 790                   &#160;
 791                 </p>
 792               </td>
 793 </tr>
 794 <tr>
 795 <td>
 796                 <p>
 797                   <code class="computeroutput"><span class="identifier">eval_frexp</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span>
 798                   <span class="identifier">cb</span><span class="special">,</span>
 799                   <span class="identifier">pi</span><span class="special">)</span></code>
 800                 </p>
 801               </td>
 802 <td>
 803                 <p>
 804                   <code class="computeroutput"><span class="keyword">void</span></code>
 805                 </p>
 806               </td>
 807 <td>
 808                 <p>
 809                   Stores values in <code class="computeroutput"><span class="identifier">b</span></code>
 810                   and <code class="computeroutput"><span class="special">*</span><span class="identifier">pi</span></code>
 811                   such that the value of <code class="computeroutput"><span class="identifier">cb</span></code>
 812                   is b * 2<sup>*pi</sup>, only required when <code class="computeroutput"><span class="identifier">B</span></code>
 813                   is a floating-point type.
 814                 </p>
 815               </td>
 816 <td>
 817                 <p>
 818                   <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">runtime_error</span></code> if the exponent
 819                   of cb is too large to be stored in an <code class="computeroutput"><span class="keyword">int</span></code>.
 820                 </p>
 821               </td>
 822 </tr>
 823 <tr>
 824 <td>
 825                 <p>
 826                   <code class="computeroutput"><span class="identifier">eval_ldexp</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span>
 827                   <span class="identifier">cb</span><span class="special">,</span>
 828                   <span class="identifier">i</span><span class="special">)</span></code>
 829                 </p>
 830               </td>
 831 <td>
 832                 <p>
 833                   <code class="computeroutput"><span class="keyword">void</span></code>
 834                 </p>
 835               </td>
 836 <td>
 837                 <p>
 838                   Stores a value in <code class="computeroutput"><span class="identifier">b</span></code>
 839                   that is cb * 2<sup>i</sup>, only required when <code class="computeroutput"><span class="identifier">B</span></code>
 840                   is a floating-point type.
 841                 </p>
 842               </td>
 843 <td>
 844                 <p>
 845                   &#160;
 846                 </p>
 847               </td>
 848 </tr>
 849 <tr>
 850 <td>
 851                 <p>
 852                   <code class="computeroutput"><span class="identifier">eval_floor</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span>
 853                   <span class="identifier">cb</span><span class="special">)</span></code>
 854                 </p>
 855               </td>
 856 <td>
 857                 <p>
 858                   <code class="computeroutput"><span class="keyword">void</span></code>
 859                 </p>
 860               </td>
 861 <td>
 862                 <p>
 863                   Stores the floor of <code class="computeroutput"><span class="identifier">cb</span></code>
 864                   in <code class="computeroutput"><span class="identifier">b</span></code>, only required
 865                   when <code class="computeroutput"><span class="identifier">B</span></code> is a floating-point
 866                   type.
 867                 </p>
 868               </td>
 869 <td>
 870                 <p>
 871                   &#160;
 872                 </p>
 873               </td>
 874 </tr>
 875 <tr>
 876 <td>
 877                 <p>
 878                   <code class="computeroutput"><span class="identifier">eval_ceil</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span>
 879                   <span class="identifier">cb</span><span class="special">)</span></code>
 880                 </p>
 881               </td>
 882 <td>
 883                 <p>
 884                   <code class="computeroutput"><span class="keyword">void</span></code>
 885                 </p>
 886               </td>
 887 <td>
 888                 <p>
 889                   Stores the ceiling of <code class="computeroutput"><span class="identifier">cb</span></code>
 890                   in <code class="computeroutput"><span class="identifier">b</span></code>, only required
 891                   when <code class="computeroutput"><span class="identifier">B</span></code> is a floating-point
 892                   type.
 893                 </p>
 894               </td>
 895 <td>
 896                 <p>
 897                   &#160;
 898                 </p>
 899               </td>
 900 </tr>
 901 <tr>
 902 <td>
 903                 <p>
 904                   <code class="computeroutput"><span class="identifier">eval_sqrt</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span>
 905                   <span class="identifier">cb</span><span class="special">)</span></code>
 906                 </p>
 907               </td>
 908 <td>
 909                 <p>
 910                   <code class="computeroutput"><span class="keyword">void</span></code>
 911                 </p>
 912               </td>
 913 <td>
 914                 <p>
 915                   Stores the square root of <code class="computeroutput"><span class="identifier">cb</span></code>
 916                   in <code class="computeroutput"><span class="identifier">b</span></code>, only required
 917                   when <code class="computeroutput"><span class="identifier">B</span></code> is a floating-point
 918                   type.
 919                 </p>
 920               </td>
 921 <td>
 922                 <p>
 923                   &#160;
 924                 </p>
 925               </td>
 926 </tr>
 927 <tr>
 928 <td>
 929                 <p>
 930                   <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">multiprecision</span><span class="special">::</span><span class="identifier">number_category</span><span class="special">&lt;</span><span class="identifier">B</span><span class="special">&gt;::</span><span class="identifier">type</span></code>
 931                 </p>
 932               </td>
 933 <td>
 934                 <p>
 935                   <code class="computeroutput"><span class="identifier">mpl</span><span class="special">::</span><span class="identifier">int_</span><span class="special">&lt;</span><span class="identifier">N</span><span class="special">&gt;</span></code>
 936                 </p>
 937               </td>
 938 <td>
 939                 <p>
 940                   <code class="computeroutput"><span class="identifier">N</span></code> is one of the
 941                   values <code class="computeroutput"><span class="identifier">number_kind_integer</span></code>,
 942                   <code class="computeroutput"><span class="identifier">number_kind_floating_point</span></code>,
 943                   <code class="computeroutput"><span class="identifier">number_kind_rational</span></code>
 944                   or <code class="computeroutput"><span class="identifier">number_kind_fixed_point</span></code>.
 945                   Defaults to <code class="computeroutput"><span class="identifier">number_kind_floating_point</span></code>.
 946                 </p>
 947               </td>
 948 <td>
 949                 <p>
 950                   &#160;
 951                 </p>
 952               </td>
 953 </tr>
 954 </tbody>
 955 </table></div>
 956 </div>
 957 <br class="table-break"><div class="table">
 958 <a name="boost_multiprecision.ref.backendconc.optional_requirements_on_the_bac"></a><p class="title"><b>Table&#160;1.9.&#160;Optional Requirements on the Backend Type</b></p>
 959 <div class="table-contents"><table class="table" summary="Optional Requirements on the Backend Type">
 960 <colgroup>
 961 <col>
 962 <col>
 963 <col>
 964 </colgroup>
 965 <thead><tr>
 966 <th>
 967                 <p>
 968                   Expression
 969                 </p>
 970               </th>
 971 <th>
 972                 <p>
 973                   Returns
 974                 </p>
 975               </th>
 976 <th>
 977                 <p>
 978                   Comments
 979                 </p>
 980               </th>
 981 <th>
 982                 <p>
 983                   Throws
 984                 </p>
 985               </th>
 986 </tr></thead>
 987 <tbody>
 988 <tr>
 989 <td>
 990                 <p>
 991                   <span class="emphasis"><em>Construct and assign:</em></span>
 992                 </p>
 993               </td>
 994 <td class="auto-generated">&#160;</td>
 995 <td class="auto-generated">&#160;</td>
 996 </tr>
 997 <tr>
 998 <td>
 999                 <p>
1000                   <code class="computeroutput"><span class="identifier">B</span><span class="special">(</span><span class="identifier">rb</span><span class="special">)</span></code>
1001                 </p>
1002               </td>
1003 <td>
1004                 <p>
1005                   <code class="computeroutput"><span class="identifier">B</span></code>
1006                 </p>
1007               </td>
1008 <td>
1009                 <p>
1010                   Move constructor. Afterwards variable <code class="computeroutput"><span class="identifier">rb</span></code>
1011                   shall be in sane state, albeit with unspecified value. Only destruction
1012                   and assignment to the moved-from variable <code class="computeroutput"><span class="identifier">rb</span></code>
1013                   need be supported after the operation.
1014                 </p>
1015               </td>
1016 <td>
1017                 <p>
1018                   <code class="computeroutput"><span class="keyword">noexcept</span></code>
1019                 </p>
1020               </td>
1021 </tr>
1022 <tr>
1023 <td>
1024                 <p>
1025                   <code class="computeroutput"><span class="identifier">b</span> <span class="special">=</span>
1026                   <span class="identifier">rb</span></code>
1027                 </p>
1028               </td>
1029 <td>
1030                 <p>
1031                   <code class="computeroutput"><span class="identifier">B</span><span class="special">&amp;</span></code>
1032                 </p>
1033               </td>
1034 <td>
1035                 <p>
1036                   Move-assign. Afterwards variable <code class="computeroutput"><span class="identifier">rb</span></code>
1037                   shall be in sane state, albeit with unspecified value. Only destruction
1038                   and assignment to the moved-from variable <code class="computeroutput"><span class="identifier">rb</span></code>
1039                   need be supported after the operation.
1040                 </p>
1041               </td>
1042 <td>
1043                 <p>
1044                   <code class="computeroutput"><span class="keyword">noexcept</span></code>
1045                 </p>
1046               </td>
1047 </tr>
1048 <tr>
1049 <td>
1050                 <p>
1051                   <code class="computeroutput"><span class="identifier">B</span><span class="special">(</span><span class="identifier">a</span><span class="special">)</span></code>
1052                 </p>
1053               </td>
1054 <td>
1055                 <p>
1056                   <code class="computeroutput"><span class="identifier">B</span></code>
1057                 </p>
1058               </td>
1059 <td>
1060                 <p>
1061                   Direct construction from an arithmetic type. The type of <code class="computeroutput"><span class="identifier">a</span></code> shall be listed in one of the
1062                   type lists <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">signed_types</span></code>, <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">unsigned_types</span></code>
1063                   or <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">float_types</span></code>. When not provided,
1064                   this operation is simulated using default-construction followed
1065                   by assignment.
1066                 </p>
1067               </td>
1068 <td>
1069                 <p>
1070                   &#160;
1071                 </p>
1072               </td>
1073 </tr>
1074 <tr>
1075 <td>
1076                 <p>
1077                   <code class="computeroutput"><span class="identifier">B</span><span class="special">(</span><span class="identifier">b2</span><span class="special">)</span></code>
1078                 </p>
1079               </td>
1080 <td>
1081                 <p>
1082                   <code class="computeroutput"><span class="identifier">B</span></code>
1083                 </p>
1084               </td>
1085 <td>
1086                 <p>
1087                   Copy constructor from a different back-end type. When not provided,
1088                   a generic interconversion routine is used. This constructor may
1089                   be <code class="computeroutput"><span class="keyword">explicit</span></code> if the
1090                   corresponding frontend constructor should also be <code class="computeroutput"><span class="keyword">explicit</span></code>.
1091                 </p>
1092               </td>
1093 <td>
1094                 <p>
1095                   &#160;
1096                 </p>
1097               </td>
1098 </tr>
1099 <tr>
1100 <td>
1101                 <p>
1102                   <code class="computeroutput"><span class="identifier">b</span> <span class="special">=</span>
1103                   <span class="identifier">b2</span></code>
1104                 </p>
1105               </td>
1106 <td>
1107                 <p>
1108                   <code class="computeroutput"><span class="identifier">b</span><span class="special">&amp;</span></code>
1109                 </p>
1110               </td>
1111 <td>
1112                 <p>
1113                   Assignment operator from a different back-end type. When not provided,
1114                   a generic interconversion routine is used.
1115                 </p>
1116               </td>
1117 <td>
1118                 <p>
1119                   &#160;
1120                 </p>
1121               </td>
1122 </tr>
1123 <tr>
1124 <td>
1125                 <p>
1126                   <code class="computeroutput"><span class="identifier">assign_components</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> <span class="identifier">a</span><span class="special">,</span> <span class="identifier">a</span><span class="special">)</span></code>
1127                 </p>
1128               </td>
1129 <td>
1130                 <p>
1131                   <code class="computeroutput"><span class="keyword">void</span></code>
1132                 </p>
1133               </td>
1134 <td>
1135                 <p>
1136                   Assigns to <code class="computeroutput"><span class="identifier">b</span></code> the
1137                   two components in the following arguments. Only applies to rational
1138                   and complex number types. When not provided, arithmetic operations
1139                   are used to synthesise the result from the two values.
1140                 </p>
1141               </td>
1142 <td>
1143                 <p>
1144                   &#160;
1145                 </p>
1146               </td>
1147 </tr>
1148 <tr>
1149 <td>
1150                 <p>
1151                   <code class="computeroutput"><span class="identifier">assign_components</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> <span class="identifier">b2</span><span class="special">,</span> <span class="identifier">b2</span><span class="special">)</span></code>
1152                 </p>
1153               </td>
1154 <td>
1155                 <p>
1156                   <code class="computeroutput"><span class="keyword">void</span></code>
1157                 </p>
1158               </td>
1159 <td>
1160                 <p>
1161                   Assigns to <code class="computeroutput"><span class="identifier">b</span></code> the
1162                   two components in the following arguments. Only applies to rational
1163                   and complex number types. When not provided, arithmetic operations
1164                   are used to synthesise the result from the two values.
1165                 </p>
1166               </td>
1167 <td>
1168                 <p>
1169                   &#160;
1170                 </p>
1171               </td>
1172 </tr>
1173 <tr>
1174 <td>
1175                 <p>
1176                   <span class="emphasis"><em>Comparisons:</em></span>
1177                 </p>
1178               </td>
1179 <td class="auto-generated">&#160;</td>
1180 <td class="auto-generated">&#160;</td>
1181 </tr>
1182 <tr>
1183 <td>
1184                 <p>
1185                   <code class="computeroutput"><span class="identifier">eval_eq</span><span class="special">(</span><span class="identifier">cb</span><span class="special">,</span>
1186                   <span class="identifier">cb2</span><span class="special">)</span></code>
1187                 </p>
1188               </td>
1189 <td>
1190                 <p>
1191                   <code class="computeroutput"><span class="keyword">bool</span></code>
1192                 </p>
1193               </td>
1194 <td>
1195                 <p>
1196                   Returns <code class="computeroutput"><span class="keyword">true</span></code> if <code class="computeroutput"><span class="identifier">cb</span></code> and <code class="computeroutput"><span class="identifier">cb2</span></code>
1197                   are equal in value. When not provided, the default implementation
1198                   returns <code class="computeroutput"><span class="identifier">cb</span><span class="special">.</span><span class="identifier">compare</span><span class="special">(</span><span class="identifier">cb2</span><span class="special">)</span>
1199                   <span class="special">==</span> <span class="number">0</span></code>.
1200                 </p>
1201               </td>
1202 <td>
1203                 <p>
1204                   <code class="computeroutput"><span class="keyword">noexcept</span></code>
1205                 </p>
1206               </td>
1207 </tr>
1208 <tr>
1209 <td>
1210                 <p>
1211                   <code class="computeroutput"><span class="identifier">eval_eq</span><span class="special">(</span><span class="identifier">cb</span><span class="special">,</span>
1212                   <span class="identifier">a</span><span class="special">)</span></code>
1213                 </p>
1214               </td>
1215 <td>
1216                 <p>
1217                   <code class="computeroutput"><span class="keyword">bool</span></code>
1218                 </p>
1219               </td>
1220 <td>
1221                 <p>
1222                   Returns <code class="computeroutput"><span class="keyword">true</span></code> if <code class="computeroutput"><span class="identifier">cb</span></code> and <code class="computeroutput"><span class="identifier">a</span></code>
1223                   are equal in value. The type of <code class="computeroutput"><span class="identifier">a</span></code>
1224                   shall be listed in one of the type lists <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">signed_types</span></code>,
1225                   <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">unsigned_types</span></code> or <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">float_types</span></code>. When not provided,
1226                   return the equivalent of <code class="computeroutput"><span class="identifier">eval_eq</span><span class="special">(</span><span class="identifier">cb</span><span class="special">,</span> <span class="identifier">B</span><span class="special">(</span><span class="identifier">a</span><span class="special">))</span></code>.
1227                 </p>
1228               </td>
1229 <td>
1230                 <p>
1231                   &#160;
1232                 </p>
1233               </td>
1234 </tr>
1235 <tr>
1236 <td>
1237                 <p>
1238                   <code class="computeroutput"><span class="identifier">eval_eq</span><span class="special">(</span><span class="identifier">a</span><span class="special">,</span>
1239                   <span class="identifier">cb</span><span class="special">)</span></code>
1240                 </p>
1241               </td>
1242 <td>
1243                 <p>
1244                   <code class="computeroutput"><span class="keyword">bool</span></code>
1245                 </p>
1246               </td>
1247 <td>
1248                 <p>
1249                   Returns <code class="computeroutput"><span class="keyword">true</span></code> if <code class="computeroutput"><span class="identifier">cb</span></code> and <code class="computeroutput"><span class="identifier">a</span></code>
1250                   are equal in value. The type of <code class="computeroutput"><span class="identifier">a</span></code>
1251                   shall be listed in one of the type lists <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">signed_types</span></code>,
1252                   <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">unsigned_types</span></code> or <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">float_types</span></code>. When not provided,
1253                   the default version returns <code class="computeroutput"><span class="identifier">eval_eq</span><span class="special">(</span><span class="identifier">cb</span><span class="special">,</span> <span class="identifier">a</span><span class="special">)</span></code>.
1254                 </p>
1255               </td>
1256 <td>
1257                 <p>
1258                   &#160;
1259                 </p>
1260               </td>
1261 </tr>
1262 <tr>
1263 <td>
1264                 <p>
1265                   <code class="computeroutput"><span class="identifier">eval_lt</span><span class="special">(</span><span class="identifier">cb</span><span class="special">,</span>
1266                   <span class="identifier">cb2</span><span class="special">)</span></code>
1267                 </p>
1268               </td>
1269 <td>
1270                 <p>
1271                   <code class="computeroutput"><span class="keyword">bool</span></code>
1272                 </p>
1273               </td>
1274 <td>
1275                 <p>
1276                   Returns <code class="computeroutput"><span class="keyword">true</span></code> if <code class="computeroutput"><span class="identifier">cb</span></code> is less than <code class="computeroutput"><span class="identifier">cb2</span></code> in value. When not provided,
1277                   the default implementation returns <code class="computeroutput"><span class="identifier">cb</span><span class="special">.</span><span class="identifier">compare</span><span class="special">(</span><span class="identifier">cb2</span><span class="special">)</span> <span class="special">&lt;</span>
1278                   <span class="number">0</span></code>.
1279                 </p>
1280               </td>
1281 <td>
1282                 <p>
1283                   <code class="computeroutput"><span class="keyword">noexcept</span></code>
1284                 </p>
1285               </td>
1286 </tr>
1287 <tr>
1288 <td>
1289                 <p>
1290                   <code class="computeroutput"><span class="identifier">eval_lt</span><span class="special">(</span><span class="identifier">cb</span><span class="special">,</span>
1291                   <span class="identifier">a</span><span class="special">)</span></code>
1292                 </p>
1293               </td>
1294 <td>
1295                 <p>
1296                   <code class="computeroutput"><span class="keyword">bool</span></code>
1297                 </p>
1298               </td>
1299 <td>
1300                 <p>
1301                   Returns <code class="computeroutput"><span class="keyword">true</span></code> if <code class="computeroutput"><span class="identifier">cb</span></code> is less than <code class="computeroutput"><span class="identifier">a</span></code> in value. The type of <code class="computeroutput"><span class="identifier">a</span></code> shall be listed in one of the
1302                   type lists <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">signed_types</span></code>, <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">unsigned_types</span></code>
1303                   or <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">float_types</span></code>. When not provided,
1304                   the default implementation returns <code class="computeroutput"><span class="identifier">eval_lt</span><span class="special">(</span><span class="identifier">cb</span><span class="special">,</span> <span class="identifier">B</span><span class="special">(</span><span class="identifier">a</span><span class="special">))</span></code>.
1305                 </p>
1306               </td>
1307 <td>
1308                 <p>
1309                   &#160;
1310                 </p>
1311               </td>
1312 </tr>
1313 <tr>
1314 <td>
1315                 <p>
1316                   <code class="computeroutput"><span class="identifier">eval_lt</span><span class="special">(</span><span class="identifier">a</span><span class="special">,</span>
1317                   <span class="identifier">cb</span><span class="special">)</span></code>
1318                 </p>
1319               </td>
1320 <td>
1321                 <p>
1322                   <code class="computeroutput"><span class="keyword">bool</span></code>
1323                 </p>
1324               </td>
1325 <td>
1326                 <p>
1327                   Returns <code class="computeroutput"><span class="keyword">true</span></code> if <code class="computeroutput"><span class="identifier">a</span></code> is less than <code class="computeroutput"><span class="identifier">cb</span></code> in value. The type of <code class="computeroutput"><span class="identifier">a</span></code> shall be listed in one of the
1328                   type lists <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">signed_types</span></code>, <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">unsigned_types</span></code>
1329                   or <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">float_types</span></code>. When not provided,
1330                   the default implementation returns <code class="computeroutput"><span class="identifier">eval_gt</span><span class="special">(</span><span class="identifier">cb</span><span class="special">,</span> <span class="identifier">a</span><span class="special">)</span></code>.
1331                 </p>
1332               </td>
1333 <td>
1334                 <p>
1335                   &#160;
1336                 </p>
1337               </td>
1338 </tr>
1339 <tr>
1340 <td>
1341                 <p>
1342                   <code class="computeroutput"><span class="identifier">eval_gt</span><span class="special">(</span><span class="identifier">cb</span><span class="special">,</span>
1343                   <span class="identifier">cb2</span><span class="special">)</span></code>
1344                 </p>
1345               </td>
1346 <td>
1347                 <p>
1348                   <code class="computeroutput"><span class="keyword">bool</span></code>
1349                 </p>
1350               </td>
1351 <td>
1352                 <p>
1353                   Returns <code class="computeroutput"><span class="keyword">true</span></code> if <code class="computeroutput"><span class="identifier">cb</span></code> is greater than <code class="computeroutput"><span class="identifier">cb2</span></code> in value. When not provided,
1354                   the default implementation returns <code class="computeroutput"><span class="identifier">cb</span><span class="special">.</span><span class="identifier">compare</span><span class="special">(</span><span class="identifier">cb2</span><span class="special">)</span> <span class="special">&gt;</span>
1355                   <span class="number">0</span></code>.
1356                 </p>
1357               </td>
1358 <td>
1359                 <p>
1360                   <code class="computeroutput"><span class="keyword">noexcept</span></code>
1361                 </p>
1362               </td>
1363 </tr>
1364 <tr>
1365 <td>
1366                 <p>
1367                   <code class="computeroutput"><span class="identifier">eval_gt</span><span class="special">(</span><span class="identifier">cb</span><span class="special">,</span>
1368                   <span class="identifier">a</span><span class="special">)</span></code>
1369                 </p>
1370               </td>
1371 <td>
1372                 <p>
1373                   <code class="computeroutput"><span class="keyword">bool</span></code>
1374                 </p>
1375               </td>
1376 <td>
1377                 <p>
1378                   Returns <code class="computeroutput"><span class="keyword">true</span></code> if <code class="computeroutput"><span class="identifier">cb</span></code> is greater than <code class="computeroutput"><span class="identifier">a</span></code> in value. The type of <code class="computeroutput"><span class="identifier">a</span></code> shall be listed in one of the
1379                   type lists <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">signed_types</span></code>, <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">unsigned_types</span></code>
1380                   or <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">float_types</span></code>. When not provided,
1381                   the default implementation returns <code class="computeroutput"><span class="identifier">eval_gt</span><span class="special">(</span><span class="identifier">cb</span><span class="special">,</span> <span class="identifier">B</span><span class="special">(</span><span class="identifier">a</span><span class="special">))</span></code>.
1382                 </p>
1383               </td>
1384 <td>
1385                 <p>
1386                   &#160;
1387                 </p>
1388               </td>
1389 </tr>
1390 <tr>
1391 <td>
1392                 <p>
1393                   <code class="computeroutput"><span class="identifier">eval_gt</span><span class="special">(</span><span class="identifier">a</span><span class="special">,</span>
1394                   <span class="identifier">cb</span><span class="special">)</span></code>
1395                 </p>
1396               </td>
1397 <td>
1398                 <p>
1399                   <code class="computeroutput"><span class="keyword">bool</span></code>
1400                 </p>
1401               </td>
1402 <td>
1403                 <p>
1404                   Returns <code class="computeroutput"><span class="keyword">true</span></code> if <code class="computeroutput"><span class="identifier">a</span></code> is greater than <code class="computeroutput"><span class="identifier">cb</span></code> in value. The type of <code class="computeroutput"><span class="identifier">a</span></code> shall be listed in one of the
1405                   type lists <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">signed_types</span></code>, <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">unsigned_types</span></code>
1406                   or <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">float_types</span></code>. When not provided,
1407                   the default implementation returns <code class="computeroutput"><span class="identifier">eval_lt</span><span class="special">(</span><span class="identifier">cb</span><span class="special">,</span> <span class="identifier">a</span><span class="special">)</span></code>.
1408                 </p>
1409               </td>
1410 <td>
1411                 <p>
1412                   &#160;
1413                 </p>
1414               </td>
1415 </tr>
1416 <tr>
1417 <td>
1418                 <p>
1419                   <code class="computeroutput"><span class="identifier">eval_is_zero</span><span class="special">(</span><span class="identifier">cb</span><span class="special">)</span></code>
1420                 </p>
1421               </td>
1422 <td>
1423                 <p>
1424                   <code class="computeroutput"><span class="keyword">bool</span></code>
1425                 </p>
1426               </td>
1427 <td>
1428                 <p>
1429                   Returns <code class="computeroutput"><span class="keyword">true</span></code> if <code class="computeroutput"><span class="identifier">cb</span></code> is zero, otherwise <code class="computeroutput"><span class="keyword">false</span></code>. The default version of this
1430                   function returns <code class="computeroutput"><span class="identifier">cb</span><span class="special">.</span><span class="identifier">compare</span><span class="special">(</span><span class="identifier">ui_type</span><span class="special">(</span><span class="number">0</span><span class="special">))</span> <span class="special">==</span>
1431                   <span class="number">0</span></code>, where <code class="computeroutput"><span class="identifier">ui_type</span></code>
1432                   is <code class="computeroutput"><span class="identifier">ui_type</span></code> is
1433                   <code class="computeroutput"><span class="keyword">typename</span> <span class="identifier">mpl</span><span class="special">::</span><span class="identifier">front</span><span class="special">&lt;</span><span class="keyword">typename</span>
1434                   <span class="identifier">B</span><span class="special">::</span><span class="identifier">unsigned_types</span><span class="special">&gt;::</span><span class="identifier">type</span></code>.
1435                 </p>
1436               </td>
1437 <td>
1438                 <p>
1439                   &#160;
1440                 </p>
1441               </td>
1442 </tr>
1443 <tr>
1444 <td>
1445                 <p>
1446                   <code class="computeroutput"><span class="identifier">eval_get_sign</span><span class="special">(</span><span class="identifier">cb</span><span class="special">)</span></code>
1447                 </p>
1448               </td>
1449 <td>
1450                 <p>
1451                   <code class="computeroutput"><span class="keyword">int</span></code>
1452                 </p>
1453               </td>
1454 <td>
1455                 <p>
1456                   Returns a value &lt; zero if <code class="computeroutput"><span class="identifier">cb</span></code>
1457                   is negative, a value &gt; zero if <code class="computeroutput"><span class="identifier">cb</span></code>
1458                   is positive, and zero if <code class="computeroutput"><span class="identifier">cb</span></code>
1459                   is zero. The default version of this function returns <code class="computeroutput"><span class="identifier">cb</span><span class="special">.</span><span class="identifier">compare</span><span class="special">(</span><span class="identifier">ui_type</span><span class="special">(</span><span class="number">0</span><span class="special">))</span></code>,
1460                   where <code class="computeroutput"><span class="identifier">ui_type</span></code> is
1461                   <code class="computeroutput"><span class="identifier">ui_type</span></code> is <code class="computeroutput"><span class="keyword">typename</span> <span class="identifier">mpl</span><span class="special">::</span><span class="identifier">front</span><span class="special">&lt;</span><span class="keyword">typename</span>
1462                   <span class="identifier">B</span><span class="special">::</span><span class="identifier">unsigned_types</span><span class="special">&gt;::</span><span class="identifier">type</span></code>.
1463                 </p>
1464               </td>
1465 <td>
1466                 <p>
1467                   &#160;
1468                 </p>
1469               </td>
1470 </tr>
1471 <tr>
1472 <td>
1473                 <p>
1474                   <span class="emphasis"><em>Basic arithmetic:</em></span>
1475                 </p>
1476               </td>
1477 <td class="auto-generated">&#160;</td>
1478 <td class="auto-generated">&#160;</td>
1479 </tr>
1480 <tr>
1481 <td>
1482                 <p>
1483                   <code class="computeroutput"><span class="identifier">eval_add</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span>
1484                   <span class="identifier">a</span><span class="special">)</span></code>
1485                 </p>
1486               </td>
1487 <td>
1488                 <p>
1489                   <code class="computeroutput"><span class="keyword">void</span></code>
1490                 </p>
1491               </td>
1492 <td>
1493                 <p>
1494                   Adds <code class="computeroutput"><span class="identifier">a</span></code> to <code class="computeroutput"><span class="identifier">b</span></code>. The type of <code class="computeroutput"><span class="identifier">a</span></code> shall be listed in one of the
1495                   type lists <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">signed_types</span></code>, <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">unsigned_types</span></code>
1496                   or <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">float_types</span></code>. When not provided,
1497                   the default version calls <code class="computeroutput"><span class="identifier">eval_add</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> <span class="identifier">B</span><span class="special">(</span><span class="identifier">a</span><span class="special">))</span></code>
1498                 </p>
1499               </td>
1500 <td>
1501                 <p>
1502                   &#160;
1503                 </p>
1504               </td>
1505 </tr>
1506 <tr>
1507 <td>
1508                 <p>
1509                   <code class="computeroutput"><span class="identifier">eval_add</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span>
1510                   <span class="identifier">cb</span><span class="special">,</span>
1511                   <span class="identifier">cb2</span><span class="special">)</span></code>
1512                 </p>
1513               </td>
1514 <td>
1515                 <p>
1516                   <code class="computeroutput"><span class="keyword">void</span></code>
1517                 </p>
1518               </td>
1519 <td>
1520                 <p>
1521                   Add <code class="computeroutput"><span class="identifier">cb</span></code> to <code class="computeroutput"><span class="identifier">cb2</span></code> and stores the result in
1522                   <code class="computeroutput"><span class="identifier">b</span></code>. When not provided,
1523                   does the equivalent of <code class="computeroutput"><span class="identifier">b</span>
1524                   <span class="special">=</span> <span class="identifier">cb</span><span class="special">;</span> <span class="identifier">eval_add</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> <span class="identifier">cb2</span><span class="special">)</span></code>.
1525                 </p>
1526               </td>
1527 <td>
1528                 <p>
1529                   &#160;
1530                 </p>
1531               </td>
1532 </tr>
1533 <tr>
1534 <td>
1535                 <p>
1536                   <code class="computeroutput"><span class="identifier">eval_add</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span>
1537                   <span class="identifier">cb</span><span class="special">,</span>
1538                   <span class="identifier">a</span><span class="special">)</span></code>
1539                 </p>
1540               </td>
1541 <td>
1542                 <p>
1543                   <code class="computeroutput"><span class="keyword">void</span></code>
1544                 </p>
1545               </td>
1546 <td>
1547                 <p>
1548                   Add <code class="computeroutput"><span class="identifier">cb</span></code> to <code class="computeroutput"><span class="identifier">a</span></code> and stores the result in <code class="computeroutput"><span class="identifier">b</span></code>. The type of <code class="computeroutput"><span class="identifier">a</span></code> shall be listed in one of the
1549                   type lists <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">signed_types</span></code>, <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">unsigned_types</span></code>
1550                   or <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">float_types</span></code>. When not provided,
1551                   does the equivalent of <code class="computeroutput"><span class="identifier">eval_add</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> <span class="identifier">cb</span><span class="special">,</span> <span class="identifier">B</span><span class="special">(</span><span class="identifier">a</span><span class="special">))</span></code>.
1552                 </p>
1553               </td>
1554 <td>
1555                 <p>
1556                   &#160;
1557                 </p>
1558               </td>
1559 </tr>
1560 <tr>
1561 <td>
1562                 <p>
1563                   <code class="computeroutput"><span class="identifier">eval_add</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span>
1564                   <span class="identifier">a</span><span class="special">,</span>
1565                   <span class="identifier">cb</span><span class="special">)</span></code>
1566                 </p>
1567               </td>
1568 <td>
1569                 <p>
1570                   <code class="computeroutput"><span class="keyword">void</span></code>
1571                 </p>
1572               </td>
1573 <td>
1574                 <p>
1575                   Add <code class="computeroutput"><span class="identifier">a</span></code> to <code class="computeroutput"><span class="identifier">cb</span></code> and stores the result in
1576                   <code class="computeroutput"><span class="identifier">b</span></code>. The type of
1577                   <code class="computeroutput"><span class="identifier">a</span></code> shall be listed
1578                   in one of the type lists <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">signed_types</span></code>,
1579                   <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">unsigned_types</span></code> or <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">float_types</span></code>. When not provided,
1580                   does the equivalent of <code class="computeroutput"><span class="identifier">eval_add</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> <span class="identifier">cb</span><span class="special">,</span> <span class="identifier">a</span><span class="special">)</span></code>.
1581                 </p>
1582               </td>
1583 <td>
1584                 <p>
1585                   &#160;
1586                 </p>
1587               </td>
1588 </tr>
1589 <tr>
1590 <td>
1591                 <p>
1592                   <code class="computeroutput"><span class="identifier">eval_subtract</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span>
1593                   <span class="identifier">a</span><span class="special">)</span></code>
1594                 </p>
1595               </td>
1596 <td>
1597                 <p>
1598                   <code class="computeroutput"><span class="keyword">void</span></code>
1599                 </p>
1600               </td>
1601 <td>
1602                 <p>
1603                   Subtracts <code class="computeroutput"><span class="identifier">a</span></code> from
1604                   <code class="computeroutput"><span class="identifier">b</span></code>. The type of
1605                   <code class="computeroutput"><span class="identifier">a</span></code> shall be listed
1606                   in one of the type lists <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">signed_types</span></code>,
1607                   <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">unsigned_types</span></code> or <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">float_types</span></code>. When not provided,
1608                   the default version calls <code class="computeroutput"><span class="identifier">eval_subtract</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> <span class="identifier">B</span><span class="special">(</span><span class="identifier">a</span><span class="special">))</span></code>
1609                 </p>
1610               </td>
1611 <td>
1612                 <p>
1613                   &#160;
1614                 </p>
1615               </td>
1616 </tr>
1617 <tr>
1618 <td>
1619                 <p>
1620                   <code class="computeroutput"><span class="identifier">eval_subtract</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span>
1621                   <span class="identifier">cb</span><span class="special">,</span>
1622                   <span class="identifier">cb2</span><span class="special">)</span></code>
1623                 </p>
1624               </td>
1625 <td>
1626                 <p>
1627                   <code class="computeroutput"><span class="keyword">void</span></code>
1628                 </p>
1629               </td>
1630 <td>
1631                 <p>
1632                   Subtracts <code class="computeroutput"><span class="identifier">cb2</span></code> from
1633                   <code class="computeroutput"><span class="identifier">cb</span></code> and stores the
1634                   result in <code class="computeroutput"><span class="identifier">b</span></code>. When
1635                   not provided, does the equivalent of <code class="computeroutput"><span class="identifier">b</span>
1636                   <span class="special">=</span> <span class="identifier">cb</span><span class="special">;</span> <span class="identifier">eval_subtract</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> <span class="identifier">cb2</span><span class="special">)</span></code>.
1637                 </p>
1638               </td>
1639 <td>
1640                 <p>
1641                   &#160;
1642                 </p>
1643               </td>
1644 </tr>
1645 <tr>
1646 <td>
1647                 <p>
1648                   <code class="computeroutput"><span class="identifier">eval_subtract</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span>
1649                   <span class="identifier">cb</span><span class="special">,</span>
1650                   <span class="identifier">a</span><span class="special">)</span></code>
1651                 </p>
1652               </td>
1653 <td>
1654                 <p>
1655                   <code class="computeroutput"><span class="keyword">void</span></code>
1656                 </p>
1657               </td>
1658 <td>
1659                 <p>
1660                   Subtracts <code class="computeroutput"><span class="identifier">a</span></code> from
1661                   <code class="computeroutput"><span class="identifier">cb</span></code> and stores the
1662                   result in <code class="computeroutput"><span class="identifier">b</span></code>. The
1663                   type of <code class="computeroutput"><span class="identifier">a</span></code> shall
1664                   be listed in one of the type lists <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">signed_types</span></code>,
1665                   <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">unsigned_types</span></code> or <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">float_types</span></code>. When not provided,
1666                   does the equivalent of <code class="computeroutput"><span class="identifier">eval_subtract</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> <span class="identifier">cb</span><span class="special">,</span> <span class="identifier">B</span><span class="special">(</span><span class="identifier">a</span><span class="special">))</span></code>.
1667                 </p>
1668               </td>
1669 <td>
1670                 <p>
1671                   &#160;
1672                 </p>
1673               </td>
1674 </tr>
1675 <tr>
1676 <td>
1677                 <p>
1678                   <code class="computeroutput"><span class="identifier">eval_subtract</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span>
1679                   <span class="identifier">a</span><span class="special">,</span>
1680                   <span class="identifier">cb</span><span class="special">)</span></code>
1681                 </p>
1682               </td>
1683 <td>
1684                 <p>
1685                   <code class="computeroutput"><span class="keyword">void</span></code>
1686                 </p>
1687               </td>
1688 <td>
1689                 <p>
1690                   Subtracts <code class="computeroutput"><span class="identifier">cb</span></code> from
1691                   <code class="computeroutput"><span class="identifier">a</span></code> and stores the
1692                   result in <code class="computeroutput"><span class="identifier">b</span></code>. The
1693                   type of <code class="computeroutput"><span class="identifier">a</span></code> shall
1694                   be listed in one of the type lists <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">signed_types</span></code>,
1695                   <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">unsigned_types</span></code> or <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">float_types</span></code>. When not provided,
1696                   does the equivalent of <code class="computeroutput"><span class="identifier">eval_subtract</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> <span class="identifier">cb</span><span class="special">,</span> <span class="identifier">a</span><span class="special">);</span> <span class="identifier">b</span><span class="special">.</span><span class="identifier">negate</span><span class="special">();</span></code>.
1697                 </p>
1698               </td>
1699 <td>
1700                 <p>
1701                   &#160;
1702                 </p>
1703               </td>
1704 </tr>
1705 <tr>
1706 <td>
1707                 <p>
1708                   <code class="computeroutput"><span class="identifier">eval_multiply</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span>
1709                   <span class="identifier">a</span><span class="special">)</span></code>
1710                 </p>
1711               </td>
1712 <td>
1713                 <p>
1714                   <code class="computeroutput"><span class="keyword">void</span></code>
1715                 </p>
1716               </td>
1717 <td>
1718                 <p>
1719                   Multiplies <code class="computeroutput"><span class="identifier">b</span></code> by
1720                   <code class="computeroutput"><span class="identifier">a</span></code>. The type of
1721                   <code class="computeroutput"><span class="identifier">a</span></code> shall be listed
1722                   in one of the type lists <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">signed_types</span></code>,
1723                   <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">unsigned_types</span></code> or <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">float_types</span></code>. When not provided,
1724                   the default version calls <code class="computeroutput"><span class="identifier">eval_multiply</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> <span class="identifier">B</span><span class="special">(</span><span class="identifier">a</span><span class="special">))</span></code>
1725                 </p>
1726               </td>
1727 <td>
1728                 <p>
1729                   &#160;
1730                 </p>
1731               </td>
1732 </tr>
1733 <tr>
1734 <td>
1735                 <p>
1736                   <code class="computeroutput"><span class="identifier">eval_multiply</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span>
1737                   <span class="identifier">cb</span><span class="special">,</span>
1738                   <span class="identifier">cb2</span><span class="special">)</span></code>
1739                 </p>
1740               </td>
1741 <td>
1742                 <p>
1743                   <code class="computeroutput"><span class="keyword">void</span></code>
1744                 </p>
1745               </td>
1746 <td>
1747                 <p>
1748                   Multiplies <code class="computeroutput"><span class="identifier">cb</span></code> by
1749                   <code class="computeroutput"><span class="identifier">cb2</span></code> and stores
1750                   the result in <code class="computeroutput"><span class="identifier">b</span></code>.
1751                   When not provided, does the equivalent of <code class="computeroutput"><span class="identifier">b</span>
1752                   <span class="special">=</span> <span class="identifier">cb</span><span class="special">;</span> <span class="identifier">eval_multiply</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> <span class="identifier">cb2</span><span class="special">)</span></code>.
1753                 </p>
1754               </td>
1755 <td>
1756                 <p>
1757                   &#160;
1758                 </p>
1759               </td>
1760 </tr>
1761 <tr>
1762 <td>
1763                 <p>
1764                   <code class="computeroutput"><span class="identifier">eval_multiply</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span>
1765                   <span class="identifier">cb</span><span class="special">,</span>
1766                   <span class="identifier">a</span><span class="special">)</span></code>
1767                 </p>
1768               </td>
1769 <td>
1770                 <p>
1771                   <code class="computeroutput"><span class="keyword">void</span></code>
1772                 </p>
1773               </td>
1774 <td>
1775                 <p>
1776                   Multiplies <code class="computeroutput"><span class="identifier">cb</span></code> by
1777                   <code class="computeroutput"><span class="identifier">a</span></code> and stores the
1778                   result in <code class="computeroutput"><span class="identifier">b</span></code>. The
1779                   type of <code class="computeroutput"><span class="identifier">a</span></code> shall
1780                   be listed in one of the type lists <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">signed_types</span></code>,
1781                   <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">unsigned_types</span></code> or <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">float_types</span></code>. When not provided,
1782                   does the equivalent of <code class="computeroutput"><span class="identifier">eval_multiply</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> <span class="identifier">cb</span><span class="special">,</span> <span class="identifier">B</span><span class="special">(</span><span class="identifier">a</span><span class="special">))</span></code>.
1783                 </p>
1784               </td>
1785 <td>
1786                 <p>
1787                   &#160;
1788                 </p>
1789               </td>
1790 </tr>
1791 <tr>
1792 <td>
1793                 <p>
1794                   <code class="computeroutput"><span class="identifier">eval_multiply</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span>
1795                   <span class="identifier">a</span><span class="special">,</span>
1796                   <span class="identifier">cb</span><span class="special">)</span></code>
1797                 </p>
1798               </td>
1799 <td>
1800                 <p>
1801                   <code class="computeroutput"><span class="keyword">void</span></code>
1802                 </p>
1803               </td>
1804 <td>
1805                 <p>
1806                   Multiplies <code class="computeroutput"><span class="identifier">a</span></code> by
1807                   <code class="computeroutput"><span class="identifier">cb</span></code> and stores the
1808                   result in <code class="computeroutput"><span class="identifier">b</span></code>. The
1809                   type of <code class="computeroutput"><span class="identifier">a</span></code> shall
1810                   be listed in one of the type lists <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">signed_types</span></code>,
1811                   <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">unsigned_types</span></code> or <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">float_types</span></code>. When not provided,
1812                   does the equivalent of <code class="computeroutput"><span class="identifier">eval_multiply</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> <span class="identifier">cb</span><span class="special">,</span> <span class="identifier">a</span><span class="special">)</span></code>.
1813                 </p>
1814               </td>
1815 <td>
1816                 <p>
1817                   &#160;
1818                 </p>
1819               </td>
1820 </tr>
1821 <tr>
1822 <td>
1823                 <p>
1824                   <code class="computeroutput"><span class="identifier">eval_multiply_add</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> <span class="identifier">cb</span><span class="special">,</span> <span class="identifier">cb2</span><span class="special">)</span></code>
1825                 </p>
1826               </td>
1827 <td>
1828                 <p>
1829                   <code class="computeroutput"><span class="keyword">void</span></code>
1830                 </p>
1831               </td>
1832 <td>
1833                 <p>
1834                   Multiplies <code class="computeroutput"><span class="identifier">cb</span></code> by
1835                   <code class="computeroutput"><span class="identifier">cb2</span></code> and adds the
1836                   result to <code class="computeroutput"><span class="identifier">b</span></code>. When
1837                   not provided does the equivalent of creating a temporary <code class="computeroutput"><span class="identifier">B</span> <span class="identifier">t</span></code>
1838                   and <code class="computeroutput"><span class="identifier">eval_multiply</span><span class="special">(</span><span class="identifier">t</span><span class="special">,</span> <span class="identifier">cb</span><span class="special">,</span> <span class="identifier">cb2</span><span class="special">)</span></code> followed by <code class="computeroutput"><span class="identifier">eval_add</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> <span class="identifier">t</span><span class="special">)</span></code>.
1839                 </p>
1840               </td>
1841 <td>
1842                 <p>
1843                   &#160;
1844                 </p>
1845               </td>
1846 </tr>
1847 <tr>
1848 <td>
1849                 <p>
1850                   <code class="computeroutput"><span class="identifier">eval_multiply_add</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> <span class="identifier">cb</span><span class="special">,</span> <span class="identifier">a</span><span class="special">)</span></code>
1851                 </p>
1852               </td>
1853 <td>
1854                 <p>
1855                   <code class="computeroutput"><span class="keyword">void</span></code>
1856                 </p>
1857               </td>
1858 <td>
1859                 <p>
1860                   Multiplies <code class="computeroutput"><span class="identifier">a</span></code> by
1861                   <code class="computeroutput"><span class="identifier">cb</span></code> and adds the
1862                   result to <code class="computeroutput"><span class="identifier">b</span></code>. The
1863                   type of <code class="computeroutput"><span class="identifier">a</span></code> shall
1864                   be listed in one of the type lists <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">signed_types</span></code>,
1865                   <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">unsigned_types</span></code> or <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">float_types</span></code>. When not provided
1866                   does the equivalent of creating a temporary <code class="computeroutput"><span class="identifier">B</span>
1867                   <span class="identifier">t</span></code> and <code class="computeroutput"><span class="identifier">eval_multiply</span><span class="special">(</span><span class="identifier">t</span><span class="special">,</span> <span class="identifier">cb</span><span class="special">,</span> <span class="identifier">a</span><span class="special">)</span></code> followed by <code class="computeroutput"><span class="identifier">eval_add</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> <span class="identifier">t</span><span class="special">)</span></code>.
1868                 </p>
1869               </td>
1870 <td>
1871                 <p>
1872                   &#160;
1873                 </p>
1874               </td>
1875 </tr>
1876 <tr>
1877 <td>
1878                 <p>
1879                   <code class="computeroutput"><span class="identifier">eval_multiply_add</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> <span class="identifier">a</span><span class="special">,</span> <span class="identifier">cb</span><span class="special">)</span></code>
1880                 </p>
1881               </td>
1882 <td>
1883                 <p>
1884                   <code class="computeroutput"><span class="keyword">void</span></code>
1885                 </p>
1886               </td>
1887 <td>
1888                 <p>
1889                   Multiplies <code class="computeroutput"><span class="identifier">a</span></code> by
1890                   <code class="computeroutput"><span class="identifier">cb</span></code> and adds the
1891                   result to <code class="computeroutput"><span class="identifier">b</span></code>. The
1892                   type of <code class="computeroutput"><span class="identifier">a</span></code> shall
1893                   be listed in one of the type lists <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">signed_types</span></code>,
1894                   <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">unsigned_types</span></code> or <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">float_types</span></code>. When not provided
1895                   does the equivalent of <code class="computeroutput"><span class="identifier">eval_multiply_add</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> <span class="identifier">cb</span><span class="special">,</span> <span class="identifier">a</span><span class="special">)</span></code>.
1896                 </p>
1897               </td>
1898 <td>
1899                 <p>
1900                   &#160;
1901                 </p>
1902               </td>
1903 </tr>
1904 <tr>
1905 <td>
1906                 <p>
1907                   <code class="computeroutput"><span class="identifier">eval_multiply_subtract</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> <span class="identifier">cb</span><span class="special">,</span> <span class="identifier">cb2</span><span class="special">)</span></code>
1908                 </p>
1909               </td>
1910 <td>
1911                 <p>
1912                   <code class="computeroutput"><span class="keyword">void</span></code>
1913                 </p>
1914               </td>
1915 <td>
1916                 <p>
1917                   Multiplies <code class="computeroutput"><span class="identifier">cb</span></code> by
1918                   <code class="computeroutput"><span class="identifier">cb2</span></code> and subtracts
1919                   the result from <code class="computeroutput"><span class="identifier">b</span></code>.
1920                   When not provided does the equivalent of creating a temporary
1921                   <code class="computeroutput"><span class="identifier">B</span> <span class="identifier">t</span></code>
1922                   and <code class="computeroutput"><span class="identifier">eval_multiply</span><span class="special">(</span><span class="identifier">t</span><span class="special">,</span> <span class="identifier">cb</span><span class="special">,</span> <span class="identifier">cb2</span><span class="special">)</span></code> followed by <code class="computeroutput"><span class="identifier">eval_subtract</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> <span class="identifier">t</span><span class="special">)</span></code>.
1923                 </p>
1924               </td>
1925 <td>
1926                 <p>
1927                   &#160;
1928                 </p>
1929               </td>
1930 </tr>
1931 <tr>
1932 <td>
1933                 <p>
1934                   <code class="computeroutput"><span class="identifier">eval_multiply_subtract</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> <span class="identifier">cb</span><span class="special">,</span> <span class="identifier">a</span><span class="special">)</span></code>
1935                 </p>
1936               </td>
1937 <td>
1938                 <p>
1939                   <code class="computeroutput"><span class="keyword">void</span></code>
1940                 </p>
1941               </td>
1942 <td>
1943                 <p>
1944                   Multiplies <code class="computeroutput"><span class="identifier">a</span></code> by
1945                   <code class="computeroutput"><span class="identifier">cb</span></code> and subtracts
1946                   the result from <code class="computeroutput"><span class="identifier">b</span></code>.
1947                   The type of <code class="computeroutput"><span class="identifier">a</span></code> shall
1948                   be listed in one of the type lists <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">signed_types</span></code>,
1949                   <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">unsigned_types</span></code> or <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">float_types</span></code>. When not provided
1950                   does the equivalent of creating a temporary <code class="computeroutput"><span class="identifier">B</span>
1951                   <span class="identifier">t</span></code> and <code class="computeroutput"><span class="identifier">eval_multiply</span><span class="special">(</span><span class="identifier">t</span><span class="special">,</span> <span class="identifier">cb</span><span class="special">,</span> <span class="identifier">a</span><span class="special">)</span></code> followed by <code class="computeroutput"><span class="identifier">eval_subtract</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> <span class="identifier">t</span><span class="special">)</span></code>.
1952                 </p>
1953               </td>
1954 <td>
1955                 <p>
1956                   &#160;
1957                 </p>
1958               </td>
1959 </tr>
1960 <tr>
1961 <td>
1962                 <p>
1963                   <code class="computeroutput"><span class="identifier">eval_multiply_subtract</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> <span class="identifier">a</span><span class="special">,</span> <span class="identifier">cb</span><span class="special">)</span></code>
1964                 </p>
1965               </td>
1966 <td>
1967                 <p>
1968                   <code class="computeroutput"><span class="keyword">void</span></code>
1969                 </p>
1970               </td>
1971 <td>
1972                 <p>
1973                   Multiplies <code class="computeroutput"><span class="identifier">a</span></code> by
1974                   <code class="computeroutput"><span class="identifier">cb</span></code> and subtracts
1975                   the result from <code class="computeroutput"><span class="identifier">b</span></code>.
1976                   The type of <code class="computeroutput"><span class="identifier">a</span></code> shall
1977                   be listed in one of the type lists <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">signed_types</span></code>,
1978                   <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">unsigned_types</span></code> or <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">float_types</span></code>. When not provided
1979                   does the equivalent of <code class="computeroutput"><span class="identifier">eval_multiply_subtract</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> <span class="identifier">cb</span><span class="special">,</span> <span class="identifier">a</span><span class="special">)</span></code>.
1980                 </p>
1981               </td>
1982 <td>
1983                 <p>
1984                   &#160;
1985                 </p>
1986               </td>
1987 </tr>
1988 <tr>
1989 <td>
1990                 <p>
1991                   <code class="computeroutput"><span class="identifier">eval_multiply_add</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> <span class="identifier">cb</span><span class="special">,</span> <span class="identifier">cb2</span><span class="special">,</span> <span class="identifier">cb3</span><span class="special">)</span></code>
1992                 </p>
1993               </td>
1994 <td>
1995                 <p>
1996                   <code class="computeroutput"><span class="keyword">void</span></code>
1997                 </p>
1998               </td>
1999 <td>
2000                 <p>
2001                   Multiplies <code class="computeroutput"><span class="identifier">cb</span></code> by
2002                   <code class="computeroutput"><span class="identifier">cb2</span></code> and adds the
2003                   result to <code class="computeroutput"><span class="identifier">cb3</span></code> storing
2004                   the result in <code class="computeroutput"><span class="identifier">b</span></code>.
2005                   When not provided does the equivalent of <code class="computeroutput"><span class="identifier">eval_multiply</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> <span class="identifier">cb</span><span class="special">,</span> <span class="identifier">cb2</span><span class="special">)</span></code> followed by <code class="computeroutput"><span class="identifier">eval_add</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> <span class="identifier">cb3</span><span class="special">)</span></code>. For brevity, only a version showing
2006                   all arguments of type <code class="computeroutput"><span class="identifier">B</span></code>
2007                   is shown here, but you can replace up to any 2 of <code class="computeroutput"><span class="identifier">cb</span></code>, <code class="computeroutput"><span class="identifier">cb2</span></code>
2008                   and <code class="computeroutput"><span class="identifier">cb3</span></code> with any
2009                   type listed in one of the type lists <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">signed_types</span></code>,
2010                   <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">unsigned_types</span></code> or <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">float_types</span></code>.
2011                 </p>
2012               </td>
2013 <td>
2014                 <p>
2015                   &#160;
2016                 </p>
2017               </td>
2018 </tr>
2019 <tr>
2020 <td>
2021                 <p>
2022                   <code class="computeroutput"><span class="identifier">eval_multiply_subtract</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> <span class="identifier">cb</span><span class="special">,</span> <span class="identifier">cb2</span><span class="special">,</span> <span class="identifier">cb3</span><span class="special">)</span></code>
2023                 </p>
2024               </td>
2025 <td>
2026                 <p>
2027                   <code class="computeroutput"><span class="keyword">void</span></code>
2028                 </p>
2029               </td>
2030 <td>
2031                 <p>
2032                   Multiplies <code class="computeroutput"><span class="identifier">cb</span></code> by
2033                   <code class="computeroutput"><span class="identifier">cb2</span></code> and subtracts
2034                   from the result <code class="computeroutput"><span class="identifier">cb3</span></code>
2035                   storing the result in <code class="computeroutput"><span class="identifier">b</span></code>.
2036                   When not provided does the equivalent of <code class="computeroutput"><span class="identifier">eval_multiply</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> <span class="identifier">cb</span><span class="special">,</span> <span class="identifier">cb2</span><span class="special">)</span></code> followed by <code class="computeroutput"><span class="identifier">eval_subtract</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> <span class="identifier">cb3</span><span class="special">)</span></code>. For brevity, only a version showing
2037                   all arguments of type <code class="computeroutput"><span class="identifier">B</span></code>
2038                   is shown here, but you can replace up to any 2 of <code class="computeroutput"><span class="identifier">cb</span></code>, <code class="computeroutput"><span class="identifier">cb2</span></code>
2039                   and <code class="computeroutput"><span class="identifier">cb3</span></code> with any
2040                   type listed in one of the type lists <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">signed_types</span></code>,
2041                   <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">unsigned_types</span></code> or <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">float_types</span></code>.
2042                 </p>
2043               </td>
2044 <td>
2045                 <p>
2046                   &#160;
2047                 </p>
2048               </td>
2049 </tr>
2050 <tr>
2051 <td>
2052                 <p>
2053                   <code class="computeroutput"><span class="identifier">eval_divide</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span>
2054                   <span class="identifier">a</span><span class="special">)</span></code>
2055                 </p>
2056               </td>
2057 <td>
2058                 <p>
2059                   <code class="computeroutput"><span class="keyword">void</span></code>
2060                 </p>
2061               </td>
2062 <td>
2063                 <p>
2064                   Divides <code class="computeroutput"><span class="identifier">b</span></code> by <code class="computeroutput"><span class="identifier">a</span></code>. The type of <code class="computeroutput"><span class="identifier">a</span></code> shall be listed in one of the
2065                   type lists <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">signed_types</span></code>, <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">unsigned_types</span></code>
2066                   or <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">float_types</span></code>. When not provided,
2067                   the default version calls <code class="computeroutput"><span class="identifier">eval_divide</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> <span class="identifier">B</span><span class="special">(</span><span class="identifier">a</span><span class="special">))</span></code>
2068                 </p>
2069               </td>
2070 <td>
2071                 <p>
2072                   <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">overflow_error</span></code> if <code class="computeroutput"><span class="identifier">a</span></code> has the value zero, and <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special">&lt;</span><span class="identifier">number</span><span class="special">&lt;</span><span class="identifier">B</span><span class="special">&gt;</span>
2073                   <span class="special">&gt;::</span><span class="identifier">has_infinity</span>
2074                   <span class="special">==</span> <span class="keyword">false</span></code>
2075                 </p>
2076               </td>
2077 </tr>
2078 <tr>
2079 <td>
2080                 <p>
2081                   <code class="computeroutput"><span class="identifier">eval_divide</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span>
2082                   <span class="identifier">cb</span><span class="special">,</span>
2083                   <span class="identifier">cb2</span><span class="special">)</span></code>
2084                 </p>
2085               </td>
2086 <td>
2087                 <p>
2088                   <code class="computeroutput"><span class="keyword">void</span></code>
2089                 </p>
2090               </td>
2091 <td>
2092                 <p>
2093                   Divides <code class="computeroutput"><span class="identifier">cb</span></code> by
2094                   <code class="computeroutput"><span class="identifier">cb2</span></code> and stores
2095                   the result in <code class="computeroutput"><span class="identifier">b</span></code>.
2096                   When not provided, does the equivalent of <code class="computeroutput"><span class="identifier">b</span>
2097                   <span class="special">=</span> <span class="identifier">cb</span><span class="special">;</span> <span class="identifier">eval_divide</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> <span class="identifier">cb2</span><span class="special">)</span></code>.
2098                 </p>
2099               </td>
2100 <td>
2101                 <p>
2102                   <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">overflow_error</span></code> if <code class="computeroutput"><span class="identifier">cb2</span></code> has the value zero, and
2103                   <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special">&lt;</span><span class="identifier">number</span><span class="special">&lt;</span><span class="identifier">B</span><span class="special">&gt;</span>
2104                   <span class="special">&gt;::</span><span class="identifier">has_infinity</span>
2105                   <span class="special">==</span> <span class="keyword">false</span></code>
2106                 </p>
2107               </td>
2108 </tr>
2109 <tr>
2110 <td>
2111                 <p>
2112                   <code class="computeroutput"><span class="identifier">eval_divide</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span>
2113                   <span class="identifier">cb</span><span class="special">,</span>
2114                   <span class="identifier">a</span><span class="special">)</span></code>
2115                 </p>
2116               </td>
2117 <td>
2118                 <p>
2119                   <code class="computeroutput"><span class="keyword">void</span></code>
2120                 </p>
2121               </td>
2122 <td>
2123                 <p>
2124                   Divides <code class="computeroutput"><span class="identifier">cb</span></code> by
2125                   <code class="computeroutput"><span class="identifier">a</span></code> and stores the
2126                   result in <code class="computeroutput"><span class="identifier">b</span></code>. The
2127                   type of <code class="computeroutput"><span class="identifier">a</span></code> shall
2128                   be listed in one of the type lists <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">signed_types</span></code>,
2129                   <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">unsigned_types</span></code> or <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">float_types</span></code>. When not provided,
2130                   does the equivalent of <code class="computeroutput"><span class="identifier">eval_divide</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> <span class="identifier">cb</span><span class="special">,</span> <span class="identifier">B</span><span class="special">(</span><span class="identifier">a</span><span class="special">))</span></code>.
2131                 </p>
2132               </td>
2133 <td>
2134                 <p>
2135                   <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">overflow_error</span></code> if <code class="computeroutput"><span class="identifier">a</span></code> has the value zero, and <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special">&lt;</span><span class="identifier">number</span><span class="special">&lt;</span><span class="identifier">B</span><span class="special">&gt;</span>
2136                   <span class="special">&gt;::</span><span class="identifier">has_infinity</span>
2137                   <span class="special">==</span> <span class="keyword">false</span></code>
2138                 </p>
2139               </td>
2140 </tr>
2141 <tr>
2142 <td>
2143                 <p>
2144                   <code class="computeroutput"><span class="identifier">eval_divide</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span>
2145                   <span class="identifier">a</span><span class="special">,</span>
2146                   <span class="identifier">cb</span><span class="special">)</span></code>
2147                 </p>
2148               </td>
2149 <td>
2150                 <p>
2151                   <code class="computeroutput"><span class="keyword">void</span></code>
2152                 </p>
2153               </td>
2154 <td>
2155                 <p>
2156                   Divides <code class="computeroutput"><span class="identifier">a</span></code> by <code class="computeroutput"><span class="identifier">cb</span></code> and stores the result in
2157                   <code class="computeroutput"><span class="identifier">b</span></code>. The type of
2158                   <code class="computeroutput"><span class="identifier">a</span></code> shall be listed
2159                   in one of the type lists <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">signed_types</span></code>,
2160                   <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">unsigned_types</span></code> or <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">float_types</span></code>. When not provided,
2161                   does the equivalent of <code class="computeroutput"><span class="identifier">eval_divide</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> <span class="identifier">B</span><span class="special">(</span><span class="identifier">a</span><span class="special">),</span> <span class="identifier">cb</span><span class="special">)</span></code>.
2162                 </p>
2163               </td>
2164 <td>
2165                 <p>
2166                   <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">overflow_error</span></code> if cb has the
2167                   value zero, and <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special">&lt;</span><span class="identifier">number</span><span class="special">&lt;</span><span class="identifier">B</span><span class="special">&gt;</span> <span class="special">&gt;::</span><span class="identifier">has_infinity</span> <span class="special">==</span>
2168                   <span class="keyword">false</span></code>
2169                 </p>
2170               </td>
2171 </tr>
2172 <tr>
2173 <td>
2174                 <p>
2175                   <code class="computeroutput"><span class="identifier">eval_increment</span><span class="special">(</span><span class="identifier">b</span><span class="special">)</span></code>
2176                 </p>
2177               </td>
2178 <td>
2179                 <p>
2180                   void
2181                 </p>
2182               </td>
2183 <td>
2184                 <p>
2185                   Increments the value of <code class="computeroutput"><span class="identifier">b</span></code>
2186                   by one. When not provided, does the equivalent of <code class="computeroutput"><span class="identifier">eval_add</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span>
2187                   <span class="keyword">static_cast</span><span class="special">&lt;</span><span class="identifier">ui_type</span><span class="special">&gt;(</span><span class="number">1u</span><span class="special">))</span></code>.
2188                   Where <code class="computeroutput"><span class="identifier">ui_type</span></code> is
2189                   <code class="computeroutput"><span class="keyword">typename</span> <span class="identifier">mpl</span><span class="special">::</span><span class="identifier">front</span><span class="special">&lt;</span><span class="keyword">typename</span>
2190                   <span class="identifier">B</span><span class="special">::</span><span class="identifier">unsigned_types</span><span class="special">&gt;::</span><span class="identifier">type</span></code>.
2191                 </p>
2192               </td>
2193 <td>
2194                 <p>
2195                   &#160;
2196                 </p>
2197               </td>
2198 </tr>
2199 <tr>
2200 <td>
2201                 <p>
2202                   <code class="computeroutput"><span class="identifier">eval_decrement</span><span class="special">(</span><span class="identifier">b</span><span class="special">)</span></code>
2203                 </p>
2204               </td>
2205 <td>
2206                 <p>
2207                   void
2208                 </p>
2209               </td>
2210 <td>
2211                 <p>
2212                   Decrements the value of <code class="computeroutput"><span class="identifier">b</span></code>
2213                   by one. When not provided, does the equivalent of <code class="computeroutput"><span class="identifier">eval_subtract</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span>
2214                   <span class="keyword">static_cast</span><span class="special">&lt;</span><span class="identifier">ui_type</span><span class="special">&gt;(</span><span class="number">1u</span><span class="special">))</span></code>.
2215                   Where <code class="computeroutput"><span class="identifier">ui_type</span></code> is
2216                   <code class="computeroutput"><span class="keyword">typename</span> <span class="identifier">mpl</span><span class="special">::</span><span class="identifier">front</span><span class="special">&lt;</span><span class="keyword">typename</span>
2217                   <span class="identifier">B</span><span class="special">::</span><span class="identifier">unsigned_types</span><span class="special">&gt;::</span><span class="identifier">type</span></code>.
2218                 </p>
2219               </td>
2220 <td>
2221                 <p>
2222                   &#160;
2223                 </p>
2224               </td>
2225 </tr>
2226 <tr>
2227 <td>
2228                 <p>
2229                   <span class="emphasis"><em>Integer specific operations:</em></span>
2230                 </p>
2231               </td>
2232 <td class="auto-generated">&#160;</td>
2233 <td class="auto-generated">&#160;</td>
2234 </tr>
2235 <tr>
2236 <td>
2237                 <p>
2238                   <code class="computeroutput"><span class="identifier">eval_modulus</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span>
2239                   <span class="identifier">a</span><span class="special">)</span></code>
2240                 </p>
2241               </td>
2242 <td>
2243                 <p>
2244                   <code class="computeroutput"><span class="keyword">void</span></code>
2245                 </p>
2246               </td>
2247 <td>
2248                 <p>
2249                   Computes <code class="computeroutput"><span class="identifier">b</span> <span class="special">%=</span>
2250                   <span class="identifier">cb</span></code>, only required when
2251                   <code class="computeroutput"><span class="identifier">B</span></code> is an integer
2252                   type. The type of <code class="computeroutput"><span class="identifier">a</span></code>
2253                   shall be listed in one of the type lists <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">signed_types</span></code>,
2254                   <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">unsigned_types</span></code> or <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">float_types</span></code>. When not provided,
2255                   the default version calls <code class="computeroutput"><span class="identifier">eval_modulus</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> <span class="identifier">B</span><span class="special">(</span><span class="identifier">a</span><span class="special">))</span></code>
2256                 </p>
2257               </td>
2258 <td>
2259                 <p>
2260                   <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">overflow_error</span></code> if <code class="computeroutput"><span class="identifier">a</span></code> has the value zero.
2261                 </p>
2262               </td>
2263 </tr>
2264 <tr>
2265 <td>
2266                 <p>
2267                   <code class="computeroutput"><span class="identifier">eval_modulus</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span>
2268                   <span class="identifier">cb</span><span class="special">,</span>
2269                   <span class="identifier">cb2</span><span class="special">)</span></code>
2270                 </p>
2271               </td>
2272 <td>
2273                 <p>
2274                   <code class="computeroutput"><span class="keyword">void</span></code>
2275                 </p>
2276               </td>
2277 <td>
2278                 <p>
2279                   Computes <code class="computeroutput"><span class="identifier">cb</span> <span class="special">%</span>
2280                   <span class="identifier">cb2</span></code> and stores the result
2281                   in <code class="computeroutput"><span class="identifier">b</span></code>, only required
2282                   when <code class="computeroutput"><span class="identifier">B</span></code> is an integer
2283                   type. When not provided, does the equivalent of <code class="computeroutput"><span class="identifier">b</span>
2284                   <span class="special">=</span> <span class="identifier">cb</span><span class="special">;</span> <span class="identifier">eval_modulus</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> <span class="identifier">cb2</span><span class="special">)</span></code>.
2285                 </p>
2286               </td>
2287 <td>
2288                 <p>
2289                   <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">overflow_error</span></code> if <code class="computeroutput"><span class="identifier">a</span></code> has the value zero.
2290                 </p>
2291               </td>
2292 </tr>
2293 <tr>
2294 <td>
2295                 <p>
2296                   <code class="computeroutput"><span class="identifier">eval_modulus</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span>
2297                   <span class="identifier">cb</span><span class="special">,</span>
2298                   <span class="identifier">a</span><span class="special">)</span></code>
2299                 </p>
2300               </td>
2301 <td>
2302                 <p>
2303                   <code class="computeroutput"><span class="keyword">void</span></code>
2304                 </p>
2305               </td>
2306 <td>
2307                 <p>
2308                   Computes <code class="computeroutput"><span class="identifier">cb</span> <span class="special">%</span>
2309                   <span class="identifier">a</span></code> and stores the result
2310                   in <code class="computeroutput"><span class="identifier">b</span></code>, only required
2311                   when <code class="computeroutput"><span class="identifier">B</span></code> is an integer
2312                   type. The type of <code class="computeroutput"><span class="identifier">a</span></code>
2313                   shall be listed in one of the type lists <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">signed_types</span></code>,
2314                   <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">unsigned_types</span></code> or <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">float_types</span></code>. When not provided,
2315                   does the equivalent of <code class="computeroutput"><span class="identifier">eval_modulus</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> <span class="identifier">cb</span><span class="special">,</span> <span class="identifier">B</span><span class="special">(</span><span class="identifier">a</span><span class="special">))</span></code>.
2316                 </p>
2317               </td>
2318 <td>
2319                 <p>
2320                   <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">overflow_error</span></code> if <code class="computeroutput"><span class="identifier">a</span></code> has the value zero.
2321                 </p>
2322               </td>
2323 </tr>
2324 <tr>
2325 <td>
2326                 <p>
2327                   <code class="computeroutput"><span class="identifier">eval_modulus</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span>
2328                   <span class="identifier">a</span><span class="special">,</span>
2329                   <span class="identifier">cb</span><span class="special">)</span></code>
2330                 </p>
2331               </td>
2332 <td>
2333                 <p>
2334                   <code class="computeroutput"><span class="keyword">void</span></code>
2335                 </p>
2336               </td>
2337 <td>
2338                 <p>
2339                   Computes <code class="computeroutput"><span class="identifier">cb</span> <span class="special">%</span>
2340                   <span class="identifier">a</span></code> and stores the result
2341                   in <code class="computeroutput"><span class="identifier">b</span></code>, only required
2342                   when <code class="computeroutput"><span class="identifier">B</span></code> is an integer
2343                   type. The type of <code class="computeroutput"><span class="identifier">a</span></code>
2344                   shall be listed in one of the type lists <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">signed_types</span></code>,
2345                   <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">unsigned_types</span></code> or <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">float_types</span></code>. When not provided,
2346                   does the equivalent of <code class="computeroutput"><span class="identifier">eval_modulus</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> <span class="identifier">B</span><span class="special">(</span><span class="identifier">a</span><span class="special">),</span> <span class="identifier">cb</span><span class="special">)</span></code>.
2347                 </p>
2348               </td>
2349 <td>
2350                 <p>
2351                   <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">overflow_error</span></code> if <code class="computeroutput"><span class="identifier">a</span></code> has the value zero.
2352                 </p>
2353               </td>
2354 </tr>
2355 <tr>
2356 <td>
2357                 <p>
2358                   <code class="computeroutput"><span class="identifier">eval_bitwise_and</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> <span class="identifier">a</span><span class="special">)</span></code>
2359                 </p>
2360               </td>
2361 <td>
2362                 <p>
2363                   <code class="computeroutput"><span class="keyword">void</span></code>
2364                 </p>
2365               </td>
2366 <td>
2367                 <p>
2368                   Computes <code class="computeroutput"><span class="identifier">b</span> <span class="special">&amp;=</span>
2369                   <span class="identifier">cb</span></code>, only required when
2370                   <code class="computeroutput"><span class="identifier">B</span></code> is an integer
2371                   type. The type of <code class="computeroutput"><span class="identifier">a</span></code>
2372                   shall be listed in one of the type lists <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">signed_types</span></code>,
2373                   <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">unsigned_types</span></code> or <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">float_types</span></code>. When not provided,
2374                   the default version calls <code class="computeroutput"><span class="identifier">eval_bitwise_and</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> <span class="identifier">B</span><span class="special">(</span><span class="identifier">a</span><span class="special">))</span></code>
2375                 </p>
2376               </td>
2377 <td>
2378                 <p>
2379                   &#160;
2380                 </p>
2381               </td>
2382 </tr>
2383 <tr>
2384 <td>
2385                 <p>
2386                   <code class="computeroutput"><span class="identifier">eval_bitwise_and</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> <span class="identifier">cb</span><span class="special">,</span> <span class="identifier">cb2</span><span class="special">)</span></code>
2387                 </p>
2388               </td>
2389 <td>
2390                 <p>
2391                   <code class="computeroutput"><span class="keyword">void</span></code>
2392                 </p>
2393               </td>
2394 <td>
2395                 <p>
2396                   Computes <code class="computeroutput"><span class="identifier">cb</span> <span class="special">&amp;</span>
2397                   <span class="identifier">cb2</span></code> and stores the result
2398                   in <code class="computeroutput"><span class="identifier">b</span></code>, only required
2399                   when <code class="computeroutput"><span class="identifier">B</span></code> is an integer
2400                   type. When not provided, does the equivalent of <code class="computeroutput"><span class="identifier">b</span>
2401                   <span class="special">=</span> <span class="identifier">cb</span><span class="special">;</span> <span class="identifier">eval_bitwise_and</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> <span class="identifier">cb2</span><span class="special">)</span></code>.
2402                 </p>
2403               </td>
2404 <td>
2405                 <p>
2406                   &#160;
2407                 </p>
2408               </td>
2409 </tr>
2410 <tr>
2411 <td>
2412                 <p>
2413                   <code class="computeroutput"><span class="identifier">eval_bitwise_and</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> <span class="identifier">cb</span><span class="special">,</span> <span class="identifier">a</span><span class="special">)</span></code>
2414                 </p>
2415               </td>
2416 <td>
2417                 <p>
2418                   <code class="computeroutput"><span class="keyword">void</span></code>
2419                 </p>
2420               </td>
2421 <td>
2422                 <p>
2423                   Computes <code class="computeroutput"><span class="identifier">cb</span> <span class="special">&amp;</span>
2424                   <span class="identifier">a</span></code> and stores the result
2425                   in <code class="computeroutput"><span class="identifier">b</span></code>, only required
2426                   when <code class="computeroutput"><span class="identifier">B</span></code> is an integer
2427                   type. The type of <code class="computeroutput"><span class="identifier">a</span></code>
2428                   shall be listed in one of the type lists <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">signed_types</span></code>,
2429                   <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">unsigned_types</span></code> or <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">float_types</span></code>. When not provided,
2430                   does the equivalent of <code class="computeroutput"><span class="identifier">eval_bitwise_and</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> <span class="identifier">cb</span><span class="special">,</span> <span class="identifier">B</span><span class="special">(</span><span class="identifier">a</span><span class="special">))</span></code>.
2431                 </p>
2432               </td>
2433 <td>
2434                 <p>
2435                   &#160;
2436                 </p>
2437               </td>
2438 </tr>
2439 <tr>
2440 <td>
2441                 <p>
2442                   <code class="computeroutput"><span class="identifier">eval_bitwise_and</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> <span class="identifier">a</span><span class="special">,</span> <span class="identifier">cb</span><span class="special">)</span></code>
2443                 </p>
2444               </td>
2445 <td>
2446                 <p>
2447                   <code class="computeroutput"><span class="keyword">void</span></code>
2448                 </p>
2449               </td>
2450 <td>
2451                 <p>
2452                   Computes <code class="computeroutput"><span class="identifier">cb</span> <span class="special">&amp;</span>
2453                   <span class="identifier">a</span></code> and stores the result
2454                   in <code class="computeroutput"><span class="identifier">b</span></code>, only required
2455                   when <code class="computeroutput"><span class="identifier">B</span></code> is an integer
2456                   type. The type of <code class="computeroutput"><span class="identifier">a</span></code>
2457                   shall be listed in one of the type lists <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">signed_types</span></code>,
2458                   <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">unsigned_types</span></code> or <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">float_types</span></code>. When not provided,
2459                   does the equivalent of <code class="computeroutput"><span class="identifier">eval_bitwise_and</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> <span class="identifier">cb</span><span class="special">,</span> <span class="identifier">a</span><span class="special">)</span></code>.
2460                 </p>
2461               </td>
2462 <td>
2463                 <p>
2464                   &#160;
2465                 </p>
2466               </td>
2467 </tr>
2468 <tr>
2469 <td>
2470                 <p>
2471                   <code class="computeroutput"><span class="identifier">eval_bitwise_or</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> <span class="identifier">a</span><span class="special">)</span></code>
2472                 </p>
2473               </td>
2474 <td>
2475                 <p>
2476                   <code class="computeroutput"><span class="keyword">void</span></code>
2477                 </p>
2478               </td>
2479 <td>
2480                 <p>
2481                   Computes <code class="computeroutput"><span class="identifier">b</span> <span class="special">|=</span>
2482                   <span class="identifier">cb</span></code>, only required when
2483                   <code class="computeroutput"><span class="identifier">B</span></code> is an integer
2484                   type. The type of <code class="computeroutput"><span class="identifier">a</span></code>
2485                   shall be listed in one of the type lists <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">signed_types</span></code>,
2486                   <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">unsigned_types</span></code> or <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">float_types</span></code>. When not provided,
2487                   the default version calls <code class="computeroutput"><span class="identifier">eval_bitwise_or</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> <span class="identifier">B</span><span class="special">(</span><span class="identifier">a</span><span class="special">))</span></code>
2488                 </p>
2489               </td>
2490 <td>
2491                 <p>
2492                   &#160;
2493                 </p>
2494               </td>
2495 </tr>
2496 <tr>
2497 <td>
2498                 <p>
2499                   <code class="computeroutput"><span class="identifier">eval_bitwise_or</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> <span class="identifier">cb</span><span class="special">,</span> <span class="identifier">cb2</span><span class="special">)</span></code>
2500                 </p>
2501               </td>
2502 <td>
2503                 <p>
2504                   <code class="computeroutput"><span class="keyword">void</span></code>
2505                 </p>
2506               </td>
2507 <td>
2508                 <p>
2509                   Computes <code class="computeroutput"><span class="identifier">cb</span> <span class="special">|</span>
2510                   <span class="identifier">cb2</span></code> and stores the result
2511                   in <code class="computeroutput"><span class="identifier">b</span></code>, only required
2512                   when <code class="computeroutput"><span class="identifier">B</span></code> is an integer
2513                   type. When not provided, does the equivalent of <code class="computeroutput"><span class="identifier">b</span>
2514                   <span class="special">=</span> <span class="identifier">cb</span><span class="special">;</span> <span class="identifier">eval_bitwise_or</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> <span class="identifier">cb2</span><span class="special">)</span></code>.
2515                 </p>
2516               </td>
2517 <td>
2518                 <p>
2519                   &#160;
2520                 </p>
2521               </td>
2522 </tr>
2523 <tr>
2524 <td>
2525                 <p>
2526                   <code class="computeroutput"><span class="identifier">eval_bitwise_or</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> <span class="identifier">cb</span><span class="special">,</span> <span class="identifier">a</span><span class="special">)</span></code>
2527                 </p>
2528               </td>
2529 <td>
2530                 <p>
2531                   <code class="computeroutput"><span class="keyword">void</span></code>
2532                 </p>
2533               </td>
2534 <td>
2535                 <p>
2536                   Computes <code class="computeroutput"><span class="identifier">cb</span> <span class="special">|</span>
2537                   <span class="identifier">a</span></code> and stores the result
2538                   in <code class="computeroutput"><span class="identifier">b</span></code>, only required
2539                   when <code class="computeroutput"><span class="identifier">B</span></code> is an integer
2540                   type. The type of <code class="computeroutput"><span class="identifier">a</span></code>
2541                   shall be listed in one of the type lists <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">signed_types</span></code>,
2542                   <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">unsigned_types</span></code> or <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">float_types</span></code>. When not provided,
2543                   does the equivalent of <code class="computeroutput"><span class="identifier">eval_bitwise_or</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> <span class="identifier">cb</span><span class="special">,</span> <span class="identifier">B</span><span class="special">(</span><span class="identifier">a</span><span class="special">))</span></code>.
2544                 </p>
2545               </td>
2546 <td>
2547                 <p>
2548                   &#160;
2549                 </p>
2550               </td>
2551 </tr>
2552 <tr>
2553 <td>
2554                 <p>
2555                   <code class="computeroutput"><span class="identifier">eval_bitwise_or</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> <span class="identifier">a</span><span class="special">,</span> <span class="identifier">cb</span><span class="special">)</span></code>
2556                 </p>
2557               </td>
2558 <td>
2559                 <p>
2560                   <code class="computeroutput"><span class="keyword">void</span></code>
2561                 </p>
2562               </td>
2563 <td>
2564                 <p>
2565                   Computes <code class="computeroutput"><span class="identifier">cb</span> <span class="special">|</span>
2566                   <span class="identifier">a</span></code> and stores the result
2567                   in <code class="computeroutput"><span class="identifier">b</span></code>, only required
2568                   when <code class="computeroutput"><span class="identifier">B</span></code> is an integer
2569                   type. The type of <code class="computeroutput"><span class="identifier">a</span></code>
2570                   shall be listed in one of the type lists <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">signed_types</span></code>,
2571                   <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">unsigned_types</span></code> or <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">float_types</span></code>. When not provided,
2572                   does the equivalent of <code class="computeroutput"><span class="identifier">eval_bitwise_or</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> <span class="identifier">cb</span><span class="special">,</span> <span class="identifier">a</span><span class="special">)</span></code>.
2573                 </p>
2574               </td>
2575 <td>
2576                 <p>
2577                   &#160;
2578                 </p>
2579               </td>
2580 </tr>
2581 <tr>
2582 <td>
2583                 <p>
2584                   <code class="computeroutput"><span class="identifier">eval_bitwise_xor</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> <span class="identifier">a</span><span class="special">)</span></code>
2585                 </p>
2586               </td>
2587 <td>
2588                 <p>
2589                   <code class="computeroutput"><span class="keyword">void</span></code>
2590                 </p>
2591               </td>
2592 <td>
2593                 <p>
2594                   Computes <code class="computeroutput"><span class="identifier">b</span> <span class="special">^=</span>
2595                   <span class="identifier">cb</span></code>, only required when
2596                   <code class="computeroutput"><span class="identifier">B</span></code> is an integer
2597                   type. The type of <code class="computeroutput"><span class="identifier">a</span></code>
2598                   shall be listed in one of the type lists <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">signed_types</span></code>,
2599                   <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">unsigned_types</span></code> or <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">float_types</span></code>. When not provided,
2600                   the default version calls <code class="computeroutput"><span class="identifier">eval_bitwise_xor</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> <span class="identifier">B</span><span class="special">(</span><span class="identifier">a</span><span class="special">))</span></code>
2601                 </p>
2602               </td>
2603 <td>
2604                 <p>
2605                   &#160;
2606                 </p>
2607               </td>
2608 </tr>
2609 <tr>
2610 <td>
2611                 <p>
2612                   <code class="computeroutput"><span class="identifier">eval_bitwise_xor</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> <span class="identifier">cb</span><span class="special">,</span> <span class="identifier">cb2</span><span class="special">)</span></code>
2613                 </p>
2614               </td>
2615 <td>
2616                 <p>
2617                   <code class="computeroutput"><span class="keyword">void</span></code>
2618                 </p>
2619               </td>
2620 <td>
2621                 <p>
2622                   Computes <code class="computeroutput"><span class="identifier">cb</span> <span class="special">^</span>
2623                   <span class="identifier">cb2</span></code> and stores the result
2624                   in <code class="computeroutput"><span class="identifier">b</span></code>, only required
2625                   when <code class="computeroutput"><span class="identifier">B</span></code> is an integer
2626                   type. When not provided, does the equivalent of <code class="computeroutput"><span class="identifier">b</span>
2627                   <span class="special">=</span> <span class="identifier">cb</span><span class="special">;</span> <span class="identifier">eval_bitwise_xor</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> <span class="identifier">cb2</span><span class="special">)</span></code>.
2628                 </p>
2629               </td>
2630 <td>
2631                 <p>
2632                   &#160;
2633                 </p>
2634               </td>
2635 </tr>
2636 <tr>
2637 <td>
2638                 <p>
2639                   <code class="computeroutput"><span class="identifier">eval_bitwise_xor</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> <span class="identifier">cb</span><span class="special">,</span> <span class="identifier">a</span><span class="special">)</span></code>
2640                 </p>
2641               </td>
2642 <td>
2643                 <p>
2644                   <code class="computeroutput"><span class="keyword">void</span></code>
2645                 </p>
2646               </td>
2647 <td>
2648                 <p>
2649                   Computes <code class="computeroutput"><span class="identifier">cb</span> <span class="special">^</span>
2650                   <span class="identifier">a</span></code> and stores the result
2651                   in <code class="computeroutput"><span class="identifier">b</span></code>, only required
2652                   when <code class="computeroutput"><span class="identifier">B</span></code> is an integer
2653                   type. The type of <code class="computeroutput"><span class="identifier">a</span></code>
2654                   shall be listed in one of the type lists <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">signed_types</span></code>,
2655                   <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">unsigned_types</span></code> or <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">float_types</span></code>. When not provided,
2656                   does the equivalent of <code class="computeroutput"><span class="identifier">eval_bitwise_xor</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> <span class="identifier">cb</span><span class="special">,</span> <span class="identifier">B</span><span class="special">(</span><span class="identifier">a</span><span class="special">))</span></code>.
2657                 </p>
2658               </td>
2659 <td>
2660                 <p>
2661                   &#160;
2662                 </p>
2663               </td>
2664 </tr>
2665 <tr>
2666 <td>
2667                 <p>
2668                   <code class="computeroutput"><span class="identifier">eval_bitwise_xor</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> <span class="identifier">a</span><span class="special">,</span> <span class="identifier">cb</span><span class="special">)</span></code>
2669                 </p>
2670               </td>
2671 <td>
2672                 <p>
2673                   <code class="computeroutput"><span class="keyword">void</span></code>
2674                 </p>
2675               </td>
2676 <td>
2677                 <p>
2678                   Computes <code class="computeroutput"><span class="identifier">a</span> <span class="special">^</span>
2679                   <span class="identifier">cb</span></code> and stores the result
2680                   in <code class="computeroutput"><span class="identifier">b</span></code>, only required
2681                   when <code class="computeroutput"><span class="identifier">B</span></code> is an integer
2682                   type. The type of <code class="computeroutput"><span class="identifier">a</span></code>
2683                   shall be listed in one of the type lists <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">signed_types</span></code>,
2684                   <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">unsigned_types</span></code> or <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">float_types</span></code>. When not provided,
2685                   does the equivalent of <code class="computeroutput"><span class="identifier">eval_bitwise_xor</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> <span class="identifier">cb</span><span class="special">,</span> <span class="identifier">a</span><span class="special">)</span></code>.
2686                 </p>
2687               </td>
2688 <td>
2689                 <p>
2690                   &#160;
2691                 </p>
2692               </td>
2693 </tr>
2694 <tr>
2695 <td>
2696                 <p>
2697                   <code class="computeroutput"><span class="identifier">eval_left_shift</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> <span class="identifier">cb</span><span class="special">,</span> <span class="identifier">ui</span><span class="special">)</span></code>
2698                 </p>
2699               </td>
2700 <td>
2701                 <p>
2702                   <code class="computeroutput"><span class="keyword">void</span></code>
2703                 </p>
2704               </td>
2705 <td>
2706                 <p>
2707                   Computes <code class="computeroutput"><span class="identifier">cb</span> <span class="special">&lt;&lt;</span>
2708                   <span class="identifier">ui</span></code> and stores the result
2709                   in <code class="computeroutput"><span class="identifier">b</span></code>, only required
2710                   when <code class="computeroutput"><span class="identifier">B</span></code> is an integer
2711                   type. When not provided, does the equivalent of <code class="computeroutput"><span class="identifier">b</span>
2712                   <span class="special">=</span> <span class="identifier">cb</span><span class="special">;</span> <span class="identifier">eval_left_shift</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> <span class="identifier">a</span><span class="special">);</span></code>.
2713                 </p>
2714               </td>
2715 <td>
2716                 <p>
2717                   &#160;
2718                 </p>
2719               </td>
2720 </tr>
2721 <tr>
2722 <td>
2723                 <p>
2724                   <code class="computeroutput"><span class="identifier">eval_right_shift</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> <span class="identifier">cb</span><span class="special">,</span> <span class="identifier">ui</span><span class="special">)</span></code>
2725                 </p>
2726               </td>
2727 <td>
2728                 <p>
2729                   <code class="computeroutput"><span class="keyword">void</span></code>
2730                 </p>
2731               </td>
2732 <td>
2733                 <p>
2734                   Computes <code class="computeroutput"><span class="identifier">cb</span> <span class="special">&gt;&gt;</span>
2735                   <span class="identifier">ui</span></code> and stores the result
2736                   in <code class="computeroutput"><span class="identifier">b</span></code>, only required
2737                   when <code class="computeroutput"><span class="identifier">B</span></code> is an integer
2738                   type. When not provided, does the equivalent of <code class="computeroutput"><span class="identifier">b</span>
2739                   <span class="special">=</span> <span class="identifier">cb</span><span class="special">;</span> <span class="identifier">eval_right_shift</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> <span class="identifier">a</span><span class="special">);</span></code>.
2740                 </p>
2741               </td>
2742 <td>
2743                 <p>
2744                   &#160;
2745                 </p>
2746               </td>
2747 </tr>
2748 <tr>
2749 <td>
2750                 <p>
2751                   <code class="computeroutput"><span class="identifier">eval_qr</span><span class="special">(</span><span class="identifier">cb</span><span class="special">,</span>
2752                   <span class="identifier">cb2</span><span class="special">,</span>
2753                   <span class="identifier">b</span><span class="special">,</span>
2754                   <span class="identifier">b2</span><span class="special">)</span></code>
2755                 </p>
2756               </td>
2757 <td>
2758                 <p>
2759                   <code class="computeroutput"><span class="keyword">void</span></code>
2760                 </p>
2761               </td>
2762 <td>
2763                 <p>
2764                   Sets <code class="computeroutput"><span class="identifier">b</span></code> to the result
2765                   of <code class="computeroutput"><span class="identifier">cb</span> <span class="special">/</span>
2766                   <span class="identifier">cb2</span></code> and <code class="computeroutput"><span class="identifier">b2</span></code> to the result of <code class="computeroutput"><span class="identifier">cb</span> <span class="special">%</span>
2767                   <span class="identifier">cb2</span></code>. Only required when
2768                   <code class="computeroutput"><span class="identifier">B</span></code> is an integer
2769                   type. The default version of this function is synthesised from
2770                   other operations above.
2771                 </p>
2772               </td>
2773 <td>
2774                 <p>
2775                   <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">overflow_error</span></code> if <code class="computeroutput"><span class="identifier">a</span></code> has the value zero.
2776                 </p>
2777               </td>
2778 </tr>
2779 <tr>
2780 <td>
2781                 <p>
2782                   <code class="computeroutput"><span class="identifier">eval_integer_modulus</span><span class="special">(</span><span class="identifier">cb</span><span class="special">,</span> <span class="identifier">ui</span><span class="special">)</span></code>
2783                 </p>
2784               </td>
2785 <td>
2786                 <p>
2787                   <code class="computeroutput"><span class="keyword">unsigned</span></code>
2788                 </p>
2789               </td>
2790 <td>
2791                 <p>
2792                   Returns the result of <code class="computeroutput"><span class="identifier">cb</span>
2793                   <span class="special">%</span> <span class="identifier">ui</span></code>.
2794                   Only required when <code class="computeroutput"><span class="identifier">B</span></code>
2795                   is an integer type. The default version of this function is synthesised
2796                   from other operations above.
2797                 </p>
2798               </td>
2799 <td>
2800                 <p>
2801                   <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">overflow_error</span></code> if <code class="computeroutput"><span class="identifier">a</span></code> has the value zero.
2802                 </p>
2803               </td>
2804 </tr>
2805 <tr>
2806 <td>
2807                 <p>
2808                   <code class="computeroutput"><span class="identifier">eval_lsb</span><span class="special">(</span><span class="identifier">cb</span><span class="special">)</span></code>
2809                 </p>
2810               </td>
2811 <td>
2812                 <p>
2813                   <code class="computeroutput"><span class="keyword">unsigned</span></code>
2814                 </p>
2815               </td>
2816 <td>
2817                 <p>
2818                   Returns the index of the least significant bit that is set. Only
2819                   required when <code class="computeroutput"><span class="identifier">B</span></code>
2820                   is an integer type. The default version of this function is synthesised
2821                   from other operations above.
2822                 </p>
2823               </td>
2824 <td>
2825                 <p>
2826                   &#160;
2827                 </p>
2828               </td>
2829 </tr>
2830 <tr>
2831 <td>
2832                 <p>
2833                   <code class="computeroutput"><span class="identifier">eval_msb</span><span class="special">(</span><span class="identifier">cb</span><span class="special">)</span></code>
2834                 </p>
2835               </td>
2836 <td>
2837                 <p>
2838                   <code class="computeroutput"><span class="keyword">unsigned</span></code>
2839                 </p>
2840               </td>
2841 <td>
2842                 <p>
2843                   Returns the index of the most significant bit that is set. Only
2844                   required when <code class="computeroutput"><span class="identifier">B</span></code>
2845                   is an integer type. The default version of this function is synthesised
2846                   from other operations above.
2847                 </p>
2848               </td>
2849 <td>
2850                 <p>
2851                   &#160;
2852                 </p>
2853               </td>
2854 </tr>
2855 <tr>
2856 <td>
2857                 <p>
2858                   <code class="computeroutput"><span class="identifier">eval_bit_test</span><span class="special">(</span><span class="identifier">cb</span><span class="special">,</span>
2859                   <span class="identifier">ui</span><span class="special">)</span></code>
2860                 </p>
2861               </td>
2862 <td>
2863                 <p>
2864                   <code class="computeroutput"><span class="keyword">bool</span></code>
2865                 </p>
2866               </td>
2867 <td>
2868                 <p>
2869                   Returns true if <code class="computeroutput"><span class="identifier">cb</span></code>
2870                   has bit <code class="computeroutput"><span class="identifier">ui</span></code> set.
2871                   Only required when <code class="computeroutput"><span class="identifier">B</span></code>
2872                   is an integer type. The default version of this function is synthesised
2873                   from other operations above.
2874                 </p>
2875               </td>
2876 <td>
2877                 <p>
2878                   &#160;
2879                 </p>
2880               </td>
2881 </tr>
2882 <tr>
2883 <td>
2884                 <p>
2885                   <code class="computeroutput"><span class="identifier">eval_bit_set</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span>
2886                   <span class="identifier">ui</span><span class="special">)</span></code>
2887                 </p>
2888               </td>
2889 <td>
2890                 <p>
2891                   <code class="computeroutput"><span class="keyword">void</span></code>
2892                 </p>
2893               </td>
2894 <td>
2895                 <p>
2896                   Sets the bit at index <code class="computeroutput"><span class="identifier">ui</span></code>
2897                   in <code class="computeroutput"><span class="identifier">b</span></code>. Only required
2898                   when <code class="computeroutput"><span class="identifier">B</span></code> is an integer
2899                   type. The default version of this function is synthesised from
2900                   other operations above.
2901                 </p>
2902               </td>
2903 <td>
2904                 <p>
2905                   &#160;
2906                 </p>
2907               </td>
2908 </tr>
2909 <tr>
2910 <td>
2911                 <p>
2912                   <code class="computeroutput"><span class="identifier">eval_bit_unset</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> <span class="identifier">ui</span><span class="special">)</span></code>
2913                 </p>
2914               </td>
2915 <td>
2916                 <p>
2917                   <code class="computeroutput"><span class="keyword">void</span></code>
2918                 </p>
2919               </td>
2920 <td>
2921                 <p>
2922                   Unsets the bit at index <code class="computeroutput"><span class="identifier">ui</span></code>
2923                   in <code class="computeroutput"><span class="identifier">b</span></code>. Only required
2924                   when <code class="computeroutput"><span class="identifier">B</span></code> is an integer
2925                   type. The default version of this function is synthesised from
2926                   other operations above.
2927                 </p>
2928               </td>
2929 <td>
2930                 <p>
2931                   &#160;
2932                 </p>
2933               </td>
2934 </tr>
2935 <tr>
2936 <td>
2937                 <p>
2938                   <code class="computeroutput"><span class="identifier">eval_bit_flip</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span>
2939                   <span class="identifier">ui</span><span class="special">)</span></code>
2940                 </p>
2941               </td>
2942 <td>
2943                 <p>
2944                   <code class="computeroutput"><span class="keyword">void</span></code>
2945                 </p>
2946               </td>
2947 <td>
2948                 <p>
2949                   Flips the bit at index <code class="computeroutput"><span class="identifier">ui</span></code>
2950                   in <code class="computeroutput"><span class="identifier">b</span></code>. Only required
2951                   when <code class="computeroutput"><span class="identifier">B</span></code> is an integer
2952                   type. The default version of this function is synthesised from
2953                   other operations above.
2954                 </p>
2955               </td>
2956 <td>
2957                 <p>
2958                   &#160;
2959                 </p>
2960               </td>
2961 </tr>
2962 <tr>
2963 <td>
2964                 <p>
2965                   <code class="computeroutput"><span class="identifier">eval_gcd</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span>
2966                   <span class="identifier">cb</span><span class="special">,</span>
2967                   <span class="identifier">cb2</span><span class="special">)</span></code>
2968                 </p>
2969               </td>
2970 <td>
2971                 <p>
2972                   <code class="computeroutput"><span class="keyword">void</span></code>
2973                 </p>
2974               </td>
2975 <td>
2976                 <p>
2977                   Sets <code class="computeroutput"><span class="identifier">b</span></code> to the greatest
2978                   common divisor of <code class="computeroutput"><span class="identifier">cb</span></code>
2979                   and <code class="computeroutput"><span class="identifier">cb2</span></code>. Only required
2980                   when <code class="computeroutput"><span class="identifier">B</span></code> is an integer
2981                   type. The default version of this function is synthesised from
2982                   other operations above.
2983                 </p>
2984               </td>
2985 <td>
2986                 <p>
2987                   &#160;
2988                 </p>
2989               </td>
2990 </tr>
2991 <tr>
2992 <td>
2993                 <p>
2994                   <code class="computeroutput"><span class="identifier">eval_lcm</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span>
2995                   <span class="identifier">cb</span><span class="special">,</span>
2996                   <span class="identifier">cb2</span><span class="special">)</span></code>
2997                 </p>
2998               </td>
2999 <td>
3000                 <p>
3001                   <code class="computeroutput"><span class="keyword">void</span></code>
3002                 </p>
3003               </td>
3004 <td>
3005                 <p>
3006                   Sets <code class="computeroutput"><span class="identifier">b</span></code> to the least
3007                   common multiple of <code class="computeroutput"><span class="identifier">cb</span></code>
3008                   and <code class="computeroutput"><span class="identifier">cb2</span></code>. Only required
3009                   when <code class="computeroutput"><span class="identifier">B</span></code> is an integer
3010                   type. The default version of this function is synthesised from
3011                   other operations above.
3012                 </p>
3013               </td>
3014 <td>
3015                 <p>
3016                   &#160;
3017                 </p>
3018               </td>
3019 </tr>
3020 <tr>
3021 <td>
3022                 <p>
3023                   <code class="computeroutput"><span class="identifier">eval_gcd</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span>
3024                   <span class="identifier">cb</span><span class="special">,</span>
3025                   <span class="identifier">a</span><span class="special">)</span></code>
3026                 </p>
3027               </td>
3028 <td>
3029                 <p>
3030                   <code class="computeroutput"><span class="keyword">void</span></code>
3031                 </p>
3032               </td>
3033 <td>
3034                 <p>
3035                   Sets <code class="computeroutput"><span class="identifier">b</span></code> to the greatest
3036                   common divisor of <code class="computeroutput"><span class="identifier">cb</span></code>
3037                   and <code class="computeroutput"><span class="identifier">cb2</span></code>. Only required
3038                   when <code class="computeroutput"><span class="identifier">B</span></code> is an integer
3039                   type. The type of <code class="computeroutput"><span class="identifier">a</span></code>
3040                   shall be listed in one of the type lists <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">signed_types</span></code>,
3041                   <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">unsigned_types</span></code> or <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">float_types</span></code>. The default version
3042                   of this function calls <code class="computeroutput"><span class="identifier">eval_gcd</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> <span class="identifier">cb</span><span class="special">,</span> <span class="identifier">B</span><span class="special">(</span><span class="identifier">a</span><span class="special">))</span></code>.
3043                 </p>
3044               </td>
3045 <td>
3046                 <p>
3047                   &#160;
3048                 </p>
3049               </td>
3050 </tr>
3051 <tr>
3052 <td>
3053                 <p>
3054                   <code class="computeroutput"><span class="identifier">eval_lcm</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span>
3055                   <span class="identifier">cb</span><span class="special">,</span>
3056                   <span class="identifier">a</span><span class="special">)</span></code>
3057                 </p>
3058               </td>
3059 <td>
3060                 <p>
3061                   <code class="computeroutput"><span class="keyword">void</span></code>
3062                 </p>
3063               </td>
3064 <td>
3065                 <p>
3066                   Sets <code class="computeroutput"><span class="identifier">b</span></code> to the least
3067                   common multiple of <code class="computeroutput"><span class="identifier">cb</span></code>
3068                   and <code class="computeroutput"><span class="identifier">cb2</span></code>. Only required
3069                   when <code class="computeroutput"><span class="identifier">B</span></code> is an integer
3070                   type. The type of <code class="computeroutput"><span class="identifier">a</span></code>
3071                   shall be listed in one of the type lists <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">signed_types</span></code>,
3072                   <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">unsigned_types</span></code> or <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">float_types</span></code>. The default version
3073                   of this function calls <code class="computeroutput"><span class="identifier">eval_lcm</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> <span class="identifier">cb</span><span class="special">,</span> <span class="identifier">B</span><span class="special">(</span><span class="identifier">a</span><span class="special">))</span></code>.
3074                 </p>
3075               </td>
3076 <td>
3077                 <p>
3078                   &#160;
3079                 </p>
3080               </td>
3081 </tr>
3082 <tr>
3083 <td>
3084                 <p>
3085                   <code class="computeroutput"><span class="identifier">eval_gcd</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span>
3086                   <span class="identifier">a</span><span class="special">,</span>
3087                   <span class="identifier">cb</span><span class="special">)</span></code>
3088                 </p>
3089               </td>
3090 <td>
3091                 <p>
3092                   <code class="computeroutput"><span class="keyword">void</span></code>
3093                 </p>
3094               </td>
3095 <td>
3096                 <p>
3097                   Sets <code class="computeroutput"><span class="identifier">b</span></code> to the greatest
3098                   common divisor of <code class="computeroutput"><span class="identifier">cb</span></code>
3099                   and <code class="computeroutput"><span class="identifier">a</span></code>. Only required
3100                   when <code class="computeroutput"><span class="identifier">B</span></code> is an integer
3101                   type. The type of <code class="computeroutput"><span class="identifier">a</span></code>
3102                   shall be listed in one of the type lists <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">signed_types</span></code>,
3103                   <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">unsigned_types</span></code> or <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">float_types</span></code>. The default version
3104                   of this function calls <code class="computeroutput"><span class="identifier">eval_gcd</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> <span class="identifier">cb</span><span class="special">,</span> <span class="identifier">a</span><span class="special">)</span></code>.
3105                 </p>
3106               </td>
3107 <td>
3108                 <p>
3109                   &#160;
3110                 </p>
3111               </td>
3112 </tr>
3113 <tr>
3114 <td>
3115                 <p>
3116                   <code class="computeroutput"><span class="identifier">eval_lcm</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span>
3117                   <span class="identifier">a</span><span class="special">,</span>
3118                   <span class="identifier">cb</span><span class="special">)</span></code>
3119                 </p>
3120               </td>
3121 <td>
3122                 <p>
3123                   <code class="computeroutput"><span class="keyword">void</span></code>
3124                 </p>
3125               </td>
3126 <td>
3127                 <p>
3128                   Sets <code class="computeroutput"><span class="identifier">b</span></code> to the least
3129                   common multiple of <code class="computeroutput"><span class="identifier">cb</span></code>
3130                   and <code class="computeroutput"><span class="identifier">a</span></code>. Only required
3131                   when <code class="computeroutput"><span class="identifier">B</span></code> is an integer
3132                   type. The type of <code class="computeroutput"><span class="identifier">a</span></code>
3133                   shall be listed in one of the type lists <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">signed_types</span></code>,
3134                   <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">unsigned_types</span></code> or <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">float_types</span></code>. The default version
3135                   of this function calls <code class="computeroutput"><span class="identifier">eval_lcm</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> <span class="identifier">cb</span><span class="special">,</span> <span class="identifier">a</span><span class="special">)</span></code>.
3136                 </p>
3137               </td>
3138 <td>
3139                 <p>
3140                   &#160;
3141                 </p>
3142               </td>
3143 </tr>
3144 <tr>
3145 <td>
3146                 <p>
3147                   <code class="computeroutput"><span class="identifier">eval_powm</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span>
3148                   <span class="identifier">cb</span><span class="special">,</span>
3149                   <span class="identifier">cb2</span><span class="special">,</span>
3150                   <span class="identifier">cb3</span><span class="special">)</span></code>
3151                 </p>
3152               </td>
3153 <td>
3154                 <p>
3155                   <code class="computeroutput"><span class="keyword">void</span></code>
3156                 </p>
3157               </td>
3158 <td>
3159                 <p>
3160                   Sets <code class="computeroutput"><span class="identifier">b</span></code> to the result
3161                   of <span class="emphasis"><em>(cb^cb2)%cb3</em></span>. The default version of this
3162                   function is synthesised from other operations above.
3163                 </p>
3164               </td>
3165 <td>
3166                 <p>
3167                   &#160;
3168                 </p>
3169               </td>
3170 </tr>
3171 <tr>
3172 <td>
3173                 <p>
3174                   <code class="computeroutput"><span class="identifier">eval_powm</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span>
3175                   <span class="identifier">cb</span><span class="special">,</span>
3176                   <span class="identifier">cb2</span><span class="special">,</span>
3177                   <span class="identifier">a</span><span class="special">)</span></code>
3178                 </p>
3179               </td>
3180 <td>
3181                 <p>
3182                   <code class="computeroutput"><span class="keyword">void</span></code>
3183                 </p>
3184               </td>
3185 <td>
3186                 <p>
3187                   Sets <code class="computeroutput"><span class="identifier">b</span></code> to the result
3188                   of <span class="emphasis"><em>(cb^cb2)%a</em></span>. The type of <code class="computeroutput"><span class="identifier">a</span></code>
3189                   shall be listed in one of the type lists <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">signed_types</span></code>,
3190                   <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">unsigned_types</span></code>. The default version
3191                   of this function is synthesised from other operations above.
3192                 </p>
3193               </td>
3194 <td>
3195                 <p>
3196                   &#160;
3197                 </p>
3198               </td>
3199 </tr>
3200 <tr>
3201 <td>
3202                 <p>
3203                   <code class="computeroutput"><span class="identifier">eval_powm</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span>
3204                   <span class="identifier">cb</span><span class="special">,</span>
3205                   <span class="identifier">a</span><span class="special">,</span>
3206                   <span class="identifier">cb2</span><span class="special">)</span></code>
3207                 </p>
3208               </td>
3209 <td>
3210                 <p>
3211                   <code class="computeroutput"><span class="keyword">void</span></code>
3212                 </p>
3213               </td>
3214 <td>
3215                 <p>
3216                   Sets <code class="computeroutput"><span class="identifier">b</span></code> to the result
3217                   of <span class="emphasis"><em>(cb^a)%cb2</em></span>. The type of <code class="computeroutput"><span class="identifier">a</span></code>
3218                   shall be listed in one of the type lists <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">signed_types</span></code>,
3219                   <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">unsigned_types</span></code>. The default version
3220                   of this function is synthesised from other operations above.
3221                 </p>
3222               </td>
3223 <td>
3224                 <p>
3225                   &#160;
3226                 </p>
3227               </td>
3228 </tr>
3229 <tr>
3230 <td>
3231                 <p>
3232                   <code class="computeroutput"><span class="identifier">eval_powm</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span>
3233                   <span class="identifier">cb</span><span class="special">,</span>
3234                   <span class="identifier">a</span><span class="special">,</span>
3235                   <span class="identifier">a2</span><span class="special">)</span></code>
3236                 </p>
3237               </td>
3238 <td>
3239                 <p>
3240                   <code class="computeroutput"><span class="keyword">void</span></code>
3241                 </p>
3242               </td>
3243 <td>
3244                 <p>
3245                   Sets <code class="computeroutput"><span class="identifier">b</span></code> to the result
3246                   of <span class="emphasis"><em>(cb^a)%a2</em></span>. The type of <code class="computeroutput"><span class="identifier">a</span></code>
3247                   shall be listed in one of the type lists <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">signed_types</span></code>,
3248                   <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">unsigned_types</span></code>. The default version
3249                   of this function is synthesised from other operations above.
3250                 </p>
3251               </td>
3252 <td>
3253                 <p>
3254                   &#160;
3255                 </p>
3256               </td>
3257 </tr>
3258 <tr>
3259 <td>
3260                 <p>
3261                   <code class="computeroutput"><span class="identifier">eval_integer_sqrt</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> <span class="identifier">cb</span><span class="special">,</span> <span class="identifier">b2</span><span class="special">)</span></code>
3262                 </p>
3263               </td>
3264 <td>
3265                 <p>
3266                   <code class="computeroutput"><span class="keyword">void</span></code>
3267                 </p>
3268               </td>
3269 <td>
3270                 <p>
3271                   Sets <code class="computeroutput"><span class="identifier">b</span></code> to the largest
3272                   integer which when squared is less than <code class="computeroutput"><span class="identifier">cb</span></code>,
3273                   also sets <code class="computeroutput"><span class="identifier">b2</span></code> to
3274                   the remainder, ie to <span class="emphasis"><em>cb - b<sup>2</sup></em></span>. The default
3275                   version of this function is synthesised from other operations above.
3276                 </p>
3277               </td>
3278 <td>
3279                 <p>
3280                   &#160;
3281                 </p>
3282               </td>
3283 </tr>
3284 <tr>
3285 <td>
3286                 <p>
3287                   <span class="emphasis"><em>Sign manipulation:</em></span>
3288                 </p>
3289               </td>
3290 <td class="auto-generated">&#160;</td>
3291 <td class="auto-generated">&#160;</td>
3292 </tr>
3293 <tr>
3294 <td>
3295                 <p>
3296                   <code class="computeroutput"><span class="identifier">eval_abs</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span>
3297                   <span class="identifier">cb</span><span class="special">)</span></code>
3298                 </p>
3299               </td>
3300 <td>
3301                 <p>
3302                   <code class="computeroutput"><span class="keyword">void</span></code>
3303                 </p>
3304               </td>
3305 <td>
3306                 <p>
3307                   Set <code class="computeroutput"><span class="identifier">b</span></code> to the absolute
3308                   value of <code class="computeroutput"><span class="identifier">cb</span></code>. The
3309                   default version of this functions assigns <code class="computeroutput"><span class="identifier">cb</span></code>
3310                   to <code class="computeroutput"><span class="identifier">b</span></code>, and then
3311                   calls <code class="computeroutput"><span class="identifier">b</span><span class="special">.</span><span class="identifier">negate</span><span class="special">()</span></code>
3312                   if <code class="computeroutput"><span class="identifier">eval_get_sign</span><span class="special">(</span><span class="identifier">cb</span><span class="special">)</span> <span class="special">&lt;</span>
3313                   <span class="number">0</span></code>.
3314                 </p>
3315               </td>
3316 <td>
3317                 <p>
3318                   &#160;
3319                 </p>
3320               </td>
3321 </tr>
3322 <tr>
3323 <td>
3324                 <p>
3325                   <code class="computeroutput"><span class="identifier">eval_fabs</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span>
3326                   <span class="identifier">cb</span><span class="special">)</span></code>
3327                 </p>
3328               </td>
3329 <td>
3330                 <p>
3331                   <code class="computeroutput"><span class="keyword">void</span></code>
3332                 </p>
3333               </td>
3334 <td>
3335                 <p>
3336                   Set <code class="computeroutput"><span class="identifier">b</span></code> to the absolute
3337                   value of <code class="computeroutput"><span class="identifier">cb</span></code>. The
3338                   default version of this functions assigns <code class="computeroutput"><span class="identifier">cb</span></code>
3339                   to <code class="computeroutput"><span class="identifier">b</span></code>, and then
3340                   calls <code class="computeroutput"><span class="identifier">b</span><span class="special">.</span><span class="identifier">negate</span><span class="special">()</span></code>
3341                   if <code class="computeroutput"><span class="identifier">eval_get_sign</span><span class="special">(</span><span class="identifier">cb</span><span class="special">)</span> <span class="special">&lt;</span>
3342                   <span class="number">0</span></code>.
3343                 </p>
3344               </td>
3345 <td>
3346                 <p>
3347                   &#160;
3348                 </p>
3349               </td>
3350 </tr>
3351 <tr>
3352 <td>
3353                 <p>
3354                   <span class="emphasis"><em>floating-point functions:</em></span>
3355                 </p>
3356               </td>
3357 <td class="auto-generated">&#160;</td>
3358 <td class="auto-generated">&#160;</td>
3359 </tr>
3360 <tr>
3361 <td>
3362                 <p>
3363                   <code class="computeroutput"><span class="identifier">eval_fpclassify</span><span class="special">(</span><span class="identifier">cb</span><span class="special">)</span></code>
3364                 </p>
3365               </td>
3366 <td>
3367                 <p>
3368                   <code class="computeroutput"><span class="keyword">int</span></code>
3369                 </p>
3370               </td>
3371 <td>
3372                 <p>
3373                   Returns one of the same values returned by <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">fpclassify</span></code>.
3374                   Only required when <code class="computeroutput"><span class="identifier">B</span></code>
3375                   is an floating-point type. The default version of this function
3376                   will only test for zero <code class="computeroutput"><span class="identifier">cb</span></code>.
3377                 </p>
3378               </td>
3379 <td>
3380                 <p>
3381                   &#160;
3382                 </p>
3383               </td>
3384 </tr>
3385 <tr>
3386 <td>
3387                 <p>
3388                   <code class="computeroutput"><span class="identifier">eval_trunc</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span>
3389                   <span class="identifier">cb</span><span class="special">)</span></code>
3390                 </p>
3391               </td>
3392 <td>
3393                 <p>
3394                   <code class="computeroutput"><span class="keyword">void</span></code>
3395                 </p>
3396               </td>
3397 <td>
3398                 <p>
3399                   Performs the equivalent operation to <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">trunc</span></code>
3400                   on argument <code class="computeroutput"><span class="identifier">cb</span></code>
3401                   and stores the result in <code class="computeroutput"><span class="identifier">b</span></code>.
3402                   Only required when <code class="computeroutput"><span class="identifier">B</span></code>
3403                   is an floating-point type. The default version of this function
3404                   is synthesised from other operations above.
3405                 </p>
3406               </td>
3407 <td>
3408                 <p>
3409                   &#160;
3410                 </p>
3411               </td>
3412 </tr>
3413 <tr>
3414 <td>
3415                 <p>
3416                   <code class="computeroutput"><span class="identifier">eval_round</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span>
3417                   <span class="identifier">cb</span><span class="special">)</span></code>
3418                 </p>
3419               </td>
3420 <td>
3421                 <p>
3422                   <code class="computeroutput"><span class="keyword">void</span></code>
3423                 </p>
3424               </td>
3425 <td>
3426                 <p>
3427                   Performs the equivalent operation to <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">round</span></code>
3428                   on argument <code class="computeroutput"><span class="identifier">cb</span></code>
3429                   and stores the result in <code class="computeroutput"><span class="identifier">b</span></code>.
3430                   Only required when <code class="computeroutput"><span class="identifier">B</span></code>
3431                   is an floating-point type. The default version of this function
3432                   is synthesised from other operations above.
3433                 </p>
3434               </td>
3435 <td>
3436                 <p>
3437                   &#160;
3438                 </p>
3439               </td>
3440 </tr>
3441 <tr>
3442 <td>
3443                 <p>
3444                   <code class="computeroutput"><span class="identifier">eval_exp</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span>
3445                   <span class="identifier">cb</span><span class="special">)</span></code>
3446                 </p>
3447               </td>
3448 <td>
3449                 <p>
3450                   <code class="computeroutput"><span class="keyword">void</span></code>
3451                 </p>
3452               </td>
3453 <td>
3454                 <p>
3455                   Performs the equivalent operation to <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">exp</span></code>
3456                   on argument <code class="computeroutput"><span class="identifier">cb</span></code>
3457                   and stores the result in <code class="computeroutput"><span class="identifier">b</span></code>.
3458                   Only required when <code class="computeroutput"><span class="identifier">B</span></code>
3459                   is an floating-point type. The default version of this function
3460                   is synthesised from other operations above.
3461                 </p>
3462               </td>
3463 <td>
3464                 <p>
3465                   &#160;
3466                 </p>
3467               </td>
3468 </tr>
3469 <tr>
3470 <td>
3471                 <p>
3472                   <code class="computeroutput"><span class="identifier">eval_exp2</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span>
3473                   <span class="identifier">cb</span><span class="special">)</span></code>
3474                 </p>
3475               </td>
3476 <td>
3477                 <p>
3478                   <code class="computeroutput"><span class="keyword">void</span></code>
3479                 </p>
3480               </td>
3481 <td>
3482                 <p>
3483                   Performs the equivalent operation to <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">exp2</span></code>
3484                   on argument <code class="computeroutput"><span class="identifier">cb</span></code>
3485                   and stores the result in <code class="computeroutput"><span class="identifier">b</span></code>.
3486                   Only required when <code class="computeroutput"><span class="identifier">B</span></code>
3487                   is an floating-point type. The default version of this function
3488                   is implemented in terms of <code class="computeroutput"><span class="identifier">eval_pow</span></code>.
3489                 </p>
3490               </td>
3491 <td>
3492                 <p>
3493                   &#160;
3494                 </p>
3495               </td>
3496 </tr>
3497 <tr>
3498 <td>
3499                 <p>
3500                   <code class="computeroutput"><span class="identifier">eval_log</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span>
3501                   <span class="identifier">cb</span><span class="special">)</span></code>
3502                 </p>
3503               </td>
3504 <td>
3505                 <p>
3506                   <code class="computeroutput"><span class="keyword">void</span></code>
3507                 </p>
3508               </td>
3509 <td>
3510                 <p>
3511                   Performs the equivalent operation to <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">log</span></code>
3512                   on argument <code class="computeroutput"><span class="identifier">cb</span></code>
3513                   and stores the result in <code class="computeroutput"><span class="identifier">b</span></code>.
3514                   Only required when <code class="computeroutput"><span class="identifier">B</span></code>
3515                   is an floating-point type. The default version of this function
3516                   is synthesised from other operations above.
3517                 </p>
3518               </td>
3519 <td>
3520                 <p>
3521                   &#160;
3522                 </p>
3523               </td>
3524 </tr>
3525 <tr>
3526 <td>
3527                 <p>
3528                   <code class="computeroutput"><span class="identifier">eval_log10</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span>
3529                   <span class="identifier">cb</span><span class="special">)</span></code>
3530                 </p>
3531               </td>
3532 <td>
3533                 <p>
3534                   <code class="computeroutput"><span class="keyword">void</span></code>
3535                 </p>
3536               </td>
3537 <td>
3538                 <p>
3539                   Performs the equivalent operation to <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">log10</span></code>
3540                   on argument <code class="computeroutput"><span class="identifier">cb</span></code>
3541                   and stores the result in <code class="computeroutput"><span class="identifier">b</span></code>.
3542                   Only required when <code class="computeroutput"><span class="identifier">B</span></code>
3543                   is an floating-point type. The default version of this function
3544                   is synthesised from other operations above.
3545                 </p>
3546               </td>
3547 <td>
3548                 <p>
3549                   &#160;
3550                 </p>
3551               </td>
3552 </tr>
3553 <tr>
3554 <td>
3555                 <p>
3556                   <code class="computeroutput"><span class="identifier">eval_sin</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span>
3557                   <span class="identifier">cb</span><span class="special">)</span></code>
3558                 </p>
3559               </td>
3560 <td>
3561                 <p>
3562                   <code class="computeroutput"><span class="keyword">void</span></code>
3563                 </p>
3564               </td>
3565 <td>
3566                 <p>
3567                   Performs the equivalent operation to <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">sin</span></code>
3568                   on argument <code class="computeroutput"><span class="identifier">cb</span></code>
3569                   and stores the result in <code class="computeroutput"><span class="identifier">b</span></code>.
3570                   Only required when <code class="computeroutput"><span class="identifier">B</span></code>
3571                   is an floating-point type. The default version of this function
3572                   is synthesised from other operations above.
3573                 </p>
3574               </td>
3575 <td>
3576                 <p>
3577                   &#160;
3578                 </p>
3579               </td>
3580 </tr>
3581 <tr>
3582 <td>
3583                 <p>
3584                   <code class="computeroutput"><span class="identifier">eval_cos</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span>
3585                   <span class="identifier">cb</span><span class="special">)</span></code>
3586                 </p>
3587               </td>
3588 <td>
3589                 <p>
3590                   <code class="computeroutput"><span class="keyword">void</span></code>
3591                 </p>
3592               </td>
3593 <td>
3594                 <p>
3595                   Performs the equivalent operation to <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">cos</span></code>
3596                   on argument <code class="computeroutput"><span class="identifier">cb</span></code>
3597                   and stores the result in <code class="computeroutput"><span class="identifier">b</span></code>.
3598                   Only required when <code class="computeroutput"><span class="identifier">B</span></code>
3599                   is an floating-point type. The default version of this function
3600                   is synthesised from other operations above.
3601                 </p>
3602               </td>
3603 <td>
3604                 <p>
3605                   &#160;
3606                 </p>
3607               </td>
3608 </tr>
3609 <tr>
3610 <td>
3611                 <p>
3612                   <code class="computeroutput"><span class="identifier">eval_tan</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span>
3613                   <span class="identifier">cb</span><span class="special">)</span></code>
3614                 </p>
3615               </td>
3616 <td>
3617                 <p>
3618                   <code class="computeroutput"><span class="keyword">void</span></code>
3619                 </p>
3620               </td>
3621 <td>
3622                 <p>
3623                   Performs the equivalent operation to <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">exp</span></code>
3624                   on argument <code class="computeroutput"><span class="identifier">cb</span></code>
3625                   and stores the result in <code class="computeroutput"><span class="identifier">b</span></code>.
3626                   Only required when <code class="computeroutput"><span class="identifier">B</span></code>
3627                   is an floating-point type. The default version of this function
3628                   is synthesised from other operations above.
3629                 </p>
3630               </td>
3631 <td>
3632                 <p>
3633                   &#160;
3634                 </p>
3635               </td>
3636 </tr>
3637 <tr>
3638 <td>
3639                 <p>
3640                   <code class="computeroutput"><span class="identifier">eval_asin</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span>
3641                   <span class="identifier">cb</span><span class="special">)</span></code>
3642                 </p>
3643               </td>
3644 <td>
3645                 <p>
3646                   <code class="computeroutput"><span class="keyword">void</span></code>
3647                 </p>
3648               </td>
3649 <td>
3650                 <p>
3651                   Performs the equivalent operation to <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">asin</span></code>
3652                   on argument <code class="computeroutput"><span class="identifier">cb</span></code>
3653                   and stores the result in <code class="computeroutput"><span class="identifier">b</span></code>.
3654                   Only required when <code class="computeroutput"><span class="identifier">B</span></code>
3655                   is an floating-point type. The default version of this function
3656                   is synthesised from other operations above.
3657                 </p>
3658               </td>
3659 <td>
3660                 <p>
3661                   &#160;
3662                 </p>
3663               </td>
3664 </tr>
3665 <tr>
3666 <td>
3667                 <p>
3668                   <code class="computeroutput"><span class="identifier">eval_acos</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span>
3669                   <span class="identifier">cb</span><span class="special">)</span></code>
3670                 </p>
3671               </td>
3672 <td>
3673                 <p>
3674                   <code class="computeroutput"><span class="keyword">void</span></code>
3675                 </p>
3676               </td>
3677 <td>
3678                 <p>
3679                   Performs the equivalent operation to <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">acos</span></code>
3680                   on argument <code class="computeroutput"><span class="identifier">cb</span></code>
3681                   and stores the result in <code class="computeroutput"><span class="identifier">b</span></code>.
3682                   Only required when <code class="computeroutput"><span class="identifier">B</span></code>
3683                   is an floating-point type. The default version of this function
3684                   is synthesised from other operations above.
3685                 </p>
3686               </td>
3687 <td>
3688                 <p>
3689                   &#160;
3690                 </p>
3691               </td>
3692 </tr>
3693 <tr>
3694 <td>
3695                 <p>
3696                   <code class="computeroutput"><span class="identifier">eval_atan</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span>
3697                   <span class="identifier">cb</span><span class="special">)</span></code>
3698                 </p>
3699               </td>
3700 <td>
3701                 <p>
3702                   <code class="computeroutput"><span class="keyword">void</span></code>
3703                 </p>
3704               </td>
3705 <td>
3706                 <p>
3707                   Performs the equivalent operation to <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">atan</span></code>
3708                   on argument <code class="computeroutput"><span class="identifier">cb</span></code>
3709                   and stores the result in <code class="computeroutput"><span class="identifier">b</span></code>.
3710                   Only required when <code class="computeroutput"><span class="identifier">B</span></code>
3711                   is an floating-point type. The default version of this function
3712                   is synthesised from other operations above.
3713                 </p>
3714               </td>
3715 <td>
3716                 <p>
3717                   &#160;
3718                 </p>
3719               </td>
3720 </tr>
3721 <tr>
3722 <td>
3723                 <p>
3724                   <code class="computeroutput"><span class="identifier">eval_sinh</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span>
3725                   <span class="identifier">cb</span><span class="special">)</span></code>
3726                 </p>
3727               </td>
3728 <td>
3729                 <p>
3730                   <code class="computeroutput"><span class="keyword">void</span></code>
3731                 </p>
3732               </td>
3733 <td>
3734                 <p>
3735                   Performs the equivalent operation to <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">sinh</span></code>
3736                   on argument <code class="computeroutput"><span class="identifier">cb</span></code>
3737                   and stores the result in <code class="computeroutput"><span class="identifier">b</span></code>.
3738                   Only required when <code class="computeroutput"><span class="identifier">B</span></code>
3739                   is an floating-point type. The default version of this function
3740                   is synthesised from other operations above.
3741                 </p>
3742               </td>
3743 <td>
3744                 <p>
3745                   &#160;
3746                 </p>
3747               </td>
3748 </tr>
3749 <tr>
3750 <td>
3751                 <p>
3752                   <code class="computeroutput"><span class="identifier">eval_cosh</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span>
3753                   <span class="identifier">cb</span><span class="special">)</span></code>
3754                 </p>
3755               </td>
3756 <td>
3757                 <p>
3758                   <code class="computeroutput"><span class="keyword">void</span></code>
3759                 </p>
3760               </td>
3761 <td>
3762                 <p>
3763                   Performs the equivalent operation to <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">cosh</span></code>
3764                   on argument <code class="computeroutput"><span class="identifier">cb</span></code>
3765                   and stores the result in <code class="computeroutput"><span class="identifier">b</span></code>.
3766                   Only required when <code class="computeroutput"><span class="identifier">B</span></code>
3767                   is an floating-point type. The default version of this function
3768                   is synthesised from other operations above.
3769                 </p>
3770               </td>
3771 <td>
3772                 <p>
3773                   &#160;
3774                 </p>
3775               </td>
3776 </tr>
3777 <tr>
3778 <td>
3779                 <p>
3780                   <code class="computeroutput"><span class="identifier">eval_tanh</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span>
3781                   <span class="identifier">cb</span><span class="special">)</span></code>
3782                 </p>
3783               </td>
3784 <td>
3785                 <p>
3786                   <code class="computeroutput"><span class="keyword">void</span></code>
3787                 </p>
3788               </td>
3789 <td>
3790                 <p>
3791                   Performs the equivalent operation to <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">tanh</span></code>
3792                   on argument <code class="computeroutput"><span class="identifier">cb</span></code>
3793                   and stores the result in <code class="computeroutput"><span class="identifier">b</span></code>.
3794                   Only required when <code class="computeroutput"><span class="identifier">B</span></code>
3795                   is an floating-point type. The default version of this function
3796                   is synthesised from other operations above.
3797                 </p>
3798               </td>
3799 <td>
3800                 <p>
3801                   &#160;
3802                 </p>
3803               </td>
3804 </tr>
3805 <tr>
3806 <td>
3807                 <p>
3808                   <code class="computeroutput"><span class="identifier">eval_fmod</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span>
3809                   <span class="identifier">cb</span><span class="special">,</span>
3810                   <span class="identifier">cb2</span><span class="special">)</span></code>
3811                 </p>
3812               </td>
3813 <td>
3814                 <p>
3815                   <code class="computeroutput"><span class="keyword">void</span></code>
3816                 </p>
3817               </td>
3818 <td>
3819                 <p>
3820                   Performs the equivalent operation to <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">fmod</span></code>
3821                   on arguments <code class="computeroutput"><span class="identifier">cb</span></code>
3822                   and <code class="computeroutput"><span class="identifier">cb2</span></code>, and store
3823                   the result in <code class="computeroutput"><span class="identifier">b</span></code>.
3824                   Only required when <code class="computeroutput"><span class="identifier">B</span></code>
3825                   is an floating-point type. The default version of this function
3826                   is synthesised from other operations above.
3827                 </p>
3828               </td>
3829 <td>
3830                 <p>
3831                   &#160;
3832                 </p>
3833               </td>
3834 </tr>
3835 <tr>
3836 <td>
3837                 <p>
3838                   <code class="computeroutput"><span class="identifier">eval_modf</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span>
3839                   <span class="identifier">cb</span><span class="special">,</span>
3840                   <span class="identifier">pb</span><span class="special">)</span></code>
3841                 </p>
3842               </td>
3843 <td>
3844                 <p>
3845                   <code class="computeroutput"><span class="keyword">void</span></code>
3846                 </p>
3847               </td>
3848 <td>
3849                 <p>
3850                   Performs the equivalent operation to <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">modf</span></code>
3851                   on argument <code class="computeroutput"><span class="identifier">cb</span></code>,
3852                   and store the integer result in <code class="computeroutput"><span class="special">*</span><span class="identifier">pb</span></code> and the fractional part in
3853                   <code class="computeroutput"><span class="identifier">b</span></code>. Only required
3854                   when <code class="computeroutput"><span class="identifier">B</span></code> is an floating-point
3855                   type. The default version of this function is synthesised from
3856                   other operations above.
3857                 </p>
3858               </td>
3859 <td>
3860                 <p>
3861                   &#160;
3862                 </p>
3863               </td>
3864 </tr>
3865 <tr>
3866 <td>
3867                 <p>
3868                   <code class="computeroutput"><span class="identifier">eval_pow</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span>
3869                   <span class="identifier">cb</span><span class="special">,</span>
3870                   <span class="identifier">cb2</span><span class="special">)</span></code>
3871                 </p>
3872               </td>
3873 <td>
3874                 <p>
3875                   <code class="computeroutput"><span class="keyword">void</span></code>
3876                 </p>
3877               </td>
3878 <td>
3879                 <p>
3880                   Performs the equivalent operation to <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">pow</span></code>
3881                   on arguments <code class="computeroutput"><span class="identifier">cb</span></code>
3882                   and <code class="computeroutput"><span class="identifier">cb2</span></code>, and store
3883                   the result in <code class="computeroutput"><span class="identifier">b</span></code>.
3884                   Only required when <code class="computeroutput"><span class="identifier">B</span></code>
3885                   is an floating-point type. The default version of this function
3886                   is synthesised from other operations above.
3887                 </p>
3888               </td>
3889 <td>
3890                 <p>
3891                   &#160;
3892                 </p>
3893               </td>
3894 </tr>
3895 <tr>
3896 <td>
3897                 <p>
3898                   <code class="computeroutput"><span class="identifier">eval_atan2</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span>
3899                   <span class="identifier">cb</span><span class="special">,</span>
3900                   <span class="identifier">cb2</span><span class="special">)</span></code>
3901                 </p>
3902               </td>
3903 <td>
3904                 <p>
3905                   <code class="computeroutput"><span class="keyword">void</span></code>
3906                 </p>
3907               </td>
3908 <td>
3909                 <p>
3910                   Performs the equivalent operation to <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">atan</span></code>
3911                   on arguments <code class="computeroutput"><span class="identifier">cb</span></code>
3912                   and <code class="computeroutput"><span class="identifier">cb2</span></code>, and store
3913                   the result in <code class="computeroutput"><span class="identifier">b</span></code>.
3914                   Only required when <code class="computeroutput"><span class="identifier">B</span></code>
3915                   is an floating-point type. The default version of this function
3916                   is synthesised from other operations above.
3917                 </p>
3918               </td>
3919 <td>
3920                 <p>
3921                   &#160;
3922                 </p>
3923               </td>
3924 </tr>
3925 <tr>
3926 <td>
3927                 <p>
3928                   <code class="computeroutput"><span class="identifier">eval_scalbn</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span>
3929                   <span class="identifier">cb</span><span class="special">,</span>
3930                   <span class="identifier">e</span><span class="special">)</span></code>
3931                 </p>
3932               </td>
3933 <td>
3934                 <p>
3935                   <code class="computeroutput"><span class="keyword">void</span></code>
3936                 </p>
3937               </td>
3938 <td>
3939                 <p>
3940                   Scales value <code class="computeroutput"><span class="identifier">cb</span></code>
3941                   by <span class="emphasis"><em>r<sup>e</sup></em></span>, where <span class="emphasis"><em>r</em></span> is the
3942                   radix of the type. The default version of this function is implemented
3943                   in terms of eval_ldexp, consequently this function must be provided
3944                   for types with a radix other than 2.
3945                 </p>
3946               </td>
3947 </tr>
3948 <tr>
3949 <td>
3950                 <p>
3951                   <code class="computeroutput"><span class="identifier">eval_scalbln</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span>
3952                   <span class="identifier">cb</span><span class="special">,</span>
3953                   <span class="identifier">e</span><span class="special">)</span></code>
3954                 </p>
3955               </td>
3956 <td>
3957                 <p>
3958                   <code class="computeroutput"><span class="keyword">void</span></code>
3959                 </p>
3960               </td>
3961 <td>
3962                 <p>
3963                   Calls <code class="computeroutput"><span class="identifier">eval_scalbn</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> <span class="identifier">cb</span><span class="special">,</span> <span class="identifier">e</span><span class="special">)</span></code>.
3964                 </p>
3965               </td>
3966 </tr>
3967 <tr>
3968 <td>
3969                 <p>
3970                   <code class="computeroutput"><span class="identifier">eval_ilogb</span><span class="special">(</span><span class="identifier">cb</span><span class="special">)</span></code>
3971                 </p>
3972               </td>
3973 <td>
3974                 <p>
3975                   <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">exponent_type</span></code>
3976                 </p>
3977               </td>
3978 <td>
3979                 <p>
3980                   Returns the exponent <span class="emphasis"><em>e</em></span> of value <code class="computeroutput"><span class="identifier">cb</span></code> such that <span class="emphasis"><em>1 &lt;=
3981                   cb*r<sup>-e</sup> &lt; r</em></span>, where <span class="emphasis"><em>r</em></span> is the radix
3982                   of type B. The default version of this function is implemented
3983                   in terms of eval_frexp, consequently this function must be provided
3984                   for types with a radix other than 2.
3985                 </p>
3986               </td>
3987 </tr>
3988 <tr>
3989 <td>
3990                 <p>
3991                   <code class="computeroutput"><span class="identifier">eval_remquo</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span>
3992                   <span class="identifier">cb</span><span class="special">,</span>
3993                   <span class="identifier">cb2</span><span class="special">,</span>
3994                   <span class="identifier">pi</span><span class="special">)</span></code>
3995                 </p>
3996               </td>
3997 <td>
3998                 <p>
3999                   <code class="computeroutput"><span class="keyword">void</span></code>
4000                 </p>
4001               </td>
4002 <td>
4003                 <p>
4004                   Sets <code class="computeroutput"><span class="identifier">b</span> <span class="special">=</span>
4005                   <span class="identifier">cb</span> <span class="special">-</span>
4006                   <span class="identifier">n</span> <span class="special">*</span>
4007                   <span class="identifier">cb2</span></code> and stores <code class="computeroutput"><span class="identifier">n</span></code> in <code class="computeroutput"><span class="special">*</span><span class="identifier">pi</span></code>.
4008                 </p>
4009               </td>
4010 </tr>
4011 <tr>
4012 <td>
4013                 <p>
4014                   <code class="computeroutput"><span class="identifier">eval_remquo</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span>
4015                   <span class="identifier">cb</span><span class="special">,</span>
4016                   <span class="identifier">a</span><span class="special">,</span>
4017                   <span class="identifier">pi</span><span class="special">)</span></code>
4018                 </p>
4019               </td>
4020 <td>
4021                 <p>
4022                   <code class="computeroutput"><span class="keyword">void</span></code>
4023                 </p>
4024               </td>
4025 <td>
4026                 <p>
4027                   Default version converts a to type B and calls the overload above.
4028                 </p>
4029               </td>
4030 </tr>
4031 <tr>
4032 <td>
4033                 <p>
4034                   <code class="computeroutput"><span class="identifier">eval_remquo</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span>
4035                   <span class="identifier">a</span><span class="special">,</span>
4036                   <span class="identifier">cb</span><span class="special">,</span>
4037                   <span class="identifier">pi</span><span class="special">)</span></code>
4038                 </p>
4039               </td>
4040 <td>
4041                 <p>
4042                   <code class="computeroutput"><span class="keyword">void</span></code>
4043                 </p>
4044               </td>
4045 <td>
4046                 <p>
4047                   Default version converts a to type B and calls the overload above.
4048                 </p>
4049               </td>
4050 </tr>
4051 <tr>
4052 <td>
4053                 <p>
4054                   <code class="computeroutput"><span class="identifier">eval_remainder</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> <span class="identifier">cb</span><span class="special">,</span> <span class="identifier">cb2</span><span class="special">)</span></code>
4055                 </p>
4056               </td>
4057 <td>
4058                 <p>
4059                   <code class="computeroutput"><span class="keyword">void</span></code>
4060                 </p>
4061               </td>
4062 <td>
4063                 <p>
4064                   Default version calls eval_remquo with a dummy final argument.
4065                 </p>
4066               </td>
4067 </tr>
4068 <tr>
4069 <td>
4070                 <p>
4071                   <code class="computeroutput"><span class="identifier">eval_remainder</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> <span class="identifier">cb</span><span class="special">,</span> <span class="identifier">a</span><span class="special">)</span></code>
4072                 </p>
4073               </td>
4074 <td>
4075                 <p>
4076                   <code class="computeroutput"><span class="keyword">void</span></code>
4077                 </p>
4078               </td>
4079 <td>
4080                 <p>
4081                   Default version calls eval_remquo with a dummy final argument.
4082                 </p>
4083               </td>
4084 </tr>
4085 <tr>
4086 <td>
4087                 <p>
4088                   <code class="computeroutput"><span class="identifier">eval_remainder</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> <span class="identifier">a</span><span class="special">,</span> <span class="identifier">cb</span><span class="special">)</span></code>
4089                 </p>
4090               </td>
4091 <td>
4092                 <p>
4093                   <code class="computeroutput"><span class="keyword">void</span></code>
4094                 </p>
4095               </td>
4096 <td>
4097                 <p>
4098                   Default version calls eval_remquo with a dummy final argument.
4099                 </p>
4100               </td>
4101 </tr>
4102 <tr>
4103 <td>
4104                 <p>
4105                   <code class="computeroutput"><span class="identifier">eval_fdim</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span>
4106                   <span class="identifier">cb</span><span class="special">,</span>
4107                   <span class="identifier">cb2</span><span class="special">)</span></code>
4108                 </p>
4109               </td>
4110 <td>
4111                 <p>
4112                   <code class="computeroutput"><span class="keyword">void</span></code>
4113                 </p>
4114               </td>
4115 <td>
4116                 <p>
4117                   Default version sets <code class="computeroutput"><span class="identifier">b</span>
4118                   <span class="special">=</span> <span class="identifier">cb</span>
4119                   <span class="special">-</span> <span class="identifier">cb2</span></code>
4120                   if <code class="computeroutput"><span class="identifier">cb</span> <span class="special">&gt;</span>
4121                   <span class="identifier">cb2</span></code> and zero otherwise.
4122                   Special cases are handled as in the C99 annex.
4123                 </p>
4124               </td>
4125 </tr>
4126 <tr>
4127 <td>
4128                 <p>
4129                   <code class="computeroutput"><span class="identifier">eval_fdim</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span>
4130                   <span class="identifier">cb</span><span class="special">,</span>
4131                   <span class="identifier">a</span><span class="special">)</span></code>
4132                 </p>
4133               </td>
4134 <td>
4135                 <p>
4136                   <code class="computeroutput"><span class="keyword">void</span></code>
4137                 </p>
4138               </td>
4139 <td>
4140                 <p>
4141                   Default version sets <code class="computeroutput"><span class="identifier">b</span>
4142                   <span class="special">=</span> <span class="identifier">cb</span>
4143                   <span class="special">-</span> <span class="identifier">cb2</span></code>
4144                   if <code class="computeroutput"><span class="identifier">cb</span> <span class="special">&gt;</span>
4145                   <span class="identifier">cb2</span></code> and zero otherwise.
4146                   Special cases are handled as in the C99 annex.
4147                 </p>
4148               </td>
4149 </tr>
4150 <tr>
4151 <td>
4152                 <p>
4153                   <code class="computeroutput"><span class="identifier">eval_fdim</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span>
4154                   <span class="identifier">a</span><span class="special">,</span>
4155                   <span class="identifier">cb</span><span class="special">)</span></code>
4156                 </p>
4157               </td>
4158 <td>
4159                 <p>
4160                   <code class="computeroutput"><span class="keyword">void</span></code>
4161                 </p>
4162               </td>
4163 <td>
4164                 <p>
4165                   Default version sets <code class="computeroutput"><span class="identifier">b</span>
4166                   <span class="special">=</span> <span class="identifier">cb</span>
4167                   <span class="special">-</span> <span class="identifier">cb2</span></code>
4168                   if <code class="computeroutput"><span class="identifier">cb</span> <span class="special">&gt;</span>
4169                   <span class="identifier">cb2</span></code> and zero otherwise.
4170                   Special cases are handled as in the C99 annex.
4171                 </p>
4172               </td>
4173 </tr>
4174 <tr>
4175 <td>
4176                 <p>
4177                   <code class="computeroutput"><span class="identifier">eval_fmax</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span>
4178                   <span class="identifier">cb</span><span class="special">,</span>
4179                   <span class="identifier">cb2</span><span class="special">)</span></code>
4180                 </p>
4181               </td>
4182 <td>
4183                 <p>
4184                   <code class="computeroutput"><span class="keyword">void</span></code>
4185                 </p>
4186               </td>
4187 <td>
4188                 <p>
4189                   Sets <code class="computeroutput"><span class="identifier">b</span></code> to the larger
4190                   of <code class="computeroutput"><span class="identifier">cb</span></code> and <code class="computeroutput"><span class="identifier">cb2</span></code>.
4191                 </p>
4192               </td>
4193 </tr>
4194 <tr>
4195 <td>
4196                 <p>
4197                   <code class="computeroutput"><span class="identifier">eval_fmax</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span>
4198                   <span class="identifier">cb</span><span class="special">,</span>
4199                   <span class="identifier">a</span><span class="special">)</span></code>
4200                 </p>
4201               </td>
4202 <td>
4203                 <p>
4204                   <code class="computeroutput"><span class="keyword">void</span></code>
4205                 </p>
4206               </td>
4207 <td>
4208                 <p>
4209                   Sets <code class="computeroutput"><span class="identifier">b</span></code> to the larger
4210                   of <code class="computeroutput"><span class="identifier">cb</span></code> and <code class="computeroutput"><span class="identifier">a</span></code>.
4211                 </p>
4212               </td>
4213 </tr>
4214 <tr>
4215 <td>
4216                 <p>
4217                   <code class="computeroutput"><span class="identifier">eval_fmax</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span>
4218                   <span class="identifier">a</span><span class="special">,</span>
4219                   <span class="identifier">cb</span><span class="special">)</span></code>
4220                 </p>
4221               </td>
4222 <td>
4223                 <p>
4224                   <code class="computeroutput"><span class="keyword">void</span></code>
4225                 </p>
4226               </td>
4227 <td>
4228                 <p>
4229                   Sets <code class="computeroutput"><span class="identifier">b</span></code> to the larger
4230                   of <code class="computeroutput"><span class="identifier">cb</span></code> and <code class="computeroutput"><span class="identifier">a</span></code>.
4231                 </p>
4232               </td>
4233 </tr>
4234 <tr>
4235 <td>
4236                 <p>
4237                   <code class="computeroutput"><span class="identifier">eval_fmin</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span>
4238                   <span class="identifier">cb</span><span class="special">,</span>
4239                   <span class="identifier">cb2</span><span class="special">)</span></code>
4240                 </p>
4241               </td>
4242 <td>
4243                 <p>
4244                   <code class="computeroutput"><span class="keyword">void</span></code>
4245                 </p>
4246               </td>
4247 <td>
4248                 <p>
4249                   Sets <code class="computeroutput"><span class="identifier">b</span></code> to the smaller
4250                   of <code class="computeroutput"><span class="identifier">cb</span></code> and <code class="computeroutput"><span class="identifier">cb2</span></code>.
4251                 </p>
4252               </td>
4253 </tr>
4254 <tr>
4255 <td>
4256                 <p>
4257                   <code class="computeroutput"><span class="identifier">eval_fmin</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span>
4258                   <span class="identifier">cb</span><span class="special">,</span>
4259                   <span class="identifier">a</span><span class="special">)</span></code>
4260                 </p>
4261               </td>
4262 <td>
4263                 <p>
4264                   <code class="computeroutput"><span class="keyword">void</span></code>
4265                 </p>
4266               </td>
4267 <td>
4268                 <p>
4269                   Sets <code class="computeroutput"><span class="identifier">b</span></code> to the smaller
4270                   of <code class="computeroutput"><span class="identifier">cb</span></code> and <code class="computeroutput"><span class="identifier">a</span></code>.
4271                 </p>
4272               </td>
4273 </tr>
4274 <tr>
4275 <td>
4276                 <p>
4277                   <code class="computeroutput"><span class="identifier">eval_fmin</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span>
4278                   <span class="identifier">a</span><span class="special">,</span>
4279                   <span class="identifier">cb</span><span class="special">)</span></code>
4280                 </p>
4281               </td>
4282 <td>
4283                 <p>
4284                   <code class="computeroutput"><span class="keyword">void</span></code>
4285                 </p>
4286               </td>
4287 <td>
4288                 <p>
4289                   Sets <code class="computeroutput"><span class="identifier">b</span></code> to the smaller
4290                   of <code class="computeroutput"><span class="identifier">cb</span></code> and <code class="computeroutput"><span class="identifier">a</span></code>.
4291                 </p>
4292               </td>
4293 </tr>
4294 <tr>
4295 <td>
4296                 <p>
4297                   <code class="computeroutput"><span class="identifier">eval_hypot</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span>
4298                   <span class="identifier">cb</span><span class="special">,</span>
4299                   <span class="identifier">cb2</span><span class="special">)</span></code>
4300                 </p>
4301               </td>
4302 <td>
4303                 <p>
4304                   <code class="computeroutput"><span class="keyword">void</span></code>
4305                 </p>
4306               </td>
4307 <td>
4308                 <p>
4309                   Sets <code class="computeroutput"><span class="identifier">b</span></code> to the square
4310                   root of the sum of the squares of <code class="computeroutput"><span class="identifier">cb</span></code>
4311                   and <code class="computeroutput"><span class="identifier">cb2</span></code> without
4312                   undue over or under flow.
4313                 </p>
4314               </td>
4315 </tr>
4316 <tr>
4317 <td>
4318                 <p>
4319                   <code class="computeroutput"><span class="identifier">eval_hypot</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span>
4320                   <span class="identifier">cb</span><span class="special">,</span>
4321                   <span class="identifier">a</span><span class="special">)</span></code>
4322                 </p>
4323               </td>
4324 <td>
4325                 <p>
4326                   <code class="computeroutput"><span class="keyword">void</span></code>
4327                 </p>
4328               </td>
4329 <td>
4330                 <p>
4331                   As above.
4332                 </p>
4333               </td>
4334 </tr>
4335 <tr>
4336 <td>
4337                 <p>
4338                   <code class="computeroutput"><span class="identifier">eval_hypot</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span>
4339                   <span class="identifier">a</span><span class="special">,</span>
4340                   <span class="identifier">cb</span><span class="special">)</span></code>
4341                 </p>
4342               </td>
4343 <td>
4344                 <p>
4345                   <code class="computeroutput"><span class="keyword">void</span></code>
4346                 </p>
4347               </td>
4348 <td>
4349                 <p>
4350                   As above.
4351                 </p>
4352               </td>
4353 </tr>
4354 <tr>
4355 <td>
4356                 <p>
4357                   <code class="computeroutput"><span class="identifier">eval_logb</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span>
4358                   <span class="identifier">cb</span><span class="special">)</span></code>
4359                 </p>
4360               </td>
4361 <td>
4362                 <p>
4363                   <code class="computeroutput"><span class="identifier">B</span><span class="special">::</span><span class="identifier">exponent_type</span></code>
4364                 </p>
4365               </td>
4366 <td>
4367                 <p>
4368                   Sets <code class="computeroutput"><span class="identifier">b</span></code> to the exponent
4369                   <span class="emphasis"><em>e</em></span> of value <code class="computeroutput"><span class="identifier">cb</span></code>
4370                   such that <span class="emphasis"><em>1 &lt;= cb*r<sup>-b</sup> &lt; r</em></span>, where <span class="emphasis"><em>r</em></span>
4371                   is the radix of type B. The default version of this function is
4372                   implemented in terms of <code class="computeroutput"><span class="identifier">eval_ilogb</span></code>.
4373                 </p>
4374               </td>
4375 </tr>
4376 <tr>
4377 <td>
4378                 <p>
4379                   <code class="computeroutput"><span class="identifier">eval_nearbyint</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> <span class="identifier">cb</span><span class="special">)</span></code>
4380                 </p>
4381               </td>
4382 <td>
4383                 <p>
4384                   <code class="computeroutput"><span class="keyword">void</span></code>
4385                 </p>
4386               </td>
4387 <td>
4388                 <p>
4389                   Calls <code class="computeroutput"><span class="identifier">eval_round</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> <span class="identifier">cb</span><span class="special">)</span></code>.
4390                 </p>
4391               </td>
4392 </tr>
4393 <tr>
4394 <td>
4395                 <p>
4396                   <code class="computeroutput"><span class="identifier">eval_rint</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span>
4397                   <span class="identifier">cb</span><span class="special">)</span></code>
4398                 </p>
4399               </td>
4400 <td>
4401                 <p>
4402                   <code class="computeroutput"><span class="keyword">void</span></code>
4403                 </p>
4404               </td>
4405 <td>
4406                 <p>
4407                   Calls <code class="computeroutput"><span class="identifier">eval_nearbyint</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span> <span class="identifier">cb</span><span class="special">)</span></code>.
4408                 </p>
4409               </td>
4410 </tr>
4411 <tr>
4412 <td>
4413                 <p>
4414                   <code class="computeroutput"><span class="identifier">eval_log2</span><span class="special">(</span><span class="identifier">b</span><span class="special">,</span>
4415                   <span class="identifier">cb</span><span class="special">)</span></code>
4416                 </p>
4417               </td>
4418 <td>
4419                 <p>
4420                   <code class="computeroutput"><span class="keyword">void</span></code>
4421                 </p>
4422               </td>
4423 <td>
4424                 <p>
4425                   Sets <code class="computeroutput"><span class="identifier">b</span></code> to the logarithm
4426                   base 2 of <code class="computeroutput"><span class="identifier">cb</span></code>.
4427                 </p>
4428               </td>
4429 </tr>
4430 <tr>
4431 <td>
4432                 <p>
4433                   <span class="emphasis"><em>hashing:</em></span>
4434                 </p>
4435               </td>
4436 <td class="auto-generated">&#160;</td>
4437 <td class="auto-generated">&#160;</td>
4438 </tr>
4439 <tr>
4440 <td>
4441                 <p>
4442                   <code class="computeroutput"><span class="identifier">hash_value</span><span class="special">(</span><span class="identifier">cb</span><span class="special">)</span></code>
4443                 </p>
4444               </td>
4445 <td>
4446                 <p>
4447                   <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">size_t</span></code>
4448                 </p>
4449               </td>
4450 <td>
4451                 <p>
4452                   Returns a hash value for the argument that is suitable for use
4453                   with <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">hash</span></code> etc. If not provided then
4454                   no automatic hashing support will be available for the number type.
4455                 </p>
4456               </td>
4457 </tr>
4458 </tbody>
4459 </table></div>
4460 </div>
4461 <br class="table-break"><p>
4462         When the tables above place no <span class="emphasis"><em>throws</em></span> requirements on
4463         an operation, then it is up to each type modelling this concept to decide
4464         when or whether throwing an exception is desirable. However, thrown exceptions
4465         should always either be the type, or inherit from the type <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">runtime_error</span></code>.
4466         For example, a floating-point type might choose to throw <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">overflow_error</span></code>
4467         whenever the result of an operation would be infinite, and <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">underflow_error</span></code>
4468         whenever it would round to zero.
4469       </p>
4470 <div class="note"><table border="0" summary="Note">
4471 <tr>
4472 <td rowspan="2" align="center" valign="top" width="25"><img alt="[Note]" src="../../../../../../doc/src/images/note.png"></td>
4473 <th align="left">Note</th>
4474 </tr>
4475 <tr><td align="left" valign="top"><p>
4476           The non-member functions are all named with an "eval_" prefix
4477           to avoid conflicts with template classes of the same name - in point of
4478           fact this naming convention shouldn't be necessary, but rather works around
4479           some compiler bugs.
4480         </p></td></tr>
4481 </table></div>
4482 <h5>
4483 <a name="boost_multiprecision.ref.backendconc.h0"></a>
4484         <span class="phrase"><a name="boost_multiprecision.ref.backendconc.overloadable_functions"></a></span><a class="link" href="backendconc.html#boost_multiprecision.ref.backendconc.overloadable_functions">Overloadable
4485         Functions</a>
4486       </h5>
4487 <p>
4488         Some of the C99 math functions do not have <code class="computeroutput"><span class="identifier">eval_</span></code>
4489         functions but must be overloaded directly: these functions are either trivial
4490         or are forwarded to the Boost.Math implementations by default. The full list
4491         of these functions is:
4492       </p>
4493 <pre class="programlisting"><span class="keyword">int</span>           <span class="identifier">sign</span>       <span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&amp;);</span>
4494 <span class="keyword">int</span>           <span class="identifier">signbit</span>    <span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&amp;);</span>
4495 <span class="emphasis"><em>number</em></span>        <span class="identifier">changesign</span> <span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&amp;);</span>
4496 <span class="emphasis"><em>number</em></span>        <span class="identifier">copysign</span>   <span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&amp;,</span> <span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&amp;);</span>
4497 <span class="emphasis"><em>number</em></span>        <span class="identifier">asinh</span>      <span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&amp;);</span>
4498 <span class="emphasis"><em>number</em></span>        <span class="identifier">acosh</span>      <span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&amp;);</span>
4499 <span class="emphasis"><em>number</em></span>        <span class="identifier">atanh</span>      <span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&amp;);</span>
4500 <span class="emphasis"><em>number</em></span>        <span class="identifier">cbrt</span>       <span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&amp;);</span>
4501 <span class="emphasis"><em>number</em></span>        <span class="identifier">erf</span>        <span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&amp;);</span>
4502 <span class="emphasis"><em>number</em></span>        <span class="identifier">erfc</span>       <span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&amp;);</span>
4503 <span class="emphasis"><em>number</em></span>        <span class="identifier">expm1</span>      <span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&amp;);</span>
4504 <span class="emphasis"><em>number</em></span>        <span class="identifier">log1p</span>      <span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&amp;);</span>
4505 <span class="emphasis"><em>number</em></span>        <span class="identifier">tgamma</span>     <span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&amp;);</span>
4506 <span class="emphasis"><em>number</em></span>        <span class="identifier">lgamma</span>     <span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&amp;);</span>
4507 <span class="keyword">long</span>          <span class="identifier">lrint</span>      <span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&amp;);</span>
4508 <span class="keyword">long</span> <span class="keyword">long</span>     <span class="identifier">llrint</span>     <span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&amp;);</span>
4509 <span class="emphasis"><em>number</em></span>        <span class="identifier">nextafter</span>  <span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&amp;,</span> <span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&amp;);</span>
4510 <span class="emphasis"><em>number</em></span>        <span class="identifier">nexttoward</span> <span class="special">(</span><span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&amp;,</span> <span class="keyword">const</span> <span class="emphasis"><em>number-or-expression-template-type</em></span><span class="special">&amp;);</span>
4511 </pre>
4512 </div>
4513 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
4514 <td align="left"></td>
4515 <td align="right"><div class="copyright-footer">Copyright &#169; 2002-2013 John Maddock and Christopher Kormanyos<p>
4516         Distributed under the Boost Software License, Version 1.0. (See accompanying
4517         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>)
4518       </p>
4519 </div></td>
4520 </tr></table>
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