sinc.hpp

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/*
 * Copyright (C) 2010-2022 The ESPResSo project
 * Copyright (C) 2002,2003,2004,2005,2006,2007,2008,2009,2010
 *   Max-Planck-Institute for Polymer Research, Theory Group
 *
 * This file is part of ESPResSo.
 *
 * ESPResSo is free software: you can redistribute it and/or modify
 * it under the terms of the GNU General Public License as published by
 * the Free Software Foundation, either version 3 of the License, or
 * (at your option) any later version.
 *
 * ESPResSo is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 * GNU General Public License for more details.
 *
 * You should have received a copy of the GNU General Public License
 * along with this program.  If not, see <http://www.gnu.org/licenses/>.
 */
 
#ifndef UTILS_MATH_SINC_HPP
#define UTILS_MATH_SINC_HPP
 
#include "utils/constants.hpp"
#include "utils/device_qualifier.hpp"
#include "utils/math/abs.hpp"
 
#include <cmath>
 
namespace Utils {
/**
 * @brief Calculates the sinc-function as sin(PI*x)/(PI*x).
 *
 * (same convention as in @cite hockney88a). In order to avoid
 * divisions by 0, arguments, whose modulus is smaller than epsi, will
 * be evaluated by an 8th order Taylor expansion of the sinc
 * function. Note that the difference between sinc(x) and this
 * expansion is smaller than 0.235e-12, if x is smaller than 0.1. (The
 * next term in the expansion is the 10th order contribution
 * PI^10/39916800 * x^10 = 0.2346...*x^12). This expansion should
 * also save time, since it reduces the number of function calls to
 * sin().
 */
template <typename T> DEVICE_QUALIFIER T sinc(T d) {
  const constexpr T epsi = T(0.1);
 
  const auto PId = pi<T>() * d;
 
  if (::Utils::abs(d) > epsi)
    return sin(PId) / PId;
 
  /* Coefficients of the Taylor expansion of sinc */
  const constexpr T c2 = T(-0.1666666666667e-0);
  const constexpr T c4 = T(0.8333333333333e-2);
  const constexpr T c6 = T(-0.1984126984127e-3);
  const constexpr T c8 = T(0.2755731922399e-5);
 
  const auto PId2 = PId * PId;
  return T(1) + PId2 * (c2 + PId2 * (c4 + PId2 * (c6 + PId2 * c8)));
}
} // namespace Utils
 
#endif