#endif
#include <boost/config.hpp>
+#include <boost/math/tools/big_constant.hpp>
#include <boost/mpl/if.hpp>
#include <boost/limits.hpp>
#include <boost/cstdint.hpp>
// 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
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>(8706.349592549009182288174442774377925882L),
- static_cast<T>(8523.650341121874633477483696775067709735L),
- static_cast<T>(3338.029219476423550899999750161289306564L),
- static_cast<T>(653.6424994294008795995653541449610986791L),
- static_cast<T>(63.99951844938187085666201263218840287667L),
- static_cast<T>(2.506628274631006311133031631822390264407L)
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 35, 8706.349592549009182288174442774377925882)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 35, 8523.650341121874633477483696775067709735)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 35, 3338.029219476423550899999750161289306564)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 35, 653.6424994294008795995653541449610986791)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 35, 63.99951844938187085666201263218840287667)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 35, 2.506628274631006311133031631822390264407))
};
static const BOOST_MATH_INT_TABLE_TYPE(T, boost::uint16_t) denom[6] = {
static_cast<boost::uint16_t>(0u),
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>(32.81244541029783471623665933780748627823L),
- static_cast<T>(32.12388941444332003446077108933558534361L),
- static_cast<T>(12.58034729455216106950851080138931470954L),
- static_cast<T>(2.463444478353241423633780693218408889251L),
- static_cast<T>(0.2412010548258800231126240760264822486599L),
- static_cast<T>(0.009446967704539249494420221613134244048319L)
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 35, 32.81244541029783471623665933780748627823)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 35, 32.12388941444332003446077108933558534361)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 35, 12.58034729455216106950851080138931470954)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 35, 2.463444478353241423633780693218408889251)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 35, 0.2412010548258800231126240760264822486599)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 35, 0.009446967704539249494420221613134244048319))
};
static const BOOST_MATH_INT_TABLE_TYPE(T, boost::uint16_t) denom[6] = {
static_cast<boost::uint16_t>(0u),
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>(2.044879010930422922760429926121241330235L),
- static_cast<T>(-2.751366405578505366591317846728753993668L),
- static_cast<T>(1.02282965224225004296750609604264824677L),
- static_cast<T>(-0.09786124911582813985028889636665335893627L),
- static_cast<T>(0.0009829742267506615183144364420540766510112L),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 35, 2.044879010930422922760429926121241330235)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 35, -2.751366405578505366591317846728753993668)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 35, 1.02282965224225004296750609604264824677)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 35, -0.09786124911582813985028889636665335893627)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 35, 0.0009829742267506615183144364420540766510112)),
};
T result = 0;
for(unsigned k = 1; k <= sizeof(d)/sizeof(d[0]); ++k)
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>(5.748142489536043490764289256167080091892L),
- static_cast<T>(-7.734074268282457156081021756682138251825L),
- static_cast<T>(2.875167944990511006997713242805893543947L),
- static_cast<T>(-0.2750873773533504542306766137703788781776L),
- static_cast<T>(0.002763134585812698552178368447708846850353L),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 35, 5.748142489536043490764289256167080091892)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 35, -7.734074268282457156081021756682138251825)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 35, 2.875167944990511006997713242805893543947)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 35, -0.2750873773533504542306766137703788781776)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 35, 0.002763134585812698552178368447708846850353)),
};
T result = 0;
T z = dz + 2;
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>(38474670393.31776828316099004518914832218L),
- static_cast<T>(36857665043.51950660081971227404959150474L),
- static_cast<T>(15889202453.72942008945006665994637853242L),
- static_cast<T>(4059208354.298834770194507810788393801607L),
- static_cast<T>(680547661.1834733286087695557084801366446L),
- static_cast<T>(78239755.00312005289816041245285376206263L),
- static_cast<T>(6246580.776401795264013335510453568106366L),
- static_cast<T>(341986.3488721347032223777872763188768288L),
- static_cast<T>(12287.19451182455120096222044424100527629L),
- static_cast<T>(261.6140441641668190791708576058805625502L),
- static_cast<T>(2.506628274631000502415573855452633787834L)
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 60, 38474670393.31776828316099004518914832218)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 60, 36857665043.51950660081971227404959150474)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 60, 15889202453.72942008945006665994637853242)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 60, 4059208354.298834770194507810788393801607)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 60, 680547661.1834733286087695557084801366446)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 60, 78239755.00312005289816041245285376206263)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 60, 6246580.776401795264013335510453568106366)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 60, 341986.3488721347032223777872763188768288)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 60, 12287.19451182455120096222044424100527629)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 60, 261.6140441641668190791708576058805625502)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 60, 2.506628274631000502415573855452633787834))
};
static const BOOST_MATH_INT_TABLE_TYPE(T, boost::uint32_t) denom[11] = {
static_cast<boost::uint32_t>(0u),
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>(709811.662581657956893540610814842699825L),
- static_cast<T>(679979.847415722640161734319823103390728L),
- static_cast<T>(293136.785721159725251629480984140341656L),
- static_cast<T>(74887.5403291467179935942448101441897121L),
- static_cast<T>(12555.29058241386295096255111537516768137L),
- static_cast<T>(1443.42992444170669746078056942194198252L),
- static_cast<T>(115.2419459613734722083208906727972935065L),
- static_cast<T>(6.30923920573262762719523981992008976989L),
- static_cast<T>(0.2266840463022436475495508977579735223818L),
- static_cast<T>(0.004826466289237661857584712046231435101741L),
- static_cast<T>(0.4624429436045378766270459638520555557321e-4L)
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 60, 709811.662581657956893540610814842699825)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 60, 679979.847415722640161734319823103390728)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 60, 293136.785721159725251629480984140341656)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 60, 74887.5403291467179935942448101441897121)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 60, 12555.29058241386295096255111537516768137)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 60, 1443.42992444170669746078056942194198252)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 60, 115.2419459613734722083208906727972935065)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 60, 6.30923920573262762719523981992008976989)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 60, 0.2266840463022436475495508977579735223818)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 60, 0.004826466289237661857584712046231435101741)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 60, 0.4624429436045378766270459638520555557321e-4))
};
static const BOOST_MATH_INT_TABLE_TYPE(T, boost::uint32_t) denom[11] = {
static_cast<boost::uint32_t>(0u),
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>(4.005853070677940377969080796551266387954L),
- static_cast<T>(-13.17044315127646469834125159673527183164L),
- static_cast<T>(17.19146865350790353683895137079288129318L),
- static_cast<T>(-11.36446409067666626185701599196274701126L),
- static_cast<T>(4.024801119349323770107694133829772634737L),
- static_cast<T>(-0.7445703262078094128346501724255463005006L),
- static_cast<T>(0.06513861351917497265045550019547857713172L),
- static_cast<T>(-0.00217899958561830354633560009312512312758L),
- static_cast<T>(0.17655204574495137651670832229571934738e-4L),
- static_cast<T>(-0.1036282091079938047775645941885460820853e-7L),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 60, 4.005853070677940377969080796551266387954)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 60, -13.17044315127646469834125159673527183164)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 60, 17.19146865350790353683895137079288129318)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 60, -11.36446409067666626185701599196274701126)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 60, 4.024801119349323770107694133829772634737)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 60, -0.7445703262078094128346501724255463005006)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 60, 0.06513861351917497265045550019547857713172)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 60, -0.00217899958561830354633560009312512312758)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 60, 0.17655204574495137651670832229571934738e-4)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 60, -0.1036282091079938047775645941885460820853e-7)),
};
T result = 0;
for(unsigned k = 1; k <= sizeof(d)/sizeof(d[0]); ++k)
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>(19.05889633808148715159575716844556056056L),
- static_cast<T>(-62.66183664701721716960978577959655644762L),
- static_cast<T>(81.7929198065004751699057192860287512027L),
- static_cast<T>(-54.06941772964234828416072865069196553015L),
- static_cast<T>(19.14904664790693019642068229478769661515L),
- static_cast<T>(-3.542488556926667589704590409095331790317L),
- static_cast<T>(0.3099140334815639910894627700232804503017L),
- static_cast<T>(-0.01036716187296241640634252431913030440825L),
- static_cast<T>(0.8399926504443119927673843789048514017761e-4L),
- static_cast<T>(-0.493038376656195010308610694048822561263e-7L),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 60, 19.05889633808148715159575716844556056056)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 60, -62.66183664701721716960978577959655644762)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 60, 81.7929198065004751699057192860287512027)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 60, -54.06941772964234828416072865069196553015)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 60, 19.14904664790693019642068229478769661515)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 60, -3.542488556926667589704590409095331790317)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 60, 0.3099140334815639910894627700232804503017)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 60, -0.01036716187296241640634252431913030440825)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 60, 0.8399926504443119927673843789048514017761e-4)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 60, -0.493038376656195010308610694048822561263e-7)),
};
T result = 0;
T z = dz + 2;
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>(44012138428004.60895436261759919070125699L),
- static_cast<T>(41590453358593.20051581730723108131357995L),
- static_cast<T>(18013842787117.99677796276038389462742949L),
- static_cast<T>(4728736263475.388896889723995205703970787L),
- static_cast<T>(837910083628.4046470415724300225777912264L),
- static_cast<T>(105583707273.4299344907359855510105321192L),
- static_cast<T>(9701363618.494999493386608345339104922694L),
- static_cast<T>(654914397.5482052641016767125048538245644L),
- static_cast<T>(32238322.94213356530668889463945849409184L),
- static_cast<T>(1128514.219497091438040721811544858643121L),
- static_cast<T>(26665.79378459858944762533958798805525125L),
- static_cast<T>(381.8801248632926870394389468349331394196L),
- static_cast<T>(2.506628274631000502415763426076722427007L)
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 72, 44012138428004.60895436261759919070125699)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 72, 41590453358593.20051581730723108131357995)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 72, 18013842787117.99677796276038389462742949)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 72, 4728736263475.388896889723995205703970787)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 72, 837910083628.4046470415724300225777912264)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 72, 105583707273.4299344907359855510105321192)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 72, 9701363618.494999493386608345339104922694)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 72, 654914397.5482052641016767125048538245644)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 72, 32238322.94213356530668889463945849409184)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 72, 1128514.219497091438040721811544858643121)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 72, 26665.79378459858944762533958798805525125)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 72, 381.8801248632926870394389468349331394196)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 72, 2.506628274631000502415763426076722427007))
};
static const BOOST_MATH_INT_TABLE_TYPE(T, boost::uint32_t) denom[13] = {
static_cast<boost::uint32_t>(0u),
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>(86091529.53418537217994842267760536134841L),
- static_cast<T>(81354505.17858011242874285785316135398567L),
- static_cast<T>(35236626.38815461910817650960734605416521L),
- static_cast<T>(9249814.988024471294683815872977672237195L),
- static_cast<T>(1639024.216687146960253839656643518985826L),
- static_cast<T>(206530.8157641225032631778026076868855623L),
- static_cast<T>(18976.70193530288915698282139308582105936L),
- static_cast<T>(1281.068909912559479885759622791374106059L),
- static_cast<T>(63.06093343420234536146194868906771599354L),
- static_cast<T>(2.207470909792527638222674678171050209691L),
- static_cast<T>(0.05216058694613505427476207805814960742102L),
- static_cast<T>(0.0007469903808915448316510079585999893674101L),
- static_cast<T>(0.4903180573459871862552197089738373164184e-5L)
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 72, 86091529.53418537217994842267760536134841)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 72, 81354505.17858011242874285785316135398567)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 72, 35236626.38815461910817650960734605416521)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 72, 9249814.988024471294683815872977672237195)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 72, 1639024.216687146960253839656643518985826)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 72, 206530.8157641225032631778026076868855623)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 72, 18976.70193530288915698282139308582105936)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 72, 1281.068909912559479885759622791374106059)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 72, 63.06093343420234536146194868906771599354)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 72, 2.207470909792527638222674678171050209691)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 72, 0.05216058694613505427476207805814960742102)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 72, 0.0007469903808915448316510079585999893674101)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 72, 0.4903180573459871862552197089738373164184e-5))
};
static const BOOST_MATH_INT_TABLE_TYPE(T, boost::uint32_t) denom[13] = {
static_cast<boost::uint32_t>(0u),
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>(4.832115561461656947793029596285626840312L),
- static_cast<T>(-19.86441536140337740383120735104359034688L),
- static_cast<T>(33.9927422807443239927197864963170585331L),
- static_cast<T>(-31.41520692249765980987427413991250886138L),
- static_cast<T>(17.0270866009599345679868972409543597821L),
- static_cast<T>(-5.5077216950865501362506920516723682167L),
- static_cast<T>(1.037811741948214855286817963800439373362L),
- static_cast<T>(-0.106640468537356182313660880481398642811L),
- static_cast<T>(0.005276450526660653288757565778182586742831L),
- static_cast<T>(-0.0001000935625597121545867453746252064770029L),
- static_cast<T>(0.462590910138598083940803704521211569234e-6L),
- static_cast<T>(-0.1735307814426389420248044907765671743012e-9L),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 72, 4.832115561461656947793029596285626840312)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 72, -19.86441536140337740383120735104359034688)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 72, 33.9927422807443239927197864963170585331)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 72, -31.41520692249765980987427413991250886138)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 72, 17.0270866009599345679868972409543597821)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 72, -5.5077216950865501362506920516723682167)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 72, 1.037811741948214855286817963800439373362)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 72, -0.106640468537356182313660880481398642811)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 72, 0.005276450526660653288757565778182586742831)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 72, -0.0001000935625597121545867453746252064770029)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 72, 0.462590910138598083940803704521211569234e-6)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 72, -0.1735307814426389420248044907765671743012e-9)),
};
T result = 0;
for(unsigned k = 1; k <= sizeof(d)/sizeof(d[0]); ++k)
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>(26.96979819614830698367887026728396466395L),
- static_cast<T>(-110.8705424709385114023884328797900204863L),
- static_cast<T>(189.7258846119231466417015694690434770085L),
- static_cast<T>(-175.3397202971107486383321670769397356553L),
- static_cast<T>(95.03437648691551457087250340903980824948L),
- static_cast<T>(-30.7406022781665264273675797983497141978L),
- static_cast<T>(5.792405601630517993355102578874590410552L),
- static_cast<T>(-0.5951993240669148697377539518639997795831L),
- static_cast<T>(0.02944979359164017509944724739946255067671L),
- static_cast<T>(-0.0005586586555377030921194246330399163602684L),
- static_cast<T>(0.2581888478270733025288922038673392636029e-5L),
- static_cast<T>(-0.9685385411006641478305219367315965391289e-9L),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 72, 26.96979819614830698367887026728396466395)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 72, -110.8705424709385114023884328797900204863)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 72, 189.7258846119231466417015694690434770085)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 72, -175.3397202971107486383321670769397356553)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 72, 95.03437648691551457087250340903980824948)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 72, -30.7406022781665264273675797983497141978)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 72, 5.792405601630517993355102578874590410552)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 72, -0.5951993240669148697377539518639997795831)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 72, 0.02944979359164017509944724739946255067671)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 72, -0.0005586586555377030921194246330399163602684)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 72, 0.2581888478270733025288922038673392636029e-5)),
+ 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);
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>(46198410803245094237463011094.12173081986L),
- static_cast<T>(43735859291852324413622037436.321513777L),
- static_cast<T>(19716607234435171720534556386.97481377748L),
- static_cast<T>(5629401471315018442177955161.245623932129L),
- static_cast<T>(1142024910634417138386281569.245580222392L),
- static_cast<T>(175048529315951173131586747.695329230778L),
- static_cast<T>(21044290245653709191654675.41581372963167L),
- static_cast<T>(2033001410561031998451380.335553678782601L),
- static_cast<T>(160394318862140953773928.8736211601848891L),
- static_cast<T>(10444944438396359705707.48957290388740896L),
- static_cast<T>(565075825801617290121.1466393747967538948L),
- static_cast<T>(25475874292116227538.99448534450411942597L),
- static_cast<T>(957135055846602154.6720835535232270205725L),
- static_cast<T>(29874506304047462.23662392445173880821515L),
- static_cast<T>(769651310384737.2749087590725764959689181L),
- static_cast<T>(16193289100889.15989633624378404096011797L),
- static_cast<T>(273781151680.6807433264462376754578933261L),
- static_cast<T>(3630485900.32917021712188739762161583295L),
- static_cast<T>(36374352.05577334277856865691538582936484L),
- static_cast<T>(258945.7742115532455441786924971194951043L),
- static_cast<T>(1167.501919472435718934219997431551246996L),
- static_cast<T>(2.50662827463100050241576528481104525333L)
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, 46198410803245094237463011094.12173081986)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, 43735859291852324413622037436.321513777)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, 19716607234435171720534556386.97481377748)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, 5629401471315018442177955161.245623932129)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, 1142024910634417138386281569.245580222392)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, 175048529315951173131586747.695329230778)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, 21044290245653709191654675.41581372963167)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, 2033001410561031998451380.335553678782601)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, 160394318862140953773928.8736211601848891)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, 10444944438396359705707.48957290388740896)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, 565075825801617290121.1466393747967538948)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, 25475874292116227538.99448534450411942597)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, 957135055846602154.6720835535232270205725)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, 29874506304047462.23662392445173880821515)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, 769651310384737.2749087590725764959689181)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, 16193289100889.15989633624378404096011797)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, 273781151680.6807433264462376754578933261)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, 3630485900.32917021712188739762161583295)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, 36374352.05577334277856865691538582936484)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, 258945.7742115532455441786924971194951043)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, 1167.501919472435718934219997431551246996)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, 2.50662827463100050241576528481104525333))
};
static const BOOST_MATH_INT_TABLE_TYPE(T, boost::uint64_t) denom[22] = {
BOOST_MATH_INT_VALUE_SUFFIX(0, uLL),
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>(6939996264376682180.277485395074954356211L),
- static_cast<T>(6570067992110214451.87201438870245659384L),
- static_cast<T>(2961859037444440551.986724631496417064121L),
- static_cast<T>(845657339772791245.3541226499766163431651L),
- static_cast<T>(171556737035449095.2475716923888737881837L),
- static_cast<T>(26296059072490867.7822441885603400926007L),
- static_cast<T>(3161305619652108.433798300149816829198706L),
- static_cast<T>(305400596026022.4774396904484542582526472L),
- static_cast<T>(24094681058862.55120507202622377623528108L),
- static_cast<T>(1569055604375.919477574824168939428328839L),
- static_cast<T>(84886558909.02047889339710230696942513159L),
- static_cast<T>(3827024985.166751989686050643579753162298L),
- static_cast<T>(143782298.9273215199098728674282885500522L),
- static_cast<T>(4487794.24541641841336786238909171265944L),
- static_cast<T>(115618.2025760830513505888216285273541959L),
- static_cast<T>(2432.580773108508276957461757328744780439L),
- static_cast<T>(41.12782532742893597168530008461874360191L),
- static_cast<T>(0.5453771709477689805460179187388702295792L),
- static_cast<T>(0.005464211062612080347167337964166505282809L),
- static_cast<T>(0.388992321263586767037090706042788910953e-4L),
- static_cast<T>(0.1753839324538447655939518484052327068859e-6L),
- static_cast<T>(0.3765495513732730583386223384116545391759e-9L)
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, 6939996264376682180.277485395074954356211)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, 6570067992110214451.87201438870245659384)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, 2961859037444440551.986724631496417064121)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, 845657339772791245.3541226499766163431651)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, 171556737035449095.2475716923888737881837)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, 26296059072490867.7822441885603400926007)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, 3161305619652108.433798300149816829198706)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, 305400596026022.4774396904484542582526472)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, 24094681058862.55120507202622377623528108)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, 1569055604375.919477574824168939428328839)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, 84886558909.02047889339710230696942513159)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, 3827024985.166751989686050643579753162298)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, 143782298.9273215199098728674282885500522)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, 4487794.24541641841336786238909171265944)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, 115618.2025760830513505888216285273541959)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, 2432.580773108508276957461757328744780439)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, 41.12782532742893597168530008461874360191)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, 0.5453771709477689805460179187388702295792)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, 0.005464211062612080347167337964166505282809)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, 0.388992321263586767037090706042788910953e-4)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, 0.1753839324538447655939518484052327068859e-6)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, 0.3765495513732730583386223384116545391759e-9))
};
static const BOOST_MATH_INT_TABLE_TYPE(T, boost::uint64_t) denom[22] = {
BOOST_MATH_INT_VALUE_SUFFIX(0, uLL),
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>(8.318998691953337183034781139546384476554L),
- static_cast<T>(-63.15415991415959158214140353299240638675L),
- static_cast<T>(217.3108224383632868591462242669081540163L),
- static_cast<T>(-448.5134281386108366899784093610397354889L),
- static_cast<T>(619.2903759363285456927248474593012711346L),
- static_cast<T>(-604.1630177420625418522025080080444177046L),
- static_cast<T>(428.8166750424646119935047118287362193314L),
- static_cast<T>(-224.6988753721310913866347429589434550302L),
- static_cast<T>(87.32181627555510833499451817622786940961L),
- static_cast<T>(-25.07866854821128965662498003029199058098L),
- static_cast<T>(5.264398125689025351448861011657789005392L),
- static_cast<T>(-0.792518936256495243383586076579921559914L),
- static_cast<T>(0.08317448364744713773350272460937904691566L),
- static_cast<T>(-0.005845345166274053157781068150827567998882L),
- static_cast<T>(0.0002599412126352082483326238522490030412391L),
- static_cast<T>(-0.6748102079670763884917431338234783496303e-5L),
- static_cast<T>(0.908824383434109002762325095643458603605e-7L),
- static_cast<T>(-0.5299325929309389890892469299969669579725e-9L),
- static_cast<T>(0.994306085859549890267983602248532869362e-12L),
- static_cast<T>(-0.3499893692975262747371544905820891835298e-15L),
- static_cast<T>(0.7260746353663365145454867069182884694961e-20L),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, 8.318998691953337183034781139546384476554)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, -63.15415991415959158214140353299240638675)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, 217.3108224383632868591462242669081540163)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, -448.5134281386108366899784093610397354889)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, 619.2903759363285456927248474593012711346)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, -604.1630177420625418522025080080444177046)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, 428.8166750424646119935047118287362193314)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, -224.6988753721310913866347429589434550302)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, 87.32181627555510833499451817622786940961)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, -25.07866854821128965662498003029199058098)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, 5.264398125689025351448861011657789005392)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, -0.792518936256495243383586076579921559914)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, 0.08317448364744713773350272460937904691566)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, -0.005845345166274053157781068150827567998882)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, 0.0002599412126352082483326238522490030412391)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, -0.6748102079670763884917431338234783496303e-5)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, 0.908824383434109002762325095643458603605e-7)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, -0.5299325929309389890892469299969669579725e-9)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, 0.994306085859549890267983602248532869362e-12)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, -0.3499893692975262747371544905820891835298e-15)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, 0.7260746353663365145454867069182884694961e-20)),
};
T result = 0;
for(unsigned k = 1; k <= sizeof(d)/sizeof(d[0]); ++k)
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>(75.39272007105208086018421070699575462226L),
- static_cast<T>(-572.3481967049935412452681346759966390319L),
- static_cast<T>(1969.426202741555335078065370698955484358L),
- static_cast<T>(-4064.74968778032030891520063865996757519L),
- static_cast<T>(5612.452614138013929794736248384309574814L),
- static_cast<T>(-5475.357667500026172903620177988213902339L),
- static_cast<T>(3886.243614216111328329547926490398103492L),
- static_cast<T>(-2036.382026072125407192448069428134470564L),
- static_cast<T>(791.3727954936062108045551843636692287652L),
- static_cast<T>(-227.2808432388436552794021219198885223122L),
- static_cast<T>(47.70974355562144229897637024320739257284L),
- static_cast<T>(-7.182373807798293545187073539819697141572L),
- static_cast<T>(0.7537866989631514559601547530490976100468L),
- static_cast<T>(-0.05297470142240154822658739758236594717787L),
- static_cast<T>(0.00235577330936380542539812701472320434133L),
- static_cast<T>(-0.6115613067659273118098229498679502138802e-4L),
- static_cast<T>(0.8236417010170941915758315020695551724181e-6L),
- static_cast<T>(-0.4802628430993048190311242611330072198089e-8L),
- static_cast<T>(0.9011113376981524418952720279739624707342e-11L),
- static_cast<T>(-0.3171854152689711198382455703658589996796e-14L),
- static_cast<T>(0.6580207998808093935798753964580596673177e-19L),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, 75.39272007105208086018421070699575462226)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, -572.3481967049935412452681346759966390319)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, 1969.426202741555335078065370698955484358)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, -4064.74968778032030891520063865996757519)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, 5612.452614138013929794736248384309574814)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, -5475.357667500026172903620177988213902339)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, 3886.243614216111328329547926490398103492)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, -2036.382026072125407192448069428134470564)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, 791.3727954936062108045551843636692287652)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, -227.2808432388436552794021219198885223122)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, 47.70974355562144229897637024320739257284)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, -7.182373807798293545187073539819697141572)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, 0.7537866989631514559601547530490976100468)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, -0.05297470142240154822658739758236594717787)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, 0.00235577330936380542539812701472320434133)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, -0.6115613067659273118098229498679502138802e-4)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, 0.8236417010170941915758315020695551724181e-6)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, -0.4802628430993048190311242611330072198089e-8)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, 0.9011113376981524418952720279739624707342e-11)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, -0.3171854152689711198382455703658589996796e-14)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 120, 0.6580207998808093935798753964580596673177e-19)),
};
T result = 0;
T z = dz + 2;
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>(553681095419291969.2230556393350368550504L),
- static_cast<T>(731918863887667017.2511276782146694632234L),
- static_cast<T>(453393234285807339.4627124634539085143364L),
- static_cast<T>(174701893724452790.3546219631779712198035L),
- static_cast<T>(46866125995234723.82897281620357050883077L),
- static_cast<T>(9281280675933215.169109622777099699054272L),
- static_cast<T>(1403600894156674.551057997617468721789536L),
- static_cast<T>(165345984157572.7305349809894046783973837L),
- static_cast<T>(15333629842677.31531822808737907246817024L),
- static_cast<T>(1123152927963.956626161137169462874517318L),
- static_cast<T>(64763127437.92329018717775593533620578237L),
- static_cast<T>(2908830362.657527782848828237106640944457L),
- static_cast<T>(99764700.56999856729959383751710026787811L),
- static_cast<T>(2525791.604886139959837791244686290089331L),
- static_cast<T>(44516.94034970167828580039370201346554872L),
- static_cast<T>(488.0063567520005730476791712814838113252L),
- static_cast<T>(2.50662827463100050241576877135758834683L)
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 553681095419291969.2230556393350368550504)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 731918863887667017.2511276782146694632234)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 453393234285807339.4627124634539085143364)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 174701893724452790.3546219631779712198035)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 46866125995234723.82897281620357050883077)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 9281280675933215.169109622777099699054272)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1403600894156674.551057997617468721789536)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 165345984157572.7305349809894046783973837)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 15333629842677.31531822808737907246817024)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1123152927963.956626161137169462874517318)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 64763127437.92329018717775593533620578237)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 2908830362.657527782848828237106640944457)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 99764700.56999856729959383751710026787811)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 2525791.604886139959837791244686290089331)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 44516.94034970167828580039370201346554872)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 488.0063567520005730476791712814838113252)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 2.50662827463100050241576877135758834683))
};
static const BOOST_MATH_INT_TABLE_TYPE(T, boost::uint64_t) denom[17] = {
BOOST_MATH_INT_VALUE_SUFFIX(0, uLL),
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>(2715894658327.717377557655133124376674911L),
- static_cast<T>(3590179526097.912105038525528721129550434L),
- static_cast<T>(2223966599737.814969312127353235818710172L),
- static_cast<T>(856940834518.9562481809925866825485883417L),
- static_cast<T>(229885871668.749072933597446453399395469L),
- static_cast<T>(45526171687.54610815813502794395753410032L),
- static_cast<T>(6884887713.165178784550917647709216424823L),
- static_cast<T>(811048596.1407531864760282453852372777439L),
- static_cast<T>(75213915.96540822314499613623119501704812L),
- static_cast<T>(5509245.417224265151697527957954952830126L),
- static_cast<T>(317673.5368435419126714931842182369574221L),
- static_cast<T>(14268.27989845035520147014373320337523596L),
- static_cast<T>(489.3618720403263670213909083601787814792L),
- static_cast<T>(12.38941330038454449295883217865458609584L),
- static_cast<T>(0.2183627389504614963941574507281683147897L),
- static_cast<T>(0.002393749522058449186690627996063983095463L),
- static_cast<T>(0.1229541408909435212800785616808830746135e-4L)
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 2715894658327.717377557655133124376674911)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 3590179526097.912105038525528721129550434)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 2223966599737.814969312127353235818710172)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 856940834518.9562481809925866825485883417)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 229885871668.749072933597446453399395469)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 45526171687.54610815813502794395753410032)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 6884887713.165178784550917647709216424823)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 811048596.1407531864760282453852372777439)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 75213915.96540822314499613623119501704812)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 5509245.417224265151697527957954952830126)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 317673.5368435419126714931842182369574221)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 14268.27989845035520147014373320337523596)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 489.3618720403263670213909083601787814792)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 12.38941330038454449295883217865458609584)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 0.2183627389504614963941574507281683147897)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 0.002393749522058449186690627996063983095463)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 0.1229541408909435212800785616808830746135e-4))
};
static const BOOST_MATH_INT_TABLE_TYPE(T, boost::uint64_t) denom[17] = {
BOOST_MATH_INT_VALUE_SUFFIX(0, uLL),
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>(4.493645054286536365763334986866616581265L),
- static_cast<T>(-16.95716370392468543800733966378143997694L),
- static_cast<T>(26.19196892983737527836811770970479846644L),
- static_cast<T>(-21.3659076437988814488356323758179283908L),
- static_cast<T>(9.913992596774556590710751047594507535764L),
- static_cast<T>(-2.62888300018780199210536267080940382158L),
- static_cast<T>(0.3807056693542503606384861890663080735588L),
- static_cast<T>(-0.02714647489697685807340312061034730486958L),
- static_cast<T>(0.0007815484715461206757220527133967191796747L),
- static_cast<T>(-0.6108630817371501052576880554048972272435e-5L),
- static_cast<T>(0.5037380238864836824167713635482801545086e-8L),
- static_cast<T>(-0.1483232144262638814568926925964858237006e-13L),
- static_cast<T>(0.1346609158752142460943888149156716841693e-14L),
- static_cast<T>(-0.660492688923978805315914918995410340796e-15L),
- static_cast<T>(0.1472114697343266749193617793755763792681e-15L),
- static_cast<T>(-0.1410901942033374651613542904678399264447e-16L),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 4.493645054286536365763334986866616581265)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -16.95716370392468543800733966378143997694)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 26.19196892983737527836811770970479846644)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -21.3659076437988814488356323758179283908)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 9.913992596774556590710751047594507535764)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -2.62888300018780199210536267080940382158)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 0.3807056693542503606384861890663080735588)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -0.02714647489697685807340312061034730486958)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 0.0007815484715461206757220527133967191796747)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -0.6108630817371501052576880554048972272435e-5)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 0.5037380238864836824167713635482801545086e-8)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -0.1483232144262638814568926925964858237006e-13)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 0.1346609158752142460943888149156716841693e-14)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -0.660492688923978805315914918995410340796e-15)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 0.1472114697343266749193617793755763792681e-15)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -0.1410901942033374651613542904678399264447e-16)),
};
T result = 0;
for(unsigned k = 1; k <= sizeof(d)/sizeof(d[0]); ++k)
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>(23.56409085052261327114594781581930373708L),
- static_cast<T>(-88.92116338946308797946237246006238652361L),
- static_cast<T>(137.3472822086847596961177383569603988797L),
- static_cast<T>(-112.0400438263562152489272966461114852861L),
- static_cast<T>(51.98768915202973863076166956576777843805L),
- static_cast<T>(-13.78552090862799358221343319574970124948L),
- static_cast<T>(1.996371068830872830250406773917646121742L),
- static_cast<T>(-0.1423525874909934506274738563671862576161L),
- static_cast<T>(0.004098338646046865122459664947239111298524L),
- static_cast<T>(-0.3203286637326511000882086573060433529094e-4L),
- static_cast<T>(0.2641536751640138646146395939004587594407e-7L),
- static_cast<T>(-0.7777876663062235617693516558976641009819e-13L),
- static_cast<T>(0.7061443477097101636871806229515157914789e-14L),
- static_cast<T>(-0.3463537849537988455590834887691613484813e-14L),
- static_cast<T>(0.7719578215795234036320348283011129450595e-15L),
- static_cast<T>(-0.7398586479708476329563577384044188912075e-16L),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 23.56409085052261327114594781581930373708)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -88.92116338946308797946237246006238652361)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 137.3472822086847596961177383569603988797)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -112.0400438263562152489272966461114852861)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 51.98768915202973863076166956576777843805)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -13.78552090862799358221343319574970124948)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 1.996371068830872830250406773917646121742)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -0.1423525874909934506274738563671862576161)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 0.004098338646046865122459664947239111298524)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -0.3203286637326511000882086573060433529094e-4)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 0.2641536751640138646146395939004587594407e-7)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -0.7777876663062235617693516558976641009819e-13)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 0.7061443477097101636871806229515157914789e-14)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -0.3463537849537988455590834887691613484813e-14)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, 0.7719578215795234036320348283011129450595e-15)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 64, -0.7398586479708476329563577384044188912075e-16)),
};
T result = 0;
T z = dz + 2;
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>(2029889364934367661624137213253.22102954656825019111612712252027267955023987678816620961507L),
- static_cast<T>(2338599599286656537526273232565.2727349714338768161421882478417543004440597874814359063158L),
- static_cast<T>(1288527989493833400335117708406.3953711906175960449186720680201425446299360322830739180195L),
- static_cast<T>(451779745834728745064649902914.550539158066332484594436145043388809847364393288132164411521L),
- static_cast<T>(113141284461097964029239556815.291212318665536114012605167994061291631013303788706545334708L),
- static_cast<T>(21533689802794625866812941616.7509064680880468667055339259146063256555368135236149614592432L),
- static_cast<T>(3235510315314840089932120340.71494940111731241353655381919722177496659303550321056514776757L),
- static_cast<T>(393537392344185475704891959.081297108513472083749083165179784098220158201055270548272414314L),
- static_cast<T>(39418265082950435024868801.5005452240816902251477336582325944930252142622315101857742955673L),
- static_cast<T>(3290158764187118871697791.05850632319194734270969161036889516414516566453884272345518372696L),
- static_cast<T>(230677110449632078321772.618245845856640677845629174549731890660612368500786684333975350954L),
- static_cast<T>(13652233645509183190158.5916189185218250859402806777406323001463296297553612462737044693697L),
- static_cast<T>(683661466754325350495.216655026531202476397782296585200982429378069417193575896602446904762L),
- static_cast<T>(28967871782219334117.0122379171041074970463982134039409352925258212207710168851968215545064L),
- static_cast<T>(1036104088560167006.2022834098572346459442601718514554488352117620272232373622553429728555L),
- static_cast<T>(31128490785613152.8380102669349814751268126141105475287632676569913936040772990253369753962L),
- static_cast<T>(779327504127342.536207878988196814811198475410572992436243686674896894543126229424358472541L),
- static_cast<T>(16067543181294.643350688789124777020407337133926174150582333950666044399234540521336771876L),
- static_cast<T>(268161795520.300916569439413185778557212729611517883948634711190170998896514639936969855484L),
- static_cast<T>(3533216359.10528191668842486732408440112703691790824611391987708562111396961696753452085068L),
- static_cast<T>(35378979.5479656110614685178752543826919239614088343789329169535932709470588426584501652577L),
- static_cast<T>(253034.881362204346444503097491737872930637147096453940375713745904094735506180552724766444L),
- static_cast<T>(1151.61895453463992438325318456328526085882924197763140514450975619271382783957699017875304L),
- static_cast<T>(2.50662827463100050241576528481104515966515623051532908941425544355490413900497467936202516L)
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 113, 2029889364934367661624137213253.22102954656825019111612712252027267955023987678816620961507)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 113, 2338599599286656537526273232565.2727349714338768161421882478417543004440597874814359063158)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 113, 1288527989493833400335117708406.3953711906175960449186720680201425446299360322830739180195)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 113, 451779745834728745064649902914.550539158066332484594436145043388809847364393288132164411521)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 113, 113141284461097964029239556815.291212318665536114012605167994061291631013303788706545334708)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 113, 21533689802794625866812941616.7509064680880468667055339259146063256555368135236149614592432)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 113, 3235510315314840089932120340.71494940111731241353655381919722177496659303550321056514776757)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 113, 393537392344185475704891959.081297108513472083749083165179784098220158201055270548272414314)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 113, 39418265082950435024868801.5005452240816902251477336582325944930252142622315101857742955673)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 113, 3290158764187118871697791.05850632319194734270969161036889516414516566453884272345518372696)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 113, 230677110449632078321772.618245845856640677845629174549731890660612368500786684333975350954)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 113, 13652233645509183190158.5916189185218250859402806777406323001463296297553612462737044693697)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 113, 683661466754325350495.216655026531202476397782296585200982429378069417193575896602446904762)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 113, 28967871782219334117.0122379171041074970463982134039409352925258212207710168851968215545064)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 113, 1036104088560167006.2022834098572346459442601718514554488352117620272232373622553429728555)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 113, 31128490785613152.8380102669349814751268126141105475287632676569913936040772990253369753962)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 113, 779327504127342.536207878988196814811198475410572992436243686674896894543126229424358472541)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 113, 16067543181294.643350688789124777020407337133926174150582333950666044399234540521336771876)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 113, 268161795520.300916569439413185778557212729611517883948634711190170998896514639936969855484)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 113, 3533216359.10528191668842486732408440112703691790824611391987708562111396961696753452085068)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 113, 35378979.5479656110614685178752543826919239614088343789329169535932709470588426584501652577)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 113, 253034.881362204346444503097491737872930637147096453940375713745904094735506180552724766444)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 113, 1151.61895453463992438325318456328526085882924197763140514450975619271382783957699017875304)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 113, 2.50662827463100050241576528481104515966515623051532908941425544355490413900497467936202516))
};
static const T denom[24] = {
- static_cast<T>(0L),
- static_cast<T>(0.112400072777760768e22L),
- static_cast<T>(0.414847677933545472e22L),
- static_cast<T>(6756146673770930688000.0L),
- static_cast<T>(6548684852703068697600.0L),
- static_cast<T>(4280722865357147142912.0L),
- static_cast<T>(2021687376910682741568.0L),
- static_cast<T>(720308216440924653696.0L),
- static_cast<T>(199321978221066137360.0L),
- static_cast<T>(43714229649594412832.0L),
- static_cast<T>(7707401101297361068.0L),
- static_cast<T>(1103230881185949736.0L),
- static_cast<T>(129006659818331295.0L),
- static_cast<T>(12363045847086207.0L),
- static_cast<T>(971250460939913.0L),
- static_cast<T>(62382416421941.0L),
- static_cast<T>(3256091103430.0L),
- static_cast<T>(136717357942.0L),
- static_cast<T>(4546047198.0L),
- static_cast<T>(116896626L),
- static_cast<T>(2240315L),
- static_cast<T>(30107L),
- static_cast<T>(253L),
- static_cast<T>(1L)
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 113, 0)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 113, 0.112400072777760768e22)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 113, 0.414847677933545472e22)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 113, 6756146673770930688000.0)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 113, 6548684852703068697600.0)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 113, 4280722865357147142912.0)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 113, 2021687376910682741568.0)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 113, 720308216440924653696.0)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 113, 199321978221066137360.0)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 113, 43714229649594412832.0)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 113, 7707401101297361068.0)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 113, 1103230881185949736.0)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 113, 129006659818331295.0)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 113, 12363045847086207.0)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 113, 971250460939913.0)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 113, 62382416421941.0)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 113, 3256091103430.0)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 113, 136717357942.0)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 113, 4546047198.0)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 113, 116896626)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 113, 2240315)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 113, 30107)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 113, 253)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 113, 1))
};
return boost::math::tools::evaluate_rational(num, denom, z);
}
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>(3035162425359883494754.02878223286972654682199012688209026810841953293372712802258398358538L),
- static_cast<T>(3496756894406430103600.16057175075063458536101374170860226963245118484234495645518505519827L),
- static_cast<T>(1926652656689320888654.01954015145958293168365236755537645929361841917596501251362171653478L),
- static_cast<T>(675517066488272766316.083023742440619929434602223726894748181327187670231286180156444871912L),
- static_cast<T>(169172853104918752780.086262749564831660238912144573032141700464995906149421555926000038492L),
- static_cast<T>(32197935167225605785.6444116302160245528783954573163541751756353183343357329404208062043808L),
- static_cast<T>(4837849542714083249.37587447454818124327561966323276633775195138872820542242539845253171632L),
- static_cast<T>(588431038090493242.308438203986649553459461798968819276505178004064031201740043314534404158L),
- static_cast<T>(58939585141634058.6206417889192563007809470547755357240808035714047014324843817783741669733L),
- static_cast<T>(4919561837722192.82991866530802080996138070630296720420704876654726991998309206256077395868L),
- static_cast<T>(344916580244240.407442753122831512004021081677987651622305356145640394384006997569631719101L),
- static_cast<T>(20413302960687.8250598845969238472629322716685686993835561234733641729957841485003560103066L),
- static_cast<T>(1022234822943.78400752460970689311934727763870970686747383486600540378889311406851534545789L),
- static_cast<T>(43313787191.9821354846952908076307094286897439975815501673706144217246093900159173598852503L),
- static_cast<T>(1549219505.59667418528481770869280437577581951167003505825834192510436144666564648361001914L),
- static_cast<T>(46544421.1998761919380541579358096705925369145324466147390364674998568485110045455014967149L),
- static_cast<T>(1165278.06807504975090675074910052763026564833951579556132777702952882101173607903881127542L),
- static_cast<T>(24024.759267256769471083727721827405338569868270177779485912486668586611981795179894572115L),
- static_cast<T>(400.965008113421955824358063769761286758463521789765880962939528760888853281920872064838918L),
- static_cast<T>(5.28299015654478269617039029170846385138134929147421558771949982217659507918482272439717603L),
- static_cast<T>(0.0528999024412510102409256676599360516359062802002483877724963720047531347449011629466149805L),
- static_cast<T>(0.000378346710654740685454266569593414561162134092347356968516522170279688139165340746957511115L),
- static_cast<T>(0.172194142179211139195966608011235161516824700287310869949928393345257114743230967204370963e-5L),
- static_cast<T>(0.374799931707148855771381263542708435935402853962736029347951399323367765509988401336565436e-8L)
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 113, 3035162425359883494754.02878223286972654682199012688209026810841953293372712802258398358538)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 113, 3496756894406430103600.16057175075063458536101374170860226963245118484234495645518505519827)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 113, 1926652656689320888654.01954015145958293168365236755537645929361841917596501251362171653478)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 113, 675517066488272766316.083023742440619929434602223726894748181327187670231286180156444871912)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 113, 169172853104918752780.086262749564831660238912144573032141700464995906149421555926000038492)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 113, 32197935167225605785.6444116302160245528783954573163541751756353183343357329404208062043808)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 113, 4837849542714083249.37587447454818124327561966323276633775195138872820542242539845253171632)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 113, 588431038090493242.308438203986649553459461798968819276505178004064031201740043314534404158)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 113, 58939585141634058.6206417889192563007809470547755357240808035714047014324843817783741669733)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 113, 4919561837722192.82991866530802080996138070630296720420704876654726991998309206256077395868)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 113, 344916580244240.407442753122831512004021081677987651622305356145640394384006997569631719101)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 113, 20413302960687.8250598845969238472629322716685686993835561234733641729957841485003560103066)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 113, 1022234822943.78400752460970689311934727763870970686747383486600540378889311406851534545789)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 113, 43313787191.9821354846952908076307094286897439975815501673706144217246093900159173598852503)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 113, 1549219505.59667418528481770869280437577581951167003505825834192510436144666564648361001914)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 113, 46544421.1998761919380541579358096705925369145324466147390364674998568485110045455014967149)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 113, 1165278.06807504975090675074910052763026564833951579556132777702952882101173607903881127542)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 113, 24024.759267256769471083727721827405338569868270177779485912486668586611981795179894572115)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 113, 400.965008113421955824358063769761286758463521789765880962939528760888853281920872064838918)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 113, 5.28299015654478269617039029170846385138134929147421558771949982217659507918482272439717603)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 113, 0.0528999024412510102409256676599360516359062802002483877724963720047531347449011629466149805)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 113, 0.000378346710654740685454266569593414561162134092347356968516522170279688139165340746957511115)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 113, 0.172194142179211139195966608011235161516824700287310869949928393345257114743230967204370963e-5)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 113, 0.374799931707148855771381263542708435935402853962736029347951399323367765509988401336565436e-8))
};
static const T denom[24] = {
- static_cast<T>(0L),
- static_cast<T>(0.112400072777760768e22L),
- static_cast<T>(0.414847677933545472e22L),
- static_cast<T>(6756146673770930688000.0L),
- static_cast<T>(6548684852703068697600.0L),
- static_cast<T>(4280722865357147142912.0L),
- static_cast<T>(2021687376910682741568.0L),
- static_cast<T>(720308216440924653696.0L),
- static_cast<T>(199321978221066137360.0L),
- static_cast<T>(43714229649594412832.0L),
- static_cast<T>(7707401101297361068.0L),
- static_cast<T>(1103230881185949736.0L),
- static_cast<T>(129006659818331295.0L),
- static_cast<T>(12363045847086207.0L),
- static_cast<T>(971250460939913.0L),
- static_cast<T>(62382416421941.0L),
- static_cast<T>(3256091103430.0L),
- static_cast<T>(136717357942.0L),
- static_cast<T>(4546047198.0L),
- static_cast<T>(116896626L),
- static_cast<T>(2240315L),
- static_cast<T>(30107L),
- static_cast<T>(253L),
- static_cast<T>(1L)
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 113, 0)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 113, 0.112400072777760768e22)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 113, 0.414847677933545472e22)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 113, 6756146673770930688000.0)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 113, 6548684852703068697600.0)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 113, 4280722865357147142912.0)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 113, 2021687376910682741568.0)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 113, 720308216440924653696.0)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 113, 199321978221066137360.0)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 113, 43714229649594412832.0)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 113, 7707401101297361068.0)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 113, 1103230881185949736.0)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 113, 129006659818331295.0)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 113, 12363045847086207.0)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 113, 971250460939913.0)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 113, 62382416421941.0)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 113, 3256091103430.0)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 113, 136717357942.0)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 113, 4546047198.0)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 113, 116896626)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 113, 2240315)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 113, 30107)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 113, 253)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 113, 1))
};
return boost::math::tools::evaluate_rational(num, denom, z);
}
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>(7.4734083002469026177867421609938203388868806387315406134072298925733950040583068760685908L),
- static_cast<T>(-50.4225805042247530267317342133388132970816607563062253708655085754357843064134941138154171L),
- static_cast<T>(152.288200621747008570784082624444625293884063492396162110698238568311211546361189979357019L),
- static_cast<T>(-271.894959539150384169327513139846971255640842175739337449692360299099322742181325023644769L),
- static_cast<T>(319.240102980202312307047586791116902719088581839891008532114107693294261542869734803906793L),
- static_cast<T>(-259.493144143048088289689500935518073716201741349569864988870534417890269467336454358361499L),
- static_cast<T>(149.747518319689708813209645403067832020714660918583227716408482877303972685262557460145835L),
- static_cast<T>(-61.9261301009341333289187201425188698128684426428003249782448828881580630606817104372760037L),
- static_cast<T>(18.3077524177286961563937379403377462608113523887554047531153187277072451294845795496072365L),
- static_cast<T>(-3.82011322251948043097070160584761236869363471824695092089556195047949392738162970152230254L),
- static_cast<T>(0.549382685505691522516705902336780999493262538301283190963770663549981309645795228539620711L),
- static_cast<T>(-0.0524814679715180697633723771076668718265358076235229045603747927518423453658004287459638024L),
- static_cast<T>(0.00315392664003333528534120626687784812050217700942910879712808180705014754163256855643360698L),
- static_cast<T>(-0.000110098373127648510519799564665442121339511198561008748083409549601095293123407080388658329L),
- static_cast<T>(0.19809382866681658224945717689377373458866950897791116315219376038432014207446832310901893e-5L),
- static_cast<T>(-0.152278977408600291408265615203504153130482270424202400677280558181047344681214058227949755e-7L),
- static_cast<T>(0.364344768076106268872239259083188037615571711218395765792787047015406264051536972018235217e-10L),
- static_cast<T>(-0.148897510480440424971521542520683536298361220674662555578951242811522959610991621951203526e-13L),
- static_cast<T>(0.261199241161582662426512749820666625442516059622425213340053324061794752786482115387573582e-18L),
- static_cast<T>(-0.780072664167099103420998436901014795601783313858454665485256897090476089641613851903791529e-24L),
- static_cast<T>(0.303465867587106629530056603454807425512962762653755513440561256044986695349304176849392735e-24L),
- static_cast<T>(-0.615420597971283870342083342286977366161772327800327789325710571275345878439656918541092056e-25L),
- static_cast<T>(0.499641233843540749369110053005439398774706583601830828776209650445427083113181961630763702e-26L),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 113, 7.4734083002469026177867421609938203388868806387315406134072298925733950040583068760685908)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 113, -50.4225805042247530267317342133388132970816607563062253708655085754357843064134941138154171)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 113, 152.288200621747008570784082624444625293884063492396162110698238568311211546361189979357019)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 113, -271.894959539150384169327513139846971255640842175739337449692360299099322742181325023644769)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 113, 319.240102980202312307047586791116902719088581839891008532114107693294261542869734803906793)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 113, -259.493144143048088289689500935518073716201741349569864988870534417890269467336454358361499)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 113, 149.747518319689708813209645403067832020714660918583227716408482877303972685262557460145835)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 113, -61.9261301009341333289187201425188698128684426428003249782448828881580630606817104372760037)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 113, 18.3077524177286961563937379403377462608113523887554047531153187277072451294845795496072365)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 113, -3.82011322251948043097070160584761236869363471824695092089556195047949392738162970152230254)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 113, 0.549382685505691522516705902336780999493262538301283190963770663549981309645795228539620711)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 113, -0.0524814679715180697633723771076668718265358076235229045603747927518423453658004287459638024)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 113, 0.00315392664003333528534120626687784812050217700942910879712808180705014754163256855643360698)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 113, -0.000110098373127648510519799564665442121339511198561008748083409549601095293123407080388658329)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 113, 0.19809382866681658224945717689377373458866950897791116315219376038432014207446832310901893e-5)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 113, -0.152278977408600291408265615203504153130482270424202400677280558181047344681214058227949755e-7)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 113, 0.364344768076106268872239259083188037615571711218395765792787047015406264051536972018235217e-10)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 113, -0.148897510480440424971521542520683536298361220674662555578951242811522959610991621951203526e-13)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 113, 0.261199241161582662426512749820666625442516059622425213340053324061794752786482115387573582e-18)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 113, -0.780072664167099103420998436901014795601783313858454665485256897090476089641613851903791529e-24)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 113, 0.303465867587106629530056603454807425512962762653755513440561256044986695349304176849392735e-24)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 113, -0.615420597971283870342083342286977366161772327800327789325710571275345878439656918541092056e-25)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 113, 0.499641233843540749369110053005439398774706583601830828776209650445427083113181961630763702e-26)),
};
T result = 0;
for(unsigned k = 1; k <= sizeof(d)/sizeof(d[0]); ++k)
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>(61.4165001061101455341808888883960361969557848005400286332291451422461117307237198559485365L),
- static_cast<T>(-414.372973678657049667308134761613915623353625332248315105320470271523320700386200587519147L),
- static_cast<T>(1251.50505818554680171298972755376376836161706773644771875668053742215217922228357204561873L),
- static_cast<T>(-2234.43389421602399514176336175766511311493214354568097811220122848998413358085613880612158L),
- static_cast<T>(2623.51647746991904821899989145639147785427273427135380151752779100215839537090464785708684L),
- static_cast<T>(-2132.51572435428751962745870184529534443305617818870214348386131243463614597272260797772423L),
- static_cast<T>(1230.62572059218405766499842067263311220019173335523810725664442147670956427061920234820189L),
- static_cast<T>(-508.90919151163744999377586956023909888833335885805154492270846381061182696305011395981929L),
- static_cast<T>(150.453184562246579758706538566480316921938628645961177699894388251635886834047343195475395L),
- static_cast<T>(-31.3937061525822497422230490071156186113405446381476081565548185848237169870395131828731397L),
- static_cast<T>(4.51482916590287954234936829724231512565732528859217337795452389161322923867318809206313688L),
- static_cast<T>(-0.431292919341108177524462194102701868233551186625103849565527515201492276412231365776131952L),
- static_cast<T>(0.0259189820815586225636729971503340447445001375909094681698918294680345547092233915092128323L),
- static_cast<T>(-0.000904788882557558697594884691337532557729219389814315972435534723829065673966567231504429712L),
- static_cast<T>(0.162793589759218213439218473348810982422449144393340433592232065020562974405674317564164312e-4L),
- static_cast<T>(-0.125142926178202562426432039899709511761368233479483128438847484617555752948755923647214487e-6L),
- static_cast<T>(0.299418680048132583204152682950097239197934281178261879500770485862852229898797687301941982e-9L),
- static_cast<T>(-0.122364035267809278675627784883078206654408225276233049012165202996967011873995261617995421e-12L),
- static_cast<T>(0.21465364366598631597052073538883430194257709353929022544344097235100199405814005393447785e-17L),
- static_cast<T>(-0.641064035802907518396608051803921688237330857546406669209280666066685733941549058513986818e-23L),
- static_cast<T>(0.249388374622173329690271566855185869111237201309011956145463506483151054813346819490278951e-23L),
- static_cast<T>(-0.505752900177513489906064295001851463338022055787536494321532352380960774349054239257683149e-24L),
- static_cast<T>(0.410605371184590959139968810080063542546949719163227555918846829816144878123034347778284006e-25L),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 113, 61.4165001061101455341808888883960361969557848005400286332291451422461117307237198559485365)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 113, -414.372973678657049667308134761613915623353625332248315105320470271523320700386200587519147)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 113, 1251.50505818554680171298972755376376836161706773644771875668053742215217922228357204561873)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 113, -2234.43389421602399514176336175766511311493214354568097811220122848998413358085613880612158)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 113, 2623.51647746991904821899989145639147785427273427135380151752779100215839537090464785708684)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 113, -2132.51572435428751962745870184529534443305617818870214348386131243463614597272260797772423)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 113, 1230.62572059218405766499842067263311220019173335523810725664442147670956427061920234820189)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 113, -508.90919151163744999377586956023909888833335885805154492270846381061182696305011395981929)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 113, 150.453184562246579758706538566480316921938628645961177699894388251635886834047343195475395)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 113, -31.3937061525822497422230490071156186113405446381476081565548185848237169870395131828731397)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 113, 4.51482916590287954234936829724231512565732528859217337795452389161322923867318809206313688)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 113, -0.431292919341108177524462194102701868233551186625103849565527515201492276412231365776131952)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 113, 0.0259189820815586225636729971503340447445001375909094681698918294680345547092233915092128323)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 113, -0.000904788882557558697594884691337532557729219389814315972435534723829065673966567231504429712)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 113, 0.162793589759218213439218473348810982422449144393340433592232065020562974405674317564164312e-4)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 113, -0.125142926178202562426432039899709511761368233479483128438847484617555752948755923647214487e-6)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 113, 0.299418680048132583204152682950097239197934281178261879500770485862852229898797687301941982e-9)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 113, -0.122364035267809278675627784883078206654408225276233049012165202996967011873995261617995421e-12)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 113, 0.21465364366598631597052073538883430194257709353929022544344097235100199405814005393447785e-17)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 113, -0.641064035802907518396608051803921688237330857546406669209280666066685733941549058513986818e-23)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 113, 0.249388374622173329690271566855185869111237201309011956145463506483151054813346819490278951e-23)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 113, -0.505752900177513489906064295001851463338022055787536494321532352380960774349054239257683149e-24)),
+ static_cast<T>(BOOST_MATH_BIG_CONSTANT(T, 113, 0.410605371184590959139968810080063542546949719163227555918846829816144878123034347778284006e-25)),
};
T result = 0;
T z = dz + 2;
} // namespace math
} // namespace boost
+#if !defined(_CRAYC) && !defined(__CUDACC__) && (!defined(__GNUC__) || (__GNUC__ > 3) || ((__GNUC__ == 3) && (__GNUC_MINOR__ > 3)))
#if (defined(_M_IX86_FP) && (_M_IX86_FP >= 2)) || defined(__SSE2__)
#include <boost/math/special_functions/detail/lanczos_sse2.hpp>
#endif
+#endif
#endif // BOOST_MATH_SPECIAL_FUNCTIONS_LANCZOS