SpecialFunctions.cc

/**************************************************************************
 * BASF2 (Belle Analysis Framework 2)                                     *
 * Copyright(C) 2016 - Belle II Collaboration                             *
 *                                                                        *
 * Author: The Belle II Collaboration                                     *
 * Contributors: Oliver Frost                                             *
 *                                                                        *
 * This software is provided "as is" without any warranty.                *
 **************************************************************************/
#include <tracking/trackFindingCDC/numerics/SpecialFunctions.h>
 
#include <boost/math/tools/precision.hpp>
#include <boost/math/special_functions/sinc.hpp>
 
#include <cmath>
 
using namespace Belle2;
using namespace TrackFindingCDC;
 
double TrackFindingCDC::sinc(double x)
{
  return boost::math::sinc_pi(x);
}
 
double TrackFindingCDC::asinc(double x)
{
  // Implementation inspired by BOOST's sinc
  BOOST_MATH_STD_USING;
 
  using namespace boost::math;
  double const taylor_n_bound = tools::forth_root_epsilon<double>();
 
  if (abs(x) >= taylor_n_bound) {
    return asin(x) / x;
  } else {
    // approximation by taylor series in x at 0 up to order 0
    double result = 1.0;
 
    double const taylor_0_bound = tools::epsilon<double>();
    if (abs(x) >= taylor_0_bound) {
      double x2 = x * x;
      // approximation by taylor series in x at 0 up to order 2
      result += x2 / 6.0;
 
      double const taylor_2_bound = tools::root_epsilon<double>();
      if (abs(x) >= taylor_2_bound) {
        // approximation by taylor series in x at 0 up to order 4
        result += x2 * x2 * (3.0 / 40.0);
      }
    }
    return result;
  }
}