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<div class="section">
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<div class="titlepage"><div><div><h2 class="title" style="clear: both">
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<a name="math_toolkit.runs_test"></a><a class="link" href="runs_test.html" title="Runs tests">Runs tests</a>
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</h2></div></div></div>
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<h4>
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<a name="math_toolkit.runs_test.h0"></a>
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<span class="phrase"><a name="math_toolkit.runs_test.synopsis"></a></span><a class="link" href="runs_test.html#math_toolkit.runs_test.synopsis">Synopsis</a>
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</h4>
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<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">statistics</span><span class="special">/</span><span class="identifier">runs_test</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span>
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<span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">statistics</span> <span class="special">{</span>
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<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">RandomAccessContainer</span><span class="special">></span>
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<span class="identifier">std</span><span class="special">::</span><span class="identifier">pair</span><span class="special"><</span><span class="identifier">Real</span><span class="special">,</span> <span class="identifier">Real</span><span class="special">></span> <span class="identifier">runs_above_and_below_threshold</span><span class="special">(</span><span class="identifier">RandomAccessContainer</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">v</span><span class="special">,</span> <span class="keyword">typename</span> <span class="identifier">RandomAccessContainer</span><span class="special">::</span><span class="identifier">value_type</span> <span class="identifier">threshold</span><span class="special">);</span>
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<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">RandomAccessContainer</span><span class="special">></span>
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<span class="identifier">std</span><span class="special">::</span><span class="identifier">pair</span><span class="special"><</span><span class="identifier">Real</span><span class="special">,</span> <span class="identifier">Real</span><span class="special">></span> <span class="identifier">runs_above_and_below_median</span><span class="special">(</span><span class="identifier">RandomAccessContainer</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">v</span><span class="special">);</span>
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<span class="special">}}}</span>
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</pre>
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<h4>
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<a name="math_toolkit.runs_test.h1"></a>
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<span class="phrase"><a name="math_toolkit.runs_test.background"></a></span><a class="link" href="runs_test.html#math_toolkit.runs_test.background">Background</a>
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</h4>
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<p>
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The "runs above and below median test" tries to determine if a sequence
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is random by looking at the number of consecutive values which exceed (or are
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below) the median of the sequence. For example, if we are given data {5, 2,
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0, 4, 7, 9, 10, 6, 1, 8, 3}, first we find the median (5), and transform the
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vector into a list of + and -'s, depending on whether the value is greater
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or less than the median. (Values equal to the median we simply ignore-this
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is a convention we have inherited from the wonderful <code class="computeroutput"><span class="identifier">randtests</span></code>
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package in R.) Hence our data vector is transformed into
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</p>
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<p>
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{-,-,-,+,+,+,-,+,-}
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</p>
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<p>
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which is 5 runs, with <span class="emphasis"><em>n</em></span><sub>a</sub> = 5 values above and <span class="emphasis"><em>n</em></span><sub>b</sub> =
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5 values below the median. <a href="https://www.itl.nist.gov/div898/handbook/eda/section3/eda35d.htm" target="_top">NIST</a>
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tells us the expected number of runs and their variance:
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</p>
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<p>
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<span class="inlinemediaobject"><object type="image/svg+xml" data="../../graphs/expected_runs_above_threshold.svg" width="418" height="45"></object></span>
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</p>
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<p>
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from which we derive the test statistic
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</p>
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<p>
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<span class="inlinemediaobject"><object type="image/svg+xml" data="../../graphs/runs_test_statistic.svg" width="115" height="42"></object></span>
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</p>
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<p>
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whose distribution we approximate as normal to extract a <span class="emphasis"><em>p</em></span>-value.
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</p>
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<p>
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An example usage is as follows:
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</p>
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<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">vector</span><span class="special">></span>
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<span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">random</span><span class="special">></span>
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<span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">statistics</span><span class="special">/</span><span class="identifier">runs_test</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span>
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<span class="identifier">std</span><span class="special">::</span><span class="identifier">random_device</span> <span class="identifier">rd</span><span class="special">;</span>
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<span class="identifier">std</span><span class="special">::</span><span class="identifier">vector</span><span class="special"><</span><span class="keyword">double</span><span class="special">></span> <span class="identifier">v</span><span class="special">{</span><span class="number">5</span><span class="special">,</span> <span class="number">2</span><span class="special">,</span> <span class="number">0</span><span class="special">,</span> <span class="number">4</span><span class="special">,</span> <span class="number">7</span><span class="special">,</span> <span class="number">9</span><span class="special">,</span> <span class="number">10</span><span class="special">,</span> <span class="number">6</span><span class="special">,</span> <span class="number">1</span><span class="special">,</span> <span class="number">8</span><span class="special">,</span> <span class="number">3</span><span class="special">};</span>
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<span class="keyword">auto</span> <span class="special">[</span><span class="identifier">t</span><span class="special">,</span> <span class="identifier">p</span><span class="special">]</span> <span class="special">=</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">statistics</span><span class="special">::</span><span class="identifier">runs_above_and_below_median</span><span class="special">(</span><span class="identifier">v</span><span class="special">);</span>
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<span class="comment">// t = -0.670820393249936919; p = 0.502334954360502017;</span>
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</pre>
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<p>
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We see that we have about a 50% chance of seeing this number of runs if the
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null hypothesis of randomness is true, and hence the assumption of randomness
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seems reasonable. As always, the test statistic is the first element of the
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pair, and the <span class="emphasis"><em>p</em></span>-value is the second element.
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</p>
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<h4>
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<a name="math_toolkit.runs_test.h2"></a>
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<span class="phrase"><a name="math_toolkit.runs_test.performance"></a></span><a class="link" href="runs_test.html#math_toolkit.runs_test.performance">Performance</a>
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</h4>
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<p>
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There are two cases: Where the threshold (typically the median) has already
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been computed, and the case where the mean and sample variance must be computed
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on the fly. Computing the median is fairly expensive (requiring a call to
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<code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">statistics</span><span class="special">::</span><span class="identifier">median</span></code>),
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and since the order of the original data must be preserved, it must allocate.
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If you believe your data to come from a distribution where the means and median
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coincide, or if you've already computed the median in the course of some other
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analysis, then you can get away with a call to <code class="computeroutput"><span class="identifier">runs_above_and_below_threshold</span></code>
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via
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</p>
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<pre class="programlisting"><span class="identifier">Real</span> <span class="identifier">threshold</span> <span class="special">=</span> <span class="number">5</span><span class="special">;</span>
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<span class="keyword">auto</span> <span class="special">[</span><span class="identifier">t</span><span class="special">,</span> <span class="identifier">p</span><span class="special">]</span> <span class="special">=</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">statistics</span><span class="special">::</span><span class="identifier">runs_above_and_below_threshold</span><span class="special">(</span><span class="identifier">v</span><span class="special">,</span> <span class="identifier">threshold</span><span class="special">);</span>
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</pre>
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<p>
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The performance differences between these two cases are obvious:
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</p>
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<pre class="programlisting"><span class="special">---------------------------------------------------------------------------------------</span>
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<span class="identifier">Benchmark</span> <span class="identifier">Time</span> <span class="identifier">Bytes</span><span class="special">/</span><span class="identifier">second</span>
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<span class="special">---------------------------------------------------------------------------------------</span>
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<span class="identifier">BMRunsAboveAndBelowMedian</span><span class="special"><</span><span class="keyword">float</span><span class="special">>/</span><span class="number">8</span> <span class="number">260</span> <span class="identifier">ns</span> <span class="number">118.421</span><span class="identifier">M</span><span class="special">/</span><span class="identifier">s</span>
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<span class="identifier">BMRunsAboveAndBelowMedian</span><span class="special"><</span><span class="keyword">float</span><span class="special">>/</span><span class="number">16</span> <span class="number">318</span> <span class="identifier">ns</span> <span class="number">192.797</span><span class="identifier">M</span><span class="special">/</span><span class="identifier">s</span>
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<span class="identifier">BMRunsAboveAndBelowMedian</span><span class="special"><</span><span class="keyword">float</span><span class="special">>/</span><span class="number">32</span> <span class="number">417</span> <span class="identifier">ns</span> <span class="number">303.509</span><span class="identifier">M</span><span class="special">/</span><span class="identifier">s</span>
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<span class="identifier">BMRunsAboveAndBelowMedian</span><span class="special"><</span><span class="keyword">float</span><span class="special">>/</span><span class="number">64</span> <span class="number">625</span> <span class="identifier">ns</span> <span class="number">390.578</span><span class="identifier">M</span><span class="special">/</span><span class="identifier">s</span>
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<span class="identifier">BMRunsAboveAndBelowMedian</span><span class="special"><</span><span class="keyword">float</span><span class="special">>/</span><span class="number">128</span> <span class="number">743</span> <span class="identifier">ns</span> <span class="number">657.827</span><span class="identifier">M</span><span class="special">/</span><span class="identifier">s</span>
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<span class="identifier">BMRunsAboveAndBelowMedian</span><span class="special"><</span><span class="keyword">float</span><span class="special">>/</span><span class="number">256</span> <span class="number">1308</span> <span class="identifier">ns</span> <span class="number">767.181</span><span class="identifier">M</span><span class="special">/</span><span class="identifier">s</span>
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<span class="identifier">BMRunsAboveAndBelowMedian</span><span class="special"><</span><span class="keyword">float</span><span class="special">>/</span><span class="number">512</span> <span class="number">1896</span> <span class="identifier">ns</span> <span class="number">1034.31</span><span class="identifier">M</span><span class="special">/</span><span class="identifier">s</span>
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<span class="identifier">BMRunsAboveAndBelowMedian</span><span class="special"><</span><span class="keyword">float</span><span class="special">>/</span><span class="number">1024</span> <span class="number">6582</span> <span class="identifier">ns</span> <span class="number">594.458</span><span class="identifier">M</span><span class="special">/</span><span class="identifier">s</span>
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<span class="identifier">BMRunsAboveAndBelowMedian</span><span class="special"><</span><span class="keyword">float</span><span class="special">>/</span><span class="number">2048</span> <span class="number">26067</span> <span class="identifier">ns</span> <span class="number">300.001</span><span class="identifier">M</span><span class="special">/</span><span class="identifier">s</span>
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<span class="identifier">BMRunsAboveAndBelowMedian</span><span class="special"><</span><span class="keyword">float</span><span class="special">>/</span><span class="number">4096</span> <span class="number">62023</span> <span class="identifier">ns</span> <span class="number">252.125</span><span class="identifier">M</span><span class="special">/</span><span class="identifier">s</span>
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<span class="identifier">BMRunsAboveAndBelowMedian</span><span class="special"><</span><span class="keyword">float</span><span class="special">>/</span><span class="number">8192</span> <span class="number">124976</span> <span class="identifier">ns</span> <span class="number">250.256</span><span class="identifier">M</span><span class="special">/</span><span class="identifier">s</span>
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<span class="identifier">BMRunsAboveAndBelowMedian</span><span class="special"><</span><span class="keyword">float</span><span class="special">>/</span><span class="number">16384</span> <span class="number">242171</span> <span class="identifier">ns</span> <span class="number">258.29</span><span class="identifier">M</span><span class="special">/</span><span class="identifier">s</span>
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<span class="identifier">BMRunsAboveAndBelowMedian</span><span class="special"><</span><span class="keyword">float</span><span class="special">>/</span><span class="number">32768</span> <span class="number">528683</span> <span class="identifier">ns</span> <span class="number">236.714</span><span class="identifier">M</span><span class="special">/</span><span class="identifier">s</span>
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<span class="identifier">BMRunsAboveAndBelowMedian</span><span class="special"><</span><span class="keyword">float</span><span class="special">>/</span><span class="number">65536</span> <span class="number">965354</span> <span class="identifier">ns</span> <span class="number">259.185</span><span class="identifier">M</span><span class="special">/</span><span class="identifier">s</span>
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<span class="identifier">BMRunsAboveAndBelowMedian</span><span class="special"><</span><span class="keyword">float</span><span class="special">>/</span><span class="number">131072</span> <span class="number">2514693</span> <span class="identifier">ns</span> <span class="number">199.068</span><span class="identifier">M</span><span class="special">/</span><span class="identifier">s</span>
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<span class="identifier">BMRunsAboveAndBelowMedian</span><span class="special"><</span><span class="keyword">float</span><span class="special">>/</span><span class="number">262144</span> <span class="number">4223084</span> <span class="identifier">ns</span> <span class="number">237.058</span><span class="identifier">M</span><span class="special">/</span><span class="identifier">s</span>
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<span class="identifier">BMRunsAboveAndBelowMedian</span><span class="special"><</span><span class="keyword">float</span><span class="special">>/</span><span class="number">524288</span> <span class="number">8638963</span> <span class="identifier">ns</span> <span class="number">231.755</span><span class="identifier">M</span><span class="special">/</span><span class="identifier">s</span>
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|
<span class="identifier">BMRunsAboveAndBelowMedian</span><span class="special"><</span><span class="keyword">float</span><span class="special">>/</span><span class="number">1048576</span> <span class="number">16215682</span> <span class="identifier">ns</span> <span class="number">246.995</span><span class="identifier">M</span><span class="special">/</span><span class="identifier">s</span>
|
|
<span class="identifier">BMRunsAboveAndBelowMedian</span><span class="special"><</span><span class="keyword">float</span><span class="special">>/</span><span class="number">2097152</span> <span class="number">39180496</span> <span class="identifier">ns</span> <span class="number">204.443</span><span class="identifier">M</span><span class="special">/</span><span class="identifier">s</span>
|
|
<span class="identifier">BMRunsAboveAndBelowMedian</span><span class="special"><</span><span class="keyword">float</span><span class="special">>/</span><span class="number">4194304</span> <span class="number">82495779</span> <span class="identifier">ns</span> <span class="number">194.307</span><span class="identifier">M</span><span class="special">/</span><span class="identifier">s</span>
|
|
<span class="identifier">BMRunsAboveAndBelowMedian</span><span class="special"><</span><span class="keyword">float</span><span class="special">>/</span><span class="number">8388608</span> <span class="number">142675936</span> <span class="identifier">ns</span> <span class="number">224.547</span><span class="identifier">M</span><span class="special">/</span><span class="identifier">s</span>
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<span class="identifier">BMRunsAboveAndBelowMedian</span><span class="special"><</span><span class="keyword">float</span><span class="special">>/</span><span class="number">16777216</span> <span class="number">287638068</span> <span class="identifier">ns</span> <span class="number">223.088</span><span class="identifier">M</span><span class="special">/</span><span class="identifier">s</span>
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<span class="identifier">BMRunsAboveAndBelowMedian</span><span class="special"><</span><span class="keyword">float</span><span class="special">></span><span class="identifier">_BigO</span> <span class="number">17.25</span> <span class="identifier">N</span>
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<span class="identifier">BMRunsAboveAndBelowMedian</span><span class="special"><</span><span class="keyword">double</span><span class="special">>/</span><span class="number">8</span> <span class="number">191</span> <span class="identifier">ns</span> <span class="number">320.129</span><span class="identifier">M</span><span class="special">/</span><span class="identifier">s</span>
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|
<span class="identifier">BMRunsAboveAndBelowMedian</span><span class="special"><</span><span class="keyword">double</span><span class="special">>/</span><span class="number">16</span> <span class="number">233</span> <span class="identifier">ns</span> <span class="number">523.526</span><span class="identifier">M</span><span class="special">/</span><span class="identifier">s</span>
|
|
<span class="identifier">BMRunsAboveAndBelowMedian</span><span class="special"><</span><span class="keyword">double</span><span class="special">>/</span><span class="number">32</span> <span class="number">334</span> <span class="identifier">ns</span> <span class="number">730.8</span><span class="identifier">M</span><span class="special">/</span><span class="identifier">s</span>
|
|
<span class="identifier">BMRunsAboveAndBelowMedian</span><span class="special"><</span><span class="keyword">double</span><span class="special">>/</span><span class="number">64</span> <span class="number">456</span> <span class="identifier">ns</span> <span class="number">1070.93</span><span class="identifier">M</span><span class="special">/</span><span class="identifier">s</span>
|
|
<span class="identifier">BMRunsAboveAndBelowMedian</span><span class="special"><</span><span class="keyword">double</span><span class="special">>/</span><span class="number">128</span> <span class="number">688</span> <span class="identifier">ns</span> <span class="number">1.38789</span><span class="identifier">G</span><span class="special">/</span><span class="identifier">s</span>
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<span class="identifier">BMRunsAboveAndBelowMedian</span><span class="special"><</span><span class="keyword">double</span><span class="special">>/</span><span class="number">256</span> <span class="number">1257</span> <span class="identifier">ns</span> <span class="number">1.51807</span><span class="identifier">G</span><span class="special">/</span><span class="identifier">s</span>
|
|
<span class="identifier">BMRunsAboveAndBelowMedian</span><span class="special"><</span><span class="keyword">double</span><span class="special">>/</span><span class="number">512</span> <span class="number">2663</span> <span class="identifier">ns</span> <span class="number">1.43406</span><span class="identifier">G</span><span class="special">/</span><span class="identifier">s</span>
|
|
<span class="identifier">BMRunsAboveAndBelowMedian</span><span class="special"><</span><span class="keyword">double</span><span class="special">>/</span><span class="number">1024</span> <span class="number">4100</span> <span class="identifier">ns</span> <span class="number">1.86266</span><span class="identifier">G</span><span class="special">/</span><span class="identifier">s</span>
|
|
<span class="identifier">BMRunsAboveAndBelowMedian</span><span class="special"><</span><span class="keyword">double</span><span class="special">>/</span><span class="number">2048</span> <span class="number">23493</span> <span class="identifier">ns</span> <span class="number">665.851</span><span class="identifier">M</span><span class="special">/</span><span class="identifier">s</span>
|
|
<span class="identifier">BMRunsAboveAndBelowMedian</span><span class="special"><</span><span class="keyword">double</span><span class="special">>/</span><span class="number">4096</span> <span class="number">57968</span> <span class="identifier">ns</span> <span class="number">539.551</span><span class="identifier">M</span><span class="special">/</span><span class="identifier">s</span>
|
|
<span class="identifier">BMRunsAboveAndBelowMedian</span><span class="special"><</span><span class="keyword">double</span><span class="special">>/</span><span class="number">8192</span> <span class="number">142272</span> <span class="identifier">ns</span> <span class="number">439.746</span><span class="identifier">M</span><span class="special">/</span><span class="identifier">s</span>
|
|
<span class="identifier">BMRunsAboveAndBelowMedian</span><span class="special"><</span><span class="keyword">double</span><span class="special">>/</span><span class="number">16384</span> <span class="number">260948</span> <span class="identifier">ns</span> <span class="number">479.639</span><span class="identifier">M</span><span class="special">/</span><span class="identifier">s</span>
|
|
<span class="identifier">BMRunsAboveAndBelowMedian</span><span class="special"><</span><span class="keyword">double</span><span class="special">>/</span><span class="number">32768</span> <span class="number">551577</span> <span class="identifier">ns</span> <span class="number">453.623</span><span class="identifier">M</span><span class="special">/</span><span class="identifier">s</span>
|
|
<span class="identifier">BMRunsAboveAndBelowMedian</span><span class="special"><</span><span class="keyword">double</span><span class="special">>/</span><span class="number">65536</span> <span class="number">1056583</span> <span class="identifier">ns</span> <span class="number">473.654</span><span class="identifier">M</span><span class="special">/</span><span class="identifier">s</span>
|
|
<span class="identifier">BMRunsAboveAndBelowMedian</span><span class="special"><</span><span class="keyword">double</span><span class="special">>/</span><span class="number">131072</span> <span class="number">2123956</span> <span class="identifier">ns</span> <span class="number">471.35</span><span class="identifier">M</span><span class="special">/</span><span class="identifier">s</span>
|
|
<span class="identifier">BMRunsAboveAndBelowMedian</span><span class="special"><</span><span class="keyword">double</span><span class="special">>/</span><span class="number">262144</span> <span class="number">5028745</span> <span class="identifier">ns</span> <span class="number">398.111</span><span class="identifier">M</span><span class="special">/</span><span class="identifier">s</span>
|
|
<span class="identifier">BMRunsAboveAndBelowMedian</span><span class="special"><</span><span class="keyword">double</span><span class="special">>/</span><span class="number">524288</span> <span class="number">10399212</span> <span class="identifier">ns</span> <span class="number">384.981</span><span class="identifier">M</span><span class="special">/</span><span class="identifier">s</span>
|
|
<span class="identifier">BMRunsAboveAndBelowMedian</span><span class="special"><</span><span class="keyword">double</span><span class="special">>/</span><span class="number">1048576</span> <span class="number">23089767</span> <span class="identifier">ns</span> <span class="number">348.496</span><span class="identifier">M</span><span class="special">/</span><span class="identifier">s</span>
|
|
<span class="identifier">BMRunsAboveAndBelowMedian</span><span class="special"><</span><span class="keyword">double</span><span class="special">>/</span><span class="number">2097152</span> <span class="number">37626884</span> <span class="identifier">ns</span> <span class="number">425.962</span><span class="identifier">M</span><span class="special">/</span><span class="identifier">s</span>
|
|
<span class="identifier">BMRunsAboveAndBelowMedian</span><span class="special"><</span><span class="keyword">double</span><span class="special">>/</span><span class="number">4194304</span> <span class="number">79281747</span> <span class="identifier">ns</span> <span class="number">404.088</span><span class="identifier">M</span><span class="special">/</span><span class="identifier">s</span>
|
|
<span class="identifier">BMRunsAboveAndBelowMedian</span><span class="special"><</span><span class="keyword">double</span><span class="special">>/</span><span class="number">8388608</span> <span class="number">172055781</span> <span class="identifier">ns</span> <span class="number">373.391</span><span class="identifier">M</span><span class="special">/</span><span class="identifier">s</span>
|
|
<span class="identifier">BMRunsAboveAndBelowMedian</span><span class="special"><</span><span class="keyword">double</span><span class="special">>/</span><span class="number">16777216</span> <span class="number">391377449</span> <span class="identifier">ns</span> <span class="number">332.01</span><span class="identifier">M</span><span class="special">/</span><span class="identifier">s</span>
|
|
<span class="identifier">BMRunsAboveAndBelowMedian</span><span class="special"><</span><span class="keyword">double</span><span class="special">></span><span class="identifier">_BigO</span> <span class="number">22.52</span> <span class="identifier">N</span>
|
|
<span class="identifier">BMRunsAboveAndBelowThreshold</span><span class="special"><</span><span class="keyword">float</span><span class="special">>/</span><span class="number">8</span> <span class="number">41.6</span> <span class="identifier">ns</span> <span class="number">739.55</span><span class="identifier">M</span><span class="special">/</span><span class="identifier">s</span>
|
|
<span class="identifier">BMRunsAboveAndBelowThreshold</span><span class="special"><</span><span class="keyword">float</span><span class="special">>/</span><span class="number">16</span> <span class="number">58.4</span> <span class="identifier">ns</span> <span class="number">1050.48</span><span class="identifier">M</span><span class="special">/</span><span class="identifier">s</span>
|
|
<span class="identifier">BMRunsAboveAndBelowThreshold</span><span class="special"><</span><span class="keyword">float</span><span class="special">>/</span><span class="number">32</span> <span class="number">66.5</span> <span class="identifier">ns</span> <span class="number">1.79606</span><span class="identifier">G</span><span class="special">/</span><span class="identifier">s</span>
|
|
<span class="identifier">BMRunsAboveAndBelowThreshold</span><span class="special"><</span><span class="keyword">float</span><span class="special">>/</span><span class="number">64</span> <span class="number">115</span> <span class="identifier">ns</span> <span class="number">2.0762</span><span class="identifier">G</span><span class="special">/</span><span class="identifier">s</span>
|
|
<span class="identifier">BMRunsAboveAndBelowThreshold</span><span class="special"><</span><span class="keyword">float</span><span class="special">>/</span><span class="number">128</span> <span class="number">198</span> <span class="identifier">ns</span> <span class="number">2.41515</span><span class="identifier">G</span><span class="special">/</span><span class="identifier">s</span>
|
|
<span class="identifier">BMRunsAboveAndBelowThreshold</span><span class="special"><</span><span class="keyword">float</span><span class="special">>/</span><span class="number">256</span> <span class="number">365</span> <span class="identifier">ns</span> <span class="number">2.61328</span><span class="identifier">G</span><span class="special">/</span><span class="identifier">s</span>
|
|
<span class="identifier">BMRunsAboveAndBelowThreshold</span><span class="special"><</span><span class="keyword">float</span><span class="special">>/</span><span class="number">512</span> <span class="number">720</span> <span class="identifier">ns</span> <span class="number">2.65053</span><span class="identifier">G</span><span class="special">/</span><span class="identifier">s</span>
|
|
<span class="identifier">BMRunsAboveAndBelowThreshold</span><span class="special"><</span><span class="keyword">float</span><span class="special">>/</span><span class="number">1024</span> <span class="number">1424</span> <span class="identifier">ns</span> <span class="number">2.68123</span><span class="identifier">G</span><span class="special">/</span><span class="identifier">s</span>
|
|
<span class="identifier">BMRunsAboveAndBelowThreshold</span><span class="special"><</span><span class="keyword">float</span><span class="special">>/</span><span class="number">2048</span> <span class="number">3009</span> <span class="identifier">ns</span> <span class="number">2.5379</span><span class="identifier">G</span><span class="special">/</span><span class="identifier">s</span>
|
|
<span class="identifier">BMRunsAboveAndBelowThreshold</span><span class="special"><</span><span class="keyword">float</span><span class="special">>/</span><span class="number">4096</span> <span class="number">16748</span> <span class="identifier">ns</span> <span class="number">933.699</span><span class="identifier">M</span><span class="special">/</span><span class="identifier">s</span>
|
|
<span class="identifier">BMRunsAboveAndBelowThreshold</span><span class="special"><</span><span class="keyword">float</span><span class="special">>/</span><span class="number">8192</span> <span class="number">40190</span> <span class="identifier">ns</span> <span class="number">778.105</span><span class="identifier">M</span><span class="special">/</span><span class="identifier">s</span>
|
|
<span class="identifier">BMRunsAboveAndBelowThreshold</span><span class="special"><</span><span class="keyword">float</span><span class="special">>/</span><span class="number">16384</span> <span class="number">86500</span> <span class="identifier">ns</span> <span class="number">723.067</span><span class="identifier">M</span><span class="special">/</span><span class="identifier">s</span>
|
|
<span class="identifier">BMRunsAboveAndBelowThreshold</span><span class="special"><</span><span class="keyword">float</span><span class="special">>/</span><span class="number">32768</span> <span class="number">176692</span> <span class="identifier">ns</span> <span class="number">708.108</span><span class="identifier">M</span><span class="special">/</span><span class="identifier">s</span>
|
|
<span class="identifier">BMRunsAboveAndBelowThreshold</span><span class="special"><</span><span class="keyword">float</span><span class="special">>/</span><span class="number">65536</span> <span class="number">356863</span> <span class="identifier">ns</span> <span class="number">701.198</span><span class="identifier">M</span><span class="special">/</span><span class="identifier">s</span>
|
|
<span class="identifier">BMRunsAboveAndBelowThreshold</span><span class="special"><</span><span class="keyword">float</span><span class="special">>/</span><span class="number">131072</span> <span class="number">714807</span> <span class="identifier">ns</span> <span class="number">700.08</span><span class="identifier">M</span><span class="special">/</span><span class="identifier">s</span>
|
|
<span class="identifier">BMRunsAboveAndBelowThreshold</span><span class="special"><</span><span class="keyword">float</span><span class="special">>/</span><span class="number">262144</span> <span class="number">1429078</span> <span class="identifier">ns</span> <span class="number">700.415</span><span class="identifier">M</span><span class="special">/</span><span class="identifier">s</span>
|
|
<span class="identifier">BMRunsAboveAndBelowThreshold</span><span class="special"><</span><span class="keyword">float</span><span class="special">>/</span><span class="number">524288</span> <span class="number">2877227</span> <span class="identifier">ns</span> <span class="number">695.785</span><span class="identifier">M</span><span class="special">/</span><span class="identifier">s</span>
|
|
<span class="identifier">BMRunsAboveAndBelowThreshold</span><span class="special"><</span><span class="keyword">float</span><span class="special">>/</span><span class="number">1048576</span> <span class="number">5795662</span> <span class="identifier">ns</span> <span class="number">691.222</span><span class="identifier">M</span><span class="special">/</span><span class="identifier">s</span>
|
|
<span class="identifier">BMRunsAboveAndBelowThreshold</span><span class="special"><</span><span class="keyword">float</span><span class="special">>/</span><span class="number">2097152</span> <span class="number">11562715</span> <span class="identifier">ns</span> <span class="number">692.427</span><span class="identifier">M</span><span class="special">/</span><span class="identifier">s</span>
|
|
<span class="identifier">BMRunsAboveAndBelowThreshold</span><span class="special"><</span><span class="keyword">float</span><span class="special">>/</span><span class="number">4194304</span> <span class="number">23364846</span> <span class="identifier">ns</span> <span class="number">686.464</span><span class="identifier">M</span><span class="special">/</span><span class="identifier">s</span>
|
|
<span class="identifier">BMRunsAboveAndBelowThreshold</span><span class="special"><</span><span class="keyword">float</span><span class="special">>/</span><span class="number">8388608</span> <span class="number">46442540</span> <span class="identifier">ns</span> <span class="number">689.871</span><span class="identifier">M</span><span class="special">/</span><span class="identifier">s</span>
|
|
<span class="identifier">BMRunsAboveAndBelowThreshold</span><span class="special"><</span><span class="keyword">float</span><span class="special">>/</span><span class="number">16777216</span> <span class="number">92284501</span> <span class="identifier">ns</span> <span class="number">694.006</span><span class="identifier">M</span><span class="special">/</span><span class="identifier">s</span>
|
|
<span class="identifier">BMRunsAboveAndBelowThreshold</span><span class="special"><</span><span class="keyword">float</span><span class="special">></span><span class="identifier">_BigO</span> <span class="number">5.51</span> <span class="identifier">N</span>
|
|
<span class="identifier">BMRunsAboveAndBelowThreshold</span><span class="special"><</span><span class="keyword">double</span><span class="special">>/</span><span class="number">8</span> <span class="number">45.1</span> <span class="identifier">ns</span> <span class="number">1.32169</span><span class="identifier">G</span><span class="special">/</span><span class="identifier">s</span>
|
|
<span class="identifier">BMRunsAboveAndBelowThreshold</span><span class="special"><</span><span class="keyword">double</span><span class="special">>/</span><span class="number">16</span> <span class="number">53.6</span> <span class="identifier">ns</span> <span class="number">2.22712</span><span class="identifier">G</span><span class="special">/</span><span class="identifier">s</span>
|
|
<span class="identifier">BMRunsAboveAndBelowThreshold</span><span class="special"><</span><span class="keyword">double</span><span class="special">>/</span><span class="number">32</span> <span class="number">71.4</span> <span class="identifier">ns</span> <span class="number">3.34079</span><span class="identifier">G</span><span class="special">/</span><span class="identifier">s</span>
|
|
<span class="identifier">BMRunsAboveAndBelowThreshold</span><span class="special"><</span><span class="keyword">double</span><span class="special">>/</span><span class="number">64</span> <span class="number">112</span> <span class="identifier">ns</span> <span class="number">4.24946</span><span class="identifier">G</span><span class="special">/</span><span class="identifier">s</span>
|
|
<span class="identifier">BMRunsAboveAndBelowThreshold</span><span class="special"><</span><span class="keyword">double</span><span class="special">>/</span><span class="number">128</span> <span class="number">196</span> <span class="identifier">ns</span> <span class="number">4.87317</span><span class="identifier">G</span><span class="special">/</span><span class="identifier">s</span>
|
|
<span class="identifier">BMRunsAboveAndBelowThreshold</span><span class="special"><</span><span class="keyword">double</span><span class="special">>/</span><span class="number">256</span> <span class="number">378</span> <span class="identifier">ns</span> <span class="number">5.04476</span><span class="identifier">G</span><span class="special">/</span><span class="identifier">s</span>
|
|
<span class="identifier">BMRunsAboveAndBelowThreshold</span><span class="special"><</span><span class="keyword">double</span><span class="special">>/</span><span class="number">512</span> <span class="number">702</span> <span class="identifier">ns</span> <span class="number">5.44134</span><span class="identifier">G</span><span class="special">/</span><span class="identifier">s</span>
|
|
<span class="identifier">BMRunsAboveAndBelowThreshold</span><span class="special"><</span><span class="keyword">double</span><span class="special">>/</span><span class="number">1024</span> <span class="number">1417</span> <span class="identifier">ns</span> <span class="number">5.3865</span><span class="identifier">G</span><span class="special">/</span><span class="identifier">s</span>
|
|
<span class="identifier">BMRunsAboveAndBelowThreshold</span><span class="special"><</span><span class="keyword">double</span><span class="special">>/</span><span class="number">2048</span> <span class="number">3031</span> <span class="identifier">ns</span> <span class="number">5.03872</span><span class="identifier">G</span><span class="special">/</span><span class="identifier">s</span>
|
|
<span class="identifier">BMRunsAboveAndBelowThreshold</span><span class="special"><</span><span class="keyword">double</span><span class="special">>/</span><span class="number">4096</span> <span class="number">16813</span> <span class="identifier">ns</span> <span class="number">1.81669</span><span class="identifier">G</span><span class="special">/</span><span class="identifier">s</span>
|
|
<span class="identifier">BMRunsAboveAndBelowThreshold</span><span class="special"><</span><span class="keyword">double</span><span class="special">>/</span><span class="number">8192</span> <span class="number">41182</span> <span class="identifier">ns</span> <span class="number">1.48565</span><span class="identifier">G</span><span class="special">/</span><span class="identifier">s</span>
|
|
<span class="identifier">BMRunsAboveAndBelowThreshold</span><span class="special"><</span><span class="keyword">double</span><span class="special">>/</span><span class="number">16384</span> <span class="number">86939</span> <span class="identifier">ns</span> <span class="number">1.40536</span><span class="identifier">G</span><span class="special">/</span><span class="identifier">s</span>
|
|
<span class="identifier">BMRunsAboveAndBelowThreshold</span><span class="special"><</span><span class="keyword">double</span><span class="special">>/</span><span class="number">32768</span> <span class="number">177255</span> <span class="identifier">ns</span> <span class="number">1.37892</span><span class="identifier">G</span><span class="special">/</span><span class="identifier">s</span>
|
|
<span class="identifier">BMRunsAboveAndBelowThreshold</span><span class="special"><</span><span class="keyword">double</span><span class="special">>/</span><span class="number">65536</span> <span class="number">356391</span> <span class="identifier">ns</span> <span class="number">1.3713</span><span class="identifier">G</span><span class="special">/</span><span class="identifier">s</span>
|
|
<span class="identifier">BMRunsAboveAndBelowThreshold</span><span class="special"><</span><span class="keyword">double</span><span class="special">>/</span><span class="number">131072</span> <span class="number">718417</span> <span class="identifier">ns</span> <span class="number">1.36057</span><span class="identifier">G</span><span class="special">/</span><span class="identifier">s</span>
|
|
<span class="identifier">BMRunsAboveAndBelowThreshold</span><span class="special"><</span><span class="keyword">double</span><span class="special">>/</span><span class="number">262144</span> <span class="number">1442288</span> <span class="identifier">ns</span> <span class="number">1.35583</span><span class="identifier">G</span><span class="special">/</span><span class="identifier">s</span>
|
|
<span class="identifier">BMRunsAboveAndBelowThreshold</span><span class="special"><</span><span class="keyword">double</span><span class="special">>/</span><span class="number">524288</span> <span class="number">2942259</span> <span class="identifier">ns</span> <span class="number">1.33217</span><span class="identifier">G</span><span class="special">/</span><span class="identifier">s</span>
|
|
<span class="identifier">BMRunsAboveAndBelowThreshold</span><span class="special"><</span><span class="keyword">double</span><span class="special">>/</span><span class="number">1048576</span> <span class="number">5870235</span> <span class="identifier">ns</span> <span class="number">1.33244</span><span class="identifier">G</span><span class="special">/</span><span class="identifier">s</span>
|
|
<span class="identifier">BMRunsAboveAndBelowThreshold</span><span class="special"><</span><span class="keyword">double</span><span class="special">>/</span><span class="number">2097152</span> <span class="number">11743081</span> <span class="identifier">ns</span> <span class="number">1.33192</span><span class="identifier">G</span><span class="special">/</span><span class="identifier">s</span>
|
|
<span class="identifier">BMRunsAboveAndBelowThreshold</span><span class="special"><</span><span class="keyword">double</span><span class="special">>/</span><span class="number">4194304</span> <span class="number">23521002</span> <span class="identifier">ns</span> <span class="number">1.32976</span><span class="identifier">G</span><span class="special">/</span><span class="identifier">s</span>
|
|
<span class="identifier">BMRunsAboveAndBelowThreshold</span><span class="special"><</span><span class="keyword">double</span><span class="special">>/</span><span class="number">8388608</span> <span class="number">46917407</span> <span class="identifier">ns</span> <span class="number">1.33339</span><span class="identifier">G</span><span class="special">/</span><span class="identifier">s</span>
|
|
<span class="identifier">BMRunsAboveAndBelowThreshold</span><span class="special"><</span><span class="keyword">double</span><span class="special">>/</span><span class="number">16777216</span> <span class="number">93823876</span> <span class="identifier">ns</span> <span class="number">1.33305</span><span class="identifier">G</span><span class="special">/</span><span class="identifier">s</span>
|
|
<span class="identifier">BMRunsAboveAndBelowThreshold</span><span class="special"><</span><span class="keyword">double</span><span class="special">></span><span class="identifier">_BigO</span> <span class="number">5.59</span> <span class="identifier">N</span> <span class="number">5.59</span> <span class="identifier">N</span>
|
|
</pre>
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</div>
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<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
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<td align="left"></td>
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<td align="right"><div class="copyright-footer">Copyright © 2006-2019 Nikhar
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Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
|
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Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
|
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Råde, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
|
|
Daryle Walker and Xiaogang Zhang<p>
|
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Distributed under the Boost Software License, Version 1.0. (See accompanying
|
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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>)
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</p>
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</div></td>
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</tr></table>
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<hr>
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