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95 lines
3.1 KiB
95 lines
3.1 KiB
// This file is part of Eigen, a lightweight C++ template library
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// for linear algebra.
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//
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// Copyright (C) 2009 Rohit Garg <rpg.314@gmail.com>
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// Copyright (C) 2009 Benoit Jacob <jacob.benoit.1@gmail.com>
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//
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// This Source Code Form is subject to the terms of the Mozilla
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// Public License v. 2.0. If a copy of the MPL was not distributed
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// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
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#ifndef STORMEIGEN_MOREVECTORIZATION_MATHFUNCTIONS_H
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#define STORMEIGEN_MOREVECTORIZATION_MATHFUNCTIONS_H
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namespace StormEigen {
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namespace internal {
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/** \internal \returns the arcsin of \a a (coeff-wise) */
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template<typename Packet> inline static Packet pasin(Packet a) { return std::asin(a); }
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#ifdef STORMEIGEN_VECTORIZE_SSE
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template<> STORMEIGEN_DONT_INLINE Packet4f pasin(Packet4f x)
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{
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_STORMEIGEN_DECLARE_CONST_Packet4f(half, 0.5);
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_STORMEIGEN_DECLARE_CONST_Packet4f(minus_half, -0.5);
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_STORMEIGEN_DECLARE_CONST_Packet4f(3half, 1.5);
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_STORMEIGEN_DECLARE_CONST_Packet4f_FROM_INT(sign_mask, 0x80000000);
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_STORMEIGEN_DECLARE_CONST_Packet4f(pi, 3.141592654);
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_STORMEIGEN_DECLARE_CONST_Packet4f(pi_over_2, 3.141592654*0.5);
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_STORMEIGEN_DECLARE_CONST_Packet4f(asin1, 4.2163199048E-2);
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_STORMEIGEN_DECLARE_CONST_Packet4f(asin2, 2.4181311049E-2);
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_STORMEIGEN_DECLARE_CONST_Packet4f(asin3, 4.5470025998E-2);
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_STORMEIGEN_DECLARE_CONST_Packet4f(asin4, 7.4953002686E-2);
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_STORMEIGEN_DECLARE_CONST_Packet4f(asin5, 1.6666752422E-1);
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Packet4f a = pabs(x);//got the absolute value
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Packet4f sign_bit= _mm_and_ps(x, p4f_sign_mask);//extracted the sign bit
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Packet4f z1,z2;//will need them during computation
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//will compute the two branches for asin
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//so first compare with half
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Packet4f branch_mask= _mm_cmpgt_ps(a, p4f_half);//this is to select which branch to take
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//both will be taken, and finally results will be merged
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//the branch for values >0.5
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{
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//the core series expansion
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z1=pmadd(p4f_minus_half,a,p4f_half);
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Packet4f x1=psqrt(z1);
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Packet4f s1=pmadd(p4f_asin1, z1, p4f_asin2);
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Packet4f s2=pmadd(s1, z1, p4f_asin3);
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Packet4f s3=pmadd(s2,z1, p4f_asin4);
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Packet4f s4=pmadd(s3,z1, p4f_asin5);
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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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z1=pmadd(temp,x1,x1);
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z1=padd(z1,z1);
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z1=psub(p4f_pi_over_2,z1);
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}
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{
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//the core series expansion
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Packet4f x2=a;
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z2=pmul(x2,x2);
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Packet4f s1=pmadd(p4f_asin1, z2, p4f_asin2);
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Packet4f s2=pmadd(s1, z2, p4f_asin3);
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Packet4f s3=pmadd(s2,z2, p4f_asin4);
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Packet4f s4=pmadd(s3,z2, p4f_asin5);
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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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z2=pmadd(temp,x2,x2);
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}
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/* select the correct result from the two branch evaluations */
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z1 = _mm_and_ps(branch_mask, z1);
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z2 = _mm_andnot_ps(branch_mask, z2);
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Packet4f z = _mm_or_ps(z1,z2);
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/* update the sign */
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return _mm_xor_ps(z, sign_bit);
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}
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#endif // STORMEIGEN_VECTORIZE_SSE
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} // end namespace internal
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} // end namespace StormEigen
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#endif // STORMEIGEN_MOREVECTORIZATION_MATHFUNCTIONS_H
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