1 // This file is part of Eigen, a lightweight C++ template library 2 // for linear algebra. 3 // 4 // Copyright (C) 2009 Rohit Garg <rpg.314 (at) gmail.com> 5 // Copyright (C) 2009 Benoit Jacob <jacob.benoit.1 (at) gmail.com> 6 // 7 // This Source Code Form is subject to the terms of the Mozilla 8 // Public License v. 2.0. If a copy of the MPL was not distributed 9 // with this file, You can obtain one at http://mozilla.org/MPL/2.0/. 10 11 #ifndef EIGEN_MOREVECTORIZATION_MATHFUNCTIONS_H 12 #define EIGEN_MOREVECTORIZATION_MATHFUNCTIONS_H 13 14 namespace Eigen { 15 16 namespace internal { 17 18 /** \internal \returns the arcsin of \a a (coeff-wise) */ 19 template<typename Packet> inline static Packet pasin(Packet a) { return std::asin(a); } 20 21 #ifdef EIGEN_VECTORIZE_SSE 22 23 template<> EIGEN_DONT_INLINE Packet4f pasin(Packet4f x) 24 { 25 _EIGEN_DECLARE_CONST_Packet4f(half, 0.5); 26 _EIGEN_DECLARE_CONST_Packet4f(minus_half, -0.5); 27 _EIGEN_DECLARE_CONST_Packet4f(3half, 1.5); 28 29 _EIGEN_DECLARE_CONST_Packet4f_FROM_INT(sign_mask, 0x80000000); 30 31 _EIGEN_DECLARE_CONST_Packet4f(pi, 3.141592654); 32 _EIGEN_DECLARE_CONST_Packet4f(pi_over_2, 3.141592654*0.5); 33 34 _EIGEN_DECLARE_CONST_Packet4f(asin1, 4.2163199048E-2); 35 _EIGEN_DECLARE_CONST_Packet4f(asin2, 2.4181311049E-2); 36 _EIGEN_DECLARE_CONST_Packet4f(asin3, 4.5470025998E-2); 37 _EIGEN_DECLARE_CONST_Packet4f(asin4, 7.4953002686E-2); 38 _EIGEN_DECLARE_CONST_Packet4f(asin5, 1.6666752422E-1); 39 40 Packet4f a = pabs(x);//got the absolute value 41 42 Packet4f sign_bit= _mm_and_ps(x, p4f_sign_mask);//extracted the sign bit 43 44 Packet4f z1,z2;//will need them during computation 45 46 47 //will compute the two branches for asin 48 //so first compare with half 49 50 Packet4f branch_mask= _mm_cmpgt_ps(a, p4f_half);//this is to select which branch to take 51 //both will be taken, and finally results will be merged 52 //the branch for values >0.5 53 54 { 55 //the core series expansion 56 z1=pmadd(p4f_minus_half,a,p4f_half); 57 Packet4f x1=psqrt(z1); 58 Packet4f s1=pmadd(p4f_asin1, z1, p4f_asin2); 59 Packet4f s2=pmadd(s1, z1, p4f_asin3); 60 Packet4f s3=pmadd(s2,z1, p4f_asin4); 61 Packet4f s4=pmadd(s3,z1, p4f_asin5); 62 Packet4f temp=pmul(s4,z1);//not really a madd but a mul by z so that the next term can be a madd 63 z1=pmadd(temp,x1,x1); 64 z1=padd(z1,z1); 65 z1=psub(p4f_pi_over_2,z1); 66 } 67 68 { 69 //the core series expansion 70 Packet4f x2=a; 71 z2=pmul(x2,x2); 72 Packet4f s1=pmadd(p4f_asin1, z2, p4f_asin2); 73 Packet4f s2=pmadd(s1, z2, p4f_asin3); 74 Packet4f s3=pmadd(s2,z2, p4f_asin4); 75 Packet4f s4=pmadd(s3,z2, p4f_asin5); 76 Packet4f temp=pmul(s4,z2);//not really a madd but a mul by z so that the next term can be a madd 77 z2=pmadd(temp,x2,x2); 78 } 79 80 /* select the correct result from the two branch evaluations */ 81 z1 = _mm_and_ps(branch_mask, z1); 82 z2 = _mm_andnot_ps(branch_mask, z2); 83 Packet4f z = _mm_or_ps(z1,z2); 84 85 /* update the sign */ 86 return _mm_xor_ps(z, sign_bit); 87 } 88 89 #endif // EIGEN_VECTORIZE_SSE 90 91 } // end namespace internal 92 93 } // end namespace Eigen 94 95 #endif // EIGEN_MOREVECTORIZATION_MATHFUNCTIONS_H 96
