libcarla/include/system/boost/math/quadrature/detail/sinh_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_SINH_SINH_DETAIL_HPP
#define BOOST_MATH_QUADRATURE_DETAIL_SINH_SINH_DETAIL_HPP

#include <cmath>
#include <string>
#include <vector>
#include <typeinfo>
#include <boost/math/constants/constants.hpp>
#include <boost/math/tools/atomic.hpp>
#include <boost/math/policies/error_handling.hpp>
#include <boost/math/special_functions/trunc.hpp>
#include <boost/math/tools/config.hpp>

#ifdef BOOST_HAS_THREADS
#include <mutex>
#endif

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


// Returns the sinh-sinh quadrature of a function f over the entire real line

template<class Real, class Policy>
class sinh_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:
    sinh_sinh_detail(size_t max_refinements);

    template<class F>
    auto integrate(const F f, Real tolerance, Real* error, Real* L1, std::size_t* levels)->decltype(std::declval<F>()(std::declval<Real>())) const;

private:
private:
   const std::vector<Real>& get_abscissa_row(std::size_t n)const
   {
#if !defined(BOOST_MATH_NO_ATOMIC_INT) && defined(BOOST_HAS_THREADS)
      if (m_committed_refinements.load() < n)
         extend_refinements();
      BOOST_MATH_ASSERT(m_committed_refinements.load() >= n);
#else
      if (m_committed_refinements < n)
         extend_refinements();
      BOOST_MATH_ASSERT(m_committed_refinements >= n);
#endif
      return m_abscissas[n];
   }
   const std::vector<Real>& get_weight_row(std::size_t n)const
   {
#if !defined(BOOST_MATH_NO_ATOMIC_INT) && defined(BOOST_HAS_THREADS)
      if (m_committed_refinements.load() < n)
         extend_refinements();
      BOOST_MATH_ASSERT(m_committed_refinements.load() >= n);
#else
      if (m_committed_refinements < n)
         extend_refinements();
      BOOST_MATH_ASSERT(m_committed_refinements >= n);
#endif
      return m_weights[n];
   }
   void init(const std::integral_constant<int, 0>&);
   void init(const std::integral_constant<int, 1>&);
   void init(const std::integral_constant<int, 2>&);
   void init(const std::integral_constant<int, 3>&);
#ifdef BOOST_HAS_FLOAT128
   void init(const std::integral_constant<int, 4>&);
#endif

   void extend_refinements()const
   {
#if !defined(BOOST_MATH_NO_ATOMIC_INT) && defined(BOOST_HAS_THREADS)
      std::lock_guard<std::mutex> guard(m_mutex);
#endif
      //
      // Check some other thread hasn't got here after we read the atomic variable, but before we got here:
      //
#if !defined(BOOST_MATH_NO_ATOMIC_INT) && defined(BOOST_HAS_THREADS)
      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;
      using constants::half_pi;

      std::size_t row = ++m_committed_refinements;

      Real h = ldexp(Real(1), -static_cast<int>(row));
      size_t k = static_cast<size_t>(boost::math::lltrunc(ceil(m_t_max / (2 * h))));
      m_abscissas[row].reserve(k);
      m_weights[row].reserve(k);
      Real arg = h;
      while (arg < m_t_max)
      {
         Real tmp = half_pi<Real>()*sinh(arg);
         Real x = sinh(tmp);
         m_abscissas[row].emplace_back(x);
         Real w = cosh(arg)*half_pi<Real>()*cosh(tmp);
         m_weights[row].emplace_back(w);
         arg += 2 * h;
      }
   }

   Real m_t_max;

   mutable std::vector<std::vector<Real>> m_abscissas;
   mutable std::vector<std::vector<Real>> m_weights;
   std::size_t                       m_max_refinements;
#if !defined(BOOST_MATH_NO_ATOMIC_INT) && defined(BOOST_HAS_THREADS)
   mutable boost::math::detail::atomic_unsigned_type      m_committed_refinements;
   mutable std::mutex m_mutex;
#else
   mutable unsigned                  m_committed_refinements;
#endif
};

template<class Real, class Policy>
sinh_sinh_detail<Real, Policy>::sinh_sinh_detail(size_t max_refinements)
   : m_abscissas(max_refinements), m_weights(max_refinements), m_max_refinements(max_refinements)
{
   init(std::integral_constant<int, initializer_selector>());
}

template<class Real, class Policy>
template<class F>
auto sinh_sinh_detail<Real, Policy>::integrate(const F f, Real tolerance, Real* error, Real* L1, std::size_t* levels)->decltype(std::declval<F>()(std::declval<Real>())) const
{
    using std::abs;
    using std::sqrt;
    using boost::math::constants::half;
    using boost::math::constants::half_pi;

    static const char* function = "boost::math::quadrature::sinh_sinh<%1%>::integrate";

    typedef decltype(f(static_cast<Real>(0))) K;
    static_assert(!std::is_integral<K>::value,
                  "The return type cannot be integral, it must be either a real or complex floating point type.");
    K y_max = f(boost::math::tools::max_value<Real>());
    if(abs(y_max) > boost::math::tools::epsilon<Real>())
    {
        return static_cast<K>(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()));
    }

    K y_min = f(-boost::math::tools::max_value<Real>());
    if(abs(y_min) > boost::math::tools::epsilon<Real>())
    {
        return static_cast<K>(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()));
    }

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

    // Uncomment the estimates to work the convergence on the command line.
    // std::cout << std::setprecision(std::numeric_limits<Real>::digits10);
    // std::cout << "First estimate : " << I0 << std::endl;
    K I1 = I0;
    Real L1_I1 = L1_I0;
    for (size_t i = 0; i < m_abscissas[1].size(); ++i)
    {
        Real x= m_abscissas[1][i];
        K yp = f(x);
        K ym = f(-x);
        I1 += (yp + ym)*m_weights[1][i];
        L1_I1 += (abs(yp) + abs(ym))*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_max_refinements; ++i)
    {
        I0 = I1;
        L1_I0 = L1_I1;

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

        Real abterm1 = 1;
        Real eps = boost::math::tools::epsilon<Real>()*L1_I1;

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

        for(size_t j = 0; j < abscissa_row.size(); ++j)
        {
            Real x = abscissa_row[j];
            K yp = f(x);
            K ym = f(-x);
            sum += (yp + ym)*weight_row[j];
            Real abterm0 = (abs(yp) + abs(ym))*weight_row[j];
            absum += abterm0;

            // We require two consecutive terms to be < eps in case we hit a zero of f.
            if (x > static_cast<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 (!(boost::math::isfinite)(L1_I1))
        {
            const char* err_msg = "The sinh_sinh quadrature evaluated your function at a singular point, leading to the value %1%.\n"
               "sinh_sinh quadrature cannot handle singularities in the domain.\n"
               "If you are sure your function has no singularities, please submit a bug against boost.math\n";
            return static_cast<K>(policies::raise_evaluation_error(function, err_msg, 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 sinh_sinh_detail<Real, Policy>::init(const std::integral_constant<int, 0>&)
{
   using std::log;
   using std::sqrt;
   using std::cosh;
   using std::sinh;
   using std::ceil;
   using boost::math::constants::two_div_pi;
   using boost::math::constants::half_pi;

   m_committed_refinements = 4;

   // 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.
   m_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 = static_cast<Real>(1) / static_cast<Real>(1 << i);
      size_t k = static_cast<size_t>(boost::math::lltrunc(ceil(m_t_max / (2 * h))));
      m_abscissas[i].reserve(k);
      m_weights[i].reserve(k);
      // We don't add 0 to the abscissas; that's treated as a special case.
      Real arg = h;
      while (arg < m_t_max)
      {
         Real tmp = half_pi<Real>()*sinh(arg);
         Real x = sinh(tmp);
         m_abscissas[i].emplace_back(x);
         Real w = cosh(arg)*half_pi<Real>()*cosh(tmp);
         m_weights[i].emplace_back(w);

         if (i != 0)
         {
            arg += 2 * h;
         }
         else
         {
            arg += h;
         }
      }
   }
}

template<class Real, class Policy>
void sinh_sinh_detail<Real, Policy>::init(const std::integral_constant<int, 1>&)
{
   m_abscissas = {
      { 3.08828742e+00f, 1.48993185e+02f, 3.41228925e+06f, 2.06932577e+18f, },
      { 9.13048763e-01f, 1.41578929e+01f, 6.70421552e+03f, 9.64172533e+10f, },
      { 4.07297690e-01f, 1.68206671e+00f, 6.15089799e+00f, 4.00396235e+01f, 7.92920025e+02f, 1.02984971e+05f, 3.03862311e+08f, 1.56544547e+14f, },
      { 1.98135272e-01f, 6.40155674e-01f, 1.24892870e+00f, 2.26608084e+00f, 4.29646270e+00f, 9.13029039e+00f, 2.31110765e+01f, 7.42770603e+01f, 3.26720921e+02f, 2.15948569e+03f, 2.41501526e+04f, 5.31819400e+05f, 2.80058686e+07f, 4.52406508e+09f, 3.08561257e+12f, 1.33882673e+16f, },
      { 9.83967894e-02f, 3.00605618e-01f, 5.19857979e-01f, 7.70362083e-01f, 1.07131137e+00f, 1.45056976e+00f, 1.95077855e+00f, 2.64003177e+00f, 3.63137237e+00f, 5.11991533e+00f, 7.45666098e+00f, 1.13022613e+01f, 1.79641069e+01f, 3.01781070e+01f, 5.40387580e+01f, 1.04107731e+02f, 2.18029520e+02f, 5.02155699e+02f, 1.28862131e+03f, 3.73921687e+03f, 1.24750730e+04f, 4.87639975e+04f, 2.28145658e+05f, 1.30877796e+06f, 9.46084663e+06f, 8.88883120e+07f, 1.12416883e+09f, 1.99127673e+10f, 5.16743469e+11f, 2.06721881e+13f, 1.35061503e+15f, 1.53854066e+17f, },
      { 4.91151004e-02f, 1.48013150e-01f, 2.48938814e-01f, 3.53325424e-01f, 4.62733557e-01f, 5.78912068e-01f, 7.03870253e-01f, 8.39965859e-01f, 9.90015066e-01f, 1.15743257e+00f, 1.34641276e+00f, 1.56216711e+00f, 1.81123885e+00f, 2.10192442e+00f, 2.44484389e+00f, 2.85372075e+00f, 3.34645891e+00f, 3.94664582e+00f, 4.68567310e+00f, 5.60576223e+00f, 6.76433234e+00f, 8.24038318e+00f, 1.01439436e+01f, 1.26302471e+01f, 1.59213040e+01f, 2.03392186e+01f, 2.63584645e+01f, 3.46892633e+01f, 4.64129147e+01f, 6.32055079e+01f, 8.77149726e+01f, 1.24209693e+02f, 1.79718635e+02f, 2.66081728e+02f, 4.03727303e+02f, 6.28811307e+02f, 1.00707984e+03f, 1.66156823e+03f, 2.82965144e+03f, 4.98438627e+03f, 9.10154693e+03f, 1.72689266e+04f, 3.41309958e+04f, 7.04566898e+04f, 1.52340422e+05f, 3.46047978e+05f, 8.28472421e+05f, 2.09759615e+06f, 5.63695080e+06f, 1.61407141e+07f, 4.94473068e+07f, 1.62781052e+08f, 5.78533297e+08f, 2.23083854e+09f, 9.38239131e+09f, 4.32814954e+10f, 2.20307274e+11f, 1.24524507e+12f, 7.86900053e+12f, 5.59953143e+13f, 4.52148695e+14f, 4.17688952e+15f, 4.45286776e+16f, 5.52914285e+17f, 8.07573252e+18f, },
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      { 1.57096255e+00f, 1.57229290e+00f, 1.57495658e+00f, 1.57895955e+00f, 1.58431079e+00f, 1.59102230e+00f, 1.59910918e+00f, 1.60858966e+00f, 1.61948515e+00f, 1.63182037e+00f, 1.64562338e+00f, 1.66092569e+00f, 1.67776241e+00f, 1.69617233e+00f, 1.71619809e+00f, 1.73788633e+00f, 1.76128784e+00f, 1.78645779e+00f, 1.81345587e+00f, 1.84234658e+00f, 1.87319943e+00f, 1.90608922e+00f, 1.94109632e+00f, 1.97830698e+00f, 2.01781368e+00f, 2.05971547e+00f, 2.10411838e+00f, 2.15113585e+00f, 2.20088916e+00f, 2.25350798e+00f, 2.30913084e+00f, 2.36790578e+00f, 2.42999091e+00f, 2.49555516e+00f, 2.56477893e+00f, 2.63785496e+00f, 2.71498915e+00f, 2.79640147e+00f, 2.88232702e+00f, 2.97301705e+00f, 3.06874019e+00f, 3.16978367e+00f, 3.27645477e+00f, 3.38908227e+00f, 3.50801806e+00f, 3.63363896e+00f, 3.76634859e+00f, 3.90657947e+00f, 4.05479525e+00f, 4.21149322e+00f, 4.37720695e+00f, 4.55250922e+00f, 4.73801517e+00f, 4.93438579e+00f, 5.14233166e+00f, 5.36261713e+00f, 5.59606472e+00f, 5.84356014e+00f, 6.10605759e+00f, 6.38458564e+00f, 6.68025373e+00f, 6.99425915e+00f, 7.32789480e+00f, 7.68255767e+00f, 8.05975815e+00f, 8.46113023e+00f, 8.88844279e+00f, 9.34361190e+00f, 9.82871448e+00f, 1.03460033e+01f, 1.08979234e+01f, 1.14871305e+01f, 1.21165112e+01f, 1.27892047e+01f, 1.35086281e+01f, 1.42785033e+01f, 1.51028871e+01f, 1.59862046e+01f, 1.69332867e+01f, 1.79494108e+01f, 1.90403465e+01f, 2.02124072e+01f, 2.14725057e+01f, 2.28282181e+01f, 2.42878539e+01f, 2.58605342e+01f, 2.75562800e+01f, 2.93861096e+01f, 3.13621485e+01f, 3.34977526e+01f, 3.58076454e+01f, 3.83080730e+01f, 4.10169773e+01f, 4.39541917e+01f, 4.71416602e+01f, 5.06036855e+01f, 5.43672075e+01f, 5.84621188e+01f, 6.29216205e+01f, 6.77826252e+01f, 7.30862125e+01f, 7.88781469e+01f, 8.52094636e+01f, 9.21371360e+01f, 9.97248336e+01f, 1.08043785e+02f, 1.17173764e+02f, 1.27204209e+02f, 1.38235512e+02f, 1.50380485e+02f, 1.63766039e+02f, 1.78535118e+02f, 1.94848913e+02f, 2.12889407e+02f, 2.32862309e+02f, 2.55000432e+02f, 2.79567594e+02f, 3.06863126e+02f, 3.37227087e+02f, 3.71046310e+02f, 4.08761417e+02f, 4.50874968e+02f, 4.97960949e+02f, 5.50675821e+02f, 6.09771424e+02f, 6.76110054e+02f, 7.50682104e+02f, 8.34626760e+02f, 9.29256285e+02f, 1.03608458e+03f, 1.15686082e+03f, 1.29360914e+03f, 1.44867552e+03f, 1.62478326e+03f, 1.82509876e+03f, 2.05330964e+03f, 2.31371761e+03f, 2.61134924e+03f, 2.95208799e+03f, 3.34283233e+03f, 3.79168493e+03f, 4.30817984e+03f, 4.90355562e+03f, 5.59108434e+03f, 6.38646863e+03f, 7.30832183e+03f, 8.37874981e+03f, 9.62405722e+03f, 1.10756067e+04f, 1.27708661e+04f, 1.47546879e+04f, 1.70808754e+04f, 1.98141031e+04f, 2.30322789e+04f, 2.68294532e+04f, 3.13194118e+04f, 3.66401221e+04f, 4.29592484e+04f, 5.04810088e+04f, 5.94547213e+04f, 7.01854788e+04f, 8.30475173e+04f, 9.85009981e+04f, 1.17113127e+05f, 1.39584798e+05f, 1.66784302e+05f, 1.99790063e+05f, 2.39944995e+05f, 2.88925794e+05f, 3.48831531e+05f, 4.22297220e+05f, 5.12639825e+05f, 6.24046488e+05f, 7.61817907e+05f, 9.32683930e+05f, 1.14521401e+06f, 1.41035265e+06f, 1.74212004e+06f, 2.15853172e+06f, 2.68280941e+06f, 3.34498056e+06f, 4.18399797e+06f, 5.25055801e+06f, 6.61086017e+06f, 8.35163942e+06f, 1.05869253e+07f, 1.34671524e+07f, 1.71914827e+07f, 2.20245345e+07f, 2.83191730e+07f, 3.65476782e+07f, 4.73445266e+07f, 6.15653406e+07f, 8.03684303e+07f, 1.05328028e+08f, 1.38592169e+08f, 1.83103699e+08f, 2.42910946e+08f, 3.23606239e+08f, 4.32947522e+08f, 5.81743297e+08f, 7.85117979e+08f, 1.06432920e+09f, 1.44938958e+09f, 1.98286647e+09f, 2.72541431e+09f, 3.76386796e+09f, 5.22313881e+09f, 7.28378581e+09f, 1.02080964e+10f, 1.43789932e+10f, 2.03583681e+10f, 2.89749983e+10f, 4.14577375e+10f, 5.96383768e+10f, 8.62622848e+10f, 1.25466705e+11f, 1.83521298e+11f, 2.69981221e+11f, 3.99492845e+11f, 5.94638056e+11f, 8.90440997e+11f, 1.34155194e+12f, 2.03376855e+12f, 3.10262796e+12f, 4.76359832e+12f, 7.36142036e+12f, 1.14512696e+13f, 1.79331419e+13f, 2.82758550e+13f, 4.48929705e+13f, 7.17780287e+13f, 1.15585510e+14f, 1.87483389e+14f, 3.06351036e+14f, 5.04340065e+14f, 8.36616340e+14f, 1.39855635e+15f, 2.35633575e+15f, 4.00176517e+15f, 6.85137
   };
#if !defined(BOOST_MATH_NO_ATOMIC_INT) && defined(BOOST_HAS_THREADS)
   m_committed_refinements = static_cast<boost::math::detail::atomic_unsigned_integer_type>(m_weights.size() - 1);
#else
   m_committed_refinements = m_weights.size() - 1;
#endif
   m_t_max = 4.03936524f;
   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 sinh_sinh_detail<Real, Policy>::init(const std::integral_constant<int, 2>&)
{
   m_abscissas = {
      { 3.088287417976322866e+00, 1.489931846492091580e+02, 3.412289247883437102e+06, 2.069325766042617791e+18, 2.087002407609475560e+50, 2.019766160717908151e+137, },
      { 9.130487626376696748e-01, 1.415789294662811592e+01, 6.704215516223276482e+03, 9.641725327150499415e+10, 2.508950760085778485e+30, 1.447263535710337145e+83, },
      { 4.072976900657586902e-01, 1.682066707021148743e+00, 6.150897986386729515e+00, 4.003962351929400222e+01, 7.929200247931026321e+02, 1.029849713330979583e+05, 3.038623109252438574e+08, 1.565445474362494869e+14, 4.042465098430219104e+23, 1.321706827429658179e+39, 4.991231782099557998e+64, 7.352943850359875966e+106, },
      { 1.981352722514781726e-01, 6.401556735005260177e-01, 1.248928698253977663e+00, 2.266080840944321232e+00, 4.296462696702327381e+00, 9.130290387099955696e+00, 2.311107653864279933e+01, 7.427706034324012430e+01, 3.267209207115258917e+02, 2.159485694311818716e+03, 2.415015262896413060e+04, 5.318194002756929158e+05, 2.800586857217043323e+07, 4.524065079794338780e+09, 3.085612573980677122e+12, 1.338826733015807478e+16, 6.254617176562341381e+20, 6.182098535814164754e+26, 3.077293649788458067e+34, 2.348957289370104303e+44, 1.148543197899469758e+57, 2.255300070010069868e+73, 1.877919500569195394e+94, 1.367473887938624280e+121, },
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      { 1.573457773573108386e+00, 1.594892755038663787e+00, 1.638536515530234742e+00, 1.705980408212213620e+00, 1.799724394608737275e+00, 1.923322854425656307e+00, 2.081597373313268178e+00, 2.280934883790070511e+00, 2.529697852387704655e+00, 2.838784782552951185e+00, 3.222395745020980612e+00, 3.699081358854235112e+00, 4.293188274330526800e+00, 5.036865356322330076e+00, 5.972871140910932199e+00, 7.158538424311077564e+00, 8.671427800892076385e+00, 1.061747360297922326e+01, 1.314285002260235600e+01, 1.645145625668428040e+01, 2.083099449998189069e+01, 2.669235989791640190e+01, 3.462993514791378189e+01, 4.551518362653662579e+01, 6.064408087764392116e+01, 8.197296917485846798e+01, 1.125020468081652564e+02, 1.569096552844714123e+02, 2.226204347868638276e+02, 3.216385489504077755e+02, 4.737574505945461739e+02, 7.122994548146997637e+02, 1.094609652686376553e+03, 1.721697789176049576e+03, 2.775924909253835146e+03, 4.595230066268149347e+03, 7.823427586641573672e+03, 1.372357435269105405e+04, 2.485188961645119553e+04, 4.655538745425972783e+04, 9.041766782135686884e+04, 1.824843964862728392e+05, 3.836800264094614027e+05, 8.426271970245168026e+05, 1.938432574158782634e+06, 4.685112849356485528e+06, 1.193528667218607927e+07, 3.215643752247989316e+07, 9.196008928386600386e+07, 2.802223178457559964e+08, 9.136110825267458886e+08, 3.200910900783148591e+09, 1.210765264234723689e+10, 4.969024745093101808e+10, 2.224315751863855216e+11, 1.092125344449313660e+12, 5.916882980019919359e+12, 3.559743438494577249e+13, 2.394353652945465191e+14, 1.813551073517501917e+15, 1.558736706166165738e+16, 1.532714875555114333e+17, 1.739274776190789212e+18, 2.298841216802216313e+19, 3.574030698837762664e+20, 6.604899705451419080e+21, 1.467155879591820659e+23, 3.964094964398509381e+24, 1.319342840595348793e+26, 5.482251971340400742e+27, 2.885137894723827518e+29, 1.952539840765392110e+31, 1.727051489032222797e+33, 2.031343507095439396e+35, 3.236074146972599980e+37, 7.120487412983497200e+39, 2.209552707411017265e+42, 9.886282647791384648e+44, 6.530514048788273529e+47, 6.530706672481546528e+50, 1.015518807431281951e+54, 2.526366773162394510e+57, 1.036450519906790297e+61, 7.241966032627135861e+64, 8.919402520769714938e+68, 2.008463619152992905e+73, 8.596914764830260020e+77, 7.290599546829495220e+82, 1.280199563216419112e+88, 4.878349285603201150e+93, 4.240828248064127940e+99, 8.869771764721598720e+105, 4.723342575741417669e+112, 6.802035963326188581e+119, 2.824531180990009549e+127, 3.621049216745982252e+135, 1.541270150334942520e+144, 2.353376995174362785e+153, },
      { 1.571461316550783294e+00, 1.576790166316938345e+00, 1.587495640370383316e+00, 1.603673956341370210e+00, 1.625471125457493943e+00, 1.653085011915939302e+00, 1.686768142525911236e+00, 1.726831323537516202e+00, 1.773648138667236602e+00, 1.827660421478661448e+00, 1.889384817044018196e+00, 1.959420572855037091e+00, 2.038458728047908923e+00, 2.127292904083847225e+00, 2.226831940199076941e+00, 2.338114664555130296e+00, 2.462327148722991304e+00, 2.600822860927085164e+00, 2.755146214814554359e+00, 2.927060108424483555e+00, 3.118578166240921951e+00, 3.332002540339506630e+00, 3.569968300410740276e+00, 3.835495653996447262e+00, 4.132051496512934885e+00, 4.463622106699067881e+00, 4.834799191008006557e+00, 5.250881957765679608e+00, 5.717998490875333124e+00, 6.243250421598568105e+00, 6.834885801226541839e+00, 7.502506202789340802e+00, 8.257315484493544201e+00, 9.112419405864642634e+00, 1.008318749543997758e+01, 1.118769134993865202e+01, 1.244723705914106881e+01, 1.388701390605507587e+01, 1.553688715915900190e+01, 1.743237000680942831e+01, 1.961581894823993424e+01, 2.213790886354273806e+01, 2.505945934677137610e+01, 2.845370377742137561e+01, 3.240911845969524834e+01, 3.703296289480230161e+01, 4.245572644746267911e+01, 4.883673480337985582e+01, 5.637124640586975420e+01, 6.529947092752610340e+01, 7.591807755694122837e+01, 8.859494252391663822e+01, 1.037881295005788124e+02, 1.220704263969226746e+02, 1.441612098131200535e+02, 1.709680191245773511e+02, 2.036410593843575570e+02, 2.436450058708723643e+02, 2.928540812182076105e+02, 3.536786019152253392e+02, 4.292343083967296939e+02, 5.235701840488733027e+02, 6.419766898003024575e+02, 7.914052083668759283e+02, 9.810422089081931637e+02, 1.223099994999740393e+03, 1.533912555427112127e+03, 1.935464013605830339e+03, 2.457534549912886852e+03, 3.140733731623635519e+03, 4.040818188564651898e+03, 5.234881599712225681e+03, 6.830294457607329226e+03, 8.977713228649887143e+03, 1.189015920967326839e+04, 1.587122387044346962e+04, 2.135711106445789331e+04, 2.897983705189681437e+04, 3.966306726795547950e+04, 5.476875193750000787e+04, 7.632356539388055680e+04, 1.073719149754976951e+05, 1.525316674555574152e+05, 2.188778434744216586e+05, 3.173624496019295608e+05, 4.651201525869328462e+05, 6.892537656280580572e+05, 1.033119885120019982e+06, 1.566887981043252499e+06, 2.405492027026531795e+06, 3.739528964815910340e+06, 5.889121154895580032e+06, 9.399046351922342030e+06, 1.520903276129653518e+07, 2.496287187293576168e+07, 4.157759259963074840e+07, 7.030705366950267312e+07, 1.207598558452493366e+08, 2.107882509464846833e+08, 3.741047199023457864e+08, 6.754494594987415572e+08, 1.241316740415880537e+09, 2.323310032649552862e+09, 4.431176019026625759e+09, 8.617446487400900130e+09, 1.709836906604031513e+10, 3.463574521880171339e+10, 7.167607123799270726e+10, 1.516347620910054079e+11, 3.281729323238950526e+11, 7.271102600298280790e+11, 1.650499552378780378e+12, 3.841338149508803917e+12, 9.173744267785176575e+12, 2.249901946357519979e+13, 5.671535089900611731e+13, 1.470742250307697019e+14, 3.927012518464311775e+14, 1.080639977391212820e+15, 3.067671466720475189e+15, 8.992386789198328428e+15, 2.724722536524592111e+16, 8.542946122263389258e+16, 2.774613718725574755e+17, 9.345299479382029121e+17, 3.267996122987731882e+18, 1.187914433455468315e+19, 4.494053408418564214e+19, 1.771706652195486743e+20, 7.288102552885931527e+20, 3.132512430816625349e+21, 1.408743767951073110e+22, 6.638294268236060414e+22, 3.282543608403565013e+23, 1.705920098038394064e+24, 9.332259385148524285e+24, 5.382727175874888312e+25, 3.278954235122093249e+26, 2.113191697957458099e+27, 1.443411041499643040e+28, 1.046864394654982423e+29, 8.077319226958905700e+29, 6.643146963432616277e+30, 5.835670121359986260e+31, 5.486890296790230798e+32, 5.533726968508261614e+33, 5.999734996418352834e+34, 7.009176119466122569e+35, 8.844061966424597499e+36, 1.208226860869605961e+38, 1.791648514311063338e+39, 2.891313916713205762e+40, 5.091457860211527298e+41, 9.810630588402496553e+42, 2.074441239147378860e+44, 4.827650116937700540e+45, 1.240287939111549029e+47, 3.528
      { 1.570962550997832611e+00, 1.572292902367211961e+00, 1.574956581912666755e+00, 1.578959553636163985e+00, 1.584310789563614305e+00, 1.591022301117035107e+00, 1.599109181186160337e+00, 1.608589657109067468e+00, 1.619485154826419743e+00, 1.631820374530739318e+00, 1.645623378191125679e+00, 1.660925689395424109e+00, 1.677762406016463717e+00, 1.696172326277082973e+00, 1.716198088860732467e+00, 1.737886327791014562e+00, 1.761287842885152410e+00, 1.786457786673686420e+00, 1.813455868772335587e+00, 1.842346578792652542e+00, 1.873199428986627521e+00, 1.906089217937612619e+00, 1.941096316736779451e+00, 1.978306979221816566e+00, 2.017813678003844337e+00, 2.059715468170813895e+00, 2.104118380732327493e+00, 2.151135848063375554e+00, 2.200889163814591418e+00, 2.253507979986114202e+00, 2.309130844113053375e+00, 2.367905779785113334e+00, 2.429990914023652954e+00, 2.495555155369085590e+00, 2.564778926893134514e+00, 2.637854958747451684e+00, 2.714989145296268067e+00, 2.796401472360280536e+00, 2.882327020626578700e+00, 2.973017051860293803e+00, 3.068740185193628238e+00, 3.169783671473487386e+00, 3.276454774427328601e+00, 3.389082268266156098e+00, 3.508018062292869136e+00, 3.633638964133530274e+00, 3.766348594369884204e+00, 3.906579466636309289e+00, 4.054795248667541120e+00, 4.211493221360917802e+00, 4.377206954666462219e+00, 4.552509221059946388e+00, 4.738015169510782826e+00, 4.934385785253587887e+00, 5.142331663338191074e+00, 5.362617126899976224e+00, 5.596064724397100194e+00, 5.843560143744373307e+00, 6.106057585381734693e+00, 6.384585640900671436e+00, 6.680253728973824449e+00, 6.994259146058412709e+00, 7.327894795748901060e+00, 7.682557667824588764e+00, 8.059758146071137270e+00, 8.461130232962342889e+00, 8.888442789395671080e+00, 9.343611899025485155e+00, 9.828714479494622022e+00, 1.034600327721380625e+01, 1.089792339849122916e+01, 1.148713054801325790e+01, 1.211651116619788555e+01, 1.278920468010096321e+01, 1.350862810871281096e+01, 1.427850329305334421e+01, 1.510288705493181327e+01, 1.598620462612703196e+01, 1.693328673269081128e+01, 1.794941076780000506e+01, 1.904034654190823159e+01, 2.021240716182964334e+01, 2.147250566192247370e+01, 2.282821809199713505e+01, 2.428785385941680425e+01, 2.586053422878117785e+01, 2.755628000354674426e+01, 2.938610955221109564e+01, 3.136214849990951329e+01, 3.349775258749912582e+01, 3.580764540799625468e+01, 3.830807296872530167e+01, 4.101697730155473447e+01, 4.395419165876113623e+01, 4.714166019494196927e+01, 5.060368545366659226e+01, 5.436720746019445252e+01, 5.846211877912138439e+01, 6.292162054058128784e+01, 6.778262518512416663e+01, 7.308621254265223015e+01, 7.887814686488147292e+01, 8.520946359734658334e+01, 9.213713603387774717e+01, 9.972483357670754649e+01, 1.080437851679046426e+02, 1.171737636088621692e+02, 1.272042089988687372e+02, 1.382355124664102373e+02, 1.503804848151483311e+02, 1.637660387526102742e+02, 1.785351181233383403e+02, 1.948489131607280604e+02, 2.128894073598352670e+02, 2.328623093447990790e+02, 2.550004322843281994e+02, 2.795675942672445782e+02, 3.068631259124280934e+02, 3.372270867451200874e+02, 3.710463099965576255e+02, 4.087614170466174911e+02, 4.508749684194593670e+02, 4.979609488959773491e+02, 5.506758209385785877e+02, 6.097714244663179092e+02, 6.761100535726473685e+02, 7.506821038741422446e+02, 8.346267600518081192e+02, 9.292562845315541998e+02, 1.036084578498234728e+03, 1.156860819661897657e+03, 1.293609142453808600e+03, 1.448675521854205144e+03, 1.624783259532197615e+03, 1.825098759915318560e+03, 2.053309635972617554e+03, 2.313717614494777200e+03, 2.611349236640186999e+03, 2.952087994093624299e+03, 3.342832332560548180e+03, 3.791684927756595099e+03, 4.308179838716318955e+03, 4.903555624570201673e+03, 5.591084343634811452e+03, 6.386468625571246341e+03, 7.308321829412979440e+03, 8.378749812799703561e+03, 9.624057218749638059e+03, 1.107560666191146008e+04, 1.277086605445904388e+04, 1.475468792019489452e+04, 1.708087537417066343e+04, 1.981410309695485051e+04, 2.303227888204754908e+04, 2.682945317928632535e+04, 3.131941178398428200e+04, 3.664012209706997997e+04, 4.295
   };
#if !defined(BOOST_MATH_NO_ATOMIC_INT) && defined(BOOST_HAS_THREADS)
   m_committed_refinements = static_cast<boost::math::detail::atomic_unsigned_integer_type>(m_weights.size() - 1);
#else
   m_committed_refinements = m_weights.size() - 1;
#endif
   m_t_max = 6.114056619798597593;
   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 sinh_sinh_detail<Real, Policy>::init(const std::integral_constant<int, 3>&)
{
   m_abscissas = {
      { 3.08828741797632286606397498241221385e+00L, 1.48993184649209158013612709175719825e+02L, 3.41228924788343710247727162226946917e+06L, 2.06932576604261779073902718911207249e+18L, 2.08700240760947556038306635808129743e+50L, 2.01976616071790815078008252209994199e+137L, 5.67213444764437168603513205349222232e+373L, 3.06198394306784061113736467298565948e+1016L, },
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      { 1.57096255099783261137673508918980377e+00L, 1.57229290236721196082451564636254803e+00L, 1.57495658191266675503402671533627186e+00L, 1.57895955363616398471678434379990522e+00L, 1.58431078956361430514416599492388597e+00L, 1.59102230111703510742216272394562613e+00L, 1.59910918118616033722590556649394763e+00L, 1.60858965710906746764504456185444654e+00L, 1.61948515482641974319339137784305225e+00L, 1.63182037453073931785527493516038124e+00L, 1.64562337819112567903033806653906069e+00L, 1.66092568939542410935608828998468834e+00L, 1.67776240601646371733138779357535047e+00L, 1.69617232627708297296989766202480515e+00L, 1.71619808886073246730768842066355199e+00L, 1.73788632779101456236627555096372654e+00L, 1.76128784288515241044102589887617560e+00L, 1.78645778667368642025315725404601102e+00L, 1.81345586877233558659749539967614045e+00L, 1.84234657879265254187280543490489739e+00L, 1.87319942898662752121993510591579920e+00L, 1.90608921793761261888076943857856180e+00L, 1.94109631673677945144587926354356120e+00L, 1.97830697922181656566949720098719647e+00L, 2.01781367800384433737712026561151498e+00L, 2.05971546817081389507270282494773392e+00L, 2.10411838073232749275747224342524909e+00L, 2.15113584806337555354918618566085438e+00L, 2.20088916381459141771044083611555369e+00L, 2.25350797998611420231160903572594743e+00L, 2.30913084411305337537709048855358397e+00L, 2.36790577978511333384857209921738492e+00L, 2.42999091402365295350102767412517845e+00L, 2.49555515536908558968587982458158759e+00L, 2.56477892689313451429557802920827974e+00L, 2.63785495874745168415081659796280588e+00L, 2.71498914529626806741705564771250802e+00L, 2.79640147236028053619149909690973720e+00L, 2.88232702062657870038560203490158574e+00L, 2.97301705186029380311201985278736098e+00L, 3.06874018519362823755119514588303156e+00L, 3.16978367147348738564623946178566521e+00L, 3.27645477442732860056345607892739085e+00L, 3.38908226826615609816107421136979984e+00L, 3.50801806229286913554992299494422526e+00L, 3.63363896413353027399263692498221540e+00L, 3.76634859436988420367634452674074607e+00L, 3.90657946663630928939225987850575005e+00L, 4.05479524866754112035397645627643742e+00L, 4.21149322136091780158052739625729631e+00L, 4.37720695466646221916071477112304019e+00L, 4.55250922105994638849140210916632132e+00L, 4.73801516951078282566987752649050466e+00L, 4.93438578525358788671420711795537458e+00L, 5.14233166333819107447595069798421539e+00L, 5.36261712689997622445803908396748884e+00L, 5.59606472439710019418213140693069575e+00L, 5.84356014374437330661446789126222075e+00L, 6.10605758538173469317727364122669467e+00L, 6.38458564090067143612732202429488542e+00L, 6.68025372897382444864907987044889317e+00L, 6.99425914605841270881961646990609410e+00L, 7.32789479574890106033548644768353338e+00L, 7.68255766782458876413667730681699443e+00L, 8.05975814607113727007240055318338450e+00L, 8.46113023296234288939356989479671723e+00L, 8.88844278939567108027044653070693778e+00L, 9.34361189902548515485066576358196470e+00L, 9.82871447949462202212030994384949241e+00L, 1.03460032772138062549383568058709409e+01L, 1.08979233984912291622835480030167114e+01L, 1.14871305480132578973614919602781370e+01L, 1.21165111661978855517781913327317255e+01L, 1.27892046801009632078942555615288463e+01L, 1.35086281087128109623831457304510920e+01L, 1.42785032930533442126932924888187804e+01L, 1.51028870549318132669071327511660921e+01L, 1.59862046261270319640752848374642080e+01L, 1.69332867326908112807352382039426796e+01L, 1.79494107678000050622926329104204826e+01L, 1.90403465419082315888820165929975494e+01L, 2.02124071618296433363312214170232623e+01L, 2.14725056619224736964251610816575600e+01L, 2.28282180919971350546248653847563966e+01L, 2.42878538594168042463845071817020910e+01L, 2.58605342287811778487151334440784950e+01L, 2.75562800035467442565131080245429614e+01L, 2.93861095522110956389210768876799587e+01L, 3.13621484999095132865600012683857137e+01L, 3.34977525874991258153646142408367963e+01L, 3.58076454079962546803810835720597110e+01L, 3.83080729687253016658377309622401176e+01L, 4.10169773015547344709659456503154667e+
   };
#if !defined(BOOST_MATH_NO_ATOMIC_INT) && defined(BOOST_HAS_THREADS)
   m_committed_refinements = static_cast<boost::math::detail::atomic_unsigned_integer_type>(m_weights.size() - 1);
#else
   m_committed_refinements = m_weights.size() - 1;
#endif
   m_t_max = 8.88600744303961370002819023592353264e+00L;
   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 sinh_sinh_detail<Real, Policy>::init(const std::integral_constant<int, 4>&)
{
   m_abscissas = {
      { 3.08828741797632286606397498241221385e+00Q, 1.48993184649209158013612709175719825e+02Q, 3.41228924788343710247727162226946917e+06Q, 2.06932576604261779073902718911207249e+18Q, 2.08700240760947556038306635808129743e+50Q, 2.01976616071790815078008252209994199e+137Q, 5.67213444764437168603513205349222232e+373Q, 3.06198394306784061113736467298565948e+1016Q, },
      { 9.13048762637669674838078869945948356e-01Q, 1.41578929466281159169215570833490092e+01Q, 6.70421551622327648231120321610008518e+03Q, 9.64172532715049941526010563818587232e+10Q, 2.50895076008577848514087028569888161e+30Q, 1.44726353571033714499079379626715686e+83Q, 3.75263401205045334128277886549019357e+226Q, 2.57846123932685341261715758547064293e+616Q, 1.25169402230987931584130068460134989e+1676Q, },
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   };
#if !defined(BOOST_MATH_NO_ATOMIC_INT) && defined(BOOST_HAS_THREADS)
   m_committed_refinements = static_cast<boost::math::detail::atomic_unsigned_integer_type>(m_weights.size() - 1);
#else
   m_committed_refinements = m_weights.size() - 1;
#endif
   m_t_max = 8.88600744303961370002819023592353264e+00Q;
   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