FM / detail

/usr/include/boost/math/quadrature/detail/

/usr/include/boost/math/quadrature/detail

Name	Size	Mode	Actions
exp_sinh_detail.hpp	549758	0644	edit dl rm
ooura_fourier_integrals_detail.hpp	23586	0644	edit dl rm
sinh_sinh_detail.hpp	274286	0644	edit dl rm
tanh_sinh_constants.hpp	26966	0644	edit dl rm
tanh_sinh_detail.hpp	280776	0644	edit dl rm

Edit: /usr/include/boost/math/quadrature/detail/tanh_sinh_constants.hpp (26966B)

// 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 boost::integral_constant<int, initializer_selector> tag_type;
                  init(tag_type());
               }

void init(const boost::integral_constant<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 boost::integral_constant<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, -0.1404309413f, -0.01295943949f, -0.0003117359716f, -7.952628853e-07f, -4.714355182e-11f, -5.415222824e-18f, -2.040300394e-29f, },
                     { 0.1943570033f, -0.4608532946f, -0.219392561f, -0.08512073674f, -0.0260331318f, -0.005944493369f, -0.0009348035442f, -9.061530486e-05f, -4.683958779e-06f, -1.072183876e-07f, -8.572949078e-10f, -1.767834693e-12f, -6.374878495e-16f, -2.442937279e-20f, -5.251546473e-26f, -2.789467162e-33f, },
                     { 0.09792388529f, 0.2878799327f, 0.4612535439f, -0.3897263425f, -0.2689819652f, -0.1766829945f, -0.1101085972f, -0.06483914248f, -0.03588783578f, -0.01854517332f, -0.008873007558f, -0.003891334562f, -0.001545791232f, -0.0005485655647f, -0.0001711779271f, -4.612899437e-05f, -1.051798518e-05f, -1.982859405e-06f, -3.011058474e-07f, -3.576091908e-08f, -3.212800902e-09f, -2.102671378e-10f, -9.606066479e-12f, -2.919026641e-13f, -5.586116639e-15f, -6.328207135e-17f, -3.956461339e-19f, -1.260975845e-21f, -1.872492175e-24f, -1.170030294e-27f, -2.740986178e-31f, -2.112282721e-35f, },
                     { 0.04905596731f, 0.1464179843f, 0.2415663195f, 0.3331422646f, 0.4199521113f, -0.4989866106f, -0.4244155094f, -0.356823241f, -0.2964499949f, -0.2433060914f, -0.1972012587f, -0.1577807536f, -0.1245646024f, -0.09698671849f, -0.07443136593f, -0.05626521395f, -0.04186397729f, -0.0306332671f, -0.02202376481f, -0.01554116883f, -0.01075156891f, -0.007283002803f, -0.004823973845f, -0.003119681872f, -0.001966663685f, -0.001206465701f, -0.0007188880782f, -0.0004152496485f, -0.0002320284004f, -0.0001251349512f, -6.498007492e-05f, -3.240693206e-05f, -1.548009773e-05f, -7.062123337e-06f, -3.06755081e-06f, -1.264528134e-06f, -4.929942806e-07f, -1.811062872e-07f, -6.244592163e-08f, -2.01254968e-08f, -6.035865798e-09f, -1.676638052e-09f, -4.292122274e-10f, -1.007222767e-10f, -2.154466259e-11f, -4.175393124e-12f, -7.284737264e-13f, -1.136386985e-13f, -1.57355351e-14f, -1.91921891e-15f, -2.044959541e-16f, -1.886958307e-17f, -1.493871649e-18f, -1.00469381e-19f, -5.679929178e-21f, -2.669103953e-22f, -1.030178138e-23f, -3.224484876e-25f, -8.0747829e-27f, -1.594654602e-28f, -2.445723975e-30f, -2.865919772e-32f, -2.521682525e-34f, -1.63551444e-36f, },
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                     { 0.01227135512f, 0.03680228095f, 0.06129788941f, 0.08573475488f, 0.1100896299f, 0.1343395153f, 0.1584617283f, 0.1824339697f, 0.2062343883f, 0.2298416433f, 0.2532349634f, 0.2763942036f, 0.2992998981f, 0.3219333097f, 0.3442764756f, 0.3663122492f, 0.3880243378f, 0.4093973357f, 0.4304167537f, 0.4510690435f, 0.4713416183f, 0.4912228687f, -0.489297826f, -0.4702300899f, -0.4515825479f, -0.4333628262f, -0.4155775577f, -0.39823239f, -0.3813319982f, -0.3648801001f, -0.3488794756f, -0.3333319877f, -0.318238608f, -0.3035994429f, -0.2894137636f, -0.275680037f, -0.2623959593f, -0.2495584902f, -0.2371638893f, -0.2252077531f, -0.2136850525f, -0.2025901721f, -0.1919169483f, -0.1816587092f, -0.1718083133f, -0.1623581887f, -0.1533003716f, -0.1446265448f, -0.1363280753f, -0.1283960505f, -0.120821315f, -0.113594505f, -0.1067060822f, -0.1001463668f, -0.09390556883f, -0.08797381831f, -0.08234119416f, -0.07699775172f, -0.07193354881f, -0.06713867034f, -0.0626032516f, -0.0583175f, -0.0542717154f, -0.050456309f, -0.0468618209f, -0.0434789361f, -0.0402984993f, -0.03731152826f, -0.0345092259f, -0.03188299107f, -0.02942442821f, -0.02712535566f, -0.02497781299f, -0.02297406711f, -0.02110661737f, -0.01936819969f, -0.01775178968f, -0.01625060483f, -0.01485810598f, -0.01356799776f, -0.01237422849f, -0.01127098916f, -0.01025271192f, -0.009314067826f, -0.008449964034f, -0.007655540506f, -0.006926166179f, -0.006257434709f, -0.005645159804f, -0.005085370197f, -0.004574304294f, -0.004108404533f, -0.003684311494f, -0.003298857801f, -0.002949061834f, -0.002632121306f, -0.002345406714f, -0.002086454715f, -0.001852961444f, -0.001642775797f, -0.001453892723f, -0.001284446528f, -0.001132704236f, -0.0009970590063f, -0.0008760236476f, -0.0007682242321f, -0.0006723938372f, -0.000587366425f, -0.0005120708762f, -0.0004455251889f, -0.0003868308567f, -0.0003351674323f, -0.0002897872882f, -0.0002500105784f, -0.0002152204083f, -0.0001848582177f, -0.0001584193765f, -0.0001354489984f, -0.0001155379702f, -9.8319198e-05f, -8.346406605e-05f, -7.067910812e-05f, -5.970288552e-05f, -5.030306831e-05f, -4.227371392e-05f, -3.543273737e-05f, -2.961956641e-05f, -2.469297451e-05f, -2.052908425e-05f, -1.701953324e-05f, -1.406979453e-05f, -1.159764317e-05f, -9.531760786e-06f, -7.810469566e-06f, -6.380587461e-06f, -5.196396351e-06f, -4.218715072e-06f, -3.414069429e-06f, -2.753951574e-06f, -2.214161365e-06f, -1.774222689e-06f, -1.416868016e-06f, -1.127584838e-06f, -8.942180042e-07f, -7.066223315e-07f, -5.563602711e-07f, -4.364397681e-07f, -3.410878407e-07f, -2.65555767e-07f, -2.059521239e-07f, -1.591002641e-07f, -1.224171449e-07f, -9.381073151e-08f, -7.159348586e-08f, -5.440972705e-08f, -4.117489851e-08f, -3.102500976e-08f, -2.327473287e-08f, -1.738282654e-08f, -1.292373523e-08f, -9.564367214e-09f, -7.045195508e-09f, -5.164949276e-09f, -3.768272997e-09f, -2.735826254e-09f, -1.976380568e-09f, -1.420541964e-09f, -1.015790099e-09f, -7.225780068e-10f, -5.112816947e-10f, -3.598270551e-10f, -2.518536224e-10f, -1.753014775e-10f, -1.213298105e-10f, -8.349395075e-11f, -5.712266027e-11f, -3.8849686e-11f, -2.626342738e-11f, -1.764649978e-11f, -1.178329832e-11f, -7.818680628e-12f, -5.154836404e-12f, -3.376501461e-12f, -2.19707447e-12f, -1.420047367e-12f, -9.115800793e-13f, -5.811306251e-13f, -3.67867911e-13f, -2.312068904e-13f, -1.442617249e-13f, -8.934966665e-14f, -5.492567772e-14f, -3.35078831e-14f, -2.02840764e-14f, -1.218279513e-14f, -7.258853736e-15f, -4.290062787e-15f, -2.514652539e-15f, -1.461687113e-15f, -8.424330958e-16f, -4.81351759e-16f, -2.726317943e-16f, -1.530442297e-16f, -8.513785725e-17f, -4.692795039e-17f, -2.562597595e-17f, -1.386133467e-17f, -7.425750192e-18f, -3.939309402e-18f, -2.069079146e-18f, -1.075828622e-18f, -5.536671017e-19f, -2.819834004e-19f, -1.421006375e-19f, -7.084243878e-20f, -3.493350557e-20f, -1.703597751e-20f, -8.214706044e-21f, -3.915973438e-21f, -1.845149816e-21f, -8.591874581e-22f, -3.953006958e-22f, -1.7966698e-22f, -8.065408821e-23f, -3.575337212e-23f, -1.564782132e-23f, -6.760041764e-24f, -2.882136323e-24f, -1.212436233e-24f, -5.031421831e-25f, -2.059286312e-25f, -8.310787798e-26f, -3.306518068e-26f, -1.296597346e-26f, -5.010091032e-27f, -1.907179385e-27f, -7.150567334e-28f, -2.639906037e-28f, -9.594664542e-29f, -3.432078099e-29f, -1.207985066e-29f, -4.182464721e-30f, -1.424153707e-30f, -4.767833382e-31f, -1.568949178e-31f, -5.073438855e-32f, -1.611691916e-32f, -5.028356694e-33f, -1.540320437e-33f, -4.631392443e-34f, -1.366470225e-34f, -3.955008527e-35f, -1.122591825e-35f, -3.123848743e-36f, -8.519540247e-37f, -2.276473481e-37f, },
                  };
                  m_weights = {
                     { 1.570796327f, 0.2300223945f, 0.0002662005138f, 1.358178427e-12f, 1.001741678e-35f, },
                     { 0.9659765794f, 0.01834316699f, 2.143120456e-07f, 2.800315102e-21f, },
                     { 1.389614759f, 0.5310782754f, 0.07638574357f, 0.002902517748f, 1.198370136e-05f, 1.163116581e-09f, 2.197079236e-16f, 1.363510331e-27f, },
                     { 1.523283719f, 1.193463026f, 0.7374378484f, 0.3604614185f, 0.1374221077f, 0.03917500549f, 0.007742601026f, 0.0009499468043f, 6.248255924e-05f, 1.826332059e-06f, 1.868728227e-08f, 4.937853878e-11f, 2.28349267e-14f, 1.122753143e-18f, 3.09765397e-24f, 2.112123344e-31f, },
                     { 1.558773356f, 1.466014427f, 1.29747575f, 1.081634985f, 0.8501728565f, 0.6304051352f, 0.4408332363f, 0.2902406793f, 0.1793244121f, 0.1034321542f, 0.05528968374f, 0.02713351001f, 0.0120835436f, 0.004816298144f, 0.001690873998f, 0.0005133938241f, 0.0001320523413f, 2.811016433e-05f, 4.823718203e-06f, 6.477756604e-07f, 6.583518513e-08f, 4.876006097e-09f, 2.521634792e-10f, 8.675931415e-12f, 1.880207173e-13f, 2.412423038e-15f, 1.708453277e-17f, 6.168256849e-20f, 1.037679724e-22f, 7.345984103e-26f, 1.949783362e-29f, 1.702438776e-33f, },
                     { 1.567781431f, 1.543881116f, 1.497226223f, 1.430008355f, 1.345278885f, 1.246701207f, 1.138272243f, 1.024044933f, 0.9078793792f, 0.7932427008f, 0.6830685163f, 0.5796781031f, 0.4847580912f, 0.3993847415f, 0.3240825396f, 0.2589046395f, 0.2035239989f, 0.1573262035f, 0.1194974113f, 0.08910313924f, 0.06515553343f, 0.04666820805f, 0.03269873273f, 0.02237947106f, 0.0149378351f, 0.009707223739f, 0.006130037632f, 0.003754250977f, 0.002225082706f, 0.001273327945f, 0.0007018595157f, 0.0003716669362f, 0.0001885644298f, 9.139081749e-05f, 4.218318384e-05f, 1.84818136e-05f, 7.659575853e-06f, 2.991661588e-06f, 1.096883513e-06f, 3.759541186e-07f, 1.199244278e-07f, 3.543477717e-08f, 9.649888896e-09f, 2.409177326e-09f, 5.48283578e-10f, 1.130605535e-10f, 2.09893354e-11f, 3.484193767e-12f, 5.134127525e-13f, 6.663992283e-14f, 7.556721776e-15f, 7.420993231e-16f, 6.252804845e-17f, 4.475759507e-18f, 2.693120661e-19f, 1.346994157e-20f, 5.533583499e-22f, 1.843546975e-23f, 4.913936871e-25f, 1.032939131e-26f, 1.686277004e-28f, 2.103305749e-30f, 1.96992098e-32f, 1.359989462e-34f, },
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                  };
                  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

cmd: