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| <div class="title">CubicInterpolation-internal.hpp</div> </div> |
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| <div class="contents"> |
| <div class="fragment"><div class="line"><a name="l00001"></a><span class="lineno"> 1</span> <span class="comment">/*</span></div> |
| <div class="line"><a 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 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 name="l00004"></a><span class="lineno"> 4</span> <span class="comment"> * distributed with this work for additional information</span></div> |
| <div class="line"><a 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 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 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 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 name="l00009"></a><span class="lineno"> 9</span> <span class="comment"> *</span></div> |
| <div class="line"><a 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 name="l00011"></a><span class="lineno"> 11</span> <span class="comment"> *</span></div> |
| <div class="line"><a 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 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 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 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 name="l00016"></a><span class="lineno"> 16</span> <span class="comment"> * specific language governing permissions and limitations</span></div> |
| <div class="line"><a name="l00017"></a><span class="lineno"> 17</span> <span class="comment"> * under the License.</span></div> |
| <div class="line"><a name="l00018"></a><span class="lineno"> 18</span> <span class="comment"> */</span></div> |
| <div class="line"><a name="l00019"></a><span class="lineno"> 19</span>  </div> |
| <div class="line"><a name="l00020"></a><span class="lineno"> 20</span> <span class="preprocessor">#ifndef _CUBICINTERPOLATION_INTERNAL_HPP_</span></div> |
| <div class="line"><a name="l00021"></a><span class="lineno"> 21</span> <span class="preprocessor">#define _CUBICINTERPOLATION_INTERNAL_HPP_</span></div> |
| <div class="line"><a name="l00022"></a><span class="lineno"> 22</span>  </div> |
| <div class="line"><a name="l00023"></a><span class="lineno"> 23</span> <span class="preprocessor">#include "CubicInterpolation.hpp"</span></div> |
| <div class="line"><a name="l00024"></a><span class="lineno"> 24</span>  </div> |
| <div class="line"><a name="l00025"></a><span class="lineno"> 25</span> <span class="preprocessor">#include <string></span></div> |
| <div class="line"><a name="l00026"></a><span class="lineno"> 26</span> <span class="preprocessor">#include <stdexcept></span></div> |
| <div class="line"><a name="l00027"></a><span class="lineno"> 27</span>  </div> |
| <div class="line"><a name="l00028"></a><span class="lineno"> 28</span> <span class="keyword">namespace </span><a class="code" href="namespacedatasketches.html">datasketches</a> {</div> |
| <div class="line"><a name="l00029"></a><span class="lineno"> 29</span>  </div> |
| <div class="line"><a name="l00030"></a><span class="lineno"> 30</span> <span class="keyword">template</span><<span class="keyword">typename</span> A></div> |
| <div class="line"><a name="l00031"></a><span class="lineno"> 31</span> <span class="keyword">static</span> <span class="keywordtype">double</span> interpolateUsingXAndYTables(<span class="keyword">const</span> <span class="keywordtype">double</span> xArr[], <span class="keyword">const</span> <span class="keywordtype">double</span> yArr[], <span class="keyword">const</span> <span class="keywordtype">int</span> offset, <span class="keyword">const</span> <span class="keywordtype">double</span> x);</div> |
| <div class="line"><a name="l00032"></a><span class="lineno"> 32</span>  </div> |
| <div class="line"><a name="l00033"></a><span class="lineno"> 33</span> <span class="keyword">template</span><<span class="keyword">typename</span> A></div> |
| <div class="line"><a name="l00034"></a><span class="lineno"> 34</span> <span class="keyword">static</span> <span class="keywordtype">double</span> cubicInterpolate(<span class="keyword">const</span> <span class="keywordtype">double</span> x0, <span class="keyword">const</span> <span class="keywordtype">double</span> y0, <span class="keyword">const</span> <span class="keywordtype">double</span> x1, <span class="keyword">const</span> <span class="keywordtype">double</span> y1,</div> |
| <div class="line"><a name="l00035"></a><span class="lineno"> 35</span>  <span class="keyword">const</span> <span class="keywordtype">double</span> x2, <span class="keyword">const</span> <span class="keywordtype">double</span> y2, <span class="keyword">const</span> <span class="keywordtype">double</span> x3, <span class="keyword">const</span> <span class="keywordtype">double</span> y3, <span class="keyword">const</span> <span class="keywordtype">double</span> x);</div> |
| <div class="line"><a name="l00036"></a><span class="lineno"> 36</span>  </div> |
| <div class="line"><a name="l00037"></a><span class="lineno"> 37</span> <span class="keyword">template</span><<span class="keyword">typename</span> A></div> |
| <div class="line"><a name="l00038"></a><span class="lineno"> 38</span> <span class="keyword">static</span> <span class="keywordtype">int</span> findStraddle(<span class="keyword">const</span> <span class="keywordtype">double</span> xArr[], <span class="keyword">const</span> <span class="keywordtype">int</span> len, <span class="keyword">const</span> <span class="keywordtype">double</span> x);</div> |
| <div class="line"><a name="l00039"></a><span class="lineno"> 39</span>  </div> |
| <div class="line"><a name="l00040"></a><span class="lineno"> 40</span> <span class="keyword">template</span><<span class="keyword">typename</span> A></div> |
| <div class="line"><a name="l00041"></a><span class="lineno"> 41</span> <span class="keyword">static</span> <span class="keywordtype">int</span> recursiveFindStraddle(<span class="keyword">const</span> <span class="keywordtype">double</span> xArr[], <span class="keyword">const</span> <span class="keywordtype">int</span> l, <span class="keyword">const</span> <span class="keywordtype">int</span> r, <span class="keyword">const</span> <span class="keywordtype">double</span> x);</div> |
| <div class="line"><a name="l00042"></a><span class="lineno"> 42</span>  </div> |
| <div class="line"><a name="l00043"></a><span class="lineno"> 43</span> <span class="keyword">template</span><<span class="keyword">typename</span> A></div> |
| <div class="line"><a name="l00044"></a><span class="lineno"> 44</span> <span class="keyword">static</span> <span class="keywordtype">double</span> interpolateUsingXArrAndYStride(<span class="keyword">const</span> <span class="keywordtype">double</span> xArr[], <span class="keyword">const</span> <span class="keywordtype">double</span> yStride,</div> |
| <div class="line"><a name="l00045"></a><span class="lineno"> 45</span>  <span class="keyword">const</span> <span class="keywordtype">int</span> offset, <span class="keyword">const</span> <span class="keywordtype">double</span> x);</div> |
| <div class="line"><a name="l00046"></a><span class="lineno"> 46</span>  </div> |
| <div class="line"><a name="l00047"></a><span class="lineno"> 47</span> <span class="keyword">const</span> <span class="keywordtype">int</span> numEntries = 40;</div> |
| <div class="line"><a name="l00048"></a><span class="lineno"> 48</span>  </div> |
| <div class="line"><a name="l00049"></a><span class="lineno"> 49</span> <span class="comment">//Computed for Coupon lgK = 26 ONLY. Designed for the cubic interpolator function.</span></div> |
| <div class="line"><a name="l00050"></a><span class="lineno"> 50</span> <span class="keyword">const</span> <span class="keywordtype">double</span> xArrComputed[numEntries] = {</div> |
| <div class="line"><a name="l00051"></a><span class="lineno"> 51</span>  0.0, 1.0, 20.0, 400.0,</div> |
| <div class="line"><a name="l00052"></a><span class="lineno"> 52</span>  8000.0, 160000.0, 300000.0, 600000.0,</div> |
| <div class="line"><a name="l00053"></a><span class="lineno"> 53</span>  900000.0, 1200000.0, 1500000.0, 1800000.0,</div> |
| <div class="line"><a name="l00054"></a><span class="lineno"> 54</span>  2100000.0, 2400000.0, 2700000.0, 3000000.0,</div> |
| <div class="line"><a name="l00055"></a><span class="lineno"> 55</span>  3300000.0, 3600000.0, 3900000.0, 4200000.0,</div> |
| <div class="line"><a name="l00056"></a><span class="lineno"> 56</span>  4500000.0, 4800000.0, 5100000.0, 5400000.0,</div> |
| <div class="line"><a name="l00057"></a><span class="lineno"> 57</span>  5700000.0, 6000000.0, 6300000.0, 6600000.0,</div> |
| <div class="line"><a name="l00058"></a><span class="lineno"> 58</span>  6900000.0, 7200000.0, 7500000.0, 7800000.0,</div> |
| <div class="line"><a name="l00059"></a><span class="lineno"> 59</span>  8100000.0, 8400000.0, 8700000.0, 9000000.0,</div> |
| <div class="line"><a name="l00060"></a><span class="lineno"> 60</span>  9300000.0, 9600000.0, 9900000.0, 10200000.0</div> |
| <div class="line"><a name="l00061"></a><span class="lineno"> 61</span> };</div> |
| <div class="line"><a name="l00062"></a><span class="lineno"> 62</span>  </div> |
| <div class="line"><a name="l00063"></a><span class="lineno"> 63</span> <span class="comment">//Computed for Coupon lgK = 26 ONLY. Designed for the cubic interpolator function.</span></div> |
| <div class="line"><a name="l00064"></a><span class="lineno"> 64</span> <span class="keyword">const</span> <span class="keywordtype">double</span> yArrComputed[numEntries] = {</div> |
| <div class="line"><a name="l00065"></a><span class="lineno"> 65</span>  0.0000000000000000, 1.0000000000000000, 20.0000009437402611, 400.0003963713384110,</div> |
| <div class="line"><a name="l00066"></a><span class="lineno"> 66</span>  8000.1589294602090376, 160063.6067763759638183, 300223.7071597663452849, 600895.5933856170158833,</div> |
| <div class="line"><a name="l00067"></a><span class="lineno"> 67</span>  902016.8065120954997838, 1203588.4983199508860707, 1505611.8245524743106216, 1808087.9449319066479802,</div> |
| <div class="line"><a name="l00068"></a><span class="lineno"> 68</span>  2111018.0231759352609515, 2414403.2270142501220107, 2718244.7282051891088486, 3022543.7025524540804327,</div> |
| <div class="line"><a name="l00069"></a><span class="lineno"> 69</span>  3327301.3299219091422856, 3632518.7942584538832307, 3938197.2836029687896371, 4244337.9901093561202288,</div> |
| <div class="line"><a name="l00070"></a><span class="lineno"> 70</span>  4550942.1100616492331028, 4858010.8438911894336343, 5165545.3961938973516226, 5473546.9757476449012756,</div> |
| <div class="line"><a name="l00071"></a><span class="lineno"> 71</span>  5782016.7955296505242586, 6090956.0727340159937739, 6400366.0287892958149314, 6710247.8893762007355690,</div> |
| <div class="line"><a name="l00072"></a><span class="lineno"> 72</span>  7020602.8844453142955899, 7331432.2482349723577499, 7642737.2192891482263803, 7954519.0404754765331745,</div> |
| <div class="line"><a name="l00073"></a><span class="lineno"> 73</span>  8266778.9590033423155546, 8579518.2264420464634895, 8892738.0987390466034412, 9206439.8362383283674717,</div> |
| <div class="line"><a name="l00074"></a><span class="lineno"> 74</span>  9520624.7036988288164139, 9835293.9703129194676876, 10150448.9097250290215015, 10466090.8000503256917000</div> |
| <div class="line"><a name="l00075"></a><span class="lineno"> 75</span> };</div> |
| <div class="line"><a name="l00076"></a><span class="lineno"> 76</span>  </div> |
| <div class="line"><a name="l00077"></a><span class="lineno"> 77</span> <span class="keyword">template</span><<span class="keyword">typename</span> A></div> |
| <div class="line"><a name="l00078"></a><span class="lineno"> 78</span> <span class="keywordtype">double</span> CubicInterpolation<A>::usingXAndYTables(<span class="keyword">const</span> <span class="keywordtype">double</span> x) {</div> |
| <div class="line"><a name="l00079"></a><span class="lineno"> 79</span>  <span class="keywordflow">return</span> usingXAndYTables(xArrComputed, yArrComputed, numEntries, x);</div> |
| <div class="line"><a name="l00080"></a><span class="lineno"> 80</span> }</div> |
| <div class="line"><a name="l00081"></a><span class="lineno"> 81</span>  </div> |
| <div class="line"><a name="l00082"></a><span class="lineno"> 82</span> <span class="keyword">template</span><<span class="keyword">typename</span> A></div> |
| <div class="line"><a name="l00083"></a><span class="lineno"> 83</span> <span class="keywordtype">double</span> CubicInterpolation<A>::usingXAndYTables(<span class="keyword">const</span> <span class="keywordtype">double</span> xArr[], <span class="keyword">const</span> <span class="keywordtype">double</span> yArr[],</div> |
| <div class="line"><a name="l00084"></a><span class="lineno"> 84</span>  <span class="keyword">const</span> <span class="keywordtype">int</span> len, <span class="keyword">const</span> <span class="keywordtype">double</span> x) {</div> |
| <div class="line"><a name="l00085"></a><span class="lineno"> 85</span>  <span class="keywordtype">int</span> offset;</div> |
| <div class="line"><a name="l00086"></a><span class="lineno"> 86</span>  <span class="keywordflow">if</span> (x < xArr[0] || x > xArr[len-1]) {</div> |
| <div class="line"><a name="l00087"></a><span class="lineno"> 87</span>  <span class="keywordflow">throw</span> std::invalid_argument(<span class="stringliteral">"x value out of range: "</span> + std::to_string(x));</div> |
| <div class="line"><a name="l00088"></a><span class="lineno"> 88</span>  }</div> |
| <div class="line"><a name="l00089"></a><span class="lineno"> 89</span>  </div> |
| <div class="line"><a name="l00090"></a><span class="lineno"> 90</span>  <span class="keywordflow">if</span> (x == xArr[len-1]) { <span class="comment">// corner case</span></div> |
| <div class="line"><a name="l00091"></a><span class="lineno"> 91</span>  <span class="keywordflow">return</span> (yArr[len-1]);</div> |
| <div class="line"><a name="l00092"></a><span class="lineno"> 92</span>  }</div> |
| <div class="line"><a name="l00093"></a><span class="lineno"> 93</span>  </div> |
| <div class="line"><a name="l00094"></a><span class="lineno"> 94</span>  offset = findStraddle<A>(xArr, len, x);</div> |
| <div class="line"><a name="l00095"></a><span class="lineno"> 95</span>  <span class="keywordflow">if</span> (offset < 0 && offset > len-2) {</div> |
| <div class="line"><a name="l00096"></a><span class="lineno"> 96</span>  <span class="keywordflow">throw</span> std::logic_error(<span class="stringliteral">"offset must be >= 0 and <= "</span> + std::to_string(len) + <span class="stringliteral">"-2"</span>);</div> |
| <div class="line"><a name="l00097"></a><span class="lineno"> 97</span>  }</div> |
| <div class="line"><a name="l00098"></a><span class="lineno"> 98</span>  </div> |
| <div class="line"><a name="l00099"></a><span class="lineno"> 99</span>  <span class="keywordflow">if</span> (offset == 0) { <span class="comment">// corner case</span></div> |
| <div class="line"><a name="l00100"></a><span class="lineno"> 100</span>  <span class="keywordflow">return</span> (interpolateUsingXAndYTables<A>(xArr, yArr, (offset-0), x));</div> |
| <div class="line"><a name="l00101"></a><span class="lineno"> 101</span>  }</div> |
| <div class="line"><a name="l00102"></a><span class="lineno"> 102</span>  <span class="keywordflow">else</span> <span class="keywordflow">if</span> (offset == numEntries-2) { <span class="comment">// corner case</span></div> |
| <div class="line"><a name="l00103"></a><span class="lineno"> 103</span>  <span class="keywordflow">return</span> (interpolateUsingXAndYTables<A>(xArr, yArr, (offset-2), x));</div> |
| <div class="line"><a name="l00104"></a><span class="lineno"> 104</span>  }</div> |
| <div class="line"><a name="l00105"></a><span class="lineno"> 105</span>  <span class="comment">// main case</span></div> |
| <div class="line"><a name="l00106"></a><span class="lineno"> 106</span>  <span class="keywordflow">return</span> (interpolateUsingXAndYTables<A>(xArr, yArr, (offset-1), x));</div> |
| <div class="line"><a name="l00107"></a><span class="lineno"> 107</span> }</div> |
| <div class="line"><a name="l00108"></a><span class="lineno"> 108</span>  </div> |
| <div class="line"><a name="l00109"></a><span class="lineno"> 109</span> <span class="comment">// In C: again-two-registers cubic_interpolate_aux L1368</span></div> |
| <div class="line"><a name="l00110"></a><span class="lineno"> 110</span> <span class="keyword">template</span><<span class="keyword">typename</span> A></div> |
| <div class="line"><a name="l00111"></a><span class="lineno"> 111</span> <span class="keyword">static</span> <span class="keywordtype">double</span> interpolateUsingXAndYTables(<span class="keyword">const</span> <span class="keywordtype">double</span> xArr[], <span class="keyword">const</span> <span class="keywordtype">double</span> yArr[],</div> |
| <div class="line"><a name="l00112"></a><span class="lineno"> 112</span>  <span class="keyword">const</span> <span class="keywordtype">int</span> offset, <span class="keyword">const</span> <span class="keywordtype">double</span> x) {</div> |
| <div class="line"><a name="l00113"></a><span class="lineno"> 113</span>  <span class="keywordflow">return</span> (cubicInterpolate<A>(xArr[offset+0], yArr[offset+0],</div> |
| <div class="line"><a name="l00114"></a><span class="lineno"> 114</span>  xArr[offset+1], yArr[offset+1],</div> |
| <div class="line"><a name="l00115"></a><span class="lineno"> 115</span>  xArr[offset+2], yArr[offset+2],</div> |
| <div class="line"><a name="l00116"></a><span class="lineno"> 116</span>  xArr[offset+3], yArr[offset+3],</div> |
| <div class="line"><a name="l00117"></a><span class="lineno"> 117</span>  x) );</div> |
| <div class="line"><a name="l00118"></a><span class="lineno"> 118</span> }</div> |
| <div class="line"><a name="l00119"></a><span class="lineno"> 119</span>  </div> |
| <div class="line"><a name="l00120"></a><span class="lineno"> 120</span> <span class="keyword">template</span><<span class="keyword">typename</span> A></div> |
| <div class="line"><a name="l00121"></a><span class="lineno"> 121</span> <span class="keyword">static</span> <span class="keyword">inline</span> <span class="keywordtype">double</span> cubicInterpolate(<span class="keyword">const</span> <span class="keywordtype">double</span> x0, <span class="keyword">const</span> <span class="keywordtype">double</span> y0,</div> |
| <div class="line"><a name="l00122"></a><span class="lineno"> 122</span>  <span class="keyword">const</span> <span class="keywordtype">double</span> x1, <span class="keyword">const</span> <span class="keywordtype">double</span> y1,</div> |
| <div class="line"><a name="l00123"></a><span class="lineno"> 123</span>  <span class="keyword">const</span> <span class="keywordtype">double</span> x2, <span class="keyword">const</span> <span class="keywordtype">double</span> y2,</div> |
| <div class="line"><a name="l00124"></a><span class="lineno"> 124</span>  <span class="keyword">const</span> <span class="keywordtype">double</span> x3, <span class="keyword">const</span> <span class="keywordtype">double</span> y3,</div> |
| <div class="line"><a name="l00125"></a><span class="lineno"> 125</span>  <span class="keyword">const</span> <span class="keywordtype">double</span> x)</div> |
| <div class="line"><a name="l00126"></a><span class="lineno"> 126</span> {</div> |
| <div class="line"><a name="l00127"></a><span class="lineno"> 127</span>  <span class="keywordtype">double</span> l0_numer = (x - x1) * (x - x2) * (x - x3);</div> |
| <div class="line"><a name="l00128"></a><span class="lineno"> 128</span>  <span class="keywordtype">double</span> l1_numer = (x - x0) * (x - x2) * (x - x3);</div> |
| <div class="line"><a name="l00129"></a><span class="lineno"> 129</span>  <span class="keywordtype">double</span> l2_numer = (x - x0) * (x - x1) * (x - x3);</div> |
| <div class="line"><a name="l00130"></a><span class="lineno"> 130</span>  <span class="keywordtype">double</span> l3_numer = (x - x0) * (x - x1) * (x - x2);</div> |
| <div class="line"><a name="l00131"></a><span class="lineno"> 131</span>  </div> |
| <div class="line"><a name="l00132"></a><span class="lineno"> 132</span>  <span class="keywordtype">double</span> l0_denom = (x0 - x1) * (x0 - x2) * (x0 - x3);</div> |
| <div class="line"><a name="l00133"></a><span class="lineno"> 133</span>  <span class="keywordtype">double</span> l1_denom = (x1 - x0) * (x1 - x2) * (x1 - x3);</div> |
| <div class="line"><a name="l00134"></a><span class="lineno"> 134</span>  <span class="keywordtype">double</span> l2_denom = (x2 - x0) * (x2 - x1) * (x2 - x3);</div> |
| <div class="line"><a name="l00135"></a><span class="lineno"> 135</span>  <span class="keywordtype">double</span> l3_denom = (x3 - x0) * (x3 - x1) * (x3 - x2);</div> |
| <div class="line"><a name="l00136"></a><span class="lineno"> 136</span>  </div> |
| <div class="line"><a name="l00137"></a><span class="lineno"> 137</span>  <span class="keywordtype">double</span> term0 = y0 * l0_numer / l0_denom;</div> |
| <div class="line"><a name="l00138"></a><span class="lineno"> 138</span>  <span class="keywordtype">double</span> term1 = y1 * l1_numer / l1_denom;</div> |
| <div class="line"><a name="l00139"></a><span class="lineno"> 139</span>  <span class="keywordtype">double</span> term2 = y2 * l2_numer / l2_denom;</div> |
| <div class="line"><a name="l00140"></a><span class="lineno"> 140</span>  <span class="keywordtype">double</span> term3 = y3 * l3_numer / l3_denom;</div> |
| <div class="line"><a name="l00141"></a><span class="lineno"> 141</span>  </div> |
| <div class="line"><a name="l00142"></a><span class="lineno"> 142</span>  <span class="keywordflow">return</span> (term0 + term1 + term2 + term3);</div> |
| <div class="line"><a name="l00143"></a><span class="lineno"> 143</span> }</div> |
| <div class="line"><a name="l00144"></a><span class="lineno"> 144</span>  </div> |
| <div class="line"><a name="l00145"></a><span class="lineno"> 145</span> <span class="comment">/* returns j such that xArr[j] <= x and x < xArr[j+1] */</span></div> |
| <div class="line"><a name="l00146"></a><span class="lineno"> 146</span> <span class="keyword">template</span><<span class="keyword">typename</span> A></div> |
| <div class="line"><a name="l00147"></a><span class="lineno"> 147</span> <span class="keyword">static</span> <span class="keywordtype">int</span> findStraddle(<span class="keyword">const</span> <span class="keywordtype">double</span> xArr[], <span class="keyword">const</span> <span class="keywordtype">int</span> len, <span class="keyword">const</span> <span class="keywordtype">double</span> x)</div> |
| <div class="line"><a name="l00148"></a><span class="lineno"> 148</span> {</div> |
| <div class="line"><a name="l00149"></a><span class="lineno"> 149</span>  <span class="keywordflow">if</span> ((len < 2) || (x < xArr[0]) || (x > xArr[len-1])) {</div> |
| <div class="line"><a name="l00150"></a><span class="lineno"> 150</span>  <span class="keywordflow">throw</span> std::logic_error(<span class="stringliteral">"invariant violated during interpolation"</span>);</div> |
| <div class="line"><a name="l00151"></a><span class="lineno"> 151</span>  }</div> |
| <div class="line"><a name="l00152"></a><span class="lineno"> 152</span>  <span class="keywordflow">return</span>(recursiveFindStraddle<A>(xArr, 0, len-1, x));</div> |
| <div class="line"><a name="l00153"></a><span class="lineno"> 153</span> }</div> |
| <div class="line"><a name="l00154"></a><span class="lineno"> 154</span>  </div> |
| <div class="line"><a name="l00155"></a><span class="lineno"> 155</span>  </div> |
| <div class="line"><a name="l00156"></a><span class="lineno"> 156</span> <span class="comment">/* the invariant here is that xArr[l] <= x && x < xArr[r] */</span></div> |
| <div class="line"><a name="l00157"></a><span class="lineno"> 157</span> <span class="keyword">template</span><<span class="keyword">typename</span> A></div> |
| <div class="line"><a name="l00158"></a><span class="lineno"> 158</span> <span class="keyword">static</span> <span class="keywordtype">int</span> recursiveFindStraddle(<span class="keyword">const</span> <span class="keywordtype">double</span> xArr[], <span class="keyword">const</span> <span class="keywordtype">int</span> l, <span class="keyword">const</span> <span class="keywordtype">int</span> r, <span class="keyword">const</span> <span class="keywordtype">double</span> x)</div> |
| <div class="line"><a name="l00159"></a><span class="lineno"> 159</span> {</div> |
| <div class="line"><a name="l00160"></a><span class="lineno"> 160</span>  <span class="keywordtype">int</span> m;</div> |
| <div class="line"><a name="l00161"></a><span class="lineno"> 161</span>  <span class="keywordflow">if</span> (l >= r) {</div> |
| <div class="line"><a name="l00162"></a><span class="lineno"> 162</span>  <span class="keywordflow">throw</span> std::logic_error(<span class="stringliteral">"lower bound not less than upper bound in search"</span>);</div> |
| <div class="line"><a name="l00163"></a><span class="lineno"> 163</span>  }</div> |
| <div class="line"><a name="l00164"></a><span class="lineno"> 164</span>  <span class="keywordflow">if</span> ((xArr[l] > x) || (x >= xArr[r])) { <span class="comment">// the invariant</span></div> |
| <div class="line"><a name="l00165"></a><span class="lineno"> 165</span>  <span class="keywordflow">throw</span> std::logic_error(<span class="stringliteral">"target value invariant violated in search"</span>);</div> |
| <div class="line"><a name="l00166"></a><span class="lineno"> 166</span>  }</div> |
| <div class="line"><a name="l00167"></a><span class="lineno"> 167</span>  </div> |
| <div class="line"><a name="l00168"></a><span class="lineno"> 168</span>  <span class="keywordflow">if</span> (l+1 == r) <span class="keywordflow">return</span> (l);</div> |
| <div class="line"><a name="l00169"></a><span class="lineno"> 169</span>  m = l + ((r-l)/2);</div> |
| <div class="line"><a name="l00170"></a><span class="lineno"> 170</span>  <span class="keywordflow">if</span> (xArr[m] <= x) <span class="keywordflow">return</span> (recursiveFindStraddle<A>(xArr, m, r, x));</div> |
| <div class="line"><a name="l00171"></a><span class="lineno"> 171</span>  <span class="keywordflow">else</span> <span class="keywordflow">return</span> (recursiveFindStraddle<A>(xArr, l, m, x));</div> |
| <div class="line"><a name="l00172"></a><span class="lineno"> 172</span> }</div> |
| <div class="line"><a name="l00173"></a><span class="lineno"> 173</span>  </div> |
| <div class="line"><a name="l00174"></a><span class="lineno"> 174</span>  </div> |
| <div class="line"><a name="l00175"></a><span class="lineno"> 175</span> <span class="comment">//Interpolate using X table and Y stride</span></div> |
| <div class="line"><a name="l00176"></a><span class="lineno"> 176</span>  </div> |
| <div class="line"><a name="l00186"></a><span class="lineno"> 186</span> <span class="comment">//In C: again-two-registers cubic_interpolate_with_x_arr_and_y_stride L1411</span></div> |
| <div class="line"><a name="l00187"></a><span class="lineno"> 187</span> <span class="comment">// Used by HllEstimators</span></div> |
| <div class="line"><a name="l00188"></a><span class="lineno"> 188</span> <span class="keyword">template</span><<span class="keyword">typename</span> A></div> |
| <div class="line"><a name="l00189"></a><span class="lineno"> 189</span> <span class="keywordtype">double</span> CubicInterpolation<A>::usingXArrAndYStride(<span class="keyword">const</span> <span class="keywordtype">double</span> xArr[], <span class="keyword">const</span> <span class="keywordtype">int</span> xArrLen,</div> |
| <div class="line"><a name="l00190"></a><span class="lineno"> 190</span>  <span class="keyword">const</span> <span class="keywordtype">double</span> yStride, <span class="keyword">const</span> <span class="keywordtype">double</span> x) {</div> |
| <div class="line"><a name="l00191"></a><span class="lineno"> 191</span>  <span class="keyword">const</span> <span class="keywordtype">int</span> xArrLenM1 = xArrLen - 1;</div> |
| <div class="line"><a name="l00192"></a><span class="lineno"> 192</span>  </div> |
| <div class="line"><a name="l00193"></a><span class="lineno"> 193</span>  <span class="keywordflow">if</span> ((xArrLen < 4) || (x < xArr[0]) || (x > xArr[xArrLenM1])) {</div> |
| <div class="line"><a name="l00194"></a><span class="lineno"> 194</span>  <span class="keywordflow">throw</span> std::logic_error(<span class="stringliteral">"impossible values during interpolaiton"</span>);</div> |
| <div class="line"><a name="l00195"></a><span class="lineno"> 195</span>  }</div> |
| <div class="line"><a name="l00196"></a><span class="lineno"> 196</span>  </div> |
| <div class="line"><a name="l00197"></a><span class="lineno"> 197</span>  <span class="keywordflow">if</span> (x == xArr[xArrLenM1]) { <span class="comment">/* corner case */</span></div> |
| <div class="line"><a name="l00198"></a><span class="lineno"> 198</span>  <span class="keywordflow">return</span> (yStride * (xArrLenM1));</div> |
| <div class="line"><a name="l00199"></a><span class="lineno"> 199</span>  }</div> |
| <div class="line"><a name="l00200"></a><span class="lineno"> 200</span>  </div> |
| <div class="line"><a name="l00201"></a><span class="lineno"> 201</span>  <span class="keyword">const</span> <span class="keywordtype">int</span> offset = findStraddle<A>(xArr, xArrLen, x); <span class="comment">//uses recursion</span></div> |
| <div class="line"><a name="l00202"></a><span class="lineno"> 202</span>  <span class="keyword">const</span> <span class="keywordtype">int</span> xArrLenM2 = xArrLen - 2;</div> |
| <div class="line"><a name="l00203"></a><span class="lineno"> 203</span>  <span class="keywordflow">if</span> ((offset < 0) || (offset > xArrLenM2)) {</div> |
| <div class="line"><a name="l00204"></a><span class="lineno"> 204</span>  <span class="keywordflow">throw</span> std::logic_error(<span class="stringliteral">"invalid offset during interpolation"</span>);</div> |
| <div class="line"><a name="l00205"></a><span class="lineno"> 205</span>  }</div> |
| <div class="line"><a name="l00206"></a><span class="lineno"> 206</span>  </div> |
| <div class="line"><a name="l00207"></a><span class="lineno"> 207</span>  <span class="keywordflow">if</span> (offset == 0) { <span class="comment">/* corner case */</span></div> |
| <div class="line"><a name="l00208"></a><span class="lineno"> 208</span>  <span class="keywordflow">return</span> (interpolateUsingXArrAndYStride<A>(xArr, yStride, (offset - 0), x));</div> |
| <div class="line"><a name="l00209"></a><span class="lineno"> 209</span>  }</div> |
| <div class="line"><a name="l00210"></a><span class="lineno"> 210</span>  <span class="keywordflow">else</span> <span class="keywordflow">if</span> (offset == xArrLenM2) { <span class="comment">/* corner case */</span></div> |
| <div class="line"><a name="l00211"></a><span class="lineno"> 211</span>  <span class="keywordflow">return</span> (interpolateUsingXArrAndYStride<A>(xArr, yStride, (offset - 2), x));</div> |
| <div class="line"><a name="l00212"></a><span class="lineno"> 212</span>  }</div> |
| <div class="line"><a name="l00213"></a><span class="lineno"> 213</span>  <span class="comment">/* main case */</span></div> |
| <div class="line"><a name="l00214"></a><span class="lineno"> 214</span>  <span class="keywordflow">return</span> (interpolateUsingXArrAndYStride<A>(xArr, yStride, (offset - 1), x));</div> |
| <div class="line"><a name="l00215"></a><span class="lineno"> 215</span> }</div> |
| <div class="line"><a name="l00216"></a><span class="lineno"> 216</span>  </div> |
| <div class="line"><a name="l00217"></a><span class="lineno"> 217</span> <span class="comment">//In C: again-two-registers cubic_interpolate_with_x_arr_and_y_stride_aux L1402</span></div> |
| <div class="line"><a name="l00218"></a><span class="lineno"> 218</span> <span class="keyword">template</span><<span class="keyword">typename</span> A></div> |
| <div class="line"><a name="l00219"></a><span class="lineno"> 219</span> <span class="keyword">static</span> <span class="keywordtype">double</span> interpolateUsingXArrAndYStride(<span class="keyword">const</span> <span class="keywordtype">double</span> xArr[], <span class="keyword">const</span> <span class="keywordtype">double</span> yStride,</div> |
| <div class="line"><a name="l00220"></a><span class="lineno"> 220</span>  <span class="keyword">const</span> <span class="keywordtype">int</span> offset, <span class="keyword">const</span> <span class="keywordtype">double</span> x) {</div> |
| <div class="line"><a name="l00221"></a><span class="lineno"> 221</span>  <span class="keywordflow">return</span> cubicInterpolate<A>(</div> |
| <div class="line"><a name="l00222"></a><span class="lineno"> 222</span>  xArr[offset + 0], yStride * (offset + 0),</div> |
| <div class="line"><a name="l00223"></a><span class="lineno"> 223</span>  xArr[offset + 1], yStride * (offset + 1),</div> |
| <div class="line"><a name="l00224"></a><span class="lineno"> 224</span>  xArr[offset + 2], yStride * (offset + 2),</div> |
| <div class="line"><a name="l00225"></a><span class="lineno"> 225</span>  xArr[offset + 3], yStride * (offset + 3),</div> |
| <div class="line"><a name="l00226"></a><span class="lineno"> 226</span>  x);</div> |
| <div class="line"><a name="l00227"></a><span class="lineno"> 227</span> }</div> |
| <div class="line"><a name="l00228"></a><span class="lineno"> 228</span>  </div> |
| <div class="line"><a name="l00229"></a><span class="lineno"> 229</span> }</div> |
| <div class="line"><a name="l00230"></a><span class="lineno"> 230</span>  </div> |
| <div class="line"><a name="l00231"></a><span class="lineno"> 231</span> <span class="preprocessor">#endif </span><span class="comment">// _CUBICINTERPOLATION_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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