1 // Copyright Nick Thompson, 2017
2 // Use, modification and distribution are subject to the
3 // Boost Software License, Version 1.0.
4 // (See accompanying file LICENSE_1_0.txt
5 // or copy at http://www.boost.org/LICENSE_1_0.txt)
6 
7 #ifndef BOOST_MATH_QUADRATURE_DETAIL_EXP_SINH_DETAIL_HPP
8 #define BOOST_MATH_QUADRATURE_DETAIL_EXP_SINH_DETAIL_HPP
9 
10 #include <cmath>
11 #include <vector>
12 #include <typeinfo>
13 #include <boost/math/constants/constants.hpp>
14 #include <boost/math/special_functions/next.hpp>
15 #include <boost/math/tools/atomic.hpp>
16 #include <boost/detail/lightweight_mutex.hpp>
17 
18 namespace boost{ namespace math{ namespace quadrature { namespace detail{
19 
20 
21 // Returns the exp-sinh quadrature of a function f over the open interval (0, infinity)
22 
23 template<class Real, class Policy>
24 class exp_sinh_detail
25 {
26    static const int initializer_selector =
27       !std::numeric_limits<Real>::is_specialized || (std::numeric_limits<Real>::radix != 2) ?
28       0 :
29       (std::numeric_limits<Real>::digits < 30) && (std::numeric_limits<Real>::max_exponent <= 128) ?
30       1 :
31       (std::numeric_limits<Real>::digits <= std::numeric_limits<double>::digits) && (std::numeric_limits<Real>::max_exponent <= std::numeric_limits<double>::max_exponent) ?
32       2 :
33       (std::numeric_limits<Real>::digits <= std::numeric_limits<long double>::digits) && (std::numeric_limits<Real>::max_exponent <= 16384) ?
34       3 :
35 #ifdef BOOST_HAS_FLOAT128
36       (std::numeric_limits<Real>::digits <= 113) && (std::numeric_limits<Real>::max_exponent <= 16384) ?
37       4 :
38 #endif
39       0;
40 public:
41     exp_sinh_detail(size_t max_refinements);
42 
43     template<class F>
44     auto integrate(const F& f, Real* error, Real* L1, const char* function, Real tolerance, std::size_t* levels)->decltype(std::declval<F>()(std::declval<Real>())) const;
45 
46 private:
get_abscissa_row(std::size_t n) const47    const std::vector<Real>& get_abscissa_row(std::size_t n)const
48    {
49 #ifndef BOOST_MATH_NO_ATOMIC_INT
50       if (m_committed_refinements.load() < n)
51          extend_refinements();
52       BOOST_ASSERT(m_committed_refinements.load() >= n);
53 #else
54       if (m_committed_refinements < n)
55          extend_refinements();
56       BOOST_ASSERT(m_committed_refinements >= n);
57 #endif
58       return m_abscissas[n];
59    }
get_weight_row(std::size_t n) const60    const std::vector<Real>& get_weight_row(std::size_t n)const
61    {
62 #ifndef BOOST_MATH_NO_ATOMIC_INT
63       if (m_committed_refinements.load() < n)
64          extend_refinements();
65       BOOST_ASSERT(m_committed_refinements.load() >= n);
66 #else
67       if (m_committed_refinements < n)
68          extend_refinements();
69       BOOST_ASSERT(m_committed_refinements >= n);
70 #endif
71       return m_weights[n];
72    }
73    void init(const mpl::int_<0>&);
74    void init(const mpl::int_<1>&);
75    void init(const mpl::int_<2>&);
76    void init(const mpl::int_<3>&);
77 #ifdef BOOST_HAS_FLOAT128
78    void init(const mpl::int_<4>&);
79 #endif
80 
extend_refinements() const81    void extend_refinements()const
82    {
83 #ifndef BOOST_MATH_NO_ATOMIC_INT
84       boost::detail::lightweight_mutex::scoped_lock guard(m_mutex);
85 #endif
86       //
87       // Check some other thread hasn't got here after we read the atomic variable, but before we got here:
88       //
89 #ifndef BOOST_MATH_NO_ATOMIC_INT
90       if (m_committed_refinements.load() >= m_max_refinements)
91          return;
92 #else
93       if (m_committed_refinements >= m_max_refinements)
94          return;
95 #endif
96 
97       using std::ldexp;
98       using std::ceil;
99       using std::sinh;
100       using std::cosh;
101       using std::exp;
102       std::size_t row  = ++m_committed_refinements;
103 
104       Real h = ldexp(Real(1), -static_cast<int>(row));
105       const Real t_max = m_t_min + m_abscissas[0].size() - 1;
106 
107       size_t k = (size_t)boost::math::lltrunc(ceil((t_max - m_t_min) / (2 * h)));
108       m_abscissas[row].reserve(k);
109       m_weights[row].reserve(k);
110       Real arg = m_t_min;
111       size_t j = 0;
112       size_t l = 2;
113       while (arg + l*h < t_max)
114       {
115          arg = m_t_min + (2 * j + 1)*h;
116          Real x = exp(constants::half_pi<Real>()*sinh(arg));
117          m_abscissas[row].emplace_back(x);
118          Real w = cosh(arg)*constants::half_pi<Real>()*x;
119          m_weights[row].emplace_back(w);
120          ++j;
121       }
122    }
123 
124     Real m_tol, m_t_min;
125 
126     mutable std::vector<std::vector<Real>> m_abscissas;
127     mutable std::vector<std::vector<Real>> m_weights;
128     std::size_t                       m_max_refinements;
129 #ifndef BOOST_MATH_NO_ATOMIC_INT
130     mutable boost::math::detail::atomic_unsigned_type      m_committed_refinements;
131     mutable boost::detail::lightweight_mutex m_mutex;
132 #else
133     mutable unsigned                  m_committed_refinements;
134 #endif
135 };
136 
137 template<class Real, class Policy>
exp_sinh_detail(size_t max_refinements)138 exp_sinh_detail<Real, Policy>::exp_sinh_detail(size_t max_refinements)
139    : m_abscissas(max_refinements), m_weights(max_refinements),
140    m_max_refinements(max_refinements)
141 {
142    init(mpl::int_<initializer_selector>());
143 }
144 template<class Real, class Policy>
145 template<class F>
integrate(const F & f,Real * error,Real * L1,const char * function,Real tolerance,std::size_t * levels)146 auto exp_sinh_detail<Real, Policy>::integrate(const F& f, Real* error, Real* L1, const char* function, Real tolerance, std::size_t* levels)->decltype(std::declval<F>()(std::declval<Real>())) const
147 {
148     typedef decltype(f(Real(0))) K;
149     using std::abs;
150     using std::floor;
151     using std::tanh;
152     using std::sinh;
153     using std::sqrt;
154     using boost::math::constants::half;
155     using boost::math::constants::half_pi;
156 
157     // This provided a nice error message for real valued integrals, but it's super awkward for complex-valued integrals:
158     /*K y_max = f(tools::max_value<Real>());
159     if(abs(y_max) > tools::epsilon<Real>() || !(boost::math::isfinite)(y_max))
160     {
161         K val = abs(y_max);
162         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%", val, Policy()));
163     }*/
164 
165     //std::cout << std::setprecision(5*std::numeric_limits<Real>::digits10);
166 
167     // Get the party started with two estimates of the integral:
168     K I0 = 0;
169     Real L1_I0 = 0;
170     for(size_t i = 0; i < m_abscissas[0].size(); ++i)
171     {
172         K y = f(m_abscissas[0][i]);
173         I0 += y*m_weights[0][i];
174         L1_I0 += abs(y)*m_weights[0][i];
175     }
176 
177     //std::cout << "First estimate : " << I0 << std::endl;
178     K I1 = I0;
179     Real L1_I1 = L1_I0;
180     for (size_t i = 0; i < m_abscissas[1].size(); ++i)
181     {
182         K y = f(m_abscissas[1][i]);
183         I1 += y*m_weights[1][i];
184         L1_I1 += abs(y)*m_weights[1][i];
185     }
186 
187     I1 *= half<Real>();
188     L1_I1 *= half<Real>();
189     Real err = abs(I0 - I1);
190     //std::cout << "Second estimate: " << I1 << " Error estimate at level " << 1 << " = " << err << std::endl;
191 
192     size_t i = 2;
193     for(; i < m_abscissas.size(); ++i)
194     {
195         I0 = I1;
196         L1_I0 = L1_I1;
197 
198         I1 = half<Real>()*I0;
199         L1_I1 = half<Real>()*L1_I0;
200         Real h = (Real) 1/ (Real) (1 << i);
201         K sum = 0;
202         Real absum = 0;
203 
204         auto abscissas_row = get_abscissa_row(i);
205         auto weight_row = get_weight_row(i);
206 
207         Real abterm1 = 1;
208         Real eps = tools::epsilon<Real>()*L1_I1;
209         for(size_t j = 0; j < m_weights[i].size(); ++j)
210         {
211             Real x = abscissas_row[j];
212             K y = f(x);
213             sum += y*weight_row[j];
214             Real abterm0 = abs(y)*weight_row[j];
215             absum += abterm0;
216 
217             // We require two consecutive terms to be < eps in case we hit a zero of f.
218             // Numerical experiments indicate that we should start this check at ~30 for floats,
219             // ~60 for doubles, and ~100 for long doubles.
220             // However, starting the check at x = 10 rather than x = 100 will only save two function evaluations.
221             if (x > (Real) 100 && abterm0 < eps && abterm1 < eps)
222             {
223                 break;
224             }
225             abterm1 = abterm0;
226         }
227 
228         I1 += sum*h;
229         L1_I1 += absum*h;
230         err = abs(I0 - I1);
231         //std::cout << "Estimate:        " << I1 << " Error estimate at level " << i  << " = " << err << std::endl;
232         // Use L1_I1 here to make it work with both complex and real valued integrands:
233         if (!isfinite(L1_I1))
234         {
235             return static_cast<K>(policies::raise_evaluation_error(function, "The exp_sinh quadrature evaluated your function at a singular point and returned %1%. Please ensure your function evaluates to a finite number over its entire domain.", I1, Policy()));
236         }
237         if (err <= tolerance*L1_I1)
238         {
239             break;
240         }
241     }
242 
243     if (error)
244     {
245         *error = err;
246     }
247 
248     if(L1)
249     {
250         *L1 = L1_I1;
251     }
252 
253     if (levels)
254     {
255        *levels = i;
256     }
257 
258     return I1;
259 }
260 
261 
262 template<class Real, class Policy>
init(const mpl::int_<0> &)263 void exp_sinh_detail<Real, Policy>::init(const mpl::int_<0>&)
264 {
265    using std::exp;
266    using std::log;
267    using std::sqrt;
268    using std::cosh;
269    using std::sinh;
270    using std::asinh;
271    using std::ceil;
272    using boost::math::constants::two_div_pi;
273    using boost::math::constants::half_pi;
274    using boost::math::constants::half;
275 
276    m_committed_refinements = 4;
277    // m_t_min is chosen such that x = exp(pi/2 sinh(-t_max)) = very small, but not too small.
278    // This is a compromise; we wish to approach a singularity at zero without hitting it through roundoff error.
279    // If we choose the small number as epsilon, we do not get close enough to the singularity to achieve high accuracy.
280    // If we choose the small number as the min(), then we round off to zero and hit the singularity.
281    // The logarithmic average of the min() and the epsilon() has been found to be a reasonable compromise, which achieves high accuracy
282    // but does not evaluate the function at the singularity.
283    Real tmp = (boost::math::tools::log_min_value<Real>() + log(boost::math::tools::epsilon<Real>()))*half<Real>();
284    m_t_min = asinh(two_div_pi<Real>()*tmp);
285 
286    // t_max is chosen to make g'(t_max) ~ sqrt(max) (g' grows faster than g).
287    // This will allow some flexibility on the users part; they can at least square a number function without overflow.
288    // But there is no unique choice; the further out we can evaluate the function, the better we can do on slowly decaying integrands.
289    const Real t_max = log(2 * two_div_pi<Real>()*log(2 * two_div_pi<Real>()*sqrt(tools::max_value<Real>())));
290 
291    for (size_t i = 0; i <= m_committed_refinements; ++i)
292    {
293       Real h = (Real)1 / (Real)(1 << i);
294       size_t k = (size_t)boost::math::lltrunc(ceil((t_max - m_t_min) / (2 * h)));
295       m_abscissas[i].reserve(k);
296       m_weights[i].reserve(k);
297       Real arg = m_t_min;
298       size_t j = 0;
299       size_t l = 2;
300       if (i == 0)
301       {
302          l = 1;
303       }
304       while (arg + l*h < t_max)
305       {
306          if (i != 0)
307          {
308             arg = m_t_min + (2 * j + 1)*h;
309          }
310          else
311          {
312             arg = m_t_min + j*h;
313          }
314          Real x = exp(half_pi<Real>()*sinh(arg));
315          m_abscissas[i].emplace_back(x);
316          Real w = cosh(arg)*half_pi<Real>()*x;
317          m_weights[i].emplace_back(w);
318          ++j;
319       }
320    }
321    /*
322    std::cout << std::setprecision(40) << m_t_min << std::endl;
323    for (unsigned i = 0; i <= m_committed_refinements; ++i)
324    {
325       std::cout << "{ ";
326       for (unsigned j = 0; j < m_abscissas[i].size(); ++j)
327          std::cout << m_abscissas[i][j] << "Q, ";
328       std::cout << " },\n";
329    }
330    for (unsigned i = 0; i <= m_committed_refinements; ++i)
331    {
332       std::cout << "{ ";
333       for (unsigned j = 0; j < m_weights[i].size(); ++j)
334          std::cout << m_weights[i][j] << "Q, ";
335       std::cout << " },\n";
336    }
337    */
338 }
339 
340 template<class Real, class Policy>
init(const mpl::int_<1> &)341 void exp_sinh_detail<Real, Policy>::init(const mpl::int_<1>&)
342 {
343    m_abscissas = {
344       { 3.47876573e-23f, 5.62503650e-09f, 9.95706124e-04f, 9.67438487e-02f, 7.43599217e-01f, 4.14293205e+00f, 1.08086768e+02f, 4.56291316e+05f, 2.70123007e+15f, },
345       { 2.41870864e-14f, 1.02534662e-05f, 1.65637566e-02f, 3.11290799e-01f, 1.64691269e+00f, 1.49800773e+01f, 2.57724301e+03f, 2.24833766e+09f, },
346       { 3.24983286e-18f, 2.51095186e-11f, 3.82035773e-07f, 1.33717837e-04f, 4.80260650e-03f, 4.41526928e-02f, 1.83045938e-01f, 4.91960276e-01f, 1.10322609e+00f, 2.53681744e+00f, 7.39791792e+00f, 3.59560256e+01f, 4.36061333e+02f, 2.49501460e+04f, 1.89216933e+07f, 1.03348694e+12f, },
347       { 1.51941172e-20f, 3.70201714e-16f, 9.67598102e-13f, 4.44773051e-10f, 5.28493928e-08f, 2.19158236e-06f, 4.00799258e-05f, 3.88011529e-04f, 2.29325538e-03f, 9.25182629e-03f, 2.78117501e-02f, 6.67553298e-02f, 1.35173168e-01f, 2.41374946e-01f, 3.94194704e-01f, 6.07196731e-01f, 9.06432514e-01f, 1.34481045e+00f, 2.03268444e+00f, 3.21243032e+00f, 5.46310949e+00f, 1.03365745e+01f, 2.26486752e+01f, 6.03727778e+01f, 2.08220266e+02f, 1.00431239e+03f, 7.47843388e+03f, 9.75279951e+04f, 2.61755592e+06f, 1.77776624e+08f, 3.98255346e+10f, 4.13443763e+13f, 3.07708133e+17f, },
348       { 7.99409438e-22f, 2.41624595e-19f, 3.73461321e-17f, 3.19397902e-15f, 1.62042378e-13f, 5.18579386e-12f, 1.10520072e-10f, 1.64548212e-09f, 1.78534009e-08f, 1.46529196e-07f, 9.40168786e-07f, 4.85507733e-06f, 2.07038029e-05f, 7.45799409e-05f, 2.31536599e-04f, 6.30580368e-04f, 1.53035449e-03f, 3.35582040e-03f, 6.73124842e-03f, 1.24856832e-02f, 2.16245309e-02f, 3.52720523e-02f, 5.45995171e-02f, 8.07587788e-02f, 1.14840025e-01f, 1.57867103e-01f, 2.10837078e-01f, 2.74805391e-01f, 3.51015955e-01f, 4.41077540e-01f, 5.47194016e-01f, 6.72466825e-01f, 8.21304567e-01f, 1.00000000e+00f, 1.21757511e+00f, 1.48706221e+00f, 1.82750536e+00f, 2.26717507e+00f, 2.84887335e+00f, 3.63893880e+00f, 4.74299876e+00f, 6.33444194e+00f, 8.70776542e+00f, 1.23825548e+01f, 1.83151803e+01f, 2.83510579e+01f, 4.62437776e+01f, 8.00917327e+01f, 1.48560852e+02f, 2.97989725e+02f, 6.53443372e+02f, 1.58584068e+03f, 4.31897162e+03f, 1.34084311e+04f, 4.83003053e+04f, 2.05969943e+05f, 1.06363880e+06f, 6.82457850e+06f, 5.60117371e+07f, 6.07724622e+08f, 9.04813016e+09f, 1.92834507e+11f, 6.17122515e+12f, 3.13089095e+14f, 2.67765347e+16f, 4.13865153e+18f, },
349       { 1.70893932e-22f, 3.56621447e-21f, 6.19138882e-20f, 9.04299298e-19f, 1.12287188e-17f, 1.19706303e-16f, 1.10583090e-15f, 8.92931857e-15f, 6.35404710e-14f, 4.01527389e-13f, 2.26955738e-12f, 1.15522811e-11f, 5.32913181e-11f, 2.24130967e-10f, 8.64254491e-10f, 3.07161058e-09f, 1.01117742e-08f, 3.09775637e-08f, 8.87004371e-08f, 2.38368096e-07f, 6.03520392e-07f, 1.44488635e-06f, 3.28212299e-06f, 7.09655821e-06f, 1.46494407e-05f, 2.89537394e-05f, 5.49357161e-05f, 1.00313252e-04f, 1.76700203e-04f, 3.00920507e-04f, 4.96484845e-04f, 7.95150594e-04f, 1.23845781e-03f, 1.87911525e-03f, 2.78210510e-03f, 4.02538552e-03f, 5.70009588e-03f, 7.91020800e-03f, 1.07716137e-02f, 1.44106884e-02f, 1.89624177e-02f, 2.45682104e-02f, 3.13735515e-02f, 3.95256605e-02f, 4.91713196e-02f, 6.04550279e-02f, 7.35176150e-02f, 8.84954195e-02f, 1.05520113e-01f, 1.24719213e-01f, 1.46217318e-01f, 1.70138063e-01f, 1.96606781e-01f, 2.25753880e-01f, 2.57718900e-01f, 2.92655274e-01f, 3.30735809e-01f, 3.72158929e-01f, 4.17155794e-01f, 4.65998399e-01f, 5.19008863e-01f, 5.76570161e-01f, 6.39138643e-01f, 7.07258781e-01f, 7.81580731e-01f, 8.62881450e-01f, 9.52090320e-01f, 1.05032052e+00f, 1.15890775e+00f, 1.27945836e+00f, 1.41390963e+00f, 1.56460576e+00f, 1.73439430e+00f, 1.92674937e+00f, 2.14593012e+00f, 2.39718593e+00f, 2.68702407e+00f, 3.02356133e+00f, 3.41698950e+00f, 3.88019661e+00f, 4.42960272e+00f, 5.08629455e+00f, 5.87757956e+00f, 6.83913514e+00f, 8.01801085e+00f, 9.47686632e+00f, 1.13000199e+01f, 1.36021823e+01f, 1.65412214e+01f, 2.03370584e+01f, 2.53000199e+01f, 3.18739815e+01f, 4.07030054e+01f, 5.27358913e+01f, 6.93929374e+01f, 9.28366010e+01f, 1.26418926e+02f, 1.75435645e+02f, 2.48423411e+02f, 3.59440052e+02f, 5.32165336e+02f, 8.07455844e+02f, 1.25762341e+03f, 2.01416017e+03f, 3.32313676e+03f, 5.65930306e+03f, 9.96877263e+03f, 1.82030939e+04f, 3.45378531e+04f, 6.82619916e+04f, 1.40913380e+05f, 3.04680844e+05f, 6.92095957e+05f, 1.65694484e+06f, 4.19519229e+06f, 1.12739016e+07f, 3.22814282e+07f, 9.88946136e+07f, 3.25562103e+08f, 1.15706659e+09f, 4.46167708e+09f, 1.87647826e+10f, 8.65629909e+10f, 4.40614549e+11f, 2.49049013e+12f, 1.57380011e+13f, 1.11990629e+14f, 9.04297390e+14f, 8.35377903e+15f, 8.90573552e+16f, 1.10582857e+18f, 1.61514650e+19f, },
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2.93241843e+00f, 3.02635449e+00f, 3.12441791e+00f, 3.22682682e+00f, 3.33381238e+00f, 3.44561973e+00f, 3.56250887e+00f, 3.68475574e+00f, 3.81265333e+00f, 3.94651282e+00f, 4.08666490e+00f, 4.23346116e+00f, 4.38727553e+00f, 4.54850596e+00f, 4.71757611e+00f, 4.89493722e+00f, 5.08107015e+00f, 5.27648761e+00f, 5.48173646e+00f, 5.69740032e+00f, 5.92410235e+00f, 6.16250823e+00f, 6.41332946e+00f, 6.67732689e+00f, 6.95531455e+00f, 7.24816384e+00f, 7.55680807e+00f, 7.88224735e+00f, 8.22555401e+00f, 8.58787841e+00f, 8.97045530e+00f, 9.37461076e+00f, 9.80176975e+00f, 1.02534643e+01f, 1.07313428e+01f, 1.12371793e+01f, 1.17728848e+01f, 1.23405187e+01f, 1.29423019e+01f, 1.35806306e+01f, 1.42580922e+01f, 1.49774818e+01f, 1.57418213e+01f, 1.65543795e+01f, 1.74186947e+01f, 1.83385994e+01f, 1.93182476e+01f, 2.03621450e+01f, 2.14751816e+01f, 2.26626686e+01f, 2.39303784e+01f, 2.52845893e+01f, 2.67321348e+01f, 2.82804577e+01f, 2.99376708e+01f, 3.17126238e+01f, 3.36149769e+01f, 3.56552840e+01f, 3.78450835e+01f, 4.01970005e+01f, 4.27248599e+01f, 4.54438126e+01f, 4.83704762e+01f, 5.15230921e+01f, 5.49217006e+01f, 5.85883374e+01f, 6.25472527e+01f, 6.68251567e+01f, 7.14514957e+01f, 7.64587609e+01f, 8.18828353e+01f, 8.77633847e+01f, 9.41442967e+01f, 1.01074176e+02f, 1.08606902e+02f, 1.16802259e+02f, 1.25726650e+02f, 1.35453899e+02f, 1.46066166e+02f, 1.57654979e+02f, 1.70322410e+02f, 1.84182406e+02f, 1.99362306e+02f, 2.16004568e+02f, 2.34268740e+02f, 2.54333703e+02f, 2.76400239e+02f, 3.00693971e+02f, 3.27468728e+02f, 3.57010397e+02f, 3.89641362e+02f, 4.25725590e+02f, 4.65674502e+02f, 5.09953726e+02f, 5.59090900e+02f, 6.13684688e+02f, 6.74415211e+02f, 7.42056139e+02f, 8.17488717e+02f, 9.01718069e+02f, 9.95892168e+02f, 1.10132394e+03f, 1.21951707e+03f, 1.35219615e+03f, 1.50134197e+03f, 1.66923291e+03f, 1.85849349e+03f, 2.07215152e+03f, 2.31370536e+03f, 2.58720328e+03f, 2.89733724e+03f, 3.24955383e+03f, 3.65018587e+03f, 4.10660860e+03f, 4.62742547e+03f, 5.22268956e+03f, 5.90416786e+03f, 6.68565726e+03f, 7.58336313e+03f, 8.61635357e+03f, 9.80710572e+03f, 1.11821637e+04f, 1.27729327e+04f, 1.46166396e+04f, 1.67574960e+04f, 1.92481112e+04f, 2.21512104e+04f, 2.55417295e+04f, 2.95093735e+04f, 3.41617487e+04f, 3.96282043e+04f, 4.60645561e+04f, 5.36589049e+04f, 6.26388223e+04f, 7.32802431e+04f, 8.59184957e+04f, 1.00962017e+05f, 1.18909442e+05f, 1.40370957e+05f, 1.66095034e+05f, 1.97001996e+05f, 2.34226253e+05f, 2.79169596e+05f, 3.33568603e+05f, 3.99580125e+05f, 4.79889989e+05f, 5.77851588e+05f, 6.97663062e+05f, 8.44594440e+05f, 1.02527965e+06f, 1.24809298e+06f, 1.52363581e+06f, 1.86536786e+06f, 2.29042802e+06f, 2.82070529e+06f, 3.48424008e+06f, 4.31706343e+06f, 5.36561882e+06f, 6.68996113e+06f, 8.36799594e+06f, 1.05011160e+07f, 1.32217203e+07f, 1.67032788e+07f, 2.11738506e+07f, 2.69343047e+07f, 3.43829654e+07f, 4.40490690e+07f, 5.66383460e+07f, 7.30953564e+07f, 9.46890531e+07f, 1.23130681e+08f, 1.60736861e+08f, 2.10656057e+08f, 2.77184338e+08f, 3.66207397e+08f, 4.85821891e+08f, 6.47212479e+08f, 8.65895044e+08f, 1.16348659e+09f, 1.57023596e+09f, 2.12865840e+09f, 2.89877917e+09f, 3.96573294e+09f, 5.45082863e+09f, 7.52773593e+09f, 1.04462776e+10f, 1.45675716e+10f, 2.04161928e+10f, 2.87579864e+10f, 4.07167363e+10f, 5.79499965e+10f, 8.29154750e+10f, 1.19276754e+11f, 1.72524570e+11f, 2.50933409e+11f, 3.67042596e+11f, 5.39962441e+11f, 7.98985690e+11f, 1.18927611e+12f, 1.78088199e+12f, 2.68310388e+12f, 4.06753710e+12f, 6.20525592e+12f, 9.52719664e+12f, 1.47228407e+13f, 2.29025392e+13f, 3.58662837e+13f, 5.65517100e+13f, 8.97859411e+13f, 1.43556057e+14f, 2.31171020e+14f, 3.74966777e+14f, 6.12702071e+14f, 1.00868013e+15f, 1.67323268e+15f, 2.79711270e+15f, 4.71267150e+15f, 8.00353033e+15f, 1.37027503e+16f, 2.36538022e+16f, 4.11734705e+16f, 7.22793757e+16f, 1.27982244e+17f, 2.28603237e+17f, 4.11976277e+17f, 7.49169358e+17f, 1.37488861e+18f, 2.54681529e+18f, 4.76248383e+18f, 8.99167123e+18f, 1.71428840e+19f, 3.30088717e+19f, 6.42020070e+19f, 1.26155602e+20f, 2.50480806e+20f, 5.02601059e+20f, 1.01935525e+21f, },
362    };
363 #ifndef BOOST_MATH_NO_ATOMIC_INT
364    m_committed_refinements = static_cast<boost::math::detail::atomic_unsigned_integer_type>(m_weights.size() - 1);
365 #else
366    m_committed_refinements = m_weights.size() - 1;
367 #endif
368    m_t_min = -4.18750000f;
369    if (m_max_refinements >= m_abscissas.size())
370    {
371       m_abscissas.resize(m_max_refinements + 1);
372       m_weights.resize(m_max_refinements + 1);
373    }
374    else
375    {
376       m_max_refinements = m_abscissas.size() - 1;
377    }
378 }
379 
380 template<class Real, class Policy>
init(const mpl::int_<2> &)381 void exp_sinh_detail<Real, Policy>::init(const mpl::int_<2>&)
382 {
383    m_abscissas = {
384       { 7.241670621354483269e-163, 2.257639733856759198e-60, 1.153241619257215165e-22, 8.747691973876861825e-09, 1.173446923800022477e-03, 1.032756936219208144e-01, 7.719261204224504866e-01, 4.355544675823585545e+00, 1.215101039066652656e+02, 6.228845436711506169e+05, 6.278613977336989392e+15, 9.127414935180233465e+42, 6.091127771174027909e+116, },
385       { 4.547459836328942014e-99, 6.678756542928857080e-37, 5.005042973041566360e-14, 1.341318484151208960e-05, 1.833875636365939263e-02, 3.257972971286326131e-01, 1.712014688483495078e+00, 1.613222549264089627e+01, 3.116246745274236447e+03, 3.751603952020919663e+09, 1.132259067258797346e+26, 6.799257464097374238e+70, },
386       { 5.314690663257815465e-127, 2.579830034615362946e-77, 3.534801062399966878e-47, 6.733941646704537777e-29, 8.265803726974829043e-18, 4.424914371157762285e-11, 5.390411046738629465e-07, 1.649389713333761449e-04, 5.463728936866216652e-03, 4.787896410534771955e-02, 1.931544616590306846e-01, 5.121421856617965197e-01, 1.144715949265016019e+00, 2.648424684387670480e+00, 7.856804169938798917e+00, 3.944731803343517708e+01, 5.060291993016831194e+02, 3.181117494063683297e+04, 2.820174654949211729e+07, 1.993745099515255184e+12, 1.943469269499068563e+20, 2.858803732300638372e+33, 1.457292199029008637e+55, 8.943565831706355607e+90, 9.016198369791554655e+149, },
387       { 8.165631636299519857e-144, 3.658949309353149331e-112, 1.635242513882908826e-87, 2.578381184977746454e-68, 2.305546416275824199e-53, 1.016725540031465162e-41, 1.191823622917539774e-32, 1.379018088205016509e-25, 4.375640088826073184e-20, 8.438464631330991606e-16, 1.838483310261119782e-12, 7.334264181393092650e-10, 7.804740587931068021e-08, 2.970395577741681504e-06, 5.081805431666579484e-05, 4.671401627620431498e-04, 2.652347404231090523e-03, 1.037409202661683856e-02, 3.045225582205323946e-02, 7.178280364982721201e-02, 1.434001065841990688e-01, 2.535640852949085796e-01, 4.113268917643175920e-01, 6.310260805648534613e-01, 9.404706503455087817e-01, 1.396267301972783068e+00, 2.116896928689963277e+00, 3.364289290471596568e+00, 5.770183960005836987e+00, 1.104863531218761752e+01, 2.460224479439805859e+01, 6.699316387888639988e+01, 2.375794092475844708e+02, 1.188092202760116066e+03, 9.269848635975416108e+03, 1.283900116155671304e+05, 3.723397798030112514e+06, 2.793667983952389721e+08, 7.112973790863854188e+10, 8.704037695808749572e+13, 8.001474015782459984e+17, 9.804091819390540578e+22, 3.342777673392873288e+29, 8.160092668471508447e+37, 4.798775331663586528e+48, 3.228614320248853938e+62, 1.836986041572136151e+80, 1.153145986877483804e+103, 2.160972586723647751e+132, },
388       { 4.825077401709435655e-153, 3.813781211050297560e-135, 2.377824349780240844e-119, 2.065817295388293122e-105, 4.132105770181358886e-93, 2.963965169989404311e-82, 1.127296662046635391e-72, 3.210346399945695041e-64, 9.282992368222161062e-57, 3.565977853916619677e-50, 2.306962519220473637e-44, 3.098751038516535098e-39, 1.039558064722960891e-34, 1.025256027381235200e-30, 3.432612000569885403e-27, 4.429681881379089961e-24, 2.464589267395236846e-21, 6.526691446363344923e-19, 8.976892324445928684e-17, 6.926277695183452225e-15, 3.208805316815751272e-13, 9.478053068835988899e-12, 1.882052586691155400e-10, 2.632616062773909009e-09, 2.703411837703917665e-08, 2.113642195965330965e-07, 1.299327029813074013e-06, 6.461189935136030673e-06, 2.665090959570723827e-05, 9.322774986189288194e-05, 2.820463407940068813e-04, 7.508613300035051413e-04, 1.786142185986551786e-03, 3.848376610765768211e-03, 7.600810651854199771e-03, 1.390873269178271700e-02, 2.380489559528694982e-02, 3.842796337748997654e-02, 5.895012901671883992e-02, 8.651391160689367948e-02, 1.221961347398101671e-01, 1.670112314557845555e-01, 2.219593619059930701e-01, 2.881200442770917241e-01, 3.667906976948184315e-01, 4.596722879563388211e-01, 5.691113093602836208e-01, 6.984190600916228379e-01, 8.523070690462583711e-01, 1.037505121571600249e+00, 1.263672635742961915e+00, 1.544788480334120896e+00, 1.901333876886441433e+00, 2.363816272813317635e+00, 2.978614980117902904e+00, 3.817957977526709364e+00, 4.997477803461245639e+00, 6.708150685706236545e+00, 9.276566033183386532e+00, 1.328332469239125539e+01, 1.980618680552458639e+01, 3.094452809319702849e+01, 5.101378787119006225e+01, 8.943523638413590523e+01, 1.682138665185088325e+02, 3.427988270281270587e+02, 7.653823671943767281e+02, 1.895993667030670343e+03, 5.285404568827643942e+03, 1.684878049282191210e+04, 6.254388805482299369e+04, 2.759556544455721132e+05, 1.481213238071008345e+06, 9.929728611179601424e+06, 8.564987764771851841e+07, 9.831650826344826952e+08, 1.560339073978569502e+10, 3.575098885016726922e+11, 1.241973798101884982e+13, 6.915106205748805839e+14, 6.571419716645131084e+16, 1.144558033138694099e+19, 3.960915669532823553e+21, 2.984410558028297842e+24, 5.430494850258846715e+27, 2.683747612498502676e+31, 4.114885708325522701e+35, 2.276004816861421600e+40, 5.387544917595833246e+45, 6.623575732955432303e+51, 5.266881304835239338e+58, 3.473234812654772210e+66, 2.517492645985977377e+75, 2.759797646289240629e+85, 6.569603829502412077e+96, 5.116181648220647995e+109, 2.073901892339407423e+124, 7.406462446666255838e+140, },
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3.548058538654277403e+32, 1.097378059358046160e+33, 3.454102978064445595e+33, 1.106745393701652323e+34, 3.610899559139069994e+34, 1.199946999283670567e+35, 4.062687014190878792e+35, 1.401835223893224514e+36, 4.931085527333162173e+36, 1.768812393284919500e+37, 6.472148293945199961e+37, 2.416453721739211922e+38, 9.208944720398123862e+38, 3.583297028622126676e+39, 1.424097482596699440e+40, 5.782627833426411524e+40, 2.399862204084363183e+41, 1.018291572042305460e+42, 4.419105414822034531e+42, 1.962126117680499311e+43, 8.916742424061253707e+43, 4.148882478294757720e+44, 1.977256529558276930e+45, 9.655300233875401080e+45, 4.832878898335598922e+46, 2.480575878223098058e+47, 1.306102809757654706e+48, 7.057565717289569232e+48, 3.915276522229618618e+49, 2.230898980943393318e+50, 1.306141334496309306e+51, 7.861021286656392627e+51, 4.865583758538451107e+52, 3.098487425915704674e+53, 2.031037614862563901e+54, 1.370999647608260200e+55, 9.534736274325001528e+55, 6.834959923166415407e+56, 5.052733546324789020e+57, 3.853810997282159979e+58, 3.034183107853208298e+59, 2.467161926009838899e+60, 2.072901039813580593e+61, 1.800563980579615383e+62, 1.617764027895344257e+63, 1.504283028250688329e+64, 1.448393206525427172e+65, 1.444855510980115799e+66, 1.494120428855029243e+67, 1.602566566107015722e+68, 1.783880504153942988e+69, 2.061999240572760738e+70, 2.476521794698572715e+71, 3.092349914153497358e+72, 4.016927238305985810e+73, 5.431607545226497387e+74, 7.650086824042822759e+75, 1.123017984114349288e+77, 1.719382952966052004e+78, 2.747335718690686674e+79, 4.584545010557684123e+80, 7.995082041539250252e+81, 1.458119909365899044e+83, 2.783001178679600175e+84, 5.562812231966194628e+85, 1.165338768982404578e+87, 2.560399126432838224e+88, 5.904549641859098192e+89, 1.430278474749838710e+91, 3.642046122956932563e+92, 9.756698571206402300e+93, 2.751946044275883051e+95, 8.179164793643197279e+96, 2.563704735086825890e+98, 8.481656496128255880e+99, 2.964260254403981007e+101, 1.095342970031208886e+103, 4.283148547584870628e+104, 1.773954352944319744e+106, 7.788991081894224760e+107, 3.628931721056821352e+109, 1.795729272516020592e+111, 9.446685151482835339e+112, 5.288263179614488101e+114, 3.153311236741401362e+116, 2.004807079683827669e+118, 1.360407192665237716e+120, 9.862825609807810517e+121, 7.647551788591128099e+123, 6.348802224871730088e+125, 5.649062361980019098e+127, 5.393248003523784781e+129, 5.530897191915703916e+131, 6.099598644640894333e+133, 7.242098433491964504e+135, 9.268083053637375570e+137, 1.279942702416040582e+140, 1.909796626960621302e+142, 3.082540300669885040e+144, 5.388809732384179657e+146, 1.021610251056626535e+149, 2.103005440072790650e+151, 4.706753990348725570e+153, 1.146834128125248991e+156, },
402    };
403 #ifndef BOOST_MATH_NO_ATOMIC_INT
404    m_committed_refinements = static_cast<boost::math::detail::atomic_unsigned_integer_type>(m_weights.size() - 1);
405 #else
406    m_committed_refinements = m_weights.size() - 1;
407 #endif
408    m_t_min = -6.164062500000000000;
409    if (m_max_refinements >= m_abscissas.size())
410    {
411       m_abscissas.resize(m_max_refinements + 1);
412       m_weights.resize(m_max_refinements + 1);
413    }
414    else
415    {
416       m_max_refinements = m_abscissas.size() - 1;
417    }
418 }
419 #if LDBL_MAX_EXP == 16384
420 template<class Real, class Policy>
init(const mpl::int_<3> &)421 void exp_sinh_detail<Real, Policy>::init(const mpl::int_<3>&)
422 {
423    m_abscissas = {
424       { 1.02756529896290544244959196973059583e-2497L, 2.56737528671961581475200468317128232e-919L, 1.17417808941462434184174780056564573e-338L, 4.82182886130634548471358754377036370e-125L, 1.85613301660646818149136526457281019e-46L, 1.52174118093087534300657777272732001e-17L, 6.75122240537294392532710530940672267e-07L, 5.94481311616464419075825632567494453e-03L, 2.00100938779037997581424620542543429e-01L, 1.17328605653712546899681147538372171e+00L, 8.18356490677287285512063117929807241e+00L, 5.59865842621965368881982340891928481e+02L, 3.69902944883650290371636082450503730e+07L, 4.05747121124517088709477132072461878e+20L, 1.07723884748977308147226626407207905e+56L, 2.07250561337258237728923403163755392e+152L, 1.09889904624000153879292638133263171e+414L, 3.02463014753652876878705286965250144e+1125L, },
425       { 3.16339947894004847541521297710937343e-1515L, 7.02786763812753004271170107158747593e-558L, 1.08465499866859733494552744914276656e-205L, 3.97220624097731753646493300738183748e-76L, 1.84145280968701148636501796762008815e-28L, 6.40886341101610144938011594904313817e-11L, 1.89200275395722467663251234615351291e-04L, 5.04892743776943294143478969573235061e-02L, 5.25946553709738448524487603870477588e-01L, 2.72635049439566736308739858009584752e+00L, 4.20081657572145199006060015525396829e+01L, 3.75221714819472331206969009243353365e+04L, 3.11642465424592079726559332629050577e+12L, 9.61947229245436139236957297153092319e+33L, 2.42007357898805628851519620917402234e+92L, 1.34351470989086331111432001407522043e+251L, 4.34937560839564995558174638985438726e+682L, 4.01820305474077838467315109614612109e+1855L, },
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6.43831323019893638007682069747894997e+236L, 3.17506717851901774760997889290937204e+240L, 1.78970981603629426034165602936202663e+244L, 1.15551435950001094003467361479483663e+248L, 8.56366431033316582912879348191377839e+251L, 7.30093770528170061921940254565023758e+255L, 7.17613138815551609337504025522760569e+259L, 8.15019404042552378087870259624107791e+263L, 1.07201229194901841245742935320285314e+268L, 1.63677814658507005123653360340510968e+272L, 2.90775562270833690431514296460636317e+276L, 6.02476179304325236422526103127046739e+280L, 1.45944561364291559252990517774206937e+285L, 4.14353248208966528107409825739318649e+289L, 1.38220972739972368321976302536673924e+294L, 5.43125471568796436605394023488404770e+298L, 2.52039989595272682474151246524004609e+303L, 1.38490332203279628724542169932072504e+308L, 9.03453415480179250943103381623811201e+312L, 7.01620311300324094081813342355630834e+317L, 6.50430483422567669743617206850738485e+322L, 7.21793562600493199951776097195343971e+327L, 9.61542788471746566451160668498411528e+332L, 1.54211655565340209996546117001243607e+338L, 2.98626205265198316430063943341329432e+343L, 7.00309320577422492544778192980108604e+348L, 1.99486089518136492496460973366880635e+354L, 6.92350663128275446878446973158773950e+359L, 2.93684755383592258491626945473185368e+365L, 1.52739293250863294426010436780725812e+371L, 9.77075509850276765943058812672579852e+376L, 7.71310608088780517993569363011828070e+382L, 7.53863036472313339350939561575995488e+388L, 9.15331385155864163687518059055937567e+394L, 1.38538605697398143363179835422022577e+401L, 2.62287133256068615930266548676255190e+407L, 6.23343982286571042809890547122705804e+413L, 1.86628588041890755929921756251934723e+420L, 7.06492694188791912037300528166794228e+426L, 3.39406886800977749230458579824930803e+433L, 2.07704891812976483907563047536681219e+440L, 1.62532865525590176989706193358042030e+447L, 1.63262112354994112352218911327913750e+454L, 2.11342684365334123128646755974119857e+461L, 3.53982137873383101244091847412793714e+468L, 7.70246700302666062188915359100825615e+475L, 2.18636422788338230254129077405708124e+483L, 8.12975261672049081897166938196495657e+490L, 3.97686557044826916151646962242652853e+498L, 2.57033035969007091507617008526033295e+506L, 2.20458407348036235529376715504150602e+514L, 2.52051509380683369529400145083533353e+522L, 3.85871376898138292734730034828559871e+530L, 7.94663225793828689108907007781152553e+538L, 2.21176541223395827472447113026924253e+547L, 8.35931033048630497134082029598865726e+555L, 4.31091797212556485985662056018893390e+564L, 3.04833317305882254988404372326531988e+573L, 2.97034828681146526635277450855709161e+582L, 4.00864404566992526097179834506253327e+591L, 7.53113144131492631353410204171028663e+600L, 1.97996763586022811207860344830247407e+610L, 7.32300332662100885299893727481183608e+619L, 3.83078680906847773947984890776183687e+629L, 2.84987258373806149506606754536239806e+639L, 3.03186631046306534459943952897407369e+649L, 4.63861318260680959360747724936035922e+659L, 1.02646622253495677529633262335412306e+670L, 3.30448344760519942319105428211388701e+680L, 1.55678514244926540491694986676104766e+691L, 1.07975219247204914347510266773073325e+702L, 1.10926415409608640204268413223928121e+713L, 1.69843188882084389205231670587156933e+724L, 3.90025209215096037836224226547246383e+735L, 1.35188796159061122898267917047667153e+747L, 7.11881895741722013661309086794573765e+758L, 5.73263787962641176699015570741387791e+770L, 7.10698682909851371094390920546530663e+782L, 1.36568905751347705631533710470350932e+795L, 4.09591384091714486453161283605440034e+807L, 1.93075428208975454032168180693618424e+820L, 1.44069783794868490577087909226154603e+833L, 1.71407451380697883211569548277738601e+846L, 3.27557874564463748685767424892341420e+859L, 1.01295195987435253561137255728975319e+873L, 5.10768437019276174029340754351596177e+886L, 4.23191986113702770379280941046346950e+900L, 5.80664714178397794019307157189161329e+914L, 1.32995815980583547946711112525038194e+929L, 5.12600842672542100652183507817331030e+943L, 3.35203762278831767267193293263751763e+958L, 3.75009417204153826893896307870937057e+973L, 7.23855050824188975713471018223024339e+988L, 2.43146178229439003194650931378387467e+1004L, 1.43376736234835679429446577737976919e+1020L, 1.49738681485939897351147361037410278e+1036L, 2.79474808763788045317059787958854766e+1052L, 9.40752795141195895210630116566470676e+1068L, 5.76455681194134988563523968421696548e+1085L, 6.49098750070655215612470119412325218e+1102L, 1.35603677524062211064037225514112165e+1120L, 5.30731596106421482379267500594247426e+1137L, 3.93020043869734370491941322540535807e+1155L, 5.56226722613029149136813618379760709e+1173L, 1.51990408820680241841102181882025951e+1192L, 8.10228003417607034858018290055212984e+1210L, 8.51521180721994744419289716417963237e+1229L, 1.78329495296502824223674285976432097e+1249L, 7.52325725334531880022021234450122858e+1268L, 6.46447702663797449769360764507187142e+1288L, 1.14411796435953528891736478925455547e+1309L, 4.21851818337788742448241659152628519e+1329L, 3.27808619028067308419286053048979085e+1350L, 5.43188779501763188996015031600338462e+1371L, 1.94236185576822902995555282219996135e+1393L, 1.51711647857248503907031482339088565e+1415L, 2.62035716514505778741231466041668281e+1437L, 1.01340333806343444348385264050569250e+1460L, 8.88786410219005270769408353397020687e+1482L, 1.79062851327433476234422894649930707e+1506L, 8.39642792144232596950658702528918677e+1529L, 9.28628794761707451127390451820966789e+1553L, 2.45536895088636462839367313490581387e+1578L, 1.57354562229875356978426356241845302e+1603L, 2.47847583619098850454983740131691503e+1628L, 9.73157119375940175602769413110414643e+1653L, 9.66320447484532719750186034583884499e+1679L, 2.46232109538721189753853963925622165e+1706L, 1.63417596934387293040006746046570718e+1733L, 2.86767794799456586471233013913198039e+1760L, 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442    };
443 #ifndef BOOST_MATH_NO_ATOMIC_INT
444    m_committed_refinements = static_cast<boost::math::detail::atomic_unsigned_integer_type>(m_weights.size() - 1);
445 #else
446    m_committed_refinements = m_weights.size() - 1;
447 #endif
448    m_t_min = -8.8984375000000L;
449    if (m_max_refinements >= m_abscissas.size())
450    {
451       m_abscissas.resize(m_max_refinements + 1);
452       m_weights.resize(m_max_refinements + 1);
453    }
454    else
455    {
456       m_max_refinements = m_abscissas.size() - 1;
457    }
458 }
459 #endif
460 #ifdef BOOST_HAS_FLOAT128
461 template<class Real, class Policy>
init(const mpl::int_<4> &)462 void exp_sinh_detail<Real, Policy>::init(const mpl::int_<4>&)
463 {
464    m_abscissas = {
465       { 2.239451308457907276646263599248028318747e-2543Q, 4.087883914826209167187520163938786544603e-936Q, 7.764136408896555253208502557716060646316e-345Q, 2.569416154701911093162209102345213640613e-127Q, 2.705458070464053854934121429341356913371e-47Q, 7.491188348021113917760090371440516887521e-18Q, 5.198294603582515693057809058359470253018e-07Q, 0.005389922804577577496651910020276229582764Q, 0.1920600417448513371971708155403009636026Q, 1.140219687292143805081229623729334820659Q, 7.806184141505854070922571674663437423603Q, 497.9910059199034049204308876883447088185Q, 27016042.73379639480428530637021605662451Q, 172966369043668599418.5877957471751383371Q, 1.061675373362961296862509492541522509127e+55Q, 3.811736521949348274993846910907815663725e+149Q, 4.031589783270233530756613072386084762687e+406Q, 1.857591496578858801010210685679553673527e+1105Q, },
466       { 6.38192460297577997296130116084380488004e-1543Q, 4.553284218142424152191512347101108073691e-568Q, 1.937062162895195937060002998269756423851e-209Q, 1.660126625033739077374114876720390220712e-77Q, 5.725718222547734673080418904622339594753e-29Q, 4.168381624810496871907721134250128161942e-11Q, 0.0001613301975005046953323705477328478299103Q, 0.0474713399587676291203429066086137662056Q, 0.5099627601758401314316521881645115690603Q, 2.636240582466121690921186199130019570689Q, 39.05613529229837860979125052359555007623Q, 30990.22477506600812220045610450185310364Q, 1857609984963.014390268032888333743476748Q, 2359106700485891760372588191034580.237445Q, 5.305502438164240038024865289303441329929e+90Q, 4.153264547632969989660655052675878016131e+246Q, 2.39549808558050342461418974153843135261e+670Q, 1.907821628968714220362207148967088886146e+1822Q, },
467       { 6.057903324174675880054786918700573277193e-1981Q, 8.656190904067090962653034260124195755274e-1202Q, 3.301911576596318022491539142850442018161e-729Q, 1.425485029898429297758878823810205941516e-442Q, 1.016496544573331920304016689793414356743e-268Q, 2.848036810989534605128535426330975462895e-163Q, 2.581928872313165828368701686010678577144e-99Q, 1.601590227152633400640250804848713890905e-60Q, 5.423190544363659530944338243992687682219e-37Q, 1.016381761828840448285257216929561921503e-22Q, 4.635725075794601084424604353869125707077e-14Q, 8.3498615886950739967156481568160331201e-09Q, 1.303868885475613415062833232828648525669e-05Q, 0.001153300807253218344728159062725073079949Q, 0.01814288911244882236930497812936819917973Q, 0.1025656071886267491128524112054469619388Q, 0.3242301173345578897587341005053281543043Q, 0.7688636442387784234265303257286061242944Q, 1.704936145319479582718350104944998619577Q, 4.332223509891009397137256165478273534279Q, 16.00424777396788542203662195209964219854Q, 119.9894477197320344196270723637925628186Q, 3053.206094606356294417950881488718170062Q, 602365.2553559583292243897621777047334194Q, 3550455773.201059364690484967711333425091Q, 5733723619916794.008354021149856937812556Q, 97490164875869638451560588.97182161070984Q, 7.132097466952214251618865223622602893458e+42Q, 4.527309308592487932893086561010303870042e+70Q, 3.115319987396348432317683626917454615693e+116Q, 1.165082263946878699920850154957972424971e+192Q, 4.61868993445541953416660351754288757642e+316Q, 1.235693446874006572643670815583618997533e+522Q, 6.085142451732094001360716852852249745666e+860Q, 1.561268268167538223129534325473369675815e+1419Q, 7.15416720524977809484490807341332912337e+2339Q, },
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483    };
484 #ifndef BOOST_MATH_NO_ATOMIC_INT
485    m_committed_refinements = static_cast<boost::math::detail::atomic_unsigned_integer_type>(m_weights.size() - 1);
486 #else
487    m_committed_refinements = m_weights.size() - 1;
488 #endif
489    m_t_min = -8.916559006047578828258918121202852111589Q;
490    if (m_max_refinements >= m_abscissas.size())
491    {
492       m_abscissas.resize(m_max_refinements + 1);
493       m_weights.resize(m_max_refinements + 1);
494    }
495    else
496    {
497       m_max_refinements = m_abscissas.size() - 1;
498    }
499    /*
500    std::cout << std::setprecision(35) << m_t_min << std::endl;
501    for (unsigned i = 0; i < m_abscissas[0].size(); ++i)
502       std::cout << m_abscissas[0][i] << ", ";
503    std::cout << std::endl;
504    for (unsigned i = 0; i < m_abscissas[0].size(); ++i)
505       std::cout << m_weights[0][i] << ", ";
506    std::cout << std::endl;
507    */
508 }
509 #endif
510 
511 }
512 }
513 }
514 }
515 #endif
516