unsupported/Eigen/src/MoreVectorization/MathFunctions.h

// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2009 Rohit Garg <rpg.314@gmail.com>
// Copyright (C) 2009 Benoit Jacob <jacob.benoit.1@gmail.com>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.

#ifndef EIGEN_MOREVECTORIZATION_MATHFUNCTIONS_H
#define EIGEN_MOREVECTORIZATION_MATHFUNCTIONS_H

// IWYU pragma: private
#include "./InternalHeaderCheck.h"

namespace Eigen {

namespace internal {

/** \internal \returns the arcsin of \a a (coeff-wise) */
template <typename Packet>
inline static Packet pasin(Packet a) {
  return std::asin(a);
}

#ifdef EIGEN_VECTORIZE_SSE

template <>
EIGEN_DONT_INLINE Packet4f pasin(Packet4f x) {
  EIGEN_DECLARE_CONST_Packet4f(half, 0.5);
  EIGEN_DECLARE_CONST_Packet4f(minus_half, -0.5);
  EIGEN_DECLARE_CONST_Packet4f(3half, 1.5);

  EIGEN_DECLARE_CONST_Packet4f_FROM_INT(sign_mask, 0x80000000);

  EIGEN_DECLARE_CONST_Packet4f(pi, 3.141592654);
  EIGEN_DECLARE_CONST_Packet4f(pi_over_2, 3.141592654 * 0.5);

  EIGEN_DECLARE_CONST_Packet4f(asin1, 4.2163199048E-2);
  EIGEN_DECLARE_CONST_Packet4f(asin2, 2.4181311049E-2);
  EIGEN_DECLARE_CONST_Packet4f(asin3, 4.5470025998E-2);
  EIGEN_DECLARE_CONST_Packet4f(asin4, 7.4953002686E-2);
  EIGEN_DECLARE_CONST_Packet4f(asin5, 1.6666752422E-1);

  Packet4f a = pabs(x);  // got the absolute value

  Packet4f sign_bit = _mm_and_ps(x, p4f_sign_mask);  // extracted the sign bit

  Packet4f z1, z2;  // will need them during computation

  // will compute the two branches for asin
  // so first compare with half

  Packet4f branch_mask = _mm_cmpgt_ps(a, p4f_half);  // this is to select which branch to take
  // both will be taken, and finally results will be merged
  // the branch for values >0.5

  {
    // the core series expansion
    z1 = pmadd(p4f_minus_half, a, p4f_half);
    Packet4f x1 = psqrt(z1);
    Packet4f s1 = pmadd(p4f_asin1, z1, p4f_asin2);
    Packet4f s2 = pmadd(s1, z1, p4f_asin3);
    Packet4f s3 = pmadd(s2, z1, p4f_asin4);
    Packet4f s4 = pmadd(s3, z1, p4f_asin5);
    Packet4f temp = pmul(s4, z1);  // not really a madd but a mul by z so that the next term can be a madd
    z1 = pmadd(temp, x1, x1);
    z1 = padd(z1, z1);
    z1 = psub(p4f_pi_over_2, z1);
  }

  {
    // the core series expansion
    Packet4f x2 = a;
    z2 = pmul(x2, x2);
    Packet4f s1 = pmadd(p4f_asin1, z2, p4f_asin2);
    Packet4f s2 = pmadd(s1, z2, p4f_asin3);
    Packet4f s3 = pmadd(s2, z2, p4f_asin4);
    Packet4f s4 = pmadd(s3, z2, p4f_asin5);
    Packet4f temp = pmul(s4, z2);  // not really a madd but a mul by z so that the next term can be a madd
    z2 = pmadd(temp, x2, x2);
  }

  /* select the correct result from the two branch evaluations */
  z1 = _mm_and_ps(branch_mask, z1);
  z2 = _mm_andnot_ps(branch_mask, z2);
  Packet4f z = _mm_or_ps(z1, z2);

  /* update the sign */
  return _mm_xor_ps(z, sign_bit);
}

#endif  // EIGEN_VECTORIZE_SSE

}  // end namespace internal

}  // end namespace Eigen

#endif  // EIGEN_MOREVECTORIZATION_MATHFUNCTIONS_H