diff options
Diffstat (limited to 'boost/math/special_functions/lanczos.hpp')
| -rw-r--r-- | boost/math/special_functions/lanczos.hpp | 55 |
1 files changed, 54 insertions, 1 deletions
diff --git a/boost/math/special_functions/lanczos.hpp b/boost/math/special_functions/lanczos.hpp index 20ff969359..ed891549f1 100644 --- a/boost/math/special_functions/lanczos.hpp +++ b/boost/math/special_functions/lanczos.hpp @@ -34,6 +34,35 @@ namespace boost{ namespace math{ namespace lanczos{ // http://my.fit.edu/~gabdo/gamma.txt and elaborated by Toth at // http://www.rskey.org/gamma.htm using NTL::RR at 1000 bit precision. // +// Begin with a small helper to force initialization of constants prior +// to main. This makes the constant initialization thread safe, even +// when called with a user-defined number type. +// +template <class Lanczos, class T> +struct lanczos_initializer +{ + struct init + { + init() + { + T t(1); + Lanczos::lanczos_sum(t); + Lanczos::lanczos_sum_expG_scaled(t); + Lanczos::lanczos_sum_near_1(t); + Lanczos::lanczos_sum_near_2(t); + Lanczos::g(); + } + void force_instantiate()const{} + }; + static const init initializer; + static void force_instantiate() + { + initializer.force_instantiate(); + } +}; +template <class Lanczos, class T> +typename lanczos_initializer<Lanczos, T>::init const lanczos_initializer<Lanczos, T>::initializer; +// // Lanczos Coefficients for N=6 G=5.581 // Max experimental error (with arbitary precision arithmetic) 9.516e-12 // Generated with compiler: Microsoft Visual C++ version 8.0 on Win32 at Mar 23 2006 @@ -47,6 +76,7 @@ struct lanczos6 : public mpl::int_<35> template <class T> static T lanczos_sum(const T& z) { + lanczos_initializer<lanczos6, T>::force_instantiate(); // Ensure our constants get initialized before main() static const T num[6] = { static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 35, 8706.349592549009182288174442774377925882)), static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 35, 8523.650341121874633477483696775067709735)), @@ -69,6 +99,7 @@ struct lanczos6 : public mpl::int_<35> template <class T> static T lanczos_sum_expG_scaled(const T& z) { + lanczos_initializer<lanczos6, T>::force_instantiate(); // Ensure our constants get initialized before main() static const T num[6] = { static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 35, 32.81244541029783471623665933780748627823)), static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 35, 32.12388941444332003446077108933558534361)), @@ -92,6 +123,7 @@ struct lanczos6 : public mpl::int_<35> template<class T> static T lanczos_sum_near_1(const T& dz) { + lanczos_initializer<lanczos6, T>::force_instantiate(); // Ensure our constants get initialized before main() static const T d[5] = { static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 35, 2.044879010930422922760429926121241330235)), static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 35, -2.751366405578505366591317846728753993668)), @@ -110,6 +142,7 @@ struct lanczos6 : public mpl::int_<35> template<class T> static T lanczos_sum_near_2(const T& dz) { + lanczos_initializer<lanczos6, T>::force_instantiate(); // Ensure our constants get initialized before main() static const T d[5] = { static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 35, 5.748142489536043490764289256167080091892)), static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 35, -7.734074268282457156081021756682138251825)), @@ -143,6 +176,7 @@ struct lanczos11 : public mpl::int_<60> template <class T> static T lanczos_sum(const T& z) { + lanczos_initializer<lanczos11, T>::force_instantiate(); // Ensure our constants get initialized before main() static const T num[11] = { static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 60, 38474670393.31776828316099004518914832218)), static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 60, 36857665043.51950660081971227404959150474)), @@ -175,6 +209,7 @@ struct lanczos11 : public mpl::int_<60> template <class T> static T lanczos_sum_expG_scaled(const T& z) { + lanczos_initializer<lanczos11, T>::force_instantiate(); // Ensure our constants get initialized before main() static const T num[11] = { static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 60, 709811.662581657956893540610814842699825)), static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 60, 679979.847415722640161734319823103390728)), @@ -208,6 +243,7 @@ struct lanczos11 : public mpl::int_<60> template<class T> static T lanczos_sum_near_1(const T& dz) { + lanczos_initializer<lanczos11, T>::force_instantiate(); // Ensure our constants get initialized before main() static const T d[10] = { static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 60, 4.005853070677940377969080796551266387954)), static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 60, -13.17044315127646469834125159673527183164)), @@ -231,6 +267,7 @@ struct lanczos11 : public mpl::int_<60> template<class T> static T lanczos_sum_near_2(const T& dz) { + lanczos_initializer<lanczos11, T>::force_instantiate(); // Ensure our constants get initialized before main() static const T d[10] = { static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 60, 19.05889633808148715159575716844556056056)), static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 60, -62.66183664701721716960978577959655644762)), @@ -269,6 +306,7 @@ struct lanczos13 : public mpl::int_<72> template <class T> static T lanczos_sum(const T& z) { + lanczos_initializer<lanczos13, T>::force_instantiate(); // Ensure our constants get initialized before main() static const T num[13] = { static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 72, 44012138428004.60895436261759919070125699)), static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 72, 41590453358593.20051581730723108131357995)), @@ -305,6 +343,7 @@ struct lanczos13 : public mpl::int_<72> template <class T> static T lanczos_sum_expG_scaled(const T& z) { + lanczos_initializer<lanczos13, T>::force_instantiate(); // Ensure our constants get initialized before main() static const T num[13] = { static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 72, 86091529.53418537217994842267760536134841)), static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 72, 81354505.17858011242874285785316135398567)), @@ -342,6 +381,7 @@ struct lanczos13 : public mpl::int_<72> template<class T> static T lanczos_sum_near_1(const T& dz) { + lanczos_initializer<lanczos13, T>::force_instantiate(); // Ensure our constants get initialized before main() static const T d[12] = { static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 72, 4.832115561461656947793029596285626840312)), static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 72, -19.86441536140337740383120735104359034688)), @@ -367,6 +407,7 @@ struct lanczos13 : public mpl::int_<72> template<class T> static T lanczos_sum_near_2(const T& dz) { + lanczos_initializer<lanczos13, T>::force_instantiate(); // Ensure our constants get initialized before main() static const T d[12] = { static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 72, 26.96979819614830698367887026728396466395)), static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 72, -110.8705424709385114023884328797900204863)), @@ -382,7 +423,7 @@ struct lanczos13 : public mpl::int_<72> static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 72, -0.9685385411006641478305219367315965391289e-9)), }; T result = 0; - T z = z = 2; + T z = dz + 2; for(unsigned k = 1; k <= sizeof(d)/sizeof(d[0]); ++k) { result += (-d[k-1]*dz)/(z + k*z + k*k - 1); @@ -407,6 +448,7 @@ struct lanczos22 : public mpl::int_<120> template <class T> static T lanczos_sum(const T& z) { + lanczos_initializer<lanczos22, T>::force_instantiate(); // Ensure our constants get initialized before main() static const T num[22] = { static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, 46198410803245094237463011094.12173081986)), static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, 43735859291852324413622037436.321513777)), @@ -461,6 +503,7 @@ struct lanczos22 : public mpl::int_<120> template <class T> static T lanczos_sum_expG_scaled(const T& z) { + lanczos_initializer<lanczos22, T>::force_instantiate(); // Ensure our constants get initialized before main() static const T num[22] = { static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, 6939996264376682180.277485395074954356211)), static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, 6570067992110214451.87201438870245659384)), @@ -516,6 +559,7 @@ struct lanczos22 : public mpl::int_<120> template<class T> static T lanczos_sum_near_1(const T& dz) { + lanczos_initializer<lanczos22, T>::force_instantiate(); // Ensure our constants get initialized before main() static const T d[21] = { static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, 8.318998691953337183034781139546384476554)), static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, -63.15415991415959158214140353299240638675)), @@ -550,6 +594,7 @@ struct lanczos22 : public mpl::int_<120> template<class T> static T lanczos_sum_near_2(const T& dz) { + lanczos_initializer<lanczos22, T>::force_instantiate(); // Ensure our constants get initialized before main() static const T d[21] = { static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, 75.39272007105208086018421070699575462226)), static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, -572.3481967049935412452681346759966390319)), @@ -830,6 +875,7 @@ struct lanczos17m64 : public mpl::int_<64> template <class T> static T lanczos_sum(const T& z) { + lanczos_initializer<lanczos17m64, T>::force_instantiate(); // Ensure our constants get initialized before main() static const T num[17] = { static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 553681095419291969.2230556393350368550504)), static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 731918863887667017.2511276782146694632234)), @@ -874,6 +920,7 @@ struct lanczos17m64 : public mpl::int_<64> template <class T> static T lanczos_sum_expG_scaled(const T& z) { + lanczos_initializer<lanczos17m64, T>::force_instantiate(); // Ensure our constants get initialized before main() static const T num[17] = { static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 2715894658327.717377557655133124376674911)), static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 3590179526097.912105038525528721129550434)), @@ -919,6 +966,7 @@ struct lanczos17m64 : public mpl::int_<64> template<class T> static T lanczos_sum_near_1(const T& dz) { + lanczos_initializer<lanczos17m64, T>::force_instantiate(); // Ensure our constants get initialized before main() static const T d[16] = { static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 4.493645054286536365763334986866616581265)), static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -16.95716370392468543800733966378143997694)), @@ -948,6 +996,7 @@ struct lanczos17m64 : public mpl::int_<64> template<class T> static T lanczos_sum_near_2(const T& dz) { + lanczos_initializer<lanczos17m64, T>::force_instantiate(); // Ensure our constants get initialized before main() static const T d[16] = { static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 23.56409085052261327114594781581930373708)), static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -88.92116338946308797946237246006238652361)), @@ -991,6 +1040,7 @@ struct lanczos24m113 : public mpl::int_<113> template <class T> static T lanczos_sum(const T& z) { + lanczos_initializer<lanczos24m113, T>::force_instantiate(); // Ensure our constants get initialized before main() static const T num[24] = { static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 113, 2029889364934367661624137213253.22102954656825019111612712252027267955023987678816620961507)), static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 113, 2338599599286656537526273232565.2727349714338768161421882478417543004440597874814359063158)), @@ -1049,6 +1099,7 @@ struct lanczos24m113 : public mpl::int_<113> template <class T> static T lanczos_sum_expG_scaled(const T& z) { + lanczos_initializer<lanczos24m113, T>::force_instantiate(); // Ensure our constants get initialized before main() static const T num[24] = { static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 113, 3035162425359883494754.02878223286972654682199012688209026810841953293372712802258398358538)), static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 113, 3496756894406430103600.16057175075063458536101374170860226963245118484234495645518505519827)), @@ -1108,6 +1159,7 @@ struct lanczos24m113 : public mpl::int_<113> template<class T> static T lanczos_sum_near_1(const T& dz) { + lanczos_initializer<lanczos24m113, T>::force_instantiate(); // Ensure our constants get initialized before main() static const T d[23] = { static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 113, 7.4734083002469026177867421609938203388868806387315406134072298925733950040583068760685908)), static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 113, -50.4225805042247530267317342133388132970816607563062253708655085754357843064134941138154171)), @@ -1144,6 +1196,7 @@ struct lanczos24m113 : public mpl::int_<113> template<class T> static T lanczos_sum_near_2(const T& dz) { + lanczos_initializer<lanczos24m113, T>::force_instantiate(); // Ensure our constants get initialized before main() static const T d[23] = { static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 113, 61.4165001061101455341808888883960361969557848005400286332291451422461117307237198559485365)), static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 113, -414.372973678657049667308134761613915623353625332248315105320470271523320700386200587519147)), |