1 | // This file is part of Eigen, a lightweight C++ template library
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2 | // for linear algebra.
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3 | //
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4 | // Copyright (C) 2009 Rohit Garg <rpg.314@gmail.com>
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5 | // Copyright (C) 2009 Benoit Jacob <jacob.benoit.1@gmail.com>
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6 | //
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7 | // This Source Code Form is subject to the terms of the Mozilla
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8 | // Public License v. 2.0. If a copy of the MPL was not distributed
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9 | // with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
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10 |
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11 | #ifndef EIGEN_MOREVECTORIZATION_MATHFUNCTIONS_H
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12 | #define EIGEN_MOREVECTORIZATION_MATHFUNCTIONS_H
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13 |
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14 | namespace Eigen {
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15 |
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16 | namespace internal {
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17 |
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18 | /** \internal \returns the arcsin of \a a (coeff-wise) */
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19 | template<typename Packet> inline static Packet pasin(Packet a) { return std::asin(a); }
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20 |
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21 | #ifdef EIGEN_VECTORIZE_SSE
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22 |
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23 | template<> EIGEN_DONT_INLINE Packet4f pasin(Packet4f x)
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24 | {
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25 | _EIGEN_DECLARE_CONST_Packet4f(half, 0.5);
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26 | _EIGEN_DECLARE_CONST_Packet4f(minus_half, -0.5);
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27 | _EIGEN_DECLARE_CONST_Packet4f(3half, 1.5);
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28 |
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29 | _EIGEN_DECLARE_CONST_Packet4f_FROM_INT(sign_mask, 0x80000000);
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30 |
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31 | _EIGEN_DECLARE_CONST_Packet4f(pi, 3.141592654);
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32 | _EIGEN_DECLARE_CONST_Packet4f(pi_over_2, 3.141592654*0.5);
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33 |
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34 | _EIGEN_DECLARE_CONST_Packet4f(asin1, 4.2163199048E-2);
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35 | _EIGEN_DECLARE_CONST_Packet4f(asin2, 2.4181311049E-2);
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36 | _EIGEN_DECLARE_CONST_Packet4f(asin3, 4.5470025998E-2);
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37 | _EIGEN_DECLARE_CONST_Packet4f(asin4, 7.4953002686E-2);
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38 | _EIGEN_DECLARE_CONST_Packet4f(asin5, 1.6666752422E-1);
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39 |
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40 | Packet4f a = pabs(x);//got the absolute value
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41 |
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42 | Packet4f sign_bit= _mm_and_ps(x, p4f_sign_mask);//extracted the sign bit
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43 |
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44 | Packet4f z1,z2;//will need them during computation
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45 |
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46 |
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47 | //will compute the two branches for asin
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48 | //so first compare with half
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49 |
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50 | Packet4f branch_mask= _mm_cmpgt_ps(a, p4f_half);//this is to select which branch to take
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51 | //both will be taken, and finally results will be merged
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52 | //the branch for values >0.5
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53 |
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54 | {
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55 | //the core series expansion
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56 | z1=pmadd(p4f_minus_half,a,p4f_half);
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57 | Packet4f x1=psqrt(z1);
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58 | Packet4f s1=pmadd(p4f_asin1, z1, p4f_asin2);
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59 | Packet4f s2=pmadd(s1, z1, p4f_asin3);
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60 | Packet4f s3=pmadd(s2,z1, p4f_asin4);
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61 | Packet4f s4=pmadd(s3,z1, p4f_asin5);
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62 | Packet4f temp=pmul(s4,z1);//not really a madd but a mul by z so that the next term can be a madd
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63 | z1=pmadd(temp,x1,x1);
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64 | z1=padd(z1,z1);
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65 | z1=psub(p4f_pi_over_2,z1);
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66 | }
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67 |
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68 | {
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69 | //the core series expansion
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70 | Packet4f x2=a;
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71 | z2=pmul(x2,x2);
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72 | Packet4f s1=pmadd(p4f_asin1, z2, p4f_asin2);
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73 | Packet4f s2=pmadd(s1, z2, p4f_asin3);
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74 | Packet4f s3=pmadd(s2,z2, p4f_asin4);
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75 | Packet4f s4=pmadd(s3,z2, p4f_asin5);
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76 | Packet4f temp=pmul(s4,z2);//not really a madd but a mul by z so that the next term can be a madd
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77 | z2=pmadd(temp,x2,x2);
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78 | }
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79 |
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80 | /* select the correct result from the two branch evaluations */
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81 | z1 = _mm_and_ps(branch_mask, z1);
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82 | z2 = _mm_andnot_ps(branch_mask, z2);
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83 | Packet4f z = _mm_or_ps(z1,z2);
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84 |
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85 | /* update the sign */
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86 | return _mm_xor_ps(z, sign_bit);
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87 | }
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88 |
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89 | #endif // EIGEN_VECTORIZE_SSE
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90 |
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91 | } // end namespace internal
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92 |
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93 | } // end namespace Eigen
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94 |
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95 | #endif // EIGEN_MOREVECTORIZATION_MATHFUNCTIONS_H
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