brintos / llvm-project-archived public Read only

1//  Copyright Takuma Yoshimura 2024.2//  Copyright Matt Borland 2024.3//  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_STATS_SASPOINT5_HPP8#define BOOST_STATS_SASPOINT5_HPP9 10#ifdef _MSC_VER11#pragma warning(push)12#pragma warning(disable : 4127) // conditional expression is constant13#endif14 15#include <boost/math/tools/config.hpp>16#include <boost/math/tools/numeric_limits.hpp>17#include <boost/math/tools/tuple.hpp>18#include <boost/math/constants/constants.hpp>19#include <boost/math/tools/big_constant.hpp>20#include <boost/math/distributions/complement.hpp>21#include <boost/math/distributions/detail/common_error_handling.hpp>22#include <boost/math/distributions/detail/derived_accessors.hpp>23#include <boost/math/tools/rational.hpp>24#include <boost/math/tools/promotion.hpp>25#include <boost/math/tools/type_traits.hpp>26#include <boost/math/policies/policy.hpp>27#include <boost/math/policies/error_handling.hpp>28 29#ifndef BOOST_MATH_HAS_NVRTC30#include <boost/math/distributions/fwd.hpp>31#include <cmath>32#endif33 34namespace boost { namespace math {35template <class RealType, class Policy>36class saspoint5_distribution;37 38namespace detail {39 40template <class RealType>41BOOST_MATH_GPU_ENABLED inline RealType saspoint5_pdf_plus_imp_prec(const RealType& x, const boost::math::integral_constant<int, 53>&)42{43    BOOST_MATH_STD_USING44    RealType result;45 46    if (x < 0.125) {47        // Rational Approximation48        // Maximum Relative Error: 7.8747e-1749        BOOST_MATH_STATIC const RealType P[13] = {50            static_cast<RealType>(6.36619772367581343076e-1),51            static_cast<RealType>(2.17275699713513462507e2),52            static_cast<RealType>(3.49063163361344578910e4),53            static_cast<RealType>(3.40332906932698464252e6),54            static_cast<RealType>(2.19485577044357440949e8),55            static_cast<RealType>(9.66086435948730562464e9),56            static_cast<RealType>(2.90571833690383003932e11),57            static_cast<RealType>(5.83089315593106044683e12),58            static_cast<RealType>(7.37911022713775715766e13),59            static_cast<RealType>(5.26757196603002476852e14),60            static_cast<RealType>(1.75780353683063527570e15),61            static_cast<RealType>(1.85883041942144306222e15),62            static_cast<RealType>(4.19828222275972713819e14),63        };64        BOOST_MATH_STATIC const RealType Q[15] = {65            static_cast<RealType>(1.),66            static_cast<RealType>(3.41295871011779138155e2),67            static_cast<RealType>(5.48907134827349102297e4),68            static_cast<RealType>(5.36641455324410261980e6),69            static_cast<RealType>(3.48045461004960397915e8),70            static_cast<RealType>(1.54920747349701741537e10),71            static_cast<RealType>(4.76490595358644532404e11),72            static_cast<RealType>(1.00104823128402735005e13),73            static_cast<RealType>(1.39703522470411802507e14),74            static_cast<RealType>(1.23724881334160220266e15),75            static_cast<RealType>(6.47437580921138359461e15),76            static_cast<RealType>(1.77627318260037604066e16),77            static_cast<RealType>(2.04792815832538146160e16),78            static_cast<RealType>(7.45102534638640681964e15),79            static_cast<RealType>(3.68496090049571174527e14),80        };81 82        result = tools::evaluate_polynomial(P, x) / tools::evaluate_polynomial(Q, x);83    }84    else if (x < 0.25) {85        RealType t = x - static_cast <RealType>(0.125);86 87        // Rational Approximation88        // Maximum Relative Error: 2.1471e-1789        BOOST_MATH_STATIC const RealType P[7] = {90            static_cast<RealType>(4.35668401768623200524e-1),91            static_cast<RealType>(7.12477357389655327116e0),92            static_cast<RealType>(4.02466317948738993787e1),93            static_cast<RealType>(9.04888497628205955839e1),94            static_cast<RealType>(7.56175387288619211460e1),95            static_cast<RealType>(1.26950253999694502457e1),96            static_cast<RealType>(-6.59304802132933325219e-1),97        };98        BOOST_MATH_STATIC const RealType Q[7] = {99            static_cast<RealType>(1.),100            static_cast<RealType>(1.98623818041545101115e1),101            static_cast<RealType>(1.52856383017632616759e2),102            static_cast<RealType>(5.70706902111659740041e2),103            static_cast<RealType>(1.06454927680197927878e3),104            static_cast<RealType>(9.13160352749764887791e2),105            static_cast<RealType>(2.58872466837209126618e2),106        };107 108        result = tools::evaluate_polynomial(P, t) / tools::evaluate_polynomial(Q, t);109    }110    else if (x < 0.5) {111        RealType t = x - static_cast <RealType>(0.25);112 113        // Rational Approximation114        // Maximum Relative Error: 5.3265e-17115        BOOST_MATH_STATIC const RealType P[8] = {116            static_cast<RealType>(2.95645445681747568732e-1),117            static_cast<RealType>(2.23779537590791610124e0),118            static_cast<RealType>(5.01302198171248036052e0),119            static_cast<RealType>(2.76363131116340641935e0),120            static_cast<RealType>(1.18134858311074670327e-1),121            static_cast<RealType>(2.00287083462139382715e-2),122            static_cast<RealType>(-7.53979800555375661516e-3),123            static_cast<RealType>(1.37294648777729527395e-3),124        };125        BOOST_MATH_STATIC const RealType Q[6] = {126            static_cast<RealType>(1.),127            static_cast<RealType>(1.02879626214781666701e1),128            static_cast<RealType>(3.85125274509784615691e1),129            static_cast<RealType>(6.18474367367800231625e1),130            static_cast<RealType>(3.77100050087302476029e1),131            static_cast<RealType>(5.41866360740066443656e0),132        };133 134        result = tools::evaluate_polynomial(P, t) / tools::evaluate_polynomial(Q, t);135    }136    else if (x < 1) {137        RealType t = x - static_cast <RealType>(0.5);138 139        // Rational Approximation140        // Maximum Relative Error: 2.7947e-17141        BOOST_MATH_STATIC const RealType P[7] = {142            static_cast<RealType>(1.70762401725206223811e-1),143            static_cast<RealType>(8.43343631021918972436e-1),144            static_cast<RealType>(1.39703819152564365627e0),145            static_cast<RealType>(8.75843324574692085009e-1),146            static_cast<RealType>(1.86199552443747562584e-1),147            static_cast<RealType>(7.35858280181579907616e-3),148            static_cast<RealType>(-1.03693607694266081126e-4),149        };150        BOOST_MATH_STATIC const RealType Q[7] = {151            static_cast<RealType>(1.),152            static_cast<RealType>(6.73363440952557318819e0),153            static_cast<RealType>(1.74288966619209299976e1),154            static_cast<RealType>(2.15943268035083671893e1),155            static_cast<RealType>(1.29818726981381859879e1),156            static_cast<RealType>(3.40707211426946022041e0),157            static_cast<RealType>(2.80229012541729457678e-1),158        };159 160        result = tools::evaluate_polynomial(P, t) / tools::evaluate_polynomial(Q, t);161    }162    else if (x < 2) {163        RealType t = x - 1;164 165        // Rational Approximation166        // Maximum Relative Error: 1.7051e-18167        BOOST_MATH_STATIC const RealType P[7] = {168            static_cast<RealType>(8.61071469126041183247e-2),169            static_cast<RealType>(1.69689585946245345838e-1),170            static_cast<RealType>(1.09494833291892212033e-1),171            static_cast<RealType>(2.76619622453130604637e-2),172            static_cast<RealType>(2.44972748006913061509e-3),173            static_cast<RealType>(4.09853605772288438003e-5),174            static_cast<RealType>(-2.63561415158954865283e-7),175        };176        BOOST_MATH_STATIC const RealType Q[7] = {177            static_cast<RealType>(1.),178            static_cast<RealType>(3.04082856018856244947e0),179            static_cast<RealType>(3.52558663323956252986e0),180            static_cast<RealType>(1.94795523079701426332e0),181            static_cast<RealType>(5.23956733400745421623e-1),182            static_cast<RealType>(6.19453597593998871667e-2),183            static_cast<RealType>(2.31061984192347753499e-3),184        };185 186        result = tools::evaluate_polynomial(P, t) / tools::evaluate_polynomial(Q, t);187    }188    else if (x < 4) {189        RealType t = x - 2;190 191        // Rational Approximation192        // Maximum Relative Error: 2.9247e-17193        BOOST_MATH_STATIC const RealType P[7] = {194            static_cast<RealType>(3.91428580496513429479e-2),195            static_cast<RealType>(4.07162484034780126757e-2),196            static_cast<RealType>(1.43342733342753081931e-2),197            static_cast<RealType>(2.01622178115394696215e-3),198            static_cast<RealType>(1.00648013467757737201e-4),199            static_cast<RealType>(9.51545046750892356441e-7),200            static_cast<RealType>(-3.56598940936439037087e-9),201        };202        BOOST_MATH_STATIC const RealType Q[7] = {203            static_cast<RealType>(1.),204            static_cast<RealType>(1.63904431617187026619e0),205            static_cast<RealType>(1.03812003196677309121e0),206            static_cast<RealType>(3.18144310790210668797e-1),207            static_cast<RealType>(4.81930155615666517263e-2),208            static_cast<RealType>(3.25435391589941361778e-3),209            static_cast<RealType>(7.01626957128181647457e-5),210        };211 212        result = tools::evaluate_polynomial(P, t) / tools::evaluate_polynomial(Q, t);213    }214    else if (x < 8) {215        RealType t = x - 4;216 217        // Rational Approximation218        // Maximum Relative Error: 2.6547e-17219        BOOST_MATH_STATIC const RealType P[7] = {220            static_cast<RealType>(1.65057384221262866484e-2),221            static_cast<RealType>(8.05429762031495873704e-3),222            static_cast<RealType>(1.35249234647852784985e-3),223            static_cast<RealType>(9.18685252682786794440e-5),224            static_cast<RealType>(2.23447790937806602674e-6),225            static_cast<RealType>(1.03176916111395079569e-8),226            static_cast<RealType>(-1.94913182592441292094e-11),227        };228        BOOST_MATH_STATIC const RealType Q[7] = {229            static_cast<RealType>(1.),230            static_cast<RealType>(8.10113554189626079232e-1),231            static_cast<RealType>(2.54175325409968367580e-1),232            static_cast<RealType>(3.87119072807894983910e-2),233            static_cast<RealType>(2.92520770162792443587e-3),234            static_cast<RealType>(9.89094130526684467420e-5),235            static_cast<RealType>(1.07148513311070719488e-6),236        };237 238        result = tools::evaluate_polynomial(P, t) / tools::evaluate_polynomial(Q, t);239    }240    else if (x < 16) {241        RealType t = x - 8;242 243        // Rational Approximation244        // Maximum Relative Error: 2.5484e-17245        BOOST_MATH_STATIC const RealType P[7] = {246            static_cast<RealType>(6.60044810497290557553e-3),247            static_cast<RealType>(1.59342644994950292031e-3),248            static_cast<RealType>(1.32429706922966110874e-4),249            static_cast<RealType>(4.45378136978435909660e-6),250            static_cast<RealType>(5.36409958111394628239e-8),251            static_cast<RealType>(1.22293787679910067873e-10),252            static_cast<RealType>(-1.16300443044165216564e-13),253        };254        BOOST_MATH_STATIC const RealType Q[7] = {255            static_cast<RealType>(1.),256            static_cast<RealType>(4.10446485803039594111e-1),257            static_cast<RealType>(6.51887342399859289520e-2),258            static_cast<RealType>(5.02151225308643905366e-3),259            static_cast<RealType>(1.91741179639551137839e-4),260            static_cast<RealType>(3.27316600311598190022e-6),261            static_cast<RealType>(1.78840301213102212857e-8),262        };263 264        result = tools::evaluate_polynomial(P, t) / tools::evaluate_polynomial(Q, t);265    }266    else if (x < 32) {267        RealType t = x - 16;268 269        // Rational Approximation270        // Maximum Relative Error: 2.9866e-17271        BOOST_MATH_STATIC const RealType P[7] = {272            static_cast<RealType>(2.54339461777955741686e-3),273            static_cast<RealType>(3.10069525357852579756e-4),274            static_cast<RealType>(1.30082682796085732756e-5),275            static_cast<RealType>(2.20715868479255585050e-7),276            static_cast<RealType>(1.33996659756026452288e-9),277            static_cast<RealType>(1.53505360463827994365e-12),278            static_cast<RealType>(-7.42649416356965421308e-16),279        };280        BOOST_MATH_STATIC const RealType Q[7] = {281            static_cast<RealType>(1.),282            static_cast<RealType>(2.09203384450859785642e-1),283            static_cast<RealType>(1.69422626897631306130e-2),284            static_cast<RealType>(6.65649059670689720386e-4),285            static_cast<RealType>(1.29654785666009849481e-5),286            static_cast<RealType>(1.12886139474560969619e-7),287            static_cast<RealType>(3.14420104899170413840e-10),288        };289 290        result = tools::evaluate_polynomial(P, t) / tools::evaluate_polynomial(Q, t);291    }292    else if (x < 64) {293        RealType t = x - 32;294 295        // Rational Approximation296        // Maximum Relative Error: 3.3581e-17297        BOOST_MATH_STATIC const RealType P[7] = {298            static_cast<RealType>(9.55085695067883584460e-4),299            static_cast<RealType>(5.86125496733202756668e-5),300            static_cast<RealType>(1.23753971325810931282e-6),301            static_cast<RealType>(1.05643819745933041408e-8),302            static_cast<RealType>(3.22502949410095015524e-11),303            static_cast<RealType>(1.85366144680157942079e-14),304            static_cast<RealType>(-4.53975807317403152058e-18),305        };306        BOOST_MATH_STATIC const RealType Q[7] = {307            static_cast<RealType>(1.),308            static_cast<RealType>(1.05980850386474826374e-1),309            static_cast<RealType>(4.34966042652000070674e-3),310            static_cast<RealType>(8.66341538387446465700e-5),311            static_cast<RealType>(8.55608082202236124363e-7),312            static_cast<RealType>(3.77719968378509293354e-9),313            static_cast<RealType>(5.33287361559571716670e-12),314        };315 316        result = tools::evaluate_polynomial(P, t) / tools::evaluate_polynomial(Q, t);317    }318    else {319        RealType t = 1 / sqrt(x);320 321        // Rational Approximation322        // Maximum Relative Error: 4.7450e-19323        BOOST_MATH_STATIC const RealType P[5] = {324            static_cast<RealType>(1.99471140200716338970e-1),325            static_cast<RealType>(-1.93310094131437487158e-2),326            static_cast<RealType>(-8.44282614309073196195e-3),327            static_cast<RealType>(3.47296024282356038069e-3),328            static_cast<RealType>(-4.05398011689821941383e-4),329        };330        BOOST_MATH_STATIC const RealType Q[5] = {331            static_cast<RealType>(1.),332            static_cast<RealType>(7.00973251258577238892e-1),333            static_cast<RealType>(2.66969681258835723157e-1),334            static_cast<RealType>(5.51785147503612200456e-2),335            static_cast<RealType>(6.50130030979966274341e-3),336        };337 338        result = tools::evaluate_polynomial(P, t) / tools::evaluate_polynomial(Q, t) * t / x;339    }340 341    return result;342}343 344 345template <class RealType>346BOOST_MATH_GPU_ENABLED inline RealType saspoint5_pdf_plus_imp_prec(const RealType& x, const boost::math::integral_constant<int, 113>&)347{348    BOOST_MATH_STD_USING349    RealType result;350 351    if (x < 0.0625) {352        // Rational Approximation353        // Maximum Relative Error: 8.8841e-35354        // LCOV_EXCL_START355        BOOST_MATH_STATIC const RealType P[27] = {356            BOOST_MATH_BIG_CONSTANT(RealType, 113, 6.36619772367581343075535053490057448138e-1),357            BOOST_MATH_BIG_CONSTANT(RealType, 113, 7.57459506929453385798277946154823008327e2),358            BOOST_MATH_BIG_CONSTANT(RealType, 113, 4.46717322844023441698710451505816706570e5),359            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.71501459971530549476153273173061194095e8),360            BOOST_MATH_BIG_CONSTANT(RealType, 113, 4.76700973495278431084530045707075552432e10),361            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.01328150775099946510145440412520620021e13),362            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.70028222513668830210058353057559790101e15),363            BOOST_MATH_BIG_CONSTANT(RealType, 113, 2.29641781943744384078006991488193839955e17),364            BOOST_MATH_BIG_CONSTANT(RealType, 113, 2.52611994112742436432957758588495082163e19),365            BOOST_MATH_BIG_CONSTANT(RealType, 113, 2.27833177267552931459542318826727288124e21),366            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.68946162731840551853993619351896931533e23),367            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.02965010233956763504899745874128908220e25),368            BOOST_MATH_BIG_CONSTANT(RealType, 113, 5.14128569264874914146628076133997950655e26),369            BOOST_MATH_BIG_CONSTANT(RealType, 113, 2.09103580386900060922163883603492216942e28),370            BOOST_MATH_BIG_CONSTANT(RealType, 113, 6.86778299087452621293332172137014749128e29),371            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.80029712249744334924217328667885673985e31),372            BOOST_MATH_BIG_CONSTANT(RealType, 113, 3.70890080432228368476255091774238573277e32),373            BOOST_MATH_BIG_CONSTANT(RealType, 113, 5.88600513999992354909078399482884993261e33),374            BOOST_MATH_BIG_CONSTANT(RealType, 113, 7.01189178534848836605739139176681647755e34),375            BOOST_MATH_BIG_CONSTANT(RealType, 113, 6.06531475170803043941021113424602440078e35),376            BOOST_MATH_BIG_CONSTANT(RealType, 113, 3.64956999370443524098457423629252855270e36),377            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.44276098283517934229787916584447559248e37),378            BOOST_MATH_BIG_CONSTANT(RealType, 113, 3.45856704224433991524661028965741649584e37),379            BOOST_MATH_BIG_CONSTANT(RealType, 113, 4.47263237190968408624388275549716907309e37),380            BOOST_MATH_BIG_CONSTANT(RealType, 113, 2.66186300951901408251743228798832386260e37),381            BOOST_MATH_BIG_CONSTANT(RealType, 113, 5.48064966533519934186356663849904556319e36),382            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.64877082086372991309408001661535573441e35),383        };384        BOOST_MATH_STATIC const RealType Q[28] = {385            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.),386            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.18981461118065892086304195732751798634e3),387            BOOST_MATH_BIG_CONSTANT(RealType, 113, 7.01761929839041982958990681130944341399e5),388            BOOST_MATH_BIG_CONSTANT(RealType, 113, 2.69465252239913021973760046507387620537e8),389            BOOST_MATH_BIG_CONSTANT(RealType, 113, 7.49221044103838155300076098325950584061e10),390            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.59327386289821190042576978177896481082e13),391            BOOST_MATH_BIG_CONSTANT(RealType, 113, 2.67528179803224728786405503232064643870e15),392            BOOST_MATH_BIG_CONSTANT(RealType, 113, 3.61672367849271591791062829736720884633e17),393            BOOST_MATH_BIG_CONSTANT(RealType, 113, 3.98395893917909208201801908435620016552e19),394            BOOST_MATH_BIG_CONSTANT(RealType, 113, 3.60025693881358827551113845076726845495e21),395            BOOST_MATH_BIG_CONSTANT(RealType, 113, 2.67730578745705562356709169493821118109e23),396            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.63843883526710042156562706339553092312e25),397            BOOST_MATH_BIG_CONSTANT(RealType, 113, 8.23075214698024188140971761421762265880e26),398            BOOST_MATH_BIG_CONSTANT(RealType, 113, 3.37775321923937393366376907114580842429e28),399            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.12444724625354796650300159037364355605e30),400            BOOST_MATH_BIG_CONSTANT(RealType, 113, 3.00860835602766063447009568106012449767e31),401            BOOST_MATH_BIG_CONSTANT(RealType, 113, 6.39614080159468893509273006948526469708e32),402            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.06547095715472468415058181351212520255e34),403            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.36755997709303811764051969789337337957e35),404            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.32519530489892818585066019217287415587e36),405            BOOST_MATH_BIG_CONSTANT(RealType, 113, 9.45230390606834183602522256278256501404e36),406            BOOST_MATH_BIG_CONSTANT(RealType, 113, 4.80344475131699029428900627020022801971e37),407            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.66469314795307459840482483320814279444e38),408            BOOST_MATH_BIG_CONSTANT(RealType, 113, 3.70209065673736156218117594311801487932e38),409            BOOST_MATH_BIG_CONSTANT(RealType, 113, 4.84490531246108754748100009460860427732e38),410            BOOST_MATH_BIG_CONSTANT(RealType, 113, 3.30215083398643966091721732133851539475e38),411            BOOST_MATH_BIG_CONSTANT(RealType, 113, 9.58032845332990262754766784625271262271e37),412            BOOST_MATH_BIG_CONSTANT(RealType, 113, 7.50461648438613634025964361513066059697e36),413        };414        // LCOV_EXCL_STOP415        result = tools::evaluate_polynomial(P, x) / tools::evaluate_polynomial(Q, x);416    }417    else if (x < 0.125) {418        RealType t = x - static_cast <RealType>(0.0625);419 420        // Rational Approximation421        // Maximum Relative Error: 3.4585e-35422        // LCOV_EXCL_START423        BOOST_MATH_STATIC const RealType P[14] = {424            BOOST_MATH_BIG_CONSTANT(RealType, 113, 5.46416716200748206779925127900698754119e-1),425            BOOST_MATH_BIG_CONSTANT(RealType, 113, 4.41771273526123373239570033672829787791e1),426            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.56142610225585235535211648703534340871e3),427            BOOST_MATH_BIG_CONSTANT(RealType, 113, 3.15655694129872563686497490176725921724e4),428            BOOST_MATH_BIG_CONSTANT(RealType, 113, 4.00791883661952751945853742455643714995e5),429            BOOST_MATH_BIG_CONSTANT(RealType, 113, 3.30252591667828615354689186280704562254e6),430            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.76168115448224677276551213052798322583e7),431            BOOST_MATH_BIG_CONSTANT(RealType, 113, 5.88534624532179841393387625270218172719e7),432            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.14740447137831585842166880265350244623e8),433            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.14904082614021239315925958812100948136e8),434            BOOST_MATH_BIG_CONSTANT(RealType, 113, 4.76866867279164114004579652405104553404e7),435            BOOST_MATH_BIG_CONSTANT(RealType, 113, 4.53475339598769347326916978463911377965e6),436            BOOST_MATH_BIG_CONSTANT(RealType, 113, -1.88896160275915786487519266368539625326e5),437            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.05543800791717482823610940401201712196e4),438        };439        BOOST_MATH_STATIC const RealType Q[13] = {440            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.),441            BOOST_MATH_BIG_CONSTANT(RealType, 113, 8.44407579416524903840331499438398472639e1),442            BOOST_MATH_BIG_CONSTANT(RealType, 113, 3.15911780811299460009161345260146251462e3),443            BOOST_MATH_BIG_CONSTANT(RealType, 113, 6.88457596285725454686358792906273558406e4),444            BOOST_MATH_BIG_CONSTANT(RealType, 113, 9.66501639812506059997744549411633476528e5),445            BOOST_MATH_BIG_CONSTANT(RealType, 113, 9.12674134216028769532305433586266118000e6),446            BOOST_MATH_BIG_CONSTANT(RealType, 113, 5.87676063477990584593444083577765264392e7),447            BOOST_MATH_BIG_CONSTANT(RealType, 113, 2.56084282739608760299329382263598821653e8),448            BOOST_MATH_BIG_CONSTANT(RealType, 113, 7.34250986378665047914811630036201995871e8),449            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.31288233106689286803200674021353188597e9),450            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.33621494302241474082474689597125896975e9),451            BOOST_MATH_BIG_CONSTANT(RealType, 113, 6.63379428046258653791600947328520263412e8),452            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.14558538557562267533922961110917101850e8),453        };454        // LCOV_EXCL_STOP455        result = tools::evaluate_polynomial(P, t) / tools::evaluate_polynomial(Q, t);456    }457    else if (x < 0.25) {458        RealType t = x - static_cast <RealType>(0.125);459 460        // Rational Approximation461        // Maximum Relative Error: 6.9278e-35462        // LCOV_EXCL_START463        BOOST_MATH_STATIC const RealType P[14] = {464            BOOST_MATH_BIG_CONSTANT(RealType, 113, 4.35668401768623200524372663239480799018e-1),465            BOOST_MATH_BIG_CONSTANT(RealType, 113, 2.30066509937988171489091367354416214000e1),466            BOOST_MATH_BIG_CONSTANT(RealType, 113, 5.05924026744937322690717755156090122074e2),467            BOOST_MATH_BIG_CONSTANT(RealType, 113, 6.12998524955326375684693500551926325112e3),468            BOOST_MATH_BIG_CONSTANT(RealType, 113, 4.52237930808361186011042950178715609183e4),469            BOOST_MATH_BIG_CONSTANT(RealType, 113, 2.10734809597587633852077152938985998879e5),470            BOOST_MATH_BIG_CONSTANT(RealType, 113, 6.20796157836149826988172603622242119074e5),471            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.12398478061053302537736799402801934778e6),472            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.17841330491647012385157454335820786724e6),473            BOOST_MATH_BIG_CONSTANT(RealType, 113, 6.46281413765362795389526259057436151953e5),474            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.52220357379402116641048490644093497829e5),475            BOOST_MATH_BIG_CONSTANT(RealType, 113, 8.51130316105543847380510577656570543736e3),476            BOOST_MATH_BIG_CONSTANT(RealType, 113, -2.32201781975497810173532067354797097401e2),477            BOOST_MATH_BIG_CONSTANT(RealType, 113, 8.96874547436310030183519174847668703774e0),478        };479        BOOST_MATH_STATIC const RealType Q[13] = {480            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.),481            BOOST_MATH_BIG_CONSTANT(RealType, 113, 5.63164311578114868477819520857286165076e1),482            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.34964379844144961683927306966955217328e3),483            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.82966031793809959278519002412667883288e4),484            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.56215285850856046267451500310816276675e5),485            BOOST_MATH_BIG_CONSTANT(RealType, 113, 8.81046679663412610005501878092824281161e5),486            BOOST_MATH_BIG_CONSTANT(RealType, 113, 3.33868038251479411246071640628518434659e6),487            BOOST_MATH_BIG_CONSTANT(RealType, 113, 8.46262495881941625571640264458627940579e6),488            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.40052628730443097561652737049917920495e7),489            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.44394803828297754346261138417756941544e7),490            BOOST_MATH_BIG_CONSTANT(RealType, 113, 8.56647617803506258343236509255155360957e6),491            BOOST_MATH_BIG_CONSTANT(RealType, 113, 2.53513095899009948733175317927025056561e6),492            BOOST_MATH_BIG_CONSTANT(RealType, 113, 2.69130675750530663088963759279778748696e5),493        };494        // LCOV_EXCL_STOP495        result = tools::evaluate_polynomial(P, t) / tools::evaluate_polynomial(Q, t);496    }497    else if (x < 0.5) {498        RealType t = x - static_cast <RealType>(0.25);499 500        // Rational Approximation501        // Maximum Relative Error: 6.9378e-36502        // LCOV_EXCL_START503        BOOST_MATH_STATIC const RealType P[14] = {504            BOOST_MATH_BIG_CONSTANT(RealType, 113, 2.95645445681747568731488283573032414811e-1),505            BOOST_MATH_BIG_CONSTANT(RealType, 113, 6.83246437763964151893665752064650172391e0),506            BOOST_MATH_BIG_CONSTANT(RealType, 113, 6.85333417559435252576820440080930004674e1),507            BOOST_MATH_BIG_CONSTANT(RealType, 113, 3.90974714199542064991001365628659054084e2),508            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.39707205668285805800884524044738261436e3),509            BOOST_MATH_BIG_CONSTANT(RealType, 113, 3.24814598419826565698241508792385416075e3),510            BOOST_MATH_BIG_CONSTANT(RealType, 113, 4.95012897118808793886195172068123345314e3),511            BOOST_MATH_BIG_CONSTANT(RealType, 113, 4.87265743900139300849404272909665705025e3),512            BOOST_MATH_BIG_CONSTANT(RealType, 113, 2.98795164648056126707212245325405968413e3),513            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.07012128790318535418330629467906917213e3),514            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.99797198893523173981812955075412130913e2),515            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.55029227544167913873724286459253168886e1),516            BOOST_MATH_BIG_CONSTANT(RealType, 113, 2.54064889901609722583601330171719819660e-1),517            BOOST_MATH_BIG_CONSTANT(RealType, 113, -1.72254289950537680833853394958874977464e-3),518        };519        BOOST_MATH_STATIC const RealType Q[14] = {520            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.),521            BOOST_MATH_BIG_CONSTANT(RealType, 113, 2.58291085070053442257438623486099473087e1),522            BOOST_MATH_BIG_CONSTANT(RealType, 113, 2.95618461039379226195473938654286975682e2),523            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.97427161745150579714266897556974326502e3),524            BOOST_MATH_BIG_CONSTANT(RealType, 113, 8.52730436681412535198281529590508861106e3),525            BOOST_MATH_BIG_CONSTANT(RealType, 113, 2.49521185356761585062135933350225236726e4),526            BOOST_MATH_BIG_CONSTANT(RealType, 113, 5.03881178612341724262911142022761966061e4),527            BOOST_MATH_BIG_CONSTANT(RealType, 113, 7.02360046338629039644581819847209730553e4),528            BOOST_MATH_BIG_CONSTANT(RealType, 113, 6.65580339066083507998465454599272345735e4),529            BOOST_MATH_BIG_CONSTANT(RealType, 113, 4.15462499626138125314518636645472893045e4),530            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.61951767959774678843021179589300545717e4),531            BOOST_MATH_BIG_CONSTANT(RealType, 113, 3.60745557054877240279811529503888551492e3),532            BOOST_MATH_BIG_CONSTANT(RealType, 113, 3.91061555870569579915258835459255406575e2),533            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.43045229010040855016672246098687100063e1),534        };535        // LCOV_EXCL_STOP536        result = tools::evaluate_polynomial(P, t) / tools::evaluate_polynomial(Q, t);537    }538    else if (x < 1) {539        RealType t = x - static_cast <RealType>(0.5);540 541        // Rational Approximation542        // Maximum Relative Error: 6.4363e-35543        // LCOV_EXCL_START544        BOOST_MATH_STATIC const RealType P[14] = {545            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.70762401725206223811383500786268939645e-1),546            BOOST_MATH_BIG_CONSTANT(RealType, 113, 2.19353011456197635663058525904929358535e0),547            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.22974648900600015961253465796487372402e1),548            BOOST_MATH_BIG_CONSTANT(RealType, 113, 3.91951696059042324975935209295355569292e1),549            BOOST_MATH_BIG_CONSTANT(RealType, 113, 7.79039444119906169910281912009369164227e1),550            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.00089963120992100860902142265631127046e2),551            BOOST_MATH_BIG_CONSTANT(RealType, 113, 8.37108883429306700857182028809960789020e1),552            BOOST_MATH_BIG_CONSTANT(RealType, 113, 4.49586566873564432788366931251358248417e1),553            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.49790521605774884174840168128255220471e1),554            BOOST_MATH_BIG_CONSTANT(RealType, 113, 2.90660338063979435668763608259382712726e0),555            BOOST_MATH_BIG_CONSTANT(RealType, 113, 2.93409982383888149064797608605579930804e-1),556            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.22802459215932860445033185874876812040e-2),557            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.07739227340181463034286653569468171767e-4),558            BOOST_MATH_BIG_CONSTANT(RealType, 113, -4.02669738424010290973023004028523684766e-7),559        };560        BOOST_MATH_STATIC const RealType Q[14] = {561            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.),562            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.46404480283267324138113869370306506431e1),563            BOOST_MATH_BIG_CONSTANT(RealType, 113, 9.54550184643308468933661600211579108422e1),564            BOOST_MATH_BIG_CONSTANT(RealType, 113, 3.63602410602063476726031476852965502123e2),565            BOOST_MATH_BIG_CONSTANT(RealType, 113, 8.94463479638213888403144706176973026333e2),566            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.48607087483870766806529883069123352339e3),567            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.69715692924508994524755312953665710218e3),568            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.33237849965272853370191827043868842100e3),569            BOOST_MATH_BIG_CONSTANT(RealType, 113, 7.08460086451666825383009487734769646087e2),570            BOOST_MATH_BIG_CONSTANT(RealType, 113, 2.47365552394788536087148438788608689300e2),571            BOOST_MATH_BIG_CONSTANT(RealType, 113, 5.38010282703940184371247559455167674975e1),572            BOOST_MATH_BIG_CONSTANT(RealType, 113, 6.67219842525655806370702248122668214685e0),573            BOOST_MATH_BIG_CONSTANT(RealType, 113, 4.01852843874982199859775136086676841910e-1),574            BOOST_MATH_BIG_CONSTANT(RealType, 113, 8.14767043526088185802569803397824432028e-3),575        };576        // LCOV_EXCL_STOP577        result = tools::evaluate_polynomial(P, t) / tools::evaluate_polynomial(Q, t);578    }579    else if (x < 2) {580        RealType t = x - 1;581 582        // Rational Approximation583        // Maximum Relative Error: 9.1244e-35584        // LCOV_EXCL_START585        BOOST_MATH_STATIC const RealType P[13] = {586            BOOST_MATH_BIG_CONSTANT(RealType, 113, 8.61071469126041183247373313827161939454e-2),587            BOOST_MATH_BIG_CONSTANT(RealType, 113, 4.35837460186564880289965856498718321896e-1),588            BOOST_MATH_BIG_CONSTANT(RealType, 113, 9.47783071967681246738651796742079530382e-1),589            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.16019502727107539284403003943433359877e0),590            BOOST_MATH_BIG_CONSTANT(RealType, 113, 8.80510046274709592896987229782879937271e-1),591            BOOST_MATH_BIG_CONSTANT(RealType, 113, 4.30456542768955299533391113704078540955e-1),592            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.36539167913428133313942008990965988621e-1),593            BOOST_MATH_BIG_CONSTANT(RealType, 113, 2.76450743657913389896743235938695682829e-2),594            BOOST_MATH_BIG_CONSTANT(RealType, 113, 3.42847090205575096649865021874905747106e-3),595            BOOST_MATH_BIG_CONSTANT(RealType, 113, 2.41380341540026027117735179862124402398e-4),596            BOOST_MATH_BIG_CONSTANT(RealType, 113, 8.40549721587212773424211923602910622515e-6),597            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.09089653391032945883918434200567278139e-7),598            BOOST_MATH_BIG_CONSTANT(RealType, 113, 2.21403900721572475664926557233205232491e-10),599        };600        BOOST_MATH_STATIC const RealType Q[14] = {601            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.),602            BOOST_MATH_BIG_CONSTANT(RealType, 113, 6.13172035933794917563324458011617112124e0),603            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.65687100738157412154132860910003018338e1),604            BOOST_MATH_BIG_CONSTANT(RealType, 113, 2.59672433683883998168388916533196510994e1),605            BOOST_MATH_BIG_CONSTANT(RealType, 113, 2.61469557815097583209668778301921207455e1),606            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.77070955301136405523492329700943077340e1),607            BOOST_MATH_BIG_CONSTANT(RealType, 113, 8.20825570431301943907348077675777546304e0),608            BOOST_MATH_BIG_CONSTANT(RealType, 113, 2.60136197167727810483751794121979805142e0),609            BOOST_MATH_BIG_CONSTANT(RealType, 113, 5.53723076053642006159503073104152703814e-1),610            BOOST_MATH_BIG_CONSTANT(RealType, 113, 7.63397465217490984394478518334313362490e-2),611            BOOST_MATH_BIG_CONSTANT(RealType, 113, 6.40577918603319523990542237990107206371e-3),612            BOOST_MATH_BIG_CONSTANT(RealType, 113, 2.94376458316662573143947719026985667328e-4),613            BOOST_MATH_BIG_CONSTANT(RealType, 113, 6.09333568224541559157192543410988474886e-6),614            BOOST_MATH_BIG_CONSTANT(RealType, 113, 3.59947287428695057506683902409023760438e-8),615        };616        // LCOV_EXCL_STOP617        result = tools::evaluate_polynomial(P, t) / tools::evaluate_polynomial(Q, t);618    }619    else if (x < 4) {620        RealType t = x - 2;621 622        // Rational Approximation623        // Maximum Relative Error: 8.1110e-35624        // LCOV_EXCL_START625        BOOST_MATH_STATIC const RealType P[13] = {626            BOOST_MATH_BIG_CONSTANT(RealType, 113, 3.91428580496513429479068747515164587814e-2),627            BOOST_MATH_BIG_CONSTANT(RealType, 113, 9.69015019070193436467106672180804948494e-2),628            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.03147451266231819912643754579290008651e-1),629            BOOST_MATH_BIG_CONSTANT(RealType, 113, 6.18825170881552297150779588545792258740e-2),630            BOOST_MATH_BIG_CONSTANT(RealType, 113, 2.30548850262278582401286533053286406505e-2),631            BOOST_MATH_BIG_CONSTANT(RealType, 113, 5.54315108501815531776138839512564427279e-3),632            BOOST_MATH_BIG_CONSTANT(RealType, 113, 8.66434584176931077662201101557716482514e-4),633            BOOST_MATH_BIG_CONSTANT(RealType, 113, 8.66158632576958238392567355014249971287e-5),634            BOOST_MATH_BIG_CONSTANT(RealType, 113, 5.31365802206301246598393821671437863818e-6),635            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.85378389166807263837732376845556856416e-7),636            BOOST_MATH_BIG_CONSTANT(RealType, 113, 3.20375363151456683883984823721339648679e-9),637            BOOST_MATH_BIG_CONSTANT(RealType, 113, 2.06637401794693307359898089790558771957e-11),638            BOOST_MATH_BIG_CONSTANT(RealType, 113, 2.08663671047376684678494625068451888284e-14),639        };640        BOOST_MATH_STATIC const RealType Q[14] = {641            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.),642            BOOST_MATH_BIG_CONSTANT(RealType, 113, 3.07443397096591141329212291707948432414e0),643            BOOST_MATH_BIG_CONSTANT(RealType, 113, 4.16665031056584124503224711639009530348e0),644            BOOST_MATH_BIG_CONSTANT(RealType, 113, 3.27666060511630720485121299731204403783e0),645            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.65646979169107732387032821262953301311e0),646            BOOST_MATH_BIG_CONSTANT(RealType, 113, 5.63594064986880863092994744424349361396e-1),647            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.31360114173642293100378020953197965181e-1),648            BOOST_MATH_BIG_CONSTANT(RealType, 113, 2.09489929949457075237756409511944811481e-2),649            BOOST_MATH_BIG_CONSTANT(RealType, 113, 2.24574519309785870806550506199124944514e-3),650            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.56048486483867679310086683710523566607e-4),651            BOOST_MATH_BIG_CONSTANT(RealType, 113, 6.60417286783794818094722636906776809193e-6),652            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.53154117367296710469692755461431646999e-7),653            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.60041713691072903334637560080298818163e-9),654            BOOST_MATH_BIG_CONSTANT(RealType, 113, 4.77381528950794767694352468734042252745e-12),655        };656        // LCOV_EXCL_STOP657        result = tools::evaluate_polynomial(P, t) / tools::evaluate_polynomial(Q, t);658    }659    else if (x < 8) {660        RealType t = x - 4;661 662        // Rational Approximation663        // Maximum Relative Error: 2.5228e-35664        // LCOV_EXCL_START665        BOOST_MATH_STATIC const RealType P[14] = {666            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.65057384221262866484014802392420311075e-2),667            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.92801687242885330588201777283015178448e-2),668            BOOST_MATH_BIG_CONSTANT(RealType, 113, 9.65508815862861196424333614846876229064e-3),669            BOOST_MATH_BIG_CONSTANT(RealType, 113, 2.71545573465295958468808641544341412235e-3),670            BOOST_MATH_BIG_CONSTANT(RealType, 113, 4.72077718130407940498710469661947719216e-4),671            BOOST_MATH_BIG_CONSTANT(RealType, 113, 5.26299620525538984108147098966692839348e-5),672            BOOST_MATH_BIG_CONSTANT(RealType, 113, 3.77971404992990847565880351976461271350e-6),673            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.71176235845517643695464740679643640241e-7),674            BOOST_MATH_BIG_CONSTANT(RealType, 113, 4.64603919225244695533557520384631958897e-9),675            BOOST_MATH_BIG_CONSTANT(RealType, 113, 6.85274347406803894317891882905083368489e-11),676            BOOST_MATH_BIG_CONSTANT(RealType, 113, 4.48564096627181435612831469651920186491e-13),677            BOOST_MATH_BIG_CONSTANT(RealType, 113, 6.90886715044580341917806394089282500340e-16),678            BOOST_MATH_BIG_CONSTANT(RealType, 113, -6.39396206221935864416563232680283312796e-19),679            BOOST_MATH_BIG_CONSTANT(RealType, 113, 8.37760675743046300528308203869876086823e-22),680        };681        BOOST_MATH_STATIC const RealType Q[13] = {682            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.),683            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.49023284463742780238035958819642738891e0),684            BOOST_MATH_BIG_CONSTANT(RealType, 113, 9.76284367953836866133894756472541395734e-1),685            BOOST_MATH_BIG_CONSTANT(RealType, 113, 3.69932155343422362573146811195224195135e-1),686            BOOST_MATH_BIG_CONSTANT(RealType, 113, 8.97593541520549770519034085640975455763e-2),687            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.45862809001322359249894968573830094537e-2),688            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.61348135835522976885804369721316193713e-3),689            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.21069949470458047530981551232427019037e-4),690            BOOST_MATH_BIG_CONSTANT(RealType, 113, 6.03132437580490629136144285669590192597e-6),691            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.91030348024641585284338958059030520141e-7),692            BOOST_MATH_BIG_CONSTANT(RealType, 113, 3.56320479309161046934628280237629402373e-9),693            BOOST_MATH_BIG_CONSTANT(RealType, 113, 3.39524198476052364627683067034422502163e-11),694            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.18666081063885228839052386515073873844e-13),695        };696        // LCOV_EXCL_STOP697        result = tools::evaluate_polynomial(P, t) / tools::evaluate_polynomial(Q, t);698    }699    else if (x < 16) {700        RealType t = x - 8;701 702        // Rational Approximation703        // Maximum Relative Error: 9.6732e-36704        // LCOV_EXCL_START705        BOOST_MATH_STATIC const RealType P[14] = {706            BOOST_MATH_BIG_CONSTANT(RealType, 113, 6.60044810497290557552736366450372523266e-3),707            BOOST_MATH_BIG_CONSTANT(RealType, 113, 4.27034183360438185616541260923634443241e-3),708            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.19813403884333707962156711479716066536e-3),709            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.91346554854771687970018076643044998737e-4),710            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.91975837766081548424458764226669789039e-5),711            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.26031304514411902758114277797443618334e-6),712            BOOST_MATH_BIG_CONSTANT(RealType, 113, 5.47127194811140370123712253347211626753e-8),713            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.55248861254135821097921903190564312000e-9),714            BOOST_MATH_BIG_CONSTANT(RealType, 113, 2.78340847719683652633864722047250151066e-11),715            BOOST_MATH_BIG_CONSTANT(RealType, 113, 2.95888612422041337572422846394029849086e-13),716            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.66363005792960308636467394552324255493e-15),717            BOOST_MATH_BIG_CONSTANT(RealType, 113, 3.93244800648299424751906591077496534948e-18),718            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.95046217952146113063614290717113024410e-21),719            BOOST_MATH_BIG_CONSTANT(RealType, 113, -4.46784746963816915795587433372284530785e-25),720        };721        BOOST_MATH_STATIC const RealType Q[14] = {722            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.),723            BOOST_MATH_BIG_CONSTANT(RealType, 113, 8.16012189991825507132967712656930682478e-1),724            BOOST_MATH_BIG_CONSTANT(RealType, 113, 2.95202772611563835130347051925062280272e-1),725            BOOST_MATH_BIG_CONSTANT(RealType, 113, 6.23801477561401113332870463345197159418e-2),726            BOOST_MATH_BIG_CONSTANT(RealType, 113, 8.54022665579711946784722766000062263305e-3),727            BOOST_MATH_BIG_CONSTANT(RealType, 113, 7.94266182294627770206082679848878391116e-4),728            BOOST_MATH_BIG_CONSTANT(RealType, 113, 5.11782839184878848480753630961211685630e-5),729            BOOST_MATH_BIG_CONSTANT(RealType, 113, 2.28827067686094594197542725283923947812e-6),730            BOOST_MATH_BIG_CONSTANT(RealType, 113, 7.00220719177374237332018587370837457299e-8),731            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.42250513143925626748132661121749401409e-9),732            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.82007216963767723991309138907689681422e-11),733            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.34214834652884406013489167210936679359e-13),734            BOOST_MATH_BIG_CONSTANT(RealType, 113, 4.85519293212465087373898447546710143008e-16),735            BOOST_MATH_BIG_CONSTANT(RealType, 113, 5.96728437809303144188312623363453475831e-19),736        };737        // LCOV_EXCL_STOP738        result = tools::evaluate_polynomial(P, t) / tools::evaluate_polynomial(Q, t);739    }740    else if (x < 32) {741        RealType t = x - 16;742 743        // Rational Approximation744        // Maximum Relative Error: 1.0113e-35745        // LCOV_EXCL_START746        BOOST_MATH_STATIC const RealType P[14] = {747            BOOST_MATH_BIG_CONSTANT(RealType, 113, 2.54339461777955741686401041938275102207e-3),748            BOOST_MATH_BIG_CONSTANT(RealType, 113, 8.17747085249877439037826121862689145081e-4),749            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.14104576580586095462211756659036062930e-4),750            BOOST_MATH_BIG_CONSTANT(RealType, 113, 9.06903778663262313120049231822412184382e-6),751            BOOST_MATH_BIG_CONSTANT(RealType, 113, 4.53115958954246158081703822428768781010e-7),752            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.48225007017630665357941682179157662142e-8),753            BOOST_MATH_BIG_CONSTANT(RealType, 113, 3.20810829523286181556951002345409843125e-10),754            BOOST_MATH_BIG_CONSTANT(RealType, 113, 4.54070972719909957155251432996372246019e-12),755            BOOST_MATH_BIG_CONSTANT(RealType, 113, 4.06258623970363729581390609798632080752e-14),756            BOOST_MATH_BIG_CONSTANT(RealType, 113, 2.15603641527498625694677136504611545743e-16),757            BOOST_MATH_BIG_CONSTANT(RealType, 113, 6.05376970060354261667000502105893106009e-19),758            BOOST_MATH_BIG_CONSTANT(RealType, 113, 7.14727542705613448694396750352455931731e-22),759            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.76883960167449461476228984331517762578e-25),760            BOOST_MATH_BIG_CONSTANT(RealType, 113, -2.03558202009465610972808653993060437679e-29),761        };762        BOOST_MATH_STATIC const RealType Q[14] = {763            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.),764            BOOST_MATH_BIG_CONSTANT(RealType, 113, 4.08809672969012756295937194823378109391e-1),765            BOOST_MATH_BIG_CONSTANT(RealType, 113, 7.41148083436617376855422685448827300528e-2),766            BOOST_MATH_BIG_CONSTANT(RealType, 113, 7.85101541143091590863368934606849033688e-3),767            BOOST_MATH_BIG_CONSTANT(RealType, 113, 5.38984899982960112626157576750593711628e-4),768            BOOST_MATH_BIG_CONSTANT(RealType, 113, 2.51437845497783812562009857096371643785e-5),769            BOOST_MATH_BIG_CONSTANT(RealType, 113, 8.12891276596072815764119699444334380521e-7),770            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.82412500887161687329929693518498698716e-8),771            BOOST_MATH_BIG_CONSTANT(RealType, 113, 2.80215715026891688444965605768621763721e-10),772            BOOST_MATH_BIG_CONSTANT(RealType, 113, 2.85838684678780184082810752634454259831e-12),773            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.83675729736846176693608812315852523556e-14),774            BOOST_MATH_BIG_CONSTANT(RealType, 113, 6.80347165008408134158968403924819637224e-17),775            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.23639219622240634094606955067799349447e-19),776            BOOST_MATH_BIG_CONSTANT(RealType, 113, 7.63446235885036169537726818244420509024e-23),777        };778        // LCOV_EXCL_STOP779        result = tools::evaluate_polynomial(P, t) / tools::evaluate_polynomial(Q, t);780    }781    else if (x < 64) {782        RealType t = x - 32;783 784        // Rational Approximation785        // Maximum Relative Error: 9.7056e-36786        // LCOV_EXCL_START787        BOOST_MATH_STATIC const RealType P[14] = {788            BOOST_MATH_BIG_CONSTANT(RealType, 113, 9.55085695067883584460317653567009454037e-4),789            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.52919532248638251721278667010429548877e-4),790            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.06266842295477991789450356745903177571e-5),791            BOOST_MATH_BIG_CONSTANT(RealType, 113, 4.20671609948319334255323512011575892813e-7),792            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.04692714549374449244320605137676408001e-8),793            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.70605481454469287545965803970738264158e-10),794            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.83960996572005209177458712170004097587e-12),795            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.29732261733491885750067029092181853751e-14),796            BOOST_MATH_BIG_CONSTANT(RealType, 113, 5.78385693918239619309147428897790440735e-17),797            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.52969197316398995616879018998891661712e-19),798            BOOST_MATH_BIG_CONSTANT(RealType, 113, 2.14063120299947677255281707434419044806e-22),799            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.25957675329657493245893497219459256248e-25),800            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.55238112862817593053765898004447484717e-29),801            BOOST_MATH_BIG_CONSTANT(RealType, 113, -8.93970406521541790658675747195982964585e-34),802        };803        BOOST_MATH_STATIC const RealType Q[14] = {804            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.),805            BOOST_MATH_BIG_CONSTANT(RealType, 113, 2.04722757068068234153968603374387493579e-1),806            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.85854131835804458353300285777969427206e-2),807            BOOST_MATH_BIG_CONSTANT(RealType, 113, 9.85809281481040288085436275150792074968e-4),808            BOOST_MATH_BIG_CONSTANT(RealType, 113, 3.38860750164285700051427698379841626305e-5),809            BOOST_MATH_BIG_CONSTANT(RealType, 113, 7.91463283601681120487987016215594255423e-7),810            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.28104952818420195583669572450494959042e-8),811            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.43912720109615655035554724090181888734e-10),812            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.10668954229813492117417896681856998595e-12),813            BOOST_MATH_BIG_CONSTANT(RealType, 113, 5.65093571330749369067212003571435698558e-15),814            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.81758227619561958470583781325371429458e-17),815            BOOST_MATH_BIG_CONSTANT(RealType, 113, 3.36970757752002915423191164330598255294e-20),816            BOOST_MATH_BIG_CONSTANT(RealType, 113, 3.06487673393164724939989217811068656932e-23),817            BOOST_MATH_BIG_CONSTANT(RealType, 113, 9.47121057452822097779067717258050172115e-27),818        };819        // LCOV_EXCL_STOP820        result = tools::evaluate_polynomial(P, t) / tools::evaluate_polynomial(Q, t);821    }822    else {823        RealType t = 1 / sqrt(x);824 825        // Rational Approximation826        // Maximum Relative Error: 7.1032e-36827        // LCOV_EXCL_START828        BOOST_MATH_STATIC const RealType P[8] = {829            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.99471140200716338969973029967190934238e-1),830            BOOST_MATH_BIG_CONSTANT(RealType, 113, 3.82846732476244747063962056024672844211e-2),831            BOOST_MATH_BIG_CONSTANT(RealType, 113, -3.69724475658159099827638225237895868258e-3),832            BOOST_MATH_BIG_CONSTANT(RealType, 113, 2.21259630917863228526439367416146293173e-3),833            BOOST_MATH_BIG_CONSTANT(RealType, 113, 3.13469812721679130825429547254346177005e-5),834            BOOST_MATH_BIG_CONSTANT(RealType, 113, -2.73237434182338329541631611908947123606e-5),835            BOOST_MATH_BIG_CONSTANT(RealType, 113, 4.72986150007117100707304201395140411630e-6),836            BOOST_MATH_BIG_CONSTANT(RealType, 113, -2.53567129749337040254350979652515879881e-7),837        };838        BOOST_MATH_STATIC const RealType Q[9] = {839            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.),840            BOOST_MATH_BIG_CONSTANT(RealType, 113, 9.89815449697874475254942178935516387239e-1),841            BOOST_MATH_BIG_CONSTANT(RealType, 113, 5.21223228867921988134838870379132038419e-1),842            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.79514417558927397512722128659468888701e-1),843            BOOST_MATH_BIG_CONSTANT(RealType, 113, 4.43331254539687594239741585764730095049e-2),844            BOOST_MATH_BIG_CONSTANT(RealType, 113, 7.99078779616201786316256750758748178864e-3),845            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.04590833634768023225748107112347131311e-3),846            BOOST_MATH_BIG_CONSTANT(RealType, 113, 9.17497990182339853998751740288392648984e-5),847            BOOST_MATH_BIG_CONSTANT(RealType, 113, 4.53420609011698705803549938558385779137e-6),848        };849        // LCOV_EXCL_STOP850        result = tools::evaluate_polynomial(P, t) / tools::evaluate_polynomial(Q, t) * t / x;851    }852 853    return result;854}855 856 857template <class RealType>858BOOST_MATH_GPU_ENABLED inline RealType saspoint5_pdf_imp_prec(const RealType& x, const boost::math::integral_constant<int, 53> &tag) {859    BOOST_MATH_STD_USING // for ADL of std functions860 861    return saspoint5_pdf_plus_imp_prec<RealType>(abs(x), tag);862}863 864template <class RealType>865BOOST_MATH_GPU_ENABLED inline RealType saspoint5_pdf_imp_prec(const RealType& x, const boost::math::integral_constant<int, 113>& tag) {866    BOOST_MATH_STD_USING // for ADL of std functions867 868    return saspoint5_pdf_plus_imp_prec<RealType>(abs(x), tag);869}870 871template <class RealType, class Policy>872BOOST_MATH_GPU_ENABLED inline RealType saspoint5_pdf_imp(const saspoint5_distribution<RealType, Policy>& dist, const RealType& x) {873    //874    // This calculates the pdf of the Saspoint5 distribution and/or its complement.875    //876 877    BOOST_MATH_STD_USING // for ADL of std functions878    constexpr auto function = "boost::math::pdf(saspoint5<%1%>&, %1%)";879    RealType result = 0;880    RealType location = dist.location();881    RealType scale = dist.scale();882 883    if (false == detail::check_location(function, location, &result, Policy()))884    {885        return result;886    }887    if (false == detail::check_scale(function, scale, &result, Policy()))888    {889        return result;890    }891    if (false == detail::check_x(function, x, &result, Policy()))892    {893        return result;894    }895 896    typedef typename tools::promote_args<RealType>::type result_type;897    typedef typename policies::precision<result_type, Policy>::type precision_type;898    typedef boost::math::integral_constant<int,899        precision_type::value <= 0 ? 0 :900        precision_type::value <= 53 ? 53 :901        precision_type::value <= 113 ? 113 : 0902    > tag_type;903 904    static_assert(tag_type::value, "The SaS point5 distribution is only implemented for types with known precision, and 113 bits or fewer in the mantissa (ie 128 bit quad-floats");905 906    RealType u = (x - location) / scale;907 908    result = saspoint5_pdf_imp_prec(u, tag_type()) / scale;909 910    return result;911}912 913template <class RealType>914BOOST_MATH_GPU_ENABLED inline RealType saspoint5_cdf_plus_imp_prec(const RealType& x, const boost::math::integral_constant<int, 53>&)915{916    BOOST_MATH_STD_USING917    RealType result;918 919    if (x < 0.5) {920        // Rational Approximation921        // Maximum Relative Error: 2.6225e-17922        BOOST_MATH_STATIC const RealType P[16] = {923            static_cast<RealType>(5.0e-1),924            static_cast<RealType>(1.11530082549581486148e2),925            static_cast<RealType>(1.18564167533523512811e4),926            static_cast<RealType>(7.51503793077701705413e5),927            static_cast<RealType>(3.05648233678438482191e7),928            static_cast<RealType>(8.12176734530090957088e8),929            static_cast<RealType>(1.39533182836234507573e10),930            static_cast<RealType>(1.50394359286077974212e11),931            static_cast<RealType>(9.79057903542935575811e11),932            static_cast<RealType>(3.73800992855150140014e12),933            static_cast<RealType>(8.12697090329432868343e12),934            static_cast<RealType>(9.63154058643818290870e12),935            static_cast<RealType>(5.77714904017642642181e12),936            static_cast<RealType>(1.53321958252091815685e12),937            static_cast<RealType>(1.36220966258718212359e11),938            static_cast<RealType>(1.70766655065405022702e9),939        };940        BOOST_MATH_STATIC const RealType Q[16] = {941            static_cast<RealType>(1.),942            static_cast<RealType>(2.24333404643898143947e2),943            static_cast<RealType>(2.39984636687021023600e4),944            static_cast<RealType>(1.53353791432086858132e6),945            static_cast<RealType>(6.30764952479861776476e7),946            static_cast<RealType>(1.70405769169309597488e9),947            static_cast<RealType>(3.00381227010195289341e10),948            static_cast<RealType>(3.37519046677507392667e11),949            static_cast<RealType>(2.35001610518109063314e12),950            static_cast<RealType>(9.90961948200767679416e12),951            static_cast<RealType>(2.47066673978544828258e13),952            static_cast<RealType>(3.51442593932882610556e13),953            static_cast<RealType>(2.68891431106117733130e13),954            static_cast<RealType>(9.99723484253582494535e12),955            static_cast<RealType>(1.49190229409236772612e12),956            static_cast<RealType>(5.68752980146893975323e10),957        };958 959        result = tools::evaluate_polynomial(P, x) / tools::evaluate_polynomial(Q, x);960    }961    else if (x < 1) {962        RealType t = x - static_cast <RealType>(0.5);963 964        // Rational Approximation965        // Maximum Relative Error: 9.2135e-19966        BOOST_MATH_STATIC const RealType P[8] = {967            static_cast<RealType>(3.31309550000758082456e-1),968            static_cast<RealType>(1.63012162307622129396e0),969            static_cast<RealType>(2.97763161467248770571e0),970            static_cast<RealType>(2.49277948739575294031e0),971            static_cast<RealType>(9.49619262302649586821e-1),972            static_cast<RealType>(1.38360148984087584165e-1),973            static_cast<RealType>(4.00812864075652334798e-3),974            static_cast<RealType>(-4.82051978765960490940e-5),975        };976        BOOST_MATH_STATIC const RealType Q[7] = {977            static_cast<RealType>(1.),978            static_cast<RealType>(5.43565383128046471592e0),979            static_cast<RealType>(1.13265160672130133152e1),980            static_cast<RealType>(1.13352316246726435292e1),981            static_cast<RealType>(5.56671465170409694873e0),982            static_cast<RealType>(1.21011708389501479550e0),983            static_cast<RealType>(8.34618282872428849500e-2),984        };985 986        result = tools::evaluate_polynomial(P, t) / tools::evaluate_polynomial(Q, t);987    }988    else if (x < 2) {989        RealType t = x - 1;990 991        // Rational Approximation992        // Maximum Relative Error: 6.4688e-17993        BOOST_MATH_STATIC const RealType P[7] = {994            static_cast<RealType>(2.71280312689343248819e-1),995            static_cast<RealType>(7.44610837974139249205e-1),996            static_cast<RealType>(7.17844128359406982825e-1),997            static_cast<RealType>(2.98789060945288850507e-1),998            static_cast<RealType>(5.22747411439102272576e-2),999            static_cast<RealType>(3.06447984437786430265e-3),1000            static_cast<RealType>(2.60407071021044908690e-5),1001        };1002        BOOST_MATH_STATIC const RealType Q[7] = {1003            static_cast<RealType>(1.),1004            static_cast<RealType>(3.06221257507188300824e0),1005            static_cast<RealType>(3.44827372231472308047e0),1006            static_cast<RealType>(1.78166113338930668519e0),1007            static_cast<RealType>(4.25580478492907232687e-1),1008            static_cast<RealType>(4.09983847731128510426e-2),1009            static_cast<RealType>(1.04343172183467651240e-3),1010        };1011 1012        result = tools::evaluate_polynomial(P, t) / tools::evaluate_polynomial(Q, t);1013    }1014    else if (x < 4) {1015        RealType t = x - 2;1016 1017        // Rational Approximation1018        // Maximum Relative Error: 8.2289e-181019        BOOST_MATH_STATIC const RealType P[7] = {1020            static_cast<RealType>(2.13928162275383716645e-1),1021            static_cast<RealType>(2.35139109235828185307e-1),1022            static_cast<RealType>(9.35967515134932733243e-2),1023            static_cast<RealType>(1.64310489592753858417e-2),1024            static_cast<RealType>(1.23186728989215889119e-3),1025            static_cast<RealType>(3.13500969261032539402e-5),1026            static_cast<RealType>(1.17021346758965979212e-7),1027        };1028        BOOST_MATH_STATIC const RealType Q[7] = {1029            static_cast<RealType>(1.),1030            static_cast<RealType>(1.28212183177829510267e0),1031            static_cast<RealType>(6.17321009406850420793e-1),1032            static_cast<RealType>(1.38400318019319970893e-1),1033            static_cast<RealType>(1.44994794535896837497e-2),1034            static_cast<RealType>(6.17774446282546623636e-4),1035            static_cast<RealType>(7.00521050169239269819e-6),1036        };1037 1038        result = tools::evaluate_polynomial(P, t) / tools::evaluate_polynomial(Q, t);1039    }1040    else if (x < 8) {1041        RealType t = x - 4;1042 1043        // Rational Approximation1044        // Maximum Relative Error: 3.7284e-171045        BOOST_MATH_STATIC const RealType P[7] = {1046            static_cast<RealType>(1.63772802979087193656e-1),1047            static_cast<RealType>(9.69009603942214234119e-2),1048            static_cast<RealType>(2.08261725719828138744e-2),1049            static_cast<RealType>(1.97965182693146960970e-3),1050            static_cast<RealType>(8.05499273532204276894e-5),1051            static_cast<RealType>(1.11401971145777879684e-6),1052            static_cast<RealType>(2.25932082770588727842e-9),1053        };1054        BOOST_MATH_STATIC const RealType Q[7] = {1055            static_cast<RealType>(1.),1056            static_cast<RealType>(6.92463563872865541733e-1),1057            static_cast<RealType>(1.80720987166755982366e-1),1058            static_cast<RealType>(2.20416647324531054557e-2),1059            static_cast<RealType>(1.26052070140663063778e-3),1060            static_cast<RealType>(2.93967534265875431639e-5),1061            static_cast<RealType>(1.82706995042259549615e-7),1062        };1063 1064        result = tools::evaluate_polynomial(P, t) / tools::evaluate_polynomial(Q, t);1065    }1066    else if (x < 16) {1067        RealType t = x - 8;1068 1069        // Rational Approximation1070        // Maximum Relative Error: 4.9609e-171071        BOOST_MATH_STATIC const RealType P[7] = {1072            static_cast<RealType>(1.22610122564874280532e-1),1073            static_cast<RealType>(3.70273222121572231593e-2),1074            static_cast<RealType>(4.06083618461789591121e-3),1075            static_cast<RealType>(1.96898134215932126299e-4),1076            static_cast<RealType>(4.08421066512186972853e-6),1077            static_cast<RealType>(2.87707419853226244584e-8),1078            static_cast<RealType>(2.96850126180387702894e-11),1079        };1080        BOOST_MATH_STATIC const RealType Q[7] = {1081            static_cast<RealType>(1.),1082            static_cast<RealType>(3.55825191301363023576e-1),1083            static_cast<RealType>(4.77251766176046719729e-2),1084            static_cast<RealType>(2.99136605131226103925e-3),1085            static_cast<RealType>(8.78895785432321899939e-5),1086            static_cast<RealType>(1.05235770624006494709e-6),1087            static_cast<RealType>(3.35423877769913468556e-9),1088        };1089 1090        result = tools::evaluate_polynomial(P, t) / tools::evaluate_polynomial(Q, t);1091    }1092    else if (x < 32) {1093        RealType t = x - 16;1094 1095        // Rational Approximation1096        // Maximum Relative Error: 5.6559e-171097        BOOST_MATH_STATIC const RealType P[7] = {1098            static_cast<RealType>(9.03056141356415077080e-2),1099            static_cast<RealType>(1.37568904417652631821e-2),1100            static_cast<RealType>(7.60947271383247418831e-4),1101            static_cast<RealType>(1.86048302967560067128e-5),1102            static_cast<RealType>(1.94537860496575427218e-7),1103            static_cast<RealType>(6.90524093915996283104e-10),1104            static_cast<RealType>(3.58808434477817122371e-13),1105        };1106        BOOST_MATH_STATIC const RealType Q[7] = {1107            static_cast<RealType>(1.),1108            static_cast<RealType>(1.80501347735272292079e-1),1109            static_cast<RealType>(1.22807958286146936376e-2),1110            static_cast<RealType>(3.90421541115275676253e-4),1111            static_cast<RealType>(5.81669449234915057779e-6),1112            static_cast<RealType>(3.53005415676201803667e-8),1113            static_cast<RealType>(5.69883025435873921433e-11),1114        };1115 1116        result = tools::evaluate_polynomial(P, t) / tools::evaluate_polynomial(Q, t);1117    }1118    else if (x < 64) {1119        RealType t = x - 32;1120 1121        // Rational Approximation1122        // Maximum Relative Error: 6.0653e-171123        BOOST_MATH_STATIC const RealType P[7] = {1124            static_cast<RealType>(6.57333571766941474226e-2),1125            static_cast<RealType>(5.02795551798163084224e-3),1126            static_cast<RealType>(1.39633616037997111325e-4),1127            static_cast<RealType>(1.71386564634533872559e-6),1128            static_cast<RealType>(8.99508156357247137439e-9),1129            static_cast<RealType>(1.60229460572297160486e-11),1130            static_cast<RealType>(4.17711709622960498456e-15),1131        };1132        BOOST_MATH_STATIC const RealType Q[7] = {1133            static_cast<RealType>(1.),1134            static_cast<RealType>(9.10198637347368265508e-2),1135            static_cast<RealType>(3.12263472357578263712e-3),1136            static_cast<RealType>(5.00524795130325614005e-5),1137            static_cast<RealType>(3.75913188747149725195e-7),1138            static_cast<RealType>(1.14970132098893394023e-9),1139            static_cast<RealType>(9.34957119271300093120e-13),1140        };1141 1142        result = tools::evaluate_polynomial(P, t) / tools::evaluate_polynomial(Q, t);1143    }1144    else {1145        RealType t = 1 / sqrt(x);1146 1147        // Rational Approximation1148        // Maximum Relative Error: 2.0104e-201149        BOOST_MATH_STATIC const RealType P[5] = {1150            static_cast<RealType>(3.98942280401432677940e-1),1151            static_cast<RealType>(8.12222388783621449146e-2),1152            static_cast<RealType>(1.68515703707271703934e-2),1153            static_cast<RealType>(2.19801627205374824460e-3),1154            static_cast<RealType>(-5.63321705854968264807e-5),1155        };1156        BOOST_MATH_STATIC const RealType Q[5] = {1157            static_cast<RealType>(1.),1158            static_cast<RealType>(6.02536240902768558315e-1),1159            static_cast<RealType>(1.99284471400121092380e-1),1160            static_cast<RealType>(3.48012577961755452113e-2),1161            static_cast<RealType>(3.38545004473058881799e-3),1162        };1163 1164        result = tools::evaluate_polynomial(P, t) / tools::evaluate_polynomial(Q, t) * t;1165    }1166 1167    return result;1168}1169 1170 1171template <class RealType>1172BOOST_MATH_GPU_ENABLED inline RealType saspoint5_cdf_plus_imp_prec(const RealType& x, const boost::math::integral_constant<int, 113>&)1173{1174    BOOST_MATH_STD_USING1175    RealType result;1176 1177    if (x < 0.125) {1178        // Rational Approximation1179        // Maximum Relative Error: 6.9340e-351180        // LCOV_EXCL_START1181        BOOST_MATH_STATIC const RealType P[30] = {1182            BOOST_MATH_BIG_CONSTANT(RealType, 113, 5.0e-1),1183            BOOST_MATH_BIG_CONSTANT(RealType, 113, 5.25520067710293108163697513129883130648e2),1184            BOOST_MATH_BIG_CONSTANT(RealType, 113, 2.70866020657515874782126804139443323023e5),1185            BOOST_MATH_BIG_CONSTANT(RealType, 113, 9.00865235319309486225795793030882782077e7),1186            BOOST_MATH_BIG_CONSTANT(RealType, 113, 2.15226363537737769449645357346965170790e10),1187            BOOST_MATH_BIG_CONSTANT(RealType, 113, 3.90371247243851280277289046301838071764e12),1188            BOOST_MATH_BIG_CONSTANT(RealType, 113, 5.55124590509169425751300134399513503679e14),1189            BOOST_MATH_BIG_CONSTANT(RealType, 113, 6.31282020412787511681760982839078664474e16),1190            BOOST_MATH_BIG_CONSTANT(RealType, 113, 5.81134278666896523873256421982740565131e18),1191            BOOST_MATH_BIG_CONSTANT(RealType, 113, 4.36154530125229747305141034242362609073e20),1192            BOOST_MATH_BIG_CONSTANT(RealType, 113, 2.67793867640429875837167908549938345465e22),1193            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.34584264816825205490037614178084070903e24),1194            BOOST_MATH_BIG_CONSTANT(RealType, 113, 5.52622279567059369718208827282730379468e25),1195            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.84678324511679577282571711018484545185e27),1196            BOOST_MATH_BIG_CONSTANT(RealType, 113, 4.99412564257799793932936828924325638617e28),1197            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.08467105431111959283045453636520222779e30),1198            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.87466808926544728702827204697734995611e31),1199            BOOST_MATH_BIG_CONSTANT(RealType, 113, 2.55020252231174414164534905191762212055e32),1200            BOOST_MATH_BIG_CONSTANT(RealType, 113, 2.69582736077420504345389671165954321163e33),1201            BOOST_MATH_BIG_CONSTANT(RealType, 113, 2.18203860972249826626461130638196586188e34),1202            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.32955733788770318392204091471121129386e35),1203            BOOST_MATH_BIG_CONSTANT(RealType, 113, 5.97972270315674052071792562126668438695e35),1204            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.93941537398987201071027348577636994465e36),1205            BOOST_MATH_BIG_CONSTANT(RealType, 113, 4.40818708062034138095495206258366082481e36),1206            BOOST_MATH_BIG_CONSTANT(RealType, 113, 6.76833406751769751643745383413977973530e36),1207            BOOST_MATH_BIG_CONSTANT(RealType, 113, 6.67873467711368838525239991688791162617e36),1208            BOOST_MATH_BIG_CONSTANT(RealType, 113, 3.94179310584115437584091984619858795365e36),1209            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.24348215908456320362232906012152922949e36),1210            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.71625432346533320597285660433110657670e35),1211            BOOST_MATH_BIG_CONSTANT(RealType, 113, 6.54662474187354179772157464533408058525e33),1212        };1213        BOOST_MATH_STATIC const RealType Q[31] = {1214            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.),1215            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.05231337496532137901354609636674085703e3),1216            BOOST_MATH_BIG_CONSTANT(RealType, 113, 5.43071888317491317900094470796567113997e5),1217            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.80864482202910830302921131771345102044e8),1218            BOOST_MATH_BIG_CONSTANT(RealType, 113, 4.32755297215862998181755216820621285536e10),1219            BOOST_MATH_BIG_CONSTANT(RealType, 113, 7.86251123527611073428156549377791985741e12),1220            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.12025543961949466786297141758805461421e15),1221            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.27681657695574252637426145112570596483e17),1222            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.17850553865715973904162289375819555884e19),1223            BOOST_MATH_BIG_CONSTANT(RealType, 113, 8.87285897504702686250962844939736867339e20),1224            BOOST_MATH_BIG_CONSTANT(RealType, 113, 5.46852796231948446334549476317560711795e22),1225            BOOST_MATH_BIG_CONSTANT(RealType, 113, 2.76101689878844725930808096548998198853e24),1226            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.14017776727845251567032313915953239178e26),1227            BOOST_MATH_BIG_CONSTANT(RealType, 113, 3.83738954971390158348334918235614003163e27),1228            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.04701345216121451992682705965658316871e29),1229            BOOST_MATH_BIG_CONSTANT(RealType, 113, 2.29994190638467725374533751141434904865e30),1230            BOOST_MATH_BIG_CONSTANT(RealType, 113, 4.03334024242845994501493644478442360593e31),1231            BOOST_MATH_BIG_CONSTANT(RealType, 113, 5.59094378123268840693978620156028975277e32),1232            BOOST_MATH_BIG_CONSTANT(RealType, 113, 6.05630254163426327113368743426054256780e33),1233            BOOST_MATH_BIG_CONSTANT(RealType, 113, 5.06008195534030444387061989883493342898e34),1234            BOOST_MATH_BIG_CONSTANT(RealType, 113, 3.21262490304347036689874956206774563906e35),1235            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.52353024633841796119920505314785365242e36),1236            BOOST_MATH_BIG_CONSTANT(RealType, 113, 5.28839143293381125956284415313626962263e36),1237            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.31074057704096457802547386358094338369e37),1238            BOOST_MATH_BIG_CONSTANT(RealType, 113, 2.24762412200364040971704861346921094354e37),1239            BOOST_MATH_BIG_CONSTANT(RealType, 113, 2.55663903116458425420509083471048286114e37),1240            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.81839283802391753865642022579846918253e37),1241            BOOST_MATH_BIG_CONSTANT(RealType, 113, 7.40026559327708207943879092058654410696e36),1242            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.48767474646810049293505781106444169229e36),1243            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.10591353097667671736865938428051885499e35),1244            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.26980708896893794012677171239610721832e33),1245        };1246        // LCOV_EXCL_STOP1247        result = tools::evaluate_polynomial(P, x) / tools::evaluate_polynomial(Q, x);1248    }1249    else if (x < 0.25) {1250        RealType t = x - static_cast <RealType>(0.125);1251 1252        // Rational Approximation1253        // Maximum Relative Error: 9.6106e-351254        // LCOV_EXCL_START1255        BOOST_MATH_STATIC const RealType P[14] = {1256            BOOST_MATH_BIG_CONSTANT(RealType, 113, 4.31887921568009055676985827521151969069e-1),1257            BOOST_MATH_BIG_CONSTANT(RealType, 113, 2.62791448964529380666250180886203090183e1),1258            BOOST_MATH_BIG_CONSTANT(RealType, 113, 6.18238045199893937316918299064825702894e2),1259            BOOST_MATH_BIG_CONSTANT(RealType, 113, 7.77274519306540522227493503092956314136e3),1260            BOOST_MATH_BIG_CONSTANT(RealType, 113, 5.89424638466340765479970877448972418958e4),1261            BOOST_MATH_BIG_CONSTANT(RealType, 113, 2.84027004420207996285174223581748706097e5),1262            BOOST_MATH_BIG_CONSTANT(RealType, 113, 8.84633134142285937075423713704784530853e5),1263            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.76780579189423063605715733542379494552e6),1264            BOOST_MATH_BIG_CONSTANT(RealType, 113, 2.19812409802969581112716039533798357401e6),1265            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.60039008588877024309600768114757310858e6),1266            BOOST_MATH_BIG_CONSTANT(RealType, 113, 6.10268260529501421009222937882726290612e5),1267            BOOST_MATH_BIG_CONSTANT(RealType, 113, 9.72169594688819848498039471657587836720e4),1268            BOOST_MATH_BIG_CONSTANT(RealType, 113, 3.27181379647139697258984772894869505788e3),1269            BOOST_MATH_BIG_CONSTANT(RealType, 113, -4.73617450590346508706222885401965820190e1),1270        };1271        BOOST_MATH_STATIC const RealType Q[13] = {1272            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.),1273            BOOST_MATH_BIG_CONSTANT(RealType, 113, 6.18558935411552146390814444666395959919e1),1274            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.49210559503096368944407109881023223654e3),1275            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.93959323596111340518285858313038058302e4),1276            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.53590607436758691037825792660167970938e5),1277            BOOST_MATH_BIG_CONSTANT(RealType, 113, 7.82700985983018132572589829602100319330e5),1278            BOOST_MATH_BIG_CONSTANT(RealType, 113, 2.62137033935442506086127262036686905276e6),1279            BOOST_MATH_BIG_CONSTANT(RealType, 113, 5.76014299715348555304267927238963139228e6),1280            BOOST_MATH_BIG_CONSTANT(RealType, 113, 8.12336796972134088340556958396544477713e6),1281            BOOST_MATH_BIG_CONSTANT(RealType, 113, 7.01952132024838508233050167059872220508e6),1282            BOOST_MATH_BIG_CONSTANT(RealType, 113, 3.41846547214877387780832317250797043384e6),1283            BOOST_MATH_BIG_CONSTANT(RealType, 113, 8.02083431572388097955901208994308271581e5),1284            BOOST_MATH_BIG_CONSTANT(RealType, 113, 6.30401057171447074343957754855656724141e4),1285        };1286        // LCOV_EXCL_STOP1287        result = tools::evaluate_polynomial(P, t) / tools::evaluate_polynomial(Q, t);1288    }1289    else if (x < 0.5) {1290        RealType t = x - static_cast <RealType>(0.25);1291 1292        // Rational Approximation1293        // Maximum Relative Error: 3.1519e-351294        // LCOV_EXCL_START1295        BOOST_MATH_STATIC const RealType P[14] = {1296            BOOST_MATH_BIG_CONSTANT(RealType, 113, 3.87119665000174806422420129219814467874e-1),1297            BOOST_MATH_BIG_CONSTANT(RealType, 113, 7.60769554551148293079169764245570645155e0),1298            BOOST_MATH_BIG_CONSTANT(RealType, 113, 6.49181979810834706538329284478129952168e1),1299            BOOST_MATH_BIG_CONSTANT(RealType, 113, 3.15722765491675871778645250624425739489e2),1300            BOOST_MATH_BIG_CONSTANT(RealType, 113, 9.65973147084701923411221710174830072860e2),1301            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.93709338011482232037110656459951914303e3),1302            BOOST_MATH_BIG_CONSTANT(RealType, 113, 2.57393131299425403017769538642434714791e3),1303            BOOST_MATH_BIG_CONSTANT(RealType, 113, 2.24110491141294379107651487490031694257e3),1304            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.23670394514211681515965192338544032862e3),1305            BOOST_MATH_BIG_CONSTANT(RealType, 113, 4.06141024932329394052395469123628405389e2),1306            BOOST_MATH_BIG_CONSTANT(RealType, 113, 7.08599362073145455095790192415468286304e1),1307            BOOST_MATH_BIG_CONSTANT(RealType, 113, 5.22746783794652085925801188098270888502e0),1308            BOOST_MATH_BIG_CONSTANT(RealType, 113, 8.19652234873414609727168969049557770989e-2),1309            BOOST_MATH_BIG_CONSTANT(RealType, 113, -5.73529976407853894192156335785920329181e-4),1310        };1311        BOOST_MATH_STATIC const RealType Q[13] = {1312            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.),1313            BOOST_MATH_BIG_CONSTANT(RealType, 113, 2.04157569499592889296640733909653747983e1),1314            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.82248883130787159161541119440215325308e2),1315            BOOST_MATH_BIG_CONSTANT(RealType, 113, 9.35191216924911901198168794737654512677e2),1316            BOOST_MATH_BIG_CONSTANT(RealType, 113, 3.05099314677808235578577204150229855903e3),1317            BOOST_MATH_BIG_CONSTANT(RealType, 113, 6.61081069236463123032873733048661305746e3),1318            BOOST_MATH_BIG_CONSTANT(RealType, 113, 9.65340645555368229718826047069323437201e3),1319            BOOST_MATH_BIG_CONSTANT(RealType, 113, 9.44526681322128674428653420882660351679e3),1320            BOOST_MATH_BIG_CONSTANT(RealType, 113, 6.03963804195353853550682049993122898950e3),1321            BOOST_MATH_BIG_CONSTANT(RealType, 113, 2.40399236835577953127465726826981753422e3),1322            BOOST_MATH_BIG_CONSTANT(RealType, 113, 5.46764755170079991793106428011388637748e2),1323            BOOST_MATH_BIG_CONSTANT(RealType, 113, 6.06384106042490712972156545051459068443e1),1324            BOOST_MATH_BIG_CONSTANT(RealType, 113, 2.27614406724572981099586665536543423891e0),1325        };1326        // LCOV_EXCL_STOP1327        result = tools::evaluate_polynomial(P, t) / tools::evaluate_polynomial(Q, t);1328    }1329    else if (x < 1) {1330        RealType t = x - static_cast <RealType>(0.5);1331 1332        // Rational Approximation1333        // Maximum Relative Error: 7.1196e-371334        // LCOV_EXCL_START1335        BOOST_MATH_STATIC const RealType P[15] = {1336            BOOST_MATH_BIG_CONSTANT(RealType, 113, 3.31309550000758082761278726632760756847e-1),1337            BOOST_MATH_BIG_CONSTANT(RealType, 113, 4.07242222531117199094690544171275415854e0),1338            BOOST_MATH_BIG_CONSTANT(RealType, 113, 2.18286763141875580859241637334381199648e1),1339            BOOST_MATH_BIG_CONSTANT(RealType, 113, 6.72102024869298528501604761974348686708e1),1340            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.31748399999514540052066169132819656757e2),1341            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.72168003284748405703923567644025252608e2),1342            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.52648991506052496046447777354251378257e2),1343            BOOST_MATH_BIG_CONSTANT(RealType, 113, 9.16777263528764704804758173026143295383e1),1344            BOOST_MATH_BIG_CONSTANT(RealType, 113, 3.66044453196259367950849328889468385159e1),1345            BOOST_MATH_BIG_CONSTANT(RealType, 113, 9.35095952392355288307377427145581700484e0),1346            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.43011308494452327007589069222668324337e0),1347            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.16582092138863383294685790744721021189e-1),1348            BOOST_MATH_BIG_CONSTANT(RealType, 113, 4.02261914949200575965813000131964695720e-3),1349            BOOST_MATH_BIG_CONSTANT(RealType, 113, 2.93943913630044161720796150617166047233e-5),1350            BOOST_MATH_BIG_CONSTANT(RealType, 113, -9.76395009419307902351328300308365369814e-8),1351        };1352        BOOST_MATH_STATIC const RealType Q[14] = {1353            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.),1354            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.28073115520716780203055949058270715651e1),1355            BOOST_MATH_BIG_CONSTANT(RealType, 113, 7.20245752585870752942356137496087189194e1),1356            BOOST_MATH_BIG_CONSTANT(RealType, 113, 2.34548337034735803039553186623067144497e2),1357            BOOST_MATH_BIG_CONSTANT(RealType, 113, 4.90925817267776213429724248532378895039e2),1358            BOOST_MATH_BIG_CONSTANT(RealType, 113, 6.92883822651628140083115301005227577059e2),1359            BOOST_MATH_BIG_CONSTANT(RealType, 113, 6.72868136219107985834601503784789993218e2),1360            BOOST_MATH_BIG_CONSTANT(RealType, 113, 4.50498744791568911029110559017896701095e2),1361            BOOST_MATH_BIG_CONSTANT(RealType, 113, 2.05178276667813671578581259848923964311e2),1362            BOOST_MATH_BIG_CONSTANT(RealType, 113, 6.16880263792490095344135867620645018480e1),1363            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.16199396397514668672304602774610890666e1),1364            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.25543193822942088303609988399416145281e0),1365            BOOST_MATH_BIG_CONSTANT(RealType, 113, 6.62522294286034117189844614005500278984e-2),1366            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.18342889744790118595835138444372660676e-3),1367        };1368        // LCOV_EXCL_STOP1369        result = tools::evaluate_polynomial(P, t) / tools::evaluate_polynomial(Q, t);1370    }1371    else if (x < 2) {1372        RealType t = x - 1;1373 1374        // Rational Approximation1375        // Maximum Relative Error: 9.5605e-361376        // LCOV_EXCL_START1377        BOOST_MATH_STATIC const RealType P[14] = {1378            BOOST_MATH_BIG_CONSTANT(RealType, 113, 2.71280312689343266367958859259591541365e-1),1379            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.49628636612698702680819948707479820292e0),1380            BOOST_MATH_BIG_CONSTANT(RealType, 113, 3.61090930375686902075245639803646265081e0),1381            BOOST_MATH_BIG_CONSTANT(RealType, 113, 5.01191924051756106307211298794294657688e0),1382            BOOST_MATH_BIG_CONSTANT(RealType, 113, 4.42496510376427957390465373165464672088e0),1383            BOOST_MATH_BIG_CONSTANT(RealType, 113, 2.59577769624139820954046058289100998534e0),1384            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.02664809521258420718170586857797408674e0),1385            BOOST_MATH_BIG_CONSTANT(RealType, 113, 2.72258711278476951299824066502536249701e-1),1386            BOOST_MATH_BIG_CONSTANT(RealType, 113, 4.72578941800687566921553416498339481887e-2),1387            BOOST_MATH_BIG_CONSTANT(RealType, 113, 5.12553368488232553360765667155702324159e-3),1388            BOOST_MATH_BIG_CONSTANT(RealType, 113, 3.20749770911901442251726681861858323649e-4),1389            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.00621121212654384864006297569770703900e-5),1390            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.18976033102817074104109472578202752346e-7),1391            BOOST_MATH_BIG_CONSTANT(RealType, 113, 2.22093548539863254922531707899658394458e-10),1392        };1393        BOOST_MATH_STATIC const RealType Q[14] = {1394            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.),1395            BOOST_MATH_BIG_CONSTANT(RealType, 113, 5.83305694892673455436552817409325835774e0),1396            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.49922543669955056754932640312490112609e1),1397            BOOST_MATH_BIG_CONSTANT(RealType, 113, 2.23488972536322019584648241457582608908e1),1398            BOOST_MATH_BIG_CONSTANT(RealType, 113, 2.14051527527038669918848981363974859889e1),1399            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.37891280136777182304388426277537358346e1),1400            BOOST_MATH_BIG_CONSTANT(RealType, 113, 6.08058775103864815769223385606687612117e0),1401            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.83305488980337433132332401784292281716e0),1402            BOOST_MATH_BIG_CONSTANT(RealType, 113, 3.71072208215804671719811563659227630554e-1),1403            BOOST_MATH_BIG_CONSTANT(RealType, 113, 4.86332040813989094594982937011005305263e-2),1404            BOOST_MATH_BIG_CONSTANT(RealType, 113, 3.87698178237970337664105782546771501188e-3),1405            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.69113555019737313680732855691540088318e-4),1406            BOOST_MATH_BIG_CONSTANT(RealType, 113, 3.31888539972217875242352157306613891243e-6),1407            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.85633766164682554126992822326956560433e-8),1408        };1409        // LCOV_EXCL_STOP1410        result = tools::evaluate_polynomial(P, t) / tools::evaluate_polynomial(Q, t);1411    }1412    else if (x < 4) {1413        RealType t = x - 2;1414 1415        // Rational Approximation1416        // Maximum Relative Error: 1.1494e-351417        // LCOV_EXCL_START1418        BOOST_MATH_STATIC const RealType P[14] = {1419            BOOST_MATH_BIG_CONSTANT(RealType, 113, 2.13928162275383718405630406427822960090e-1),1420            BOOST_MATH_BIG_CONSTANT(RealType, 113, 5.90742307267701162395764574873947997211e-1),1421            BOOST_MATH_BIG_CONSTANT(RealType, 113, 7.13821826367941514387521090205756466068e-1),1422            BOOST_MATH_BIG_CONSTANT(RealType, 113, 4.96186879146063565484800486550739025293e-1),1423            BOOST_MATH_BIG_CONSTANT(RealType, 113, 2.19438785955706463753454881511977831603e-1),1424            BOOST_MATH_BIG_CONSTANT(RealType, 113, 6.44969124820016994689518539612465708536e-2),1425            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.27841835070651018079759230944461773079e-2),1426            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.69952429132675045239242077293594666305e-3),1427            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.47919853099168659881487026035933933068e-4),1428            BOOST_MATH_BIG_CONSTANT(RealType, 113, 8.04644774117864306055402364094681541437e-6),1429            BOOST_MATH_BIG_CONSTANT(RealType, 113, 2.52604718870921084048756263996119841957e-7),1430            BOOST_MATH_BIG_CONSTANT(RealType, 113, 3.97610950633031564892821158058978809537e-9),1431            BOOST_MATH_BIG_CONSTANT(RealType, 113, 2.35934159016861180185992558083703785765e-11),1432            BOOST_MATH_BIG_CONSTANT(RealType, 113, 2.21044098237798939057079316997065892072e-14),1433        };1434        BOOST_MATH_STATIC const RealType Q[14] = {1435            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.),1436            BOOST_MATH_BIG_CONSTANT(RealType, 113, 2.94437702178976797218081686254875998984e0),1437            BOOST_MATH_BIG_CONSTANT(RealType, 113, 3.82068837586514484653828718675654460991e0),1438            BOOST_MATH_BIG_CONSTANT(RealType, 113, 2.87606058269189306593797764456467061128e0),1439            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.39130528408903116343256483948950693356e0),1440            BOOST_MATH_BIG_CONSTANT(RealType, 113, 4.52792074489091396425713962375223436022e-1),1441            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.00892233011840867583848470677898363716e-1),1442            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.53717105060592851173320646706141911461e-2),1443            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.57293857675930200001382624769341451561e-3),1444            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.04219251796696135508847408131139677925e-4),1445            BOOST_MATH_BIG_CONSTANT(RealType, 113, 4.20053006131133304932740325113068767057e-6),1446            BOOST_MATH_BIG_CONSTANT(RealType, 113, 9.26384707028090985155079342718673255493e-8),1447            BOOST_MATH_BIG_CONSTANT(RealType, 113, 9.19146442700994823924806249608315505708e-10),1448            BOOST_MATH_BIG_CONSTANT(RealType, 113, 2.59879298772002950043508762057850408213e-12),1449        };1450        // LCOV_EXCL_STOP1451        result = tools::evaluate_polynomial(P, t) / tools::evaluate_polynomial(Q, t);1452    }1453    else if (x < 8) {1454        RealType t = x - 4;1455 1456        // Rational Approximation1457        // Maximum Relative Error: 1.9710e-351458        // LCOV_EXCL_START1459        BOOST_MATH_STATIC const RealType P[14] = {1460            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.63772802979087199762340235165979751298e-1),1461            BOOST_MATH_BIG_CONSTANT(RealType, 113, 2.31941534705372320785274994658709390116e-1),1462            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.43643960022585762678456016437621064500e-1),1463            BOOST_MATH_BIG_CONSTANT(RealType, 113, 5.11415302325466272779041471612529728187e-2),1464            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.15767742459744253874067896740220951622e-2),1465            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.74049309186016489825053763513176160256e-3),1466            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.76349898574685150849080543168157785281e-4),1467            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.19757202370729036627932327405149840205e-5),1468            BOOST_MATH_BIG_CONSTANT(RealType, 113, 5.32067727965321839898287320520750897894e-7),1469            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.47636340015260789807543414080472136575e-8),1470            BOOST_MATH_BIG_CONSTANT(RealType, 113, 2.36236727340568181129875213546468908164e-10),1471            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.89379573960280486883733996547662506245e-12),1472            BOOST_MATH_BIG_CONSTANT(RealType, 113, 5.71832232038263988173042637335112603365e-15),1473            BOOST_MATH_BIG_CONSTANT(RealType, 113, 2.72380245500539326441037770757072641975e-18),1474        };1475        BOOST_MATH_STATIC const RealType Q[14] = {1476            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.),1477            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.51702400281458104713682413542736419584e0),1478            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.01375164846907815766683647295932603968e0),1479            BOOST_MATH_BIG_CONSTANT(RealType, 113, 3.92796007869834847612192314006582598557e-1),1480            BOOST_MATH_BIG_CONSTANT(RealType, 113, 9.77580441164023725582659445614058463183e-2),1481            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.63592331843149724480258804892989851727e-2),1482            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.87334158717610115008450674967492650941e-3),1483            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.46596056941432875244263245821845070102e-4),1484            BOOST_MATH_BIG_CONSTANT(RealType, 113, 7.69980051560936361597177347949112822752e-6),1485            BOOST_MATH_BIG_CONSTANT(RealType, 113, 2.61690034211585843423761830218320365457e-7),1486            BOOST_MATH_BIG_CONSTANT(RealType, 113, 5.40619773800285766355596852314940341504e-9),1487            BOOST_MATH_BIG_CONSTANT(RealType, 113, 6.10624533319804091814643828283820958419e-11),1488            BOOST_MATH_BIG_CONSTANT(RealType, 113, 3.10009654621246392691126133176423833259e-13),1489            BOOST_MATH_BIG_CONSTANT(RealType, 113, 4.48070591106986983088640496621926852293e-16),1490        };1491        // LCOV_EXCL_STOP1492        result = tools::evaluate_polynomial(P, t) / tools::evaluate_polynomial(Q, t);1493    }1494    else if (x < 16) {1495        RealType t = x - 8;1496 1497        // Rational Approximation1498        // Maximum Relative Error: 5.2049e-361499        // LCOV_EXCL_START1500        BOOST_MATH_STATIC const RealType P[14] = {1501            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.22610122564874286614786819620499101143e-1),1502            BOOST_MATH_BIG_CONSTANT(RealType, 113, 8.30352481858382230273216195795534959290e-2),1503            BOOST_MATH_BIG_CONSTANT(RealType, 113, 2.45933050053542949214164590814846222512e-2),1504            BOOST_MATH_BIG_CONSTANT(RealType, 113, 4.18776888646200567321599584635465632591e-3),1505            BOOST_MATH_BIG_CONSTANT(RealType, 113, 4.53421996228923143480455729204878676265e-4),1506            BOOST_MATH_BIG_CONSTANT(RealType, 113, 3.26075686557831306993734433164305349875e-5),1507            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.58045762501721375879877727645933749122e-6),1508            BOOST_MATH_BIG_CONSTANT(RealType, 113, 5.13469629033419341069106781092024950086e-8),1509            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.09157226556088521407323375433512662525e-9),1510            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.44961350323527660188267669752380722085e-11),1511            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.11052101325523147964890915835024505324e-13),1512            BOOST_MATH_BIG_CONSTANT(RealType, 113, 4.26421404354976214191891992583151033361e-16),1513            BOOST_MATH_BIG_CONSTANT(RealType, 113, 6.17133505681224996657291059553060754343e-19),1514            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.41010917905686427164414364663355769988e-22),1515        };1516        BOOST_MATH_STATIC const RealType Q[14] = {1517            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.),1518            BOOST_MATH_BIG_CONSTANT(RealType, 113, 7.31062773739451672808456319166347015167e-1),1519            BOOST_MATH_BIG_CONSTANT(RealType, 113, 2.35386721434011881226168110614121649232e-1),1520            BOOST_MATH_BIG_CONSTANT(RealType, 113, 4.39357338312443465616015226804775178232e-2),1521            BOOST_MATH_BIG_CONSTANT(RealType, 113, 5.26630144036271792027494677957363535353e-3),1522            BOOST_MATH_BIG_CONSTANT(RealType, 113, 4.24340476859846183414651435036807677467e-4),1523            BOOST_MATH_BIG_CONSTANT(RealType, 113, 2.33917136421389571662908749253850939876e-5),1524            BOOST_MATH_BIG_CONSTANT(RealType, 113, 8.80972141456523767244381195690041498939e-7),1525            BOOST_MATH_BIG_CONSTANT(RealType, 113, 2.22653625120465488656616983786525028119e-8),1526            BOOST_MATH_BIG_CONSTANT(RealType, 113, 3.64072452032620505897896978124863889812e-10),1527            BOOST_MATH_BIG_CONSTANT(RealType, 113, 3.61842001579321492488462230987972104386e-12),1528            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.96631619425501661980194304605724632777e-14),1529            BOOST_MATH_BIG_CONSTANT(RealType, 113, 4.80392324086028812772385536034034039168e-17),1530            BOOST_MATH_BIG_CONSTANT(RealType, 113, 3.34254502871215949266781048808984963366e-20),1531        };1532        // LCOV_EXCL_STOP1533        result = tools::evaluate_polynomial(P, t) / tools::evaluate_polynomial(Q, t);1534    }1535    else if (x < 32) {1536        RealType t = x - 16;1537 1538        // Rational Approximation1539        // Maximum Relative Error: 1.7434e-351540        // LCOV_EXCL_START1541        BOOST_MATH_STATIC const RealType P[14] = {1542            BOOST_MATH_BIG_CONSTANT(RealType, 113, 9.03056141356415128156562790092782153630e-2),1543            BOOST_MATH_BIG_CONSTANT(RealType, 113, 3.15331583242023443256381237551843296356e-2),1544            BOOST_MATH_BIG_CONSTANT(RealType, 113, 4.81847913073640285776566199343276995613e-3),1545            BOOST_MATH_BIG_CONSTANT(RealType, 113, 4.23578443960486030170636772457627141406e-4),1546            BOOST_MATH_BIG_CONSTANT(RealType, 113, 2.36906354316016270165240908809929957836e-5),1547            BOOST_MATH_BIG_CONSTANT(RealType, 113, 8.80584421020238085239890207672296651219e-7),1548            BOOST_MATH_BIG_CONSTANT(RealType, 113, 2.20726437845755296397071540583729544203e-8),1549            BOOST_MATH_BIG_CONSTANT(RealType, 113, 3.71042563703818585243207722641746283288e-10),1550            BOOST_MATH_BIG_CONSTANT(RealType, 113, 4.08307373360265947158569900625482137206e-12),1551            BOOST_MATH_BIG_CONSTANT(RealType, 113, 2.80776566500233755365518221977875432763e-14),1552            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.11405351639704510305055492207286172753e-16),1553            BOOST_MATH_BIG_CONSTANT(RealType, 113, 2.21575609293568296049921888011966327905e-19),1554            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.66081982641748223969990279975752576675e-22),1555            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.96483118060215455299182487430511998831e-26),1556        };1557        BOOST_MATH_STATIC const RealType Q[14] = {1558            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.),1559            BOOST_MATH_BIG_CONSTANT(RealType, 113, 3.77347004038951368607085827825968614455e-1),1560            BOOST_MATH_BIG_CONSTANT(RealType, 113, 6.27559305780716801070924630708599448466e-2),1561            BOOST_MATH_BIG_CONSTANT(RealType, 113, 6.05452382624230160738008550961679711827e-3),1562            BOOST_MATH_BIG_CONSTANT(RealType, 113, 3.75369667590360521677018734348769796476e-4),1563            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.56551290985905942229892419848093494661e-5),1564            BOOST_MATH_BIG_CONSTANT(RealType, 113, 4.46972102361871185271727958608184616388e-7),1565            BOOST_MATH_BIG_CONSTANT(RealType, 113, 8.72423917010499649257775199140781647069e-9),1566            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.14337306905269302583746182007852069459e-10),1567            BOOST_MATH_BIG_CONSTANT(RealType, 113, 9.69949885309711859563395555285232232606e-13),1568            BOOST_MATH_BIG_CONSTANT(RealType, 113, 5.00318719634300754237920041312234711548e-15),1569            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.41139664927184402637020651515172315287e-17),1570            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.79013190225240505774959477465594797961e-20),1571            BOOST_MATH_BIG_CONSTANT(RealType, 113, 6.46536966503325413797061462062918707370e-24),1572        };1573        // LCOV_EXCL_STOP1574        result = tools::evaluate_polynomial(P, t) / tools::evaluate_polynomial(Q, t);1575    }1576    else if (x < 64) {1577        RealType t = x - 32;1578 1579        // Rational Approximation1580        // Maximum Relative Error: 2.0402e-351581        // LCOV_EXCL_START1582        BOOST_MATH_STATIC const RealType P[14] = {1583            BOOST_MATH_BIG_CONSTANT(RealType, 113, 6.57333571766941514095434647381791040479e-2),1584            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.15416685251021339933358981066948923001e-2),1585            BOOST_MATH_BIG_CONSTANT(RealType, 113, 8.86806753164417557035166075399588122481e-4),1586            BOOST_MATH_BIG_CONSTANT(RealType, 113, 3.91972616817770660098405128729991574724e-5),1587            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.10225768760715861978198010761036882002e-6),1588            BOOST_MATH_BIG_CONSTANT(RealType, 113, 2.05986998674039047865566990469266534338e-8),1589            BOOST_MATH_BIG_CONSTANT(RealType, 113, 2.59572646670205456333051888086612875871e-10),1590            BOOST_MATH_BIG_CONSTANT(RealType, 113, 2.19347294198055585461131949159508730257e-12),1591            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.21328285448498841418774425071549974153e-14),1592            BOOST_MATH_BIG_CONSTANT(RealType, 113, 4.19331596847283822557042655221763459728e-17),1593            BOOST_MATH_BIG_CONSTANT(RealType, 113, 8.36128017817576942059191451016251062072e-20),1594            BOOST_MATH_BIG_CONSTANT(RealType, 113, 8.35600223942735523925477855247725326228e-23),1595            BOOST_MATH_BIG_CONSTANT(RealType, 113, 3.14658948592500290756690769268766876322e-26),1596            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.86984591055448991335081550609451649866e-30),1597        };1598        BOOST_MATH_STATIC const RealType Q[14] = {1599            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.),1600            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.90112824856612652807095815199496602262e-1),1601            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.59291524937386142936420775839969648652e-2),1602            BOOST_MATH_BIG_CONSTANT(RealType, 113, 7.74245361925275011235694006013677228467e-4),1603            BOOST_MATH_BIG_CONSTANT(RealType, 113, 2.41828589449615478387532599798645159282e-5),1604            BOOST_MATH_BIG_CONSTANT(RealType, 113, 5.08088176420557205743676774127863572768e-7),1605            BOOST_MATH_BIG_CONSTANT(RealType, 113, 7.30760429417424419297000535744450830697e-9),1606            BOOST_MATH_BIG_CONSTANT(RealType, 113, 7.18464910867914234357511605329900284981e-11),1607            BOOST_MATH_BIG_CONSTANT(RealType, 113, 4.74255540513281299503596269087176674333e-13),1608            BOOST_MATH_BIG_CONSTANT(RealType, 113, 2.02616028440371294233330747672966435921e-15),1609            BOOST_MATH_BIG_CONSTANT(RealType, 113, 5.26276597941744408946918920573146445795e-18),1610            BOOST_MATH_BIG_CONSTANT(RealType, 113, 7.47463109867603732992337779860914933775e-21),1611            BOOST_MATH_BIG_CONSTANT(RealType, 113, 4.77217411888267832243050973915295217582e-24),1612            BOOST_MATH_BIG_CONSTANT(RealType, 113, 8.67397425207383164084527830512920206074e-28),1613        };1614        // LCOV_EXCL_STOP1615        result = tools::evaluate_polynomial(P, t) / tools::evaluate_polynomial(Q, t);1616    }1617    else {1618        RealType t = 1 / sqrt(x);1619 1620        // Rational Approximation1621        // Maximum Relative Error: 9.2612e-351622        // LCOV_EXCL_START1623        BOOST_MATH_STATIC const RealType P[9] = {1624            BOOST_MATH_BIG_CONSTANT(RealType, 113, 3.98942280401432677939946059934381868476e-1),1625            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.33908701314796522684603310107061150444e-1),1626            BOOST_MATH_BIG_CONSTANT(RealType, 113, 2.92120397142832495974006972404741124398e-2),1627            BOOST_MATH_BIG_CONSTANT(RealType, 113, 6.15463147603421962834297353867930971657e-3),1628            BOOST_MATH_BIG_CONSTANT(RealType, 113, 4.44488751006069172847577645328482300099e-4),1629            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.44057582804743599116332797864164802887e-5),1630            BOOST_MATH_BIG_CONSTANT(RealType, 113, 4.02968018188491417839349438941039867033e-6),1631            BOOST_MATH_BIG_CONSTANT(RealType, 113, -4.75092244933846337077999183310087492887e-7),1632            BOOST_MATH_BIG_CONSTANT(RealType, 113, 2.35099582728548602389917143511323566818e-8),1633        };1634        BOOST_MATH_STATIC const RealType Q[7] = {1635            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.),1636            BOOST_MATH_BIG_CONSTANT(RealType, 113, 7.34601617336219074065534356705298927390e-1),1637            BOOST_MATH_BIG_CONSTANT(RealType, 113, 2.82954035780824611941899463895040327299e-1),1638            BOOST_MATH_BIG_CONSTANT(RealType, 113, 6.70929001162671283123255408612494541378e-2),1639            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.05508596604210030533747793197422815105e-2),1640            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.02913299057943756875992272236063124608e-3),1641            BOOST_MATH_BIG_CONSTANT(RealType, 113, 5.37824426836648736125759177846682556245e-5),1642        };1643        // LCOV_EXCL_STOP1644        result = tools::evaluate_polynomial(P, t) / tools::evaluate_polynomial(Q, t) * t;1645    }1646 1647    return result;1648}1649 1650template <class RealType>1651BOOST_MATH_GPU_ENABLED inline RealType saspoint5_cdf_imp_prec(const RealType& x, bool complement, const boost::math::integral_constant<int, 53>& tag) {1652    if (x >= 0) {1653        return complement ? saspoint5_cdf_plus_imp_prec(x, tag) : 1 - saspoint5_cdf_plus_imp_prec(x, tag);1654    }1655    else if (x <= 0) {1656        return complement ? 1 - saspoint5_cdf_plus_imp_prec(-x, tag) : saspoint5_cdf_plus_imp_prec(-x, tag);1657    }1658    else {1659        return boost::math::numeric_limits<RealType>::quiet_NaN();1660    }1661}1662 1663template <class RealType>1664BOOST_MATH_GPU_ENABLED inline RealType saspoint5_cdf_imp_prec(const RealType& x, bool complement, const boost::math::integral_constant<int, 113>& tag) {1665    if (x >= 0) {1666        return complement ? saspoint5_cdf_plus_imp_prec(x, tag) : 1 - saspoint5_cdf_plus_imp_prec(x, tag);1667    }1668    else if (x <= 0) {1669        return complement ? 1 - saspoint5_cdf_plus_imp_prec(-x, tag) : saspoint5_cdf_plus_imp_prec(-x, tag);1670    }1671    else {1672        return boost::math::numeric_limits<RealType>::quiet_NaN();1673    }1674}1675 1676template <class RealType, class Policy>1677BOOST_MATH_GPU_ENABLED inline RealType saspoint5_cdf_imp(const saspoint5_distribution<RealType, Policy>& dist, const RealType& x, bool complement) {1678    //1679    // This calculates the cdf of the Saspoint5 distribution and/or its complement.1680    //1681 1682    BOOST_MATH_STD_USING // for ADL of std functions1683    constexpr auto function = "boost::math::cdf(saspoint5<%1%>&, %1%)";1684    RealType result = 0;1685    RealType location = dist.location();1686    RealType scale = dist.scale();1687 1688    if (false == detail::check_location(function, location, &result, Policy()))1689    {1690        return result;1691    }1692    if (false == detail::check_scale(function, scale, &result, Policy()))1693    {1694        return result;1695    }1696    if (false == detail::check_x(function, x, &result, Policy()))1697    {1698        return result;1699    }1700 1701    typedef typename tools::promote_args<RealType>::type result_type;1702    typedef typename policies::precision<result_type, Policy>::type precision_type;1703    typedef boost::math::integral_constant<int,1704        precision_type::value <= 0 ? 0 :1705        precision_type::value <= 53 ? 53 :1706        precision_type::value <= 113 ? 113 : 01707    > tag_type;1708 1709    static_assert(tag_type::value, "The SaS point5 distribution is only implemented for types with known precision, and 113 bits or fewer in the mantissa (ie 128 bit quad-floats");1710 1711    RealType u = (x - location) / scale;1712 1713    result = saspoint5_cdf_imp_prec(u, complement, tag_type());1714 1715    return result;1716}1717 1718template <class RealType>1719BOOST_MATH_GPU_ENABLED inline RealType saspoint5_quantile_upper_imp_prec(const RealType& p, const boost::math::integral_constant<int, 53>&)1720{1721    BOOST_MATH_STD_USING1722    RealType result;1723 1724    if (ilogb(p) >= -2) {1725        RealType u = -log2(ldexp(p, 1));1726 1727        if (u < 0.125) {1728            // Rational Approximation1729            // Maximum Relative Error: 4.2616e-171730            BOOST_MATH_STATIC const RealType P[13] = {1731                static_cast<RealType>(1.36099130643975127045e-1),1732                static_cast<RealType>(2.19634434498311523885e1),1733                static_cast<RealType>(1.70276954848343179287e3),1734                static_cast<RealType>(8.02187341786354339306e4),1735                static_cast<RealType>(2.48750112198456813443e6),1736                static_cast<RealType>(5.20617858300443231437e7),1737                static_cast<RealType>(7.31202030685167303439e8),1738                static_cast<RealType>(6.66061403138355591915e9),1739                static_cast<RealType>(3.65687892725590813998e10),1740                static_cast<RealType>(1.06061776220305595494e11),1741                static_cast<RealType>(1.23930642673461465346e11),1742                static_cast<RealType>(1.49986408149520127078e10),1743                static_cast<RealType>(-6.17325587219357123900e8),1744            };1745            BOOST_MATH_STATIC const RealType Q[13] = {1746                static_cast<RealType>(1.),1747                static_cast<RealType>(1.63111146753825227716e2),1748                static_cast<RealType>(1.27864461509685444043e4),1749                static_cast<RealType>(6.10371533241799228037e5),1750                static_cast<RealType>(1.92422115963507708309e7),1751                static_cast<RealType>(4.11544185502250709497e8),1752                static_cast<RealType>(5.95343302992055062258e9),1753                static_cast<RealType>(5.65615858889758369947e10),1754                static_cast<RealType>(3.30833154992293143503e11),1755                static_cast<RealType>(1.06032392136054207216e12),1756                static_cast<RealType>(1.50071282012095447931e12),1757                static_cast<RealType>(5.43552396263989180433e11),1758                static_cast<RealType>(9.57434915768660935004e10),1759            };1760 1761            result = u * tools::evaluate_polynomial(P, u) / (tools::evaluate_polynomial(Q, u) * (p * p));1762        }1763        else if (u < 0.25) {1764            RealType t = u - static_cast <RealType>(0.125);1765 1766            // Rational Approximation1767            // Maximum Relative Error: 2.3770e-191768            BOOST_MATH_STATIC const RealType P[8] = {1769                static_cast<RealType>(1.46698650748920243698e-2),1770                static_cast<RealType>(3.58380131788385557227e-1),1771                static_cast<RealType>(3.39153750029553194566e0),1772                static_cast<RealType>(1.55457424873957272207e1),1773                static_cast<RealType>(3.44403897039657057261e1),1774                static_cast<RealType>(3.01881531964962975320e1),1775                static_cast<RealType>(2.77679052294606319767e0),1776                static_cast<RealType>(-7.76665288232972435969e-2),1777            };1778            BOOST_MATH_STATIC const RealType Q[7] = {1779                static_cast<RealType>(1.),1780                static_cast<RealType>(1.72584280323876188464e1),1781                static_cast<RealType>(1.11983518800147654866e2),1782                static_cast<RealType>(3.25969893054048132145e2),1783                static_cast<RealType>(3.91978809680672051666e2),1784                static_cast<RealType>(1.29874252720714897530e2),1785                static_cast<RealType>(2.08740114519610102248e1),1786            };1787 1788            result = tools::evaluate_polynomial(P, t) / (tools::evaluate_polynomial(Q, t) * (p * p));1789        }1790        else if (u < 0.5) {1791            RealType t = u - static_cast <RealType>(0.25);1792 1793            // Rational Approximation1794            // Maximum Relative Error: 9.2445e-181795            BOOST_MATH_STATIC const RealType P[8] = {1796                static_cast<RealType>(2.69627866689346445458e-2),1797                static_cast<RealType>(3.23091180507445216811e-1),1798                static_cast<RealType>(1.42164019533549860681e0),1799                static_cast<RealType>(2.74613170828120023406e0),1800                static_cast<RealType>(2.07865023346180997996e0),1801                static_cast<RealType>(2.53267176863740856907e-1),1802                static_cast<RealType>(-2.55816250186301841152e-2),1803                static_cast<RealType>(3.02683750470398342224e-3),1804            };1805            BOOST_MATH_STATIC const RealType Q[6] = {1806                static_cast<RealType>(1.),1807                static_cast<RealType>(8.55049920135376003042e0),1808                static_cast<RealType>(2.48726119139047911316e1),1809                static_cast<RealType>(2.79519589592198994574e1),1810                static_cast<RealType>(9.88212916161823866098e0),1811                static_cast<RealType>(1.39749417956251951564e0),1812            };1813 1814            result = tools::evaluate_polynomial(P, t) / (tools::evaluate_polynomial(Q, t) * (p * p));1815        }1816        else {1817            RealType t = u - static_cast <RealType>(0.5);1818 1819            // Rational Approximation1820            // Maximum Relative Error: 2.2918e-201821            BOOST_MATH_STATIC const RealType P[9] = {1822                static_cast<RealType>(4.79518653373241051274e-2),1823                static_cast<RealType>(3.81837125793765918564e-1),1824                static_cast<RealType>(1.13370353708146321188e0),1825                static_cast<RealType>(1.55218145762186846509e0),1826                static_cast<RealType>(9.60938271141036509605e-1),1827                static_cast<RealType>(2.11811755464425606950e-1),1828                static_cast<RealType>(8.84533960603915742831e-3),1829                static_cast<RealType>(1.73314614571009160225e-3),1830                static_cast<RealType>(-3.63491208733876986098e-5),1831            };1832            BOOST_MATH_STATIC const RealType Q[8] = {1833                static_cast<RealType>(1.),1834                static_cast<RealType>(6.36954463000253710936e0),1835                static_cast<RealType>(1.40601897306833147611e1),1836                static_cast<RealType>(1.33838075106916667084e1),1837                static_cast<RealType>(5.60958095533108032859e0),1838                static_cast<RealType>(1.11796035623375210182e0),1839                static_cast<RealType>(1.12508482637488861060e-1),1840                static_cast<RealType>(5.18503975949799718538e-3),1841            };1842 1843            result = tools::evaluate_polynomial(P, t) / (tools::evaluate_polynomial(Q, t) * (p * p));1844        }1845    }1846    else if (ilogb(p) >= -4) {1847        RealType t = -log2(ldexp(p, 2));1848 1849        // Rational Approximation1850        // Maximum Relative Error: 4.2057e-181851        BOOST_MATH_STATIC const RealType P[10] = {1852            static_cast<RealType>(8.02395484493329835881e-2),1853            static_cast<RealType>(2.46132933068351274622e-1),1854            static_cast<RealType>(2.81820176867119231101e-1),1855            static_cast<RealType>(1.47754061028371025893e-1),1856            static_cast<RealType>(3.54638964490281023406e-2),1857            static_cast<RealType>(3.99998730093393774294e-3),1858            static_cast<RealType>(3.81581928434827040262e-4),1859            static_cast<RealType>(1.82520920154354221101e-5),1860            static_cast<RealType>(-2.06151396745690348445e-7),1861            static_cast<RealType>(6.77986548138011345849e-9),1862        };1863        BOOST_MATH_STATIC const RealType Q[8] = {1864            static_cast<RealType>(1.),1865            static_cast<RealType>(2.39244329037830026691e0),1866            static_cast<RealType>(2.12683465416376620896e0),1867            static_cast<RealType>(9.02612272334554457823e-1),1868            static_cast<RealType>(2.06667959191488815314e-1),1869            static_cast<RealType>(2.79328968525257867541e-2),1870            static_cast<RealType>(2.28216286216537879937e-3),1871            static_cast<RealType>(1.04195690531437767679e-4),1872        };1873 1874        result = tools::evaluate_polynomial(P, t) / (tools::evaluate_polynomial(Q, t) * (p * p));1875    }1876    else if (ilogb(p) >= -8) {1877        RealType t = -log2(ldexp(p, 4));1878 1879        // Rational Approximation1880        // Maximum Relative Error: 3.3944e-171881        BOOST_MATH_STATIC const RealType P[9] = {1882            static_cast<RealType>(1.39293493266195561875e-1),1883            static_cast<RealType>(1.26741380938661691592e-1),1884            static_cast<RealType>(4.31117040307200265931e-2),1885            static_cast<RealType>(7.50528269269498076949e-3),1886            static_cast<RealType>(8.63100497178570310436e-4),1887            static_cast<RealType>(6.75686286034521991703e-5),1888            static_cast<RealType>(3.11102625473120771882e-6),1889            static_cast<RealType>(9.63513655399980075083e-8),1890            static_cast<RealType>(-6.40223609013005302318e-11),1891        };1892        BOOST_MATH_STATIC const RealType Q[8] = {1893            static_cast<RealType>(1.),1894            static_cast<RealType>(8.11234548272888947555e-1),1895            static_cast<RealType>(2.63525516991753831892e-1),1896            static_cast<RealType>(4.77118226533147280522e-2),1897            static_cast<RealType>(5.46090741266888954909e-3),1898            static_cast<RealType>(4.15325425646862026425e-4),1899            static_cast<RealType>(2.02377681998442384863e-5),1900            static_cast<RealType>(5.79823311154876056655e-7),1901        };1902 1903        result = tools::evaluate_polynomial(P, t) / (tools::evaluate_polynomial(Q, t) * (p * p));1904    }1905    else if (ilogb(p) >= -16) {1906        RealType t = -log2(ldexp(p, 8));1907 1908        // Rational Approximation1909        // Maximum Relative Error: 4.1544e-171910        BOOST_MATH_STATIC const RealType P[9] = {1911            static_cast<RealType>(1.57911660613037760235e-1),1912            static_cast<RealType>(5.59740955695099219682e-2),1913            static_cast<RealType>(8.92895854008560399142e-3),1914            static_cast<RealType>(8.88795299273855801726e-4),1915            static_cast<RealType>(5.66358335596607738071e-5),1916            static_cast<RealType>(2.46733195253941569922e-6),1917            static_cast<RealType>(6.44829870181825872501e-8),1918            static_cast<RealType>(7.62193242864380357931e-10),1919            static_cast<RealType>(-7.82035413331699873450e-14),1920        };1921        BOOST_MATH_STATIC const RealType Q[8] = {1922            static_cast<RealType>(1.),1923            static_cast<RealType>(3.49007782566002620811e-1),1924            static_cast<RealType>(5.65303702876260444572e-2),1925            static_cast<RealType>(5.54316442661801299351e-3),1926            static_cast<RealType>(3.58498995501703237922e-4),1927            static_cast<RealType>(1.53872913968336341278e-5),1928            static_cast<RealType>(4.08512152326482573624e-7),1929            static_cast<RealType>(4.72959615756470826429e-9),1930        };1931 1932        result = tools::evaluate_polynomial(P, t) / (tools::evaluate_polynomial(Q, t) * (p * p));1933    }1934    else if (ilogb(p) >= -32) {1935        RealType t = -log2(ldexp(p, 16));1936 1937        // Rational Approximation1938        // Maximum Relative Error: 8.5877e-181939        BOOST_MATH_STATIC const RealType P[10] = {1940            static_cast<RealType>(1.59150086070234563099e-1),1941            static_cast<RealType>(6.07144002506911115092e-2),1942            static_cast<RealType>(1.10026443723891740392e-2),1943            static_cast<RealType>(1.24892739209332398698e-3),1944            static_cast<RealType>(9.82922518655171276487e-5),1945            static_cast<RealType>(5.58366837526347222893e-6),1946            static_cast<RealType>(2.29005408647580194007e-7),1947            static_cast<RealType>(6.44325718317518336404e-9),1948            static_cast<RealType>(1.05110361316230054467e-10),1949            static_cast<RealType>(1.48083450629432857655e-18),1950        };1951        BOOST_MATH_STATIC const RealType Q[9] = {1952            static_cast<RealType>(1.),1953            static_cast<RealType>(3.81470315977341203351e-1),1954            static_cast<RealType>(6.91330250512167919573e-2),1955            static_cast<RealType>(7.84712209182587717077e-3),1956            static_cast<RealType>(6.17595479676821181012e-4),1957            static_cast<RealType>(3.50829361179041199953e-5),1958            static_cast<RealType>(1.43889153071571504712e-6),1959            static_cast<RealType>(4.04840254888235877998e-8),1960            static_cast<RealType>(6.60429636407045050112e-10),1961        };1962 1963        result = tools::evaluate_polynomial(P, t) / (tools::evaluate_polynomial(Q, t) * (p * p));1964    }1965    else if (ilogb(p) >= -64) {1966        RealType t = -log2(ldexp(p, 32));1967 1968        // Rational Approximation1969        // Maximum Relative Error: 8.7254e-171970        BOOST_MATH_STATIC const RealType P[9] = {1971            static_cast<RealType>(1.59154943017783026201e-1),1972            static_cast<RealType>(6.91506515614472069475e-2),1973            static_cast<RealType>(1.44590186111155933843e-2),1974            static_cast<RealType>(1.92616138327724025421e-3),1975            static_cast<RealType>(1.79640147906775699469e-4),1976            static_cast<RealType>(1.30852535070639833809e-5),1977            static_cast<RealType>(5.55259657884038297268e-7),1978            static_cast<RealType>(3.50107118687544980820e-8),1979            static_cast<RealType>(-1.47102592933729597720e-22),1980        };1981        BOOST_MATH_STATIC const RealType Q[8] = {1982            static_cast<RealType>(1.),1983            static_cast<RealType>(4.34486357752330500669e-1),1984            static_cast<RealType>(9.08486933075320995164e-2),1985            static_cast<RealType>(1.21024289017243304241e-2),1986            static_cast<RealType>(1.12871233794777525784e-3),1987            static_cast<RealType>(8.22170725751776749123e-5),1988            static_cast<RealType>(3.48879932410650101194e-6),1989            static_cast<RealType>(2.19978790407451988423e-7),1990        };1991 1992        result = tools::evaluate_polynomial(P, t) / (tools::evaluate_polynomial(Q, t) * (p * p));1993    }1994    else {1995        result = 1 / (p * p * constants::two_pi<RealType>());1996    }1997 1998    return result;1999}2000 2001 2002template <class RealType>2003BOOST_MATH_GPU_ENABLED inline RealType saspoint5_quantile_upper_imp_prec(const RealType& p, const boost::math::integral_constant<int, 113>&)2004{2005    BOOST_MATH_STD_USING2006    RealType result;2007 2008    if (ilogb(p) >= -2) {2009        RealType u = -log2(ldexp(p, 1));2010 2011        if (u < 0.125) {2012            // Rational Approximation2013            // Maximum Relative Error: 2.5675e-362014            // LCOV_EXCL_START2015            BOOST_MATH_STATIC const RealType P[31] = {2016                BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.36099130643975133156293056139850872219e-1),2017                BOOST_MATH_BIG_CONSTANT(RealType, 113, 9.03940482189350763127508703926866548690e1),2018                BOOST_MATH_BIG_CONSTANT(RealType, 113, 3.00518276893354880480781640750482315271e4),2019                BOOST_MATH_BIG_CONSTANT(RealType, 113, 6.55844903094077096941027360107304259099e6),2020                BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.04507684135310729583474324660276395831e9),2021                BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.28519957085041757616278379578781441623e11),2022                BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.26054173986187219679917530171252145632e13),2023                BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.00693075272502479915569708465960917906e15),2024                BOOST_MATH_BIG_CONSTANT(RealType, 113, 6.64153695410984136395853200311209462775e16),2025                BOOST_MATH_BIG_CONSTANT(RealType, 113, 3.64993034609287363745840801813540992383e18),2026                BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.68080300629977787949474098413155901197e20),2027                BOOST_MATH_BIG_CONSTANT(RealType, 113, 6.50632142671665246974634799849090331338e21),2028                BOOST_MATH_BIG_CONSTANT(RealType, 113, 2.11943753054362349397013211631038480307e23),2029                BOOST_MATH_BIG_CONSTANT(RealType, 113, 5.80601829873419334580289886671478701625e24),2030                BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.33441650581633426542372642262736818512e26),2031                BOOST_MATH_BIG_CONSTANT(RealType, 113, 2.56279427934163518272441555879970370340e27),2032                BOOST_MATH_BIG_CONSTANT(RealType, 113, 4.08899113985387092689705022477814364717e28),2033                BOOST_MATH_BIG_CONSTANT(RealType, 113, 5.37750989391907347952902900750138805007e29),2034                BOOST_MATH_BIG_CONSTANT(RealType, 113, 5.76961267256299304213687639380275530721e30),2035                BOOST_MATH_BIG_CONSTANT(RealType, 113, 4.98417586455955659885944915688130612888e31),2036                BOOST_MATH_BIG_CONSTANT(RealType, 113, 3.40932923796679251232655132670811114351e32),2037                BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.80810239916688876216017180714744912573e33),2038                BOOST_MATH_BIG_CONSTANT(RealType, 113, 7.23907429566810200929293428832485038147e33),2039                BOOST_MATH_BIG_CONSTANT(RealType, 113, 2.11441754640405256305951569489818422227e34),2040                BOOST_MATH_BIG_CONSTANT(RealType, 113, 4.30534222360394829628175800718529342304e34),2041                BOOST_MATH_BIG_CONSTANT(RealType, 113, 5.73301799323855143458670230536670073483e34),2042                BOOST_MATH_BIG_CONSTANT(RealType, 113, 4.53142592196246595846485130434777396548e34),2043                BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.81719621726393542967303806360105998384e34),2044                BOOST_MATH_BIG_CONSTANT(RealType, 113, 3.00188544550531824809437206713326495544e33),2045                BOOST_MATH_BIG_CONSTANT(RealType, 113, 2.62706943144847786115732327787879709587e32),2046                BOOST_MATH_BIG_CONSTANT(RealType, 113, 2.32129438774563059735783287456769609571e31),2047            };2048            BOOST_MATH_STATIC const RealType Q[32] = {2049                BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.),2050                BOOST_MATH_BIG_CONSTANT(RealType, 113, 6.65910866673514847742559406762379054364e2),2051                BOOST_MATH_BIG_CONSTANT(RealType, 113, 2.21954860438789969160116317316418373146e5),2052                BOOST_MATH_BIG_CONSTANT(RealType, 113, 4.85684385746348850219351196129081986508e7),2053                BOOST_MATH_BIG_CONSTANT(RealType, 113, 7.76131116920014625994371306210585646224e9),2054                BOOST_MATH_BIG_CONSTANT(RealType, 113, 9.57402411617965582839975369786525269977e11),2055                BOOST_MATH_BIG_CONSTANT(RealType, 113, 9.42213951996062253608905591667405322835e13),2056                BOOST_MATH_BIG_CONSTANT(RealType, 113, 7.55477693883842522631954327528060778834e15),2057                BOOST_MATH_BIG_CONSTANT(RealType, 113, 5.00397907346473927493255003955380711046e17),2058                BOOST_MATH_BIG_CONSTANT(RealType, 113, 2.76305959503723486331556274939198109922e19),2059                BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.27926540483498824808520492399128682366e21),2060                BOOST_MATH_BIG_CONSTANT(RealType, 113, 4.98253913105291675445666919447864520248e22),2061                BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.63457445658532249936389003141915626894e24),2062                BOOST_MATH_BIG_CONSTANT(RealType, 113, 4.51446616633910582673057455450707805902e25),2063                BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.04744823698010333311911891992022528040e27),2064                BOOST_MATH_BIG_CONSTANT(RealType, 113, 2.03400927415310540137351756981742318263e28),2065                BOOST_MATH_BIG_CONSTANT(RealType, 113, 3.28761940359662123632247441327784689568e29),2066                BOOST_MATH_BIG_CONSTANT(RealType, 113, 4.39016138777648624292953560568071708327e30),2067                BOOST_MATH_BIG_CONSTANT(RealType, 113, 4.79639567867465767764785448609833337532e31),2068                BOOST_MATH_BIG_CONSTANT(RealType, 113, 4.23406781975678544311073661662680006588e32),2069                BOOST_MATH_BIG_CONSTANT(RealType, 113, 2.97261483656310352862554580475760827374e33),2070                BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.62715040832592600542933595577003951697e34),2071                BOOST_MATH_BIG_CONSTANT(RealType, 113, 6.77359945057399130202830211722221279906e34),2072                BOOST_MATH_BIG_CONSTANT(RealType, 113, 2.07842295432910751940058270741081867701e35),2073                BOOST_MATH_BIG_CONSTANT(RealType, 113, 4.51739306780247334064265249344359460675e35),2074                BOOST_MATH_BIG_CONSTANT(RealType, 113, 6.60574331076505049588401700048488577194e35),2075                BOOST_MATH_BIG_CONSTANT(RealType, 113, 6.08286808700840316336961663635580879141e35),2076                BOOST_MATH_BIG_CONSTANT(RealType, 113, 3.27661033115008662284071342245200272702e35),2077                BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.00465576791024249023365007797010262700e35),2078                BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.83311248273885136105510175099322638440e34),2079                BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.96635220211386288597285960837372073054e33),2080                BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.23849744128418288892902205619933047730e32),2081            };2082            // LCOV_EXCL_STOP2083            result = u * tools::evaluate_polynomial(P, u) / (tools::evaluate_polynomial(Q, u) * (p * p));2084        }2085        else if (u < 0.25) {2086            RealType t = u - static_cast <RealType>(0.125);2087 2088            // Rational Approximation2089            // Maximum Relative Error: 9.0663e-362090            // LCOV_EXCL_START2091            BOOST_MATH_STATIC const RealType P[13] = {2092                BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.46698650748920243663487731226111319705e-2),2093                BOOST_MATH_BIG_CONSTANT(RealType, 113, 6.39021286045890143123252180276484388346e-1),2094                BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.21933242816562043224009451007344301143e1),2095                BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.33741547463966207206741888477702151242e2),2096                BOOST_MATH_BIG_CONSTANT(RealType, 113, 9.29556944160837955334643715180923663741e2),2097                BOOST_MATH_BIG_CONSTANT(RealType, 113, 4.25261081330476435844217173674285740857e3),2098                BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.28690563577245995896389783271544510833e4),2099                BOOST_MATH_BIG_CONSTANT(RealType, 113, 2.51764495004238264050843085122188741180e4),2100                BOOST_MATH_BIG_CONSTANT(RealType, 113, 3.00501773552098137637598813101153206656e4),2101                BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.93991776883375928647775429233323885440e4),2102                BOOST_MATH_BIG_CONSTANT(RealType, 113, 5.13059418708769178567954713937745050279e3),2103                BOOST_MATH_BIG_CONSTANT(RealType, 113, 2.41565791250614170744069436181282300453e2),2104                BOOST_MATH_BIG_CONSTANT(RealType, 113, 3.35838723365672196069179944509778281549e1),2105            };2106            BOOST_MATH_STATIC const RealType Q[13] = {2107                BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.),2108                BOOST_MATH_BIG_CONSTANT(RealType, 113, 3.63888803456697300467924455320638435538e1),2109                BOOST_MATH_BIG_CONSTANT(RealType, 113, 5.74785179836182339383932806919167693991e2),2110                BOOST_MATH_BIG_CONSTANT(RealType, 113, 5.15133301804008879476562749311747788645e3),2111                BOOST_MATH_BIG_CONSTANT(RealType, 113, 2.87361675398393057971764841741518474061e4),2112                BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.02992617475892211368309739891693879676e5),2113                BOOST_MATH_BIG_CONSTANT(RealType, 113, 2.36356854400440662641546588001882412251e5),2114                BOOST_MATH_BIG_CONSTANT(RealType, 113, 3.35807552915245783626759227539698719908e5),2115                BOOST_MATH_BIG_CONSTANT(RealType, 113, 2.75959389290929178190646034566377062463e5),2116                BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.18514088996371641206828142820042918681e5),2117                BOOST_MATH_BIG_CONSTANT(RealType, 113, 2.54881978220293930450469794941944831047e4),2118                BOOST_MATH_BIG_CONSTANT(RealType, 113, 2.83958740186543542804045767758191509433e3),2119                BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.26637084978098507405883170227585648985e2),2120            };2121            // LCOV_EXCL_STOP2122            result = tools::evaluate_polynomial(P, t) / (tools::evaluate_polynomial(Q, t) * (p * p));2123        }2124        else if (u < 0.5) {2125            RealType t = u - static_cast <RealType>(0.25);2126 2127            // Rational Approximation2128            // Maximum Relative Error: 7.1265e-352129            // LCOV_EXCL_START2130            BOOST_MATH_STATIC const RealType P[14] = {2131                BOOST_MATH_BIG_CONSTANT(RealType, 113, 2.69627866689346442965083437425920959525e-2),2132                BOOST_MATH_BIG_CONSTANT(RealType, 113, 6.28948812330446670380449765578224539665e-1),2133                BOOST_MATH_BIG_CONSTANT(RealType, 113, 6.38832694133021352110245148952631526683e0),2134                BOOST_MATH_BIG_CONSTANT(RealType, 113, 3.70206624753427831733487031852769976576e1),2135                BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.34677850226082773550206949299306677736e2),2136                BOOST_MATH_BIG_CONSTANT(RealType, 113, 3.18657422004942861459539366963056149110e2),2137                BOOST_MATH_BIG_CONSTANT(RealType, 113, 4.90933843076824719761937043667767333536e2),2138                BOOST_MATH_BIG_CONSTANT(RealType, 113, 4.78597771586582252472927601403235921029e2),2139                BOOST_MATH_BIG_CONSTANT(RealType, 113, 2.76489020985978559079198751910122765603e2),2140                BOOST_MATH_BIG_CONSTANT(RealType, 113, 8.37662018494780327201390375334403954354e1),2141                BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.11303058491765900888068268844399186476e1),2142                BOOST_MATH_BIG_CONSTANT(RealType, 113, 8.38147649159947518976483710606042789880e-1),2143                BOOST_MATH_BIG_CONSTANT(RealType, 113, 7.81260575060831053615857196033574207714e-2),2144                BOOST_MATH_BIG_CONSTANT(RealType, 113, -1.26783311530618626413866321968979725353e-3),2145            };2146            BOOST_MATH_STATIC const RealType Q[13] = {2147                BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.),2148                BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.98941943311823528497840052715295329781e1),2149                BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.70142252619301982454969690308614487433e2),2150                BOOST_MATH_BIG_CONSTANT(RealType, 113, 8.17472255695869018956165466705137979540e2),2151                BOOST_MATH_BIG_CONSTANT(RealType, 113, 2.42016169942136311355803413981032780219e3),2152                BOOST_MATH_BIG_CONSTANT(RealType, 113, 4.55874385736597452997483327962434131932e3),2153                BOOST_MATH_BIG_CONSTANT(RealType, 113, 5.45782883079400958761816030672202996788e3),2154                BOOST_MATH_BIG_CONSTANT(RealType, 113, 4.05272877129840019671123017296056938361e3),2155                BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.79833037593794381103412381177370862105e3),2156                BOOST_MATH_BIG_CONSTANT(RealType, 113, 4.67388248713896792948592889733513376054e2),2157                BOOST_MATH_BIG_CONSTANT(RealType, 113, 7.19952164110429183557842014635391021832e1),2158                BOOST_MATH_BIG_CONSTANT(RealType, 113, 6.43813483967503071358907030110791934870e0),2159                BOOST_MATH_BIG_CONSTANT(RealType, 113, 3.21327682641358836049127780506729428797e-1),2160            };2161            // LCOV_EXCL_STOP2162            result = tools::evaluate_polynomial(P, t) / (tools::evaluate_polynomial(Q, t) * (p * p));2163        }2164        else {2165            RealType t = u - static_cast <RealType>(0.5);2166 2167            // Rational Approximation2168            // Maximum Relative Error: 2.7048e-372169            // LCOV_EXCL_START2170            BOOST_MATH_STATIC const RealType P[15] = {2171                BOOST_MATH_BIG_CONSTANT(RealType, 113, 4.79518653373241051262822702930040975338e-2),2172                BOOST_MATH_BIG_CONSTANT(RealType, 113, 5.62230291299220868262265687829866364204e-1),2173                BOOST_MATH_BIG_CONSTANT(RealType, 113, 2.87315544620612697712513318458226575394e0),2174                BOOST_MATH_BIG_CONSTANT(RealType, 113, 8.38993950875334507399211313740958438201e0),2175                BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.54257654902026056547861805085572437922e1),2176                BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.85673656862223617197701693270067722169e1),2177                BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.47842193222521213922734312546590337064e1),2178                BOOST_MATH_BIG_CONSTANT(RealType, 113, 7.76640627287007744941009407221495229316e0),2179                BOOST_MATH_BIG_CONSTANT(RealType, 113, 2.71884893887802925773271837595143776207e0),2180                BOOST_MATH_BIG_CONSTANT(RealType, 113, 6.87432154629995817972739015224205530101e-1),2181                BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.44664933176248007092868241686074743562e-1),2182                BOOST_MATH_BIG_CONSTANT(RealType, 113, 2.32094739938150047092982705610586287965e-2),2183                BOOST_MATH_BIG_CONSTANT(RealType, 113, 2.18537678581395571564129512698022192316e-3),2184                BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.99365265557355974918712592061740510276e-4),2185                BOOST_MATH_BIG_CONSTANT(RealType, 113, 7.66467016868206844419002547523627548705e-6),2186            };2187            BOOST_MATH_STATIC const RealType Q[15] = {2188                BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.),2189                BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.01315080955831561204744043759079263546e1),2190                BOOST_MATH_BIG_CONSTANT(RealType, 113, 4.43409077070585581955481063438385546913e1),2191                BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.09863540097812452102765922256432103612e2),2192                BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.69971336507400724019217277303598318934e2),2193                BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.71444880426858110981683485927452024652e2),2194                BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.15252748520663939799185721687082682973e2),2195                BOOST_MATH_BIG_CONSTANT(RealType, 113, 5.28399989835264172624148638350889215004e1),2196                BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.73464700365199500083227290575797895127e1),2197                BOOST_MATH_BIG_CONSTANT(RealType, 113, 4.40421770918884020099427978511354197438e0),2198                BOOST_MATH_BIG_CONSTANT(RealType, 113, 8.97023025282119988988976542004620759235e-1),2199                BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.38774609088015115009880504176630591783e-1),2200                BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.52748138528630655371589047000668876440e-2),2201                BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.13088455793478303045390386135591069087e-3),2202                BOOST_MATH_BIG_CONSTANT(RealType, 113, 5.18220605549460262119565543089703387122e-5),2203            };2204            // LCOV_EXCL_STOP2205            result = tools::evaluate_polynomial(P, t) / (tools::evaluate_polynomial(Q, t) * (p * p));2206        }2207    }2208    else if (ilogb(p) >= -4) {2209        RealType t = -log2(ldexp(p, 2));2210 2211        // Rational Approximation2212        // Maximum Relative Error: 3.8969e-352213        // LCOV_EXCL_START2214        BOOST_MATH_STATIC const RealType P[18] = {2215            BOOST_MATH_BIG_CONSTANT(RealType, 113, 8.02395484493329839255216366819344305871e-2),2216            BOOST_MATH_BIG_CONSTANT(RealType, 113, 5.02703992140456336967688958960484716694e-1),2217            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.38779662796374026809611637926067177436e0),2218            BOOST_MATH_BIG_CONSTANT(RealType, 113, 2.22326903547451397450399124548020897393e0),2219            BOOST_MATH_BIG_CONSTANT(RealType, 113, 2.29321119874906326000117036864856138032e0),2220            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.60045794013093831332658415095234082115e0),2221            BOOST_MATH_BIG_CONSTANT(RealType, 113, 7.75863216252160126657107771372004587438e-1),2222            BOOST_MATH_BIG_CONSTANT(RealType, 113, 2.65658718311497180532644775193008407069e-1),2223            BOOST_MATH_BIG_CONSTANT(RealType, 113, 6.53225259384404343896446164609240157391e-2),2224            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.17876243295156782920260122855798305258e-2),2225            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.59647007234516896762020830535717539733e-3),2226            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.64519789656979327339865975091579252352e-4),2227            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.29566724776730544346201080459027524931e-5),2228            BOOST_MATH_BIG_CONSTANT(RealType, 113, 7.40979492647851412567441418477263395917e-7),2229            BOOST_MATH_BIG_CONSTANT(RealType, 113, 2.78894057948338305679452471174923939381e-8),2230            BOOST_MATH_BIG_CONSTANT(RealType, 113, 7.97064244496171921075006182915678263370e-10),2231            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.13496588267213644899739513941375650458e-13),2232            BOOST_MATH_BIG_CONSTANT(RealType, 113, 3.75224691413667093006312591320754720811e-14),2233        };2234        BOOST_MATH_STATIC const RealType Q[17] = {2235            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.),2236            BOOST_MATH_BIG_CONSTANT(RealType, 113, 5.59000688626663121310675150262772434285e0),2237            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.37518060227321498297232252379976917550e1),2238            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.96559443266702775026538144474892076437e1),2239            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.81865210018244220041408788510705356696e1),2240            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.15188291931842064325756652570456168425e1),2241            BOOST_MATH_BIG_CONSTANT(RealType, 113, 5.16909307081950035111952362482113369939e0),2242            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.68454509269150307761046136063890222011e0),2243            BOOST_MATH_BIG_CONSTANT(RealType, 113, 4.06391236761753712424925832120306727169e-1),2244            BOOST_MATH_BIG_CONSTANT(RealType, 113, 7.35744804731044427608283991933125506859e-2),2245            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.00655928177646208520006978937806043639e-2),2246            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.04093230988242553633939757013466501271e-3),2247            BOOST_MATH_BIG_CONSTANT(RealType, 113, 8.07921031269974885975846184199640060403e-5),2248            BOOST_MATH_BIG_CONSTANT(RealType, 113, 4.61356596082773699708092475561216104426e-6),2249            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.83968520269928804453766899533464507543e-7),2250            BOOST_MATH_BIG_CONSTANT(RealType, 113, 4.44620973323561344735660659502096499899e-9),2251            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.84398925760354259350870730551452956164e-11),2252        };2253        // LCOV_EXCL_STOP2254        result = tools::evaluate_polynomial(P, t) / (tools::evaluate_polynomial(Q, t) * (p * p));2255    }2256    else if (ilogb(p) >= -8) {2257        RealType t = -log2(ldexp(p, 4));2258 2259        // Rational Approximation2260        // Maximum Relative Error: 4.0176e-352261        // LCOV_EXCL_START2262        BOOST_MATH_STATIC const RealType P[17] = {2263            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.39293493266195566603513288406748830312e-1),2264            BOOST_MATH_BIG_CONSTANT(RealType, 113, 2.75724665658983779947977436518056682748e-1),2265            BOOST_MATH_BIG_CONSTANT(RealType, 113, 2.42437549740894393207094008058345312893e-1),2266            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.26189619865771499663660627120168211026e-1),2267            BOOST_MATH_BIG_CONSTANT(RealType, 113, 4.38952430871711360962228087792821341859e-2),2268            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.09604487371653920602809626594722822237e-2),2269            BOOST_MATH_BIG_CONSTANT(RealType, 113, 2.06215021409396534038209460967790566899e-3),2270            BOOST_MATH_BIG_CONSTANT(RealType, 113, 3.02245531075243838209245241246011523536e-4),2271            BOOST_MATH_BIG_CONSTANT(RealType, 113, 3.52822482024384335373072062232322682354e-5),2272            BOOST_MATH_BIG_CONSTANT(RealType, 113, 3.32527687997718638700761890588399465467e-6),2273            BOOST_MATH_BIG_CONSTANT(RealType, 113, 2.54799997015944073019842889902521208940e-7),2274            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.59368565314052950335981455903474908073e-8),2275            BOOST_MATH_BIG_CONSTANT(RealType, 113, 8.09459594346367728583560281313278117879e-10),2276            BOOST_MATH_BIG_CONSTANT(RealType, 113, 3.30296867679720593932307487485758431355e-11),2277            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.04594079707862644415224596859620253913e-12),2278            BOOST_MATH_BIG_CONSTANT(RealType, 113, 2.40274507498190913768918372242285652373e-14),2279            BOOST_MATH_BIG_CONSTANT(RealType, 113, 3.48644117815971872777609922455371868747e-16),2280        };2281        BOOST_MATH_STATIC const RealType Q[17] = {2282            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.),2283            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.88079839671202113888025645668230104601e0),2284            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.58898753182105924446845274197682915131e0),2285            BOOST_MATH_BIG_CONSTANT(RealType, 113, 8.05418719178760837974322764299800701708e-1),2286            BOOST_MATH_BIG_CONSTANT(RealType, 113, 2.76439568495464423890950166804368135632e-1),2287            BOOST_MATH_BIG_CONSTANT(RealType, 113, 6.87661284201828717694596419805804620767e-2),2288            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.29462021166220769918154388930589492957e-2),2289            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.89960014717788045459266868996575581278e-3),2290            BOOST_MATH_BIG_CONSTANT(RealType, 113, 2.21759236630028632465777310665839652757e-4),2291            BOOST_MATH_BIG_CONSTANT(RealType, 113, 2.08884467282860764261728614542418632608e-5),2292            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.60098870889198704716300891829788260654e-6),2293            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.00120123451682223443624210304146589040e-7),2294            BOOST_MATH_BIG_CONSTANT(RealType, 113, 5.08868117923724451329261971335574401646e-9),2295            BOOST_MATH_BIG_CONSTANT(RealType, 113, 2.07346130275947166224129347124306950150e-10),2296            BOOST_MATH_BIG_CONSTANT(RealType, 113, 6.57848230665832873347797099944091265220e-12),2297            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.50841502849442327828534131901583916707e-13),2298            BOOST_MATH_BIG_CONSTANT(RealType, 113, 2.19165038770000448560339443014882434202e-15),2299        };2300        // LCOV_EXCL_STOP2301        result = tools::evaluate_polynomial(P, t) / (tools::evaluate_polynomial(Q, t) * (p * p));2302    }2303    else if (ilogb(p) >= -16) {2304        RealType t = -log2(ldexp(p, 8));2305 2306        // Rational Approximation2307        // Maximum Relative Error: 4.1682e-362308        // LCOV_EXCL_START2309        BOOST_MATH_STATIC const RealType P[17] = {2310            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.57911660613037766795694241662819364797e-1),2311            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.28799302413396670477035614399187456630e-1),2312            BOOST_MATH_BIG_CONSTANT(RealType, 113, 4.87488304496324715063356722168914018093e-2),2313            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.15106082041721012436439208357739139578e-2),2314            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.91744691940169259573871742836817806248e-3),2315            BOOST_MATH_BIG_CONSTANT(RealType, 113, 2.40707390548486625606656777332664791183e-4),2316            BOOST_MATH_BIG_CONSTANT(RealType, 113, 2.37047148097688601398129659532643297674e-5),2317            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.88039545021930711122085375901243257574e-6),2318            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.22254460725736448552173288004145978774e-7),2319            BOOST_MATH_BIG_CONSTANT(RealType, 113, 6.58462349007293730244197837509157696852e-9),2320            BOOST_MATH_BIG_CONSTANT(RealType, 113, 2.95242372547984999431208546685672497090e-10),2321            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.10113734998651793201123616276573169622e-11),2322            BOOST_MATH_BIG_CONSTANT(RealType, 113, 3.38963677413425618019569452771868834246e-13),2323            BOOST_MATH_BIG_CONSTANT(RealType, 113, 8.45242599273032563942546507899265865936e-15),2324            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.64855118157117311049698715635863670233e-16),2325            BOOST_MATH_BIG_CONSTANT(RealType, 113, 2.31679318790012894619592273346600264199e-18),2326            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.97289727214495789126072009268721022605e-20),2327        };2328        BOOST_MATH_STATIC const RealType Q[17] = {2329            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.),2330            BOOST_MATH_BIG_CONSTANT(RealType, 113, 8.10184661848812835285809771940181522329e-1),2331            BOOST_MATH_BIG_CONSTANT(RealType, 113, 3.06179300560230499194426573196970342618e-1),2332            BOOST_MATH_BIG_CONSTANT(RealType, 113, 7.23171547302923911058112454487643162794e-2),2333            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.20486436116678834807354529081908850425e-2),2334            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.51239574861351183874145649960640500707e-3),2335            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.48939385253081273966380467344920741615e-4),2336            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.18148716720470800170115047757600735127e-5),2337            BOOST_MATH_BIG_CONSTANT(RealType, 113, 7.68156131480770927662478944117713742978e-7),2338            BOOST_MATH_BIG_CONSTANT(RealType, 113, 4.13720275846166334505537351224097058812e-8),2339            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.85505701632948614345319635028225905820e-9),2340            BOOST_MATH_BIG_CONSTANT(RealType, 113, 6.91876669388212587242659571229471930880e-11),2341            BOOST_MATH_BIG_CONSTANT(RealType, 113, 2.12971661051277278610784329698988278013e-12),2342            BOOST_MATH_BIG_CONSTANT(RealType, 113, 5.31096179726750865531615367639563072055e-14),2343            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.03579138802970748888093188937926461893e-15),2344            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.45570688568663643410924100311054014175e-17),2345            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.23959804461200982866930072222355142173e-19),2346        };2347        // LCOV_EXCL_STOP2348        result = tools::evaluate_polynomial(P, t) / (tools::evaluate_polynomial(Q, t) * (p * p));2349    }2350    else if (ilogb(p) >= -32) {2351        RealType t = -log2(ldexp(p, 16));2352 2353        // Rational Approximation2354        // Maximum Relative Error: 6.2158e-372355        // LCOV_EXCL_START2356        BOOST_MATH_STATIC const RealType P[17] = {2357            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.59150086070234561732507586188017224084e-1),2358            BOOST_MATH_BIG_CONSTANT(RealType, 113, 6.80849532387385837583114307010320459997e-2),2359            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.41158479406270598752210344238285334672e-2),2360            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.88824037165656723581890282427897772492e-3),2361            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.82912940787568736176030025420621547622e-4),2362            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.36469458704261637785603215754389736108e-5),2363            BOOST_MATH_BIG_CONSTANT(RealType, 113, 8.13801486421774537025334682673091205328e-7),2364            BOOST_MATH_BIG_CONSTANT(RealType, 113, 3.97058432407176502984043208925327069250e-8),2365            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.60823277541385163663463406307766614689e-9),2366            BOOST_MATH_BIG_CONSTANT(RealType, 113, 5.45016369260792040947272022706860047646e-11),2367            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.54846457278644736871929319230398689553e-12),2368            BOOST_MATH_BIG_CONSTANT(RealType, 113, 3.67291749890916930953794688556299297735e-14),2369            BOOST_MATH_BIG_CONSTANT(RealType, 113, 7.18742803398417392282841454979723852423e-16),2370            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.13337431668170547244474715030235433597e-17),2371            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.37782648734897338547414800391203459036e-19),2372            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.17863064141234633971470839644872485483e-21),2373            BOOST_MATH_BIG_CONSTANT(RealType, 113, 5.58768205048500915346781559321978174829e-24),2374        };2375        BOOST_MATH_STATIC const RealType Q[17] = {2376            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.),2377            BOOST_MATH_BIG_CONSTANT(RealType, 113, 4.27782279546086824129750042200649907991e-1),2378            BOOST_MATH_BIG_CONSTANT(RealType, 113, 8.86934772625607907724733810228981095894e-2),2379            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.18640923531164938140838239032346416143e-2),2380            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.14927915778694317602192656254187608215e-3),2381            BOOST_MATH_BIG_CONSTANT(RealType, 113, 8.57462121236985574785071163024761935943e-5),2382            BOOST_MATH_BIG_CONSTANT(RealType, 113, 5.11326475640883361512750692176665937785e-6),2383            BOOST_MATH_BIG_CONSTANT(RealType, 113, 2.49479333407835032831192117009600622344e-7),2384            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.01048164044583907219965175201239136609e-8),2385            BOOST_MATH_BIG_CONSTANT(RealType, 113, 3.42444147056333448589159611785359705792e-10),2386            BOOST_MATH_BIG_CONSTANT(RealType, 113, 9.72928365136507710372724683325279209464e-12),2387            BOOST_MATH_BIG_CONSTANT(RealType, 113, 2.30776323450676114149657959931149982200e-13),2388            BOOST_MATH_BIG_CONSTANT(RealType, 113, 4.51599272091669693373558919762006698549e-15),2389            BOOST_MATH_BIG_CONSTANT(RealType, 113, 7.12120236145539526122748260176385899774e-17),2390            BOOST_MATH_BIG_CONSTANT(RealType, 113, 8.65713807525694136400636427188839379484e-19),2391            BOOST_MATH_BIG_CONSTANT(RealType, 113, 7.40555520515542383952495965093730818381e-21),2392            BOOST_MATH_BIG_CONSTANT(RealType, 113, 3.51084407433793180162386990118245623958e-23),2393        };2394        // LCOV_EXCL_STOP2395        result = tools::evaluate_polynomial(P, t) / (tools::evaluate_polynomial(Q, t) * (p * p));2396    }2397    else if (ilogb(p) >= -64) {2398        RealType t = -log2(ldexp(p, 32));2399 2400        // Rational Approximation2401        // Maximum Relative Error: 9.8515e-352402        // LCOV_EXCL_START2403        BOOST_MATH_STATIC const RealType P[18] = {2404            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.59154943017783040087729009335921759322e-1),2405            BOOST_MATH_BIG_CONSTANT(RealType, 113, 6.35955784629344586058432079844665517425e-2),2406            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.24333525582177610783141409282489279582e-2),2407            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.58257137499954581519132407255793210808e-3),2408            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.47191495695958634792434622715063010854e-4),2409            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.06408464185207904662485396901099847317e-5),2410            BOOST_MATH_BIG_CONSTANT(RealType, 113, 6.20796977470988464880970001894205834196e-7),2411            BOOST_MATH_BIG_CONSTANT(RealType, 113, 2.99451680244976178843047944033382023574e-8),2412            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.21331607817814211329055723244764031561e-9),2413            BOOST_MATH_BIG_CONSTANT(RealType, 113, 4.16997758215752306644496702331954449485e-11),2414            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.22151810180865778439184946086488092970e-12),2415            BOOST_MATH_BIG_CONSTANT(RealType, 113, 3.05017329554372903197056366604190738772e-14),2416            BOOST_MATH_BIG_CONSTANT(RealType, 113, 6.45919279055502465343977575104142733356e-16),2417            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.14611865933281087898817644094411667861e-17),2418            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.66574579315129285098834562564888533591e-19),2419            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.90098275536617376789480602467351545227e-21),2420            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.56200324658873566425094389271790730206e-23),2421            BOOST_MATH_BIG_CONSTANT(RealType, 113, 7.35526648761411463124801128103381691418e-26),2422        };2423        BOOST_MATH_STATIC const RealType Q[18] = {2424            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.),2425            BOOST_MATH_BIG_CONSTANT(RealType, 113, 3.99582804063194774835771688139366152937e-1),2426            BOOST_MATH_BIG_CONSTANT(RealType, 113, 7.81210581320456331960539046132284190053e-2),2427            BOOST_MATH_BIG_CONSTANT(RealType, 113, 9.94358920922810097599951120081974275145e-3),2428            BOOST_MATH_BIG_CONSTANT(RealType, 113, 9.24831443209858422294319043037419780210e-4),2429            BOOST_MATH_BIG_CONSTANT(RealType, 113, 6.68584098673893150929178892200446909375e-5),2430            BOOST_MATH_BIG_CONSTANT(RealType, 113, 3.90058244779420124535106788512940199547e-6),2431            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.88151039746201934320258158884886191886e-7),2432            BOOST_MATH_BIG_CONSTANT(RealType, 113, 7.62348975553160355852344937226490493460e-9),2433            BOOST_MATH_BIG_CONSTANT(RealType, 113, 2.62007418751593938350474825754731470453e-10),2434            BOOST_MATH_BIG_CONSTANT(RealType, 113, 7.67502458979132962529935588245058477825e-12),2435            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.91648040348401277706598232576212305626e-13),2436            BOOST_MATH_BIG_CONSTANT(RealType, 113, 4.05843052379331618504561151714467880641e-15),2437            BOOST_MATH_BIG_CONSTANT(RealType, 113, 7.20127592059771206959014911028588129920e-17),2438            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.04661894930286305556240859086772458465e-18),2439            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.19442269177165740287568170417649762849e-20),2440            BOOST_MATH_BIG_CONSTANT(RealType, 113, 9.81435584873372180820418114652670864136e-23),2441            BOOST_MATH_BIG_CONSTANT(RealType, 113, 4.62145023253666168339801687459484937001e-25),2442        };2443        // LCOV_EXCL_STOP2444        result = tools::evaluate_polynomial(P, t) / (tools::evaluate_polynomial(Q, t) * (p * p));2445    }2446    else if (ilogb(p) >= -128) {2447        RealType t = -log2(ldexp(p, 64));2448 2449        // Rational Approximation2450        // Maximum Relative Error: 2.2157e-352451        // LCOV_EXCL_START2452        BOOST_MATH_STATIC const RealType P[18] = {2453            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.59154943091895335751628149866310390641e-1),2454            BOOST_MATH_BIG_CONSTANT(RealType, 113, 6.91164927854420277537616294413463565970e-2),2455            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.47557801928232619499125670863084398577e-2),2456            BOOST_MATH_BIG_CONSTANT(RealType, 113, 2.06172621625221091203249391660455847328e-3),2457            BOOST_MATH_BIG_CONSTANT(RealType, 113, 2.11720157411653968975956625234656001375e-4),2458            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.70086412127379161257840749700428137407e-5),2459            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.11069186177775505692019195793079552937e-6),2460            BOOST_MATH_BIG_CONSTANT(RealType, 113, 6.04581765901792649215653828121992908775e-8),2461            BOOST_MATH_BIG_CONSTANT(RealType, 113, 2.78996797234624395264657873201296117159e-9),2462            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.10365978021268853654282661591051834468e-10),2463            BOOST_MATH_BIG_CONSTANT(RealType, 113, 3.76744621013787434243259445839624450867e-12),2464            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.11110170303355425599446515240949433934e-13),2465            BOOST_MATH_BIG_CONSTANT(RealType, 113, 2.83669090335022069229153919882930282425e-15),2466            BOOST_MATH_BIG_CONSTANT(RealType, 113, 6.09633460833089193733622172621696983652e-17),2467            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.16200852052266861122422190933586966917e-18),2468            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.47795810090424252745150042033544310609e-20),2469            BOOST_MATH_BIG_CONSTANT(RealType, 113, 2.35722092370326505616747155207965300634e-22),2470            BOOST_MATH_BIG_CONSTANT(RealType, 113, 8.98381676423023212724768510437325359364e-51),2471        };2472        BOOST_MATH_STATIC const RealType Q[17] = {2473            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.),2474            BOOST_MATH_BIG_CONSTANT(RealType, 113, 4.34271731953273239691423485699928257808e-1),2475            BOOST_MATH_BIG_CONSTANT(RealType, 113, 9.27133013035186849140772481980360839559e-2),2476            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.29542078693828543560388747333519393752e-2),2477            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.33027698228265344561650492600955601983e-3),2478            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.06868444562964057795387778972002636261e-4),2479            BOOST_MATH_BIG_CONSTANT(RealType, 113, 6.97868278672593071151212650783507879919e-6),2480            BOOST_MATH_BIG_CONSTANT(RealType, 113, 3.79869926850283188785885503049178903204e-7),2481            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.75298857713475428388051708713106549590e-8),2482            BOOST_MATH_BIG_CONSTANT(RealType, 113, 6.93449891515741631942400181171061740767e-10),2483            BOOST_MATH_BIG_CONSTANT(RealType, 113, 2.36715626731277089044713008494971829270e-11),2484            BOOST_MATH_BIG_CONSTANT(RealType, 113, 6.98125789528264426960496891930942311971e-13),2485            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.78234546049400950544724588355539821858e-14),2486            BOOST_MATH_BIG_CONSTANT(RealType, 113, 3.83044000387150792693434128054414524740e-16),2487            BOOST_MATH_BIG_CONSTANT(RealType, 113, 7.30111486296552039483196431122555524886e-18),2488            BOOST_MATH_BIG_CONSTANT(RealType, 113, 9.28628462422858135083238952377446358986e-20),2489            BOOST_MATH_BIG_CONSTANT(RealType, 113, 1.48108558735886480298604270981393793162e-21),2490        };2491        // LCOV_EXCL_STOP2492        result = tools::evaluate_polynomial(P, t) / (tools::evaluate_polynomial(Q, t) * (p * p));2493    }2494    else {2495        result = 1 / (p * p * constants::two_pi<RealType>());2496    }2497 2498    return result;2499}2500 2501template <class RealType>2502BOOST_MATH_GPU_ENABLED inline RealType saspoint5_quantile_imp_prec(const RealType& p, bool complement, const boost::math::integral_constant<int, 53>& tag)2503{2504    if (p > 0.5) {2505        return !complement ? saspoint5_quantile_upper_imp_prec(1 - p, tag) : -saspoint5_quantile_upper_imp_prec(1 - p, tag);2506    }2507 2508    return complement ? saspoint5_quantile_upper_imp_prec(p, tag) : -saspoint5_quantile_upper_imp_prec(p, tag);2509}2510 2511template <class RealType>2512BOOST_MATH_GPU_ENABLED inline RealType saspoint5_quantile_imp_prec(const RealType& p, bool complement, const boost::math::integral_constant<int, 113>& tag)2513{2514    if (p > 0.5) {2515        return !complement ? saspoint5_quantile_upper_imp_prec(1 - p, tag) : -saspoint5_quantile_upper_imp_prec(1 - p, tag);2516    }2517 2518    return complement ? saspoint5_quantile_upper_imp_prec(p, tag) : -saspoint5_quantile_upper_imp_prec(p, tag);2519}2520 2521template <class RealType, class Policy>2522BOOST_MATH_GPU_ENABLED inline RealType saspoint5_quantile_imp(const saspoint5_distribution<RealType, Policy>& dist, const RealType& p, bool complement)2523{2524    // This routine implements the quantile for the Saspoint5 distribution,2525    // the value p may be the probability, or its complement if complement=true.2526 2527    constexpr auto function = "boost::math::quantile(saspoint5<%1%>&, %1%)";2528    BOOST_MATH_STD_USING // for ADL of std functions2529 2530    RealType result = 0;2531    RealType scale = dist.scale();2532    RealType location = dist.location();2533 2534    if (false == detail::check_location(function, location, &result, Policy()))2535    {2536        return result;2537    }2538    if (false == detail::check_scale(function, scale, &result, Policy()))2539    {2540        return result;2541    }2542    if (false == detail::check_probability(function, p, &result, Policy()))2543    {2544        return result;2545    }2546 2547    typedef typename tools::promote_args<RealType>::type result_type;2548    typedef typename policies::precision<result_type, Policy>::type precision_type;2549    typedef boost::math::integral_constant<int,2550        precision_type::value <= 0 ? 0 :2551        precision_type::value <= 53 ? 53 :2552        precision_type::value <= 113 ? 113 : 02553    > tag_type;2554 2555    static_assert(tag_type::value, "The SaS point5 distribution is only implemented for types with known precision, and 113 bits or fewer in the mantissa (ie 128 bit quad-floats");2556 2557    result = location + scale * saspoint5_quantile_imp_prec(p, complement, tag_type());2558 2559    return result;2560}2561 2562template <class RealType>2563BOOST_MATH_GPU_ENABLED inline RealType saspoint5_entropy_imp_prec(const boost::math::integral_constant<int, 53>&)2564{2565    return static_cast<RealType>(3.63992444568030649573);2566}2567 2568template <class RealType>2569BOOST_MATH_GPU_ENABLED inline RealType saspoint5_entropy_imp_prec(const boost::math::integral_constant<int, 113>&)2570{2571    return BOOST_MATH_BIG_CONSTANT(RealType, 113, 3.6399244456803064957308496039071853510);2572}2573 2574template <class RealType, class Policy>2575BOOST_MATH_GPU_ENABLED inline RealType saspoint5_entropy_imp(const saspoint5_distribution<RealType, Policy>& dist)2576{2577    // This implements the entropy for the Saspoint5 distribution,2578 2579    constexpr auto function = "boost::math::entropy(saspoint5<%1%>&, %1%)";2580    BOOST_MATH_STD_USING // for ADL of std functions2581 2582    RealType result = 0;2583    RealType scale = dist.scale();2584 2585    if (false == detail::check_scale(function, scale, &result, Policy()))2586    {2587        return result;2588    }2589 2590    typedef typename tools::promote_args<RealType>::type result_type;2591    typedef typename policies::precision<result_type, Policy>::type precision_type;2592    typedef boost::math::integral_constant<int,2593        precision_type::value <= 0 ? 0 :2594        precision_type::value <= 53 ? 53 :2595        precision_type::value <= 113 ? 113 : 02596    > tag_type;2597 2598    static_assert(tag_type::value, "The SaS point5 distribution is only implemented for types with known precision, and 113 bits or fewer in the mantissa (ie 128 bit quad-floats");2599 2600    result = saspoint5_entropy_imp_prec<RealType>(tag_type()) + log(scale);2601 2602    return result;2603}2604 2605} // detail2606 2607template <class RealType = double, class Policy = policies::policy<> >2608class saspoint5_distribution2609{2610    public:2611    typedef RealType value_type;2612    typedef Policy policy_type;2613 2614    BOOST_MATH_GPU_ENABLED saspoint5_distribution(RealType l_location = 0, RealType l_scale = 1)2615        : mu(l_location), c(l_scale)2616    {2617        constexpr auto function = "boost::math::saspoint5_distribution<%1%>::saspoint5_distribution";2618        RealType result = 0;2619        detail::check_location(function, l_location, &result, Policy());2620        detail::check_scale(function, l_scale, &result, Policy());2621    } // saspoint5_distribution2622 2623    BOOST_MATH_GPU_ENABLED RealType location()const2624    {2625        return mu;2626    }2627    BOOST_MATH_GPU_ENABLED RealType scale()const2628    {2629        return c;2630    }2631 2632    private:2633    RealType mu;    // The location parameter.2634    RealType c;     // The scale parameter.2635};2636 2637typedef saspoint5_distribution<double> saspoint5;2638 2639#ifdef __cpp_deduction_guides2640template <class RealType>2641saspoint5_distribution(RealType) -> saspoint5_distribution<typename boost::math::tools::promote_args<RealType>::type>;2642template <class RealType>2643saspoint5_distribution(RealType, RealType) -> saspoint5_distribution<typename boost::math::tools::promote_args<RealType>::type>;2644#endif2645 2646template <class RealType, class Policy>2647BOOST_MATH_GPU_ENABLED inline const boost::math::pair<RealType, RealType> range(const saspoint5_distribution<RealType, Policy>&)2648{ // Range of permissible values for random variable x.2649    BOOST_MATH_IF_CONSTEXPR (boost::math::numeric_limits<RealType>::has_infinity)2650    {2651        return boost::math::pair<RealType, RealType>(-boost::math::numeric_limits<RealType>::infinity(), boost::math::numeric_limits<RealType>::infinity()); // - to + infinity.2652    }2653    else2654    { // Can only use max_value.2655        using boost::math::tools::max_value;2656        return boost::math::pair<RealType, RealType>(-max_value<RealType>(), max_value<RealType>()); // - to + max.2657    }2658}2659 2660template <class RealType, class Policy>2661BOOST_MATH_GPU_ENABLED inline const boost::math::pair<RealType, RealType> support(const saspoint5_distribution<RealType, Policy>&)2662{ // Range of supported values for random variable x.2663   // This is range where cdf rises from 0 to 1, and outside it, the pdf is zero.2664    BOOST_MATH_IF_CONSTEXPR (boost::math::numeric_limits<RealType>::has_infinity)2665    {2666        return boost::math::pair<RealType, RealType>(-boost::math::numeric_limits<RealType>::infinity(), boost::math::numeric_limits<RealType>::infinity()); // - to + infinity.2667    }2668    else2669    { // Can only use max_value.2670        using boost::math::tools::max_value;2671        return boost::math::pair<RealType, RealType>(-tools::max_value<RealType>(), max_value<RealType>()); // - to + max.2672    }2673}2674 2675template <class RealType, class Policy>2676BOOST_MATH_GPU_ENABLED inline RealType pdf(const saspoint5_distribution<RealType, Policy>& dist, const RealType& x)2677{2678    return detail::saspoint5_pdf_imp(dist, x);2679} // pdf2680 2681template <class RealType, class Policy>2682BOOST_MATH_GPU_ENABLED inline RealType cdf(const saspoint5_distribution<RealType, Policy>& dist, const RealType& x)2683{2684    return detail::saspoint5_cdf_imp(dist, x, false);2685} // cdf2686 2687template <class RealType, class Policy>2688BOOST_MATH_GPU_ENABLED inline RealType quantile(const saspoint5_distribution<RealType, Policy>& dist, const RealType& p)2689{2690    return detail::saspoint5_quantile_imp(dist, p, false);2691} // quantile2692 2693template <class RealType, class Policy>2694BOOST_MATH_GPU_ENABLED inline RealType cdf(const complemented2_type<saspoint5_distribution<RealType, Policy>, RealType>& c)2695{2696    return detail::saspoint5_cdf_imp(c.dist, c.param, true);2697} //  cdf complement2698 2699template <class RealType, class Policy>2700BOOST_MATH_GPU_ENABLED inline RealType quantile(const complemented2_type<saspoint5_distribution<RealType, Policy>, RealType>& c)2701{2702    return detail::saspoint5_quantile_imp(c.dist, c.param, true);2703} // quantile complement2704 2705template <class RealType, class Policy>2706BOOST_MATH_GPU_ENABLED inline RealType mean(const saspoint5_distribution<RealType, Policy> &dist)2707{2708    // There is no mean:2709    typedef typename Policy::assert_undefined_type assert_type;2710    static_assert(assert_type::value == 0, "The SaS point5 Distribution has no mean");2711 2712    return policies::raise_domain_error<RealType>(2713        "boost::math::mean(saspoint5<%1%>&)",2714        "The SaS point5 distribution does not have a mean: "2715        "the only possible return value is %1%.",2716        boost::math::numeric_limits<RealType>::quiet_NaN(), Policy());2717}2718 2719template <class RealType, class Policy>2720BOOST_MATH_GPU_ENABLED inline RealType variance(const saspoint5_distribution<RealType, Policy>& /*dist*/)2721{2722    // There is no variance:2723    typedef typename Policy::assert_undefined_type assert_type;2724    static_assert(assert_type::value == 0, "The SaS point5 Distribution has no variance");2725 2726    return policies::raise_domain_error<RealType>(2727        "boost::math::variance(saspoint5<%1%>&)",2728        "The SaS point5 distribution does not have a variance: "2729        "the only possible return value is %1%.",2730        boost::math::numeric_limits<RealType>::quiet_NaN(), Policy());2731}2732 2733template <class RealType, class Policy>2734BOOST_MATH_GPU_ENABLED inline RealType mode(const saspoint5_distribution<RealType, Policy>& dist)2735{2736    return dist.location();2737}2738 2739template <class RealType, class Policy>2740BOOST_MATH_GPU_ENABLED inline RealType median(const saspoint5_distribution<RealType, Policy>& dist)2741{2742    return dist.location();2743}2744 2745template <class RealType, class Policy>2746BOOST_MATH_GPU_ENABLED inline RealType skewness(const saspoint5_distribution<RealType, Policy>& /*dist*/)2747{2748    // There is no skewness:2749    typedef typename Policy::assert_undefined_type assert_type;2750    static_assert(assert_type::value == 0, "The SaS point5 Distribution has no skewness");2751 2752    return policies::raise_domain_error<RealType>(2753        "boost::math::skewness(saspoint5<%1%>&)",2754        "The SaS point5 distribution does not have a skewness: "2755        "the only possible return value is %1%.",2756        boost::math::numeric_limits<RealType>::quiet_NaN(), Policy()); // infinity?2757}2758 2759template <class RealType, class Policy>2760BOOST_MATH_GPU_ENABLED inline RealType kurtosis(const saspoint5_distribution<RealType, Policy>& /*dist*/)2761{2762    // There is no kurtosis:2763    typedef typename Policy::assert_undefined_type assert_type;2764    static_assert(assert_type::value == 0, "The SaS point5 Distribution has no kurtosis");2765 2766    return policies::raise_domain_error<RealType>(2767        "boost::math::kurtosis(saspoint5<%1%>&)",2768        "The SaS point5 distribution does not have a kurtosis: "2769        "the only possible return value is %1%.",2770        boost::math::numeric_limits<RealType>::quiet_NaN(), Policy());2771}2772 2773template <class RealType, class Policy>2774BOOST_MATH_GPU_ENABLED inline RealType kurtosis_excess(const saspoint5_distribution<RealType, Policy>& /*dist*/)2775{2776    // There is no kurtosis excess:2777    typedef typename Policy::assert_undefined_type assert_type;2778    static_assert(assert_type::value == 0, "The SaS point5 Distribution has no kurtosis excess");2779 2780    return policies::raise_domain_error<RealType>(2781        "boost::math::kurtosis_excess(saspoint5<%1%>&)",2782        "The SaS point5 distribution does not have a kurtosis: "2783        "the only possible return value is %1%.",2784        boost::math::numeric_limits<RealType>::quiet_NaN(), Policy());2785}2786 2787template <class RealType, class Policy>2788BOOST_MATH_GPU_ENABLED inline RealType entropy(const saspoint5_distribution<RealType, Policy>& dist)2789{2790    return detail::saspoint5_entropy_imp(dist);2791}2792 2793}} // namespaces2794 2795 2796#endif // BOOST_STATS_SASPOINT5_HPP2797