boost/math/constants/constants.hpp
// Copyright John Maddock 2005-2006, 2011. // Copyright Paul A. Bristow 2006-2011. // Use, modification and distribution are subject to the // Boost Software License, Version 1.0. (See accompanying file // LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) #ifndef BOOST_MATH_CONSTANTS_CONSTANTS_INCLUDED #define BOOST_MATH_CONSTANTS_CONSTANTS_INCLUDED #include <boost/math/tools/config.hpp> #include <boost/math/policies/policy.hpp> #include <boost/math/tools/precision.hpp> #ifdef BOOST_MSVC #pragma warning(push) #pragma warning(disable: 4127 4701) #endif #include <boost/lexical_cast.hpp> #ifdef BOOST_MSVC #pragma warning(pop) #endif #include <boost/mpl/if.hpp> #include <boost/mpl/and.hpp> #include <boost/mpl/int.hpp> #include <boost/type_traits/is_convertible.hpp> namespace boost{ namespace math { namespace constants { // To permit other calculations at about 100 decimal digits with NTL::RR type, // it is obviously necessary to define constants to this accuracy. // However, some compilers do not accept decimal digits strings as long as this. // So the constant is split into two parts, with the 1st containing at least // long double precision, and the 2nd zero if not needed or known. // The 3rd part permits an exponent to be provided if necessary (use zero if none) - // the other two parameters may only contain decimal digits (and sign and decimal point), // and may NOT include an exponent like 1.234E99. // The second digit string is only used if T is a User-Defined Type, // when the constant is converted to a long string literal and lexical_casted to type T. // (This is necessary because you can't use a numeric constant // since even a long double might not have enough digits). enum construction_method { construct_from_float = 1, construct_from_double = 2, construct_from_long_double = 3, construct_from_string = 4 }; // // Max number of binary digits in the string representations // of our constants: // BOOST_STATIC_CONSTANT(int, max_string_digits = (101 * 1000L) / 301L); template <class Real, class Policy> struct construction_traits { private: typedef typename policies::precision<Real, Policy>::type t1; typedef typename policies::precision<float, Policy>::type t2; typedef typename policies::precision<double, Policy>::type t3; typedef typename policies::precision<long double, Policy>::type t4; public: typedef typename mpl::if_< mpl::and_<boost::is_convertible<float, Real>, mpl::bool_< t1::value <= t2::value>, mpl::bool_<0 != t1::value> >, mpl::int_<construct_from_float>, typename mpl::if_< mpl::and_<boost::is_convertible<double, Real>, mpl::bool_< t1::value <= t3::value>, mpl::bool_<0 != t1::value> >, mpl::int_<construct_from_double>, typename mpl::if_< mpl::and_<boost::is_convertible<long double, Real>, mpl::bool_< t1::value <= t4::value>, mpl::bool_<0 != t1::value> >, mpl::int_<construct_from_long_double>, typename mpl::if_< mpl::and_<mpl::bool_< t1::value <= max_string_digits>, mpl::bool_<0 != t1::value> >, mpl::int_<construct_from_string>, mpl::int_<t1::value> >::type >::type >::type >::type type; }; #ifdef BOOST_HAS_THREADS #define BOOST_MATH_CONSTANT_THREAD_HELPER(name, prefix) \ boost::once_flag f = BOOST_ONCE_INIT;\ boost::call_once(f, &BOOST_JOIN(BOOST_JOIN(string_, get_), name)<T>); #else #define BOOST_MATH_CONSTANT_THREAD_HELPER(name, prefix) #endif namespace detail{ template <class Real> Real convert_from_string(const char* p, const mpl::false_&) { return boost::lexical_cast<Real>(p); } template <class Real> const char* convert_from_string(const char* p, const mpl::true_&) { return p; } template <class T, T (*F)(BOOST_EXPLICIT_TEMPLATE_TYPE_SPEC(T))> struct constant_initializer { static void force_instantiate() { init.force_instantiate(); } private: struct initializer { initializer() { F( #ifdef BOOST_NO_EXPLICIT_FUNCTION_TEMPLATE_ARGUMENTS 0 #endif ); } void force_instantiate()const{} }; static const initializer init; }; template <class T, T (*F)(BOOST_EXPLICIT_TEMPLATE_TYPE_SPEC(T))> typename constant_initializer<T, F>::initializer const constant_initializer<T, F>::init; template <class T, int N, T (*F)(BOOST_MATH_EXPLICIT_TEMPLATE_TYPE_SPEC(mpl::int_<N>) BOOST_MATH_APPEND_EXPLICIT_TEMPLATE_TYPE_SPEC(T))> struct constant_initializer2 { static void force_instantiate() { init.force_instantiate(); } private: struct initializer { initializer() { F( #ifdef BOOST_NO_EXPLICIT_FUNCTION_TEMPLATE_ARGUMENTS mpl::int_<N>() , 0 #endif ); } void force_instantiate()const{} }; static const initializer init; }; template <class T, int N, T (*F)(BOOST_MATH_EXPLICIT_TEMPLATE_TYPE_SPEC(mpl::int_<N>) BOOST_MATH_APPEND_EXPLICIT_TEMPLATE_TYPE_SPEC(T))> typename constant_initializer2<T, N, F>::initializer const constant_initializer2<T, N, F>::init; } #define BOOST_DEFINE_MATH_CONSTANT(name, x, y)\ namespace detail{\ template <class T> struct BOOST_JOIN(constant_, name){\ private:\ /* The default implementations come next: */ \ static inline T get_from_string()\ {\ static const T result = convert_from_string<T>(y, boost::is_convertible<const char*, T>());\ return result;\ }\ /* This one is for very high precision that is none the less known at compile time: */ \ template <int N> static T compute(BOOST_MATH_EXPLICIT_TEMPLATE_TYPE_SPEC(mpl::int_<N>));\ /* public getters come next */\ public:\ static inline T get(const mpl::int_<construct_from_string>&)\ {\ constant_initializer<T, & BOOST_JOIN(constant_, name)<T>::get_from_string >::force_instantiate();\ return get_from_string();\ }\ static inline BOOST_CONSTEXPR T get(const mpl::int_<construct_from_float>)\ { return BOOST_JOIN(x, F); }\ static inline BOOST_CONSTEXPR T get(const mpl::int_<construct_from_double>&)\ { return x; }\ static inline BOOST_CONSTEXPR T get(const mpl::int_<construct_from_long_double>&)\ { return BOOST_JOIN(x, L); }\ template <int N> static inline T get(const mpl::int_<N>& n)\ {\ constant_initializer2<T, N, & BOOST_JOIN(constant_, name)<T>::template compute<N> >::force_instantiate();\ return compute<N>(); \ }\ /* This one is for true arbitary precision, which may well vary at runtime: */ \ static inline T get(const mpl::int_<0>&)\ { return tools::digits<T>() > max_string_digits ? compute<0>() : get(mpl::int_<construct_from_string>()); }\ }; /* end of struct */\ } /* namespace detail */ \ \ \ /* The actual forwarding function: */ \ template <class T, class Policy> inline BOOST_CONSTEXPR T name(BOOST_MATH_EXPLICIT_TEMPLATE_TYPE_SPEC(T) BOOST_MATH_APPEND_EXPLICIT_TEMPLATE_TYPE_SPEC(Policy))\ { return detail:: BOOST_JOIN(constant_, name)<T>::get(typename construction_traits<T, Policy>::type()); }\ template <class T> inline BOOST_CONSTEXPR T name(BOOST_MATH_EXPLICIT_TEMPLATE_TYPE_SPEC(T))\ { return name<T, boost::math::policies::policy<> >(); }\ \ \ /* Now the namespace specific versions: */ \ } namespace float_constants{ static const float name = BOOST_JOIN(x, F); }\ namespace double_constants{ static const double name = x; } \ namespace long_double_constants{ static const long double name = BOOST_JOIN(x, L); }\ namespace constants{ BOOST_DEFINE_MATH_CONSTANT(half, 5.000000000000000000000000000000000000e-01, "5.00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-01") BOOST_DEFINE_MATH_CONSTANT(third, 3.333333333333333333333333333333333333e-01, "3.33333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333e-01") BOOST_DEFINE_MATH_CONSTANT(twothirds, 6.666666666666666666666666666666666666e-01, "6.66666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666667e-01") BOOST_DEFINE_MATH_CONSTANT(two_thirds, 6.666666666666666666666666666666666666e-01, "6.66666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666666667e-01") BOOST_DEFINE_MATH_CONSTANT(three_quarters, 7.500000000000000000000000000000000000e-01, "7.50000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-01") BOOST_DEFINE_MATH_CONSTANT(root_two, 1.414213562373095048801688724209698078e+00, "1.41421356237309504880168872420969807856967187537694807317667973799073247846210703885038753432764157273501384623e+00") BOOST_DEFINE_MATH_CONSTANT(root_three, 1.732050807568877293527446341505872366e+00, "1.73205080756887729352744634150587236694280525381038062805580697945193301690880003708114618675724857567562614142e+00") BOOST_DEFINE_MATH_CONSTANT(half_root_two, 7.071067811865475244008443621048490392e-01, "7.07106781186547524400844362104849039284835937688474036588339868995366239231053519425193767163820786367506923115e-01") BOOST_DEFINE_MATH_CONSTANT(ln_two, 6.931471805599453094172321214581765680e-01, "6.93147180559945309417232121458176568075500134360255254120680009493393621969694715605863326996418687542001481021e-01") BOOST_DEFINE_MATH_CONSTANT(ln_ln_two, -3.665129205816643270124391582326694694e-01, "-3.66512920581664327012439158232669469454263447837105263053677713670561615319352738549455822856698908358302523045e-01") BOOST_DEFINE_MATH_CONSTANT(root_ln_four, 1.177410022515474691011569326459699637e+00, "1.17741002251547469101156932645969963774738568938582053852252575650002658854698492680841813836877081106747157858e+00") BOOST_DEFINE_MATH_CONSTANT(one_div_root_two, 7.071067811865475244008443621048490392e-01, "7.07106781186547524400844362104849039284835937688474036588339868995366239231053519425193767163820786367506923115e-01") BOOST_DEFINE_MATH_CONSTANT(pi, 3.141592653589793238462643383279502884e+00, "3.14159265358979323846264338327950288419716939937510582097494459230781640628620899862803482534211706798214808651e+00") BOOST_DEFINE_MATH_CONSTANT(half_pi, 1.570796326794896619231321691639751442e+00, "1.57079632679489661923132169163975144209858469968755291048747229615390820314310449931401741267105853399107404326e+00") BOOST_DEFINE_MATH_CONSTANT(third_pi, 1.047197551196597746154214461093167628e+00, "1.04719755119659774615421446109316762806572313312503527365831486410260546876206966620934494178070568932738269550e+00") BOOST_DEFINE_MATH_CONSTANT(sixth_pi, 5.235987755982988730771072305465838140e-01, "5.23598775598298873077107230546583814032861566562517636829157432051302734381034833104672470890352844663691347752e-01") BOOST_DEFINE_MATH_CONSTANT(two_pi, 6.283185307179586476925286766559005768e+00, "6.28318530717958647692528676655900576839433879875021164194988918461563281257241799725606965068423413596429617303e+00") BOOST_DEFINE_MATH_CONSTANT(two_thirds_pi, 2.094395102393195492308428922186335256e+00, "2.09439510239319549230842892218633525613144626625007054731662972820521093752413933241868988356141137865476539101e+00") BOOST_DEFINE_MATH_CONSTANT(three_quarters_pi, 2.356194490192344928846982537459627163e+00, "2.35619449019234492884698253745962716314787704953132936573120844423086230471465674897102611900658780098661106488e+00") BOOST_DEFINE_MATH_CONSTANT(four_thirds_pi, 4.188790204786390984616857844372670512e+00, "4.18879020478639098461685784437267051226289253250014109463325945641042187504827866483737976712282275730953078202e+00") BOOST_DEFINE_MATH_CONSTANT(one_div_two_pi, 1.591549430918953357688837633725143620e-01, "1.59154943091895335768883763372514362034459645740456448747667344058896797634226535090113802766253085956072842727e-01") BOOST_DEFINE_MATH_CONSTANT(one_div_root_two_pi, 3.989422804014326779399460599343818684e-01, "3.98942280401432677939946059934381868475858631164934657665925829670657925899301838501252333907306936430302558863e-01") BOOST_DEFINE_MATH_CONSTANT(root_pi, 1.772453850905516027298167483341145182e+00, "1.77245385090551602729816748334114518279754945612238712821380778985291128459103218137495065673854466541622682362e+00") BOOST_DEFINE_MATH_CONSTANT(root_half_pi, 1.253314137315500251207882642405522626e+00, "1.25331413731550025120788264240552262650349337030496915831496178817114682730392098747329791918902863305800498633e+00") BOOST_DEFINE_MATH_CONSTANT(root_two_pi, 2.506628274631000502415765284811045253e+00, "2.50662827463100050241576528481104525300698674060993831662992357634229365460784197494659583837805726611600997267e+00") BOOST_DEFINE_MATH_CONSTANT(one_div_root_pi, 5.641895835477562869480794515607725858e-01, "5.64189583547756286948079451560772585844050629328998856844085721710642468441493414486743660202107363443028347906e-01") BOOST_DEFINE_MATH_CONSTANT(root_one_div_pi, 5.641895835477562869480794515607725858e-01, "5.64189583547756286948079451560772585844050629328998856844085721710642468441493414486743660202107363443028347906e-01") BOOST_DEFINE_MATH_CONSTANT(pi_minus_three, 1.415926535897932384626433832795028841e-01, "1.41592653589793238462643383279502884197169399375105820974944592307816406286208998628034825342117067982148086513e-01") BOOST_DEFINE_MATH_CONSTANT(four_minus_pi, 8.584073464102067615373566167204971158e-01, "8.58407346410206761537356616720497115802830600624894179025055407692183593713791001371965174657882932017851913487e-01") BOOST_DEFINE_MATH_CONSTANT(pow23_four_minus_pi, 7.953167673715975443483953350568065807e-01, "7.95316767371597544348395335056806580727639173327713205445302234388856268267518187590758006888600828436839800178e-01") BOOST_DEFINE_MATH_CONSTANT(pi_pow_e, 2.245915771836104547342715220454373502e+01, "2.24591577183610454734271522045437350275893151339966922492030025540669260403991179123185197527271430315314500731e+01") BOOST_DEFINE_MATH_CONSTANT(pi_sqr, 9.869604401089358618834490999876151135e+00, "9.86960440108935861883449099987615113531369940724079062641334937622004482241920524300177340371855223182402591377e+00") BOOST_DEFINE_MATH_CONSTANT(pi_sqr_div_six, 1.644934066848226436472415166646025189e+00, "1.64493406684822643647241516664602518921894990120679843773555822937000747040320087383362890061975870530400431896e+00") BOOST_DEFINE_MATH_CONSTANT(pi_cubed, 3.100627668029982017547631506710139520e+01, "3.10062766802998201754763150671013952022252885658851076941445381038063949174657060375667010326028861930301219616e+01") BOOST_DEFINE_MATH_CONSTANT(cbrt_pi, 1.464591887561523263020142527263790391e+00, "1.46459188756152326302014252726379039173859685562793717435725593713839364979828626614568206782035382089750397002e+00") BOOST_DEFINE_MATH_CONSTANT(one_div_cbrt_pi, 6.827840632552956814670208331581645981e-01, "6.82784063255295681467020833158164598108367515632448804042681583118899226433403918237673501922595519865685577274e-01") BOOST_DEFINE_MATH_CONSTANT(e, 2.718281828459045235360287471352662497e+00, "2.71828182845904523536028747135266249775724709369995957496696762772407663035354759457138217852516642742746639193e+00") BOOST_DEFINE_MATH_CONSTANT(exp_minus_half, 6.065306597126334236037995349911804534e-01, "6.06530659712633423603799534991180453441918135487186955682892158735056519413748423998647611507989456026423789794e-01") BOOST_DEFINE_MATH_CONSTANT(e_pow_pi, 2.314069263277926900572908636794854738e+01, "2.31406926327792690057290863679485473802661062426002119934450464095243423506904527835169719970675492196759527048e+01") BOOST_DEFINE_MATH_CONSTANT(root_e, 1.648721270700128146848650787814163571e+00, "1.64872127070012814684865078781416357165377610071014801157507931164066102119421560863277652005636664300286663776e+00") BOOST_DEFINE_MATH_CONSTANT(log10_e, 4.342944819032518276511289189166050822e-01, "4.34294481903251827651128918916605082294397005803666566114453783165864649208870774729224949338431748318706106745e-01") BOOST_DEFINE_MATH_CONSTANT(one_div_log10_e, 2.302585092994045684017991454684364207e+00, "2.30258509299404568401799145468436420760110148862877297603332790096757260967735248023599720508959829834196778404e+00") BOOST_DEFINE_MATH_CONSTANT(ln_ten, 2.302585092994045684017991454684364207e+00, "2.30258509299404568401799145468436420760110148862877297603332790096757260967735248023599720508959829834196778404e+00") BOOST_DEFINE_MATH_CONSTANT(degree, 1.745329251994329576923690768488612713e-02, "1.74532925199432957692369076848861271344287188854172545609719144017100911460344944368224156963450948221230449251e-02") BOOST_DEFINE_MATH_CONSTANT(radian, 5.729577951308232087679815481410517033e+01, "5.72957795130823208767981548141051703324054724665643215491602438612028471483215526324409689958511109441862233816e+01") BOOST_DEFINE_MATH_CONSTANT(sin_one, 8.414709848078965066525023216302989996e-01, "8.41470984807896506652502321630298999622563060798371065672751709991910404391239668948639743543052695854349037908e-01") BOOST_DEFINE_MATH_CONSTANT(cos_one, 5.403023058681397174009366074429766037e-01, "5.40302305868139717400936607442976603732310420617922227670097255381100394774471764517951856087183089343571731160e-01") BOOST_DEFINE_MATH_CONSTANT(sinh_one, 1.175201193643801456882381850595600815e+00, "1.17520119364380145688238185059560081515571798133409587022956541301330756730432389560711745208962339184041953333e+00") BOOST_DEFINE_MATH_CONSTANT(cosh_one, 1.543080634815243778477905620757061682e+00, "1.54308063481524377847790562075706168260152911236586370473740221471076906304922369896426472643554303558704685860e+00") BOOST_DEFINE_MATH_CONSTANT(phi, 1.618033988749894848204586834365638117e+00, "1.61803398874989484820458683436563811772030917980576286213544862270526046281890244970720720418939113748475408808e+00") BOOST_DEFINE_MATH_CONSTANT(ln_phi, 4.812118250596034474977589134243684231e-01, "4.81211825059603447497758913424368423135184334385660519661018168840163867608221774412009429122723474997231839958e-01") BOOST_DEFINE_MATH_CONSTANT(one_div_ln_phi, 2.078086921235027537601322606117795767e+00, "2.07808692123502753760132260611779576774219226778328348027813992191974386928553540901445615414453604821933918634e+00") BOOST_DEFINE_MATH_CONSTANT(euler, 5.772156649015328606065120900824024310e-01, "5.77215664901532860606512090082402431042159335939923598805767234884867726777664670936947063291746749514631447250e-01") BOOST_DEFINE_MATH_CONSTANT(one_div_euler, 1.732454714600633473583025315860829681e+00, "1.73245471460063347358302531586082968115577655226680502204843613287065531408655243008832840219409928068072365714e+00") BOOST_DEFINE_MATH_CONSTANT(euler_sqr, 3.331779238077186743183761363552442266e-01, "3.33177923807718674318376136355244226659417140249629743150833338002265793695756669661263268631715977303039565603e-01") BOOST_DEFINE_MATH_CONSTANT(zeta_two, 1.644934066848226436472415166646025189e+00, "1.64493406684822643647241516664602518921894990120679843773555822937000747040320087383362890061975870530400431896e+00") BOOST_DEFINE_MATH_CONSTANT(zeta_three, 1.202056903159594285399738161511449990e+00, "1.20205690315959428539973816151144999076498629234049888179227155534183820578631309018645587360933525814619915780e+00") BOOST_DEFINE_MATH_CONSTANT(catalan, 9.159655941772190150546035149323841107e-01, "9.15965594177219015054603514932384110774149374281672134266498119621763019776254769479356512926115106248574422619e-01") BOOST_DEFINE_MATH_CONSTANT(glaisher, 1.282427129100622636875342568869791727e+00, "1.28242712910062263687534256886979172776768892732500119206374002174040630885882646112973649195820237439420646120e+00") BOOST_DEFINE_MATH_CONSTANT(khinchin, 2.685452001065306445309714835481795693e+00, "2.68545200106530644530971483548179569382038229399446295305115234555721885953715200280114117493184769799515346591e+00") BOOST_DEFINE_MATH_CONSTANT(extreme_value_skewness, 1.139547099404648657492793019389846112e+00, "1.13954709940464865749279301938984611208759979583655182472165571008524800770607068570718754688693851501894272049e+00") BOOST_DEFINE_MATH_CONSTANT(rayleigh_skewness, 6.311106578189371381918993515442277798e-01, "6.31110657818937138191899351544227779844042203134719497658094585692926819617473725459905027032537306794400047264e-01") BOOST_DEFINE_MATH_CONSTANT(rayleigh_kurtosis, 3.245089300687638062848660410619754415e+00, "3.24508930068763806284866041061975441541706673178920936177133764493367904540874159051490619368679348977426462633e+00") BOOST_DEFINE_MATH_CONSTANT(rayleigh_kurtosis_excess, 2.450893006876380628486604106197544154e-01, "2.45089300687638062848660410619754415417066731789209361771337644933679045408741590514906193686793489774264626328e-01") BOOST_DEFINE_MATH_CONSTANT(two_div_pi, 6.366197723675813430755350534900574481e-01, "6.36619772367581343075535053490057448137838582961825794990669376235587190536906140360455211065012343824291370907e-01") BOOST_DEFINE_MATH_CONSTANT(root_two_div_pi, 7.978845608028653558798921198687637369e-01, "7.97884560802865355879892119868763736951717262329869315331851659341315851798603677002504667814613872860605117725e-01") } // namespace constants } // namespace math } // namespace boost // // We deliberately include this *after* all the declarations above, // that way the calculation routines can call on other constants above: // #include <boost/math/constants/calculate_constants.hpp> #endif // BOOST_MATH_CONSTANTS_CONSTANTS_INCLUDED