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<div class="ChapSects"><a href="chapA.html#X82113B3184F76F58">A <span class="Heading">Some Benchmarks</span></a>
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<h3>A <span class="Heading">Some Benchmarks</span></h3>

<p>Some of the key subroutines have been improved in version 1.2 of <strong class="pkg">CRIME</strong>, resulting in a significant speedup of many basic calculations.</p>

<p>The numbers in the following table compare the runtimes of the 1.1 and 1.2 versions of the functions listed in the column headers on all the groups of size 16. All functions were executed on a 2.4 GHz AMD64 processor with 12 GB of RAM. The number in the first column of every row is the Small Group Library number of the group used in that row, so the group used in row <code class="keyw">n</code> is <code class="keyw">SmallGroup(16,n)</code>. The upper number in each box is the runtime for the 1.1 version, whereas the lower number is the runtime for the 1.2 version.</p>

<div class="pcenter"><table class="GAPDocTable">
<tr>
<td class="tdcenter">Group</td>
<td class="tdcenter"><code class="keyw">ProjectiveResolution</code></td>
<td class="tdcenter"><code class="keyw">CohomologyGenerators</code></td>
<td class="tdcenter"><code class="keyw">CohomologyRelators</code></td>
</tr>
<tr>
<td class="tdcenter">1</td>
<td class="tdcenter">0:00:00.424</td>
<td class="tdcenter">0:00:00.040</td>
<td class="tdcenter">0:00:00.092</td>
</tr>
<tr>
<td class="tdcenter"></td>
<td class="tdcenter">0:00:00.380</td>
<td class="tdcenter">0:00:00.016</td>
<td class="tdcenter">0:00:00.012</td>
</tr>
<tr>
<td class="tdcenter">2</td>
<td class="tdcenter">0:00:00.436</td>
<td class="tdcenter">0:00:01.472</td>
<td class="tdcenter">0:00:05.848</td>
</tr>
<tr>
<td class="tdcenter"></td>
<td class="tdcenter">0:00:00.072</td>
<td class="tdcenter">0:00:00.116</td>
<td class="tdcenter">0:00:00.396</td>
</tr>
<tr>
<td class="tdcenter">3</td>
<td class="tdcenter">0:00:02.752</td>
<td class="tdcenter">0:00:11.469</td>
<td class="tdcenter">0:00:42.887</td>
</tr>
<tr>
<td class="tdcenter"></td>
<td class="tdcenter">0:00:00.352</td>
<td class="tdcenter">0:00:01.192</td>
<td class="tdcenter">0:00:01.944</td>
</tr>
<tr>
<td class="tdcenter">4</td>
<td class="tdcenter">0:00:00.480</td>
<td class="tdcenter">0:00:01.456</td>
<td class="tdcenter">0:00:06.320</td>
</tr>
<tr>
<td class="tdcenter"></td>
<td class="tdcenter">0:00:00.068</td>
<td class="tdcenter">0:00:00.116</td>
<td class="tdcenter">0:00:00.316</td>
</tr>
<tr>
<td class="tdcenter">5</td>
<td class="tdcenter">0:00:00.480</td>
<td class="tdcenter">0:00:01.136</td>
<td class="tdcenter">0:00:06.045</td>
</tr>
<tr>
<td class="tdcenter"></td>
<td class="tdcenter">0:00:00.080</td>
<td class="tdcenter">0:00:00.096</td>
<td class="tdcenter">0:00:00.296</td>
</tr>
<tr>
<td class="tdcenter">6</td>
<td class="tdcenter">0:00:00.204</td>
<td class="tdcenter">0:00:00.724</td>
<td class="tdcenter">0:00:01.892</td>
</tr>
<tr>
<td class="tdcenter"></td>
<td class="tdcenter">0:00:00.036</td>
<td class="tdcenter">0:00:00.072</td>
<td class="tdcenter">0:00:00.116</td>
</tr>
<tr>
<td class="tdcenter">7</td>
<td class="tdcenter">0:00:00.504</td>
<td class="tdcenter">0:00:01.156</td>
<td class="tdcenter">0:00:06.140</td>
</tr>
<tr>
<td class="tdcenter"></td>
<td class="tdcenter">0:00:00.088</td>
<td class="tdcenter">0:00:00.100</td>
<td class="tdcenter">0:00:00.344</td>
</tr>
<tr>
<td class="tdcenter">8</td>
<td class="tdcenter">0:00:00.192</td>
<td class="tdcenter">0:00:00.704</td>
<td class="tdcenter">0:00:01.800</td>
</tr>
<tr>
<td class="tdcenter"></td>
<td class="tdcenter">0:00:00.036</td>
<td class="tdcenter">0:00:00.064</td>
<td class="tdcenter">0:00:00.120</td>
</tr>
<tr>
<td class="tdcenter">9</td>
<td class="tdcenter">0:00:00.060</td>
<td class="tdcenter">0:00:00.100</td>
<td class="tdcenter">0:00:00.284</td>
</tr>
<tr>
<td class="tdcenter"></td>
<td class="tdcenter">0:00:00.020</td>
<td class="tdcenter">0:00:00.012</td>
<td class="tdcenter">0:00:00.028</td>
</tr>
<tr>
<td class="tdcenter">10</td>
<td class="tdcenter">0:00:10.161</td>
<td class="tdcenter">0:00:34.326</td>
<td class="tdcenter">0:03:07.104</td>
</tr>
<tr>
<td class="tdcenter"></td>
<td class="tdcenter">0:00:01.524</td>
<td class="tdcenter">0:00:04.252</td>
<td class="tdcenter">0:00:08.089</td>
</tr>
<tr>
<td class="tdcenter">11</td>
<td class="tdcenter">0:00:10.397</td>
<td class="tdcenter">0:00:32.354</td>
<td class="tdcenter">0:03:07.355</td>
</tr>
<tr>
<td class="tdcenter"></td>
<td class="tdcenter">0:00:01.716</td>
<td class="tdcenter">0:00:04.584</td>
<td class="tdcenter">0:00:08.021</td>
</tr>
<tr>
<td class="tdcenter">12</td>
<td class="tdcenter">0:00:01.184</td>
<td class="tdcenter">0:00:04.613</td>
<td class="tdcenter">0:00:20.789</td>
</tr>
<tr>
<td class="tdcenter"></td>
<td class="tdcenter">0:00:00.192</td>
<td class="tdcenter">0:00:00.544</td>
<td class="tdcenter">0:00:00.984</td>
</tr>
<tr>
<td class="tdcenter">13</td>
<td class="tdcenter">0:00:01.152</td>
<td class="tdcenter">0:00:04.496</td>
<td class="tdcenter">0:00:20.990</td>
</tr>
<tr>
<td class="tdcenter"></td>
<td class="tdcenter">0:00:00.196</td>
<td class="tdcenter">0:00:00.472</td>
<td class="tdcenter">0:00:01.072</td>
</tr>
<tr>
<td class="tdcenter">14</td>
<td class="tdcenter">0:03:26.817</td>
<td class="tdcenter">0:07:37.960</td>
<td class="tdcenter">0:56:39.273</td>
</tr>
<tr>
<td class="tdcenter"></td>
<td class="tdcenter">0:00:41.919</td>
<td class="tdcenter">0:02:07.399</td>
<td class="tdcenter">0:01:54.752</td>
</tr>
</table><br />
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