xref: /dports/devel/boost-docs/boost_1_72_0/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/detail/lightweight_mutex.hpp>

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
   {
#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;
      using constants::half_pi;

      std::size_t row = ++m_committed_refinements;

      Real h = ldexp(Real(1), -static_cast<int>(row));
      size_t k = (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;
#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>
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(mpl::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(Real(0))) K;
    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 = (Real) 1/ (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 > (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 mpl::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 = (Real)1 / (Real)(1 << i);
      size_t k = (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 mpl::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, 6.85137513e+15f, 1.18269011e+16f, 2.05867353e+16f, 3.61396878e+16f, 6.39911218e+16f, 1.14301619e+17f, 2.05988138e+17f, 3.74584679e+17f, 6.87444303e+17f, 1.27340764e+18f, 2.38124192e+18f, 4.49583562e+18f, 8.57144202e+18f, 1.65044358e+19f, 3.21010035e+19f, 6.30778012e+19f, 1.25240403e+20f, 2.51300530e+20f, 5.09677626e+20f, },
   };
#ifndef BOOST_MATH_NO_ATOMIC_INT
   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 mpl::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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      { 1.570962550997832611e+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, 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3.654767820268344932e+07, 4.734452657230626106e+07, 6.156534063509513873e+07, 8.036843026897869248e+07, 1.053280284359690289e+08, 1.385921689084126286e+08, 1.831036985925683524e+08, 2.429109457458640820e+08, 3.236062393759667463e+08, 4.329475218599986663e+08, 5.817432967962929479e+08, 7.851179789388191786e+08, 1.064329197627075307e+09, 1.449389582912945485e+09, 1.982866469377991849e+09, 2.725414314698094324e+09, 3.763867964111621444e+09, 5.223138814950990937e+09, 7.283785810644397704e+09, 1.020809642381158743e+10, 1.437899318470510521e+10, 2.035836812543633578e+10, 2.897499827080027444e+10, 4.145773751645494878e+10, 5.963837683872426287e+10, 8.626228483915530800e+10, 1.254667045389825180e+11, 1.835212982264913186e+11, 2.699812207400151604e+11, 3.994928452151922954e+11, 5.946380558701434550e+11, 8.904409967424091107e+11, 1.341551941677775838e+12, 2.033768550332151892e+12, 3.102627959875753214e+12, 4.763598321705862063e+12, 7.361420360560813584e+12, 1.145126961456557423e+13, 1.793314186996273926e+13, 2.827585501285792232e+13, 4.489297053678444669e+13, 7.177802872658499571e+13, 1.155855098545820625e+14, 1.874833886367883093e+14, 3.063510356402174454e+14, 5.043400653005970242e+14, 8.366163396892429890e+14, 1.398556351640947289e+15, 2.356335749516164682e+15, 4.001765167382637456e+15, 6.851375128404941445e+15, 1.182690111761543990e+16, 2.058673527013806443e+16, 3.613968784314904633e+16, 6.399112184394213551e+16, 1.143016185628376923e+17, 2.059881383915666443e+17, 3.745846788353680914e+17, 6.874443034683149068e+17, 1.273407643613485314e+18, 2.381241916829895366e+18, 4.495835617307108399e+18, 8.571442024901952701e+18, 1.650443584181656965e+19, 3.210100352421317851e+19, 6.307780124442703091e+19, 1.252404031157661279e+20, 2.513005295649985394e+20, 5.096776255690838436e+20, 1.045019200016673046e+21, 2.166476479260878466e+21, 4.542138145678395463e+21, 9.632082324449137128e+21, 2.066386536688254528e+22, 4.485529785554428251e+22, 9.853879573610977508e+22, 2.191158874464374408e+23, 4.932835964390971668e+23, 1.124501529971774363e+24, 2.596269136156756008e+24, 6.072292938313625501e+24, 1.438989066308003836e+25, 3.455841956406570469e+25, 8.412655191713576490e+25, 2.076289061650816510e+26, 5.196515024640220322e+26, 1.319173194089644043e+27, 3.397455895980380794e+27, 8.879057454438503591e+27, 2.355272361492064126e+28, 6.342762007722624824e+28, 1.734531093990859705e+29, 4.817893170606830871e+29, 1.359597346490148232e+30, 3.898969689906500392e+30, 1.136542986529989936e+31, 3.368450043991780017e+31, 1.015304084709817260e+32, 3.113144376221918237e+32, 9.713072739730140403e+32, 3.084517643581725946e+33, 9.972682139820497284e+33, 3.283625052288491586e+34, 1.101378785390827536e+35, 3.764333367592714297e+35, 1.311403465938242926e+36, 4.658135710682813672e+36, 1.687517347470511392e+37, 6.237053685018323490e+37, 2.352571314427744869e+38, 9.058938240219699936e+38, 3.562249097611136071e+39, 1.430959291578558210e+40, 5.873974584984375049e+40, 2.464828549811283787e+41, 1.057649203090855628e+42, 4.642475639281078035e+42, 2.085287118272421779e+43, 9.588439985186632177e+43, 4.514982011246092280e+44, 2.177974048341973204e+45, 1.076720976822900458e+46, 5.457267432929085589e+46, 2.836869270455781134e+47, 1.513103201392011626e+48, 8.283974667225617075e+48, 4.657239491995971344e+49, 2.689796370712836937e+50, 1.596597846911970388e+51, 9.744154538256586629e+51, 6.117238394843313065e+52, 3.952049650585241827e+53, 2.628701592074258213e+54, 1.800990196502679393e+55, 1.271554462563068383e+56, 9.255880104477760711e+56, 6.949737920133919393e+57, 5.385167200769965621e+58, 4.308493668102978774e+59, 3.560951557542178371e+60, 3.041888528384649992e+61, 2.687094441930837189e+62, 2.455920538900000855e+63, 2.323648254168641537e+64, 2.277129741584892331e+65, 2.312633552913224734e+66, 2.435407592981291129e+67, 2.660910388822465246e+68, 3.018105943423533920e+69, 3.555823489510192503e+70, 4.354188877793849013e+71, 5.544975795511813315e+72, 7.348276481909886336e+73, 1.013998025722423261e+75, 1.457911462244607943e+76, 2.185488876819505295e+77, 3.418022153286623008e+78, 5.580843920601835728e+79, 9.519586502799733908e+80, 1.697573578247197786e+82, 3.166906670990180014e+83, 6.185099106418675430e+84, 1.265541134386934377e+86, 2.714828965877756899e+87, 6.110386802964494082e+88, 1.444054086171083239e+90, 3.586083726638388165e+91, 9.365231868063239600e+92, 2.574080116205122449e+94, 7.452134689862302719e+95, 2.274309903836169819e+97, 7.323011134121164749e+98, 2.489816421737932462e+100, 8.946533386359281588e+101, 3.400401372391165979e+103, 1.368288186208928217e+105, 5.834277489829591931e+106, 2.638486937672383424e+108, 1.266728882767139521e+110, 6.462225178314182803e+111, 3.506432320607573604e+113, 2.025608933943268165e+115, 1.247041677084784707e+117, 8.189865188405279038e+118, 5.743610894406099965e+120, 4.305808934084489763e+122, 3.454156966079496755e+124, 2.968316601530352737e+126, 2.735456242372183592e+128, 2.706317176690077847e+130, 2.877679916342060385e+132, 3.292412878268106390e+134, 4.057840961953725969e+136, 5.393783049105737324e+138, 7.741523901672235406e+140, 1.201209962310668456e+143, 2.017456079556807301e+145, 3.672176623483062526e+147, 7.253163798058577630e+149, 1.556591535302570570e+152, 3.634399832790394885e+154, },
   };
#ifndef BOOST_MATH_NO_ATOMIC_INT
   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 mpl::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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3.29340233091271285034548969456076701e+664L, 8.78384225704905897945003526718634352e+674L, 3.41824790512159692619674889187554870e+685L, 1.95247619547378795632466874007982924e+696L, 1.64685615123975037569921507294781182e+707L, 2.06385512057306929298128483493412318e+718L, 3.86691162964076111860523245198584961e+729L, 1.09008736553561747232882422664193409e+741L, 4.65333391196364819411904308657257877e+752L, 3.02768585771015415481330091322447912e+764L, 3.02262040534180824988954474846992913e+776L, 4.66133722640174567906974646266839244e+788L, 1.11806119156969171229108916233644999e+801L, 4.20019655376202192049844032418033555e+813L, 2.48880615873773868126893696694455625e+826L, 2.34286193142054643224145247339492426e+839L, 3.52941162196327496812531706159176164e+852L, 8.57183106082165907783781027353105401e+865L, 3.38163627323872188047900717079347979e+879L, 2.18363447282104345585022834572887531e+893L, 2.32596275137292895223293068081362090e+907L, 4.11925247272574761366980289309686003e+921L, 1.22265489460258041690738897372130823e+936L, 6.13184165651799059701146847592463464e+950L, 5.23922303275545560334122760478493484e+965L, 7.69087233862553980667730597006685190e+980L, 1.95622275953749870274795206909257068e+996L, 8.69670052895401378378113763338699958e+1011L, 6.81715148318539616903616353647181598e+1027L, 9.50697711954141544724599553989093262e+1043L, 2.38019733682587370869498352841844428e+1060L, 1.07973324919847346937291516197684901e+1077L, 8.95814284819025403820872820042945790e+1093L, 1.37229192661307043018958002675397831e+1111L, 3.91918794622242371528673544888524419e+1128L, 2.10730218913863433412315532873510194e+1146L, 2.15459607934366008026324206138837528e+1164L, 4.23163839295623007237154131840451677e+1182L, 1.61294441956204958952970453918741185e+1201L, 1.20568335528354973250479511763057854e+1220L, 1.78630819666459637235669417819650103e+1239L, 5.30233997012953850434143324467683139e+1258L, 3.18800705045665419646272046839479382e+1278L, 3.92589619613994835597705628928304867e+1298L, 1.00145056975313260959947278741812233e+1319L, 5.35268808912615454171856125906228237e+1339L, 6.06491960606218539467705074145131193e+1360L, 1.47410187506507259371724909079906759e+1382L, 7.77855372825975976779550291054389078e+1403L, 9.02071339187528665617085297107535931e+1425L, 2.32776342394968427168699373890370933e+1448L, 1.35351409374730203846799381939288903e+1471L, 1.79625881886715571166142200348072039e+1494L, 5.51189494978629938318487744451579809e+1517L, 3.96270198063441303687686251379779681e+1541L, 6.76492837567767494547614386605795924e+1565L, 2.77991073110506719318274536923711255e+1590L, 2.78805951202715437087943440518839779e+1615L, 6.92116280606414755524296394791409952e+1640L, 4.31380309053366092943951122004431463e+1666L, 6.84923073262139995438889690748178280e+1692L, 2.81137418164430829179092468240459910e+1719L, 3.02821524237655652451836921974619657e+1746L, 8.69048903533522694231765189726868666e+1773L, 6.74828063313306417588175763238310325e+1801L, 1.44026065844141159256872926595644247e+1830L, 8.58426091495439408178371839859019039e+1858L, 1.45211919400936944187225846047638548e+1888L, 7.08718013380970011842483247147601395e+1917L, 1.01475962220405902523641440040104610e+1948L, 4.33542978691578087509838132034723750e+1978L, 5.62285772227295495777726116212032065e+2009L, 2.25285072921565445630031609130087435e+2041L, 2.83839050906274298341210206309759282e+2073L, 1.14501659579022194588844609345877849e+2106L, 1.50629562239998305958408533546634030e+2139L, 6.58342161306998815751663631350733541e+2172L, 9.74198999952210922892973281379349494e+2206L, 4.97552704772088889228035264268694867e+2241L, 8.94330619882842342247706838649878784e+2276L, 5.77072420156026800834371478648673792e+2312L, 1.36388225285320494361282201451878478e+2349L, 1.20508189950290985406298094670730466e+2386L, 4.06413362486490272506766749982212198e+2423L, 5.34308092015215251528601382597439463e+2461L, },
   };
#ifndef BOOST_MATH_NO_ATOMIC_INT
   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 mpl::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, },
      { 4.07297690065758690150573950473604675e-01Q, 1.68206670702114874332932330092838356e+00Q, 6.15089798638672951539668935798437533e+00Q, 4.00396235192940022205839866641270319e+01Q, 7.92920024793102632052902471550336177e+02Q, 1.02984971333097958319686053784919407e+05Q, 3.03862310925243857437932941891415841e+08Q, 1.56544547436249486913719231527597560e+14Q, 4.04246509843021910355659662715183671e+23Q, 1.32170682742965817915034577861235933e+39Q, 4.99123178209955799774620736137366103e+64Q, 7.35294385035987596594501676609562008e+106Q, 2.45145417229813114714431821340237112e+176Q, 1.03030479197459267961759023741376327e+291Q, 9.88478945193556730604342445576518136e+479Q, 3.74498116076433060427765453233124618e+791Q, 1.90292390713026708045766158039087796e+1305Q, 1.72712488231809244721915842027236657e+2152Q, },
      { 1.98135272251478172615235718398538323e-01Q, 6.40155673500526017670785720911319502e-01Q, 1.24892869825397766254802900819319987e+00Q, 2.26608084094432123181038001270985037e+00Q, 4.29646269670232738148137717958679987e+00Q, 9.13029038709995569641811827045549232e+00Q, 2.31110765386427993316995139635470937e+01Q, 7.42770603432401243012214481410240677e+01Q, 3.26720920711525891697790966796945063e+02Q, 2.15948569431181871552028449867301828e+03Q, 2.41501526289641306037808670196966696e+04Q, 5.31819400275692915826269282626844010e+05Q, 2.80058685721704332307817790755562305e+07Q, 4.52406507979433877971977526863358905e+09Q, 3.08561257398067712180174566763237112e+12Q, 1.33882673301580747789133427708622972e+16Q, 6.25461717656234138147247754416652254e+20Q, 6.18209853581416475394863999233554548e+26Q, 3.07729364978845806686511011060697837e+34Q, 2.34895728937010430290698332595743680e+44Q, 1.14854319789946975790127332653552673e+57Q, 2.25530007001006986846545694404767295e+73Q, 1.87791950056919539419801461538703336e+94Q, 1.36747388793862427976781689638282239e+121Q, 4.24212177246407592514720294750151286e+155Q, 8.23473099012134325391170623028607158e+199Q, 6.06134211888406631001019923425936351e+256Q, 6.32519197436029413652766295658658263e+329Q, 3.61942292928205643948383705201563065e+423Q, 8.82464433126646489632943769283758364e+543Q, 3.35512488018651738642854323317447493e+698Q, 1.02411434678684822400261582079656500e+897Q, 7.40716670979374017620610271197945784e+1151Q, 1.30455147283895162835186634827124464e+1479Q, 2.02948723345659016173510134582487641e+1899Q, 6.99019443250345564805134094483457477e+2438Q, },
      { 9.83967894006732033862249554537934739e-02Q, 3.00605617659955035122465185012715805e-01Q, 5.19857978994938490000644785900799951e-01Q, 7.70362083298887700858583505753306721e-01Q, 1.07131136964131183026831222500748063e+00Q, 1.45056975808899844502126797109703210e+00Q, 1.95077854952036033400296546339240312e+00Q, 2.64003177369555146770080103921424631e+00Q, 3.63137237366741227331951933364601985e+00Q, 5.11991533090335057003526222543242753e+00Q, 7.45666098140488328926087222725984231e+00Q, 1.13022612688997262443461342203136009e+01Q, 1.79641069247277254966592982669611020e+01Q, 3.01781070460189822236726995418068214e+01Q, 5.40387580031237056709826662540066860e+01Q, 1.04107731447746954767459980678311109e+02Q, 2.18029520120262807725988909352359830e+02Q, 5.02155698625910164594509258651311707e+02Q, 1.28862131099822242045586488612672886e+03Q, 3.73921687080054832376623401153054636e+03Q, 1.24750729702019123239464970064060864e+04Q, 4.87639975322669212414357357061002683e+04Q, 2.28145658221913012154676335814417144e+05Q, 1.30877796006484301664040981436471740e+06Q, 9.46084663420966407698078336053299177e+06Q, 8.88883120363727962245667776649286152e+07Q, 1.12416882897434413447175648471746990e+09Q, 1.99127672953214446985509145592687205e+10Q, 5.16743469106098464964433058111638245e+11Q, 2.06721881420399088776240044545119948e+13Q, 1.35061503318410040604770421574064883e+15Q, 1.53854066283650818848773859278941683e+17Q, 3.29074729054035066052820102585085173e+19Q, 1.43729138188449881561963100200796631e+22Q, 1.40983244553034728562740932242727657e+25Q, 3.45913548027797144127990544649862792e+28Q, 2.39872058234095409213724024023509754e+32Q, 5.39880660461729295997086364918754801e+36Q, 4.61334000258062860955942270137550165e+41Q, 1.78768590966790245678294238939560892e+47Q, 3.84198437012433853552557148945213178e+53Q, 5.75279795570858370009870455748773410e+60Q, 7.77181203842728655149182334288749850e+68Q, 1.26967304420408162635234502672130357e+78Q, 3.49567677376573156773252547632961336e+88Q, 2.36251947497169244454694635287097330e+100Q, 6.00214389327365112307366927985587840e+113Q, 9.29071630346415553922675334522602561e+128Q, 1.51444223803384709004933819608345315e+146Q, 4.83290204410990250226310317342789471e+165Q, 6.09623012864338569215560315517200736e+187Q, 6.73889214277659359787962707085479315e+212Q, 1.60917893672694484647176104023542732e+241Q, 2.30724123468764987944582372785293125e+273Q, 6.32636439816284705814531208407868829e+309Q, 1.23274815890184688792156489065830724e+351Q, 7.55519778823055185901318833981345378e+397Q, 7.85730655106759111844772008129590573e+450Q, 9.36328400229780321059086898529742817e+510Q, 1.11332545426270395766246494603539938e+579Q, 1.53432069979625061288117473415446630e+656Q, 3.94622553764411915381186808199466267e+743Q, 4.41554290953392996069257034424439949e+842Q, 7.62037777854651720247173134262034607e+954Q, 1.15650294539918196985498353779647134e+1082Q, 1.50761161209705395018419027031866347e+1226Q, 3.03485088181756935935831645680716816e+1389Q, 3.38561189018537177501905611143498298e+1574Q, 1.64407968993192526511230001818530622e+1784Q, 6.63148743223242467667800355907041029e+2021Q, 1.15911606715877477373516464924821476e+2291Q, },
      { 4.91151003502902493004859475143401791e-02Q, 1.48013149674360733270682895306542340e-01Q, 2.48938813740683685679302156785267041e-01Q, 3.53325423692668437764413545980527251e-01Q, 4.62733556612235325924240102411897269e-01Q, 5.78912068164096306746325958452873475e-01Q, 7.03870253386062779930091622585657886e-01Q, 8.39965859144650568772715366992985538e-01Q, 9.90015066424437614655918533324528544e-01Q, 1.15743257014369913143250540144278056e+00Q, 1.34641275918536176274682426896283388e+00Q, 1.56216711390133555099139972670978661e+00Q, 1.81123885278232337973709010374295886e+00Q, 2.10192441900655030086142289233010995e+00Q, 2.44484388558419793403331221069953203e+00Q, 2.85372074663291502355627105440782037e+00Q, 3.34645891095535078662878051589922609e+00Q, 3.94664582105783838715586741669722603e+00Q, 4.68567310159667852940801410152900804e+00Q, 5.60576223090815117543658276010994803e+00Q, 6.76433233683057420359243855855175747e+00Q, 8.24038317537998522052755780107530197e+00Q, 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3.29340233091271285034548969456076701e+664Q, 8.78384225704905897945003526718634352e+674Q, 3.41824790512159692619674889187554870e+685Q, 1.95247619547378795632466874007982924e+696Q, 1.64685615123975037569921507294781182e+707Q, 2.06385512057306929298128483493412318e+718Q, 3.86691162964076111860523245198584961e+729Q, 1.09008736553561747232882422664193409e+741Q, 4.65333391196364819411904308657257877e+752Q, 3.02768585771015415481330091322447912e+764Q, 3.02262040534180824988954474846992913e+776Q, 4.66133722640174567906974646266839244e+788Q, 1.11806119156969171229108916233644999e+801Q, 4.20019655376202192049844032418033555e+813Q, 2.48880615873773868126893696694455625e+826Q, 2.34286193142054643224145247339492426e+839Q, 3.52941162196327496812531706159176164e+852Q, 8.57183106082165907783781027353105401e+865Q, 3.38163627323872188047900717079347979e+879Q, 2.18363447282104345585022834572887531e+893Q, 2.32596275137292895223293068081362090e+907Q, 4.11925247272574761366980289309686003e+921Q, 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3.92589619613994835597705628928304867e+1298Q, 1.00145056975313260959947278741812233e+1319Q, 5.35268808912615454171856125906228237e+1339Q, 6.06491960606218539467705074145131193e+1360Q, 1.47410187506507259371724909079906759e+1382Q, 7.77855372825975976779550291054389078e+1403Q, 9.02071339187528665617085297107535931e+1425Q, 2.32776342394968427168699373890370933e+1448Q, 1.35351409374730203846799381939288903e+1471Q, 1.79625881886715571166142200348072039e+1494Q, 5.51189494978629938318487744451579809e+1517Q, 3.96270198063441303687686251379779681e+1541Q, 6.76492837567767494547614386605795924e+1565Q, 2.77991073110506719318274536923711255e+1590Q, 2.78805951202715437087943440518839779e+1615Q, 6.92116280606414755524296394791409952e+1640Q, 4.31380309053366092943951122004431463e+1666Q, 6.84923073262139995438889690748178280e+1692Q, 2.81137418164430829179092468240459910e+1719Q, 3.02821524237655652451836921974619657e+1746Q, 8.69048903533522694231765189726868666e+1773Q, 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   };
#ifndef BOOST_MATH_NO_ATOMIC_INT
   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