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  26 <div class="titlepage"><div><div><h3 class="title">
  27 <a name="boost_multiprecision.perf.int_real_world"></a><a class="link" href="int_real_world.html" title="Integer Real World Tests">Integer Real
  28       World Tests</a>
  29 </h3></div></div></div>
  30 <p>
  31         The first set of <a href="../../../../performance/voronoi_performance.cpp" target="_top">tests</a>
  32         measure the times taken to execute the multiprecision part of the Voronoi-diagram
  33         builder from Boost.Polygon. The tests mainly create a large number of temporaries
  34         "just in case" multiprecision arithmetic is required, for comparison,
  35         also included in the tests is Boost.Polygon's own partial-multiprecision
  36         integer type which was custom written for this specific task:
  37       </p>
  38 <div class="informaltable"><table class="table">
  39 <colgroup>
  40 <col>
  41 <col>
  42 </colgroup>
  43 <thead><tr>
  44 <th>
  45                 <p>
  46                   Integer Type
  47                 </p>
  48               </th>
  49 <th>
  50                 <p>
  51                   Relative Performance (Actual time in parenthesis)
  52                 </p>
  53               </th>
  54 </tr></thead>
  55 <tbody>
  56 <tr>
  57 <td>
  58                 <p>
  59                   polygon::detail::extended_int
  60                 </p>
  61               </td>
  62 <td>
  63                 <p>
  64                   1(0.138831s)
  65                 </p>
  66               </td>
  67 </tr>
  68 <tr>
  69 <td>
  70                 <p>
  71                   int256_t
  72                 </p>
  73               </td>
  74 <td>
  75                 <p>
  76                   1.19247(0.165551s)
  77                 </p>
  78               </td>
  79 </tr>
  80 <tr>
  81 <td>
  82                 <p>
  83                   int512_t
  84                 </p>
  85               </td>
  86 <td>
  87                 <p>
  88                   1.23301(0.17118s)
  89                 </p>
  90               </td>
  91 </tr>
  92 <tr>
  93 <td>
  94                 <p>
  95                   int1024_t
  96                 </p>
  97               </td>
  98 <td>
  99                 <p>
 100                   1.21463(0.168628s)
 101                 </p>
 102               </td>
 103 </tr>
 104 <tr>
 105 <td>
 106                 <p>
 107                   checked_int256_t
 108                 </p>
 109               </td>
 110 <td>
 111                 <p>
 112                   1.31711(0.182855s)
 113                 </p>
 114               </td>
 115 </tr>
 116 <tr>
 117 <td>
 118                 <p>
 119                   checked_int512_t
 120                 </p>
 121               </td>
 122 <td>
 123                 <p>
 124                   1.57413(0.218538s)
 125                 </p>
 126               </td>
 127 </tr>
 128 <tr>
 129 <td>
 130                 <p>
 131                   checked_int1024_t
 132                 </p>
 133               </td>
 134 <td>
 135                 <p>
 136                   1.36992(0.190187s)
 137                 </p>
 138               </td>
 139 </tr>
 140 <tr>
 141 <td>
 142                 <p>
 143                   cpp_int
 144                 </p>
 145               </td>
 146 <td>
 147                 <p>
 148                   1.63244(0.226632s)
 149                 </p>
 150               </td>
 151 </tr>
 152 <tr>
 153 <td>
 154                 <p>
 155                   mpz_int
 156                 </p>
 157               </td>
 158 <td>
 159                 <p>
 160                   5.42511(0.753172s)
 161                 </p>
 162               </td>
 163 </tr>
 164 <tr>
 165 <td>
 166                 <p>
 167                   tom_int
 168                 </p>
 169               </td>
 170 <td>
 171                 <p>
 172                   29.0793(4.03709s)
 173                 </p>
 174               </td>
 175 </tr>
 176 </tbody>
 177 </table></div>
 178 <p>
 179         Note how for this use case, any dynamic allocation is a performance killer.
 180       </p>
 181 <p>
 182         The next <a href="../../../../performance/miller_rabin_performance.cpp" target="_top">tests</a>
 183         measure the time taken to generate 1000 128-bit random numbers and test for
 184         primality using the Miller Rabin test. This is primarily a test of modular-exponentiation
 185         since that is the rate limiting step:
 186       </p>
 187 <div class="informaltable"><table class="table">
 188 <colgroup>
 189 <col>
 190 <col>
 191 </colgroup>
 192 <thead><tr>
 193 <th>
 194                 <p>
 195                   Integer Type
 196                 </p>
 197               </th>
 198 <th>
 199                 <p>
 200                   Relative Performance (Actual time in parenthesis)
 201                 </p>
 202               </th>
 203 </tr></thead>
 204 <tbody>
 205 <tr>
 206 <td>
 207                 <p>
 208                   cpp_int
 209                 </p>
 210               </td>
 211 <td>
 212                 <p>
 213                   5.25827(0.379597s)
 214                 </p>
 215               </td>
 216 </tr>
 217 <tr>
 218 <td>
 219                 <p>
 220                   cpp_int (no Expression templates)
 221                 </p>
 222               </td>
 223 <td>
 224                 <p>
 225                   5.15675(0.372268s)
 226                 </p>
 227               </td>
 228 </tr>
 229 <tr>
 230 <td>
 231                 <p>
 232                   cpp_int (128-bit cache)
 233                 </p>
 234               </td>
 235 <td>
 236                 <p>
 237                   5.10882(0.368808s)
 238                 </p>
 239               </td>
 240 </tr>
 241 <tr>
 242 <td>
 243                 <p>
 244                   cpp_int (256-bit cache)
 245                 </p>
 246               </td>
 247 <td>
 248                 <p>
 249                   5.50623(0.397497s)
 250                 </p>
 251               </td>
 252 </tr>
 253 <tr>
 254 <td>
 255                 <p>
 256                   cpp_int (512-bit cache)
 257                 </p>
 258               </td>
 259 <td>
 260                 <p>
 261                   4.82257(0.348144s)
 262                 </p>
 263               </td>
 264 </tr>
 265 <tr>
 266 <td>
 267                 <p>
 268                   cpp_int (1024-bit cache)
 269                 </p>
 270               </td>
 271 <td>
 272                 <p>
 273                   5.00053(0.360991s)
 274                 </p>
 275               </td>
 276 </tr>
 277 <tr>
 278 <td>
 279                 <p>
 280                   int1024_t
 281                 </p>
 282               </td>
 283 <td>
 284                 <p>
 285                   4.37589(0.315897s)
 286                 </p>
 287               </td>
 288 </tr>
 289 <tr>
 290 <td>
 291                 <p>
 292                   checked_int1024_t
 293                 </p>
 294               </td>
 295 <td>
 296                 <p>
 297                   4.52396(0.326587s)
 298                 </p>
 299               </td>
 300 </tr>
 301 <tr>
 302 <td>
 303                 <p>
 304                   mpz_int
 305                 </p>
 306               </td>
 307 <td>
 308                 <p>
 309                   1(0.0721905s)
 310                 </p>
 311               </td>
 312 </tr>
 313 <tr>
 314 <td>
 315                 <p>
 316                   mpz_int (no Expression templates)
 317                 </p>
 318               </td>
 319 <td>
 320                 <p>
 321                   1.0248(0.0739806s)
 322                 </p>
 323               </td>
 324 </tr>
 325 <tr>
 326 <td>
 327                 <p>
 328                   tom_int
 329                 </p>
 330               </td>
 331 <td>
 332                 <p>
 333                   2.60673(0.188181s)
 334                 </p>
 335               </td>
 336 </tr>
 337 <tr>
 338 <td>
 339                 <p>
 340                   tom_int (no Expression templates)
 341                 </p>
 342               </td>
 343 <td>
 344                 <p>
 345                   2.64997(0.191303s)
 346                 </p>
 347               </td>
 348 </tr>
 349 </tbody>
 350 </table></div>
 351 <p>
 352         It's interesting to note that expression templates have little effect here
 353         - perhaps because the actual expressions involved are relatively trivial
 354         in this case - so the time taken for multiplication and division tends to
 355         dominate. Also note how increasing the internal cache size used by <code class="computeroutput"><span class="identifier">cpp_int</span></code> is quite effective in this case
 356         in cutting out memory allocations altogether - cutting about a third off
 357         the total runtime. Finally the much quicker times from GMP and tommath are
 358         down to their much better modular-exponentiation algorithms (GMP's is about
 359         5x faster). That's an issue which needs to be addressed in a future release
 360         for <a class="link" href="../tut/ints/cpp_int.html" title="cpp_int">cpp_int</a>.
 361       </p>
 362 <p>
 363         Test code was compiled with Microsoft Visual Studio 2010 with all optimisations
 364         turned on (/Ox), and used MPIR-2.3.0 and <a href="http://www.mpfr.org" target="_top">MPFR</a>-3.0.0.
 365         The tests were run on 32-bit Windows Vista machine.
 366       </p>
 367 </div>
 368 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 369 <td align="left"></td>
 370 <td align="right"><div class="copyright-footer">Copyright &#169; 2002-2013 John Maddock and Christopher Kormanyos<p>
 371         Distributed under the Boost Software License, Version 1.0. (See accompanying
 372         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>)
 373       </p>
 374 </div></td>
 375 </tr></table>
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