path: root/boost/math/quadrature/detail/exp_sinh_detail.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_EXP_SINH_DETAIL_HPP
#define BOOST_MATH_QUADRATURE_DETAIL_EXP_SINH_DETAIL_HPP

#include <cmath>
#include <vector>
#include <typeinfo>
#include <boost/math/constants/constants.hpp>
#include <boost/math/special_functions/next.hpp>
#include <boost/math/tools/atomic.hpp>
#include <boost/detail/lightweight_mutex.hpp>

namespace boost{ namespace math{ namespace quadrature { namespace detail{


// Returns the exp-sinh quadrature of a function f over the open interval (0, infinity)

template<class Real, class Policy>
class exp_sinh_detail
{
   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 :
      (std::numeric_limits<Real>::digits <= std::numeric_limits<double>::digits) && (std::numeric_limits<Real>::max_exponent <= std::numeric_limits<double>::max_exponent) ?
      2 :
      (std::numeric_limits<Real>::digits <= std::numeric_limits<long double>::digits) && (std::numeric_limits<Real>::max_exponent <= 16384) ?
      3 :
#ifdef BOOST_HAS_FLOAT128
      (std::numeric_limits<Real>::digits <= 113) && (std::numeric_limits<Real>::max_exponent <= 16384) ?
      4 :
#endif
      0;
public:
    exp_sinh_detail(size_t max_refinements);

    template<class F>
    Real integrate(const F& f, Real* error, Real* L1, const char* function, Real tolerance, std::size_t* levels) const;

private:
   const std::vector<Real>& get_abscissa_row(std::size_t n)const
   {
#ifndef BOOST_MATH_NO_ATOMIC_INT
      if (m_committed_refinements.load() < n)
         extend_refinements();
      BOOST_ASSERT(m_committed_refinements.load() >= n);
#else
      if (m_committed_refinements < n)
         extend_refinements();
      BOOST_ASSERT(m_committed_refinements >= n);
#endif
      return m_abscissas[n];
   }
   const std::vector<Real>& get_weight_row(std::size_t n)const
   {
#ifndef BOOST_MATH_NO_ATOMIC_INT
      if (m_committed_refinements.load() < n)
         extend_refinements();
      BOOST_ASSERT(m_committed_refinements.load() >= n);
#else
      if (m_committed_refinements < n)
         extend_refinements();
      BOOST_ASSERT(m_committed_refinements >= n);
#endif
      return m_weights[n];
   }
   void init(const mpl::int_<0>&);
   void init(const mpl::int_<1>&);
   void init(const mpl::int_<2>&);
   void init(const mpl::int_<3>&);
#ifdef BOOST_HAS_FLOAT128
   void init(const mpl::int_<4>&);
#endif

   void extend_refinements()const
   {
#ifndef BOOST_MATH_NO_ATOMIC_INT
      boost::detail::lightweight_mutex::scoped_lock guard(m_mutex);
#endif
      //
      // Check some other thread hasn't got here after we read the atomic variable, but before we got here:
      //
#ifndef BOOST_MATH_NO_ATOMIC_INT
      if (m_committed_refinements.load() >= m_max_refinements)
         return;
#else
      if (m_committed_refinements >= m_max_refinements)
         return;
#endif

      using std::ldexp;
      using std::ceil;
      using std::sinh;
      using std::cosh;
      using std::exp;
      std::size_t row  = ++m_committed_refinements;

      Real h = ldexp(Real(1), -static_cast<int>(row));
      const Real t_max = m_t_min + m_abscissas[0].size() - 1;

      size_t k = (size_t)boost::math::lltrunc(ceil((t_max - m_t_min) / (2 * h)));
      m_abscissas[row].reserve(k);
      m_weights[row].reserve(k);
      Real arg = m_t_min;
      size_t j = 0;
      size_t l = 2;
      while (arg + l*h < t_max)
      {
         arg = m_t_min + (2 * j + 1)*h;
         Real x = exp(constants::half_pi<Real>()*sinh(arg));
         m_abscissas[row].emplace_back(x);
         Real w = cosh(arg)*constants::half_pi<Real>()*x;
         m_weights[row].emplace_back(w);
         ++j;
      }
   }

    Real m_tol, m_t_min;

    mutable std::vector<std::vector<Real>> m_abscissas;
    mutable std::vector<std::vector<Real>> m_weights;
    std::size_t                       m_max_refinements;
#ifndef BOOST_MATH_NO_ATOMIC_INT
    mutable boost::math::detail::atomic_unsigned_type      m_committed_refinements;
    mutable boost::detail::lightweight_mutex m_mutex;
#else
    mutable unsigned                  m_committed_refinements;
#endif
};

template<class Real, class Policy>
exp_sinh_detail<Real, Policy>::exp_sinh_detail(size_t max_refinements) 
   : m_abscissas(max_refinements), m_weights(max_refinements),
   m_max_refinements(max_refinements)
{
   init(mpl::int_<initializer_selector>());
}
template<class Real, class Policy>
template<class F>
Real exp_sinh_detail<Real, Policy>::integrate(const F& f, Real* error, Real* L1, const char* function, Real tolerance, std::size_t* levels) const
{
    using std::abs;
    using std::floor;
    using std::tanh;
    using std::sinh;
    using std::sqrt;
    using boost::math::constants::half;
    using boost::math::constants::half_pi;

    Real y_max = f(tools::max_value<Real>());
    if(abs(y_max) > tools::epsilon<Real>() || !(boost::math::isfinite)(y_max))
    {
       return policies::raise_domain_error(function, "The function you are trying to integrate does not go to zero at infinity, and instead evaluates to %1%", y_max, Policy());
    }

    //std::cout << std::setprecision(5*std::numeric_limits<Real>::digits10);

    // Get the party started with two estimates of the integral:
    Real I0 = 0;
    Real L1_I0 = 0;
    for(size_t i = 0; i < m_abscissas[0].size(); ++i)
    {
        Real y = f(m_abscissas[0][i]);
        I0 += y*m_weights[0][i];
        L1_I0 += abs(y)*m_weights[0][i];
    }

    //std::cout << "First estimate : " << I0 << std::endl;
    Real I1 = I0;
    Real L1_I1 = L1_I0;
    for (size_t i = 0; i < m_abscissas[1].size(); ++i)
    {
        Real y = f(m_abscissas[1][i]);
        I1 += y*m_weights[1][i];
        L1_I1 += abs(y)*m_weights[1][i];
    }

    I1 *= half<Real>();
    L1_I1 *= half<Real>();
    Real err = abs(I0 - I1);
    //std::cout << "Second estimate: " << I1 << " Error estimate at level " << 1 << " = " << err << std::endl;

    size_t i = 2;
    for(; i < m_abscissas.size(); ++i)
    {
        I0 = I1;
        L1_I0 = L1_I1;

        I1 = half<Real>()*I0;
        L1_I1 = half<Real>()*L1_I0;
        Real h = (Real) 1/ (Real) (1 << i);
        Real sum = 0;
        Real absum = 0;

        auto abscissas_row = get_abscissa_row(i);
        auto weight_row = get_weight_row(i);

        Real abterm1 = 1;
        Real eps = tools::epsilon<Real>()*L1_I1;
        for(size_t j = 0; j < m_weights[i].size(); ++j)
        {
            Real x = abscissas_row[j];
            Real y = f(x);
            sum += y*weight_row[j];
            Real abterm0 = abs(y)*weight_row[j];
            absum += abterm0;

            // We require two consecutive terms to be < eps in case we hit a zero of f.
            // Numerical experiments indicate that we should start this check at ~30 for floats,
            // ~60 for doubles, and ~100 for long doubles.
            // However, starting the check at x = 10 rather than x = 100 will only save two function evaluations.
            if (x > (Real) 100 && abterm0 < eps && abterm1 < eps)
            {
                break;
            }
            abterm1 = abterm0;
        }

        I1 += sum*h;
        L1_I1 += absum*h;
        err = abs(I0 - I1);
        //std::cout << "Estimate:        " << I1 << " Error estimate at level " << i  << " = " << err << std::endl;
        if (!isfinite(I1))
        {
            return policies::raise_evaluation_error(function, "The exp_sinh quadrature evaluated your function at a singular point and returned %1%. Please ensure your function evaluates to a finite number over its entire domain.", I1, Policy());
        }
        if (err <= tolerance*L1_I1)
        {
            break;
        }
    }

    if (error)
    {
        *error = err;
    }

    if(L1)
    {
        *L1 = L1_I1;
    }

    if (levels)
    {
       *levels = i;
    }

    return I1;
}


template<class Real, class Policy>
void exp_sinh_detail<Real, Policy>::init(const mpl::int_<0>&)
{
   using std::exp;
   using std::log;
   using std::sqrt;
   using std::cosh;
   using std::sinh;
   using std::asinh;
   using std::ceil;
   using boost::math::constants::two_div_pi;
   using boost::math::constants::half_pi;
   using boost::math::constants::half;

   m_committed_refinements = 4;
   // m_t_min is chosen such that x = exp(pi/2 sinh(-t_max)) = very small, but not too small.
   // This is a compromise; we wish to approach a singularity at zero without hitting it through roundoff error.
   // If we choose the small number as epsilon, we do not get close enough to the singularity to achieve high accuracy.
   // If we choose the small number as the min(), then we round off to zero and hit the singularity.
   // The logarithmic average of the min() and the epsilon() has been found to be a reasonable compromise, which achieves high accuracy
   // but does not evaluate the function at the singularity.
   Real tmp = (boost::math::tools::log_min_value<Real>() + log(boost::math::tools::epsilon<Real>()))*half<Real>();
   m_t_min = asinh(two_div_pi<Real>()*tmp);

   // t_max is chosen to make g'(t_max) ~ sqrt(max) (g' grows faster than g).
   // This will allow some flexibility on the users part; they can at least square a number function without overflow.
   // But there is no unique choice; the further out we can evaluate the function, the better we can do on slowly decaying integrands.
   const Real t_max = log(2 * two_div_pi<Real>()*log(2 * two_div_pi<Real>()*sqrt(tools::max_value<Real>())));

   for (size_t i = 0; i <= 4; ++i)
   {
      Real h = (Real)1 / (Real)(1 << i);
      size_t k = (size_t)boost::math::lltrunc(ceil((t_max - m_t_min) / (2 * h)));
      m_abscissas[i].reserve(k);
      m_weights[i].reserve(k);
      Real arg = m_t_min;
      size_t j = 0;
      size_t l = 2;
      if (i == 0)
      {
         l = 1;
      }
      while (arg + l*h < t_max)
      {
         if (i != 0)
         {
            arg = m_t_min + (2 * j + 1)*h;
         }
         else
         {
            arg = m_t_min + j*h;
         }
         Real x = exp(half_pi<Real>()*sinh(arg));
         m_abscissas[i].emplace_back(x);
         Real w = cosh(arg)*half_pi<Real>()*x;
         m_weights[i].emplace_back(w);
         ++j;
      }
   }
/*
   std::cout << std::setprecision(18) << m_t_min << std::endl;
   for (unsigned i = 0; i < m_abscissas[0].size(); ++i)
      std::cout << m_abscissas[0][i] << ", ";
   std::cout << std::endl;
   */
}

template<class Real, class Policy>
void exp_sinh_detail<Real, Policy>::init(const mpl::int_<1>&)
{
   m_abscissas = {
      { 3.47876573e-23f, 5.62503650e-09f, 9.95706124e-04f, 9.67438487e-02f, 7.43599217e-01f, 4.14293205e+00f, 1.08086768e+02f, 4.56291316e+05f, 2.70123007e+15f, },
      { 2.41870864e-14f, 1.02534662e-05f, 1.65637566e-02f, 3.11290799e-01f, 1.64691269e+00f, 1.49800773e+01f, 2.57724301e+03f, 2.24833766e+09f, },
      { 3.24983286e-18f, 2.51095186e-11f, 3.82035773e-07f, 1.33717837e-04f, 4.80260650e-03f, 4.41526928e-02f, 1.83045938e-01f, 4.91960276e-01f, 1.10322609e+00f, 2.53681744e+00f, 7.39791792e+00f, 3.59560256e+01f, 4.36061333e+02f, 2.49501460e+04f, 1.89216933e+07f, 1.03348694e+12f, },
      { 1.51941172e-20f, 3.70201714e-16f, 9.67598102e-13f, 4.44773051e-10f, 5.28493928e-08f, 2.19158236e-06f, 4.00799258e-05f, 3.88011529e-04f, 2.29325538e-03f, 9.25182629e-03f, 2.78117501e-02f, 6.67553298e-02f, 1.35173168e-01f, 2.41374946e-01f, 3.94194704e-01f, 6.07196731e-01f, 9.06432514e-01f, 1.34481045e+00f, 2.03268444e+00f, 3.21243032e+00f, 5.46310949e+00f, 1.03365745e+01f, 2.26486752e+01f, 6.03727778e+01f, 2.08220266e+02f, 1.00431239e+03f, 7.47843388e+03f, 9.75279951e+04f, 2.61755592e+06f, 1.77776624e+08f, 3.98255346e+10f, 4.13443763e+13f, 3.07708133e+17f, },
      { 7.99409438e-22f, 2.41624595e-19f, 3.73461321e-17f, 3.19397902e-15f, 1.62042378e-13f, 5.18579386e-12f, 1.10520072e-10f, 1.64548212e-09f, 1.78534009e-08f, 1.46529196e-07f, 9.40168786e-07f, 4.85507733e-06f, 2.07038029e-05f, 7.45799409e-05f, 2.31536599e-04f, 6.30580368e-04f, 1.53035449e-03f, 3.35582040e-03f, 6.73124842e-03f, 1.24856832e-02f, 2.16245309e-02f, 3.52720523e-02f, 5.45995171e-02f, 8.07587788e-02f, 1.14840025e-01f, 1.57867103e-01f, 2.10837078e-01f, 2.74805391e-01f, 3.51015955e-01f, 4.41077540e-01f, 5.47194016e-01f, 6.72466825e-01f, 8.21304567e-01f, 1.00000000e+00f, 1.21757511e+00f, 1.48706221e+00f, 1.82750536e+00f, 2.26717507e+00f, 2.84887335e+00f, 3.63893880e+00f, 4.74299876e+00f, 6.33444194e+00f, 8.70776542e+00f, 1.23825548e+01f, 1.83151803e+01f, 2.83510579e+01f, 4.62437776e+01f, 8.00917327e+01f, 1.48560852e+02f, 2.97989725e+02f, 6.53443372e+02f, 1.58584068e+03f, 4.31897162e+03f, 1.34084311e+04f, 4.83003053e+04f, 2.05969943e+05f, 1.06363880e+06f, 6.82457850e+06f, 5.60117371e+07f, 6.07724622e+08f, 9.04813016e+09f, 1.92834507e+11f, 6.17122515e+12f, 3.13089095e+14f, 2.67765347e+16f, 4.13865153e+18f, },
      { 1.70893932e-22f, 3.56621447e-21f, 6.19138882e-20f, 9.04299298e-19f, 1.12287188e-17f, 1.19706303e-16f, 1.10583090e-15f, 8.92931857e-15f, 6.35404710e-14f, 4.01527389e-13f, 2.26955738e-12f, 1.15522811e-11f, 5.32913181e-11f, 2.24130967e-10f, 8.64254491e-10f, 3.07161058e-09f, 1.01117742e-08f, 3.09775637e-08f, 8.87004371e-08f, 2.38368096e-07f, 6.03520392e-07f, 1.44488635e-06f, 3.28212299e-06f, 7.09655821e-06f, 1.46494407e-05f, 2.89537394e-05f, 5.49357161e-05f, 1.00313252e-04f, 1.76700203e-04f, 3.00920507e-04f, 4.96484845e-04f, 7.95150594e-04f, 1.23845781e-03f, 1.87911525e-03f, 2.78210510e-03f, 4.02538552e-03f, 5.70009588e-03f, 7.91020800e-03f, 1.07716137e-02f, 1.44106884e-02f, 1.89624177e-02f, 2.45682104e-02f, 3.13735515e-02f, 3.95256605e-02f, 4.91713196e-02f, 6.04550279e-02f, 7.35176150e-02f, 8.84954195e-02f, 1.05520113e-01f, 1.24719213e-01f, 1.46217318e-01f, 1.70138063e-01f, 1.96606781e-01f, 2.25753880e-01f, 2.57718900e-01f, 2.92655274e-01f, 3.30735809e-01f, 3.72158929e-01f, 4.17155794e-01f, 4.65998399e-01f, 5.19008863e-01f, 5.76570161e-01f, 6.39138643e-01f, 7.07258781e-01f, 7.81580731e-01f, 8.62881450e-01f, 9.52090320e-01f, 1.05032052e+00f, 1.15890775e+00f, 1.27945836e+00f, 1.41390963e+00f, 1.56460576e+00f, 1.73439430e+00f, 1.92674937e+00f, 2.14593012e+00f, 2.39718593e+00f, 2.68702407e+00f, 3.02356133e+00f, 3.41698950e+00f, 3.88019661e+00f, 4.42960272e+00f, 5.08629455e+00f, 5.87757956e+00f, 6.83913514e+00f, 8.01801085e+00f, 9.47686632e+00f, 1.13000199e+01f, 1.36021823e+01f, 1.65412214e+01f, 2.03370584e+01f, 2.53000199e+01f, 3.18739815e+01f, 4.07030054e+01f, 5.27358913e+01f, 6.93929374e+01f, 9.28366010e+01f, 1.26418926e+02f, 1.75435645e+02f, 2.48423411e+02f, 3.59440052e+02f, 5.32165336e+02f, 8.07455844e+02f, 1.25762341e+03f, 2.01416017e+03f, 3.32313676e+03f, 5.65930306e+03f, 9.96877263e+03f, 1.82030939e+04f, 3.45378531e+04f, 6.82619916e+04f, 1.40913380e+05f, 3.04680844e+05f, 6.92095957e+05f, 1.65694484e+06f, 4.19519229e+06f, 1.12739016e+07f, 3.22814282e+07f, 9.88946136e+07f, 3.25562103e+08f, 1.15706659e+09f, 4.46167708e+09f, 1.87647826e+10f, 8.65629909e+10f, 4.40614549e+11f, 2.49049013e+12f, 1.57380011e+13f, 1.11990629e+14f, 9.04297390e+14f, 8.35377903e+15f, 8.90573552e+16f, 1.10582857e+18f, 1.61514650e+19f, },
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2.93241843e+00f, 3.02635449e+00f, 3.12441791e+00f, 3.22682682e+00f, 3.33381238e+00f, 3.44561973e+00f, 3.56250887e+00f, 3.68475574e+00f, 3.81265333e+00f, 3.94651282e+00f, 4.08666490e+00f, 4.23346116e+00f, 4.38727553e+00f, 4.54850596e+00f, 4.71757611e+00f, 4.89493722e+00f, 5.08107015e+00f, 5.27648761e+00f, 5.48173646e+00f, 5.69740032e+00f, 5.92410235e+00f, 6.16250823e+00f, 6.41332946e+00f, 6.67732689e+00f, 6.95531455e+00f, 7.24816384e+00f, 7.55680807e+00f, 7.88224735e+00f, 8.22555401e+00f, 8.58787841e+00f, 8.97045530e+00f, 9.37461076e+00f, 9.80176975e+00f, 1.02534643e+01f, 1.07313428e+01f, 1.12371793e+01f, 1.17728848e+01f, 1.23405187e+01f, 1.29423019e+01f, 1.35806306e+01f, 1.42580922e+01f, 1.49774818e+01f, 1.57418213e+01f, 1.65543795e+01f, 1.74186947e+01f, 1.83385994e+01f, 1.93182476e+01f, 2.03621450e+01f, 2.14751816e+01f, 2.26626686e+01f, 2.39303784e+01f, 2.52845893e+01f, 2.67321348e+01f, 2.82804577e+01f, 2.99376708e+01f, 3.17126238e+01f, 3.36149769e+01f, 3.56552840e+01f, 3.78450835e+01f, 4.01970005e+01f, 4.27248599e+01f, 4.54438126e+01f, 4.83704762e+01f, 5.15230921e+01f, 5.49217006e+01f, 5.85883374e+01f, 6.25472527e+01f, 6.68251567e+01f, 7.14514957e+01f, 7.64587609e+01f, 8.18828353e+01f, 8.77633847e+01f, 9.41442967e+01f, 1.01074176e+02f, 1.08606902e+02f, 1.16802259e+02f, 1.25726650e+02f, 1.35453899e+02f, 1.46066166e+02f, 1.57654979e+02f, 1.70322410e+02f, 1.84182406e+02f, 1.99362306e+02f, 2.16004568e+02f, 2.34268740e+02f, 2.54333703e+02f, 2.76400239e+02f, 3.00693971e+02f, 3.27468728e+02f, 3.57010397e+02f, 3.89641362e+02f, 4.25725590e+02f, 4.65674502e+02f, 5.09953726e+02f, 5.59090900e+02f, 6.13684688e+02f, 6.74415211e+02f, 7.42056139e+02f, 8.17488717e+02f, 9.01718069e+02f, 9.95892168e+02f, 1.10132394e+03f, 1.21951707e+03f, 1.35219615e+03f, 1.50134197e+03f, 1.66923291e+03f, 1.85849349e+03f, 2.07215152e+03f, 2.31370536e+03f, 2.58720328e+03f, 2.89733724e+03f, 3.24955383e+03f, 3.65018587e+03f, 4.10660860e+03f, 4.62742547e+03f, 5.22268956e+03f, 5.90416786e+03f, 6.68565726e+03f, 7.58336313e+03f, 8.61635357e+03f, 9.80710572e+03f, 1.11821637e+04f, 1.27729327e+04f, 1.46166396e+04f, 1.67574960e+04f, 1.92481112e+04f, 2.21512104e+04f, 2.55417295e+04f, 2.95093735e+04f, 3.41617487e+04f, 3.96282043e+04f, 4.60645561e+04f, 5.36589049e+04f, 6.26388223e+04f, 7.32802431e+04f, 8.59184957e+04f, 1.00962017e+05f, 1.18909442e+05f, 1.40370957e+05f, 1.66095034e+05f, 1.97001996e+05f, 2.34226253e+05f, 2.79169596e+05f, 3.33568603e+05f, 3.99580125e+05f, 4.79889989e+05f, 5.77851588e+05f, 6.97663062e+05f, 8.44594440e+05f, 1.02527965e+06f, 1.24809298e+06f, 1.52363581e+06f, 1.86536786e+06f, 2.29042802e+06f, 2.82070529e+06f, 3.48424008e+06f, 4.31706343e+06f, 5.36561882e+06f, 6.68996113e+06f, 8.36799594e+06f, 1.05011160e+07f, 1.32217203e+07f, 1.67032788e+07f, 2.11738506e+07f, 2.69343047e+07f, 3.43829654e+07f, 4.40490690e+07f, 5.66383460e+07f, 7.30953564e+07f, 9.46890531e+07f, 1.23130681e+08f, 1.60736861e+08f, 2.10656057e+08f, 2.77184338e+08f, 3.66207397e+08f, 4.85821891e+08f, 6.47212479e+08f, 8.65895044e+08f, 1.16348659e+09f, 1.57023596e+09f, 2.12865840e+09f, 2.89877917e+09f, 3.96573294e+09f, 5.45082863e+09f, 7.52773593e+09f, 1.04462776e+10f, 1.45675716e+10f, 2.04161928e+10f, 2.87579864e+10f, 4.07167363e+10f, 5.79499965e+10f, 8.29154750e+10f, 1.19276754e+11f, 1.72524570e+11f, 2.50933409e+11f, 3.67042596e+11f, 5.39962441e+11f, 7.98985690e+11f, 1.18927611e+12f, 1.78088199e+12f, 2.68310388e+12f, 4.06753710e+12f, 6.20525592e+12f, 9.52719664e+12f, 1.47228407e+13f, 2.29025392e+13f, 3.58662837e+13f, 5.65517100e+13f, 8.97859411e+13f, 1.43556057e+14f, 2.31171020e+14f, 3.74966777e+14f, 6.12702071e+14f, 1.00868013e+15f, 1.67323268e+15f, 2.79711270e+15f, 4.71267150e+15f, 8.00353033e+15f, 1.37027503e+16f, 2.36538022e+16f, 4.11734705e+16f, 7.22793757e+16f, 1.27982244e+17f, 2.28603237e+17f, 4.11976277e+17f, 7.49169358e+17f, 1.37488861e+18f, 2.54681529e+18f, 4.76248383e+18f, 8.99167123e+18f, 1.71428840e+19f, 3.30088717e+19f, 6.42020070e+19f, 1.26155602e+20f, 2.50480806e+20f, 5.02601059e+20f, 1.01935525e+21f, },
   };
   m_committed_refinements = static_cast<boost::math::detail::atomic_unsigned_integer_type>(m_weights.size() - 1);
   m_t_min = -4.18750000f;
   if (m_max_refinements >= m_abscissas.size())
   {
      m_abscissas.resize(m_max_refinements + 1);
      m_weights.resize(m_max_refinements + 1);
   }
   else
   {
      m_max_refinements = m_abscissas.size() - 1;
   }
}

template<class Real, class Policy>
void exp_sinh_detail<Real, Policy>::init(const mpl::int_<2>&)
{
   m_abscissas = {
      { 7.241670621354483269e-163, 2.257639733856759198e-60, 1.153241619257215165e-22, 8.747691973876861825e-09, 1.173446923800022477e-03, 1.032756936219208144e-01, 7.719261204224504866e-01, 4.355544675823585545e+00, 1.215101039066652656e+02, 6.228845436711506169e+05, 6.278613977336989392e+15, 9.127414935180233465e+42, 6.091127771174027909e+116, },
      { 4.547459836328942014e-99, 6.678756542928857080e-37, 5.005042973041566360e-14, 1.341318484151208960e-05, 1.833875636365939263e-02, 3.257972971286326131e-01, 1.712014688483495078e+00, 1.613222549264089627e+01, 3.116246745274236447e+03, 3.751603952020919663e+09, 1.132259067258797346e+26, 6.799257464097374238e+70, },
      { 5.314690663257815465e-127, 2.579830034615362946e-77, 3.534801062399966878e-47, 6.733941646704537777e-29, 8.265803726974829043e-18, 4.424914371157762285e-11, 5.390411046738629465e-07, 1.649389713333761449e-04, 5.463728936866216652e-03, 4.787896410534771955e-02, 1.931544616590306846e-01, 5.121421856617965197e-01, 1.144715949265016019e+00, 2.648424684387670480e+00, 7.856804169938798917e+00, 3.944731803343517708e+01, 5.060291993016831194e+02, 3.181117494063683297e+04, 2.820174654949211729e+07, 1.993745099515255184e+12, 1.943469269499068563e+20, 2.858803732300638372e+33, 1.457292199029008637e+55, 8.943565831706355607e+90, 9.016198369791554655e+149, },
      { 8.165631636299519857e-144, 3.658949309353149331e-112, 1.635242513882908826e-87, 2.578381184977746454e-68, 2.305546416275824199e-53, 1.016725540031465162e-41, 1.191823622917539774e-32, 1.379018088205016509e-25, 4.375640088826073184e-20, 8.438464631330991606e-16, 1.838483310261119782e-12, 7.334264181393092650e-10, 7.804740587931068021e-08, 2.970395577741681504e-06, 5.081805431666579484e-05, 4.671401627620431498e-04, 2.652347404231090523e-03, 1.037409202661683856e-02, 3.045225582205323946e-02, 7.178280364982721201e-02, 1.434001065841990688e-01, 2.535640852949085796e-01, 4.113268917643175920e-01, 6.310260805648534613e-01, 9.404706503455087817e-01, 1.396267301972783068e+00, 2.116896928689963277e+00, 3.364289290471596568e+00, 5.770183960005836987e+00, 1.104863531218761752e+01, 2.460224479439805859e+01, 6.699316387888639988e+01, 2.375794092475844708e+02, 1.188092202760116066e+03, 9.269848635975416108e+03, 1.283900116155671304e+05, 3.723397798030112514e+06, 2.793667983952389721e+08, 7.112973790863854188e+10, 8.704037695808749572e+13, 8.001474015782459984e+17, 9.804091819390540578e+22, 3.342777673392873288e+29, 8.160092668471508447e+37, 4.798775331663586528e+48, 3.228614320248853938e+62, 1.836986041572136151e+80, 1.153145986877483804e+103, 2.160972586723647751e+132, },
      { 4.825077401709435655e-153, 3.813781211050297560e-135, 2.377824349780240844e-119, 2.065817295388293122e-105, 4.132105770181358886e-93, 2.963965169989404311e-82, 1.127296662046635391e-72, 3.210346399945695041e-64, 9.282992368222161062e-57, 3.565977853916619677e-50, 2.306962519220473637e-44, 3.098751038516535098e-39, 1.039558064722960891e-34, 1.025256027381235200e-30, 3.432612000569885403e-27, 4.429681881379089961e-24, 2.464589267395236846e-21, 6.526691446363344923e-19, 8.976892324445928684e-17, 6.926277695183452225e-15, 3.208805316815751272e-13, 9.478053068835988899e-12, 1.882052586691155400e-10, 2.632616062773909009e-09, 2.703411837703917665e-08, 2.113642195965330965e-07, 1.299327029813074013e-06, 6.461189935136030673e-06, 2.665090959570723827e-05, 9.322774986189288194e-05, 2.820463407940068813e-04, 7.508613300035051413e-04, 1.786142185986551786e-03, 3.848376610765768211e-03, 7.600810651854199771e-03, 1.390873269178271700e-02, 2.380489559528694982e-02, 3.842796337748997654e-02, 5.895012901671883992e-02, 8.651391160689367948e-02, 1.221961347398101671e-01, 1.670112314557845555e-01, 2.219593619059930701e-01, 2.881200442770917241e-01, 3.667906976948184315e-01, 4.596722879563388211e-01, 5.691113093602836208e-01, 6.984190600916228379e-01, 8.523070690462583711e-01, 1.037505121571600249e+00, 1.263672635742961915e+00, 1.544788480334120896e+00, 1.901333876886441433e+00, 2.363816272813317635e+00, 2.978614980117902904e+00, 3.817957977526709364e+00, 4.997477803461245639e+00, 6.708150685706236545e+00, 9.276566033183386532e+00, 1.328332469239125539e+01, 1.980618680552458639e+01, 3.094452809319702849e+01, 5.101378787119006225e+01, 8.943523638413590523e+01, 1.682138665185088325e+02, 3.427988270281270587e+02, 7.653823671943767281e+02, 1.895993667030670343e+03, 5.285404568827643942e+03, 1.684878049282191210e+04, 6.254388805482299369e+04, 2.759556544455721132e+05, 1.481213238071008345e+06, 9.929728611179601424e+06, 8.564987764771851841e+07, 9.831650826344826952e+08, 1.560339073978569502e+10, 3.575098885016726922e+11, 1.241973798101884982e+13, 6.915106205748805839e+14, 6.571419716645131084e+16, 1.144558033138694099e+19, 3.960915669532823553e+21, 2.984410558028297842e+24, 5.430494850258846715e+27, 2.683747612498502676e+31, 4.114885708325522701e+35, 2.276004816861421600e+40, 5.387544917595833246e+45, 6.623575732955432303e+51, 5.266881304835239338e+58, 3.473234812654772210e+66, 2.517492645985977377e+75, 2.759797646289240629e+85, 6.569603829502412077e+96, 5.116181648220647995e+109, 2.073901892339407423e+124, 7.406462446666255838e+140, },
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1.113229743930062164e+00, 1.137646231695313314e+00, 1.162770615670420260e+00, 1.188635146483979071e+00, 1.215273585336112390e+00, 1.242721280043529050e+00, 1.271015245815510799e+00, 1.300194251072644711e+00, 1.330298908642019971e+00, 1.361371772686240192e+00, 1.393457441749111730e+00, 1.426602668328411758e+00, 1.460856475415888358e+00, 1.496270280476785338e+00, 1.532898027375920169e+00, 1.570796326794896619e+00, 1.610024605725646420e+00, 1.650645266669431435e+00, 1.692723857217988332e+00, 1.736329250744977731e+00, 1.781533838991654903e+00, 1.828413737391087381e+00, 1.877049004040720448e+00, 1.927523873304087635e+00, 1.979927005099477087e+00, 2.034351751016940433e+00, 2.090896438495766214e+00, 2.149664674393090421e+00, 2.210765669381402212e+00, 2.274314584729113927e+00, 2.340432903144970240e+00, 2.409248825504827076e+00, 2.480897695429288043e+00, 2.555522453844001656e+00, 2.633274125832370887e+00, 2.714312342284411608e+00, 2.798805899057066353e+00, 2.886933356592141886e+00, 2.978883683190077867e+00, 3.074856945413050211e+00, 3.175065049391765683e+00, 3.279732537139255280e+00, 3.389097442334834102e+00, 3.503412210435275865e+00, 3.622944688401595705e+00, 3.747979189802462585e+00, 3.878817641573403805e+00, 4.015780819279312670e+00, 4.159209678351536168e+00, 4.309466789455788368e+00, 4.466937886899736897e+00, 4.632033539816493591e+00, 4.805190956770360727e+00, 4.986875935432896972e+00, 5.177584970080537688e+00, 5.377847530880629761e+00, 5.588228530273088035e+00, 5.809330993233640059e+00, 6.041798949837089488e+00, 6.286320570342285919e+00, 6.543631565013652661e+00, 6.814518873098582608e+00, 7.099824667819718682e+00, 7.400450706942931008e+00, 7.717363061475788814e+00, 8.051597258371279584e+00, 8.404263876795383951e+00, 8.776554641607500109e+00, 9.169749062247565207e+00, 9.585221670276993889e+00, 1.002444991444300704e+01, 1.048902277839603856e+01, 1.098065019316492606e+01, 1.150117332427169985e+01, 1.205257582204547280e+01, 1.263699613338454324e+01, 1.325674098404332380e+01, 1.391430015262873368e+01, 1.461236267104086712e+01, 1.535383460126837531e+01, 1.614185855545811846e+01, 1.697983514525758524e+01, 1.787144656784601339e+01, 1.882068256013178484e+01, 1.983186897964764985e+01, 2.090969930111845450e+01, 2.205926935196095527e+01, 2.328611564861881683e+01, 2.459625773922860138e+01, 2.599624500732998276e+01, 2.749320844694889238e+01, 2.909491798228195984e+01, 3.080984597641076715e+01, 3.264723765414180400e+01, 3.461718925554321861e+01, 3.673073484057443067e+01, 3.899994278315456980e+01, 4.143802312713618427e+01, 4.405944712930142330e+01, 4.688008048840357439e+01, 4.991733195758662298e+01, 5.319031926387298369e+01, 5.672005451703465811e+01, 6.052965158594831140e+01, 6.464455825915836491e+01, 6.909281639443131774e+01, 7.390535370725211687e+01, 7.911631135942343489e+01, 8.476341209659472308e+01, 9.088837435982152722e+01, 9.753737857533253823e+01, 1.047615927251647361e+02, 1.126177653386554197e+02, 1.211688952437418817e+02, 1.304849888043593828e+02, 1.406439169773708701e+02, 1.517323863863765989e+02, 1.638470407739824279e+02, 1.770957117100033620e+02, 1.915988403612775885e+02, 2.074910955409497265e+02, 2.249232172361061194e+02, 2.440641194630869936e+02, 2.651032917390266964e+02, 2.882535448280364212e+02, 3.137541538897424513e+02, 3.418744609277612322e+02, 3.729180087461214321e+02, 4.072272907593818790e+02, 4.451892153103389878e+02, 4.872414000388630927e+02, 5.338794318098249932e+02, 5.856652513400113117e+02, 6.432368496766822816e+02, 7.073194969336578611e+02, 7.787387632221277236e+02, 8.584356387770406827e+02, 9.474841163944599543e+02, 1.047111666301969297e+03, 1.158723113719277435e+03, 1.283928525349707755e+03, 1.424575826189363437e+03, 1.582789006393775706e+03, 1.761012944445459235e+03, 1.962066073573121788e+03, 2.189202360708354222e+03, 2.446184360349559652e+03, 2.737369460761187093e+03, 3.067811870808767638e+03, 3.443383419509962754e+03, 3.870916878218207705e+03, 4.358376293464465508e+03, 4.915059769420260559e+03, 5.551841303216967404e+03, 6.281459704453426129e+03, 7.118864385205665710e+03, 8.081629967627799596e+03, 9.190454321738597280e+03, 1.046975794051835702e+04, 1.194840663946247320e+04, 1.366058463062104793e+04, 1.564685131637809273e+04, 1.795542299179967539e+04, 2.064373043744082514e+04, 2.378031563732670807e+04, 2.744714621995650953e+04, 3.174244552480722739e+04, 3.678416050731336226e+04, 4.271422037773508051e+04, 4.970377768100323981e+04, 5.795967273138576164e+04, 6.773242484608792593e+04, 7.932613346949942761e+04, 9.311077397156915450e+04, 1.095375030536372224e+05, 1.291577556735669526e+05, 1.526471301608741586e+05, 1.808353350969648289e+05, 2.147438294770164181e+05, 2.556332515573999948e+05, 3.050633345562097502e+05, 3.649687926665853954e+05, 4.377556866857485380e+05, 5.264241222943208736e+05, 6.347248990108319410e+05, 7.673600526542426466e+05, 9.302403050337502786e+05, 1.130816502666451845e+06, 1.378507531155523742e+06, 1.685254393964162275e+06, 2.066239770168639390e+06, 2.540825270229354918e+06, 3.133775962036416630e+06, 3.876865148275802393e+06, 4.810984054018349430e+06, 5.988924089534678664e+06, 7.479057929608060924e+06, 9.370225698693408867e+06, 1.177824230977510661e+07, 1.485459301432580619e+07, 1.879809270383398104e+07, 2.387057334436346400e+07, 3.041806552258603202e+07, 3.889950046843262151e+07, 4.992574374586696017e+07, 6.431287504495613210e+07, 8.315518519925858136e+07, 1.079255664704117961e+08, 1.406141073390035115e+08, 1.839201785677305607e+08, 2.415197116904975365e+08, 3.184386015381112281e+08, 4.215765018929686736e+08, 5.604446356915114550e+08, 7.482094398046911572e+08, 1.003175129668246151e+09, 1.350898918997482870e+09, 1.827222165053491590e+09, 2.482633480831760933e+09, 3.388577637234919719e+09, 4.646620065299105644e+09, 6.401821801566297122e+09, 8.862352038053251473e+09, 1.232838602859196811e+10, 1.723489297480180023e+10, 2.421530528469447376e+10, 3.419673813208063025e+10, 4.854312364622606540e+10, 6.927149043760342676e+10, 9.938049490186203616e+10, 1.433521424759854145e+11, 2.079221734483088227e+11, 3.032695241820108158e+11, 4.448631503727710431e+11, 6.563458646477901051e+11, 9.740635696398910980e+11, 1.454220520059656158e+12, 2.184250688898627320e+12, 3.300999104757560757e+12, 5.019970485022749012e+12, 7.682676299017607834e+12, 1.183376596003983872e+13, 1.834748853557035315e+13, 2.863639312458363586e+13, 4.499803892715039958e+13, 7.119486876989154498e+13, 1.134307017980122346e+14, 1.820065782363618395e+14, 2.941484500615394037e+14, 4.788707305890930382e+14, 7.854025036928623551e+14, 1.297894304619860251e+15, 2.161279954782425640e+15, 3.627102147035003834e+15, 6.135342933440950378e+15, 1.046170006362244506e+16, 1.798477357839665686e+16, 3.117473412332331475e+16, 5.449445073049184222e+16, 9.607515505017978212e+16, 1.708589224452677852e+17, 3.065429751110228665e+17, 5.549227437451149511e+17, 1.013730232778046314e+18, 1.869059895876405824e+18, 3.478549552381578424e+18, 6.535992245975463763e+18, 1.240019272261066308e+19, 2.375828866910936629e+19, 4.597682433604432625e+19, 8.988106816837128428e+19, 1.775302379393632263e+20, 3.543413304390973486e+20, 7.148061397675525327e+20, 1.457620510577186305e+21, 3.005137124879829797e+21, 6.265024861633250697e+21, 1.320979941090283816e+22, 2.817487535902146221e+22, 6.079933041429805231e+22, 1.327658853647212083e+23, 2.934311759183641318e+23, 6.565087216807130026e+23, 1.487212273437937650e+24, 3.411840196076788128e+24, 7.928189928797018762e+24, 1.866451877029704857e+25, 4.452521859886739549e+25, 1.076545435174977662e+26, 2.638685681190697586e+26, 6.557908470244186498e+26, 1.652952243735585721e+27, 4.226383395914916199e+27, 1.096450394268080148e+28, 2.886822082999286080e+28, 7.715480389344015925e+28, 2.093728789309964846e+29, 5.770275789447655037e+29, 1.615463845391781140e+30, 4.595470055795608691e+30, 1.328629392686523255e+31, 3.905079681530784219e+31, 1.167134024271997252e+32, 3.548058538654277403e+32, 1.097378059358046160e+33, 3.454102978064445595e+33, 1.106745393701652323e+34, 3.610899559139069994e+34, 1.199946999283670567e+35, 4.062687014190878792e+35, 1.401835223893224514e+36, 4.931085527333162173e+36, 1.768812393284919500e+37, 6.472148293945199961e+37, 2.416453721739211922e+38, 9.208944720398123862e+38, 3.583297028622126676e+39, 1.424097482596699440e+40, 5.782627833426411524e+40, 2.399862204084363183e+41, 1.018291572042305460e+42, 4.419105414822034531e+42, 1.962126117680499311e+43, 8.916742424061253707e+43, 4.148882478294757720e+44, 1.977256529558276930e+45, 9.655300233875401080e+45, 4.832878898335598922e+46, 2.480575878223098058e+47, 1.306102809757654706e+48, 7.057565717289569232e+48, 3.915276522229618618e+49, 2.230898980943393318e+50, 1.306141334496309306e+51, 7.861021286656392627e+51, 4.865583758538451107e+52, 3.098487425915704674e+53, 2.031037614862563901e+54, 1.370999647608260200e+55, 9.534736274325001528e+55, 6.834959923166415407e+56, 5.052733546324789020e+57, 3.853810997282159979e+58, 3.034183107853208298e+59, 2.467161926009838899e+60, 2.072901039813580593e+61, 1.800563980579615383e+62, 1.617764027895344257e+63, 1.504283028250688329e+64, 1.448393206525427172e+65, 1.444855510980115799e+66, 1.494120428855029243e+67, 1.602566566107015722e+68, 1.783880504153942988e+69, 2.061999240572760738e+70, 2.476521794698572715e+71, 3.092349914153497358e+72, 4.016927238305985810e+73, 5.431607545226497387e+74, 7.650086824042822759e+75, 1.123017984114349288e+77, 1.719382952966052004e+78, 2.747335718690686674e+79, 4.584545010557684123e+80, 7.995082041539250252e+81, 1.458119909365899044e+83, 2.783001178679600175e+84, 5.562812231966194628e+85, 1.165338768982404578e+87, 2.560399126432838224e+88, 5.904549641859098192e+89, 1.430278474749838710e+91, 3.642046122956932563e+92, 9.756698571206402300e+93, 2.751946044275883051e+95, 8.179164793643197279e+96, 2.563704735086825890e+98, 8.481656496128255880e+99, 2.964260254403981007e+101, 1.095342970031208886e+103, 4.283148547584870628e+104, 1.773954352944319744e+106, 7.788991081894224760e+107, 3.628931721056821352e+109, 1.795729272516020592e+111, 9.446685151482835339e+112, 5.288263179614488101e+114, 3.153311236741401362e+116, 2.004807079683827669e+118, 1.360407192665237716e+120, 9.862825609807810517e+121, 7.647551788591128099e+123, 6.348802224871730088e+125, 5.649062361980019098e+127, 5.393248003523784781e+129, 5.530897191915703916e+131, 6.099598644640894333e+133, 7.242098433491964504e+135, 9.268083053637375570e+137, 1.279942702416040582e+140, 1.909796626960621302e+142, 3.082540300669885040e+144, 5.388809732384179657e+146, 1.021610251056626535e+149, 2.103005440072790650e+151, 4.706753990348725570e+153, 1.146834128125248991e+156, },
   };
   m_committed_refinements = static_cast<boost::math::detail::atomic_unsigned_integer_type>(m_weights.size() - 1);
   m_t_min = -6.164062500000000000;
   if (m_max_refinements >= m_abscissas.size())
   {
      m_abscissas.resize(m_max_refinements + 1);
      m_weights.resize(m_max_refinements + 1);
   }
   else
   {
      m_max_refinements = m_abscissas.size() - 1;
   }
}
#if LDBL_MAX_EXP == 16384
template<class Real, class Policy>
void exp_sinh_detail<Real, Policy>::init(const mpl::int_<3>&)
{
   m_abscissas = {
      { 1.02756529896290544244959196973059583e-2497L, 2.56737528671961581475200468317128232e-919L, 1.17417808941462434184174780056564573e-338L, 4.82182886130634548471358754377036370e-125L, 1.85613301660646818149136526457281019e-46L, 1.52174118093087534300657777272732001e-17L, 6.75122240537294392532710530940672267e-07L, 5.94481311616464419075825632567494453e-03L, 2.00100938779037997581424620542543429e-01L, 1.17328605653712546899681147538372171e+00L, 8.18356490677287285512063117929807241e+00L, 5.59865842621965368881982340891928481e+02L, 3.69902944883650290371636082450503730e+07L, 4.05747121124517088709477132072461878e+20L, 1.07723884748977308147226626407207905e+56L, 2.07250561337258237728923403163755392e+152L, 1.09889904624000153879292638133263171e+414L, 3.02463014753652876878705286965250144e+1125L, },
      { 3.16339947894004847541521297710937343e-1515L, 7.02786763812753004271170107158747593e-558L, 1.08465499866859733494552744914276656e-205L, 3.97220624097731753646493300738183748e-76L, 1.84145280968701148636501796762008815e-28L, 6.40886341101610144938011594904313817e-11L, 1.89200275395722467663251234615351291e-04L, 5.04892743776943294143478969573235061e-02L, 5.25946553709738448524487603870477588e-01L, 2.72635049439566736308739858009584752e+00L, 4.20081657572145199006060015525396829e+01L, 3.75221714819472331206969009243353365e+04L, 3.11642465424592079726559332629050577e+12L, 9.61947229245436139236957297153092319e+33L, 2.42007357898805628851519620917402234e+92L, 1.34351470989086331111432001407522043e+251L, 4.34937560839564995558174638985438726e+682L, 4.01820305474077838467315109614612109e+1855L, },
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1.36040719266523771611516008331762962e+120L, 9.86282560980781051743602195410395887e+121L, 7.64755178859112809938428139017982021e+123L, 6.34880222487173008841344329862213996e+125L, 5.64906236198001909791959175488227229e+127L, 5.39324800352378478055022039572371179e+129L, 5.53089719191570391565414448432944942e+131L, 6.09959864464089433289271654904908851e+133L, 7.24209843349196450391058906977712497e+135L, 9.26808305363737556950784175210077690e+137L, 1.27994270241604058214925694813276489e+140L, 1.90979662696062130244831484512150929e+142L, 3.08254030066988503957988563764712878e+144L, 5.38880973238417965706179354197373928e+146L, 1.02161025105662653467101460483765248e+149L, 2.10300544007279065014421211807768152e+151L, 4.70675399034872557015773705065650223e+153L, 1.14683412812524899101968167573148610e+156L, 3.04620262376779901134561159740015427e+158L, 8.83255301555740088857655282843830654e+160L, 2.79951315833790052768515917244690507e+163L, 9.71307000884329724595836237775132776e+165L, 3.69425449543187541186652254254454177e+168L, 1.54248755204034481247092284401752383e+171L, 7.08075007659653083674442572183052884e+173L, 3.57888569536270290704774796012385631e+176L, 1.99473765641034107285413476042860568e+179L, 1.22789700989638770500092926180435793e+182L, 8.36095001442791620159284429240141671e+184L, 6.30749438488829733664127973626729614e+187L, 5.28039699582730274851611343025005913e+190L, 4.91356459266260178144685151251583280e+193L, 5.09061556382806163145943155929283695e+196L, 5.88195913486315120755496558081929324e+199L, 7.59272859182451584412681161192886089e+202L, 1.09687154447604565252927157604063023e+206L, 1.77650105264457177914887205035954057e+209L, 3.23153511879574325299022213712900198e+212L, 6.61424415330008555964088497876375007e+215L, 1.52611134962392865764465743843181152e+219L, 3.97691502072254861067816109956158434e+222L, 1.17271592685350180601663411607927347e+226L, 3.92076851079784438154800269803529292e+229L, 1.48915601904650135853122181753421959e+233L, 6.43831323019893638007682069747894997e+236L, 3.17506717851901774760997889290937204e+240L, 1.78970981603629426034165602936202663e+244L, 1.15551435950001094003467361479483663e+248L, 8.56366431033316582912879348191377839e+251L, 7.30093770528170061921940254565023758e+255L, 7.17613138815551609337504025522760569e+259L, 8.15019404042552378087870259624107791e+263L, 1.07201229194901841245742935320285314e+268L, 1.63677814658507005123653360340510968e+272L, 2.90775562270833690431514296460636317e+276L, 6.02476179304325236422526103127046739e+280L, 1.45944561364291559252990517774206937e+285L, 4.14353248208966528107409825739318649e+289L, 1.38220972739972368321976302536673924e+294L, 5.43125471568796436605394023488404770e+298L, 2.52039989595272682474151246524004609e+303L, 1.38490332203279628724542169932072504e+308L, 9.03453415480179250943103381623811201e+312L, 7.01620311300324094081813342355630834e+317L, 6.50430483422567669743617206850738485e+322L, 7.21793562600493199951776097195343971e+327L, 9.61542788471746566451160668498411528e+332L, 1.54211655565340209996546117001243607e+338L, 2.98626205265198316430063943341329432e+343L, 7.00309320577422492544778192980108604e+348L, 1.99486089518136492496460973366880635e+354L, 6.92350663128275446878446973158773950e+359L, 2.93684755383592258491626945473185368e+365L, 1.52739293250863294426010436780725812e+371L, 9.77075509850276765943058812672579852e+376L, 7.71310608088780517993569363011828070e+382L, 7.53863036472313339350939561575995488e+388L, 9.15331385155864163687518059055937567e+394L, 1.38538605697398143363179835422022577e+401L, 2.62287133256068615930266548676255190e+407L, 6.23343982286571042809890547122705804e+413L, 1.86628588041890755929921756251934723e+420L, 7.06492694188791912037300528166794228e+426L, 3.39406886800977749230458579824930803e+433L, 2.07704891812976483907563047536681219e+440L, 1.62532865525590176989706193358042030e+447L, 1.63262112354994112352218911327913750e+454L, 2.11342684365334123128646755974119857e+461L, 3.53982137873383101244091847412793714e+468L, 7.70246700302666062188915359100825615e+475L, 2.18636422788338230254129077405708124e+483L, 8.12975261672049081897166938196495657e+490L, 3.97686557044826916151646962242652853e+498L, 2.57033035969007091507617008526033295e+506L, 2.20458407348036235529376715504150602e+514L, 2.52051509380683369529400145083533353e+522L, 3.85871376898138292734730034828559871e+530L, 7.94663225793828689108907007781152553e+538L, 2.21176541223395827472447113026924253e+547L, 8.35931033048630497134082029598865726e+555L, 4.31091797212556485985662056018893390e+564L, 3.04833317305882254988404372326531988e+573L, 2.97034828681146526635277450855709161e+582L, 4.00864404566992526097179834506253327e+591L, 7.53113144131492631353410204171028663e+600L, 1.97996763586022811207860344830247407e+610L, 7.32300332662100885299893727481183608e+619L, 3.83078680906847773947984890776183687e+629L, 2.84987258373806149506606754536239806e+639L, 3.03186631046306534459943952897407369e+649L, 4.63861318260680959360747724936035922e+659L, 1.02646622253495677529633262335412306e+670L, 3.30448344760519942319105428211388701e+680L, 1.55678514244926540491694986676104766e+691L, 1.07975219247204914347510266773073325e+702L, 1.10926415409608640204268413223928121e+713L, 1.69843188882084389205231670587156933e+724L, 3.90025209215096037836224226547246383e+735L, 1.35188796159061122898267917047667153e+747L, 7.11881895741722013661309086794573765e+758L, 5.73263787962641176699015570741387791e+770L, 7.10698682909851371094390920546530663e+782L, 1.36568905751347705631533710470350932e+795L, 4.09591384091714486453161283605440034e+807L, 1.93075428208975454032168180693618424e+820L, 1.44069783794868490577087909226154603e+833L, 1.71407451380697883211569548277738601e+846L, 3.27557874564463748685767424892341420e+859L, 1.01295195987435253561137255728975319e+873L, 5.10768437019276174029340754351596177e+886L, 4.23191986113702770379280941046346950e+900L, 5.80664714178397794019307157189161329e+914L, 1.32995815980583547946711112525038194e+929L, 5.12600842672542100652183507817331030e+943L, 3.35203762278831767267193293263751763e+958L, 3.75009417204153826893896307870937057e+973L, 7.23855050824188975713471018223024339e+988L, 2.43146178229439003194650931378387467e+1004L, 1.43376736234835679429446577737976919e+1020L, 1.49738681485939897351147361037410278e+1036L, 2.79474808763788045317059787958854766e+1052L, 9.40752795141195895210630116566470676e+1068L, 5.76455681194134988563523968421696548e+1085L, 6.49098750070655215612470119412325218e+1102L, 1.35603677524062211064037225514112165e+1120L, 5.30731596106421482379267500594247426e+1137L, 3.93020043869734370491941322540535807e+1155L, 5.56226722613029149136813618379760709e+1173L, 1.51990408820680241841102181882025951e+1192L, 8.10228003417607034858018290055212984e+1210L, 8.51521180721994744419289716417963237e+1229L, 1.78329495296502824223674285976432097e+1249L, 7.52325725334531880022021234450122858e+1268L, 6.46447702663797449769360764507187142e+1288L, 1.14411796435953528891736478925455547e+1309L, 4.21851818337788742448241659152628519e+1329L, 3.27808619028067308419286053048979085e+1350L, 5.43188779501763188996015031600338462e+1371L, 1.94236185576822902995555282219996135e+1393L, 1.51711647857248503907031482339088565e+1415L, 2.62035716514505778741231466041668281e+1437L, 1.01340333806343444348385264050569250e+1460L, 8.88786410219005270769408353397020687e+1482L, 1.79062851327433476234422894649930707e+1506L, 8.39642792144232596950658702528918677e+1529L, 9.28628794761707451127390451820966789e+1553L, 2.45536895088636462839367313490581387e+1578L, 1.57354562229875356978426356241845302e+1603L, 2.47847583619098850454983740131691503e+1628L, 9.73157119375940175602769413110414643e+1653L, 9.66320447484532719750186034583884499e+1679L, 2.46232109538721189753853963925622165e+1706L, 1.63417596934387293040006746046570718e+1733L, 2.86767794799456586471233013913198039e+1760L, 1.35110548955493375904544893914917995e+1788L, 1.73592152545700077097814839827674920e+1816L, 6.17893831026015926230407301367680801e+1844L, 6.19169576655007716364858612984691562e+1873L, 1.77539961419331109157892833779912252e+1903L, 1.48102931564535770775910220632570312e+1933L, 3.65523833138677287346435504279580939e+1963L, 2.71500576533505130343548298805675281e+1994L, 6.17538661057993294979124427622665421e+2025L, 4.37773911614056336228335278244614535e+2057L, 9.84696637606677900175890481086698860e+2089L, 7.15679932872021171306956409599896671e+2122L, 1.71206538074954819527676482193571839e+2156L, 1.37358203471630226464631105286036694e+2190L, 3.76701670663930120912543386433302245e+2224L, 3.60043887764831236838085599723119708e+2259L, 1.22311399177140229476034440208616729e+2295L, 1.50662485913882109231872682750679813e+2331L, 6.86720031172136555587682118613084257e+2367L, 1.18233110675109495729851537371527994e+2405L, 7.85186218386652904615339091354671418e+2442L, },
   };
   m_committed_refinements = static_cast<boost::math::detail::atomic_unsigned_integer_type>(m_weights.size() - 1);
   m_t_min = -8.8984375000000L;
   if (m_max_refinements >= m_abscissas.size())
   {
      m_abscissas.resize(m_max_refinements + 1);
      m_weights.resize(m_max_refinements + 1);
   }
   else
   {
      m_max_refinements = m_abscissas.size() - 1;
   }
}
#endif
#ifdef BOOST_HAS_FLOAT128
template<class Real, class Policy>
void exp_sinh_detail<Real, Policy>::init(const mpl::int_<4>&)
{
   m_abscissas = {
      { 1.02756529896290544244959196973059583e-2497Q, 2.56737528671961581475200468317128232e-919Q, 1.17417808941462434184174780056564573e-338Q, 4.82182886130634548471358754377036370e-125Q, 1.85613301660646818149136526457281019e-46Q, 1.52174118093087534300657777272732001e-17Q, 6.75122240537294392532710530940672267e-07Q, 5.94481311616464419075825632567494453e-03Q, 2.00100938779037997581424620542543429e-01Q, 1.17328605653712546899681147538372171e+00Q, 8.18356490677287285512063117929807241e+00Q, 5.59865842621965368881982340891928481e+02Q, 3.69902944883650290371636082450503730e+07Q, 4.05747121124517088709477132072461878e+20Q, 1.07723884748977308147226626407207905e+56Q, 2.07250561337258237728923403163755392e+152Q, 1.09889904624000153879292638133263171e+414Q, 3.02463014753652876878705286965250144e+1125Q, },
      { 3.16339947894004847541521297710937343e-1515Q, 7.02786763812753004271170107158747593e-558Q, 1.08465499866859733494552744914276656e-205Q, 3.97220624097731753646493300738183748e-76Q, 1.84145280968701148636501796762008815e-28Q, 6.40886341101610144938011594904313817e-11Q, 1.89200275395722467663251234615351291e-04Q, 5.04892743776943294143478969573235061e-02Q, 5.25946553709738448524487603870477588e-01Q, 2.72635049439566736308739858009584752e+00Q, 4.20081657572145199006060015525396829e+01Q, 3.75221714819472331206969009243353365e+04Q, 3.11642465424592079726559332629050577e+12Q, 9.61947229245436139236957297153092319e+33Q, 2.42007357898805628851519620917402234e+92Q, 1.34351470989086331111432001407522043e+251Q, 4.34937560839564995558174638985438726e+682Q, 4.01820305474077838467315109614612109e+1855Q, },
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   };
   m_committed_refinements = static_cast<boost::math::detail::atomic_unsigned_integer_type>(m_weights.size() - 1);
   m_t_min = -8.89265635039934944849389055479809884Q;
   if (m_max_refinements >= m_abscissas.size())
   {
      m_abscissas.resize(m_max_refinements + 1);
      m_weights.resize(m_max_refinements + 1);
   }
   else
   {
      m_max_refinements = m_abscissas.size() - 1;
   }
}
#endif

}
}
}
}
#endif