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| <div class="headertitle"><div class="title">HarmonicNumbers-internal.hpp</div></div> |
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| <div class="fragment"><div class="line"><a id="l00001" name="l00001"></a><span class="lineno"> 1</span><span class="comment">/*</span></div> |
| <div class="line"><a id="l00002" name="l00002"></a><span class="lineno"> 2</span><span class="comment"> * Licensed to the Apache Software Foundation (ASF) under one</span></div> |
| <div class="line"><a id="l00003" name="l00003"></a><span class="lineno"> 3</span><span class="comment"> * or more contributor license agreements. See the NOTICE file</span></div> |
| <div class="line"><a id="l00004" name="l00004"></a><span class="lineno"> 4</span><span class="comment"> * distributed with this work for additional information</span></div> |
| <div class="line"><a id="l00005" name="l00005"></a><span class="lineno"> 5</span><span class="comment"> * regarding copyright ownership. The ASF licenses this file</span></div> |
| <div class="line"><a id="l00006" name="l00006"></a><span class="lineno"> 6</span><span class="comment"> * to you under the Apache License, Version 2.0 (the</span></div> |
| <div class="line"><a id="l00007" name="l00007"></a><span class="lineno"> 7</span><span class="comment"> * "License"); you may not use this file except in compliance</span></div> |
| <div class="line"><a id="l00008" name="l00008"></a><span class="lineno"> 8</span><span class="comment"> * with the License. You may obtain a copy of the License at</span></div> |
| <div class="line"><a id="l00009" name="l00009"></a><span class="lineno"> 9</span><span class="comment"> *</span></div> |
| <div class="line"><a id="l00010" name="l00010"></a><span class="lineno"> 10</span><span class="comment"> * http://www.apache.org/licenses/LICENSE-2.0</span></div> |
| <div class="line"><a id="l00011" name="l00011"></a><span class="lineno"> 11</span><span class="comment"> *</span></div> |
| <div class="line"><a id="l00012" name="l00012"></a><span class="lineno"> 12</span><span class="comment"> * Unless required by applicable law or agreed to in writing,</span></div> |
| <div class="line"><a id="l00013" name="l00013"></a><span class="lineno"> 13</span><span class="comment"> * software distributed under the License is distributed on an</span></div> |
| <div class="line"><a id="l00014" name="l00014"></a><span class="lineno"> 14</span><span class="comment"> * "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY</span></div> |
| <div class="line"><a id="l00015" name="l00015"></a><span class="lineno"> 15</span><span class="comment"> * KIND, either express or implied. See the License for the</span></div> |
| <div class="line"><a id="l00016" name="l00016"></a><span class="lineno"> 16</span><span class="comment"> * specific language governing permissions and limitations</span></div> |
| <div class="line"><a id="l00017" name="l00017"></a><span class="lineno"> 17</span><span class="comment"> * under the License.</span></div> |
| <div class="line"><a id="l00018" name="l00018"></a><span class="lineno"> 18</span><span class="comment"> */</span></div> |
| <div class="line"><a id="l00019" name="l00019"></a><span class="lineno"> 19</span> </div> |
| <div class="line"><a id="l00020" name="l00020"></a><span class="lineno"> 20</span><span class="preprocessor">#ifndef _HARMONICNUMBERS_INTERNAL_HPP_</span></div> |
| <div class="line"><a id="l00021" name="l00021"></a><span class="lineno"> 21</span><span class="preprocessor">#define _HARMONICNUMBERS_INTERNAL_HPP_</span></div> |
| <div class="line"><a id="l00022" name="l00022"></a><span class="lineno"> 22</span> </div> |
| <div class="line"><a id="l00023" name="l00023"></a><span class="lineno"> 23</span><span class="preprocessor">#include "HarmonicNumbers.hpp"</span></div> |
| <div class="line"><a id="l00024" name="l00024"></a><span class="lineno"> 24</span> </div> |
| <div class="line"><a id="l00025" name="l00025"></a><span class="lineno"> 25</span><span class="preprocessor">#include <cmath></span></div> |
| <div class="line"><a id="l00026" name="l00026"></a><span class="lineno"> 26</span> </div> |
| <div class="line"><a id="l00027" name="l00027"></a><span class="lineno"> 27</span><span class="keyword">namespace </span><a class="code hl_namespace" href="namespacedatasketches.html">datasketches</a> {</div> |
| <div class="line"><a id="l00028" name="l00028"></a><span class="lineno"> 28</span> </div> |
| <div class="line"><a id="l00029" name="l00029"></a><span class="lineno"> 29</span><span class="keyword">template</span><<span class="keyword">typename</span> A></div> |
| <div class="line"><a id="l00030" name="l00030"></a><span class="lineno"> 30</span><span class="keywordtype">double</span> HarmonicNumbers<A>::getBitMapEstimate(<span class="keyword">const</span> <span class="keywordtype">int</span> bitVectorLength, <span class="keyword">const</span> <span class="keywordtype">int</span> numBitsSet) {</div> |
| <div class="line"><a id="l00031" name="l00031"></a><span class="lineno"> 31</span> <span class="keywordflow">return</span> (bitVectorLength * (harmonicNumber(bitVectorLength) - harmonicNumber(bitVectorLength - numBitsSet)));</div> |
| <div class="line"><a id="l00032" name="l00032"></a><span class="lineno"> 32</span>}</div> |
| <div class="line"><a id="l00033" name="l00033"></a><span class="lineno"> 33</span> </div> |
| <div class="line"><a id="l00034" name="l00034"></a><span class="lineno"> 34</span><span class="keyword">static</span> <span class="keyword">const</span> <span class="keywordtype">int</span> NUM_EXACT_HARMONIC_NUMBERS = 25;</div> |
| <div class="line"><a id="l00035" name="l00035"></a><span class="lineno"> 35</span> </div> |
| <div class="line"><a id="l00036" name="l00036"></a><span class="lineno"> 36</span><span class="keyword">static</span> <span class="keywordtype">double</span> tableOfExactHarmonicNumbers[] = {</div> |
| <div class="line"><a id="l00037" name="l00037"></a><span class="lineno"> 37</span> 0.0, <span class="comment">// 0</span></div> |
| <div class="line"><a id="l00038" name="l00038"></a><span class="lineno"> 38</span> 1.0, <span class="comment">// 1</span></div> |
| <div class="line"><a id="l00039" name="l00039"></a><span class="lineno"> 39</span> 1.5, <span class="comment">// 2</span></div> |
| <div class="line"><a id="l00040" name="l00040"></a><span class="lineno"> 40</span> 11.0 / 6.0, <span class="comment">// 3</span></div> |
| <div class="line"><a id="l00041" name="l00041"></a><span class="lineno"> 41</span> 25.0 / 12.0, <span class="comment">// 4</span></div> |
| <div class="line"><a id="l00042" name="l00042"></a><span class="lineno"> 42</span> 137.0 / 60.0, <span class="comment">// 5</span></div> |
| <div class="line"><a id="l00043" name="l00043"></a><span class="lineno"> 43</span> 49.0 / 20.0, <span class="comment">// 6</span></div> |
| <div class="line"><a id="l00044" name="l00044"></a><span class="lineno"> 44</span> 363.0 / 140.0, <span class="comment">// 7</span></div> |
| <div class="line"><a id="l00045" name="l00045"></a><span class="lineno"> 45</span> 761.0 / 280.0, <span class="comment">// 8</span></div> |
| <div class="line"><a id="l00046" name="l00046"></a><span class="lineno"> 46</span> 7129.0 / 2520.0, <span class="comment">// 9</span></div> |
| <div class="line"><a id="l00047" name="l00047"></a><span class="lineno"> 47</span> 7381.0 / 2520.0, <span class="comment">// 10</span></div> |
| <div class="line"><a id="l00048" name="l00048"></a><span class="lineno"> 48</span> 83711.0 / 27720.0, <span class="comment">// 11</span></div> |
| <div class="line"><a id="l00049" name="l00049"></a><span class="lineno"> 49</span> 86021.0 / 27720.0, <span class="comment">// 12</span></div> |
| <div class="line"><a id="l00050" name="l00050"></a><span class="lineno"> 50</span> 1145993.0 / 360360.0, <span class="comment">// 13</span></div> |
| <div class="line"><a id="l00051" name="l00051"></a><span class="lineno"> 51</span> 1171733.0 / 360360.0, <span class="comment">// 14</span></div> |
| <div class="line"><a id="l00052" name="l00052"></a><span class="lineno"> 52</span> 1195757.0 / 360360.0, <span class="comment">// 15</span></div> |
| <div class="line"><a id="l00053" name="l00053"></a><span class="lineno"> 53</span> 2436559.0 / 720720.0, <span class="comment">// 16</span></div> |
| <div class="line"><a id="l00054" name="l00054"></a><span class="lineno"> 54</span> 42142223.0 / 12252240.0, <span class="comment">// 17</span></div> |
| <div class="line"><a id="l00055" name="l00055"></a><span class="lineno"> 55</span> 14274301.0 / 4084080.0, <span class="comment">// 18</span></div> |
| <div class="line"><a id="l00056" name="l00056"></a><span class="lineno"> 56</span> 275295799.0 / 77597520.0, <span class="comment">// 19</span></div> |
| <div class="line"><a id="l00057" name="l00057"></a><span class="lineno"> 57</span> 55835135.0 / 15519504.0, <span class="comment">// 20</span></div> |
| <div class="line"><a id="l00058" name="l00058"></a><span class="lineno"> 58</span> 18858053.0 / 5173168.0, <span class="comment">// 21</span></div> |
| <div class="line"><a id="l00059" name="l00059"></a><span class="lineno"> 59</span> 19093197.0 / 5173168.0, <span class="comment">// 22</span></div> |
| <div class="line"><a id="l00060" name="l00060"></a><span class="lineno"> 60</span> 444316699.0 / 118982864.0, <span class="comment">// 23</span></div> |
| <div class="line"><a id="l00061" name="l00061"></a><span class="lineno"> 61</span> 1347822955.0 / 356948592.0 <span class="comment">// 24</span></div> |
| <div class="line"><a id="l00062" name="l00062"></a><span class="lineno"> 62</span> };</div> |
| <div class="line"><a id="l00063" name="l00063"></a><span class="lineno"> 63</span> </div> |
| <div class="line"><a id="l00064" name="l00064"></a><span class="lineno"> 64</span><span class="keyword">static</span> <span class="keyword">const</span> <span class="keywordtype">double</span> EULER_MASCHERONI_CONSTANT = 0.577215664901532860606512090082;</div> |
| <div class="line"><a id="l00065" name="l00065"></a><span class="lineno"> 65</span> </div> |
| <div class="line"><a id="l00066" name="l00066"></a><span class="lineno"> 66</span><span class="keyword">template</span><<span class="keyword">typename</span> A></div> |
| <div class="line"><a id="l00067" name="l00067"></a><span class="lineno"> 67</span><span class="keywordtype">double</span> HarmonicNumbers<A>::harmonicNumber(<span class="keyword">const</span> uint64_t x_i) {</div> |
| <div class="line"><a id="l00068" name="l00068"></a><span class="lineno"> 68</span> <span class="keywordflow">if</span> (x_i < NUM_EXACT_HARMONIC_NUMBERS) {</div> |
| <div class="line"><a id="l00069" name="l00069"></a><span class="lineno"> 69</span> <span class="keywordflow">return</span> tableOfExactHarmonicNumbers[x_i];</div> |
| <div class="line"><a id="l00070" name="l00070"></a><span class="lineno"> 70</span> } <span class="keywordflow">else</span> {</div> |
| <div class="line"><a id="l00071" name="l00071"></a><span class="lineno"> 71</span> <span class="keywordtype">double</span> x = <span class="keyword">static_cast<</span><span class="keywordtype">double</span><span class="keyword">></span>(x_i);</div> |
| <div class="line"><a id="l00072" name="l00072"></a><span class="lineno"> 72</span> <span class="keywordtype">double</span> invSq = 1.0 / (x * x);</div> |
| <div class="line"><a id="l00073" name="l00073"></a><span class="lineno"> 73</span> <span class="keywordtype">double</span> sum = log(x) + EULER_MASCHERONI_CONSTANT + (1.0 / (2.0 * x));</div> |
| <div class="line"><a id="l00074" name="l00074"></a><span class="lineno"> 74</span> <span class="comment">/* note: the number of terms included from this series expansion is appropriate</span></div> |
| <div class="line"><a id="l00075" name="l00075"></a><span class="lineno"> 75</span><span class="comment"> for the size of the exact table (25) and the precision of doubles */</span></div> |
| <div class="line"><a id="l00076" name="l00076"></a><span class="lineno"> 76</span> <span class="keywordtype">double</span> pow = invSq; <span class="comment">// now n^-2</span></div> |
| <div class="line"><a id="l00077" name="l00077"></a><span class="lineno"> 77</span> sum -= pow * (1.0 / 12.0);</div> |
| <div class="line"><a id="l00078" name="l00078"></a><span class="lineno"> 78</span> pow *= invSq; <span class="comment">// now n^-4</span></div> |
| <div class="line"><a id="l00079" name="l00079"></a><span class="lineno"> 79</span> sum += pow * (1.0 / 120.0);</div> |
| <div class="line"><a id="l00080" name="l00080"></a><span class="lineno"> 80</span> pow *= invSq; <span class="comment">/* now n^-6 */</span></div> |
| <div class="line"><a id="l00081" name="l00081"></a><span class="lineno"> 81</span> sum -= pow * (1.0 / 252.0);</div> |
| <div class="line"><a id="l00082" name="l00082"></a><span class="lineno"> 82</span> pow *= invSq; <span class="comment">/* now n^-8 */</span></div> |
| <div class="line"><a id="l00083" name="l00083"></a><span class="lineno"> 83</span> sum += pow * (1.0 / 240.0);</div> |
| <div class="line"><a id="l00084" name="l00084"></a><span class="lineno"> 84</span> <span class="keywordflow">return</span> sum;</div> |
| <div class="line"><a id="l00085" name="l00085"></a><span class="lineno"> 85</span> }</div> |
| <div class="line"><a id="l00086" name="l00086"></a><span class="lineno"> 86</span>}</div> |
| <div class="line"><a id="l00087" name="l00087"></a><span class="lineno"> 87</span> </div> |
| <div class="line"><a id="l00088" name="l00088"></a><span class="lineno"> 88</span>}</div> |
| <div class="line"><a id="l00089" name="l00089"></a><span class="lineno"> 89</span> </div> |
| <div class="line"><a id="l00090" name="l00090"></a><span class="lineno"> 90</span><span class="preprocessor">#endif </span><span class="comment">// _HARMONICNUMBERS_INTERNAL_HPP_</span></div> |
| <div class="ttc" id="anamespacedatasketches_html"><div class="ttname"><a href="namespacedatasketches.html">datasketches</a></div><div class="ttdoc">DataSketches namespace.</div><div class="ttdef"><b>Definition</b> binomial_bounds.hpp:38</div></div> |
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