src/MoreVectorization/MathFunctions.h

0001 // This file is part of Eigen, a lightweight C++ template library
0002 // for linear algebra.
0003 //
0004 // Copyright (C) 2009 Rohit Garg <rpg.314@gmail.com>
0005 // Copyright (C) 2009 Benoit Jacob <jacob.benoit.1@gmail.com>
0006 //
0007 // This Source Code Form is subject to the terms of the Mozilla
0008 // Public License v. 2.0. If a copy of the MPL was not distributed
0009 // with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
0010
0011 #ifndef EIGEN_MOREVECTORIZATION_MATHFUNCTIONS_H
0012 #define EIGEN_MOREVECTORIZATION_MATHFUNCTIONS_H
0013
0014 namespace Eigen {
0015
0016 namespace internal {
0017
0018 /** \internal \returns the arcsin of \a a (coeff-wise) */
0019 template<typename Packet> inline static Packet pasin(Packet a) { return std::asin(a); }
0020
0021 #ifdef EIGEN_VECTORIZE_SSE
0022
0023 template<> EIGEN_DONT_INLINE Packet4f pasin(Packet4f x)
0024 {
0025   _EIGEN_DECLARE_CONST_Packet4f(half, 0.5);
0026   _EIGEN_DECLARE_CONST_Packet4f(minus_half, -0.5);
0027   _EIGEN_DECLARE_CONST_Packet4f(3half, 1.5);
0028
0029   _EIGEN_DECLARE_CONST_Packet4f_FROM_INT(sign_mask, 0x80000000);
0030
0031   _EIGEN_DECLARE_CONST_Packet4f(pi, 3.141592654);
0032   _EIGEN_DECLARE_CONST_Packet4f(pi_over_2, 3.141592654*0.5);
0033
0034   _EIGEN_DECLARE_CONST_Packet4f(asin1, 4.2163199048E-2);
0035   _EIGEN_DECLARE_CONST_Packet4f(asin2, 2.4181311049E-2);
0036   _EIGEN_DECLARE_CONST_Packet4f(asin3, 4.5470025998E-2);
0037   _EIGEN_DECLARE_CONST_Packet4f(asin4, 7.4953002686E-2);
0038   _EIGEN_DECLARE_CONST_Packet4f(asin5, 1.6666752422E-1);
0039
0040   Packet4f a = pabs(x);//got the absolute value
0041
0042   Packet4f sign_bit= _mm_and_ps(x, p4f_sign_mask);//extracted the sign bit
0043
0044   Packet4f z1,z2;//will need them during computation
0045
0046
0047 //will compute the two branches for asin
0048 //so first compare with half
0049
0050   Packet4f branch_mask= _mm_cmpgt_ps(a, p4f_half);//this is to select which branch to take
0051 //both will be taken, and finally results will be merged
0052 //the branch for values >0.5
0053
0054     {
0055 //the core series expansion
0056     z1=pmadd(p4f_minus_half,a,p4f_half);
0057     Packet4f x1=psqrt(z1);
0058     Packet4f s1=pmadd(p4f_asin1, z1, p4f_asin2);
0059     Packet4f s2=pmadd(s1, z1, p4f_asin3);
0060     Packet4f s3=pmadd(s2,z1, p4f_asin4);
0061     Packet4f s4=pmadd(s3,z1, p4f_asin5);
0062     Packet4f temp=pmul(s4,z1);//not really a madd but a mul by z so that the next term can be a madd
0063     z1=pmadd(temp,x1,x1);
0064     z1=padd(z1,z1);
0065     z1=psub(p4f_pi_over_2,z1);
0066     }
0067
0068     {
0069 //the core series expansion
0070     Packet4f x2=a;
0071     z2=pmul(x2,x2);
0072     Packet4f s1=pmadd(p4f_asin1, z2, p4f_asin2);
0073     Packet4f s2=pmadd(s1, z2, p4f_asin3);
0074     Packet4f s3=pmadd(s2,z2, p4f_asin4);
0075     Packet4f s4=pmadd(s3,z2, p4f_asin5);
0076     Packet4f temp=pmul(s4,z2);//not really a madd but a mul by z so that the next term can be a madd
0077     z2=pmadd(temp,x2,x2);
0078     }
0079
0080 /* select the correct result from the two branch evaluations */
0081   z1  = _mm_and_ps(branch_mask, z1);
0082   z2  = _mm_andnot_ps(branch_mask, z2);
0083   Packet4f z  = _mm_or_ps(z1,z2);
0084
0085 /* update the sign */
0086   return _mm_xor_ps(z, sign_bit);
0087 }
0088
0089 #endif // EIGEN_VECTORIZE_SSE
0090
0091 } // end namespace internal
0092
0093 } // end namespace Eigen
0094
0095 #endif // EIGEN_MOREVECTORIZATION_MATHFUNCTIONS_H