EVOLUTION-MANAGER

Edit File: tanh_sinh_constants.hpp

// Copyright Nick Thompson, 2017 // Use, modification and distribution are subject to the // Boost Software License, Version 1.0. // (See accompanying file LICENSE_1_0.txt // or copy at http://www.boost.org/LICENSE_1_0.txt) #ifndef BOOST_MATH_QUADRATURE_DETAIL_TANH_SINH_CONSTANTS_HPP #define BOOST_MATH_QUADRATURE_DETAIL_TANH_SINH_CONSTANTS_HPP #include <boost/type_traits/is_constructible.hpp> #include <boost/lexical_cast.hpp> namespace boost { namespace math { namespace quadrature { namespace detail { template <class Real> inline Real abscissa_at_t(const Real& t) { using std::tanh; using std::sinh; return tanh(constants::half_pi<Real>()*sinh(t)); } template <class Real> inline Real weight_at_t(const Real& t) { using std::cosh; using std::sinh; Real cs = cosh(constants::half_pi<Real>() * sinh(t)); return constants::half_pi<Real>() * cosh(t) / (cs * cs); } template <class Real> inline Real abscissa_complement_at_t(const Real& t) { using std::cosh; using std::exp; using std::sinh; Real u2 = constants::half_pi<Real>() * sinh(t); return 1 / (exp(u2) *cosh(u2)); } template <class Real> inline Real t_from_abscissa_complement(const Real& x) { using std::log; using std::sqrt; Real l = log(sqrt((2 - x) / x)); return log((sqrt(4 * l * l + constants::pi<Real>() * constants::pi<Real>()) + 2 * l) / constants::pi<Real>()); }; template<class Real, int precision> class tanh_sinh_detail_constants { static const int initializer_selector = !std::numeric_limits<Real>::is_specialized || (std::numeric_limits<Real>::radix != 2) ? 0 : (std::numeric_limits<Real>::digits < 30) && (std::numeric_limits<Real>::max_exponent <= 128) ? 1 : 0; public: tanh_sinh_detail_constants(std::size_t max_refinements, std::size_t initial_commit = 4) : m_max_refinements(max_refinements), m_committed_refinements(initial_commit) { typedef mpl::int_<initializer_selector> tag_type; init(tag_type()); } void init(const mpl::int_<0>&) { using std::tanh; using std::sinh; using std::asinh; using std::atanh; using boost::math::constants::half_pi; using boost::math::constants::pi; using boost::math::constants::two_div_pi; m_inital_row_length = 7; std::size_t first_complement = 0; m_t_max = m_inital_row_length; m_t_crossover = t_from_abscissa_complement(Real(0.5f)); m_abscissas.assign(m_max_refinements + 1, std::vector<Real>()); m_weights.assign(m_max_refinements + 1, std::vector<Real>()); m_first_complements.assign(m_max_refinements + 1, 0); // // First row is special: // Real h = m_t_max / m_inital_row_length; std::vector<Real> temp(m_inital_row_length + 1, Real(0)); for (std::size_t i = 0; i < m_inital_row_length; ++i) { Real t = h * i; if ((first_complement < 0) && (t < m_t_crossover)) first_complement = i; temp[i] = t < m_t_crossover ? abscissa_at_t(t) : -abscissa_complement_at_t(t); } temp[m_inital_row_length] = abscissa_complement_at_t(m_t_max); m_abscissas[0].swap(temp); m_first_complements[0] = first_complement; temp.assign(m_inital_row_length + 1, Real(0)); for (std::size_t i = 0; i < m_inital_row_length; ++i) temp[i] = weight_at_t(Real(h * i)); temp[m_inital_row_length] = weight_at_t(m_t_max); m_weights[0].swap(temp); for (std::size_t row = 1; row <= m_committed_refinements; ++row) { h /= 2; first_complement = 0; for (Real pos = h; pos < m_t_max; pos += 2 * h) { if (pos < m_t_crossover) ++first_complement; temp.push_back(pos < m_t_crossover ? abscissa_at_t(pos) : -abscissa_complement_at_t(pos)); } m_abscissas[row].swap(temp); m_first_complements[row] = first_complement; for (Real pos = h; pos < m_t_max; pos += 2 * h) temp.push_back(weight_at_t(pos)); m_weights[row].swap(temp); } } void init(const mpl::int_<1>&) { m_inital_row_length = 4; m_abscissas.reserve(m_max_refinements + 1); m_weights.reserve(m_max_refinements + 1); m_first_complements.reserve(m_max_refinements + 1); m_abscissas = { { 0.0f, -0.04863203593f, -2.252280754e-05f, -4.294161056e-14f, -1.167648898e-37f, }, { -0.3257285078f, -0.002485143543f, -1.112433512e-08f, -5.378491591e-23f, }, { 0.3772097382f, 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1.87127733e-19f, 8.955739455e-20f, 4.235742852e-20f, 1.979436202e-20f, 9.138078558e-21f, 4.166641158e-21f, 1.876075055e-21f, 8.339901949e-22f, 3.659575236e-22f, 1.584785218e-22f, 6.771575694e-23f, 2.854281708e-23f, 1.186583858e-23f, 4.864069936e-24f, 1.965643419e-24f, 7.829165625e-25f, 3.072789229e-25f, 1.188107615e-25f, 4.524619749e-26f, 1.696710187e-26f, 6.263641003e-27f, 2.275790793e-27f, 8.136077716e-28f, 2.861306549e-28f, 9.896184197e-29f, 3.365200893e-29f, 1.124807055e-29f, 3.694460433e-30f, 1.192093301e-30f, 3.777757876e-31f, 1.175436379e-31f, 3.589879078e-32f, 1.075842686e-32f, 3.162835126e-33f, 9.118674189e-34f, 2.577393168e-34f, 7.139829504e-35f, 1.937828921e-35f, }, }; m_first_complements = { 1, 0, 1, 1, 3, 5, 11, 22, }; while (m_abscissas.size() <= m_committed_refinements) extend_refinements(); m_committed_refinements = m_abscissas.size() - 1; if (m_max_refinements >= m_abscissas.size()) { m_abscissas.resize(m_max_refinements + 1); m_weights.resize(m_max_refinements + 1); m_first_complements.resize(m_max_refinements + 1); } else { m_max_refinements = m_abscissas.size() - 1; } m_t_max = m_inital_row_length; m_t_crossover = t_from_abscissa_complement(Real(0.5f)); } void extend_refinements()const { ++m_committed_refinements; std::size_t row = m_committed_refinements; Real h = ldexp(Real(1), -static_cast<int>(row)); std::size_t first_complement = 0; for (Real pos = h; pos < m_t_max; pos += 2 * h) { if (pos < m_t_crossover) ++first_complement; m_abscissas[row].push_back(pos < m_t_crossover ? abscissa_at_t(pos) : -abscissa_complement_at_t(pos)); } m_first_complements[row] = first_complement; for (Real pos = h; pos < m_t_max; pos += 2 * h) m_weights[row].push_back(weight_at_t(pos)); } const std::vector<Real>& get_abscissa_row(std::size_t n)const { if (m_committed_refinements < n) extend_refinements(); BOOST_ASSERT(m_committed_refinements >= n); return m_abscissas[n]; } const std::vector<Real>& get_weight_row(std::size_t n)const { if (m_committed_refinements < n) extend_refinements(); BOOST_ASSERT(m_committed_refinements >= n); return m_weights[n]; } std::size_t get_first_complement_index(std::size_t n)const { if (m_committed_refinements < n) extend_refinements(); BOOST_ASSERT(m_committed_refinements >= n); return m_first_complements[n]; } protected: mutable std::vector<std::vector<Real>> m_abscissas; mutable std::vector<std::vector<Real>> m_weights; mutable std::vector<std::size_t> m_first_complements; std::size_t m_max_refinements, m_inital_row_length; mutable std::size_t m_committed_refinements; Real m_t_max, m_t_crossover; }; } } } } #endif