math/quadrature/gauss_kronrod.hpp

0001 //  Copyright John Maddock 2017.
0002 //  Copyright Nick Thompson 2017.
0003 //  Use, modification and distribution are subject to the
0004 //  Boost Software License, Version 1.0. (See accompanying file
0005 //  LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
0006
0007 #ifndef BOOST_MATH_QUADRATURE_GAUSS_KRONROD_HPP
0008 #define BOOST_MATH_QUADRATURE_GAUSS_KRONROD_HPP
0009
0010 #ifdef _MSC_VER
0011 #pragma once
0012 #pragma warning(push)
0013 #pragma warning(disable: 4127)
0014 #endif
0015
0016 #include <array>
0017 #include <vector>
0018 #include <algorithm>
0019 #include <boost/math/special_functions/legendre.hpp>
0020 #include <boost/math/special_functions/legendre_stieltjes.hpp>
0021 #include <boost/math/quadrature/gauss.hpp>
0022
0023 namespace boost { namespace math{ namespace quadrature{ namespace detail{
0024
0025 #ifndef BOOST_MATH_GAUSS_NO_COMPUTE_ON_DEMAND
0026
0027 template <class Real, unsigned N, unsigned tag>
0028 class gauss_kronrod_detail
0029 {
0030    static legendre_stieltjes<Real> const& get_legendre_stieltjes()
0031    {
0032       static const legendre_stieltjes<Real> data((N - 1) / 2 + 1);
0033       return data;
0034    }
0035    static std::vector<Real> calculate_abscissa()
0036    {
0037       static std::vector<Real> result = boost::math::legendre_p_zeros<Real>((N - 1) / 2);
0038       const legendre_stieltjes<Real> E = get_legendre_stieltjes();
0039       std::vector<Real> ls_zeros = E.zeros();
0040       result.insert(result.end(), ls_zeros.begin(), ls_zeros.end());
0041       std::sort(result.begin(), result.end());
0042       return result;
0043    }
0044    static std::vector<Real> calculate_weights()
0045    {
0046       std::vector<Real> result(abscissa().size(), 0);
0047       unsigned gauss_order = (N - 1) / 2;
0048       unsigned gauss_start = gauss_order & 1 ? 0 : 1;
0049       const legendre_stieltjes<Real>& E = get_legendre_stieltjes();
0050
0051       for (unsigned i = gauss_start; i < abscissa().size(); i += 2)
0052       {
0053          Real x = abscissa()[i];
0054          Real p = boost::math::legendre_p_prime(gauss_order, x);
0055          Real gauss_weight = 2 / ((1 - x * x) * p * p);
0056          result[i] = gauss_weight + static_cast<Real>(2) / (static_cast<Real>(gauss_order + 1) * legendre_p_prime(gauss_order, x) * E(x));
0057       }
0058       for (unsigned i = gauss_start ? 0 : 1; i < abscissa().size(); i += 2)
0059       {
0060          Real x = abscissa()[i];
0061          result[i] = static_cast<Real>(2) / (static_cast<Real>(gauss_order + 1) * legendre_p(gauss_order, x) * E.prime(x));
0062       }
0063       return result;
0064    }
0065 public:
0066    static const std::vector<Real>& abscissa()
0067    {
0068       static std::vector<Real> data = calculate_abscissa();
0069       return data;
0070    }
0071    static const std::vector<Real>& weights()
0072    {
0073       static std::vector<Real> data = calculate_weights();
0074       return data;
0075    }
0076 };
0077
0078 #else
0079
0080 template <class Real, unsigned N, unsigned tag>
0081 class gauss_kronrod_detail;
0082
0083 #endif
0084
0085 template <class T>
0086 class gauss_kronrod_detail<T, 15, 0>
0087 {
0088 public:
0089    static std::array<T, 8> const & abscissa()
0090    {
0091       static constexpr std::array<T, 8> data = {
0092          0.000000000e+00f,
0093          2.077849550e-01f,
0094          4.058451514e-01f,
0095          5.860872355e-01f,
0096          7.415311856e-01f,
0097          8.648644234e-01f,
0098          9.491079123e-01f,
0099          9.914553711e-01f,
0100       };
0101       return data;
0102    }
0103    static std::array<T, 8> const & weights()
0104    {
0105       static constexpr std::array<T, 8> data = {
0106          2.094821411e-01f,
0107          2.044329401e-01f,
0108          1.903505781e-01f,
0109          1.690047266e-01f,
0110          1.406532597e-01f,
0111          1.047900103e-01f,
0112          6.309209263e-02f,
0113          2.293532201e-02f,
0114       };
0115       return data;
0116    }
0117 };
0118
0119 template <class T>
0120 class gauss_kronrod_detail<T, 15, 1>
0121 {
0122 public:
0123    static std::array<T, 8> const & abscissa()
0124    {
0125       static constexpr std::array<T, 8> data = {
0126          0.00000000000000000e+00,
0127          2.07784955007898468e-01,
0128          4.05845151377397167e-01,
0129          5.86087235467691130e-01,
0130          7.41531185599394440e-01,
0131          8.64864423359769073e-01,
0132          9.49107912342758525e-01,
0133          9.91455371120812639e-01,
0134       };
0135       return data;
0136    }
0137    static std::array<T, 8> const & weights()
0138    {
0139       static constexpr std::array<T, 8> data = {
0140          2.09482141084727828e-01,
0141          2.04432940075298892e-01,
0142          1.90350578064785410e-01,
0143          1.69004726639267903e-01,
0144          1.40653259715525919e-01,
0145          1.04790010322250184e-01,
0146          6.30920926299785533e-02,
0147          2.29353220105292250e-02,
0148       };
0149       return data;
0150    }
0151 };
0152
0153 template <class T>
0154 class gauss_kronrod_detail<T, 15, 2>
0155 {
0156 public:
0157    static std::array<T, 8> const & abscissa()
0158    {
0159       static constexpr std::array<T, 8> data = {
0160          0.00000000000000000000000000000000000e+00L,
0161          2.07784955007898467600689403773244913e-01L,
0162          4.05845151377397166906606412076961463e-01L,
0163          5.86087235467691130294144838258729598e-01L,
0164          7.41531185599394439863864773280788407e-01L,
0165          8.64864423359769072789712788640926201e-01L,
0166          9.49107912342758524526189684047851262e-01L,
0167          9.91455371120812639206854697526328517e-01L,
0168       };
0169       return data;
0170    }
0171    static std::array<T, 8> const & weights()
0172    {
0173       static constexpr std::array<T, 8> data = {
0174          2.09482141084727828012999174891714264e-01L,
0175          2.04432940075298892414161999234649085e-01L,
0176          1.90350578064785409913256402421013683e-01L,
0177          1.69004726639267902826583426598550284e-01L,
0178          1.40653259715525918745189590510237920e-01L,
0179          1.04790010322250183839876322541518017e-01L,
0180          6.30920926299785532907006631892042867e-02L,
0181          2.29353220105292249637320080589695920e-02L,
0182       };
0183       return data;
0184    }
0185 };
0186
0187 #ifdef BOOST_HAS_FLOAT128
0188 template <class T>
0189 class gauss_kronrod_detail<T, 15, 3>
0190 {
0191 public:
0192    static std::array<T, 8> const & abscissa()
0193    {
0194       static const std::array<T, 8> data = {
0195          0.00000000000000000000000000000000000e+00Q,
0196          2.07784955007898467600689403773244913e-01Q,
0197          4.05845151377397166906606412076961463e-01Q,
0198          5.86087235467691130294144838258729598e-01Q,
0199          7.41531185599394439863864773280788407e-01Q,
0200          8.64864423359769072789712788640926201e-01Q,
0201          9.49107912342758524526189684047851262e-01Q,
0202          9.91455371120812639206854697526328517e-01Q,
0203       };
0204       return data;
0205    }
0206    static std::array<T, 8> const & weights()
0207    {
0208       static const std::array<T, 8> data = {
0209          2.09482141084727828012999174891714264e-01Q,
0210          2.04432940075298892414161999234649085e-01Q,
0211          1.90350578064785409913256402421013683e-01Q,
0212          1.69004726639267902826583426598550284e-01Q,
0213          1.40653259715525918745189590510237920e-01Q,
0214          1.04790010322250183839876322541518017e-01Q,
0215          6.30920926299785532907006631892042867e-02Q,
0216          2.29353220105292249637320080589695920e-02Q,
0217       };
0218       return data;
0219    }
0220 };
0221 #endif
0222
0223 template <class T>
0224 class gauss_kronrod_detail<T, 15, 4>
0225 {
0226 public:
0227    static  std::array<T, 8> const & abscissa()
0228    {
0229       static  std::array<T, 8> data = {
0230          BOOST_MATH_HUGE_CONSTANT(T, 0, 0.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+00),
0231          BOOST_MATH_HUGE_CONSTANT(T, 0, 2.0778495500789846760068940377324491347978440714517064971384573461986693844943520226910343227183698530560857645062738e-01),
0232          BOOST_MATH_HUGE_CONSTANT(T, 0, 4.0584515137739716690660641207696146334738201409937012638704325179466381322612565532831268972774658776528675866604802e-01),
0233          BOOST_MATH_HUGE_CONSTANT(T, 0, 5.8608723546769113029414483825872959843678075060436095130499289319880373607444407464511674498935942098956811555121368e-01),
0234          BOOST_MATH_HUGE_CONSTANT(T, 0, 7.4153118559939443986386477328078840707414764714139026011995535196742987467218051379282683236686324705969251809311201e-01),
0235          BOOST_MATH_HUGE_CONSTANT(T, 0, 8.6486442335976907278971278864092620121097230707408814860145771276706770813259572103585847859604590541475281326027862e-01),
0236          BOOST_MATH_HUGE_CONSTANT(T, 0, 9.4910791234275852452618968404785126240077093767061778354876910391306333035484014080573077002792572414430073966699522e-01),
0237          BOOST_MATH_HUGE_CONSTANT(T, 0, 9.9145537112081263920685469752632851664204433837033470129108741357244173934653407235924503509626841760744349505339308e-01),
0238       };
0239       return data;
0240    }
0241    static  std::array<T, 8> const & weights()
0242    {
0243       static  std::array<T, 8> data = {
0244          BOOST_MATH_HUGE_CONSTANT(T, 0, 2.0948214108472782801299917489171426369776208022370431671299800656137515132325648616816908211675949102392971459688215e-01),
0245          BOOST_MATH_HUGE_CONSTANT(T, 0, 2.0443294007529889241416199923464908471651760418071835742447095312045467698546598879348374292009347554167803659293064e-01),
0246          BOOST_MATH_HUGE_CONSTANT(T, 0, 1.9035057806478540991325640242101368282607807545535835588544088036744058072410212679605964605106377593834568683551139e-01),
0247          BOOST_MATH_HUGE_CONSTANT(T, 0, 1.6900472663926790282658342659855028410624490030294424149734006755695680921619029112936702403855359908156070095656537e-01),
0248          BOOST_MATH_HUGE_CONSTANT(T, 0, 1.4065325971552591874518959051023792039988975724799857556174546893312708093090950408097379122415555910759700350860143e-01),
0249          BOOST_MATH_HUGE_CONSTANT(T, 0, 1.0479001032225018383987632254151801744375665421383061189339065133963746321576289524167571627509311333949422518201492e-01),
0250          BOOST_MATH_HUGE_CONSTANT(T, 0, 6.3092092629978553290700663189204286665071157211550707113605545146983997477964874928199170264504441995865872491871943e-02),
0251          BOOST_MATH_HUGE_CONSTANT(T, 0, 2.2935322010529224963732008058969591993560811275746992267507430254711815787976075946156368168156289483493617134063245e-02),
0252       };
0253       return data;
0254    }
0255 };
0256
0257 template <class T>
0258 class gauss_kronrod_detail<T, 21, 0>
0259 {
0260 public:
0261    static std::array<T, 11> const & abscissa()
0262    {
0263       static constexpr std::array<T, 11> data = {
0264          0.000000000e+00f,
0265          1.488743390e-01f,
0266          2.943928627e-01f,
0267          4.333953941e-01f,
0268          5.627571347e-01f,
0269          6.794095683e-01f,
0270          7.808177266e-01f,
0271          8.650633667e-01f,
0272          9.301574914e-01f,
0273          9.739065285e-01f,
0274          9.956571630e-01f,
0275       };
0276       return data;
0277    }
0278    static std::array<T, 11> const & weights()
0279    {
0280       static constexpr std::array<T, 11> data = {
0281          1.494455540e-01f,
0282          1.477391049e-01f,
0283          1.427759386e-01f,
0284          1.347092173e-01f,
0285          1.234919763e-01f,
0286          1.093871588e-01f,
0287          9.312545458e-02f,
0288          7.503967481e-02f,
0289          5.475589657e-02f,
0290          3.255816231e-02f,
0291          1.169463887e-02f,
0292       };
0293       return data;
0294    }
0295 };
0296
0297 template <class T>
0298 class gauss_kronrod_detail<T, 21, 1>
0299 {
0300 public:
0301    static std::array<T, 11> const & abscissa()
0302    {
0303       static constexpr std::array<T, 11> data = {
0304          0.00000000000000000e+00,
0305          1.48874338981631211e-01,
0306          2.94392862701460198e-01,
0307          4.33395394129247191e-01,
0308          5.62757134668604683e-01,
0309          6.79409568299024406e-01,
0310          7.80817726586416897e-01,
0311          8.65063366688984511e-01,
0312          9.30157491355708226e-01,
0313          9.73906528517171720e-01,
0314          9.95657163025808081e-01,
0315       };
0316       return data;
0317    }
0318    static std::array<T, 11> const & weights()
0319    {
0320       static constexpr std::array<T, 11> data = {
0321          1.49445554002916906e-01,
0322          1.47739104901338491e-01,
0323          1.42775938577060081e-01,
0324          1.34709217311473326e-01,
0325          1.23491976262065851e-01,
0326          1.09387158802297642e-01,
0327          9.31254545836976055e-02,
0328          7.50396748109199528e-02,
0329          5.47558965743519960e-02,
0330          3.25581623079647275e-02,
0331          1.16946388673718743e-02,
0332       };
0333       return data;
0334    }
0335 };
0336
0337 template <class T>
0338 class gauss_kronrod_detail<T, 21, 2>
0339 {
0340 public:
0341    static std::array<T, 11> const & abscissa()
0342    {
0343       static constexpr std::array<T, 11> data = {
0344          0.00000000000000000000000000000000000e+00L,
0345          1.48874338981631210884826001129719985e-01L,
0346          2.94392862701460198131126603103865566e-01L,
0347          4.33395394129247190799265943165784162e-01L,
0348          5.62757134668604683339000099272694141e-01L,
0349          6.79409568299024406234327365114873576e-01L,
0350          7.80817726586416897063717578345042377e-01L,
0351          8.65063366688984510732096688423493049e-01L,
0352          9.30157491355708226001207180059508346e-01L,
0353          9.73906528517171720077964012084452053e-01L,
0354          9.95657163025808080735527280689002848e-01L,
0355       };
0356       return data;
0357    }
0358    static std::array<T, 11> const & weights()
0359    {
0360       static constexpr std::array<T, 11> data = {
0361          1.49445554002916905664936468389821204e-01L,
0362          1.47739104901338491374841515972068046e-01L,
0363          1.42775938577060080797094273138717061e-01L,
0364          1.34709217311473325928054001771706833e-01L,
0365          1.23491976262065851077958109831074160e-01L,
0366          1.09387158802297641899210590325804960e-01L,
0367          9.31254545836976055350654650833663444e-02L,
0368          7.50396748109199527670431409161900094e-02L,
0369          5.47558965743519960313813002445801764e-02L,
0370          3.25581623079647274788189724593897606e-02L,
0371          1.16946388673718742780643960621920484e-02L,
0372       };
0373       return data;
0374    }
0375 };
0376
0377 #ifdef BOOST_HAS_FLOAT128
0378 template <class T>
0379 class gauss_kronrod_detail<T, 21, 3>
0380 {
0381 public:
0382    static std::array<T, 11> const & abscissa()
0383    {
0384       static const std::array<T, 11> data = {
0385          0.00000000000000000000000000000000000e+00Q,
0386          1.48874338981631210884826001129719985e-01Q,
0387          2.94392862701460198131126603103865566e-01Q,
0388          4.33395394129247190799265943165784162e-01Q,
0389          5.62757134668604683339000099272694141e-01Q,
0390          6.79409568299024406234327365114873576e-01Q,
0391          7.80817726586416897063717578345042377e-01Q,
0392          8.65063366688984510732096688423493049e-01Q,
0393          9.30157491355708226001207180059508346e-01Q,
0394          9.73906528517171720077964012084452053e-01Q,
0395          9.95657163025808080735527280689002848e-01Q,
0396       };
0397       return data;
0398    }
0399    static std::array<T, 11> const & weights()
0400    {
0401       static const std::array<T, 11> data = {
0402          1.49445554002916905664936468389821204e-01Q,
0403          1.47739104901338491374841515972068046e-01Q,
0404          1.42775938577060080797094273138717061e-01Q,
0405          1.34709217311473325928054001771706833e-01Q,
0406          1.23491976262065851077958109831074160e-01Q,
0407          1.09387158802297641899210590325804960e-01Q,
0408          9.31254545836976055350654650833663444e-02Q,
0409          7.50396748109199527670431409161900094e-02Q,
0410          5.47558965743519960313813002445801764e-02Q,
0411          3.25581623079647274788189724593897606e-02Q,
0412          1.16946388673718742780643960621920484e-02Q,
0413       };
0414       return data;
0415    }
0416 };
0417 #endif
0418
0419 template <class T>
0420 class gauss_kronrod_detail<T, 21, 4>
0421 {
0422 public:
0423    static  std::array<T, 11> const & abscissa()
0424    {
0425       static  std::array<T, 11> data = {
0426          BOOST_MATH_HUGE_CONSTANT(T, 0, 0.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+00),
0427          BOOST_MATH_HUGE_CONSTANT(T, 0, 1.4887433898163121088482600112971998461756485942069169570798925351590361735566852137117762979946369123003116080525534e-01),
0428          BOOST_MATH_HUGE_CONSTANT(T, 0, 2.9439286270146019813112660310386556616268662515695791864888229172724611166332737888445523178268237359119185139299872e-01),
0429          BOOST_MATH_HUGE_CONSTANT(T, 0, 4.3339539412924719079926594316578416220007183765624649650270151314376698907770350122510275795011772122368293504099894e-01),
0430          BOOST_MATH_HUGE_CONSTANT(T, 0, 5.6275713466860468333900009927269414084301388194196695886034621458779266353216327549712087854169992422106448211158815e-01),
0431          BOOST_MATH_HUGE_CONSTANT(T, 0, 6.7940956829902440623432736511487357576929471183480946766481718895255857539507492461507857357048037949983390204739932e-01),
0432          BOOST_MATH_HUGE_CONSTANT(T, 0, 7.8081772658641689706371757834504237716340752029815717974694859999505607982761420654526977234238996241110129779403362e-01),
0433          BOOST_MATH_HUGE_CONSTANT(T, 0, 8.6506336668898451073209668842349304852754301496533045252195973184537475513805556135679072894604577069440463108641177e-01),
0434          BOOST_MATH_HUGE_CONSTANT(T, 0, 9.3015749135570822600120718005950834622516790998193924230349406866828415983091673055011194572851007884702013619684320e-01),
0435          BOOST_MATH_HUGE_CONSTANT(T, 0, 9.7390652851717172007796401208445205342826994669238211923121206669659520323463615962572356495626855625823304251877421e-01),
0436          BOOST_MATH_HUGE_CONSTANT(T, 0, 9.9565716302580808073552728068900284792126058721947892436337916111757023046774867357152325996912076724298149077812671e-01),
0437       };
0438       return data;
0439    }
0440    static  std::array<T, 11> const & weights()
0441    {
0442       static  std::array<T, 11> data = {
0443          BOOST_MATH_HUGE_CONSTANT(T, 0, 1.4944555400291690566493646838982120374523631668747280383560851873698964478511841925721030705689540264726493367634340e-01),
0444          BOOST_MATH_HUGE_CONSTANT(T, 0, 1.4773910490133849137484151597206804552373162548520660451819195439885993016735696405732703959182882254268727823258502e-01),
0445          BOOST_MATH_HUGE_CONSTANT(T, 0, 1.4277593857706008079709427313871706088597905653190555560741004743970770449909340027811131706283756428281146832304737e-01),
0446          BOOST_MATH_HUGE_CONSTANT(T, 0, 1.3470921731147332592805400177170683276099191300855971406636668491320291400121282036676953159488271772384389604997640e-01),
0447          BOOST_MATH_HUGE_CONSTANT(T, 0, 1.2349197626206585107795810983107415951230034952864832764467994120974054238975454689681538622363738230836484113389878e-01),
0448          BOOST_MATH_HUGE_CONSTANT(T, 0, 1.0938715880229764189921059032580496027181329983434522007819675829826550372891432168683899432674553842507906611591517e-01),
0449          BOOST_MATH_HUGE_CONSTANT(T, 0, 9.3125454583697605535065465083366344390018828880760031970085038760177735672200775237414123061615827474831165614953012e-02),
0450          BOOST_MATH_HUGE_CONSTANT(T, 0, 7.5039674810919952767043140916190009395219382000910088173697048048430404342858495178813808730646554086856929327903059e-02),
0451          BOOST_MATH_HUGE_CONSTANT(T, 0, 5.4755896574351996031381300244580176373721114058333557524432615804784098927818975325116301569003298086458722055550981e-02),
0452          BOOST_MATH_HUGE_CONSTANT(T, 0, 3.2558162307964727478818972459389760617388939845662609571537504232714121820165498692381607605384626494546068817765276e-02),
0453          BOOST_MATH_HUGE_CONSTANT(T, 0, 1.1694638867371874278064396062192048396217332481931888927598147525622222058064992651806736704969967250888097490233242e-02),
0454       };
0455       return data;
0456    }
0457 };
0458
0459 template <class T>
0460 class gauss_kronrod_detail<T, 31, 0>
0461 {
0462 public:
0463    static std::array<T, 16> const & abscissa()
0464    {
0465       static constexpr std::array<T, 16> data = {
0466          0.000000000e+00f,
0467          1.011420669e-01f,
0468          2.011940940e-01f,
0469          2.991800072e-01f,
0470          3.941513471e-01f,
0471          4.850818636e-01f,
0472          5.709721726e-01f,
0473          6.509967413e-01f,
0474          7.244177314e-01f,
0475          7.904185014e-01f,
0476          8.482065834e-01f,
0477          8.972645323e-01f,
0478          9.372733924e-01f,
0479          9.677390757e-01f,
0480          9.879925180e-01f,
0481          9.980022987e-01f,
0482       };
0483       return data;
0484    }
0485    static std::array<T, 16> const & weights()
0486    {
0487       static constexpr std::array<T, 16> data = {
0488          1.013300070e-01f,
0489          1.007698455e-01f,
0490          9.917359872e-02f,
0491          9.664272698e-02f,
0492          9.312659817e-02f,
0493          8.856444306e-02f,
0494          8.308050282e-02f,
0495          7.684968076e-02f,
0496          6.985412132e-02f,
0497          6.200956780e-02f,
0498          5.348152469e-02f,
0499          4.458975132e-02f,
0500          3.534636079e-02f,
0501          2.546084733e-02f,
0502          1.500794733e-02f,
0503          5.377479873e-03f,
0504       };
0505       return data;
0506    }
0507 };
0508
0509 template <class T>
0510 class gauss_kronrod_detail<T, 31, 1>
0511 {
0512 public:
0513    static std::array<T, 16> const & abscissa()
0514    {
0515       static constexpr std::array<T, 16> data = {
0516          0.00000000000000000e+00,
0517          1.01142066918717499e-01,
0518          2.01194093997434522e-01,
0519          2.99180007153168812e-01,
0520          3.94151347077563370e-01,
0521          4.85081863640239681e-01,
0522          5.70972172608538848e-01,
0523          6.50996741297416971e-01,
0524          7.24417731360170047e-01,
0525          7.90418501442465933e-01,
0526          8.48206583410427216e-01,
0527          8.97264532344081901e-01,
0528          9.37273392400705904e-01,
0529          9.67739075679139134e-01,
0530          9.87992518020485428e-01,
0531          9.98002298693397060e-01,
0532       };
0533       return data;
0534    }
0535    static std::array<T, 16> const & weights()
0536    {
0537       static constexpr std::array<T, 16> data = {
0538          1.01330007014791549e-01,
0539          1.00769845523875595e-01,
0540          9.91735987217919593e-02,
0541          9.66427269836236785e-02,
0542          9.31265981708253212e-02,
0543          8.85644430562117706e-02,
0544          8.30805028231330210e-02,
0545          7.68496807577203789e-02,
0546          6.98541213187282587e-02,
0547          6.20095678006706403e-02,
0548          5.34815246909280873e-02,
0549          4.45897513247648766e-02,
0550          3.53463607913758462e-02,
0551          2.54608473267153202e-02,
0552          1.50079473293161225e-02,
0553          5.37747987292334899e-03,
0554       };
0555       return data;
0556    }
0557 };
0558
0559 template <class T>
0560 class gauss_kronrod_detail<T, 31, 2>
0561 {
0562 public:
0563    static std::array<T, 16> const & abscissa()
0564    {
0565       static constexpr std::array<T, 16> data = {
0566          0.00000000000000000000000000000000000e+00L,
0567          1.01142066918717499027074231447392339e-01L,
0568          2.01194093997434522300628303394596208e-01L,
0569          2.99180007153168812166780024266388963e-01L,
0570          3.94151347077563369897207370981045468e-01L,
0571          4.85081863640239680693655740232350613e-01L,
0572          5.70972172608538847537226737253910641e-01L,
0573          6.50996741297416970533735895313274693e-01L,
0574          7.24417731360170047416186054613938010e-01L,
0575          7.90418501442465932967649294817947347e-01L,
0576          8.48206583410427216200648320774216851e-01L,
0577          8.97264532344081900882509656454495883e-01L,
0578          9.37273392400705904307758947710209471e-01L,
0579          9.67739075679139134257347978784337225e-01L,
0580          9.87992518020485428489565718586612581e-01L,
0581          9.98002298693397060285172840152271209e-01L,
0582       };
0583       return data;
0584    }
0585    static std::array<T, 16> const & weights()
0586    {
0587       static constexpr std::array<T, 16> data = {
0588          1.01330007014791549017374792767492547e-01L,
0589          1.00769845523875595044946662617569722e-01L,
0590          9.91735987217919593323931734846031311e-02L,
0591          9.66427269836236785051799076275893351e-02L,
0592          9.31265981708253212254868727473457186e-02L,
0593          8.85644430562117706472754436937743032e-02L,
0594          8.30805028231330210382892472861037896e-02L,
0595          7.68496807577203788944327774826590067e-02L,
0596          6.98541213187282587095200770991474758e-02L,
0597          6.20095678006706402851392309608029322e-02L,
0598          5.34815246909280872653431472394302968e-02L,
0599          4.45897513247648766082272993732796902e-02L,
0600          3.53463607913758462220379484783600481e-02L,
0601          2.54608473267153201868740010196533594e-02L,
0602          1.50079473293161225383747630758072681e-02L,
0603          5.37747987292334898779205143012764982e-03L,
0604       };
0605       return data;
0606    }
0607 };
0608
0609 #ifdef BOOST_HAS_FLOAT128
0610 template <class T>
0611 class gauss_kronrod_detail<T, 31, 3>
0612 {
0613 public:
0614    static std::array<T, 16> const & abscissa()
0615    {
0616       static const std::array<T, 16> data = {
0617          0.00000000000000000000000000000000000e+00Q,
0618          1.01142066918717499027074231447392339e-01Q,
0619          2.01194093997434522300628303394596208e-01Q,
0620          2.99180007153168812166780024266388963e-01Q,
0621          3.94151347077563369897207370981045468e-01Q,
0622          4.85081863640239680693655740232350613e-01Q,
0623          5.70972172608538847537226737253910641e-01Q,
0624          6.50996741297416970533735895313274693e-01Q,
0625          7.24417731360170047416186054613938010e-01Q,
0626          7.90418501442465932967649294817947347e-01Q,
0627          8.48206583410427216200648320774216851e-01Q,
0628          8.97264532344081900882509656454495883e-01Q,
0629          9.37273392400705904307758947710209471e-01Q,
0630          9.67739075679139134257347978784337225e-01Q,
0631          9.87992518020485428489565718586612581e-01Q,
0632          9.98002298693397060285172840152271209e-01Q,
0633       };
0634       return data;
0635    }
0636    static std::array<T, 16> const & weights()
0637    {
0638       static const std::array<T, 16> data = {
0639          1.01330007014791549017374792767492547e-01Q,
0640          1.00769845523875595044946662617569722e-01Q,
0641          9.91735987217919593323931734846031311e-02Q,
0642          9.66427269836236785051799076275893351e-02Q,
0643          9.31265981708253212254868727473457186e-02Q,
0644          8.85644430562117706472754436937743032e-02Q,
0645          8.30805028231330210382892472861037896e-02Q,
0646          7.68496807577203788944327774826590067e-02Q,
0647          6.98541213187282587095200770991474758e-02Q,
0648          6.20095678006706402851392309608029322e-02Q,
0649          5.34815246909280872653431472394302968e-02Q,
0650          4.45897513247648766082272993732796902e-02Q,
0651          3.53463607913758462220379484783600481e-02Q,
0652          2.54608473267153201868740010196533594e-02Q,
0653          1.50079473293161225383747630758072681e-02Q,
0654          5.37747987292334898779205143012764982e-03Q,
0655       };
0656       return data;
0657    }
0658 };
0659 #endif
0660
0661 template <class T>
0662 class gauss_kronrod_detail<T, 31, 4>
0663 {
0664 public:
0665    static  std::array<T, 16> const & abscissa()
0666    {
0667       static  std::array<T, 16> data = {
0668          BOOST_MATH_HUGE_CONSTANT(T, 0, 0.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+00),
0669          BOOST_MATH_HUGE_CONSTANT(T, 0, 1.0114206691871749902707423144739233878745105740164180495800189504151097862454083050931321451540380998341273193681967e-01),
0670          BOOST_MATH_HUGE_CONSTANT(T, 0, 2.0119409399743452230062830339459620781283645446263767961594972460994823900302018760183625806752105908967902257386509e-01),
0671          BOOST_MATH_HUGE_CONSTANT(T, 0, 2.9918000715316881216678002426638896266160338274382080184125545738918081102513884467602322020157243563662094470221235e-01),
0672          BOOST_MATH_HUGE_CONSTANT(T, 0, 3.9415134707756336989720737098104546836275277615869825503116534395160895778696141797549711416165976202589352169635648e-01),
0673          BOOST_MATH_HUGE_CONSTANT(T, 0, 4.8508186364023968069365574023235061286633893089407312129367943604080239955167155974371848690848595275551258416303565e-01),
0674          BOOST_MATH_HUGE_CONSTANT(T, 0, 5.7097217260853884753722673725391064123838639628274960485326541705419537986975857948341462856982614477912646497026257e-01),
0675          BOOST_MATH_HUGE_CONSTANT(T, 0, 6.5099674129741697053373589531327469254694822609259966708966160576093305841043840794460394747228060367236079289132544e-01),
0676          BOOST_MATH_HUGE_CONSTANT(T, 0, 7.2441773136017004741618605461393800963089929458410256355142342070412378167792521899610109760313432626923598549381925e-01),
0677          BOOST_MATH_HUGE_CONSTANT(T, 0, 7.9041850144246593296764929481794734686214051995697617332365280643308302974631807059994738664225445530963711137343440e-01),
0678          BOOST_MATH_HUGE_CONSTANT(T, 0, 8.4820658341042721620064832077421685136625617473699263409572755876067507517414548519760771975082148085090373835713340e-01),
0679          BOOST_MATH_HUGE_CONSTANT(T, 0, 8.9726453234408190088250965645449588283177871149442786763972687601078537721473771221195399661919716123038835639691946e-01),
0680          BOOST_MATH_HUGE_CONSTANT(T, 0, 9.3727339240070590430775894771020947124399627351530445790136307635020297379704552795054758617426808659746824044603157e-01),
0681          BOOST_MATH_HUGE_CONSTANT(T, 0, 9.6773907567913913425734797878433722528335733730013163797468062226335804249452174804319385048203118506304424717089291e-01),
0682          BOOST_MATH_HUGE_CONSTANT(T, 0, 9.8799251802048542848956571858661258114697281712376148999999751558738843736901942471272205036831914497667516843990079e-01),
0683          BOOST_MATH_HUGE_CONSTANT(T, 0, 9.9800229869339706028517284015227120907340644231555723034839427970683348682837134566648979907760125278631896777136104e-01),
0684       };
0685       return data;
0686    }
0687    static  std::array<T, 16> const & weights()
0688    {
0689       static  std::array<T, 16> data = {
0690          BOOST_MATH_HUGE_CONSTANT(T, 0, 1.0133000701479154901737479276749254677092627259659629246734858372174107615774696665932418050683956749891773195816338e-01),
0691          BOOST_MATH_HUGE_CONSTANT(T, 0, 1.0076984552387559504494666261756972191634838013536373069278929029488122760822761077475060185965408326901925180106227e-01),
0692          BOOST_MATH_HUGE_CONSTANT(T, 0, 9.9173598721791959332393173484603131059567260816713281734860095693651563064308745717056680128223790739026832596087552e-02),
0693          BOOST_MATH_HUGE_CONSTANT(T, 0, 9.6642726983623678505179907627589335136656568630495198973407668882934392359962841826511402504664592185391687490319950e-02),
0694          BOOST_MATH_HUGE_CONSTANT(T, 0, 9.3126598170825321225486872747345718561927881321317330560285879189052002874531855060114908990458716740695847509343865e-02),
0695          BOOST_MATH_HUGE_CONSTANT(T, 0, 8.8564443056211770647275443693774303212266732690655967817996052574877144544749814260718837576325109922207832119243346e-02),
0696          BOOST_MATH_HUGE_CONSTANT(T, 0, 8.3080502823133021038289247286103789601554188253368717607281604875233630643885056057630789228337088859687986285569521e-02),
0697          BOOST_MATH_HUGE_CONSTANT(T, 0, 7.6849680757720378894432777482659006722109101167947000584089097112470821092034084418224731527690291913686588446455555e-02),
0698          BOOST_MATH_HUGE_CONSTANT(T, 0, 6.9854121318728258709520077099147475786045435140671549698798093177992675624987998849748628778570667518643649536771245e-02),
0699          BOOST_MATH_HUGE_CONSTANT(T, 0, 6.2009567800670640285139230960802932190400004210329723569147829395618376206272317333030584268303808639229575334680414e-02),
0700          BOOST_MATH_HUGE_CONSTANT(T, 0, 5.3481524690928087265343147239430296771554760947116739813222888752727413616259625439714812475198987513183153639571249e-02),
0701          BOOST_MATH_HUGE_CONSTANT(T, 0, 4.4589751324764876608227299373279690223256649667921096570980823211805450700059906366455036418897149593261561551176267e-02),
0702          BOOST_MATH_HUGE_CONSTANT(T, 0, 3.5346360791375846222037948478360048122630678992420820868148023340902501837247680978434662724296810081131106317333086e-02),
0703          BOOST_MATH_HUGE_CONSTANT(T, 0, 2.5460847326715320186874001019653359397271745046864640508377984982400903447009185267605205778819712848080691366407461e-02),
0704          BOOST_MATH_HUGE_CONSTANT(T, 0, 1.5007947329316122538374763075807268094639436437387634979291759700896494746154334398961710227490402528151677469993935e-02),
0705          BOOST_MATH_HUGE_CONSTANT(T, 0, 5.3774798729233489877920514301276498183080402431284197876486169536848635554354599213793172596490038991436925569025913e-03),
0706       };
0707       return data;
0708    }
0709 };
0710
0711 template <class T>
0712 class gauss_kronrod_detail<T, 41, 0>
0713 {
0714 public:
0715    static std::array<T, 21> const & abscissa()
0716    {
0717       static constexpr std::array<T, 21> data = {
0718          0.000000000e+00f,
0719          7.652652113e-02f,
0720          1.526054652e-01f,
0721          2.277858511e-01f,
0722          3.016278681e-01f,
0723          3.737060887e-01f,
0724          4.435931752e-01f,
0725          5.108670020e-01f,
0726          5.751404468e-01f,
0727          6.360536807e-01f,
0728          6.932376563e-01f,
0729          7.463319065e-01f,
0730          7.950414288e-01f,
0731          8.391169718e-01f,
0732          8.782768113e-01f,
0733          9.122344283e-01f,
0734          9.408226338e-01f,
0735          9.639719273e-01f,
0736          9.815078775e-01f,
0737          9.931285992e-01f,
0738          9.988590316e-01f,
0739       };
0740       return data;
0741    }
0742    static std::array<T, 21> const & weights()
0743    {
0744       static constexpr std::array<T, 21> data = {
0745          7.660071192e-02f,
0746          7.637786767e-02f,
0747          7.570449768e-02f,
0748          7.458287540e-02f,
0749          7.303069033e-02f,
0750          7.105442355e-02f,
0751          6.864867293e-02f,
0752          6.583459713e-02f,
0753          6.265323755e-02f,
0754          5.911140088e-02f,
0755          5.519510535e-02f,
0756          5.094457392e-02f,
0757          4.643482187e-02f,
0758          4.166887333e-02f,
0759          3.660016976e-02f,
0760          3.128730678e-02f,
0761          2.588213360e-02f,
0762          2.038837346e-02f,
0763          1.462616926e-02f,
0764          8.600269856e-03f,
0765          3.073583719e-03f,
0766       };
0767       return data;
0768    }
0769 };
0770
0771 template <class T>
0772 class gauss_kronrod_detail<T, 41, 1>
0773 {
0774 public:
0775    static std::array<T, 21> const & abscissa()
0776    {
0777       static constexpr std::array<T, 21> data = {
0778          0.00000000000000000e+00,
0779          7.65265211334973338e-02,
0780          1.52605465240922676e-01,
0781          2.27785851141645078e-01,
0782          3.01627868114913004e-01,
0783          3.73706088715419561e-01,
0784          4.43593175238725103e-01,
0785          5.10867001950827098e-01,
0786          5.75140446819710315e-01,
0787          6.36053680726515025e-01,
0788          6.93237656334751385e-01,
0789          7.46331906460150793e-01,
0790          7.95041428837551198e-01,
0791          8.39116971822218823e-01,
0792          8.78276811252281976e-01,
0793          9.12234428251325906e-01,
0794          9.40822633831754754e-01,
0795          9.63971927277913791e-01,
0796          9.81507877450250259e-01,
0797          9.93128599185094925e-01,
0798          9.98859031588277664e-01,
0799       };
0800       return data;
0801    }
0802    static std::array<T, 21> const & weights()
0803    {
0804       static constexpr std::array<T, 21> data = {
0805          7.66007119179996564e-02,
0806          7.63778676720807367e-02,
0807          7.57044976845566747e-02,
0808          7.45828754004991890e-02,
0809          7.30306903327866675e-02,
0810          7.10544235534440683e-02,
0811          6.86486729285216193e-02,
0812          6.58345971336184221e-02,
0813          6.26532375547811680e-02,
0814          5.91114008806395724e-02,
0815          5.51951053482859947e-02,
0816          5.09445739237286919e-02,
0817          4.64348218674976747e-02,
0818          4.16688733279736863e-02,
0819          3.66001697582007980e-02,
0820          3.12873067770327990e-02,
0821          2.58821336049511588e-02,
0822          2.03883734612665236e-02,
0823          1.46261692569712530e-02,
0824          8.60026985564294220e-03,
0825          3.07358371852053150e-03,
0826       };
0827       return data;
0828    }
0829 };
0830
0831 template <class T>
0832 class gauss_kronrod_detail<T, 41, 2>
0833 {
0834 public:
0835    static std::array<T, 21> const & abscissa()
0836    {
0837       static constexpr std::array<T, 21> data = {
0838          0.00000000000000000000000000000000000e+00L,
0839          7.65265211334973337546404093988382110e-02L,
0840          1.52605465240922675505220241022677528e-01L,
0841          2.27785851141645078080496195368574625e-01L,
0842          3.01627868114913004320555356858592261e-01L,
0843          3.73706088715419560672548177024927237e-01L,
0844          4.43593175238725103199992213492640108e-01L,
0845          5.10867001950827098004364050955250998e-01L,
0846          5.75140446819710315342946036586425133e-01L,
0847          6.36053680726515025452836696226285937e-01L,
0848          6.93237656334751384805490711845931533e-01L,
0849          7.46331906460150792614305070355641590e-01L,
0850          7.95041428837551198350638833272787943e-01L,
0851          8.39116971822218823394529061701520685e-01L,
0852          8.78276811252281976077442995113078467e-01L,
0853          9.12234428251325905867752441203298113e-01L,
0854          9.40822633831754753519982722212443380e-01L,
0855          9.63971927277913791267666131197277222e-01L,
0856          9.81507877450250259193342994720216945e-01L,
0857          9.93128599185094924786122388471320278e-01L,
0858          9.98859031588277663838315576545863010e-01L,
0859       };
0860       return data;
0861    }
0862    static std::array<T, 21> const & weights()
0863    {
0864       static constexpr std::array<T, 21> data = {
0865          7.66007119179996564450499015301017408e-02L,
0866          7.63778676720807367055028350380610018e-02L,
0867          7.57044976845566746595427753766165583e-02L,
0868          7.45828754004991889865814183624875286e-02L,
0869          7.30306903327866674951894176589131128e-02L,
0870          7.10544235534440683057903617232101674e-02L,
0871          6.86486729285216193456234118853678017e-02L,
0872          6.58345971336184221115635569693979431e-02L,
0873          6.26532375547811680258701221742549806e-02L,
0874          5.91114008806395723749672206485942171e-02L,
0875          5.51951053482859947448323724197773292e-02L,
0876          5.09445739237286919327076700503449487e-02L,
0877          4.64348218674976747202318809261075168e-02L,
0878          4.16688733279736862637883059368947380e-02L,
0879          3.66001697582007980305572407072110085e-02L,
0880          3.12873067770327989585431193238007379e-02L,
0881          2.58821336049511588345050670961531430e-02L,
0882          2.03883734612665235980102314327547051e-02L,
0883          1.46261692569712529837879603088683562e-02L,
0884          8.60026985564294219866178795010234725e-03L,
0885          3.07358371852053150121829324603098749e-03L,
0886       };
0887       return data;
0888    }
0889 };
0890
0891 #ifdef BOOST_HAS_FLOAT128
0892 template <class T>
0893 class gauss_kronrod_detail<T, 41, 3>
0894 {
0895 public:
0896    static std::array<T, 21> const & abscissa()
0897    {
0898       static const std::array<T, 21> data = {
0899          0.00000000000000000000000000000000000e+00Q,
0900          7.65265211334973337546404093988382110e-02Q,
0901          1.52605465240922675505220241022677528e-01Q,
0902          2.27785851141645078080496195368574625e-01Q,
0903          3.01627868114913004320555356858592261e-01Q,
0904          3.73706088715419560672548177024927237e-01Q,
0905          4.43593175238725103199992213492640108e-01Q,
0906          5.10867001950827098004364050955250998e-01Q,
0907          5.75140446819710315342946036586425133e-01Q,
0908          6.36053680726515025452836696226285937e-01Q,
0909          6.93237656334751384805490711845931533e-01Q,
0910          7.46331906460150792614305070355641590e-01Q,
0911          7.95041428837551198350638833272787943e-01Q,
0912          8.39116971822218823394529061701520685e-01Q,
0913          8.78276811252281976077442995113078467e-01Q,
0914          9.12234428251325905867752441203298113e-01Q,
0915          9.40822633831754753519982722212443380e-01Q,
0916          9.63971927277913791267666131197277222e-01Q,
0917          9.81507877450250259193342994720216945e-01Q,
0918          9.93128599185094924786122388471320278e-01Q,
0919          9.98859031588277663838315576545863010e-01Q,
0920       };
0921       return data;
0922    }
0923    static std::array<T, 21> const & weights()
0924    {
0925       static const std::array<T, 21> data = {
0926          7.66007119179996564450499015301017408e-02Q,
0927          7.63778676720807367055028350380610018e-02Q,
0928          7.57044976845566746595427753766165583e-02Q,
0929          7.45828754004991889865814183624875286e-02Q,
0930          7.30306903327866674951894176589131128e-02Q,
0931          7.10544235534440683057903617232101674e-02Q,
0932          6.86486729285216193456234118853678017e-02Q,
0933          6.58345971336184221115635569693979431e-02Q,
0934          6.26532375547811680258701221742549806e-02Q,
0935          5.91114008806395723749672206485942171e-02Q,
0936          5.51951053482859947448323724197773292e-02Q,
0937          5.09445739237286919327076700503449487e-02Q,
0938          4.64348218674976747202318809261075168e-02Q,
0939          4.16688733279736862637883059368947380e-02Q,
0940          3.66001697582007980305572407072110085e-02Q,
0941          3.12873067770327989585431193238007379e-02Q,
0942          2.58821336049511588345050670961531430e-02Q,
0943          2.03883734612665235980102314327547051e-02Q,
0944          1.46261692569712529837879603088683562e-02Q,
0945          8.60026985564294219866178795010234725e-03Q,
0946          3.07358371852053150121829324603098749e-03Q,
0947       };
0948       return data;
0949    }
0950 };
0951 #endif
0952
0953 template <class T>
0954 class gauss_kronrod_detail<T, 41, 4>
0955 {
0956 public:
0957    static  std::array<T, 21> const & abscissa()
0958    {
0959       static  std::array<T, 21> data = {
0960          BOOST_MATH_HUGE_CONSTANT(T, 0, 0.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+00),
0961          BOOST_MATH_HUGE_CONSTANT(T, 0, 7.6526521133497333754640409398838211004796266813497500804795244384256342048336978241545114181556215606998505646364133e-02),
0962          BOOST_MATH_HUGE_CONSTANT(T, 0, 1.5260546524092267550522024102267752791167622481841730660174156703809133685751696356987995886397049724808931527012542e-01),
0963          BOOST_MATH_HUGE_CONSTANT(T, 0, 2.2778585114164507808049619536857462474308893768292747231463573920717134186355582779495212519096870803177373131560430e-01),
0964          BOOST_MATH_HUGE_CONSTANT(T, 0, 3.0162786811491300432055535685859226061539650501373092456926374427956957435978384116066498234762220215751079886015902e-01),
0965          BOOST_MATH_HUGE_CONSTANT(T, 0, 3.7370608871541956067254817702492723739574632170568271182794861351564576437305952789589568363453337894476772208852815e-01),
0966          BOOST_MATH_HUGE_CONSTANT(T, 0, 4.4359317523872510319999221349264010784010101082300309613315028346299543059315258601993479156987847429893626854030516e-01),
0967          BOOST_MATH_HUGE_CONSTANT(T, 0, 5.1086700195082709800436405095525099842549132920242683347234861989473497039076572814403168305086777919832943068843526e-01),
0968          BOOST_MATH_HUGE_CONSTANT(T, 0, 5.7514044681971031534294603658642513281381264014771682537415885495717468074720062012357788489049470208285175093670561e-01),
0969          BOOST_MATH_HUGE_CONSTANT(T, 0, 6.3605368072651502545283669622628593674338911679936846393944662254654126258543013255870319549576130658211710937772596e-01),
0970          BOOST_MATH_HUGE_CONSTANT(T, 0, 6.9323765633475138480549071184593153338642585141021417904687378454301191710739219011546672416325022748282227809465165e-01),
0971          BOOST_MATH_HUGE_CONSTANT(T, 0, 7.4633190646015079261430507035564159031073067956917644413954590606853535503815506468110411362064752061238490065167656e-01),
0972          BOOST_MATH_HUGE_CONSTANT(T, 0, 7.9504142883755119835063883327278794295938959911578029703855163894322697871710382866701777890251824617748545658564370e-01),
0973          BOOST_MATH_HUGE_CONSTANT(T, 0, 8.3911697182221882339452906170152068532962936506563737325249272553286109399932480991922934056595764922060422035306914e-01),
0974          BOOST_MATH_HUGE_CONSTANT(T, 0, 8.7827681125228197607744299511307846671124526828251164853898086998248145904743220740840261624245683876748360309079747e-01),
0975          BOOST_MATH_HUGE_CONSTANT(T, 0, 9.1223442825132590586775244120329811304918479742369177479588221915807089120871907893644472619292138737876039175464603e-01),
0976          BOOST_MATH_HUGE_CONSTANT(T, 0, 9.4082263383175475351998272221244338027429557377965291059536839973186796006557571220888218676776618448841584569497535e-01),
0977          BOOST_MATH_HUGE_CONSTANT(T, 0, 9.6397192727791379126766613119727722191206032780618885606353759389204158078438305698001812525596471563131043491596423e-01),
0978          BOOST_MATH_HUGE_CONSTANT(T, 0, 9.8150787745025025919334299472021694456725093981023759869077533318793098857465723460898060491887511355706497739384103e-01),
0979          BOOST_MATH_HUGE_CONSTANT(T, 0, 9.9312859918509492478612238847132027822264713090165589614818413121798471762775378083944940249657220927472894034724419e-01),
0980          BOOST_MATH_HUGE_CONSTANT(T, 0, 9.9885903158827766383831557654586300999957020432629666866666860339324411793311982967839129772854179884971700274369367e-01),
0981       };
0982       return data;
0983    }
0984    static  std::array<T, 21> const & weights()
0985    {
0986       static  std::array<T, 21> data = {
0987          BOOST_MATH_HUGE_CONSTANT(T, 0, 7.6600711917999656445049901530101740827932500628670118055485349620314721456712029449597396569857880493210849110825276e-02),
0988          BOOST_MATH_HUGE_CONSTANT(T, 0, 7.6377867672080736705502835038061001800801036764945996714946431116936745542061941050008345047482501253320401746334511e-02),
0989          BOOST_MATH_HUGE_CONSTANT(T, 0, 7.5704497684556674659542775376616558263363155900414326194855223272348838596099414841886740468379707283366777797425290e-02),
0990          BOOST_MATH_HUGE_CONSTANT(T, 0, 7.4582875400499188986581418362487528616116493572092273080047040726969899567887364227664202642942357104526915332274625e-02),
0991          BOOST_MATH_HUGE_CONSTANT(T, 0, 7.3030690332786667495189417658913112760626845234552742380174250771849743831660040966804802312464527721645765620253776e-02),
0992          BOOST_MATH_HUGE_CONSTANT(T, 0, 7.1054423553444068305790361723210167412912159322210143921628270586407381879789525901086146473278095159807542174985045e-02),
0993          BOOST_MATH_HUGE_CONSTANT(T, 0, 6.8648672928521619345623411885367801715489704958239860400434264173923806029589970941711224257967651039544669425313433e-02),
0994          BOOST_MATH_HUGE_CONSTANT(T, 0, 6.5834597133618422111563556969397943147223506343381443709751749639944420314384296347503523810096842402960802728781816e-02),
0995          BOOST_MATH_HUGE_CONSTANT(T, 0, 6.2653237554781168025870122174254980585819744698897886186553324157100424088919284503451596742588386343548162830898103e-02),
0996          BOOST_MATH_HUGE_CONSTANT(T, 0, 5.9111400880639572374967220648594217136419365977042191748388047204015262840407696611508732839851952697839735487615776e-02),
0997          BOOST_MATH_HUGE_CONSTANT(T, 0, 5.5195105348285994744832372419777329194753456228153116909812131213177827707884692917845453999535518818940813085110223e-02),
0998          BOOST_MATH_HUGE_CONSTANT(T, 0, 5.0944573923728691932707670050344948664836365809262579747517140086119113476866735641054822574173198900379392130050979e-02),
0999          BOOST_MATH_HUGE_CONSTANT(T, 0, 4.6434821867497674720231880926107516842127071007077929289994127933243222585938804392953931185146446072587020288747981e-02),
1000          BOOST_MATH_HUGE_CONSTANT(T, 0, 4.1668873327973686263788305936894738043960843153010324860966353235271889596379726462208702081068715463576895020003842e-02),
1001          BOOST_MATH_HUGE_CONSTANT(T, 0, 3.6600169758200798030557240707211008487453496747498001651070009441973280061489266074044986901436324295513243878212345e-02),
1002          BOOST_MATH_HUGE_CONSTANT(T, 0, 3.1287306777032798958543119323800737887769280362813337359554598005322423266047996771926031069705049476071896145456496e-02),
1003          BOOST_MATH_HUGE_CONSTANT(T, 0, 2.5882133604951158834505067096153142999479118048674944526997797755374306421629440393392427198869345793286369198147609e-02),
1004          BOOST_MATH_HUGE_CONSTANT(T, 0, 2.0388373461266523598010231432754705122838627940185929365371868214433006532030353671253640300679157504987977281782909e-02),
1005          BOOST_MATH_HUGE_CONSTANT(T, 0, 1.4626169256971252983787960308868356163881050162249770342103474631076960029748751959380482484308382288261238476948520e-02),
1006          BOOST_MATH_HUGE_CONSTANT(T, 0, 8.6002698556429421986617879501023472521289227667077976622450602031426535362696437838448828009554532025301579670206091e-03),
1007          BOOST_MATH_HUGE_CONSTANT(T, 0, 3.0735837185205315012182932460309874880335046882543449198461628212114333665590378156706265241414469306987988292234740e-03),
1008       };
1009       return data;
1010    }
1011 };
1012
1013 template <class T>
1014 class gauss_kronrod_detail<T, 51, 0>
1015 {
1016 public:
1017    static std::array<T, 26> const & abscissa()
1018    {
1019       static constexpr std::array<T, 26> data = {
1020          0.000000000e+00f,
1021          6.154448301e-02f,
1022          1.228646926e-01f,
1023          1.837189394e-01f,
1024          2.438668837e-01f,
1025          3.030895389e-01f,
1026          3.611723058e-01f,
1027          4.178853822e-01f,
1028          4.730027314e-01f,
1029          5.263252843e-01f,
1030          5.776629302e-01f,
1031          6.268100990e-01f,
1032          6.735663685e-01f,
1033          7.177664068e-01f,
1034          7.592592630e-01f,
1035          7.978737980e-01f,
1036          8.334426288e-01f,
1037          8.658470653e-01f,
1038          8.949919979e-01f,
1039          9.207471153e-01f,
1040          9.429745712e-01f,
1041          9.616149864e-01f,
1042          9.766639215e-01f,
1043          9.880357945e-01f,
1044          9.955569698e-01f,
1045          9.992621050e-01f,
1046       };
1047       return data;
1048    }
1049    static std::array<T, 26> const & weights()
1050    {
1051       static constexpr std::array<T, 26> data = {
1052          6.158081807e-02f,
1053          6.147118987e-02f,
1054          6.112850972e-02f,
1055          6.053945538e-02f,
1056          5.972034032e-02f,
1057          5.868968002e-02f,
1058          5.743711636e-02f,
1059          5.595081122e-02f,
1060          5.425112989e-02f,
1061          5.236288581e-02f,
1062          5.027767908e-02f,
1063          4.798253714e-02f,
1064          4.550291305e-02f,
1065          4.287284502e-02f,
1066          4.008382550e-02f,
1067          3.711627148e-02f,
1068          3.400213027e-02f,
1069          3.079230017e-02f,
1070          2.747531759e-02f,
1071          2.400994561e-02f,
1072          2.043537115e-02f,
1073          1.684781771e-02f,
1074          1.323622920e-02f,
1075          9.473973386e-03f,
1076          5.561932135e-03f,
1077          1.987383892e-03f,
1078       };
1079       return data;
1080    }
1081 };
1082
1083 template <class T>
1084 class gauss_kronrod_detail<T, 51, 1>
1085 {
1086 public:
1087    static std::array<T, 26> const & abscissa()
1088    {
1089       static constexpr std::array<T, 26> data = {
1090          0.00000000000000000e+00,
1091          6.15444830056850789e-02,
1092          1.22864692610710396e-01,
1093          1.83718939421048892e-01,
1094          2.43866883720988432e-01,
1095          3.03089538931107830e-01,
1096          3.61172305809387838e-01,
1097          4.17885382193037749e-01,
1098          4.73002731445714961e-01,
1099          5.26325284334719183e-01,
1100          5.77662930241222968e-01,
1101          6.26810099010317413e-01,
1102          6.73566368473468364e-01,
1103          7.17766406813084388e-01,
1104          7.59259263037357631e-01,
1105          7.97873797998500059e-01,
1106          8.33442628760834001e-01,
1107          8.65847065293275595e-01,
1108          8.94991997878275369e-01,
1109          9.20747115281701562e-01,
1110          9.42974571228974339e-01,
1111          9.61614986425842512e-01,
1112          9.76663921459517511e-01,
1113          9.88035794534077248e-01,
1114          9.95556969790498098e-01,
1115          9.99262104992609834e-01,
1116       };
1117       return data;
1118    }
1119    static std::array<T, 26> const & weights()
1120    {
1121       static constexpr std::array<T, 26> data = {
1122          6.15808180678329351e-02,
1123          6.14711898714253167e-02,
1124          6.11285097170530483e-02,
1125          6.05394553760458629e-02,
1126          5.97203403241740600e-02,
1127          5.86896800223942080e-02,
1128          5.74371163615678329e-02,
1129          5.59508112204123173e-02,
1130          5.42511298885454901e-02,
1131          5.23628858064074759e-02,
1132          5.02776790807156720e-02,
1133          4.79825371388367139e-02,
1134          4.55029130499217889e-02,
1135          4.28728450201700495e-02,
1136          4.00838255040323821e-02,
1137          3.71162714834155436e-02,
1138          3.40021302743293378e-02,
1139          3.07923001673874889e-02,
1140          2.74753175878517378e-02,
1141          2.40099456069532162e-02,
1142          2.04353711458828355e-02,
1143          1.68478177091282982e-02,
1144          1.32362291955716748e-02,
1145          9.47397338617415161e-03,
1146          5.56193213535671376e-03,
1147          1.98738389233031593e-03,
1148       };
1149       return data;
1150    }
1151 };
1152
1153 template <class T>
1154 class gauss_kronrod_detail<T, 51, 2>
1155 {
1156 public:
1157    static std::array<T, 26> const & abscissa()
1158    {
1159       static constexpr std::array<T, 26> data = {
1160          0.00000000000000000000000000000000000e+00L,
1161          6.15444830056850788865463923667966313e-02L,
1162          1.22864692610710396387359818808036806e-01L,
1163          1.83718939421048892015969888759528416e-01L,
1164          2.43866883720988432045190362797451586e-01L,
1165          3.03089538931107830167478909980339329e-01L,
1166          3.61172305809387837735821730127640667e-01L,
1167          4.17885382193037748851814394594572487e-01L,
1168          4.73002731445714960522182115009192041e-01L,
1169          5.26325284334719182599623778158010178e-01L,
1170          5.77662930241222967723689841612654067e-01L,
1171          6.26810099010317412788122681624517881e-01L,
1172          6.73566368473468364485120633247622176e-01L,
1173          7.17766406813084388186654079773297781e-01L,
1174          7.59259263037357630577282865204360976e-01L,
1175          7.97873797998500059410410904994306569e-01L,
1176          8.33442628760834001421021108693569569e-01L,
1177          8.65847065293275595448996969588340088e-01L,
1178          8.94991997878275368851042006782804954e-01L,
1179          9.20747115281701561746346084546330632e-01L,
1180          9.42974571228974339414011169658470532e-01L,
1181          9.61614986425842512418130033660167242e-01L,
1182          9.76663921459517511498315386479594068e-01L,
1183          9.88035794534077247637331014577406227e-01L,
1184          9.95556969790498097908784946893901617e-01L,
1185          9.99262104992609834193457486540340594e-01L,
1186       };
1187       return data;
1188    }
1189    static std::array<T, 26> const & weights()
1190    {
1191       static constexpr std::array<T, 26> data = {
1192          6.15808180678329350787598242400645532e-02L,
1193          6.14711898714253166615441319652641776e-02L,
1194          6.11285097170530483058590304162927119e-02L,
1195          6.05394553760458629453602675175654272e-02L,
1196          5.97203403241740599790992919325618538e-02L,
1197          5.86896800223942079619741758567877641e-02L,
1198          5.74371163615678328535826939395064720e-02L,
1199          5.59508112204123173082406863827473468e-02L,
1200          5.42511298885454901445433704598756068e-02L,
1201          5.23628858064074758643667121378727149e-02L,
1202          5.02776790807156719633252594334400844e-02L,
1203          4.79825371388367139063922557569147550e-02L,
1204          4.55029130499217889098705847526603930e-02L,
1205          4.28728450201700494768957924394951611e-02L,
1206          4.00838255040323820748392844670756464e-02L,
1207          3.71162714834155435603306253676198760e-02L,
1208          3.40021302743293378367487952295512032e-02L,
1209          3.07923001673874888911090202152285856e-02L,
1210          2.74753175878517378029484555178110786e-02L,
1211          2.40099456069532162200924891648810814e-02L,
1212          2.04353711458828354565682922359389737e-02L,
1213          1.68478177091282982315166675363363158e-02L,
1214          1.32362291955716748136564058469762381e-02L,
1215          9.47397338617415160720771052365532387e-03L,
1216          5.56193213535671375804023690106552207e-03L,
1217          1.98738389233031592650785188284340989e-03L,
1218       };
1219       return data;
1220    }
1221 };
1222
1223 #ifdef BOOST_HAS_FLOAT128
1224 template <class T>
1225 class gauss_kronrod_detail<T, 51, 3>
1226 {
1227 public:
1228    static std::array<T, 26> const & abscissa()
1229    {
1230       static const std::array<T, 26> data = {
1231          0.00000000000000000000000000000000000e+00Q,
1232          6.15444830056850788865463923667966313e-02Q,
1233          1.22864692610710396387359818808036806e-01Q,
1234          1.83718939421048892015969888759528416e-01Q,
1235          2.43866883720988432045190362797451586e-01Q,
1236          3.03089538931107830167478909980339329e-01Q,
1237          3.61172305809387837735821730127640667e-01Q,
1238          4.17885382193037748851814394594572487e-01Q,
1239          4.73002731445714960522182115009192041e-01Q,
1240          5.26325284334719182599623778158010178e-01Q,
1241          5.77662930241222967723689841612654067e-01Q,
1242          6.26810099010317412788122681624517881e-01Q,
1243          6.73566368473468364485120633247622176e-01Q,
1244          7.17766406813084388186654079773297781e-01Q,
1245          7.59259263037357630577282865204360976e-01Q,
1246          7.97873797998500059410410904994306569e-01Q,
1247          8.33442628760834001421021108693569569e-01Q,
1248          8.65847065293275595448996969588340088e-01Q,
1249          8.94991997878275368851042006782804954e-01Q,
1250          9.20747115281701561746346084546330632e-01Q,
1251          9.42974571228974339414011169658470532e-01Q,
1252          9.61614986425842512418130033660167242e-01Q,
1253          9.76663921459517511498315386479594068e-01Q,
1254          9.88035794534077247637331014577406227e-01Q,
1255          9.95556969790498097908784946893901617e-01Q,
1256          9.99262104992609834193457486540340594e-01Q,
1257       };
1258       return data;
1259    }
1260    static std::array<T, 26> const & weights()
1261    {
1262       static const std::array<T, 26> data = {
1263          6.15808180678329350787598242400645532e-02Q,
1264          6.14711898714253166615441319652641776e-02Q,
1265          6.11285097170530483058590304162927119e-02Q,
1266          6.05394553760458629453602675175654272e-02Q,
1267          5.97203403241740599790992919325618538e-02Q,
1268          5.86896800223942079619741758567877641e-02Q,
1269          5.74371163615678328535826939395064720e-02Q,
1270          5.59508112204123173082406863827473468e-02Q,
1271          5.42511298885454901445433704598756068e-02Q,
1272          5.23628858064074758643667121378727149e-02Q,
1273          5.02776790807156719633252594334400844e-02Q,
1274          4.79825371388367139063922557569147550e-02Q,
1275          4.55029130499217889098705847526603930e-02Q,
1276          4.28728450201700494768957924394951611e-02Q,
1277          4.00838255040323820748392844670756464e-02Q,
1278          3.71162714834155435603306253676198760e-02Q,
1279          3.40021302743293378367487952295512032e-02Q,
1280          3.07923001673874888911090202152285856e-02Q,
1281          2.74753175878517378029484555178110786e-02Q,
1282          2.40099456069532162200924891648810814e-02Q,
1283          2.04353711458828354565682922359389737e-02Q,
1284          1.68478177091282982315166675363363158e-02Q,
1285          1.32362291955716748136564058469762381e-02Q,
1286          9.47397338617415160720771052365532387e-03Q,
1287          5.56193213535671375804023690106552207e-03Q,
1288          1.98738389233031592650785188284340989e-03Q,
1289       };
1290       return data;
1291    }
1292 };
1293 #endif
1294
1295 template <class T>
1296 class gauss_kronrod_detail<T, 51, 4>
1297 {
1298 public:
1299    static  std::array<T, 26> const & abscissa()
1300    {
1301       static  std::array<T, 26> data = {
1302          BOOST_MATH_HUGE_CONSTANT(T, 0, 0.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+00),
1303          BOOST_MATH_HUGE_CONSTANT(T, 0, 6.1544483005685078886546392366796631281724348039823545274305431751687279361558658545141048781022691067898008423227288e-02),
1304          BOOST_MATH_HUGE_CONSTANT(T, 0, 1.2286469261071039638735981880803680553220534604978373842389353789270883496885841582643884994633105537597765980412320e-01),
1305          BOOST_MATH_HUGE_CONSTANT(T, 0, 1.8371893942104889201596988875952841578528447834990555215034512653236752851109815617651867160645591242103823539931527e-01),
1306          BOOST_MATH_HUGE_CONSTANT(T, 0, 2.4386688372098843204519036279745158640563315632598447642113565325038747278585595067977636776325034060327548499765742e-01),
1307          BOOST_MATH_HUGE_CONSTANT(T, 0, 3.0308953893110783016747890998033932920041937876655194685731578452573120372337209717349617882111662416355753711853559e-01),
1308          BOOST_MATH_HUGE_CONSTANT(T, 0, 3.6117230580938783773582173012764066742207834704337506979457877784674538239569654860329531506093761400789294612122812e-01),
1309          BOOST_MATH_HUGE_CONSTANT(T, 0, 4.1788538219303774885181439459457248709336998140069528034955785068796932076966599548717224205109797297615032607570119e-01),
1310          BOOST_MATH_HUGE_CONSTANT(T, 0, 4.7300273144571496052218211500919204133181773846162729090723082769560327584128603010315684778279363544192787010704498e-01),
1311          BOOST_MATH_HUGE_CONSTANT(T, 0, 5.2632528433471918259962377815801017803683252320191114313002425180471455022502695302371008520604638341970901082293650e-01),
1312          BOOST_MATH_HUGE_CONSTANT(T, 0, 5.7766293024122296772368984161265406739573503929151825664548350776102301275263202227671659646579649084013116066120581e-01),
1313          BOOST_MATH_HUGE_CONSTANT(T, 0, 6.2681009901031741278812268162451788101954628995068510806525222008437260184181183053045236423845198752346149030569920e-01),
1314          BOOST_MATH_HUGE_CONSTANT(T, 0, 6.7356636847346836448512063324762217588341672807274931705965696177828773684928421158196368568030932194044282149314388e-01),
1315          BOOST_MATH_HUGE_CONSTANT(T, 0, 7.1776640681308438818665407977329778059771167555515582423493486823991612820974965089522905953765860328116692570706602e-01),
1316          BOOST_MATH_HUGE_CONSTANT(T, 0, 7.5925926303735763057728286520436097638752201889833412091838973544501862882026240760763679724185230331463919586229073e-01),
1317          BOOST_MATH_HUGE_CONSTANT(T, 0, 7.9787379799850005941041090499430656940863230009338267661706934499488650817643824077118950314443984031474353711531825e-01),
1318          BOOST_MATH_HUGE_CONSTANT(T, 0, 8.3344262876083400142102110869356956946096411382352078602086471546171813247709012525322973947759168107133491065937347e-01),
1319          BOOST_MATH_HUGE_CONSTANT(T, 0, 8.6584706529327559544899696958834008820284409402823690293965213246691432948180280120756708738064779055576005302835351e-01),
1320          BOOST_MATH_HUGE_CONSTANT(T, 0, 8.9499199787827536885104200678280495417455484975358390306170168295917151090119945137118600693039178162093726882638296e-01),
1321          BOOST_MATH_HUGE_CONSTANT(T, 0, 9.2074711528170156174634608454633063157457035996277199700642836501131385042631212407808952281702820179915510491592339e-01),
1322          BOOST_MATH_HUGE_CONSTANT(T, 0, 9.4297457122897433941401116965847053190520157060899014192745249713729532254404926130890521815127348327109666786665572e-01),
1323          BOOST_MATH_HUGE_CONSTANT(T, 0, 9.6161498642584251241813003366016724169212642963709676666624520141292893281185666917636407790823210892689040877316178e-01),
1324          BOOST_MATH_HUGE_CONSTANT(T, 0, 9.7666392145951751149831538647959406774537055531440674467098742731616386753588055389644670948300617866819865983054648e-01),
1325          BOOST_MATH_HUGE_CONSTANT(T, 0, 9.8803579453407724763733101457740622707248415209160748131449972199405186821347293686245404742032360498210710718706868e-01),
1326          BOOST_MATH_HUGE_CONSTANT(T, 0, 9.9555696979049809790878494689390161725756264940480817121080493113293348134372793448728802635294700756868258870429256e-01),
1327          BOOST_MATH_HUGE_CONSTANT(T, 0, 9.9926210499260983419345748654034059370452496042279618586228697762904524428167719073818746102238075978747461480736921e-01),
1328       };
1329       return data;
1330    }
1331    static  std::array<T, 26> const & weights()
1332    {
1333       static  std::array<T, 26> data = {
1334          BOOST_MATH_HUGE_CONSTANT(T, 0, 6.1580818067832935078759824240064553190436936903140808056908996403358367244202623293256774502185186717703954810463664e-02),
1335          BOOST_MATH_HUGE_CONSTANT(T, 0, 6.1471189871425316661544131965264177586537962876885022711111683500151700796198726558483367566537422877227096643444043e-02),
1336          BOOST_MATH_HUGE_CONSTANT(T, 0, 6.1128509717053048305859030416292711922678552321960938357322028070390133769952032831204895569347757809858568165047769e-02),
1337          BOOST_MATH_HUGE_CONSTANT(T, 0, 6.0539455376045862945360267517565427162312365710457079923487043144554747810689514408013582515489930908693681447570811e-02),
1338          BOOST_MATH_HUGE_CONSTANT(T, 0, 5.9720340324174059979099291932561853835363045476189975483372207816149988460708299020779612375010639778624011960832019e-02),
1339          BOOST_MATH_HUGE_CONSTANT(T, 0, 5.8689680022394207961974175856787764139795646254828315293243700305012569486054157617049685031506591863121580010947248e-02),
1340          BOOST_MATH_HUGE_CONSTANT(T, 0, 5.7437116361567832853582693939506471994832856823896682976509412313367495727224381199978598247737089593472710899482737e-02),
1341          BOOST_MATH_HUGE_CONSTANT(T, 0, 5.5950811220412317308240686382747346820271035112771802428932791066115158268338607019365831655460314732208940609352540e-02),
1342          BOOST_MATH_HUGE_CONSTANT(T, 0, 5.4251129888545490144543370459875606826076838441263383072163293312936923476650934130242315028422047795830492882862973e-02),
1343          BOOST_MATH_HUGE_CONSTANT(T, 0, 5.2362885806407475864366712137872714887351550723707596350905793656046659248541276597504566497990926306481919129870507e-02),
1344          BOOST_MATH_HUGE_CONSTANT(T, 0, 5.0277679080715671963325259433440084440587630604775975142050968279743014641141402310302584542633557037153607386127936e-02),
1345          BOOST_MATH_HUGE_CONSTANT(T, 0, 4.7982537138836713906392255756914754983592207423271169651235865196757913880334117810235517477328110033499422471098658e-02),
1346          BOOST_MATH_HUGE_CONSTANT(T, 0, 4.5502913049921788909870584752660393043707768935695327316724254392794299567957035458208970599641697203261236226745020e-02),
1347          BOOST_MATH_HUGE_CONSTANT(T, 0, 4.2872845020170049476895792439495161101999504199883328877919242515738957655253932048951366960802592343905647433925806e-02),
1348          BOOST_MATH_HUGE_CONSTANT(T, 0, 4.0083825504032382074839284467075646401410549266591308713115878386835777315058451955614116158949614066927183232852042e-02),
1349          BOOST_MATH_HUGE_CONSTANT(T, 0, 3.7116271483415543560330625367619875995997802688047764805628702762773009669395760582294525748583875707140577080663373e-02),
1350          BOOST_MATH_HUGE_CONSTANT(T, 0, 3.4002130274329337836748795229551203225670528250050443083264193121524339063344855010257660547708022429300203676502386e-02),
1351          BOOST_MATH_HUGE_CONSTANT(T, 0, 3.0792300167387488891109020215228585600877162393292487644544830559965388047996492709248618249084851477787538356572832e-02),
1352          BOOST_MATH_HUGE_CONSTANT(T, 0, 2.7475317587851737802948455517811078614796013288710603199613621069727810352835469926107822047433566792405123805901196e-02),
1353          BOOST_MATH_HUGE_CONSTANT(T, 0, 2.4009945606953216220092489164881081392931528209659330290734972342536012282191913069778658241972047765300060007037359e-02),
1354          BOOST_MATH_HUGE_CONSTANT(T, 0, 2.0435371145882835456568292235938973678758006097668937220074531550163622566841885855957623103354443247806459277197725e-02),
1355          BOOST_MATH_HUGE_CONSTANT(T, 0, 1.6847817709128298231516667536336315840402654624706139411175769276842182270078960078544597372646532637619276509222462e-02),
1356          BOOST_MATH_HUGE_CONSTANT(T, 0, 1.3236229195571674813656405846976238077578084997863654732213860488560614587634395544002156258192582265590155862296710e-02),
1357          BOOST_MATH_HUGE_CONSTANT(T, 0, 9.4739733861741516072077105236553238716453268483726334971394029603529306140359023187904705754719643032594360138998941e-03),
1358          BOOST_MATH_HUGE_CONSTANT(T, 0, 5.5619321353567137580402369010655220701769295496290984052961210793810038857581724171021610100708799763006942755331129e-03),
1359          BOOST_MATH_HUGE_CONSTANT(T, 0, 1.9873838923303159265078518828434098894299804282505973837653346298985629336820118753523093675303476883723992297810124e-03),
1360       };
1361       return data;
1362    }
1363 };
1364
1365 template <class T>
1366 class gauss_kronrod_detail<T, 61, 0>
1367 {
1368 public:
1369    static std::array<T, 31> const & abscissa()
1370    {
1371       static constexpr std::array<T, 31> data = {
1372          0.000000000e+00f,
1373          5.147184256e-02f,
1374          1.028069380e-01f,
1375          1.538699136e-01f,
1376          2.045251167e-01f,
1377          2.546369262e-01f,
1378          3.040732023e-01f,
1379          3.527047255e-01f,
1380          4.004012548e-01f,
1381          4.470337695e-01f,
1382          4.924804679e-01f,
1383          5.366241481e-01f,
1384          5.793452358e-01f,
1385          6.205261830e-01f,
1386          6.600610641e-01f,
1387          6.978504948e-01f,
1388          7.337900625e-01f,
1389          7.677774321e-01f,
1390          7.997278358e-01f,
1391          8.295657624e-01f,
1392          8.572052335e-01f,
1393          8.825605358e-01f,
1394          9.055733077e-01f,
1395          9.262000474e-01f,
1396          9.443744447e-01f,
1397          9.600218650e-01f,
1398          9.731163225e-01f,
1399          9.836681233e-01f,
1400          9.916309969e-01f,
1401          9.968934841e-01f,
1402          9.994844101e-01f,
1403       };
1404       return data;
1405    }
1406    static std::array<T, 31> const & weights()
1407    {
1408       static constexpr std::array<T, 31> data = {
1409          5.149472943e-02f,
1410          5.142612854e-02f,
1411          5.122154785e-02f,
1412          5.088179590e-02f,
1413          5.040592140e-02f,
1414          4.979568343e-02f,
1415          4.905543456e-02f,
1416          4.818586176e-02f,
1417          4.718554657e-02f,
1418          4.605923827e-02f,
1419          4.481480013e-02f,
1420          4.345253970e-02f,
1421          4.196981022e-02f,
1422          4.037453895e-02f,
1423          3.867894562e-02f,
1424          3.688236465e-02f,
1425          3.497933803e-02f,
1426          3.298144706e-02f,
1427          3.090725756e-02f,
1428          2.875404877e-02f,
1429          2.650995488e-02f,
1430          2.419116208e-02f,
1431          2.182803582e-02f,
1432          1.941414119e-02f,
1433          1.692088919e-02f,
1434          1.436972951e-02f,
1435          1.182301525e-02f,
1436          9.273279660e-03f,
1437          6.630703916e-03f,
1438          3.890461127e-03f,
1439          1.389013699e-03f,
1440       };
1441       return data;
1442    }
1443 };
1444
1445 template <class T>
1446 class gauss_kronrod_detail<T, 61, 1>
1447 {
1448 public:
1449    static std::array<T, 31> const & abscissa()
1450    {
1451       static constexpr std::array<T, 31> data = {
1452          0.00000000000000000e+00,
1453          5.14718425553176958e-02,
1454          1.02806937966737030e-01,
1455          1.53869913608583547e-01,
1456          2.04525116682309891e-01,
1457          2.54636926167889846e-01,
1458          3.04073202273625077e-01,
1459          3.52704725530878113e-01,
1460          4.00401254830394393e-01,
1461          4.47033769538089177e-01,
1462          4.92480467861778575e-01,
1463          5.36624148142019899e-01,
1464          5.79345235826361692e-01,
1465          6.20526182989242861e-01,
1466          6.60061064126626961e-01,
1467          6.97850494793315797e-01,
1468          7.33790062453226805e-01,
1469          7.67777432104826195e-01,
1470          7.99727835821839083e-01,
1471          8.29565762382768397e-01,
1472          8.57205233546061099e-01,
1473          8.82560535792052682e-01,
1474          9.05573307699907799e-01,
1475          9.26200047429274326e-01,
1476          9.44374444748559979e-01,
1477          9.60021864968307512e-01,
1478          9.73116322501126268e-01,
1479          9.83668123279747210e-01,
1480          9.91630996870404595e-01,
1481          9.96893484074649540e-01,
1482          9.99484410050490638e-01,
1483       };
1484       return data;
1485    }
1486    static std::array<T, 31> const & weights()
1487    {
1488       static constexpr std::array<T, 31> data = {
1489          5.14947294294515676e-02,
1490          5.14261285374590259e-02,
1491          5.12215478492587722e-02,
1492          5.08817958987496065e-02,
1493          5.04059214027823468e-02,
1494          4.97956834270742064e-02,
1495          4.90554345550297789e-02,
1496          4.81858617570871291e-02,
1497          4.71855465692991539e-02,
1498          4.60592382710069881e-02,
1499          4.48148001331626632e-02,
1500          4.34525397013560693e-02,
1501          4.19698102151642461e-02,
1502          4.03745389515359591e-02,
1503          3.86789456247275930e-02,
1504          3.68823646518212292e-02,
1505          3.49793380280600241e-02,
1506          3.29814470574837260e-02,
1507          3.09072575623877625e-02,
1508          2.87540487650412928e-02,
1509          2.65099548823331016e-02,
1510          2.41911620780806014e-02,
1511          2.18280358216091923e-02,
1512          1.94141411939423812e-02,
1513          1.69208891890532726e-02,
1514          1.43697295070458048e-02,
1515          1.18230152534963417e-02,
1516          9.27327965951776343e-03,
1517          6.63070391593129217e-03,
1518          3.89046112709988405e-03,
1519          1.38901369867700762e-03,
1520       };
1521       return data;
1522    }
1523 };
1524
1525 template <class T>
1526 class gauss_kronrod_detail<T, 61, 2>
1527 {
1528 public:
1529    static std::array<T, 31> const & abscissa()
1530    {
1531       static constexpr std::array<T, 31> data = {
1532          0.00000000000000000000000000000000000e+00L,
1533          5.14718425553176958330252131667225737e-02L,
1534          1.02806937966737030147096751318000592e-01L,
1535          1.53869913608583546963794672743255920e-01L,
1536          2.04525116682309891438957671002024710e-01L,
1537          2.54636926167889846439805129817805108e-01L,
1538          3.04073202273625077372677107199256554e-01L,
1539          3.52704725530878113471037207089373861e-01L,
1540          4.00401254830394392535476211542660634e-01L,
1541          4.47033769538089176780609900322854000e-01L,
1542          4.92480467861778574993693061207708796e-01L,
1543          5.36624148142019899264169793311072794e-01L,
1544          5.79345235826361691756024932172540496e-01L,
1545          6.20526182989242861140477556431189299e-01L,
1546          6.60061064126626961370053668149270753e-01L,
1547          6.97850494793315796932292388026640068e-01L,
1548          7.33790062453226804726171131369527646e-01L,
1549          7.67777432104826194917977340974503132e-01L,
1550          7.99727835821839083013668942322683241e-01L,
1551          8.29565762382768397442898119732501916e-01L,
1552          8.57205233546061098958658510658943857e-01L,
1553          8.82560535792052681543116462530225590e-01L,
1554          9.05573307699907798546522558925958320e-01L,
1555          9.26200047429274325879324277080474004e-01L,
1556          9.44374444748559979415831324037439122e-01L,
1557          9.60021864968307512216871025581797663e-01L,
1558          9.73116322501126268374693868423706885e-01L,
1559          9.83668123279747209970032581605662802e-01L,
1560          9.91630996870404594858628366109485725e-01L,
1561          9.96893484074649540271630050918695283e-01L,
1562          9.99484410050490637571325895705810819e-01L,
1563       };
1564       return data;
1565    }
1566    static std::array<T, 31> const & weights()
1567    {
1568       static constexpr std::array<T, 31> data = {
1569          5.14947294294515675583404336470993075e-02L,
1570          5.14261285374590259338628792157812598e-02L,
1571          5.12215478492587721706562826049442083e-02L,
1572          5.08817958987496064922974730498046919e-02L,
1573          5.04059214027823468408930856535850289e-02L,
1574          4.97956834270742063578115693799423285e-02L,
1575          4.90554345550297788875281653672381736e-02L,
1576          4.81858617570871291407794922983045926e-02L,
1577          4.71855465692991539452614781810994865e-02L,
1578          4.60592382710069881162717355593735806e-02L,
1579          4.48148001331626631923555516167232438e-02L,
1580          4.34525397013560693168317281170732581e-02L,
1581          4.19698102151642461471475412859697578e-02L,
1582          4.03745389515359591119952797524681142e-02L,
1583          3.86789456247275929503486515322810503e-02L,
1584          3.68823646518212292239110656171359677e-02L,
1585          3.49793380280600241374996707314678751e-02L,
1586          3.29814470574837260318141910168539275e-02L,
1587          3.09072575623877624728842529430922726e-02L,
1588          2.87540487650412928439787853543342111e-02L,
1589          2.65099548823331016106017093350754144e-02L,
1590          2.41911620780806013656863707252320268e-02L,
1591          2.18280358216091922971674857383389934e-02L,
1592          1.94141411939423811734089510501284559e-02L,
1593          1.69208891890532726275722894203220924e-02L,
1594          1.43697295070458048124514324435800102e-02L,
1595          1.18230152534963417422328988532505929e-02L,
1596          9.27327965951776342844114689202436042e-03L,
1597          6.63070391593129217331982636975016813e-03L,
1598          3.89046112709988405126720184451550328e-03L,
1599          1.38901369867700762455159122675969968e-03L,
1600       };
1601       return data;
1602    }
1603 };
1604
1605 #ifdef BOOST_HAS_FLOAT128
1606 template <class T>
1607 class gauss_kronrod_detail<T, 61, 3>
1608 {
1609 public:
1610    static std::array<T, 31> const & abscissa()
1611    {
1612       static const std::array<T, 31> data = {
1613          0.00000000000000000000000000000000000e+00Q,
1614          5.14718425553176958330252131667225737e-02Q,
1615          1.02806937966737030147096751318000592e-01Q,
1616          1.53869913608583546963794672743255920e-01Q,
1617          2.04525116682309891438957671002024710e-01Q,
1618          2.54636926167889846439805129817805108e-01Q,
1619          3.04073202273625077372677107199256554e-01Q,
1620          3.52704725530878113471037207089373861e-01Q,
1621          4.00401254830394392535476211542660634e-01Q,
1622          4.47033769538089176780609900322854000e-01Q,
1623          4.92480467861778574993693061207708796e-01Q,
1624          5.36624148142019899264169793311072794e-01Q,
1625          5.79345235826361691756024932172540496e-01Q,
1626          6.20526182989242861140477556431189299e-01Q,
1627          6.60061064126626961370053668149270753e-01Q,
1628          6.97850494793315796932292388026640068e-01Q,
1629          7.33790062453226804726171131369527646e-01Q,
1630          7.67777432104826194917977340974503132e-01Q,
1631          7.99727835821839083013668942322683241e-01Q,
1632          8.29565762382768397442898119732501916e-01Q,
1633          8.57205233546061098958658510658943857e-01Q,
1634          8.82560535792052681543116462530225590e-01Q,
1635          9.05573307699907798546522558925958320e-01Q,
1636          9.26200047429274325879324277080474004e-01Q,
1637          9.44374444748559979415831324037439122e-01Q,
1638          9.60021864968307512216871025581797663e-01Q,
1639          9.73116322501126268374693868423706885e-01Q,
1640          9.83668123279747209970032581605662802e-01Q,
1641          9.91630996870404594858628366109485725e-01Q,
1642          9.96893484074649540271630050918695283e-01Q,
1643          9.99484410050490637571325895705810819e-01Q,
1644       };
1645       return data;
1646    }
1647    static std::array<T, 31> const & weights()
1648    {
1649       static const std::array<T, 31> data = {
1650          5.14947294294515675583404336470993075e-02Q,
1651          5.14261285374590259338628792157812598e-02Q,
1652          5.12215478492587721706562826049442083e-02Q,
1653          5.08817958987496064922974730498046919e-02Q,
1654          5.04059214027823468408930856535850289e-02Q,
1655          4.97956834270742063578115693799423285e-02Q,
1656          4.90554345550297788875281653672381736e-02Q,
1657          4.81858617570871291407794922983045926e-02Q,
1658          4.71855465692991539452614781810994865e-02Q,
1659          4.60592382710069881162717355593735806e-02Q,
1660          4.48148001331626631923555516167232438e-02Q,
1661          4.34525397013560693168317281170732581e-02Q,
1662          4.19698102151642461471475412859697578e-02Q,
1663          4.03745389515359591119952797524681142e-02Q,
1664          3.86789456247275929503486515322810503e-02Q,
1665          3.68823646518212292239110656171359677e-02Q,
1666          3.49793380280600241374996707314678751e-02Q,
1667          3.29814470574837260318141910168539275e-02Q,
1668          3.09072575623877624728842529430922726e-02Q,
1669          2.87540487650412928439787853543342111e-02Q,
1670          2.65099548823331016106017093350754144e-02Q,
1671          2.41911620780806013656863707252320268e-02Q,
1672          2.18280358216091922971674857383389934e-02Q,
1673          1.94141411939423811734089510501284559e-02Q,
1674          1.69208891890532726275722894203220924e-02Q,
1675          1.43697295070458048124514324435800102e-02Q,
1676          1.18230152534963417422328988532505929e-02Q,
1677          9.27327965951776342844114689202436042e-03Q,
1678          6.63070391593129217331982636975016813e-03Q,
1679          3.89046112709988405126720184451550328e-03Q,
1680          1.38901369867700762455159122675969968e-03Q,
1681       };
1682       return data;
1683    }
1684 };
1685 #endif
1686
1687 template <class T>
1688 class gauss_kronrod_detail<T, 61, 4>
1689 {
1690 public:
1691    static  std::array<T, 31> const & abscissa()
1692    {
1693       static  std::array<T, 31> data = {
1694          BOOST_MATH_HUGE_CONSTANT(T, 0, 0.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+00),
1695          BOOST_MATH_HUGE_CONSTANT(T, 0, 5.1471842555317695833025213166722573749141453666569564255160843987964755210427109055870090707285485841217089963590678e-02),
1696          BOOST_MATH_HUGE_CONSTANT(T, 0, 1.0280693796673703014709675131800059247190133296515840552101946914632788253917872738234797140786490207720254922664913e-01),
1697          BOOST_MATH_HUGE_CONSTANT(T, 0, 1.5386991360858354696379467274325592041855197124433846171896298291578714851081610139692310651074078557990111754952062e-01),
1698          BOOST_MATH_HUGE_CONSTANT(T, 0, 2.0452511668230989143895767100202470952410426459556377447604465028350321894663245495592565235317147819577892124850607e-01),
1699          BOOST_MATH_HUGE_CONSTANT(T, 0, 2.5463692616788984643980512981780510788278930330251842616428597508896353156907880290636628138423620257595521678255758e-01),
1700          BOOST_MATH_HUGE_CONSTANT(T, 0, 3.0407320227362507737267710719925655353115778980946272844421536998312150442387767304001423699909778588529370119457430e-01),
1701          BOOST_MATH_HUGE_CONSTANT(T, 0, 3.5270472553087811347103720708937386065363100802142562659418446890026941623319107866436039675211352945165817827083104e-01),
1702          BOOST_MATH_HUGE_CONSTANT(T, 0, 4.0040125483039439253547621154266063361104593297078395983186610656429170689311759061175527015710247383961903284673474e-01),
1703          BOOST_MATH_HUGE_CONSTANT(T, 0, 4.4703376953808917678060990032285400016240759386142440975447738172761535172858420700400688872124189834257262048739699e-01),
1704          BOOST_MATH_HUGE_CONSTANT(T, 0, 4.9248046786177857499369306120770879564426564096318697026073340982988422546396352776837047452262025983265531109327026e-01),
1705          BOOST_MATH_HUGE_CONSTANT(T, 0, 5.3662414814201989926416979331107279416417800693029710545274348291201490861897837863114116009718990258091585830703557e-01),
1706          BOOST_MATH_HUGE_CONSTANT(T, 0, 5.7934523582636169175602493217254049590705158881215289208126016612312833567812241903809970751783808208940322061083509e-01),
1707          BOOST_MATH_HUGE_CONSTANT(T, 0, 6.2052618298924286114047755643118929920736469282952813259505117012433531497488911774115258445532782106478789996137481e-01),
1708          BOOST_MATH_HUGE_CONSTANT(T, 0, 6.6006106412662696137005366814927075303835037480883390955067197339904937499734522076788020517029688190998858739703079e-01),
1709          BOOST_MATH_HUGE_CONSTANT(T, 0, 6.9785049479331579693229238802664006838235380065395465637972284673997672124315996069538163644008904690545069439941341e-01),
1710          BOOST_MATH_HUGE_CONSTANT(T, 0, 7.3379006245322680472617113136952764566938172775468549208701399518300016463613325382024664531597318795933262446521430e-01),
1711          BOOST_MATH_HUGE_CONSTANT(T, 0, 7.6777743210482619491797734097450313169488361723290845320649438736515857017299504505260960258623968420224697596501719e-01),
1712          BOOST_MATH_HUGE_CONSTANT(T, 0, 7.9972783582183908301366894232268324073569842937778450923647349548686662567326007229195202524185356472023967927713548e-01),
1713          BOOST_MATH_HUGE_CONSTANT(T, 0, 8.2956576238276839744289811973250191643906869617034167880695298345365650658958163508295244350814016004371545455777732e-01),
1714          BOOST_MATH_HUGE_CONSTANT(T, 0, 8.5720523354606109895865851065894385682080017062359612850504551739119887225712932688031120704657195642614071367390794e-01),
1715          BOOST_MATH_HUGE_CONSTANT(T, 0, 8.8256053579205268154311646253022559005668914714648423206832605312161626269519165572921583828573210485349058106849548e-01),
1716          BOOST_MATH_HUGE_CONSTANT(T, 0, 9.0557330769990779854652255892595831956897536366222841356404766397803760239449631913585074426842574155323901785046522e-01),
1717          BOOST_MATH_HUGE_CONSTANT(T, 0, 9.2620004742927432587932427708047400408647453682532906091103713367942299565110232681677288015055886244486106298320068e-01),
1718          BOOST_MATH_HUGE_CONSTANT(T, 0, 9.4437444474855997941583132403743912158564371496498093181748940139520917000657342753448871376849848523800667868447591e-01),
1719          BOOST_MATH_HUGE_CONSTANT(T, 0, 9.6002186496830751221687102558179766293035921740392339948566167242493995770706842922718944370380002378239172677454384e-01),
1720          BOOST_MATH_HUGE_CONSTANT(T, 0, 9.7311632250112626837469386842370688488763796428343933853755850185624118958166838288308561708261486365954975485787212e-01),
1721          BOOST_MATH_HUGE_CONSTANT(T, 0, 9.8366812327974720997003258160566280194031785470971136351718001015114429536479104370207597166035471368057762560137209e-01),
1722          BOOST_MATH_HUGE_CONSTANT(T, 0, 9.9163099687040459485862836610948572485050033374616325510019923349807489603260796605556191495843575227494654783755353e-01),
1723          BOOST_MATH_HUGE_CONSTANT(T, 0, 9.9689348407464954027163005091869528334088203811775079010809429780238769521016374081588201955806171741257405095963817e-01),
1724          BOOST_MATH_HUGE_CONSTANT(T, 0, 9.9948441005049063757132589570581081946887394701850801923632642830748016674843587830656468823145435723317885056396548e-01),
1725       };
1726       return data;
1727    }
1728    static  std::array<T, 31> const & weights()
1729    {
1730       static  std::array<T, 31> data = {
1731          BOOST_MATH_HUGE_CONSTANT(T, 0, 5.1494729429451567558340433647099307532736880396464168074637323362474083844397567724480716864880173808112573901197920e-02),
1732          BOOST_MATH_HUGE_CONSTANT(T, 0, 5.1426128537459025933862879215781259829552034862395987263855824172761589259406892072066110681184224608133314131500422e-02),
1733          BOOST_MATH_HUGE_CONSTANT(T, 0, 5.1221547849258772170656282604944208251146952425246327553509056805511015401279553971190412722969308620984161625812560e-02),
1734          BOOST_MATH_HUGE_CONSTANT(T, 0, 5.0881795898749606492297473049804691853384914260919239920771942080972542646780575571132056254070929858650733836163479e-02),
1735          BOOST_MATH_HUGE_CONSTANT(T, 0, 5.0405921402782346840893085653585028902197018251622233664243959211066713308635283713447747907973700791599900911248852e-02),
1736          BOOST_MATH_HUGE_CONSTANT(T, 0, 4.9795683427074206357811569379942328539209602813696108951047392842948482646220377655098341924089250200477846596263918e-02),
1737          BOOST_MATH_HUGE_CONSTANT(T, 0, 4.9055434555029778887528165367238173605887405295296569579490717901328215644590555247522873065246297467067324397612445e-02),
1738          BOOST_MATH_HUGE_CONSTANT(T, 0, 4.8185861757087129140779492298304592605799236108429800057373350872433793583969368428942672063270298939865425225579922e-02),
1739          BOOST_MATH_HUGE_CONSTANT(T, 0, 4.7185546569299153945261478181099486482884807300628457194141861551725533289490897029020276525603515502104799540544222e-02),
1740          BOOST_MATH_HUGE_CONSTANT(T, 0, 4.6059238271006988116271735559373580594692875571824924004732379492293604006446052672252973438978639166425766841417488e-02),
1741          BOOST_MATH_HUGE_CONSTANT(T, 0, 4.4814800133162663192355551616723243757431392796373009889680201194063503947907899189061064792111919040540351834527742e-02),
1742          BOOST_MATH_HUGE_CONSTANT(T, 0, 4.3452539701356069316831728117073258074603308631703168064888805495738640839573863333942084117196541456054957383622173e-02),
1743          BOOST_MATH_HUGE_CONSTANT(T, 0, 4.1969810215164246147147541285969757790088656718992374820388720323852655511200365790379948462006156953358103259681948e-02),
1744          BOOST_MATH_HUGE_CONSTANT(T, 0, 4.0374538951535959111995279752468114216126062126030255633998289613810846761059740961836828802959573901107306640876603e-02),
1745          BOOST_MATH_HUGE_CONSTANT(T, 0, 3.8678945624727592950348651532281050250923629821553846790376130679337402056620700554139109487533759557982632153728099e-02),
1746          BOOST_MATH_HUGE_CONSTANT(T, 0, 3.6882364651821229223911065617135967736955164781030337670005198584196134970154169862584193360751243227989492571664973e-02),
1747          BOOST_MATH_HUGE_CONSTANT(T, 0, 3.4979338028060024137499670731467875097226912794818719972208457232177786702008744219498470603846784465175225933802357e-02),
1748          BOOST_MATH_HUGE_CONSTANT(T, 0, 3.2981447057483726031814191016853927510599291213858385714519347641452316582381008804994515341969205985818543200837577e-02),
1749          BOOST_MATH_HUGE_CONSTANT(T, 0, 3.0907257562387762472884252943092272635270458523807153426840486964022086189874056947717446328187131273807982629114591e-02),
1750          BOOST_MATH_HUGE_CONSTANT(T, 0, 2.8754048765041292843978785354334211144679160542074930035102280759132174815469834227854660515366003136772757344886331e-02),
1751          BOOST_MATH_HUGE_CONSTANT(T, 0, 2.6509954882333101610601709335075414366517579522748565770867438338472138903658077617652522759934474895733739329287706e-02),
1752          BOOST_MATH_HUGE_CONSTANT(T, 0, 2.4191162078080601365686370725232026760391377828182462432228943562944885267501070688006470962871743661192935455117297e-02),
1753          BOOST_MATH_HUGE_CONSTANT(T, 0, 2.1828035821609192297167485738338993401507296056834912773630422358720439403382559079356058602393879803560534375378340e-02),
1754          BOOST_MATH_HUGE_CONSTANT(T, 0, 1.9414141193942381173408951050128455851421014191431525770276066536497179079025540486072726114628763606440143557769099e-02),
1755          BOOST_MATH_HUGE_CONSTANT(T, 0, 1.6920889189053272627572289420322092368566703783835191139883410840546679978551861043620089451681146020853650713611444e-02),
1756          BOOST_MATH_HUGE_CONSTANT(T, 0, 1.4369729507045804812451432443580010195841899895001505873565899403000198662495821906144274682894222591414503342336172e-02),
1757          BOOST_MATH_HUGE_CONSTANT(T, 0, 1.1823015253496341742232898853250592896264406250607818326302431548265365155855182739401700032519141448997853772603766e-02),
1758          BOOST_MATH_HUGE_CONSTANT(T, 0, 9.2732796595177634284411468920243604212700249381931076964956469143626665557434385492325784596343112153704094886248672e-03),
1759          BOOST_MATH_HUGE_CONSTANT(T, 0, 6.6307039159312921733198263697501681336283882177812585973955597357837568277731921327731815844512598157843672104469554e-03),
1760          BOOST_MATH_HUGE_CONSTANT(T, 0, 3.8904611270998840512672018445155032785151429848864649214200101281144733676455451061226273655941038347210163533085954e-03),
1761          BOOST_MATH_HUGE_CONSTANT(T, 0, 1.3890136986770076245515912267596996810488412919632724534411055332301367130989865366956251556423820479579333920310978e-03),
1762       };
1763       return data;
1764    }
1765 };
1766
1767 }
1768
1769 template <class Real, unsigned N, class Policy = boost::math::policies::policy<> >
1770 class gauss_kronrod : public detail::gauss_kronrod_detail<Real, N, detail::gauss_constant_category<Real>::value>
1771 {
1772    typedef detail::gauss_kronrod_detail<Real, N, detail::gauss_constant_category<Real>::value> base;
1773 public:
1774   typedef Real value_type;
1775 private:
1776    template <class F>
1777    static auto integrate_non_adaptive_m1_1(F f, Real* error = nullptr, Real* pL1 = nullptr)->decltype(std::declval<F>()(std::declval<Real>()))
1778    {
1779       typedef decltype(f(Real(0))) K;
1780       using std::abs;
1781       unsigned gauss_start = 2;
1782       unsigned kronrod_start = 1;
1783       unsigned gauss_order = (N - 1) / 2;
1784       K kronrod_result = 0;
1785       K gauss_result = 0;
1786       K fp, fm;
1787       if (gauss_order & 1)
1788       {
1789          fp = f(value_type(0));
1790          kronrod_result = fp * base::weights()[0];
1791          gauss_result += fp * gauss<Real, (N - 1) / 2>::weights()[0];
1792       }
1793       else
1794       {
1795          fp = f(value_type(0));
1796          kronrod_result = fp * base::weights()[0];
1797          gauss_start = 1;
1798          kronrod_start = 2;
1799       }
1800       Real L1 = abs(kronrod_result);
1801       for (unsigned i = gauss_start; i < base::abscissa().size(); i += 2)
1802       {
1803          fp = f(base::abscissa()[i]);
1804          fm = f(-base::abscissa()[i]);
1805          kronrod_result += (fp + fm) * base::weights()[i];
1806          L1 += (abs(fp) + abs(fm)) *  base::weights()[i];
1807          gauss_result += (fp + fm) * gauss<Real, (N - 1) / 2>::weights()[i / 2];
1808       }
1809       for (unsigned i = kronrod_start; i < base::abscissa().size(); i += 2)
1810       {
1811          fp = f(base::abscissa()[i]);
1812          fm = f(-base::abscissa()[i]);
1813          kronrod_result += (fp + fm) * base::weights()[i];
1814          L1 += (abs(fp) + abs(fm)) *  base::weights()[i];
1815       }
1816       if (pL1)
1817          *pL1 = L1;
1818       if (error)
1819          *error = (std::max)(static_cast<Real>(abs(kronrod_result - gauss_result)), static_cast<Real>(abs(kronrod_result * tools::epsilon<Real>() * Real(2))));
1820       return kronrod_result;
1821    }
1822
1823    template <class F>
1824    struct recursive_info
1825    {
1826       F f;
1827       Real tol;
1828    };
1829
1830    template <class F>
1831    static auto recursive_adaptive_integrate(const recursive_info<F>* info, Real a, Real b, unsigned max_levels, Real abs_tol, Real* error, Real* L1)->decltype(std::declval<F>()(std::declval<Real>()))
1832    {
1833       typedef decltype(info->f(Real(a))) K;
1834       using std::abs;
1835       Real error_local;
1836       Real mean = (b + a) / 2;
1837       Real scale = (b - a) / 2;
1838       auto ff = [&](const Real& x)->K
1839       {
1840          return info->f(scale * x + mean);
1841       };
1842       K r1 = integrate_non_adaptive_m1_1(ff, &error_local, L1);
1843       K estimate = scale * r1;
1844
1845       K tmp = estimate * info->tol;
1846       Real abs_tol1 = abs(tmp);
1847       if (abs_tol == 0)
1848          abs_tol = abs_tol1;
1849
1850       if (max_levels && (abs_tol1 < error_local) && (abs_tol < error_local))
1851       {
1852          Real mid = (a + b) / 2;
1853          Real L1_local;
1854          estimate = recursive_adaptive_integrate(info, a, mid, max_levels - 1, abs_tol / 2, error, L1);
1855          estimate += recursive_adaptive_integrate(info, mid, b, max_levels - 1, abs_tol / 2, &error_local, &L1_local);
1856          if (error)
1857             *error += error_local;
1858          if (L1)
1859             *L1 += L1_local;
1860          return estimate;
1861       }
1862       if(L1)
1863          *L1 *= scale;
1864       if (error)
1865          *error = error_local;
1866       return estimate;
1867    }
1868
1869 public:
1870    template <class F>
1871    static auto integrate(F f, Real a, Real b, unsigned max_depth = 15, Real tol = tools::root_epsilon<Real>(), Real* error = nullptr, Real* pL1 = nullptr)->decltype(std::declval<F>()(std::declval<Real>()))
1872    {
1873       typedef decltype(f(a)) K;
1874       static_assert(!std::is_integral<K>::value,
1875                   "The return type cannot be integral, it must be either a real or complex floating point type.");
1876       static const char* function = "boost::math::quadrature::gauss_kronrod<%1%>::integrate(f, %1%, %1%)";
1877       if (!(boost::math::isnan)(a) && !(boost::math::isnan)(b))
1878       {
1879          // Infinite limits:
1880          if ((a <= -tools::max_value<Real>()) && (b >= tools::max_value<Real>()))
1881          {
1882             auto u = [&](const Real& t)->K
1883             {
1884                Real t_sq = t*t;
1885                Real inv = 1 / (1 - t_sq);
1886                Real w = (1 + t_sq)*inv*inv;
1887                Real arg = t*inv;
1888                K res = f(arg)*w;
1889                return res;
1890             };
1891             recursive_info<decltype(u)> info = { u, tol };
1892             K res = recursive_adaptive_integrate(&info, Real(-1), Real(1), max_depth, Real(0), error, pL1);
1893             return res;
1894          }
1895
1896          // Right limit is infinite:
1897          if ((boost::math::isfinite)(a) && (b >= tools::max_value<Real>()))
1898          {
1899             auto u = [&](const Real& t)->K
1900             {
1901                Real z = 1 / (t + 1);
1902                Real arg = 2 * z + a - 1;
1903                K res = f(arg)*z*z;
1904                return res;
1905             };
1906             recursive_info<decltype(u)> info = { u, tol };
1907             K Q = Real(2) * recursive_adaptive_integrate(&info, Real(-1), Real(1), max_depth, Real(0), error, pL1);
1908             if (pL1)
1909             {
1910                *pL1 *= 2;
1911             }
1912             return Q;
1913          }
1914
1915          if ((boost::math::isfinite)(b) && (a <= -tools::max_value<Real>()))
1916          {
1917             auto v = [&](const Real& t)->K
1918             {
1919                Real z = 1 / (t + 1);
1920                Real arg = 2 * z - 1;
1921                return f(b - arg) * z * z;
1922             };
1923             recursive_info<decltype(v)> info = { v, tol };
1924             K Q = Real(2) * recursive_adaptive_integrate(&info, Real(-1), Real(1), max_depth, Real(0), error, pL1);
1925             if (pL1)
1926             {
1927                *pL1 *= 2;
1928             }
1929             return Q;
1930          }
1931
1932          if ((boost::math::isfinite)(a) && (boost::math::isfinite)(b))
1933          {
1934             if (a==b)
1935             {
1936                return K(0);
1937             }
1938             recursive_info<F> info = { f, tol };
1939             if (b < a)
1940             {
1941                return -recursive_adaptive_integrate(&info, b, a, max_depth, Real(0), error, pL1);
1942             }
1943             return recursive_adaptive_integrate(&info, a, b, max_depth, Real(0), error, pL1);
1944          }
1945       }
1946       return static_cast<K>(policies::raise_domain_error(function, "The domain of integration is not sensible; please check the bounds.", a, Policy()));
1947    }
1948 };
1949
1950 } // namespace quadrature
1951 } // namespace math
1952 } // namespace boost
1953
1954 #ifdef _MSC_VER
1955 #pragma warning(pop)
1956 #endif
1957
1958 #endif // BOOST_MATH_QUADRATURE_GAUSS_KRONROD_HPP