EVOLUTION-MANAGER

Edit File: 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, }, { 2.45471558e-02f, 7.37246687e-02f, 1.23152531e-01f, 1.73000138e-01f, 2.23440665e-01f, 2.74652655e-01f, 3.26821679e-01f, 3.80142101e-01f, 4.34818964e-01f, 4.91070037e-01f, 5.49128046e-01f, 6.09243132e-01f, 6.71685571e-01f, 7.36748805e-01f, 8.04752842e-01f, 8.76048080e-01f, 9.51019635e-01f, 1.03009224e+00f, 1.11373586e+00f, 1.20247203e+00f, 1.29688123e+00f, 1.39761124e+00f, 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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, }, { 9.839678940067320339e-02, 3.006056176599550351e-01, 5.198579789949384900e-01, 7.703620832988877009e-01, 1.071311369641311830e+00, 1.450569758088998445e+00, 1.950778549520360334e+00, 2.640031773695551468e+00, 3.631372373667412273e+00, 5.119915330903350570e+00, 7.456660981404883289e+00, 1.130226126889972624e+01, 1.796410692472772550e+01, 3.017810704601898222e+01, 5.403875800312370567e+01, 1.041077314477469548e+02, 2.180295201202628077e+02, 5.021556986259101646e+02, 1.288621310998222420e+03, 3.739216870800548324e+03, 1.247507297020191232e+04, 4.876399753226692124e+04, 2.281456582219130122e+05, 1.308777960064843017e+06, 9.460846634209664077e+06, 8.888831203637279622e+07, 1.124168828974344134e+09, 1.991276729532144470e+10, 5.167434691060984650e+11, 2.067218814203990888e+13, 1.350615033184100406e+15, 1.538540662836508188e+17, 3.290747290540350661e+19, 1.437291381884498816e+22, 1.409832445530347286e+25, 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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, }, { 9.13048762637669674838078869945948356e-01L, 1.41578929466281159169215570833490092e+01L, 6.70421551622327648231120321610008518e+03L, 9.64172532715049941526010563818587232e+10L, 2.50895076008577848514087028569888161e+30L, 1.44726353571033714499079379626715686e+83L, 3.75263401205045334128277886549019357e+226L, 2.57846123932685341261715758547064293e+616L, 1.25169402230987931584130068460134989e+1676L, }, { 4.07297690065758690150573950473604675e-01L, 1.68206670702114874332932330092838356e+00L, 6.15089798638672951539668935798437533e+00L, 4.00396235192940022205839866641270319e+01L, 7.92920024793102632052902471550336177e+02L, 1.02984971333097958319686053784919407e+05L, 3.03862310925243857437932941891415841e+08L, 1.56544547436249486913719231527597560e+14L, 4.04246509843021910355659662715183671e+23L, 1.32170682742965817915034577861235933e+39L, 4.99123178209955799774620736137366103e+64L, 7.35294385035987596594501676609562008e+106L, 2.45145417229813114714431821340237112e+176L, 1.03030479197459267961759023741376327e+291L, 9.88478945193556730604342445576518136e+479L, 3.74498116076433060427765453233124618e+791L, 1.90292390713026708045766158039087796e+1305L, 1.72712488231809244721915842027236657e+2152L, }, { 1.98135272251478172615235718398538323e-01L, 6.40155673500526017670785720911319502e-01L, 1.24892869825397766254802900819319987e+00L, 2.26608084094432123181038001270985037e+00L, 4.29646269670232738148137717958679987e+00L, 9.13029038709995569641811827045549232e+00L, 2.31110765386427993316995139635470937e+01L, 7.42770603432401243012214481410240677e+01L, 3.26720920711525891697790966796945063e+02L, 2.15948569431181871552028449867301828e+03L, 2.41501526289641306037808670196966696e+04L, 5.31819400275692915826269282626844010e+05L, 2.80058685721704332307817790755562305e+07L, 4.52406507979433877971977526863358905e+09L, 3.08561257398067712180174566763237112e+12L, 1.33882673301580747789133427708622972e+16L, 6.25461717656234138147247754416652254e+20L, 6.18209853581416475394863999233554548e+26L, 3.07729364978845806686511011060697837e+34L, 2.34895728937010430290698332595743680e+44L, 1.14854319789946975790127332653552673e+57L, 2.25530007001006986846545694404767295e+73L, 1.87791950056919539419801461538703336e+94L, 1.36747388793862427976781689638282239e+121L, 4.24212177246407592514720294750151286e+155L, 8.23473099012134325391170623028607158e+199L, 6.06134211888406631001019923425936351e+256L, 6.32519197436029413652766295658658263e+329L, 3.61942292928205643948383705201563065e+423L, 8.82464433126646489632943769283758364e+543L, 3.35512488018651738642854323317447493e+698L, 1.02411434678684822400261582079656500e+897L, 7.40716670979374017620610271197945784e+1151L, 1.30455147283895162835186634827124464e+1479L, 2.02948723345659016173510134582487641e+1899L, 6.99019443250345564805134094483457477e+2438L, }, { 9.83967894006732033862249554537934739e-02L, 3.00605617659955035122465185012715805e-01L, 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1.64407968993192526511230001818530622e+1784L, 6.63148743223242467667800355907041029e+2021L, 1.15911606715877477373516464924821476e+2291L, }, { 4.91151003502902493004859475143401791e-02L, 1.48013149674360733270682895306542340e-01L, 2.48938813740683685679302156785267041e-01L, 3.53325423692668437764413545980527251e-01L, 4.62733556612235325924240102411897269e-01L, 5.78912068164096306746325958452873475e-01L, 7.03870253386062779930091622585657886e-01L, 8.39965859144650568772715366992985538e-01L, 9.90015066424437614655918533324528544e-01L, 1.15743257014369913143250540144278056e+00L, 1.34641275918536176274682426896283388e+00L, 1.56216711390133555099139972670978661e+00L, 1.81123885278232337973709010374295886e+00L, 2.10192441900655030086142289233010995e+00L, 2.44484388558419793403331221069953203e+00L, 2.85372074663291502355627105440782037e+00L, 3.34645891095535078662878051589922609e+00L, 3.94664582105783838715586741669722603e+00L, 4.68567310159667852940801410152900804e+00L, 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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, 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1.45211919400936944187225846047638548e+1888Q, 7.08718013380970011842483247147601395e+1917Q, 1.01475962220405902523641440040104610e+1948Q, 4.33542978691578087509838132034723750e+1978Q, 5.62285772227295495777726116212032065e+2009Q, 2.25285072921565445630031609130087435e+2041Q, 2.83839050906274298341210206309759282e+2073Q, 1.14501659579022194588844609345877849e+2106Q, 1.50629562239998305958408533546634030e+2139Q, 6.58342161306998815751663631350733541e+2172Q, 9.74198999952210922892973281379349494e+2206Q, 4.97552704772088889228035264268694867e+2241Q, 8.94330619882842342247706838649878784e+2276Q, 5.77072420156026800834371478648673792e+2312Q, 1.36388225285320494361282201451878478e+2349Q, 1.20508189950290985406298094670730466e+2386Q, 4.06413362486490272506766749982212198e+2423Q, 5.34308092015215251528601382597439463e+2461Q, }, }; #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