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1// Copyright John Maddock 2017.2// Copyright Nick Thompson 2017.3// Use, modification and distribution are subject to the4// Boost Software License, Version 1.0. (See accompanying file5// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)6 7#ifndef BOOST_MATH_QUADRATURE_GAUSS_KRONROD_HPP8#define BOOST_MATH_QUADRATURE_GAUSS_KRONROD_HPP9 10#ifdef _MSC_VER11#pragma once12#pragma warning(push)13#pragma warning(disable: 4127)14#endif15 16#include <array>17#include <vector>18#include <algorithm>19#include <boost/math/special_functions/legendre.hpp>20#include <boost/math/special_functions/legendre_stieltjes.hpp>21#include <boost/math/quadrature/gauss.hpp>22 23namespace boost { namespace math{ namespace quadrature{ namespace detail{24 25#ifndef BOOST_MATH_GAUSS_NO_COMPUTE_ON_DEMAND26 27template <class Real, unsigned N, unsigned tag>28class gauss_kronrod_detail29{30 static legendre_stieltjes<Real> const& get_legendre_stieltjes()31 {32 static const legendre_stieltjes<Real> data((N - 1) / 2 + 1);33 return data;34 }35 static std::vector<Real> calculate_abscissa()36 {37 static std::vector<Real> result = boost::math::legendre_p_zeros<Real>((N - 1) / 2);38 const legendre_stieltjes<Real> E = get_legendre_stieltjes();39 std::vector<Real> ls_zeros = E.zeros();40 result.insert(result.end(), ls_zeros.begin(), ls_zeros.end());41 std::sort(result.begin(), result.end());42 return result;43 }44 static std::vector<Real> calculate_weights()45 {46 std::vector<Real> result(abscissa().size(), 0);47 unsigned gauss_order = (N - 1) / 2;48 unsigned gauss_start = gauss_order & 1 ? 0 : 1;49 const legendre_stieltjes<Real>& E = get_legendre_stieltjes();50 51 for (unsigned i = gauss_start; i < abscissa().size(); i += 2)52 {53 Real x = abscissa()[i];54 Real p = boost::math::legendre_p_prime(gauss_order, x);55 Real gauss_weight = 2 / ((1 - x * x) * p * p);56 result[i] = gauss_weight + static_cast<Real>(2) / (static_cast<Real>(gauss_order + 1) * legendre_p_prime(gauss_order, x) * E(x));57 }58 for (unsigned i = gauss_start ? 0 : 1; i < abscissa().size(); i += 2)59 {60 Real x = abscissa()[i];61 result[i] = static_cast<Real>(2) / (static_cast<Real>(gauss_order + 1) * legendre_p(gauss_order, x) * E.prime(x));62 }63 return result;64 }65public:66 static const std::vector<Real>& abscissa()67 {68 static std::vector<Real> data = calculate_abscissa();69 return data;70 }71 static const std::vector<Real>& weights()72 {73 static std::vector<Real> data = calculate_weights();74 return data;75 }76};77 78#else79 80template <class Real, unsigned N, unsigned tag>81class gauss_kronrod_detail;82 83#endif84 85#ifndef BOOST_HAS_FLOAT12886template <class T>87class gauss_kronrod_detail<T, 15, 0>88{89 using storage_type = typename gauss_constant_category<T>::storage_type;90public:91 static std::array<storage_type, 8> const & abscissa()92 {93 static constexpr std::array<storage_type, 8> data = {94 static_cast<storage_type>(0.00000000000000000000000000000000000e+00L),95 static_cast<storage_type>(2.07784955007898467600689403773244913e-01L),96 static_cast<storage_type>(4.05845151377397166906606412076961463e-01L),97 static_cast<storage_type>(5.86087235467691130294144838258729598e-01L),98 static_cast<storage_type>(7.41531185599394439863864773280788407e-01L),99 static_cast<storage_type>(8.64864423359769072789712788640926201e-01L),100 static_cast<storage_type>(9.49107912342758524526189684047851262e-01L),101 static_cast<storage_type>(9.91455371120812639206854697526328517e-01L),102 };103 return data;104 }105 static std::array<storage_type, 8> const & weights()106 {107 static constexpr std::array<storage_type, 8> data = {108 static_cast<storage_type>(2.09482141084727828012999174891714264e-01L),109 static_cast<storage_type>(2.04432940075298892414161999234649085e-01L),110 static_cast<storage_type>(1.90350578064785409913256402421013683e-01L),111 static_cast<storage_type>(1.69004726639267902826583426598550284e-01L),112 static_cast<storage_type>(1.40653259715525918745189590510237920e-01L),113 static_cast<storage_type>(1.04790010322250183839876322541518017e-01L),114 static_cast<storage_type>(6.30920926299785532907006631892042867e-02L),115 static_cast<storage_type>(2.29353220105292249637320080589695920e-02L),116 };117 return data;118 }119};120 121#else122template <class T>123class gauss_kronrod_detail<T, 15, 0>124{125 using storage_type = typename gauss_constant_category<T>::storage_type;126public:127 static std::array<storage_type, 8> const & abscissa()128 {129 static const std::array<storage_type, 8> data = {130 static_cast<storage_type>(0.00000000000000000000000000000000000e+00Q),131 static_cast<storage_type>(2.07784955007898467600689403773244913e-01Q),132 static_cast<storage_type>(4.05845151377397166906606412076961463e-01Q),133 static_cast<storage_type>(5.86087235467691130294144838258729598e-01Q),134 static_cast<storage_type>(7.41531185599394439863864773280788407e-01Q),135 static_cast<storage_type>(8.64864423359769072789712788640926201e-01Q),136 static_cast<storage_type>(9.49107912342758524526189684047851262e-01Q),137 static_cast<storage_type>(9.91455371120812639206854697526328517e-01Q),138 };139 return data;140 }141 static std::array<storage_type, 8> const & weights()142 {143 static const std::array<storage_type, 8> data = {144 static_cast<storage_type>(2.09482141084727828012999174891714264e-01Q),145 static_cast<storage_type>(2.04432940075298892414161999234649085e-01Q),146 static_cast<storage_type>(1.90350578064785409913256402421013683e-01Q),147 static_cast<storage_type>(1.69004726639267902826583426598550284e-01Q),148 static_cast<storage_type>(1.40653259715525918745189590510237920e-01Q),149 static_cast<storage_type>(1.04790010322250183839876322541518017e-01Q),150 static_cast<storage_type>(6.30920926299785532907006631892042867e-02Q),151 static_cast<storage_type>(2.29353220105292249637320080589695920e-02Q),152 };153 return data;154 }155};156#endif157 158template <class T>159class gauss_kronrod_detail<T, 15, 4>160{161public:162 static std::array<T, 8> const & abscissa()163 {164 static std::array<T, 8> data = { // LCOV_EXCL_START165 BOOST_MATH_HUGE_CONSTANT(T, 0, 0.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+00),166 BOOST_MATH_HUGE_CONSTANT(T, 0, 2.0778495500789846760068940377324491347978440714517064971384573461986693844943520226910343227183698530560857645062738e-01),167 BOOST_MATH_HUGE_CONSTANT(T, 0, 4.0584515137739716690660641207696146334738201409937012638704325179466381322612565532831268972774658776528675866604802e-01),168 BOOST_MATH_HUGE_CONSTANT(T, 0, 5.8608723546769113029414483825872959843678075060436095130499289319880373607444407464511674498935942098956811555121368e-01),169 BOOST_MATH_HUGE_CONSTANT(T, 0, 7.4153118559939443986386477328078840707414764714139026011995535196742987467218051379282683236686324705969251809311201e-01),170 BOOST_MATH_HUGE_CONSTANT(T, 0, 8.6486442335976907278971278864092620121097230707408814860145771276706770813259572103585847859604590541475281326027862e-01),171 BOOST_MATH_HUGE_CONSTANT(T, 0, 9.4910791234275852452618968404785126240077093767061778354876910391306333035484014080573077002792572414430073966699522e-01),172 BOOST_MATH_HUGE_CONSTANT(T, 0, 9.9145537112081263920685469752632851664204433837033470129108741357244173934653407235924503509626841760744349505339308e-01),173 }; // LCOV_EXCL_STOP174 return data;175 }176 static std::array<T, 8> const & weights()177 {178 static std::array<T, 8> data = { // LCOV_EXCL_START179 BOOST_MATH_HUGE_CONSTANT(T, 0, 2.0948214108472782801299917489171426369776208022370431671299800656137515132325648616816908211675949102392971459688215e-01),180 BOOST_MATH_HUGE_CONSTANT(T, 0, 2.0443294007529889241416199923464908471651760418071835742447095312045467698546598879348374292009347554167803659293064e-01),181 BOOST_MATH_HUGE_CONSTANT(T, 0, 1.9035057806478540991325640242101368282607807545535835588544088036744058072410212679605964605106377593834568683551139e-01),182 BOOST_MATH_HUGE_CONSTANT(T, 0, 1.6900472663926790282658342659855028410624490030294424149734006755695680921619029112936702403855359908156070095656537e-01),183 BOOST_MATH_HUGE_CONSTANT(T, 0, 1.4065325971552591874518959051023792039988975724799857556174546893312708093090950408097379122415555910759700350860143e-01),184 BOOST_MATH_HUGE_CONSTANT(T, 0, 1.0479001032225018383987632254151801744375665421383061189339065133963746321576289524167571627509311333949422518201492e-01),185 BOOST_MATH_HUGE_CONSTANT(T, 0, 6.3092092629978553290700663189204286665071157211550707113605545146983997477964874928199170264504441995865872491871943e-02),186 BOOST_MATH_HUGE_CONSTANT(T, 0, 2.2935322010529224963732008058969591993560811275746992267507430254711815787976075946156368168156289483493617134063245e-02),187 }; // LCOV_EXCL_STOP188 return data;189 }190};191 192 193#ifndef BOOST_HAS_FLOAT128194template <class T>195class gauss_kronrod_detail<T, 21, 0>196{197 using storage_type = typename gauss_constant_category<T>::storage_type;198public:199 static std::array<storage_type, 11> const & abscissa()200 {201 static constexpr std::array<storage_type, 11> data = {202 static_cast<storage_type>(0.00000000000000000000000000000000000e+00L),203 static_cast<storage_type>(1.48874338981631210884826001129719985e-01L),204 static_cast<storage_type>(2.94392862701460198131126603103865566e-01L),205 static_cast<storage_type>(4.33395394129247190799265943165784162e-01L),206 static_cast<storage_type>(5.62757134668604683339000099272694141e-01L),207 static_cast<storage_type>(6.79409568299024406234327365114873576e-01L),208 static_cast<storage_type>(7.80817726586416897063717578345042377e-01L),209 static_cast<storage_type>(8.65063366688984510732096688423493049e-01L),210 static_cast<storage_type>(9.30157491355708226001207180059508346e-01L),211 static_cast<storage_type>(9.73906528517171720077964012084452053e-01L),212 static_cast<storage_type>(9.95657163025808080735527280689002848e-01L),213 };214 return data;215 }216 static std::array<storage_type, 11> const & weights()217 {218 static constexpr std::array<storage_type, 11> data = {219 static_cast<storage_type>(1.49445554002916905664936468389821204e-01L),220 static_cast<storage_type>(1.47739104901338491374841515972068046e-01L),221 static_cast<storage_type>(1.42775938577060080797094273138717061e-01L),222 static_cast<storage_type>(1.34709217311473325928054001771706833e-01L),223 static_cast<storage_type>(1.23491976262065851077958109831074160e-01L),224 static_cast<storage_type>(1.09387158802297641899210590325804960e-01L),225 static_cast<storage_type>(9.31254545836976055350654650833663444e-02L),226 static_cast<storage_type>(7.50396748109199527670431409161900094e-02L),227 static_cast<storage_type>(5.47558965743519960313813002445801764e-02L),228 static_cast<storage_type>(3.25581623079647274788189724593897606e-02L),229 static_cast<storage_type>(1.16946388673718742780643960621920484e-02L),230 };231 return data;232 }233};234 235#else236template <class T>237class gauss_kronrod_detail<T, 21, 0>238{239 using storage_type = typename gauss_constant_category<T>::storage_type;240public:241 static std::array<storage_type, 11> const & abscissa()242 {243 static const std::array<storage_type, 11> data = {244 static_cast<storage_type>(0.00000000000000000000000000000000000e+00Q),245 static_cast<storage_type>(1.48874338981631210884826001129719985e-01Q),246 static_cast<storage_type>(2.94392862701460198131126603103865566e-01Q),247 static_cast<storage_type>(4.33395394129247190799265943165784162e-01Q),248 static_cast<storage_type>(5.62757134668604683339000099272694141e-01Q),249 static_cast<storage_type>(6.79409568299024406234327365114873576e-01Q),250 static_cast<storage_type>(7.80817726586416897063717578345042377e-01Q),251 static_cast<storage_type>(8.65063366688984510732096688423493049e-01Q),252 static_cast<storage_type>(9.30157491355708226001207180059508346e-01Q),253 static_cast<storage_type>(9.73906528517171720077964012084452053e-01Q),254 static_cast<storage_type>(9.95657163025808080735527280689002848e-01Q),255 };256 return data;257 }258 static std::array<storage_type, 11> const & weights()259 {260 static const std::array<storage_type, 11> data = {261 static_cast<storage_type>(1.49445554002916905664936468389821204e-01Q),262 static_cast<storage_type>(1.47739104901338491374841515972068046e-01Q),263 static_cast<storage_type>(1.42775938577060080797094273138717061e-01Q),264 static_cast<storage_type>(1.34709217311473325928054001771706833e-01Q),265 static_cast<storage_type>(1.23491976262065851077958109831074160e-01Q),266 static_cast<storage_type>(1.09387158802297641899210590325804960e-01Q),267 static_cast<storage_type>(9.31254545836976055350654650833663444e-02Q),268 static_cast<storage_type>(7.50396748109199527670431409161900094e-02Q),269 static_cast<storage_type>(5.47558965743519960313813002445801764e-02Q),270 static_cast<storage_type>(3.25581623079647274788189724593897606e-02Q),271 static_cast<storage_type>(1.16946388673718742780643960621920484e-02Q),272 };273 return data;274 }275};276#endif277 278template <class T>279class gauss_kronrod_detail<T, 21, 4>280{281public:282 static std::array<T, 11> const & abscissa()283 {284 static std::array<T, 11> data = { // LCOV_EXCL_START285 BOOST_MATH_HUGE_CONSTANT(T, 0, 0.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+00),286 BOOST_MATH_HUGE_CONSTANT(T, 0, 1.4887433898163121088482600112971998461756485942069169570798925351590361735566852137117762979946369123003116080525534e-01),287 BOOST_MATH_HUGE_CONSTANT(T, 0, 2.9439286270146019813112660310386556616268662515695791864888229172724611166332737888445523178268237359119185139299872e-01),288 BOOST_MATH_HUGE_CONSTANT(T, 0, 4.3339539412924719079926594316578416220007183765624649650270151314376698907770350122510275795011772122368293504099894e-01),289 BOOST_MATH_HUGE_CONSTANT(T, 0, 5.6275713466860468333900009927269414084301388194196695886034621458779266353216327549712087854169992422106448211158815e-01),290 BOOST_MATH_HUGE_CONSTANT(T, 0, 6.7940956829902440623432736511487357576929471183480946766481718895255857539507492461507857357048037949983390204739932e-01),291 BOOST_MATH_HUGE_CONSTANT(T, 0, 7.8081772658641689706371757834504237716340752029815717974694859999505607982761420654526977234238996241110129779403362e-01),292 BOOST_MATH_HUGE_CONSTANT(T, 0, 8.6506336668898451073209668842349304852754301496533045252195973184537475513805556135679072894604577069440463108641177e-01),293 BOOST_MATH_HUGE_CONSTANT(T, 0, 9.3015749135570822600120718005950834622516790998193924230349406866828415983091673055011194572851007884702013619684320e-01),294 BOOST_MATH_HUGE_CONSTANT(T, 0, 9.7390652851717172007796401208445205342826994669238211923121206669659520323463615962572356495626855625823304251877421e-01),295 BOOST_MATH_HUGE_CONSTANT(T, 0, 9.9565716302580808073552728068900284792126058721947892436337916111757023046774867357152325996912076724298149077812671e-01),296 }; // LCOV_EXCL_STOP297 return data;298 }299 static std::array<T, 11> const & weights()300 {301 static std::array<T, 11> data = { // LCOV_EXCL_START302 BOOST_MATH_HUGE_CONSTANT(T, 0, 1.4944555400291690566493646838982120374523631668747280383560851873698964478511841925721030705689540264726493367634340e-01),303 BOOST_MATH_HUGE_CONSTANT(T, 0, 1.4773910490133849137484151597206804552373162548520660451819195439885993016735696405732703959182882254268727823258502e-01),304 BOOST_MATH_HUGE_CONSTANT(T, 0, 1.4277593857706008079709427313871706088597905653190555560741004743970770449909340027811131706283756428281146832304737e-01),305 BOOST_MATH_HUGE_CONSTANT(T, 0, 1.3470921731147332592805400177170683276099191300855971406636668491320291400121282036676953159488271772384389604997640e-01),306 BOOST_MATH_HUGE_CONSTANT(T, 0, 1.2349197626206585107795810983107415951230034952864832764467994120974054238975454689681538622363738230836484113389878e-01),307 BOOST_MATH_HUGE_CONSTANT(T, 0, 1.0938715880229764189921059032580496027181329983434522007819675829826550372891432168683899432674553842507906611591517e-01),308 BOOST_MATH_HUGE_CONSTANT(T, 0, 9.3125454583697605535065465083366344390018828880760031970085038760177735672200775237414123061615827474831165614953012e-02),309 BOOST_MATH_HUGE_CONSTANT(T, 0, 7.5039674810919952767043140916190009395219382000910088173697048048430404342858495178813808730646554086856929327903059e-02),310 BOOST_MATH_HUGE_CONSTANT(T, 0, 5.4755896574351996031381300244580176373721114058333557524432615804784098927818975325116301569003298086458722055550981e-02),311 BOOST_MATH_HUGE_CONSTANT(T, 0, 3.2558162307964727478818972459389760617388939845662609571537504232714121820165498692381607605384626494546068817765276e-02),312 BOOST_MATH_HUGE_CONSTANT(T, 0, 1.1694638867371874278064396062192048396217332481931888927598147525622222058064992651806736704969967250888097490233242e-02),313 }; // LCOV_EXCL_STOP314 return data;315 }316};317 318 319#ifndef BOOST_HAS_FLOAT128320template <class T>321class gauss_kronrod_detail<T, 31, 0>322{323 using storage_type = typename gauss_constant_category<T>::storage_type;324public:325 static std::array<storage_type, 16> const & abscissa()326 {327 static constexpr std::array<storage_type, 16> data = {328 static_cast<storage_type>(0.00000000000000000000000000000000000e+00L),329 static_cast<storage_type>(1.01142066918717499027074231447392339e-01L),330 static_cast<storage_type>(2.01194093997434522300628303394596208e-01L),331 static_cast<storage_type>(2.99180007153168812166780024266388963e-01L),332 static_cast<storage_type>(3.94151347077563369897207370981045468e-01L),333 static_cast<storage_type>(4.85081863640239680693655740232350613e-01L),334 static_cast<storage_type>(5.70972172608538847537226737253910641e-01L),335 static_cast<storage_type>(6.50996741297416970533735895313274693e-01L),336 static_cast<storage_type>(7.24417731360170047416186054613938010e-01L),337 static_cast<storage_type>(7.90418501442465932967649294817947347e-01L),338 static_cast<storage_type>(8.48206583410427216200648320774216851e-01L),339 static_cast<storage_type>(8.97264532344081900882509656454495883e-01L),340 static_cast<storage_type>(9.37273392400705904307758947710209471e-01L),341 static_cast<storage_type>(9.67739075679139134257347978784337225e-01L),342 static_cast<storage_type>(9.87992518020485428489565718586612581e-01L),343 static_cast<storage_type>(9.98002298693397060285172840152271209e-01L),344 };345 return data;346 }347 static std::array<storage_type, 16> const & weights()348 {349 static constexpr std::array<storage_type, 16> data = {350 static_cast<storage_type>(1.01330007014791549017374792767492547e-01L),351 static_cast<storage_type>(1.00769845523875595044946662617569722e-01L),352 static_cast<storage_type>(9.91735987217919593323931734846031311e-02L),353 static_cast<storage_type>(9.66427269836236785051799076275893351e-02L),354 static_cast<storage_type>(9.31265981708253212254868727473457186e-02L),355 static_cast<storage_type>(8.85644430562117706472754436937743032e-02L),356 static_cast<storage_type>(8.30805028231330210382892472861037896e-02L),357 static_cast<storage_type>(7.68496807577203788944327774826590067e-02L),358 static_cast<storage_type>(6.98541213187282587095200770991474758e-02L),359 static_cast<storage_type>(6.20095678006706402851392309608029322e-02L),360 static_cast<storage_type>(5.34815246909280872653431472394302968e-02L),361 static_cast<storage_type>(4.45897513247648766082272993732796902e-02L),362 static_cast<storage_type>(3.53463607913758462220379484783600481e-02L),363 static_cast<storage_type>(2.54608473267153201868740010196533594e-02L),364 static_cast<storage_type>(1.50079473293161225383747630758072681e-02L),365 static_cast<storage_type>(5.37747987292334898779205143012764982e-03L),366 };367 return data;368 }369};370 371#else372 373template <class T>374class gauss_kronrod_detail<T, 31, 0>375{376 using storage_type = typename gauss_constant_category<T>::storage_type;377public:378 static std::array<storage_type, 16> const & abscissa()379 {380 static const std::array<storage_type, 16> data = {381 static_cast<storage_type>(0.00000000000000000000000000000000000e+00Q),382 static_cast<storage_type>(1.01142066918717499027074231447392339e-01Q),383 static_cast<storage_type>(2.01194093997434522300628303394596208e-01Q),384 static_cast<storage_type>(2.99180007153168812166780024266388963e-01Q),385 static_cast<storage_type>(3.94151347077563369897207370981045468e-01Q),386 static_cast<storage_type>(4.85081863640239680693655740232350613e-01Q),387 static_cast<storage_type>(5.70972172608538847537226737253910641e-01Q),388 static_cast<storage_type>(6.50996741297416970533735895313274693e-01Q),389 static_cast<storage_type>(7.24417731360170047416186054613938010e-01Q),390 static_cast<storage_type>(7.90418501442465932967649294817947347e-01Q),391 static_cast<storage_type>(8.48206583410427216200648320774216851e-01Q),392 static_cast<storage_type>(8.97264532344081900882509656454495883e-01Q),393 static_cast<storage_type>(9.37273392400705904307758947710209471e-01Q),394 static_cast<storage_type>(9.67739075679139134257347978784337225e-01Q),395 static_cast<storage_type>(9.87992518020485428489565718586612581e-01Q),396 static_cast<storage_type>(9.98002298693397060285172840152271209e-01Q),397 };398 return data;399 }400 static std::array<storage_type, 16> const & weights()401 {402 static const std::array<storage_type, 16> data = {403 static_cast<storage_type>(1.01330007014791549017374792767492547e-01Q),404 static_cast<storage_type>(1.00769845523875595044946662617569722e-01Q),405 static_cast<storage_type>(9.91735987217919593323931734846031311e-02Q),406 static_cast<storage_type>(9.66427269836236785051799076275893351e-02Q),407 static_cast<storage_type>(9.31265981708253212254868727473457186e-02Q),408 static_cast<storage_type>(8.85644430562117706472754436937743032e-02Q),409 static_cast<storage_type>(8.30805028231330210382892472861037896e-02Q),410 static_cast<storage_type>(7.68496807577203788944327774826590067e-02Q),411 static_cast<storage_type>(6.98541213187282587095200770991474758e-02Q),412 static_cast<storage_type>(6.20095678006706402851392309608029322e-02Q),413 static_cast<storage_type>(5.34815246909280872653431472394302968e-02Q),414 static_cast<storage_type>(4.45897513247648766082272993732796902e-02Q),415 static_cast<storage_type>(3.53463607913758462220379484783600481e-02Q),416 static_cast<storage_type>(2.54608473267153201868740010196533594e-02Q),417 static_cast<storage_type>(1.50079473293161225383747630758072681e-02Q),418 static_cast<storage_type>(5.37747987292334898779205143012764982e-03Q),419 };420 return data;421 }422};423#endif424 425template <class T>426class gauss_kronrod_detail<T, 31, 4>427{428public:429 static std::array<T, 16> const & abscissa()430 {431 static std::array<T, 16> data = { // LCOV_EXCL_START432 BOOST_MATH_HUGE_CONSTANT(T, 0, 0.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+00),433 BOOST_MATH_HUGE_CONSTANT(T, 0, 1.0114206691871749902707423144739233878745105740164180495800189504151097862454083050931321451540380998341273193681967e-01),434 BOOST_MATH_HUGE_CONSTANT(T, 0, 2.0119409399743452230062830339459620781283645446263767961594972460994823900302018760183625806752105908967902257386509e-01),435 BOOST_MATH_HUGE_CONSTANT(T, 0, 2.9918000715316881216678002426638896266160338274382080184125545738918081102513884467602322020157243563662094470221235e-01),436 BOOST_MATH_HUGE_CONSTANT(T, 0, 3.9415134707756336989720737098104546836275277615869825503116534395160895778696141797549711416165976202589352169635648e-01),437 BOOST_MATH_HUGE_CONSTANT(T, 0, 4.8508186364023968069365574023235061286633893089407312129367943604080239955167155974371848690848595275551258416303565e-01),438 BOOST_MATH_HUGE_CONSTANT(T, 0, 5.7097217260853884753722673725391064123838639628274960485326541705419537986975857948341462856982614477912646497026257e-01),439 BOOST_MATH_HUGE_CONSTANT(T, 0, 6.5099674129741697053373589531327469254694822609259966708966160576093305841043840794460394747228060367236079289132544e-01),440 BOOST_MATH_HUGE_CONSTANT(T, 0, 7.2441773136017004741618605461393800963089929458410256355142342070412378167792521899610109760313432626923598549381925e-01),441 BOOST_MATH_HUGE_CONSTANT(T, 0, 7.9041850144246593296764929481794734686214051995697617332365280643308302974631807059994738664225445530963711137343440e-01),442 BOOST_MATH_HUGE_CONSTANT(T, 0, 8.4820658341042721620064832077421685136625617473699263409572755876067507517414548519760771975082148085090373835713340e-01),443 BOOST_MATH_HUGE_CONSTANT(T, 0, 8.9726453234408190088250965645449588283177871149442786763972687601078537721473771221195399661919716123038835639691946e-01),444 BOOST_MATH_HUGE_CONSTANT(T, 0, 9.3727339240070590430775894771020947124399627351530445790136307635020297379704552795054758617426808659746824044603157e-01),445 BOOST_MATH_HUGE_CONSTANT(T, 0, 9.6773907567913913425734797878433722528335733730013163797468062226335804249452174804319385048203118506304424717089291e-01),446 BOOST_MATH_HUGE_CONSTANT(T, 0, 9.8799251802048542848956571858661258114697281712376148999999751558738843736901942471272205036831914497667516843990079e-01),447 BOOST_MATH_HUGE_CONSTANT(T, 0, 9.9800229869339706028517284015227120907340644231555723034839427970683348682837134566648979907760125278631896777136104e-01),448 }; // LCOV_EXCL_STOP449 return data;450 }451 static std::array<T, 16> const & weights()452 {453 static std::array<T, 16> data = { // LCOV_EXCL_START454 BOOST_MATH_HUGE_CONSTANT(T, 0, 1.0133000701479154901737479276749254677092627259659629246734858372174107615774696665932418050683956749891773195816338e-01),455 BOOST_MATH_HUGE_CONSTANT(T, 0, 1.0076984552387559504494666261756972191634838013536373069278929029488122760822761077475060185965408326901925180106227e-01),456 BOOST_MATH_HUGE_CONSTANT(T, 0, 9.9173598721791959332393173484603131059567260816713281734860095693651563064308745717056680128223790739026832596087552e-02),457 BOOST_MATH_HUGE_CONSTANT(T, 0, 9.6642726983623678505179907627589335136656568630495198973407668882934392359962841826511402504664592185391687490319950e-02),458 BOOST_MATH_HUGE_CONSTANT(T, 0, 9.3126598170825321225486872747345718561927881321317330560285879189052002874531855060114908990458716740695847509343865e-02),459 BOOST_MATH_HUGE_CONSTANT(T, 0, 8.8564443056211770647275443693774303212266732690655967817996052574877144544749814260718837576325109922207832119243346e-02),460 BOOST_MATH_HUGE_CONSTANT(T, 0, 8.3080502823133021038289247286103789601554188253368717607281604875233630643885056057630789228337088859687986285569521e-02),461 BOOST_MATH_HUGE_CONSTANT(T, 0, 7.6849680757720378894432777482659006722109101167947000584089097112470821092034084418224731527690291913686588446455555e-02),462 BOOST_MATH_HUGE_CONSTANT(T, 0, 6.9854121318728258709520077099147475786045435140671549698798093177992675624987998849748628778570667518643649536771245e-02),463 BOOST_MATH_HUGE_CONSTANT(T, 0, 6.2009567800670640285139230960802932190400004210329723569147829395618376206272317333030584268303808639229575334680414e-02),464 BOOST_MATH_HUGE_CONSTANT(T, 0, 5.3481524690928087265343147239430296771554760947116739813222888752727413616259625439714812475198987513183153639571249e-02),465 BOOST_MATH_HUGE_CONSTANT(T, 0, 4.4589751324764876608227299373279690223256649667921096570980823211805450700059906366455036418897149593261561551176267e-02),466 BOOST_MATH_HUGE_CONSTANT(T, 0, 3.5346360791375846222037948478360048122630678992420820868148023340902501837247680978434662724296810081131106317333086e-02),467 BOOST_MATH_HUGE_CONSTANT(T, 0, 2.5460847326715320186874001019653359397271745046864640508377984982400903447009185267605205778819712848080691366407461e-02),468 BOOST_MATH_HUGE_CONSTANT(T, 0, 1.5007947329316122538374763075807268094639436437387634979291759700896494746154334398961710227490402528151677469993935e-02),469 BOOST_MATH_HUGE_CONSTANT(T, 0, 5.3774798729233489877920514301276498183080402431284197876486169536848635554354599213793172596490038991436925569025913e-03),470 }; // LCOV_EXCL_STOP471 return data;472 }473};474 475#ifndef BOOST_HAS_FLOAT128476 477template <class T>478class gauss_kronrod_detail<T, 41, 0>479{480 using storage_type = typename gauss_constant_category<T>::storage_type;481public:482 static std::array<storage_type, 21> const & abscissa()483 {484 static constexpr std::array<storage_type, 21> data = {485 static_cast<storage_type>(0.00000000000000000000000000000000000e+00L),486 static_cast<storage_type>(7.65265211334973337546404093988382110e-02L),487 static_cast<storage_type>(1.52605465240922675505220241022677528e-01L),488 static_cast<storage_type>(2.27785851141645078080496195368574625e-01L),489 static_cast<storage_type>(3.01627868114913004320555356858592261e-01L),490 static_cast<storage_type>(3.73706088715419560672548177024927237e-01L),491 static_cast<storage_type>(4.43593175238725103199992213492640108e-01L),492 static_cast<storage_type>(5.10867001950827098004364050955250998e-01L),493 static_cast<storage_type>(5.75140446819710315342946036586425133e-01L),494 static_cast<storage_type>(6.36053680726515025452836696226285937e-01L),495 static_cast<storage_type>(6.93237656334751384805490711845931533e-01L),496 static_cast<storage_type>(7.46331906460150792614305070355641590e-01L),497 static_cast<storage_type>(7.95041428837551198350638833272787943e-01L),498 static_cast<storage_type>(8.39116971822218823394529061701520685e-01L),499 static_cast<storage_type>(8.78276811252281976077442995113078467e-01L),500 static_cast<storage_type>(9.12234428251325905867752441203298113e-01L),501 static_cast<storage_type>(9.40822633831754753519982722212443380e-01L),502 static_cast<storage_type>(9.63971927277913791267666131197277222e-01L),503 static_cast<storage_type>(9.81507877450250259193342994720216945e-01L),504 static_cast<storage_type>(9.93128599185094924786122388471320278e-01L),505 static_cast<storage_type>(9.98859031588277663838315576545863010e-01L),506 };507 return data;508 }509 static std::array<storage_type, 21> const & weights()510 {511 static constexpr std::array<storage_type, 21> data = {512 static_cast<storage_type>(7.66007119179996564450499015301017408e-02L),513 static_cast<storage_type>(7.63778676720807367055028350380610018e-02L),514 static_cast<storage_type>(7.57044976845566746595427753766165583e-02L),515 static_cast<storage_type>(7.45828754004991889865814183624875286e-02L),516 static_cast<storage_type>(7.30306903327866674951894176589131128e-02L),517 static_cast<storage_type>(7.10544235534440683057903617232101674e-02L),518 static_cast<storage_type>(6.86486729285216193456234118853678017e-02L),519 static_cast<storage_type>(6.58345971336184221115635569693979431e-02L),520 static_cast<storage_type>(6.26532375547811680258701221742549806e-02L),521 static_cast<storage_type>(5.91114008806395723749672206485942171e-02L),522 static_cast<storage_type>(5.51951053482859947448323724197773292e-02L),523 static_cast<storage_type>(5.09445739237286919327076700503449487e-02L),524 static_cast<storage_type>(4.64348218674976747202318809261075168e-02L),525 static_cast<storage_type>(4.16688733279736862637883059368947380e-02L),526 static_cast<storage_type>(3.66001697582007980305572407072110085e-02L),527 static_cast<storage_type>(3.12873067770327989585431193238007379e-02L),528 static_cast<storage_type>(2.58821336049511588345050670961531430e-02L),529 static_cast<storage_type>(2.03883734612665235980102314327547051e-02L),530 static_cast<storage_type>(1.46261692569712529837879603088683562e-02L),531 static_cast<storage_type>(8.60026985564294219866178795010234725e-03L),532 static_cast<storage_type>(3.07358371852053150121829324603098749e-03L),533 };534 return data;535 }536};537 538#else539 540template <class T>541class gauss_kronrod_detail<T, 41, 0>542{543 using storage_type = typename gauss_constant_category<T>::storage_type;544public:545 static std::array<storage_type, 21> const & abscissa()546 {547 static const std::array<storage_type, 21> data = {548 static_cast<storage_type>(0.00000000000000000000000000000000000e+00Q),549 static_cast<storage_type>(7.65265211334973337546404093988382110e-02Q),550 static_cast<storage_type>(1.52605465240922675505220241022677528e-01Q),551 static_cast<storage_type>(2.27785851141645078080496195368574625e-01Q),552 static_cast<storage_type>(3.01627868114913004320555356858592261e-01Q),553 static_cast<storage_type>(3.73706088715419560672548177024927237e-01Q),554 static_cast<storage_type>(4.43593175238725103199992213492640108e-01Q),555 static_cast<storage_type>(5.10867001950827098004364050955250998e-01Q),556 static_cast<storage_type>(5.75140446819710315342946036586425133e-01Q),557 static_cast<storage_type>(6.36053680726515025452836696226285937e-01Q),558 static_cast<storage_type>(6.93237656334751384805490711845931533e-01Q),559 static_cast<storage_type>(7.46331906460150792614305070355641590e-01Q),560 static_cast<storage_type>(7.95041428837551198350638833272787943e-01Q),561 static_cast<storage_type>(8.39116971822218823394529061701520685e-01Q),562 static_cast<storage_type>(8.78276811252281976077442995113078467e-01Q),563 static_cast<storage_type>(9.12234428251325905867752441203298113e-01Q),564 static_cast<storage_type>(9.40822633831754753519982722212443380e-01Q),565 static_cast<storage_type>(9.63971927277913791267666131197277222e-01Q),566 static_cast<storage_type>(9.81507877450250259193342994720216945e-01Q),567 static_cast<storage_type>(9.93128599185094924786122388471320278e-01Q),568 static_cast<storage_type>(9.98859031588277663838315576545863010e-01Q),569 };570 return data;571 }572 static std::array<storage_type, 21> const & weights()573 {574 static const std::array<storage_type, 21> data = {575 static_cast<storage_type>(7.66007119179996564450499015301017408e-02Q),576 static_cast<storage_type>(7.63778676720807367055028350380610018e-02Q),577 static_cast<storage_type>(7.57044976845566746595427753766165583e-02Q),578 static_cast<storage_type>(7.45828754004991889865814183624875286e-02Q),579 static_cast<storage_type>(7.30306903327866674951894176589131128e-02Q),580 static_cast<storage_type>(7.10544235534440683057903617232101674e-02Q),581 static_cast<storage_type>(6.86486729285216193456234118853678017e-02Q),582 static_cast<storage_type>(6.58345971336184221115635569693979431e-02Q),583 static_cast<storage_type>(6.26532375547811680258701221742549806e-02Q),584 static_cast<storage_type>(5.91114008806395723749672206485942171e-02Q),585 static_cast<storage_type>(5.51951053482859947448323724197773292e-02Q),586 static_cast<storage_type>(5.09445739237286919327076700503449487e-02Q),587 static_cast<storage_type>(4.64348218674976747202318809261075168e-02Q),588 static_cast<storage_type>(4.16688733279736862637883059368947380e-02Q),589 static_cast<storage_type>(3.66001697582007980305572407072110085e-02Q),590 static_cast<storage_type>(3.12873067770327989585431193238007379e-02Q),591 static_cast<storage_type>(2.58821336049511588345050670961531430e-02Q),592 static_cast<storage_type>(2.03883734612665235980102314327547051e-02Q),593 static_cast<storage_type>(1.46261692569712529837879603088683562e-02Q),594 static_cast<storage_type>(8.60026985564294219866178795010234725e-03Q),595 static_cast<storage_type>(3.07358371852053150121829324603098749e-03Q),596 };597 return data;598 }599};600#endif601 602template <class T>603class gauss_kronrod_detail<T, 41, 4>604{605public:606 static std::array<T, 21> const & abscissa()607 {608 static std::array<T, 21> data = { // LCOV_EXCL_START609 BOOST_MATH_HUGE_CONSTANT(T, 0, 0.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+00),610 BOOST_MATH_HUGE_CONSTANT(T, 0, 7.6526521133497333754640409398838211004796266813497500804795244384256342048336978241545114181556215606998505646364133e-02),611 BOOST_MATH_HUGE_CONSTANT(T, 0, 1.5260546524092267550522024102267752791167622481841730660174156703809133685751696356987995886397049724808931527012542e-01),612 BOOST_MATH_HUGE_CONSTANT(T, 0, 2.2778585114164507808049619536857462474308893768292747231463573920717134186355582779495212519096870803177373131560430e-01),613 BOOST_MATH_HUGE_CONSTANT(T, 0, 3.0162786811491300432055535685859226061539650501373092456926374427956957435978384116066498234762220215751079886015902e-01),614 BOOST_MATH_HUGE_CONSTANT(T, 0, 3.7370608871541956067254817702492723739574632170568271182794861351564576437305952789589568363453337894476772208852815e-01),615 BOOST_MATH_HUGE_CONSTANT(T, 0, 4.4359317523872510319999221349264010784010101082300309613315028346299543059315258601993479156987847429893626854030516e-01),616 BOOST_MATH_HUGE_CONSTANT(T, 0, 5.1086700195082709800436405095525099842549132920242683347234861989473497039076572814403168305086777919832943068843526e-01),617 BOOST_MATH_HUGE_CONSTANT(T, 0, 5.7514044681971031534294603658642513281381264014771682537415885495717468074720062012357788489049470208285175093670561e-01),618 BOOST_MATH_HUGE_CONSTANT(T, 0, 6.3605368072651502545283669622628593674338911679936846393944662254654126258543013255870319549576130658211710937772596e-01),619 BOOST_MATH_HUGE_CONSTANT(T, 0, 6.9323765633475138480549071184593153338642585141021417904687378454301191710739219011546672416325022748282227809465165e-01),620 BOOST_MATH_HUGE_CONSTANT(T, 0, 7.4633190646015079261430507035564159031073067956917644413954590606853535503815506468110411362064752061238490065167656e-01),621 BOOST_MATH_HUGE_CONSTANT(T, 0, 7.9504142883755119835063883327278794295938959911578029703855163894322697871710382866701777890251824617748545658564370e-01),622 BOOST_MATH_HUGE_CONSTANT(T, 0, 8.3911697182221882339452906170152068532962936506563737325249272553286109399932480991922934056595764922060422035306914e-01),623 BOOST_MATH_HUGE_CONSTANT(T, 0, 8.7827681125228197607744299511307846671124526828251164853898086998248145904743220740840261624245683876748360309079747e-01),624 BOOST_MATH_HUGE_CONSTANT(T, 0, 9.1223442825132590586775244120329811304918479742369177479588221915807089120871907893644472619292138737876039175464603e-01),625 BOOST_MATH_HUGE_CONSTANT(T, 0, 9.4082263383175475351998272221244338027429557377965291059536839973186796006557571220888218676776618448841584569497535e-01),626 BOOST_MATH_HUGE_CONSTANT(T, 0, 9.6397192727791379126766613119727722191206032780618885606353759389204158078438305698001812525596471563131043491596423e-01),627 BOOST_MATH_HUGE_CONSTANT(T, 0, 9.8150787745025025919334299472021694456725093981023759869077533318793098857465723460898060491887511355706497739384103e-01),628 BOOST_MATH_HUGE_CONSTANT(T, 0, 9.9312859918509492478612238847132027822264713090165589614818413121798471762775378083944940249657220927472894034724419e-01),629 BOOST_MATH_HUGE_CONSTANT(T, 0, 9.9885903158827766383831557654586300999957020432629666866666860339324411793311982967839129772854179884971700274369367e-01),630 }; // LCOV_EXCL_STOP631 return data;632 }633 static std::array<T, 21> const & weights()634 {635 static std::array<T, 21> data = { // LCOV_EXCL_START636 BOOST_MATH_HUGE_CONSTANT(T, 0, 7.6600711917999656445049901530101740827932500628670118055485349620314721456712029449597396569857880493210849110825276e-02),637 BOOST_MATH_HUGE_CONSTANT(T, 0, 7.6377867672080736705502835038061001800801036764945996714946431116936745542061941050008345047482501253320401746334511e-02),638 BOOST_MATH_HUGE_CONSTANT(T, 0, 7.5704497684556674659542775376616558263363155900414326194855223272348838596099414841886740468379707283366777797425290e-02),639 BOOST_MATH_HUGE_CONSTANT(T, 0, 7.4582875400499188986581418362487528616116493572092273080047040726969899567887364227664202642942357104526915332274625e-02),640 BOOST_MATH_HUGE_CONSTANT(T, 0, 7.3030690332786667495189417658913112760626845234552742380174250771849743831660040966804802312464527721645765620253776e-02),641 BOOST_MATH_HUGE_CONSTANT(T, 0, 7.1054423553444068305790361723210167412912159322210143921628270586407381879789525901086146473278095159807542174985045e-02),642 BOOST_MATH_HUGE_CONSTANT(T, 0, 6.8648672928521619345623411885367801715489704958239860400434264173923806029589970941711224257967651039544669425313433e-02),643 BOOST_MATH_HUGE_CONSTANT(T, 0, 6.5834597133618422111563556969397943147223506343381443709751749639944420314384296347503523810096842402960802728781816e-02),644 BOOST_MATH_HUGE_CONSTANT(T, 0, 6.2653237554781168025870122174254980585819744698897886186553324157100424088919284503451596742588386343548162830898103e-02),645 BOOST_MATH_HUGE_CONSTANT(T, 0, 5.9111400880639572374967220648594217136419365977042191748388047204015262840407696611508732839851952697839735487615776e-02),646 BOOST_MATH_HUGE_CONSTANT(T, 0, 5.5195105348285994744832372419777329194753456228153116909812131213177827707884692917845453999535518818940813085110223e-02),647 BOOST_MATH_HUGE_CONSTANT(T, 0, 5.0944573923728691932707670050344948664836365809262579747517140086119113476866735641054822574173198900379392130050979e-02),648 BOOST_MATH_HUGE_CONSTANT(T, 0, 4.6434821867497674720231880926107516842127071007077929289994127933243222585938804392953931185146446072587020288747981e-02),649 BOOST_MATH_HUGE_CONSTANT(T, 0, 4.1668873327973686263788305936894738043960843153010324860966353235271889596379726462208702081068715463576895020003842e-02),650 BOOST_MATH_HUGE_CONSTANT(T, 0, 3.6600169758200798030557240707211008487453496747498001651070009441973280061489266074044986901436324295513243878212345e-02),651 BOOST_MATH_HUGE_CONSTANT(T, 0, 3.1287306777032798958543119323800737887769280362813337359554598005322423266047996771926031069705049476071896145456496e-02),652 BOOST_MATH_HUGE_CONSTANT(T, 0, 2.5882133604951158834505067096153142999479118048674944526997797755374306421629440393392427198869345793286369198147609e-02),653 BOOST_MATH_HUGE_CONSTANT(T, 0, 2.0388373461266523598010231432754705122838627940185929365371868214433006532030353671253640300679157504987977281782909e-02),654 BOOST_MATH_HUGE_CONSTANT(T, 0, 1.4626169256971252983787960308868356163881050162249770342103474631076960029748751959380482484308382288261238476948520e-02),655 BOOST_MATH_HUGE_CONSTANT(T, 0, 8.6002698556429421986617879501023472521289227667077976622450602031426535362696437838448828009554532025301579670206091e-03),656 BOOST_MATH_HUGE_CONSTANT(T, 0, 3.0735837185205315012182932460309874880335046882543449198461628212114333665590378156706265241414469306987988292234740e-03),657 }; // LCOV_EXCL_STOP658 return data;659 }660};661 662#ifndef BOOST_HAS_FLOAT128663 664template <class T>665class gauss_kronrod_detail<T, 51, 0>666{667 using storage_type = typename gauss_constant_category<T>::storage_type;668public:669 static std::array<storage_type, 26> const & abscissa()670 {671 static constexpr std::array<storage_type, 26> data = {672 static_cast<storage_type>(0.00000000000000000000000000000000000e+00L),673 static_cast<storage_type>(6.15444830056850788865463923667966313e-02L),674 static_cast<storage_type>(1.22864692610710396387359818808036806e-01L),675 static_cast<storage_type>(1.83718939421048892015969888759528416e-01L),676 static_cast<storage_type>(2.43866883720988432045190362797451586e-01L),677 static_cast<storage_type>(3.03089538931107830167478909980339329e-01L),678 static_cast<storage_type>(3.61172305809387837735821730127640667e-01L),679 static_cast<storage_type>(4.17885382193037748851814394594572487e-01L),680 static_cast<storage_type>(4.73002731445714960522182115009192041e-01L),681 static_cast<storage_type>(5.26325284334719182599623778158010178e-01L),682 static_cast<storage_type>(5.77662930241222967723689841612654067e-01L),683 static_cast<storage_type>(6.26810099010317412788122681624517881e-01L),684 static_cast<storage_type>(6.73566368473468364485120633247622176e-01L),685 static_cast<storage_type>(7.17766406813084388186654079773297781e-01L),686 static_cast<storage_type>(7.59259263037357630577282865204360976e-01L),687 static_cast<storage_type>(7.97873797998500059410410904994306569e-01L),688 static_cast<storage_type>(8.33442628760834001421021108693569569e-01L),689 static_cast<storage_type>(8.65847065293275595448996969588340088e-01L),690 static_cast<storage_type>(8.94991997878275368851042006782804954e-01L),691 static_cast<storage_type>(9.20747115281701561746346084546330632e-01L),692 static_cast<storage_type>(9.42974571228974339414011169658470532e-01L),693 static_cast<storage_type>(9.61614986425842512418130033660167242e-01L),694 static_cast<storage_type>(9.76663921459517511498315386479594068e-01L),695 static_cast<storage_type>(9.88035794534077247637331014577406227e-01L),696 static_cast<storage_type>(9.95556969790498097908784946893901617e-01L),697 static_cast<storage_type>(9.99262104992609834193457486540340594e-01L),698 };699 return data;700 }701 static std::array<storage_type, 26> const & weights()702 {703 static constexpr std::array<storage_type, 26> data = {704 static_cast<storage_type>(6.15808180678329350787598242400645532e-02L),705 static_cast<storage_type>(6.14711898714253166615441319652641776e-02L),706 static_cast<storage_type>(6.11285097170530483058590304162927119e-02L),707 static_cast<storage_type>(6.05394553760458629453602675175654272e-02L),708 static_cast<storage_type>(5.97203403241740599790992919325618538e-02L),709 static_cast<storage_type>(5.86896800223942079619741758567877641e-02L),710 static_cast<storage_type>(5.74371163615678328535826939395064720e-02L),711 static_cast<storage_type>(5.59508112204123173082406863827473468e-02L),712 static_cast<storage_type>(5.42511298885454901445433704598756068e-02L),713 static_cast<storage_type>(5.23628858064074758643667121378727149e-02L),714 static_cast<storage_type>(5.02776790807156719633252594334400844e-02L),715 static_cast<storage_type>(4.79825371388367139063922557569147550e-02L),716 static_cast<storage_type>(4.55029130499217889098705847526603930e-02L),717 static_cast<storage_type>(4.28728450201700494768957924394951611e-02L),718 static_cast<storage_type>(4.00838255040323820748392844670756464e-02L),719 static_cast<storage_type>(3.71162714834155435603306253676198760e-02L),720 static_cast<storage_type>(3.40021302743293378367487952295512032e-02L),721 static_cast<storage_type>(3.07923001673874888911090202152285856e-02L),722 static_cast<storage_type>(2.74753175878517378029484555178110786e-02L),723 static_cast<storage_type>(2.40099456069532162200924891648810814e-02L),724 static_cast<storage_type>(2.04353711458828354565682922359389737e-02L),725 static_cast<storage_type>(1.68478177091282982315166675363363158e-02L),726 static_cast<storage_type>(1.32362291955716748136564058469762381e-02L),727 static_cast<storage_type>(9.47397338617415160720771052365532387e-03L),728 static_cast<storage_type>(5.56193213535671375804023690106552207e-03L),729 static_cast<storage_type>(1.98738389233031592650785188284340989e-03L),730 };731 return data;732 }733};734 735#else736 737template <class T>738class gauss_kronrod_detail<T, 51, 3>739{740 using storage_type = typename gauss_constant_category<T>::storage_type;741public:742 static std::array<storage_type, 26> const & abscissa()743 {744 static const std::array<storage_type, 26> data = {745 static_cast<storage_type>(0.00000000000000000000000000000000000e+00Q),746 static_cast<storage_type>(6.15444830056850788865463923667966313e-02Q),747 static_cast<storage_type>(1.22864692610710396387359818808036806e-01Q),748 static_cast<storage_type>(1.83718939421048892015969888759528416e-01Q),749 static_cast<storage_type>(2.43866883720988432045190362797451586e-01Q),750 static_cast<storage_type>(3.03089538931107830167478909980339329e-01Q),751 static_cast<storage_type>(3.61172305809387837735821730127640667e-01Q),752 static_cast<storage_type>(4.17885382193037748851814394594572487e-01Q),753 static_cast<storage_type>(4.73002731445714960522182115009192041e-01Q),754 static_cast<storage_type>(5.26325284334719182599623778158010178e-01Q),755 static_cast<storage_type>(5.77662930241222967723689841612654067e-01Q),756 static_cast<storage_type>(6.26810099010317412788122681624517881e-01Q),757 static_cast<storage_type>(6.73566368473468364485120633247622176e-01Q),758 static_cast<storage_type>(7.17766406813084388186654079773297781e-01Q),759 static_cast<storage_type>(7.59259263037357630577282865204360976e-01Q),760 static_cast<storage_type>(7.97873797998500059410410904994306569e-01Q),761 static_cast<storage_type>(8.33442628760834001421021108693569569e-01Q),762 static_cast<storage_type>(8.65847065293275595448996969588340088e-01Q),763 static_cast<storage_type>(8.94991997878275368851042006782804954e-01Q),764 static_cast<storage_type>(9.20747115281701561746346084546330632e-01Q),765 static_cast<storage_type>(9.42974571228974339414011169658470532e-01Q),766 static_cast<storage_type>(9.61614986425842512418130033660167242e-01Q),767 static_cast<storage_type>(9.76663921459517511498315386479594068e-01Q),768 static_cast<storage_type>(9.88035794534077247637331014577406227e-01Q),769 static_cast<storage_type>(9.95556969790498097908784946893901617e-01Q),770 static_cast<storage_type>(9.99262104992609834193457486540340594e-01Q),771 };772 return data;773 }774 static std::array<storage_type, 26> const & weights()775 {776 static const std::array<storage_type, 26> data = {777 static_cast<storage_type>(6.15808180678329350787598242400645532e-02Q),778 static_cast<storage_type>(6.14711898714253166615441319652641776e-02Q),779 static_cast<storage_type>(6.11285097170530483058590304162927119e-02Q),780 static_cast<storage_type>(6.05394553760458629453602675175654272e-02Q),781 static_cast<storage_type>(5.97203403241740599790992919325618538e-02Q),782 static_cast<storage_type>(5.86896800223942079619741758567877641e-02Q),783 static_cast<storage_type>(5.74371163615678328535826939395064720e-02Q),784 static_cast<storage_type>(5.59508112204123173082406863827473468e-02Q),785 static_cast<storage_type>(5.42511298885454901445433704598756068e-02Q),786 static_cast<storage_type>(5.23628858064074758643667121378727149e-02Q),787 static_cast<storage_type>(5.02776790807156719633252594334400844e-02Q),788 static_cast<storage_type>(4.79825371388367139063922557569147550e-02Q),789 static_cast<storage_type>(4.55029130499217889098705847526603930e-02Q),790 static_cast<storage_type>(4.28728450201700494768957924394951611e-02Q),791 static_cast<storage_type>(4.00838255040323820748392844670756464e-02Q),792 static_cast<storage_type>(3.71162714834155435603306253676198760e-02Q),793 static_cast<storage_type>(3.40021302743293378367487952295512032e-02Q),794 static_cast<storage_type>(3.07923001673874888911090202152285856e-02Q),795 static_cast<storage_type>(2.74753175878517378029484555178110786e-02Q),796 static_cast<storage_type>(2.40099456069532162200924891648810814e-02Q),797 static_cast<storage_type>(2.04353711458828354565682922359389737e-02Q),798 static_cast<storage_type>(1.68478177091282982315166675363363158e-02Q),799 static_cast<storage_type>(1.32362291955716748136564058469762381e-02Q),800 static_cast<storage_type>(9.47397338617415160720771052365532387e-03Q),801 static_cast<storage_type>(5.56193213535671375804023690106552207e-03Q),802 static_cast<storage_type>(1.98738389233031592650785188284340989e-03Q),803 };804 return data;805 }806};807#endif808 809template <class T>810class gauss_kronrod_detail<T, 51, 4>811{812public:813 static std::array<T, 26> const & abscissa()814 {815 static std::array<T, 26> data = { // LCOV_EXCL_START816 BOOST_MATH_HUGE_CONSTANT(T, 0, 0.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+00),817 BOOST_MATH_HUGE_CONSTANT(T, 0, 6.1544483005685078886546392366796631281724348039823545274305431751687279361558658545141048781022691067898008423227288e-02),818 BOOST_MATH_HUGE_CONSTANT(T, 0, 1.2286469261071039638735981880803680553220534604978373842389353789270883496885841582643884994633105537597765980412320e-01),819 BOOST_MATH_HUGE_CONSTANT(T, 0, 1.8371893942104889201596988875952841578528447834990555215034512653236752851109815617651867160645591242103823539931527e-01),820 BOOST_MATH_HUGE_CONSTANT(T, 0, 2.4386688372098843204519036279745158640563315632598447642113565325038747278585595067977636776325034060327548499765742e-01),821 BOOST_MATH_HUGE_CONSTANT(T, 0, 3.0308953893110783016747890998033932920041937876655194685731578452573120372337209717349617882111662416355753711853559e-01),822 BOOST_MATH_HUGE_CONSTANT(T, 0, 3.6117230580938783773582173012764066742207834704337506979457877784674538239569654860329531506093761400789294612122812e-01),823 BOOST_MATH_HUGE_CONSTANT(T, 0, 4.1788538219303774885181439459457248709336998140069528034955785068796932076966599548717224205109797297615032607570119e-01),824 BOOST_MATH_HUGE_CONSTANT(T, 0, 4.7300273144571496052218211500919204133181773846162729090723082769560327584128603010315684778279363544192787010704498e-01),825 BOOST_MATH_HUGE_CONSTANT(T, 0, 5.2632528433471918259962377815801017803683252320191114313002425180471455022502695302371008520604638341970901082293650e-01),826 BOOST_MATH_HUGE_CONSTANT(T, 0, 5.7766293024122296772368984161265406739573503929151825664548350776102301275263202227671659646579649084013116066120581e-01),827 BOOST_MATH_HUGE_CONSTANT(T, 0, 6.2681009901031741278812268162451788101954628995068510806525222008437260184181183053045236423845198752346149030569920e-01),828 BOOST_MATH_HUGE_CONSTANT(T, 0, 6.7356636847346836448512063324762217588341672807274931705965696177828773684928421158196368568030932194044282149314388e-01),829 BOOST_MATH_HUGE_CONSTANT(T, 0, 7.1776640681308438818665407977329778059771167555515582423493486823991612820974965089522905953765860328116692570706602e-01),830 BOOST_MATH_HUGE_CONSTANT(T, 0, 7.5925926303735763057728286520436097638752201889833412091838973544501862882026240760763679724185230331463919586229073e-01),831 BOOST_MATH_HUGE_CONSTANT(T, 0, 7.9787379799850005941041090499430656940863230009338267661706934499488650817643824077118950314443984031474353711531825e-01),832 BOOST_MATH_HUGE_CONSTANT(T, 0, 8.3344262876083400142102110869356956946096411382352078602086471546171813247709012525322973947759168107133491065937347e-01),833 BOOST_MATH_HUGE_CONSTANT(T, 0, 8.6584706529327559544899696958834008820284409402823690293965213246691432948180280120756708738064779055576005302835351e-01),834 BOOST_MATH_HUGE_CONSTANT(T, 0, 8.9499199787827536885104200678280495417455484975358390306170168295917151090119945137118600693039178162093726882638296e-01),835 BOOST_MATH_HUGE_CONSTANT(T, 0, 9.2074711528170156174634608454633063157457035996277199700642836501131385042631212407808952281702820179915510491592339e-01),836 BOOST_MATH_HUGE_CONSTANT(T, 0, 9.4297457122897433941401116965847053190520157060899014192745249713729532254404926130890521815127348327109666786665572e-01),837 BOOST_MATH_HUGE_CONSTANT(T, 0, 9.6161498642584251241813003366016724169212642963709676666624520141292893281185666917636407790823210892689040877316178e-01),838 BOOST_MATH_HUGE_CONSTANT(T, 0, 9.7666392145951751149831538647959406774537055531440674467098742731616386753588055389644670948300617866819865983054648e-01),839 BOOST_MATH_HUGE_CONSTANT(T, 0, 9.8803579453407724763733101457740622707248415209160748131449972199405186821347293686245404742032360498210710718706868e-01),840 BOOST_MATH_HUGE_CONSTANT(T, 0, 9.9555696979049809790878494689390161725756264940480817121080493113293348134372793448728802635294700756868258870429256e-01),841 BOOST_MATH_HUGE_CONSTANT(T, 0, 9.9926210499260983419345748654034059370452496042279618586228697762904524428167719073818746102238075978747461480736921e-01),842 }; // LCOV_EXCL_STOP843 return data;844 }845 static std::array<T, 26> const & weights()846 {847 static std::array<T, 26> data = { // LCOV_EXCL_START848 BOOST_MATH_HUGE_CONSTANT(T, 0, 6.1580818067832935078759824240064553190436936903140808056908996403358367244202623293256774502185186717703954810463664e-02),849 BOOST_MATH_HUGE_CONSTANT(T, 0, 6.1471189871425316661544131965264177586537962876885022711111683500151700796198726558483367566537422877227096643444043e-02),850 BOOST_MATH_HUGE_CONSTANT(T, 0, 6.1128509717053048305859030416292711922678552321960938357322028070390133769952032831204895569347757809858568165047769e-02),851 BOOST_MATH_HUGE_CONSTANT(T, 0, 6.0539455376045862945360267517565427162312365710457079923487043144554747810689514408013582515489930908693681447570811e-02),852 BOOST_MATH_HUGE_CONSTANT(T, 0, 5.9720340324174059979099291932561853835363045476189975483372207816149988460708299020779612375010639778624011960832019e-02),853 BOOST_MATH_HUGE_CONSTANT(T, 0, 5.8689680022394207961974175856787764139795646254828315293243700305012569486054157617049685031506591863121580010947248e-02),854 BOOST_MATH_HUGE_CONSTANT(T, 0, 5.7437116361567832853582693939506471994832856823896682976509412313367495727224381199978598247737089593472710899482737e-02),855 BOOST_MATH_HUGE_CONSTANT(T, 0, 5.5950811220412317308240686382747346820271035112771802428932791066115158268338607019365831655460314732208940609352540e-02),856 BOOST_MATH_HUGE_CONSTANT(T, 0, 5.4251129888545490144543370459875606826076838441263383072163293312936923476650934130242315028422047795830492882862973e-02),857 BOOST_MATH_HUGE_CONSTANT(T, 0, 5.2362885806407475864366712137872714887351550723707596350905793656046659248541276597504566497990926306481919129870507e-02),858 BOOST_MATH_HUGE_CONSTANT(T, 0, 5.0277679080715671963325259433440084440587630604775975142050968279743014641141402310302584542633557037153607386127936e-02),859 BOOST_MATH_HUGE_CONSTANT(T, 0, 4.7982537138836713906392255756914754983592207423271169651235865196757913880334117810235517477328110033499422471098658e-02),860 BOOST_MATH_HUGE_CONSTANT(T, 0, 4.5502913049921788909870584752660393043707768935695327316724254392794299567957035458208970599641697203261236226745020e-02),861 BOOST_MATH_HUGE_CONSTANT(T, 0, 4.2872845020170049476895792439495161101999504199883328877919242515738957655253932048951366960802592343905647433925806e-02),862 BOOST_MATH_HUGE_CONSTANT(T, 0, 4.0083825504032382074839284467075646401410549266591308713115878386835777315058451955614116158949614066927183232852042e-02),863 BOOST_MATH_HUGE_CONSTANT(T, 0, 3.7116271483415543560330625367619875995997802688047764805628702762773009669395760582294525748583875707140577080663373e-02),864 BOOST_MATH_HUGE_CONSTANT(T, 0, 3.4002130274329337836748795229551203225670528250050443083264193121524339063344855010257660547708022429300203676502386e-02),865 BOOST_MATH_HUGE_CONSTANT(T, 0, 3.0792300167387488891109020215228585600877162393292487644544830559965388047996492709248618249084851477787538356572832e-02),866 BOOST_MATH_HUGE_CONSTANT(T, 0, 2.7475317587851737802948455517811078614796013288710603199613621069727810352835469926107822047433566792405123805901196e-02),867 BOOST_MATH_HUGE_CONSTANT(T, 0, 2.4009945606953216220092489164881081392931528209659330290734972342536012282191913069778658241972047765300060007037359e-02),868 BOOST_MATH_HUGE_CONSTANT(T, 0, 2.0435371145882835456568292235938973678758006097668937220074531550163622566841885855957623103354443247806459277197725e-02),869 BOOST_MATH_HUGE_CONSTANT(T, 0, 1.6847817709128298231516667536336315840402654624706139411175769276842182270078960078544597372646532637619276509222462e-02),870 BOOST_MATH_HUGE_CONSTANT(T, 0, 1.3236229195571674813656405846976238077578084997863654732213860488560614587634395544002156258192582265590155862296710e-02),871 BOOST_MATH_HUGE_CONSTANT(T, 0, 9.4739733861741516072077105236553238716453268483726334971394029603529306140359023187904705754719643032594360138998941e-03),872 BOOST_MATH_HUGE_CONSTANT(T, 0, 5.5619321353567137580402369010655220701769295496290984052961210793810038857581724171021610100708799763006942755331129e-03),873 BOOST_MATH_HUGE_CONSTANT(T, 0, 1.9873838923303159265078518828434098894299804282505973837653346298985629336820118753523093675303476883723992297810124e-03),874 }; // LCOV_EXCL_STOP875 return data;876 }877};878 879#ifndef BOOST_HAS_FLOAT128880 881template <class T>882class gauss_kronrod_detail<T, 61, 0>883{884 using storage_type = typename gauss_constant_category<T>::storage_type;885public:886 static std::array<storage_type, 31> const & abscissa()887 {888 static constexpr std::array<storage_type, 31> data = {889 static_cast<storage_type>(0.00000000000000000000000000000000000e+00L),890 static_cast<storage_type>(5.14718425553176958330252131667225737e-02L),891 static_cast<storage_type>(1.02806937966737030147096751318000592e-01L),892 static_cast<storage_type>(1.53869913608583546963794672743255920e-01L),893 static_cast<storage_type>(2.04525116682309891438957671002024710e-01L),894 static_cast<storage_type>(2.54636926167889846439805129817805108e-01L),895 static_cast<storage_type>(3.04073202273625077372677107199256554e-01L),896 static_cast<storage_type>(3.52704725530878113471037207089373861e-01L),897 static_cast<storage_type>(4.00401254830394392535476211542660634e-01L),898 static_cast<storage_type>(4.47033769538089176780609900322854000e-01L),899 static_cast<storage_type>(4.92480467861778574993693061207708796e-01L),900 static_cast<storage_type>(5.36624148142019899264169793311072794e-01L),901 static_cast<storage_type>(5.79345235826361691756024932172540496e-01L),902 static_cast<storage_type>(6.20526182989242861140477556431189299e-01L),903 static_cast<storage_type>(6.60061064126626961370053668149270753e-01L),904 static_cast<storage_type>(6.97850494793315796932292388026640068e-01L),905 static_cast<storage_type>(7.33790062453226804726171131369527646e-01L),906 static_cast<storage_type>(7.67777432104826194917977340974503132e-01L),907 static_cast<storage_type>(7.99727835821839083013668942322683241e-01L),908 static_cast<storage_type>(8.29565762382768397442898119732501916e-01L),909 static_cast<storage_type>(8.57205233546061098958658510658943857e-01L),910 static_cast<storage_type>(8.82560535792052681543116462530225590e-01L),911 static_cast<storage_type>(9.05573307699907798546522558925958320e-01L),912 static_cast<storage_type>(9.26200047429274325879324277080474004e-01L),913 static_cast<storage_type>(9.44374444748559979415831324037439122e-01L),914 static_cast<storage_type>(9.60021864968307512216871025581797663e-01L),915 static_cast<storage_type>(9.73116322501126268374693868423706885e-01L),916 static_cast<storage_type>(9.83668123279747209970032581605662802e-01L),917 static_cast<storage_type>(9.91630996870404594858628366109485725e-01L),918 static_cast<storage_type>(9.96893484074649540271630050918695283e-01L),919 static_cast<storage_type>(9.99484410050490637571325895705810819e-01L),920 };921 return data;922 }923 static std::array<storage_type, 31> const & weights()924 {925 static constexpr std::array<storage_type, 31> data = {926 static_cast<storage_type>(5.14947294294515675583404336470993075e-02L),927 static_cast<storage_type>(5.14261285374590259338628792157812598e-02L),928 static_cast<storage_type>(5.12215478492587721706562826049442083e-02L),929 static_cast<storage_type>(5.08817958987496064922974730498046919e-02L),930 static_cast<storage_type>(5.04059214027823468408930856535850289e-02L),931 static_cast<storage_type>(4.97956834270742063578115693799423285e-02L),932 static_cast<storage_type>(4.90554345550297788875281653672381736e-02L),933 static_cast<storage_type>(4.81858617570871291407794922983045926e-02L),934 static_cast<storage_type>(4.71855465692991539452614781810994865e-02L),935 static_cast<storage_type>(4.60592382710069881162717355593735806e-02L),936 static_cast<storage_type>(4.48148001331626631923555516167232438e-02L),937 static_cast<storage_type>(4.34525397013560693168317281170732581e-02L),938 static_cast<storage_type>(4.19698102151642461471475412859697578e-02L),939 static_cast<storage_type>(4.03745389515359591119952797524681142e-02L),940 static_cast<storage_type>(3.86789456247275929503486515322810503e-02L),941 static_cast<storage_type>(3.68823646518212292239110656171359677e-02L),942 static_cast<storage_type>(3.49793380280600241374996707314678751e-02L),943 static_cast<storage_type>(3.29814470574837260318141910168539275e-02L),944 static_cast<storage_type>(3.09072575623877624728842529430922726e-02L),945 static_cast<storage_type>(2.87540487650412928439787853543342111e-02L),946 static_cast<storage_type>(2.65099548823331016106017093350754144e-02L),947 static_cast<storage_type>(2.41911620780806013656863707252320268e-02L),948 static_cast<storage_type>(2.18280358216091922971674857383389934e-02L),949 static_cast<storage_type>(1.94141411939423811734089510501284559e-02L),950 static_cast<storage_type>(1.69208891890532726275722894203220924e-02L),951 static_cast<storage_type>(1.43697295070458048124514324435800102e-02L),952 static_cast<storage_type>(1.18230152534963417422328988532505929e-02L),953 static_cast<storage_type>(9.27327965951776342844114689202436042e-03L),954 static_cast<storage_type>(6.63070391593129217331982636975016813e-03L),955 static_cast<storage_type>(3.89046112709988405126720184451550328e-03L),956 static_cast<storage_type>(1.38901369867700762455159122675969968e-03L),957 };958 return data;959 }960};961 962#else963 964template <class T>965class gauss_kronrod_detail<T, 61, 0>966{967 using storage_type = typename gauss_constant_category<T>::storage_type;968public:969 static std::array<storage_type, 31> const & abscissa()970 {971 static const std::array<storage_type, 31> data = {972 static_cast<storage_type>(0.00000000000000000000000000000000000e+00Q),973 static_cast<storage_type>(5.14718425553176958330252131667225737e-02Q),974 static_cast<storage_type>(1.02806937966737030147096751318000592e-01Q),975 static_cast<storage_type>(1.53869913608583546963794672743255920e-01Q),976 static_cast<storage_type>(2.04525116682309891438957671002024710e-01Q),977 static_cast<storage_type>(2.54636926167889846439805129817805108e-01Q),978 static_cast<storage_type>(3.04073202273625077372677107199256554e-01Q),979 static_cast<storage_type>(3.52704725530878113471037207089373861e-01Q),980 static_cast<storage_type>(4.00401254830394392535476211542660634e-01Q),981 static_cast<storage_type>(4.47033769538089176780609900322854000e-01Q),982 static_cast<storage_type>(4.92480467861778574993693061207708796e-01Q),983 static_cast<storage_type>(5.36624148142019899264169793311072794e-01Q),984 static_cast<storage_type>(5.79345235826361691756024932172540496e-01Q),985 static_cast<storage_type>(6.20526182989242861140477556431189299e-01Q),986 static_cast<storage_type>(6.60061064126626961370053668149270753e-01Q),987 static_cast<storage_type>(6.97850494793315796932292388026640068e-01Q),988 static_cast<storage_type>(7.33790062453226804726171131369527646e-01Q),989 static_cast<storage_type>(7.67777432104826194917977340974503132e-01Q),990 static_cast<storage_type>(7.99727835821839083013668942322683241e-01Q),991 static_cast<storage_type>(8.29565762382768397442898119732501916e-01Q),992 static_cast<storage_type>(8.57205233546061098958658510658943857e-01Q),993 static_cast<storage_type>(8.82560535792052681543116462530225590e-01Q),994 static_cast<storage_type>(9.05573307699907798546522558925958320e-01Q),995 static_cast<storage_type>(9.26200047429274325879324277080474004e-01Q),996 static_cast<storage_type>(9.44374444748559979415831324037439122e-01Q),997 static_cast<storage_type>(9.60021864968307512216871025581797663e-01Q),998 static_cast<storage_type>(9.73116322501126268374693868423706885e-01Q),999 static_cast<storage_type>(9.83668123279747209970032581605662802e-01Q),1000 static_cast<storage_type>(9.91630996870404594858628366109485725e-01Q),1001 static_cast<storage_type>(9.96893484074649540271630050918695283e-01Q),1002 static_cast<storage_type>(9.99484410050490637571325895705810819e-01Q),1003 };1004 return data;1005 }1006 static std::array<storage_type, 31> const & weights()1007 {1008 static const std::array<storage_type, 31> data = {1009 static_cast<storage_type>(5.14947294294515675583404336470993075e-02Q),1010 static_cast<storage_type>(5.14261285374590259338628792157812598e-02Q),1011 static_cast<storage_type>(5.12215478492587721706562826049442083e-02Q),1012 static_cast<storage_type>(5.08817958987496064922974730498046919e-02Q),1013 static_cast<storage_type>(5.04059214027823468408930856535850289e-02Q),1014 static_cast<storage_type>(4.97956834270742063578115693799423285e-02Q),1015 static_cast<storage_type>(4.90554345550297788875281653672381736e-02Q),1016 static_cast<storage_type>(4.81858617570871291407794922983045926e-02Q),1017 static_cast<storage_type>(4.71855465692991539452614781810994865e-02Q),1018 static_cast<storage_type>(4.60592382710069881162717355593735806e-02Q),1019 static_cast<storage_type>(4.48148001331626631923555516167232438e-02Q),1020 static_cast<storage_type>(4.34525397013560693168317281170732581e-02Q),1021 static_cast<storage_type>(4.19698102151642461471475412859697578e-02Q),1022 static_cast<storage_type>(4.03745389515359591119952797524681142e-02Q),1023 static_cast<storage_type>(3.86789456247275929503486515322810503e-02Q),1024 static_cast<storage_type>(3.68823646518212292239110656171359677e-02Q),1025 static_cast<storage_type>(3.49793380280600241374996707314678751e-02Q),1026 static_cast<storage_type>(3.29814470574837260318141910168539275e-02Q),1027 static_cast<storage_type>(3.09072575623877624728842529430922726e-02Q),1028 static_cast<storage_type>(2.87540487650412928439787853543342111e-02Q),1029 static_cast<storage_type>(2.65099548823331016106017093350754144e-02Q),1030 static_cast<storage_type>(2.41911620780806013656863707252320268e-02Q),1031 static_cast<storage_type>(2.18280358216091922971674857383389934e-02Q),1032 static_cast<storage_type>(1.94141411939423811734089510501284559e-02Q),1033 static_cast<storage_type>(1.69208891890532726275722894203220924e-02Q),1034 static_cast<storage_type>(1.43697295070458048124514324435800102e-02Q),1035 static_cast<storage_type>(1.18230152534963417422328988532505929e-02Q),1036 static_cast<storage_type>(9.27327965951776342844114689202436042e-03Q),1037 static_cast<storage_type>(6.63070391593129217331982636975016813e-03Q),1038 static_cast<storage_type>(3.89046112709988405126720184451550328e-03Q),1039 static_cast<storage_type>(1.38901369867700762455159122675969968e-03Q),1040 };1041 return data;1042 }1043};1044#endif1045 1046template <class T>1047class gauss_kronrod_detail<T, 61, 4>1048{1049public:1050 static std::array<T, 31> const & abscissa()1051 {1052 static std::array<T, 31> data = { // LCOV_EXCL_START1053 BOOST_MATH_HUGE_CONSTANT(T, 0, 0.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+00),1054 BOOST_MATH_HUGE_CONSTANT(T, 0, 5.1471842555317695833025213166722573749141453666569564255160843987964755210427109055870090707285485841217089963590678e-02),1055 BOOST_MATH_HUGE_CONSTANT(T, 0, 1.0280693796673703014709675131800059247190133296515840552101946914632788253917872738234797140786490207720254922664913e-01),1056 BOOST_MATH_HUGE_CONSTANT(T, 0, 1.5386991360858354696379467274325592041855197124433846171896298291578714851081610139692310651074078557990111754952062e-01),1057 BOOST_MATH_HUGE_CONSTANT(T, 0, 2.0452511668230989143895767100202470952410426459556377447604465028350321894663245495592565235317147819577892124850607e-01),1058 BOOST_MATH_HUGE_CONSTANT(T, 0, 2.5463692616788984643980512981780510788278930330251842616428597508896353156907880290636628138423620257595521678255758e-01),1059 BOOST_MATH_HUGE_CONSTANT(T, 0, 3.0407320227362507737267710719925655353115778980946272844421536998312150442387767304001423699909778588529370119457430e-01),1060 BOOST_MATH_HUGE_CONSTANT(T, 0, 3.5270472553087811347103720708937386065363100802142562659418446890026941623319107866436039675211352945165817827083104e-01),1061 BOOST_MATH_HUGE_CONSTANT(T, 0, 4.0040125483039439253547621154266063361104593297078395983186610656429170689311759061175527015710247383961903284673474e-01),1062 BOOST_MATH_HUGE_CONSTANT(T, 0, 4.4703376953808917678060990032285400016240759386142440975447738172761535172858420700400688872124189834257262048739699e-01),1063 BOOST_MATH_HUGE_CONSTANT(T, 0, 4.9248046786177857499369306120770879564426564096318697026073340982988422546396352776837047452262025983265531109327026e-01),1064 BOOST_MATH_HUGE_CONSTANT(T, 0, 5.3662414814201989926416979331107279416417800693029710545274348291201490861897837863114116009718990258091585830703557e-01),1065 BOOST_MATH_HUGE_CONSTANT(T, 0, 5.7934523582636169175602493217254049590705158881215289208126016612312833567812241903809970751783808208940322061083509e-01),1066 BOOST_MATH_HUGE_CONSTANT(T, 0, 6.2052618298924286114047755643118929920736469282952813259505117012433531497488911774115258445532782106478789996137481e-01),1067 BOOST_MATH_HUGE_CONSTANT(T, 0, 6.6006106412662696137005366814927075303835037480883390955067197339904937499734522076788020517029688190998858739703079e-01),1068 BOOST_MATH_HUGE_CONSTANT(T, 0, 6.9785049479331579693229238802664006838235380065395465637972284673997672124315996069538163644008904690545069439941341e-01),1069 BOOST_MATH_HUGE_CONSTANT(T, 0, 7.3379006245322680472617113136952764566938172775468549208701399518300016463613325382024664531597318795933262446521430e-01),1070 BOOST_MATH_HUGE_CONSTANT(T, 0, 7.6777743210482619491797734097450313169488361723290845320649438736515857017299504505260960258623968420224697596501719e-01),1071 BOOST_MATH_HUGE_CONSTANT(T, 0, 7.9972783582183908301366894232268324073569842937778450923647349548686662567326007229195202524185356472023967927713548e-01),1072 BOOST_MATH_HUGE_CONSTANT(T, 0, 8.2956576238276839744289811973250191643906869617034167880695298345365650658958163508295244350814016004371545455777732e-01),1073 BOOST_MATH_HUGE_CONSTANT(T, 0, 8.5720523354606109895865851065894385682080017062359612850504551739119887225712932688031120704657195642614071367390794e-01),1074 BOOST_MATH_HUGE_CONSTANT(T, 0, 8.8256053579205268154311646253022559005668914714648423206832605312161626269519165572921583828573210485349058106849548e-01),1075 BOOST_MATH_HUGE_CONSTANT(T, 0, 9.0557330769990779854652255892595831956897536366222841356404766397803760239449631913585074426842574155323901785046522e-01),1076 BOOST_MATH_HUGE_CONSTANT(T, 0, 9.2620004742927432587932427708047400408647453682532906091103713367942299565110232681677288015055886244486106298320068e-01),1077 BOOST_MATH_HUGE_CONSTANT(T, 0, 9.4437444474855997941583132403743912158564371496498093181748940139520917000657342753448871376849848523800667868447591e-01),1078 BOOST_MATH_HUGE_CONSTANT(T, 0, 9.6002186496830751221687102558179766293035921740392339948566167242493995770706842922718944370380002378239172677454384e-01),1079 BOOST_MATH_HUGE_CONSTANT(T, 0, 9.7311632250112626837469386842370688488763796428343933853755850185624118958166838288308561708261486365954975485787212e-01),1080 BOOST_MATH_HUGE_CONSTANT(T, 0, 9.8366812327974720997003258160566280194031785470971136351718001015114429536479104370207597166035471368057762560137209e-01),1081 BOOST_MATH_HUGE_CONSTANT(T, 0, 9.9163099687040459485862836610948572485050033374616325510019923349807489603260796605556191495843575227494654783755353e-01),1082 BOOST_MATH_HUGE_CONSTANT(T, 0, 9.9689348407464954027163005091869528334088203811775079010809429780238769521016374081588201955806171741257405095963817e-01),1083 BOOST_MATH_HUGE_CONSTANT(T, 0, 9.9948441005049063757132589570581081946887394701850801923632642830748016674843587830656468823145435723317885056396548e-01),1084 }; // LCOV_EXCL_STOP1085 return data;1086 }1087 static std::array<T, 31> const & weights()1088 {1089 static std::array<T, 31> data = { // LCOV_EXCL_START1090 BOOST_MATH_HUGE_CONSTANT(T, 0, 5.1494729429451567558340433647099307532736880396464168074637323362474083844397567724480716864880173808112573901197920e-02),1091 BOOST_MATH_HUGE_CONSTANT(T, 0, 5.1426128537459025933862879215781259829552034862395987263855824172761589259406892072066110681184224608133314131500422e-02),1092 BOOST_MATH_HUGE_CONSTANT(T, 0, 5.1221547849258772170656282604944208251146952425246327553509056805511015401279553971190412722969308620984161625812560e-02),1093 BOOST_MATH_HUGE_CONSTANT(T, 0, 5.0881795898749606492297473049804691853384914260919239920771942080972542646780575571132056254070929858650733836163479e-02),1094 BOOST_MATH_HUGE_CONSTANT(T, 0, 5.0405921402782346840893085653585028902197018251622233664243959211066713308635283713447747907973700791599900911248852e-02),1095 BOOST_MATH_HUGE_CONSTANT(T, 0, 4.9795683427074206357811569379942328539209602813696108951047392842948482646220377655098341924089250200477846596263918e-02),1096 BOOST_MATH_HUGE_CONSTANT(T, 0, 4.9055434555029778887528165367238173605887405295296569579490717901328215644590555247522873065246297467067324397612445e-02),1097 BOOST_MATH_HUGE_CONSTANT(T, 0, 4.8185861757087129140779492298304592605799236108429800057373350872433793583969368428942672063270298939865425225579922e-02),1098 BOOST_MATH_HUGE_CONSTANT(T, 0, 4.7185546569299153945261478181099486482884807300628457194141861551725533289490897029020276525603515502104799540544222e-02),1099 BOOST_MATH_HUGE_CONSTANT(T, 0, 4.6059238271006988116271735559373580594692875571824924004732379492293604006446052672252973438978639166425766841417488e-02),1100 BOOST_MATH_HUGE_CONSTANT(T, 0, 4.4814800133162663192355551616723243757431392796373009889680201194063503947907899189061064792111919040540351834527742e-02),1101 BOOST_MATH_HUGE_CONSTANT(T, 0, 4.3452539701356069316831728117073258074603308631703168064888805495738640839573863333942084117196541456054957383622173e-02),1102 BOOST_MATH_HUGE_CONSTANT(T, 0, 4.1969810215164246147147541285969757790088656718992374820388720323852655511200365790379948462006156953358103259681948e-02),1103 BOOST_MATH_HUGE_CONSTANT(T, 0, 4.0374538951535959111995279752468114216126062126030255633998289613810846761059740961836828802959573901107306640876603e-02),1104 BOOST_MATH_HUGE_CONSTANT(T, 0, 3.8678945624727592950348651532281050250923629821553846790376130679337402056620700554139109487533759557982632153728099e-02),1105 BOOST_MATH_HUGE_CONSTANT(T, 0, 3.6882364651821229223911065617135967736955164781030337670005198584196134970154169862584193360751243227989492571664973e-02),1106 BOOST_MATH_HUGE_CONSTANT(T, 0, 3.4979338028060024137499670731467875097226912794818719972208457232177786702008744219498470603846784465175225933802357e-02),1107 BOOST_MATH_HUGE_CONSTANT(T, 0, 3.2981447057483726031814191016853927510599291213858385714519347641452316582381008804994515341969205985818543200837577e-02),1108 BOOST_MATH_HUGE_CONSTANT(T, 0, 3.0907257562387762472884252943092272635270458523807153426840486964022086189874056947717446328187131273807982629114591e-02),1109 BOOST_MATH_HUGE_CONSTANT(T, 0, 2.8754048765041292843978785354334211144679160542074930035102280759132174815469834227854660515366003136772757344886331e-02),1110 BOOST_MATH_HUGE_CONSTANT(T, 0, 2.6509954882333101610601709335075414366517579522748565770867438338472138903658077617652522759934474895733739329287706e-02),1111 BOOST_MATH_HUGE_CONSTANT(T, 0, 2.4191162078080601365686370725232026760391377828182462432228943562944885267501070688006470962871743661192935455117297e-02),1112 BOOST_MATH_HUGE_CONSTANT(T, 0, 2.1828035821609192297167485738338993401507296056834912773630422358720439403382559079356058602393879803560534375378340e-02),1113 BOOST_MATH_HUGE_CONSTANT(T, 0, 1.9414141193942381173408951050128455851421014191431525770276066536497179079025540486072726114628763606440143557769099e-02),1114 BOOST_MATH_HUGE_CONSTANT(T, 0, 1.6920889189053272627572289420322092368566703783835191139883410840546679978551861043620089451681146020853650713611444e-02),1115 BOOST_MATH_HUGE_CONSTANT(T, 0, 1.4369729507045804812451432443580010195841899895001505873565899403000198662495821906144274682894222591414503342336172e-02),1116 BOOST_MATH_HUGE_CONSTANT(T, 0, 1.1823015253496341742232898853250592896264406250607818326302431548265365155855182739401700032519141448997853772603766e-02),1117 BOOST_MATH_HUGE_CONSTANT(T, 0, 9.2732796595177634284411468920243604212700249381931076964956469143626665557434385492325784596343112153704094886248672e-03),1118 BOOST_MATH_HUGE_CONSTANT(T, 0, 6.6307039159312921733198263697501681336283882177812585973955597357837568277731921327731815844512598157843672104469554e-03),1119 BOOST_MATH_HUGE_CONSTANT(T, 0, 3.8904611270998840512672018445155032785151429848864649214200101281144733676455451061226273655941038347210163533085954e-03),1120 BOOST_MATH_HUGE_CONSTANT(T, 0, 1.3890136986770076245515912267596996810488412919632724534411055332301367130989865366956251556423820479579333920310978e-03),1121 }; // LCOV_EXCL_STOP1122 return data;1123 }1124};1125 1126}1127 1128template <class Real, unsigned N, class Policy = boost::math::policies::policy<> >1129class gauss_kronrod : public detail::gauss_kronrod_detail<Real, N, detail::gauss_constant_category<Real>::value>1130{1131 typedef detail::gauss_kronrod_detail<Real, N, detail::gauss_constant_category<Real>::value> base;1132public:1133 typedef Real value_type;1134private:1135 template <class F>1136 static auto integrate_non_adaptive_m1_1(F f, Real* error = nullptr, Real* pL1 = nullptr)->decltype(std::declval<F>()(std::declval<Real>()))1137 {1138 typedef decltype(f(Real(0))) K;1139 using std::abs;1140 unsigned gauss_start = 2;1141 unsigned kronrod_start = 1;1142 unsigned gauss_order = (N - 1) / 2;1143 K kronrod_result = 0;1144 K gauss_result = 0;1145 K fp, fm;1146 if (gauss_order & 1)1147 {1148 fp = f(value_type(0));1149 kronrod_result = fp * static_cast<Real>(base::weights()[0]);1150 gauss_result += fp * static_cast<Real>(gauss<Real, (N - 1) / 2>::weights()[0]);1151 }1152 else1153 {1154 fp = f(value_type(0));1155 kronrod_result = fp * static_cast<Real>(base::weights()[0]);1156 gauss_start = 1;1157 kronrod_start = 2;1158 }1159 Real L1 = abs(kronrod_result);1160 for (unsigned i = gauss_start; i < base::abscissa().size(); i += 2)1161 {1162 fp = f(static_cast<Real>(base::abscissa()[i]));1163 fm = f(static_cast<Real>(-base::abscissa()[i]));1164 kronrod_result += (fp + fm) * static_cast<Real>(base::weights()[i]);1165 L1 += (abs(fp) + abs(fm)) * static_cast<Real>(base::weights()[i]);1166 gauss_result += (fp + fm) * static_cast<Real>(gauss<Real, (N - 1) / 2>::weights()[i / 2]);1167 }1168 for (unsigned i = kronrod_start; i < base::abscissa().size(); i += 2)1169 {1170 fp = f(static_cast<Real>(base::abscissa()[i]));1171 fm = f(static_cast<Real>(-base::abscissa()[i]));1172 kronrod_result += (fp + fm) * static_cast<Real>(base::weights()[i]);1173 L1 += (abs(fp) + abs(fm)) * static_cast<Real>(base::weights()[i]);1174 }1175 if (pL1)1176 *pL1 = L1;1177 if (error)1178 *error = (std::max)(static_cast<Real>(abs(kronrod_result - gauss_result)), static_cast<Real>(abs(kronrod_result * tools::epsilon<Real>() * Real(2))));1179 return kronrod_result;1180 }1181 1182 template <class F>1183 struct recursive_info1184 {1185 F f;1186 Real tol;1187 };1188 1189 template <class F>1190 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>()))1191 {1192 typedef decltype(info->f(Real(a))) K;1193 using std::abs;1194 Real error_local;1195 Real mean = (b + a) / 2;1196 Real scale = (b - a) / 2;1197 auto ff = [&](const Real& x)->K1198 {1199 return info->f(scale * x + mean);1200 };1201 K r1 = integrate_non_adaptive_m1_1(ff, &error_local, L1);1202 K estimate = scale * r1;1203 1204 K tmp = estimate * info->tol;1205 Real abs_tol1 = abs(tmp);1206 if (abs_tol == 0)1207 abs_tol = abs_tol1;1208 1209 if (max_levels && (abs_tol1 < error_local) && (abs_tol < error_local))1210 {1211 Real mid = (a + b) / 2;1212 Real L1_local;1213 estimate = recursive_adaptive_integrate(info, a, mid, max_levels - 1, abs_tol / 2, error, L1);1214 estimate += recursive_adaptive_integrate(info, mid, b, max_levels - 1, abs_tol / 2, &error_local, &L1_local);1215 if (error)1216 *error += error_local;1217 if (L1)1218 *L1 += L1_local;1219 return estimate;1220 }1221 if(L1)1222 *L1 *= scale;1223 if (error)1224 *error = error_local;1225 return estimate;1226 }1227 1228public:1229 template <class F>1230 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>()))1231 {1232 typedef decltype(f(a)) K;1233 static_assert(!std::is_integral<K>::value,1234 "The return type cannot be integral, it must be either a real or complex floating point type.");1235 static const char* function = "boost::math::quadrature::gauss_kronrod<%1%>::integrate(f, %1%, %1%)";1236 if (!(boost::math::isnan)(a) && !(boost::math::isnan)(b))1237 {1238 // Infinite limits:1239 if ((a <= -tools::max_value<Real>()) && (b >= tools::max_value<Real>()))1240 {1241 auto u = [&](const Real& t)->K1242 {1243 Real t_sq = t*t;1244 Real inv = 1 / (1 - t_sq);1245 Real w = (1 + t_sq)*inv*inv;1246 Real arg = t*inv;1247 K res = f(arg)*w;1248 return res;1249 };1250 recursive_info<decltype(u)> info = { u, tol };1251 K res = recursive_adaptive_integrate(&info, Real(-1), Real(1), max_depth, Real(0), error, pL1);1252 return res;1253 }1254 1255 // Right limit is infinite:1256 if ((boost::math::isfinite)(a) && (b >= tools::max_value<Real>()))1257 {1258 auto u = [&](const Real& t)->K1259 {1260 Real z = 1 / (t + 1);1261 Real arg = 2 * z + a - 1;1262 K res = f(arg)*z*z;1263 return res;1264 };1265 recursive_info<decltype(u)> info = { u, tol };1266 K Q = Real(2) * recursive_adaptive_integrate(&info, Real(-1), Real(1), max_depth, Real(0), error, pL1);1267 if (pL1)1268 {1269 *pL1 *= 2;1270 }1271 return Q;1272 }1273 1274 if ((boost::math::isfinite)(b) && (a <= -tools::max_value<Real>()))1275 {1276 auto v = [&](const Real& t)->K1277 {1278 Real z = 1 / (t + 1);1279 Real arg = 2 * z - 1;1280 return f(b - arg) * z * z;1281 };1282 recursive_info<decltype(v)> info = { v, tol };1283 K Q = Real(2) * recursive_adaptive_integrate(&info, Real(-1), Real(1), max_depth, Real(0), error, pL1);1284 if (pL1)1285 {1286 *pL1 *= 2;1287 }1288 return Q;1289 }1290 1291 if ((boost::math::isfinite)(a) && (boost::math::isfinite)(b))1292 {1293 if (a==b)1294 {1295 return K(0);1296 }1297 recursive_info<F> info = { f, tol };1298 if (b < a)1299 {1300 return -recursive_adaptive_integrate(&info, b, a, max_depth, Real(0), error, pL1);1301 }1302 return recursive_adaptive_integrate(&info, a, b, max_depth, Real(0), error, pL1);1303 }1304 }1305 return static_cast<K>(policies::raise_domain_error(function, "The domain of integration is not sensible; please check the bounds.", a, Policy()));1306 }1307};1308 1309} // namespace quadrature1310} // namespace math1311} // namespace boost1312 1313#ifdef _MSC_VER1314#pragma warning(pop)1315#endif1316 1317#endif // BOOST_MATH_QUADRATURE_GAUSS_KRONROD_HPP1318