AS_erfc_part.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_AC_ERF_PART_HPP
#define UTILS_MATH_AC_ERF_PART_HPP
 
namespace Utils {
/** Approximate \f$ \exp(d^2) \mathrm{erfc}(d)\f$ by applying a formula from
 *  @cite abramowitz65a chapter 7.
 */
template <typename T> constexpr T AS_erfc_part(T d) {
  T const constexpr a1 = 0.254829592;
  T const constexpr a2 = -0.284496736;
  T const constexpr a3 = 1.421413741;
  T const constexpr a4 = -1.453152027;
  T const constexpr a5 = 1.061405429;
  T const constexpr p = 0.3275911;
 
  auto const t = 1.0 / (1.0 + p * d);
 
  return t * (a1 + t * (a2 + t * (a3 + t * (a4 + t * a5))));
}
} // namespace Utils
 
#endif