Quelle MathFunctions.h Sprache: C

// 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

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

quality100%

¤ Dauer der Verarbeitung: 0.21 Sekunden (vorverarbeitet) ¤

Wurzel

Suchen

Beweissystem der NASA

Beweissystem Isabelle

NIST Cobol Testsuite

Cephes Mathematical Library

Wiener Entwicklungsmethode

Haftungshinweis

Die Informationen auf dieser Webseite wurden nach bestem Wissen sorgfältig zusammengestellt. Es wird jedoch weder Vollständigkeit, noch Richtigkeit, noch Qualität der bereit gestellten Informationen zugesichert.

Bemerkung:

Die farbliche Syntaxdarstellung ist noch experimentell.