math/constants/constants.hpp

0001 //  Copyright John Maddock 2005-2006, 2011.
0002 //  Copyright Paul A. Bristow 2006-2011.
0003 //  Use, modification and distribution are subject to the
0004 //  Boost Software License, Version 1.0. (See accompanying file
0005 //  LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
0006
0007 #ifndef BOOST_MATH_CONSTANTS_CONSTANTS_INCLUDED
0008 #define BOOST_MATH_CONSTANTS_CONSTANTS_INCLUDED
0009
0010 #include <boost/math/tools/config.hpp>
0011 #include <boost/math/tools/cxx03_warn.hpp>
0012 #include <boost/math/policies/policy.hpp>
0013 #include <boost/math/tools/precision.hpp>
0014 #include <boost/math/tools/convert_from_string.hpp>
0015 #ifdef _MSC_VER
0016 #pragma warning(push)
0017 #pragma warning(disable: 4127 4701)
0018 #endif
0019 #ifdef _MSC_VER
0020 #pragma warning(pop)
0021 #endif
0022 #include <utility>
0023 #include <type_traits>
0024
0025 #if defined(__GNUC__) && defined(BOOST_MATH_USE_FLOAT128)
0026 //
0027 // This is the only way we can avoid
0028 // warning: non-standard suffix on floating constant [-Wpedantic]
0029 // when building with -Wall -pedantic.  Neither __extension__
0030 // nor #pragma diagnostic ignored work :(
0031 //
0032 #pragma GCC system_header
0033 #endif
0034
0035 namespace boost{ namespace math
0036 {
0037   namespace constants
0038   {
0039     // To permit other calculations at about 100 decimal digits with some UDT,
0040     // it is obviously necessary to define constants to this accuracy.
0041
0042     // However, some compilers do not accept decimal digits strings as long as this.
0043     // So the constant is split into two parts, with the 1st containing at least
0044     // long double precision, and the 2nd zero if not needed or known.
0045     // The 3rd part permits an exponent to be provided if necessary (use zero if none) -
0046     // the other two parameters may only contain decimal digits (and sign and decimal point),
0047     // and may NOT include an exponent like 1.234E99.
0048     // The second digit string is only used if T is a User-Defined Type,
0049     // when the constant is converted to a long string literal and lexical_casted to type T.
0050     // (This is necessary because you can't use a numeric constant
0051     // since even a long double might not have enough digits).
0052
0053    enum construction_method
0054    {
0055       construct_from_float = 1,
0056       construct_from_double = 2,
0057       construct_from_long_double = 3,
0058       construct_from_string = 4,
0059       construct_from_float128 = 5,
0060       // Must be the largest value above:
0061       construct_max = construct_from_float128
0062    };
0063
0064    //
0065    // Traits class determines how to convert from string based on whether T has a constructor
0066    // from const char* or not:
0067    //
0068    template <int N>
0069    struct dummy_size{};
0070
0071    //
0072    // Max number of binary digits in the string representations of our constants:
0073    //
0074    static constexpr int max_string_digits = (101 * 1000L) / 301L;
0075
0076    template <typename Real, typename Policy>
0077    struct construction_traits
0078    {
0079    private:
0080       using real_precision = typename policies::precision<Real, Policy>::type;
0081       using float_precision = typename policies::precision<float, Policy>::type;
0082       using double_precision = typename policies::precision<double, Policy>::type;
0083       using long_double_precision = typename policies::precision<long double, Policy>::type;
0084    public:
0085       using type = std::integral_constant<int,
0086          (0 == real_precision::value) ? 0 :
0087          std::is_convertible<float, Real>::value && (real_precision::value <= float_precision::value)? construct_from_float :
0088          std::is_convertible<double, Real>::value && (real_precision::value <= double_precision::value)? construct_from_double :
0089          std::is_convertible<long double, Real>::value && (real_precision::value <= long_double_precision::value)? construct_from_long_double :
0090 #ifdef BOOST_MATH_USE_FLOAT128
0091          std::is_convertible<BOOST_MATH_FLOAT128_TYPE, Real>::value && (real_precision::value <= 113) ? construct_from_float128 :
0092 #endif
0093          (real_precision::value <= max_string_digits) ? construct_from_string : real_precision::value
0094       >;
0095    };
0096
0097 #ifdef BOOST_HAS_THREADS
0098 #define BOOST_MATH_CONSTANT_THREAD_HELPER(name, prefix) \
0099       boost::once_flag f = BOOST_ONCE_INIT;\
0100       boost::call_once(f, &BOOST_JOIN(BOOST_JOIN(string_, get_), name)<T>);
0101 #else
0102 #define BOOST_MATH_CONSTANT_THREAD_HELPER(name, prefix)
0103 #endif
0104
0105    namespace detail{
0106
0107       template <class Real, class Policy = boost::math::policies::policy<> >
0108       struct constant_return
0109       {
0110          using construct_type = typename construction_traits<Real, Policy>::type;
0111          using type = typename std::conditional<
0112             (construct_type::value == construct_from_string) || (construct_type::value > construct_max),
0113             const Real&, Real>::type;
0114       };
0115
0116       template <typename T, const T& (*F)()>
0117       struct constant_initializer
0118       {
0119          static void force_instantiate()
0120          {
0121             init.force_instantiate();
0122          }
0123       private:
0124          struct initializer
0125          {
0126             initializer()
0127             {
0128                F();
0129             }
0130             void force_instantiate()const{}
0131          };
0132          static const initializer init;
0133       };
0134
0135       template <typename T, const T& (*F)()>
0136       typename constant_initializer<T, F>::initializer const constant_initializer<T, F>::init;
0137
0138       template <typename T, int N, const T& (*F)(BOOST_MATH_EXPLICIT_TEMPLATE_TYPE_SPEC((std::integral_constant<int, N>)) BOOST_MATH_APPEND_EXPLICIT_TEMPLATE_TYPE_SPEC(T))>
0139       struct constant_initializer2
0140       {
0141          static void force_instantiate()
0142          {
0143             init.force_instantiate();
0144          }
0145       private:
0146          struct initializer
0147          {
0148             initializer()
0149             {
0150                F();
0151             }
0152             void force_instantiate()const{}
0153          };
0154          static const initializer init;
0155       };
0156
0157       template <typename T, int N, const T& (*F)(BOOST_MATH_EXPLICIT_TEMPLATE_TYPE_SPEC((std::integral_constant<int, N>)) BOOST_MATH_APPEND_EXPLICIT_TEMPLATE_TYPE_SPEC(T))>
0158       typename constant_initializer2<T, N, F>::initializer const constant_initializer2<T, N, F>::init;
0159
0160    }
0161
0162 #ifdef BOOST_MATH_USE_FLOAT128
0163 #  define BOOST_MATH_FLOAT128_CONSTANT_OVERLOAD(x) \
0164    static inline constexpr T get(const std::integral_constant<int, construct_from_float128>&) noexcept\
0165    { return BOOST_JOIN(x, Q); }
0166 #else
0167 #  define BOOST_MATH_FLOAT128_CONSTANT_OVERLOAD(x)
0168 #endif
0169
0170 #ifdef BOOST_NO_CXX11_THREAD_LOCAL
0171 #  define BOOST_MATH_PRECOMPUTE_IF_NOT_LOCAL(constant_, name)       constant_initializer<T, & BOOST_JOIN(constant_, name)<T>::get_from_variable_precision>::force_instantiate();
0172 #else
0173 #  define BOOST_MATH_PRECOMPUTE_IF_NOT_LOCAL(constant_, name)
0174 #endif
0175
0176 #define BOOST_DEFINE_MATH_CONSTANT(name, x, y)\
0177    namespace detail{\
0178    template <typename T> struct BOOST_JOIN(constant_, name){\
0179    private:\
0180    /* The default implementations come next: */ \
0181    static inline const T& get_from_string()\
0182    {\
0183       static const T result(boost::math::tools::convert_from_string<T>(y));\
0184       return result;\
0185    }\
0186    /* This one is for very high precision that is none the less known at compile time: */ \
0187    template <int N> static T compute(BOOST_MATH_EXPLICIT_TEMPLATE_TYPE_SPEC((std::integral_constant<int, N>)));\
0188    template <int N> static inline const T& get_from_compute(BOOST_MATH_EXPLICIT_TEMPLATE_TYPE_SPEC((std::integral_constant<int, N>)))\
0189    {\
0190       static const T result = compute<N>();\
0191       return result;\
0192    }\
0193    static inline const T& get_from_variable_precision()\
0194    {\
0195       static BOOST_MATH_THREAD_LOCAL int digits = 0;\
0196       static BOOST_MATH_THREAD_LOCAL T value;\
0197       int current_digits = boost::math::tools::digits<T>();\
0198       if(digits != current_digits)\
0199       {\
0200          value = current_digits > max_string_digits ? compute<0>() : T(boost::math::tools::convert_from_string<T>(y));\
0201          digits = current_digits; \
0202       }\
0203       return value;\
0204    }\
0205    /* public getters come next */\
0206    public:\
0207    static inline const T& get(const std::integral_constant<int, construct_from_string>&)\
0208    {\
0209       constant_initializer<T, & BOOST_JOIN(constant_, name)<T>::get_from_string >::force_instantiate();\
0210       return get_from_string();\
0211    }\
0212    static inline constexpr T get(const std::integral_constant<int, construct_from_float>) noexcept\
0213    { return BOOST_JOIN(x, F); }\
0214    static inline constexpr T get(const std::integral_constant<int, construct_from_double>&) noexcept\
0215    { return x; }\
0216    static inline constexpr T get(const std::integral_constant<int, construct_from_long_double>&) noexcept\
0217    { return BOOST_JOIN(x, L); }\
0218    BOOST_MATH_FLOAT128_CONSTANT_OVERLOAD(x) \
0219    template <int N> static inline const T& get(const std::integral_constant<int, N>&)\
0220    {\
0221       constant_initializer2<T, N, & BOOST_JOIN(constant_, name)<T>::template get_from_compute<N> >::force_instantiate();\
0222       return get_from_compute<N>(); \
0223    }\
0224    /* This one is for true arbitrary precision, which may well vary at runtime: */ \
0225    static inline T get(const std::integral_constant<int, 0>&)\
0226    {\
0227       BOOST_MATH_PRECOMPUTE_IF_NOT_LOCAL(constant_, name)\
0228       return get_from_variable_precision(); }\
0229    }; /* end of struct */\
0230    } /* namespace detail */ \
0231    \
0232    \
0233    /* The actual forwarding function: */ \
0234    template <typename T, typename Policy> inline constexpr typename detail::constant_return<T, Policy>::type name(BOOST_MATH_EXPLICIT_TEMPLATE_TYPE_SPEC(T) BOOST_MATH_APPEND_EXPLICIT_TEMPLATE_TYPE_SPEC(Policy)) BOOST_MATH_NOEXCEPT(T)\
0235    { return detail:: BOOST_JOIN(constant_, name)<T>::get(typename construction_traits<T, Policy>::type()); }\
0236    template <typename T> inline constexpr typename detail::constant_return<T>::type name(BOOST_MATH_EXPLICIT_TEMPLATE_TYPE_SPEC(T)) BOOST_MATH_NOEXCEPT(T)\
0237    { return name<T, boost::math::policies::policy<> >(); }\
0238    \
0239    \
0240    /* Now the namespace specific versions: */ \
0241    } namespace float_constants{ static constexpr float name = BOOST_JOIN(x, F); }\
0242    namespace double_constants{ static constexpr double name = x; } \
0243    namespace long_double_constants{ static constexpr long double name = BOOST_JOIN(x, L); }\
0244    namespace constants{
0245
0246   BOOST_DEFINE_MATH_CONSTANT(half, 5.000000000000000000000000000000000000e-01, "5.00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-01")
0247   BOOST_DEFINE_MATH_CONSTANT(third, 3.333333333333333333333333333333333333e-01, "3.33333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333e-01")
0248   BOOST_DEFINE_MATH_CONSTANT(twothirds, 6.666666666666666666666666666666666666e-01, "6.66666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666667e-01")
0249   BOOST_DEFINE_MATH_CONSTANT(two_thirds, 6.666666666666666666666666666666666666e-01, "6.66666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666667e-01")
0250   BOOST_DEFINE_MATH_CONSTANT(sixth, 1.666666666666666666666666666666666666e-01, "1.66666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666667e-01")
0251   BOOST_DEFINE_MATH_CONSTANT(three_quarters, 7.500000000000000000000000000000000000e-01, "7.50000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-01")
0252   BOOST_DEFINE_MATH_CONSTANT(root_two, 1.414213562373095048801688724209698078e+00, "1.41421356237309504880168872420969807856967187537694807317667973799073247846210703885038753432764157273501384623e+00")
0253   BOOST_DEFINE_MATH_CONSTANT(root_three, 1.732050807568877293527446341505872366e+00, "1.73205080756887729352744634150587236694280525381038062805580697945193301690880003708114618675724857567562614142e+00")
0254   BOOST_DEFINE_MATH_CONSTANT(half_root_two, 7.071067811865475244008443621048490392e-01, "7.07106781186547524400844362104849039284835937688474036588339868995366239231053519425193767163820786367506923115e-01")
0255   BOOST_DEFINE_MATH_CONSTANT(ln_two, 6.931471805599453094172321214581765680e-01, "6.93147180559945309417232121458176568075500134360255254120680009493393621969694715605863326996418687542001481021e-01")
0256   BOOST_DEFINE_MATH_CONSTANT(ln_ln_two, -3.665129205816643270124391582326694694e-01, "-3.66512920581664327012439158232669469454263447837105263053677713670561615319352738549455822856698908358302523045e-01")
0257   BOOST_DEFINE_MATH_CONSTANT(root_ln_four, 1.177410022515474691011569326459699637e+00, "1.17741002251547469101156932645969963774738568938582053852252575650002658854698492680841813836877081106747157858e+00")
0258   BOOST_DEFINE_MATH_CONSTANT(one_div_root_two, 7.071067811865475244008443621048490392e-01, "7.07106781186547524400844362104849039284835937688474036588339868995366239231053519425193767163820786367506923115e-01")
0259   BOOST_DEFINE_MATH_CONSTANT(pi, 3.141592653589793238462643383279502884e+00, "3.14159265358979323846264338327950288419716939937510582097494459230781640628620899862803482534211706798214808651e+00")
0260   BOOST_DEFINE_MATH_CONSTANT(half_pi, 1.570796326794896619231321691639751442e+00, "1.57079632679489661923132169163975144209858469968755291048747229615390820314310449931401741267105853399107404326e+00")
0261   BOOST_DEFINE_MATH_CONSTANT(third_pi, 1.047197551196597746154214461093167628e+00, "1.04719755119659774615421446109316762806572313312503527365831486410260546876206966620934494178070568932738269550e+00")
0262   BOOST_DEFINE_MATH_CONSTANT(sixth_pi, 5.235987755982988730771072305465838140e-01, "5.23598775598298873077107230546583814032861566562517636829157432051302734381034833104672470890352844663691347752e-01")
0263   BOOST_DEFINE_MATH_CONSTANT(two_pi, 6.283185307179586476925286766559005768e+00, "6.28318530717958647692528676655900576839433879875021164194988918461563281257241799725606965068423413596429617303e+00")
0264   BOOST_DEFINE_MATH_CONSTANT(two_thirds_pi, 2.094395102393195492308428922186335256e+00, "2.09439510239319549230842892218633525613144626625007054731662972820521093752413933241868988356141137865476539101e+00")
0265   BOOST_DEFINE_MATH_CONSTANT(three_quarters_pi, 2.356194490192344928846982537459627163e+00, "2.35619449019234492884698253745962716314787704953132936573120844423086230471465674897102611900658780098661106488e+00")
0266   BOOST_DEFINE_MATH_CONSTANT(four_thirds_pi, 4.188790204786390984616857844372670512e+00, "4.18879020478639098461685784437267051226289253250014109463325945641042187504827866483737976712282275730953078202e+00")
0267   BOOST_DEFINE_MATH_CONSTANT(one_div_two_pi, 1.591549430918953357688837633725143620e-01, "1.59154943091895335768883763372514362034459645740456448747667344058896797634226535090113802766253085956072842727e-01")
0268   BOOST_DEFINE_MATH_CONSTANT(one_div_root_two_pi, 3.989422804014326779399460599343818684e-01, "3.98942280401432677939946059934381868475858631164934657665925829670657925899301838501252333907306936430302558863e-01")
0269   BOOST_DEFINE_MATH_CONSTANT(root_pi, 1.772453850905516027298167483341145182e+00, "1.77245385090551602729816748334114518279754945612238712821380778985291128459103218137495065673854466541622682362e+00")
0270   BOOST_DEFINE_MATH_CONSTANT(root_half_pi, 1.253314137315500251207882642405522626e+00, "1.25331413731550025120788264240552262650349337030496915831496178817114682730392098747329791918902863305800498633e+00")
0271   BOOST_DEFINE_MATH_CONSTANT(root_two_pi, 2.506628274631000502415765284811045253e+00, "2.50662827463100050241576528481104525300698674060993831662992357634229365460784197494659583837805726611600997267e+00")
0272   BOOST_DEFINE_MATH_CONSTANT(log_root_two_pi, 9.189385332046727417803297364056176398e-01, "9.18938533204672741780329736405617639861397473637783412817151540482765695927260397694743298635954197622005646625e-01")
0273   BOOST_DEFINE_MATH_CONSTANT(one_div_root_pi, 5.641895835477562869480794515607725858e-01, "5.64189583547756286948079451560772585844050629328998856844085721710642468441493414486743660202107363443028347906e-01")
0274   BOOST_DEFINE_MATH_CONSTANT(root_one_div_pi, 5.641895835477562869480794515607725858e-01, "5.64189583547756286948079451560772585844050629328998856844085721710642468441493414486743660202107363443028347906e-01")
0275   BOOST_DEFINE_MATH_CONSTANT(pi_minus_three, 1.415926535897932384626433832795028841e-01, "1.41592653589793238462643383279502884197169399375105820974944592307816406286208998628034825342117067982148086513e-01")
0276   BOOST_DEFINE_MATH_CONSTANT(four_minus_pi, 8.584073464102067615373566167204971158e-01, "8.58407346410206761537356616720497115802830600624894179025055407692183593713791001371965174657882932017851913487e-01")
0277   //BOOST_DEFINE_MATH_CONSTANT(pow23_four_minus_pi, 7.953167673715975443483953350568065807e-01, "7.95316767371597544348395335056806580727639173327713205445302234388856268267518187590758006888600828436839800178e-01")
0278   BOOST_DEFINE_MATH_CONSTANT(pi_pow_e, 2.245915771836104547342715220454373502e+01, "2.24591577183610454734271522045437350275893151339966922492030025540669260403991179123185197527271430315314500731e+01")
0279   BOOST_DEFINE_MATH_CONSTANT(pi_sqr, 9.869604401089358618834490999876151135e+00, "9.86960440108935861883449099987615113531369940724079062641334937622004482241920524300177340371855223182402591377e+00")
0280   BOOST_DEFINE_MATH_CONSTANT(pi_sqr_div_six, 1.644934066848226436472415166646025189e+00, "1.64493406684822643647241516664602518921894990120679843773555822937000747040320087383362890061975870530400431896e+00")
0281   BOOST_DEFINE_MATH_CONSTANT(pi_cubed, 3.100627668029982017547631506710139520e+01, "3.10062766802998201754763150671013952022252885658851076941445381038063949174657060375667010326028861930301219616e+01")
0282   BOOST_DEFINE_MATH_CONSTANT(cbrt_pi, 1.464591887561523263020142527263790391e+00, "1.46459188756152326302014252726379039173859685562793717435725593713839364979828626614568206782035382089750397002e+00")
0283   BOOST_DEFINE_MATH_CONSTANT(one_div_cbrt_pi, 6.827840632552956814670208331581645981e-01, "6.82784063255295681467020833158164598108367515632448804042681583118899226433403918237673501922595519865685577274e-01")
0284   BOOST_DEFINE_MATH_CONSTANT(log2_e, 1.44269504088896340735992468100189213742664595415298, "1.44269504088896340735992468100189213742664595415298593413544940693110921918118507988552662289350634449699751830965e+00")
0285   BOOST_DEFINE_MATH_CONSTANT(e, 2.718281828459045235360287471352662497e+00, "2.71828182845904523536028747135266249775724709369995957496696762772407663035354759457138217852516642742746639193e+00")
0286   BOOST_DEFINE_MATH_CONSTANT(exp_minus_half, 6.065306597126334236037995349911804534e-01, "6.06530659712633423603799534991180453441918135487186955682892158735056519413748423998647611507989456026423789794e-01")
0287   BOOST_DEFINE_MATH_CONSTANT(exp_minus_one, 3.678794411714423215955237701614608674e-01, "3.67879441171442321595523770161460867445811131031767834507836801697461495744899803357147274345919643746627325277e-01")
0288   BOOST_DEFINE_MATH_CONSTANT(e_pow_pi, 2.314069263277926900572908636794854738e+01, "2.31406926327792690057290863679485473802661062426002119934450464095243423506904527835169719970675492196759527048e+01")
0289   BOOST_DEFINE_MATH_CONSTANT(root_e, 1.648721270700128146848650787814163571e+00, "1.64872127070012814684865078781416357165377610071014801157507931164066102119421560863277652005636664300286663776e+00")
0290   BOOST_DEFINE_MATH_CONSTANT(log10_e, 4.342944819032518276511289189166050822e-01, "4.34294481903251827651128918916605082294397005803666566114453783165864649208870774729224949338431748318706106745e-01")
0291   BOOST_DEFINE_MATH_CONSTANT(one_div_log10_e, 2.302585092994045684017991454684364207e+00, "2.30258509299404568401799145468436420760110148862877297603332790096757260967735248023599720508959829834196778404e+00")
0292   BOOST_DEFINE_MATH_CONSTANT(ln_ten, 2.302585092994045684017991454684364207e+00, "2.30258509299404568401799145468436420760110148862877297603332790096757260967735248023599720508959829834196778404e+00")
0293   BOOST_DEFINE_MATH_CONSTANT(degree, 1.745329251994329576923690768488612713e-02, "1.74532925199432957692369076848861271344287188854172545609719144017100911460344944368224156963450948221230449251e-02")
0294   BOOST_DEFINE_MATH_CONSTANT(radian, 5.729577951308232087679815481410517033e+01, "5.72957795130823208767981548141051703324054724665643215491602438612028471483215526324409689958511109441862233816e+01")
0295   BOOST_DEFINE_MATH_CONSTANT(sin_one, 8.414709848078965066525023216302989996e-01, "8.41470984807896506652502321630298999622563060798371065672751709991910404391239668948639743543052695854349037908e-01")
0296   BOOST_DEFINE_MATH_CONSTANT(cos_one, 5.403023058681397174009366074429766037e-01, "5.40302305868139717400936607442976603732310420617922227670097255381100394774471764517951856087183089343571731160e-01")
0297   BOOST_DEFINE_MATH_CONSTANT(sinh_one, 1.175201193643801456882381850595600815e+00, "1.17520119364380145688238185059560081515571798133409587022956541301330756730432389560711745208962339184041953333e+00")
0298   BOOST_DEFINE_MATH_CONSTANT(cosh_one, 1.543080634815243778477905620757061682e+00, "1.54308063481524377847790562075706168260152911236586370473740221471076906304922369896426472643554303558704685860e+00")
0299   BOOST_DEFINE_MATH_CONSTANT(phi, 1.618033988749894848204586834365638117e+00, "1.61803398874989484820458683436563811772030917980576286213544862270526046281890244970720720418939113748475408808e+00")
0300   BOOST_DEFINE_MATH_CONSTANT(ln_phi, 4.812118250596034474977589134243684231e-01, "4.81211825059603447497758913424368423135184334385660519661018168840163867608221774412009429122723474997231839958e-01")
0301   BOOST_DEFINE_MATH_CONSTANT(one_div_ln_phi, 2.078086921235027537601322606117795767e+00, "2.07808692123502753760132260611779576774219226778328348027813992191974386928553540901445615414453604821933918634e+00")
0302   BOOST_DEFINE_MATH_CONSTANT(euler, 5.772156649015328606065120900824024310e-01, "5.77215664901532860606512090082402431042159335939923598805767234884867726777664670936947063291746749514631447250e-01")
0303   BOOST_DEFINE_MATH_CONSTANT(one_div_euler, 1.732454714600633473583025315860829681e+00, "1.73245471460063347358302531586082968115577655226680502204843613287065531408655243008832840219409928068072365714e+00")
0304   BOOST_DEFINE_MATH_CONSTANT(euler_sqr, 3.331779238077186743183761363552442266e-01, "3.33177923807718674318376136355244226659417140249629743150833338002265793695756669661263268631715977303039565603e-01")
0305   BOOST_DEFINE_MATH_CONSTANT(zeta_two, 1.644934066848226436472415166646025189e+00, "1.64493406684822643647241516664602518921894990120679843773555822937000747040320087383362890061975870530400431896e+00")
0306   BOOST_DEFINE_MATH_CONSTANT(zeta_three, 1.202056903159594285399738161511449990e+00, "1.20205690315959428539973816151144999076498629234049888179227155534183820578631309018645587360933525814619915780e+00")
0307   BOOST_DEFINE_MATH_CONSTANT(catalan, 9.159655941772190150546035149323841107e-01, "9.15965594177219015054603514932384110774149374281672134266498119621763019776254769479356512926115106248574422619e-01")
0308   BOOST_DEFINE_MATH_CONSTANT(glaisher, 1.282427129100622636875342568869791727e+00, "1.28242712910062263687534256886979172776768892732500119206374002174040630885882646112973649195820237439420646120e+00")
0309   BOOST_DEFINE_MATH_CONSTANT(khinchin, 2.685452001065306445309714835481795693e+00, "2.68545200106530644530971483548179569382038229399446295305115234555721885953715200280114117493184769799515346591e+00")
0310   BOOST_DEFINE_MATH_CONSTANT(extreme_value_skewness, 1.139547099404648657492793019389846112e+00, "1.13954709940464865749279301938984611208759979583655182472165571008524800770607068570718754688693851501894272049e+00")
0311   BOOST_DEFINE_MATH_CONSTANT(rayleigh_skewness, 6.311106578189371381918993515442277798e-01, "6.31110657818937138191899351544227779844042203134719497658094585692926819617473725459905027032537306794400047264e-01")
0312   BOOST_DEFINE_MATH_CONSTANT(rayleigh_kurtosis, 3.245089300687638062848660410619754415e+00, "3.24508930068763806284866041061975441541706673178920936177133764493367904540874159051490619368679348977426462633e+00")
0313   BOOST_DEFINE_MATH_CONSTANT(rayleigh_kurtosis_excess, 2.450893006876380628486604106197544154e-01, "2.45089300687638062848660410619754415417066731789209361771337644933679045408741590514906193686793489774264626328e-01")
0314
0315   BOOST_DEFINE_MATH_CONSTANT(two_div_pi, 6.366197723675813430755350534900574481e-01, "6.36619772367581343075535053490057448137838582961825794990669376235587190536906140360455211065012343824291370907e-01")
0316   BOOST_DEFINE_MATH_CONSTANT(root_two_div_pi, 7.978845608028653558798921198687637369e-01, "7.97884560802865355879892119868763736951717262329869315331851659341315851798603677002504667814613872860605117725e-01")
0317   BOOST_DEFINE_MATH_CONSTANT(quarter_pi, 0.785398163397448309615660845819875721049292, "0.785398163397448309615660845819875721049292349843776455243736148076954101571552249657008706335529266995537021628320576661773")
0318   BOOST_DEFINE_MATH_CONSTANT(one_div_pi, 0.3183098861837906715377675267450287240689192, "0.31830988618379067153776752674502872406891929148091289749533468811779359526845307018022760553250617191214568545351")
0319   BOOST_DEFINE_MATH_CONSTANT(two_div_root_pi, 1.12837916709551257389615890312154517168810125, "1.12837916709551257389615890312154517168810125865799771368817144342128493688298682897348732040421472688605669581272")
0320
0321 #if __cplusplus >= 201103L || (defined(_MSC_VER) && _MSC_VER >= 1900)
0322   BOOST_DEFINE_MATH_CONSTANT(first_feigenbaum, 4.66920160910299067185320382046620161725818557747576863274,  "4.6692016091029906718532038204662016172581855774757686327456513430041343302113147371386897440239480138171")
0323   BOOST_DEFINE_MATH_CONSTANT(plastic, 1.324717957244746025960908854478097340734404056901733364534, "1.32471795724474602596090885447809734073440405690173336453401505030282785124554759405469934798178728032991")
0324   BOOST_DEFINE_MATH_CONSTANT(gauss, 0.834626841674073186281429732799046808993993013490347002449, "0.83462684167407318628142973279904680899399301349034700244982737010368199270952641186969116035127532412906785")
0325   BOOST_DEFINE_MATH_CONSTANT(dottie, 0.739085133215160641655312087673873404013411758900757464965, "0.739085133215160641655312087673873404013411758900757464965680635773284654883547594599376106931766531849801246")
0326   BOOST_DEFINE_MATH_CONSTANT(reciprocal_fibonacci, 3.35988566624317755317201130291892717968890513, "3.35988566624317755317201130291892717968890513373196848649555381532513031899668338361541621645679008729704")
0327   BOOST_DEFINE_MATH_CONSTANT(laplace_limit, 0.662743419349181580974742097109252907056233549115022417, "0.66274341934918158097474209710925290705623354911502241752039253499097185308651127724965480259895818168")
0328 #endif
0329
0330 template <typename T>
0331 inline constexpr T tau() {  return two_pi<T>(); }
0332
0333 } // namespace constants
0334 } // namespace math
0335 } // namespace boost
0336
0337 //
0338 // We deliberately include this *after* all the declarations above,
0339 // that way the calculation routines can call on other constants above:
0340 //
0341 #include <boost/math/constants/calculate_constants.hpp>
0342
0343 #endif // BOOST_MATH_CONSTANTS_CONSTANTS_INCLUDED
0344
0345