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<div class="title">MathFunctions.h</div> </div>
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<div class="fragment"><div class="line"><a name="l00001"></a><span class="lineno"> 1</span> <span class="comment">// This file is part of Eigen, a lightweight C++ template library</span></div>
<div class="line"><a name="l00002"></a><span class="lineno"> 2</span> <span class="comment">// for linear algebra.</span></div>
<div class="line"><a name="l00003"></a><span class="lineno"> 3</span> <span class="comment">//</span></div>
<div class="line"><a name="l00004"></a><span class="lineno"> 4</span> <span class="comment">// Copyright (C) 2009 Rohit Garg <rpg.314@gmail.com></span></div>
<div class="line"><a name="l00005"></a><span class="lineno"> 5</span> <span class="comment">// Copyright (C) 2009 Benoit Jacob <jacob.benoit.1@gmail.com></span></div>
<div class="line"><a name="l00006"></a><span class="lineno"> 6</span> <span class="comment">//</span></div>
<div class="line"><a name="l00007"></a><span class="lineno"> 7</span> <span class="comment">// This Source Code Form is subject to the terms of the Mozilla</span></div>
<div class="line"><a name="l00008"></a><span class="lineno"> 8</span> <span class="comment">// Public License v. 2.0. If a copy of the MPL was not distributed</span></div>
<div class="line"><a name="l00009"></a><span class="lineno"> 9</span> <span class="comment">// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.</span></div>
<div class="line"><a name="l00010"></a><span class="lineno"> 10</span> </div>
<div class="line"><a name="l00011"></a><span class="lineno"> 11</span> <span class="preprocessor">#ifndef EIGEN_MOREVECTORIZATION_MATHFUNCTIONS_H</span></div>
<div class="line"><a name="l00012"></a><span class="lineno"> 12</span> <span class="preprocessor"></span><span class="preprocessor">#define EIGEN_MOREVECTORIZATION_MATHFUNCTIONS_H</span></div>
<div class="line"><a name="l00013"></a><span class="lineno"> 13</span> <span class="preprocessor"></span></div>
<div class="line"><a name="l00014"></a><span class="lineno"> 14</span> <span class="keyword">namespace </span>Eigen { </div>
<div class="line"><a name="l00015"></a><span class="lineno"> 15</span> </div>
<div class="line"><a name="l00016"></a><span class="lineno"> 16</span> <span class="keyword">namespace </span>internal {</div>
<div class="line"><a name="l00017"></a><span class="lineno"> 17</span> </div>
<div class="line"><a name="l00019"></a><span class="lineno"> 19</span> <span class="keyword">template</span><<span class="keyword">typename</span> Packet> <span class="keyword">inline</span> <span class="keyword">static</span> Packet pasin(Packet a) { <span class="keywordflow">return</span> std::asin(a); }</div>
<div class="line"><a name="l00020"></a><span class="lineno"> 20</span> </div>
<div class="line"><a name="l00021"></a><span class="lineno"> 21</span> <span class="preprocessor">#ifdef EIGEN_VECTORIZE_SSE</span></div>
<div class="line"><a name="l00022"></a><span class="lineno"> 22</span> <span class="preprocessor"></span></div>
<div class="line"><a name="l00023"></a><span class="lineno"> 23</span> <span class="keyword">template</span><> EIGEN_DONT_INLINE Packet4f pasin(Packet4f x)</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>  _EIGEN_DECLARE_CONST_Packet4f(half, 0.5);</div>
<div class="line"><a name="l00026"></a><span class="lineno"> 26</span>  _EIGEN_DECLARE_CONST_Packet4f(minus_half, -0.5);</div>
<div class="line"><a name="l00027"></a><span class="lineno"> 27</span>  _EIGEN_DECLARE_CONST_Packet4f(3half, 1.5);</div>
<div class="line"><a name="l00028"></a><span class="lineno"> 28</span> </div>
<div class="line"><a name="l00029"></a><span class="lineno"> 29</span>  _EIGEN_DECLARE_CONST_Packet4f_FROM_INT(sign_mask, 0x80000000);</div>
<div class="line"><a name="l00030"></a><span class="lineno"> 30</span> </div>
<div class="line"><a name="l00031"></a><span class="lineno"> 31</span>  _EIGEN_DECLARE_CONST_Packet4f(pi, 3.141592654);</div>
<div class="line"><a name="l00032"></a><span class="lineno"> 32</span>  _EIGEN_DECLARE_CONST_Packet4f(pi_over_2, 3.141592654*0.5);</div>
<div class="line"><a name="l00033"></a><span class="lineno"> 33</span> </div>
<div class="line"><a name="l00034"></a><span class="lineno"> 34</span>  _EIGEN_DECLARE_CONST_Packet4f(asin1, 4.2163199048E-2);</div>
<div class="line"><a name="l00035"></a><span class="lineno"> 35</span>  _EIGEN_DECLARE_CONST_Packet4f(asin2, 2.4181311049E-2);</div>
<div class="line"><a name="l00036"></a><span class="lineno"> 36</span>  _EIGEN_DECLARE_CONST_Packet4f(asin3, 4.5470025998E-2);</div>
<div class="line"><a name="l00037"></a><span class="lineno"> 37</span>  _EIGEN_DECLARE_CONST_Packet4f(asin4, 7.4953002686E-2);</div>
<div class="line"><a name="l00038"></a><span class="lineno"> 38</span>  _EIGEN_DECLARE_CONST_Packet4f(asin5, 1.6666752422E-1);</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>  Packet4f a = pabs(x);<span class="comment">//got the absolute value</span></div>
<div class="line"><a name="l00041"></a><span class="lineno"> 41</span> </div>
<div class="line"><a name="l00042"></a><span class="lineno"> 42</span>  Packet4f sign_bit= _mm_and_ps(x, p4f_sign_mask);<span class="comment">//extracted the sign bit</span></div>
<div class="line"><a name="l00043"></a><span class="lineno"> 43</span> </div>
<div class="line"><a name="l00044"></a><span class="lineno"> 44</span>  Packet4f z1,z2;<span class="comment">//will need them during computation </span></div>
<div class="line"><a name="l00045"></a><span class="lineno"> 45</span> </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="comment">//will compute the two branches for asin</span></div>
<div class="line"><a name="l00048"></a><span class="lineno"> 48</span> <span class="comment">//so first compare with half</span></div>
<div class="line"><a name="l00049"></a><span class="lineno"> 49</span> </div>
<div class="line"><a name="l00050"></a><span class="lineno"> 50</span>  Packet4f branch_mask= _mm_cmpgt_ps(a, p4f_half);<span class="comment">//this is to select which branch to take</span></div>
<div class="line"><a name="l00051"></a><span class="lineno"> 51</span> <span class="comment">//both will be taken, and finally results will be merged</span></div>
<div class="line"><a name="l00052"></a><span class="lineno"> 52</span> <span class="comment">//the branch for values >0.5</span></div>
<div class="line"><a name="l00053"></a><span class="lineno"> 53</span> </div>
<div class="line"><a name="l00054"></a><span class="lineno"> 54</span>  {</div>
<div class="line"><a name="l00055"></a><span class="lineno"> 55</span> <span class="comment">//the core series expansion </span></div>
<div class="line"><a name="l00056"></a><span class="lineno"> 56</span>  z1=pmadd(p4f_minus_half,a,p4f_half);</div>
<div class="line"><a name="l00057"></a><span class="lineno"> 57</span>  Packet4f x1=psqrt(z1);</div>
<div class="line"><a name="l00058"></a><span class="lineno"> 58</span>  Packet4f s1=pmadd(p4f_asin1, z1, p4f_asin2);</div>
<div class="line"><a name="l00059"></a><span class="lineno"> 59</span>  Packet4f s2=pmadd(s1, z1, p4f_asin3);</div>
<div class="line"><a name="l00060"></a><span class="lineno"> 60</span>  Packet4f s3=pmadd(s2,z1, p4f_asin4);</div>
<div class="line"><a name="l00061"></a><span class="lineno"> 61</span>  Packet4f s4=pmadd(s3,z1, p4f_asin5);</div>
<div class="line"><a name="l00062"></a><span class="lineno"> 62</span>  Packet4f temp=pmul(s4,z1);<span class="comment">//not really a madd but a mul by z so that the next term can be a madd</span></div>
<div class="line"><a name="l00063"></a><span class="lineno"> 63</span>  z1=pmadd(temp,x1,x1);</div>
<div class="line"><a name="l00064"></a><span class="lineno"> 64</span>  z1=padd(z1,z1);</div>
<div class="line"><a name="l00065"></a><span class="lineno"> 65</span>  z1=psub(p4f_pi_over_2,z1);</div>
<div class="line"><a name="l00066"></a><span class="lineno"> 66</span>  }</div>
<div class="line"><a name="l00067"></a><span class="lineno"> 67</span> </div>
<div class="line"><a name="l00068"></a><span class="lineno"> 68</span>  {</div>
<div class="line"><a name="l00069"></a><span class="lineno"> 69</span> <span class="comment">//the core series expansion </span></div>
<div class="line"><a name="l00070"></a><span class="lineno"> 70</span>  Packet4f x2=a;</div>
<div class="line"><a name="l00071"></a><span class="lineno"> 71</span>  z2=pmul(x2,x2);</div>
<div class="line"><a name="l00072"></a><span class="lineno"> 72</span>  Packet4f s1=pmadd(p4f_asin1, z2, p4f_asin2);</div>
<div class="line"><a name="l00073"></a><span class="lineno"> 73</span>  Packet4f s2=pmadd(s1, z2, p4f_asin3);</div>
<div class="line"><a name="l00074"></a><span class="lineno"> 74</span>  Packet4f s3=pmadd(s2,z2, p4f_asin4);</div>
<div class="line"><a name="l00075"></a><span class="lineno"> 75</span>  Packet4f s4=pmadd(s3,z2, p4f_asin5);</div>
<div class="line"><a name="l00076"></a><span class="lineno"> 76</span>  Packet4f temp=pmul(s4,z2);<span class="comment">//not really a madd but a mul by z so that the next term can be a madd</span></div>
<div class="line"><a name="l00077"></a><span class="lineno"> 77</span>  z2=pmadd(temp,x2,x2);</div>
<div class="line"><a name="l00078"></a><span class="lineno"> 78</span>  }</div>
<div class="line"><a name="l00079"></a><span class="lineno"> 79</span> </div>
<div class="line"><a name="l00080"></a><span class="lineno"> 80</span> <span class="comment">/* select the correct result from the two branch evaluations */</span></div>
<div class="line"><a name="l00081"></a><span class="lineno"> 81</span>  z1 = _mm_and_ps(branch_mask, z1);</div>
<div class="line"><a name="l00082"></a><span class="lineno"> 82</span>  z2 = _mm_andnot_ps(branch_mask, z2);</div>
<div class="line"><a name="l00083"></a><span class="lineno"> 83</span>  Packet4f z = _mm_or_ps(z1,z2);</div>
<div class="line"><a name="l00084"></a><span class="lineno"> 84</span> </div>
<div class="line"><a name="l00085"></a><span class="lineno"> 85</span> <span class="comment">/* update the sign */</span></div>
<div class="line"><a name="l00086"></a><span class="lineno"> 86</span>  <span class="keywordflow">return</span> _mm_xor_ps(z, sign_bit);</div>
<div class="line"><a name="l00087"></a><span class="lineno"> 87</span> }</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> <span class="preprocessor">#endif // EIGEN_VECTORIZE_SSE</span></div>
<div class="line"><a name="l00090"></a><span class="lineno"> 90</span> <span class="preprocessor"></span></div>
<div class="line"><a name="l00091"></a><span class="lineno"> 91</span> } <span class="comment">// end namespace internal</span></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> } <span class="comment">// end namespace Eigen</span></div>
<div class="line"><a name="l00094"></a><span class="lineno"> 94</span> </div>
<div class="line"><a name="l00095"></a><span class="lineno"> 95</span> <span class="preprocessor">#endif // EIGEN_MOREVECTORIZATION_MATHFUNCTIONS_H</span></div>
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