[ceph.git] / ceph / src / boost / libs / math / include / boost / math / bindings / detail / big_digamma.hpp

//  (C) Copyright John Maddock 2006-8.
//  Use, modification and distribution are subject to the
//  Boost Software License, Version 1.0. (See accompanying file
//  LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)

#ifndef BOOST_MATH_NTL_DIGAMMA
#define BOOST_MATH_NTL_DIGAMMA

#include <boost/math/tools/rational.hpp>
#include <boost/math/policies/error_handling.hpp>
#include <boost/math/constants/constants.hpp>
#include <boost/lexical_cast.hpp>

namespace boost{ namespace math{ namespace detail{

template <class T>
T big_digamma_helper(T x)
{
      static const T P[61] = {
         boost::lexical_cast<T>("0.6660133691143982067148122682345055274952e81"),
         boost::lexical_cast<T>("0.6365271516829242456324234577164675383137e81"),
         boost::lexical_cast<T>("0.2991038873096202943405966144203628966976e81"),
         boost::lexical_cast<T>("0.9211116495503170498076013367421231351115e80"),
         boost::lexical_cast<T>("0.2090792764676090716286400360584443891749e80"),
         boost::lexical_cast<T>("0.3730037777359591428226035156377978092809e79"),
         boost::lexical_cast<T>("0.5446396536956682043376492370432031543834e78"),
         boost::lexical_cast<T>("0.6692523966335177847425047827449069256345e77"),
         boost::lexical_cast<T>("0.7062543624100864681625612653756619116848e76"),
         boost::lexical_cast<T>("0.6499914905966283735005256964443226879158e75"),
         boost::lexical_cast<T>("0.5280364564853225211197557708655426736091e74"),
         boost::lexical_cast<T>("0.3823205608981176913075543599005095206953e73"),
         boost::lexical_cast<T>("0.2486733714214237704739129972671154532415e72"),
         boost::lexical_cast<T>("0.1462562139602039577983434547171318011675e71"),
         boost::lexical_cast<T>("0.7821169065036815012381267259559910324285e69"),
         boost::lexical_cast<T>("0.3820552182348155468636157988764435365078e68"),
         boost::lexical_cast<T>("0.1711618296983598244658239925535632505062e67"),
         boost::lexical_cast<T>("0.7056661618357643731419080738521475204245e65"),
         boost::lexical_cast<T>("0.2685246896473614017356264531791459936036e64"),
         boost::lexical_cast<T>("0.9455168125599643085283071944864977592391e62"),
         boost::lexical_cast<T>("0.3087541626972538362237309145177486236219e61"),
         boost::lexical_cast<T>("0.9367928873352980208052601301625005737407e59"),
         boost::lexical_cast<T>("0.2645306130689794942883818547314327466007e58"),
         boost::lexical_cast<T>("0.6961815141171454309161007351079576190079e56"),
         boost::lexical_cast<T>("0.1709637824471794552313802669803885946843e55"),
         boost::lexical_cast<T>("0.3921553258481531526663112728778759311158e53"),
         boost::lexical_cast<T>("0.8409006354449988687714450897575728228696e51"),
         boost::lexical_cast<T>("0.1686755204461325935742097669030363344927e50"),
         boost::lexical_cast<T>("0.3166653542877070999007425197729038754254e48"),
         boost::lexical_cast<T>("0.5566029092358215049069560272835654229637e46"),
         boost::lexical_cast<T>("0.9161766287916328133080586672953875116242e44"),
         boost::lexical_cast<T>("1412317772330871298317974693514430627922000"),
         boost::lexical_cast<T>("20387991986727877473732570146112459874790"),
         boost::lexical_cast<T>("275557928713904105182512535678580359839.3"),
         boost::lexical_cast<T>("3485719851040516559072031256589598330.723"),
         boost::lexical_cast<T>("41247046743564028399938106707656877.40859"),
         boost::lexical_cast<T>("456274078125709314602601667471879.0147312"),
         boost::lexical_cast<T>("4714450683242899367025707077155.310613012"),
         boost::lexical_cast<T>("45453933537925041680009544258.75073849996"),
         boost::lexical_cast<T>("408437900487067278846361972.302331241052"),
         boost::lexical_cast<T>("3415719344386166273085838.705771571751035"),
         boost::lexical_cast<T>("26541502879185876562320.93134691487351145"),
         boost::lexical_cast<T>("191261415065918713661.1571433274648417668"),
         boost::lexical_cast<T>("1275349770108718421.645275944284937551702"),
         boost::lexical_cast<T>("7849171120971773.318910987434906905704272"),
         boost::lexical_cast<T>("44455946386549.80866460312682983576538056"),
         boost::lexical_cast<T>("230920362395.3198137186361608905136598046"),
         boost::lexical_cast<T>("1095700096.240863858624279930600654130254"),
         boost::lexical_cast<T>("4727085.467506050153744334085516289728134"),
         boost::lexical_cast<T>("18440.75118859447173303252421991479005424"),
         boost::lexical_cast<T>("64.62515887799460295677071749181651317052"),
         boost::lexical_cast<T>("0.201851568864688406206528472883512147547"),
         boost::lexical_cast<T>("0.0005565091674187978029138500039504078098143"),
         boost::lexical_cast<T>("0.1338097668312907986354698683493366559613e-5"),
         boost::lexical_cast<T>("0.276308225077464312820179030238305271638e-8"),
         boost::lexical_cast<T>("0.4801582970473168520375942100071070575043e-11"),
         boost::lexical_cast<T>("0.6829184144212920949740376186058541800175e-14"),
         boost::lexical_cast<T>("0.7634080076358511276617829524639455399182e-17"),
         boost::lexical_cast<T>("0.6290035083727140966418512608156646142409e-20"),
         boost::lexical_cast<T>("0.339652245667538733044036638506893821352e-23"),
         boost::lexical_cast<T>("0.9017518064256388530773585529891677854909e-27")
      };
      static const T Q[61] = {
         boost::lexical_cast<T>("0"),
         boost::lexical_cast<T>("0.1386831185456898357379390197203894063459e81"),
         boost::lexical_cast<T>("0.6467076379487574703291056110838151259438e81"),
         boost::lexical_cast<T>("0.1394967823848615838336194279565285465161e82"),
         boost::lexical_cast<T>("0.1872927317344192945218570366455046340458e82"),
         boost::lexical_cast<T>("0.1772461045338946243584650759986310355937e82"),
         boost::lexical_cast<T>("0.1267294892200258648315971144069595555118e82"),
         boost::lexical_cast<T>("0.7157764838362416821508872117623058626589e81"),
         boost::lexical_cast<T>("0.329447266909948668265277828268378274513e81"),
         boost::lexical_cast<T>("0.1264376077317689779509250183194342571207e81"),
         boost::lexical_cast<T>("0.4118230304191980787640446056583623228873e80"),
         boost::lexical_cast<T>("0.1154393529762694616405952270558316515261e80"),
         boost::lexical_cast<T>("0.281655612889423906125295485693696744275e79"),
         boost::lexical_cast<T>("0.6037483524928743102724159846414025482077e78"),
         boost::lexical_cast<T>("0.1145927995397835468123576831800276999614e78"),
         boost::lexical_cast<T>("0.1938624296151985600348534009382865995154e77"),
         boost::lexical_cast<T>("0.293980925856227626211879961219188406675e76"),
         boost::lexical_cast<T>("0.4015574518216966910319562902099567437832e75"),
         boost::lexical_cast<T>("0.4961475457509727343545565970423431880907e74"),
         boost::lexical_cast<T>("0.5565482348278933960215521991000378896338e73"),
         boost::lexical_cast<T>("0.5686112924615820754631098622770303094938e72"),
         boost::lexical_cast<T>("0.5305988545844796293285410303747469932856e71"),
         boost::lexical_cast<T>("0.4533363413802585060568537458067343491358e70"),
         boost::lexical_cast<T>("0.3553932059473516064068322757331575565718e69"),
         boost::lexical_cast<T>("0.2561198565218704414618802902533972354203e68"),
         boost::lexical_cast<T>("0.1699519313292900324098102065697454295572e67"),
         boost::lexical_cast<T>("0.1039830160862334505389615281373574959236e66"),
         boost::lexical_cast<T>("0.5873082967977428281000961954715372504986e64"),
         boost::lexical_cast<T>("0.3065255179030575882202133042549783442446e63"),
         boost::lexical_cast<T>("0.1479494813481364701208655943688307245459e62"),
         boost::lexical_cast<T>("0.6608150467921598615495180659808895663164e60"),
         boost::lexical_cast<T>("0.2732535313770902021791888953487787496976e59"),
         boost::lexical_cast<T>("0.1046402297662493314531194338414508049069e58"),
         boost::lexical_cast<T>("0.3711375077192882936085049147920021549622e56"),
         boost::lexical_cast<T>("0.1219154482883895482637944309702972234576e55"),
         boost::lexical_cast<T>("0.3708359374149458741391374452286837880162e53"),
         boost::lexical_cast<T>("0.1044095509971707189716913168889769471468e52"),
         boost::lexical_cast<T>("0.271951506225063286130946773813524945052e50"),
         boost::lexical_cast<T>("0.6548016291215163843464133978454065823866e48"),
         boost::lexical_cast<T>("0.1456062447610542135403751730809295219344e47"),
         boost::lexical_cast<T>("0.2986690175077969760978388356833006028929e45"),
         boost::lexical_cast<T>("5643149706574013350061247429006443326844000"),
         boost::lexical_cast<T>("98047545414467090421964387960743688053480"),
         boost::lexical_cast<T>("1563378767746846395507385099301468978550"),
         boost::lexical_cast<T>("22823360528584500077862274918382796495"),
         boost::lexical_cast<T>("304215527004115213046601295970388750"),
         boost::lexical_cast<T>("3690289075895685793844344966820325"),
         boost::lexical_cast<T>("40584512015702371433911456606050"),
         boost::lexical_cast<T>("402834190897282802772754873905"),
         boost::lexical_cast<T>("3589522158493606918146495750"),
         boost::lexical_cast<T>("28530557707503483723634725"),
         boost::lexical_cast<T>("200714561335055753000730"),
         boost::lexical_cast<T>("1237953783437761888641"),
         boost::lexical_cast<T>("6614698701445762950"),
         boost::lexical_cast<T>("30155495647727505"),
         boost::lexical_cast<T>("114953256021450"),
         boost::lexical_cast<T>("356398020013"),
         boost::lexical_cast<T>("863113950"),
         boost::lexical_cast<T>("1531345"),
         boost::lexical_cast<T>("1770"),
         boost::lexical_cast<T>("1")
      };
      static const T PD[60] = {
         boost::lexical_cast<T>("0.6365271516829242456324234577164675383137e81"),
         2*boost::lexical_cast<T>("0.2991038873096202943405966144203628966976e81"),
         3*boost::lexical_cast<T>("0.9211116495503170498076013367421231351115e80"),
         4*boost::lexical_cast<T>("0.2090792764676090716286400360584443891749e80"),
         5*boost::lexical_cast<T>("0.3730037777359591428226035156377978092809e79"),
         6*boost::lexical_cast<T>("0.5446396536956682043376492370432031543834e78"),
         7*boost::lexical_cast<T>("0.6692523966335177847425047827449069256345e77"),
         8*boost::lexical_cast<T>("0.7062543624100864681625612653756619116848e76"),
         9*boost::lexical_cast<T>("0.6499914905966283735005256964443226879158e75"),
         10*boost::lexical_cast<T>("0.5280364564853225211197557708655426736091e74"),
         11*boost::lexical_cast<T>("0.3823205608981176913075543599005095206953e73"),
         12*boost::lexical_cast<T>("0.2486733714214237704739129972671154532415e72"),
         13*boost::lexical_cast<T>("0.1462562139602039577983434547171318011675e71"),
         14*boost::lexical_cast<T>("0.7821169065036815012381267259559910324285e69"),
         15*boost::lexical_cast<T>("0.3820552182348155468636157988764435365078e68"),
         16*boost::lexical_cast<T>("0.1711618296983598244658239925535632505062e67"),
         17*boost::lexical_cast<T>("0.7056661618357643731419080738521475204245e65"),
         18*boost::lexical_cast<T>("0.2685246896473614017356264531791459936036e64"),
         19*boost::lexical_cast<T>("0.9455168125599643085283071944864977592391e62"),
         20*boost::lexical_cast<T>("0.3087541626972538362237309145177486236219e61"),
         21*boost::lexical_cast<T>("0.9367928873352980208052601301625005737407e59"),
         22*boost::lexical_cast<T>("0.2645306130689794942883818547314327466007e58"),
         23*boost::lexical_cast<T>("0.6961815141171454309161007351079576190079e56"),
         24*boost::lexical_cast<T>("0.1709637824471794552313802669803885946843e55"),
         25*boost::lexical_cast<T>("0.3921553258481531526663112728778759311158e53"),
         26*boost::lexical_cast<T>("0.8409006354449988687714450897575728228696e51"),
         27*boost::lexical_cast<T>("0.1686755204461325935742097669030363344927e50"),
         28*boost::lexical_cast<T>("0.3166653542877070999007425197729038754254e48"),
         29*boost::lexical_cast<T>("0.5566029092358215049069560272835654229637e46"),
         30*boost::lexical_cast<T>("0.9161766287916328133080586672953875116242e44"),
         31*boost::lexical_cast<T>("1412317772330871298317974693514430627922000"),
         32*boost::lexical_cast<T>("20387991986727877473732570146112459874790"),
         33*boost::lexical_cast<T>("275557928713904105182512535678580359839.3"),
         34*boost::lexical_cast<T>("3485719851040516559072031256589598330.723"),
         35*boost::lexical_cast<T>("41247046743564028399938106707656877.40859"),
         36*boost::lexical_cast<T>("456274078125709314602601667471879.0147312"),
         37*boost::lexical_cast<T>("4714450683242899367025707077155.310613012"),
         38*boost::lexical_cast<T>("45453933537925041680009544258.75073849996"),
         39*boost::lexical_cast<T>("408437900487067278846361972.302331241052"),
         40*boost::lexical_cast<T>("3415719344386166273085838.705771571751035"),
         41*boost::lexical_cast<T>("26541502879185876562320.93134691487351145"),
         42*boost::lexical_cast<T>("191261415065918713661.1571433274648417668"),
         43*boost::lexical_cast<T>("1275349770108718421.645275944284937551702"),
         44*boost::lexical_cast<T>("7849171120971773.318910987434906905704272"),
         45*boost::lexical_cast<T>("44455946386549.80866460312682983576538056"),
         46*boost::lexical_cast<T>("230920362395.3198137186361608905136598046"),
         47*boost::lexical_cast<T>("1095700096.240863858624279930600654130254"),
         48*boost::lexical_cast<T>("4727085.467506050153744334085516289728134"),
         49*boost::lexical_cast<T>("18440.75118859447173303252421991479005424"),
         50*boost::lexical_cast<T>("64.62515887799460295677071749181651317052"),
         51*boost::lexical_cast<T>("0.201851568864688406206528472883512147547"),
         52*boost::lexical_cast<T>("0.0005565091674187978029138500039504078098143"),
         53*boost::lexical_cast<T>("0.1338097668312907986354698683493366559613e-5"),
         54*boost::lexical_cast<T>("0.276308225077464312820179030238305271638e-8"),
         55*boost::lexical_cast<T>("0.4801582970473168520375942100071070575043e-11"),
         56*boost::lexical_cast<T>("0.6829184144212920949740376186058541800175e-14"),
         57*boost::lexical_cast<T>("0.7634080076358511276617829524639455399182e-17"),
         58*boost::lexical_cast<T>("0.6290035083727140966418512608156646142409e-20"),
         59*boost::lexical_cast<T>("0.339652245667538733044036638506893821352e-23"),
         60*boost::lexical_cast<T>("0.9017518064256388530773585529891677854909e-27")
      };
      static const T QD[60] = {
         boost::lexical_cast<T>("0.1386831185456898357379390197203894063459e81"),
         2*boost::lexical_cast<T>("0.6467076379487574703291056110838151259438e81"),
         3*boost::lexical_cast<T>("0.1394967823848615838336194279565285465161e82"),
         4*boost::lexical_cast<T>("0.1872927317344192945218570366455046340458e82"),
         5*boost::lexical_cast<T>("0.1772461045338946243584650759986310355937e82"),
         6*boost::lexical_cast<T>("0.1267294892200258648315971144069595555118e82"),
         7*boost::lexical_cast<T>("0.7157764838362416821508872117623058626589e81"),
         8*boost::lexical_cast<T>("0.329447266909948668265277828268378274513e81"),
         9*boost::lexical_cast<T>("0.1264376077317689779509250183194342571207e81"),
         10*boost::lexical_cast<T>("0.4118230304191980787640446056583623228873e80"),
         11*boost::lexical_cast<T>("0.1154393529762694616405952270558316515261e80"),
         12*boost::lexical_cast<T>("0.281655612889423906125295485693696744275e79"),
         13*boost::lexical_cast<T>("0.6037483524928743102724159846414025482077e78"),
         14*boost::lexical_cast<T>("0.1145927995397835468123576831800276999614e78"),
         15*boost::lexical_cast<T>("0.1938624296151985600348534009382865995154e77"),
         16*boost::lexical_cast<T>("0.293980925856227626211879961219188406675e76"),
         17*boost::lexical_cast<T>("0.4015574518216966910319562902099567437832e75"),
         18*boost::lexical_cast<T>("0.4961475457509727343545565970423431880907e74"),
         19*boost::lexical_cast<T>("0.5565482348278933960215521991000378896338e73"),
         20*boost::lexical_cast<T>("0.5686112924615820754631098622770303094938e72"),
         21*boost::lexical_cast<T>("0.5305988545844796293285410303747469932856e71"),
         22*boost::lexical_cast<T>("0.4533363413802585060568537458067343491358e70"),
         23*boost::lexical_cast<T>("0.3553932059473516064068322757331575565718e69"),
         24*boost::lexical_cast<T>("0.2561198565218704414618802902533972354203e68"),
         25*boost::lexical_cast<T>("0.1699519313292900324098102065697454295572e67"),
         26*boost::lexical_cast<T>("0.1039830160862334505389615281373574959236e66"),
         27*boost::lexical_cast<T>("0.5873082967977428281000961954715372504986e64"),
         28*boost::lexical_cast<T>("0.3065255179030575882202133042549783442446e63"),
         29*boost::lexical_cast<T>("0.1479494813481364701208655943688307245459e62"),
         30*boost::lexical_cast<T>("0.6608150467921598615495180659808895663164e60"),
         31*boost::lexical_cast<T>("0.2732535313770902021791888953487787496976e59"),
         32*boost::lexical_cast<T>("0.1046402297662493314531194338414508049069e58"),
         33*boost::lexical_cast<T>("0.3711375077192882936085049147920021549622e56"),
         34*boost::lexical_cast<T>("0.1219154482883895482637944309702972234576e55"),
         35*boost::lexical_cast<T>("0.3708359374149458741391374452286837880162e53"),
         36*boost::lexical_cast<T>("0.1044095509971707189716913168889769471468e52"),
         37*boost::lexical_cast<T>("0.271951506225063286130946773813524945052e50"),
         38*boost::lexical_cast<T>("0.6548016291215163843464133978454065823866e48"),
         39*boost::lexical_cast<T>("0.1456062447610542135403751730809295219344e47"),
         40*boost::lexical_cast<T>("0.2986690175077969760978388356833006028929e45"),
         41*boost::lexical_cast<T>("5643149706574013350061247429006443326844000"),
         42*boost::lexical_cast<T>("98047545414467090421964387960743688053480"),
         43*boost::lexical_cast<T>("1563378767746846395507385099301468978550"),
         44*boost::lexical_cast<T>("22823360528584500077862274918382796495"),
         45*boost::lexical_cast<T>("304215527004115213046601295970388750"),
         46*boost::lexical_cast<T>("3690289075895685793844344966820325"),
         47*boost::lexical_cast<T>("40584512015702371433911456606050"),
         48*boost::lexical_cast<T>("402834190897282802772754873905"),
         49*boost::lexical_cast<T>("3589522158493606918146495750"),
         50*boost::lexical_cast<T>("28530557707503483723634725"),
         51*boost::lexical_cast<T>("200714561335055753000730"),
         52*boost::lexical_cast<T>("1237953783437761888641"),
         53*boost::lexical_cast<T>("6614698701445762950"),
         54*boost::lexical_cast<T>("30155495647727505"),
         55*boost::lexical_cast<T>("114953256021450"),
         56*boost::lexical_cast<T>("356398020013"),
         57*boost::lexical_cast<T>("863113950"),
         58*boost::lexical_cast<T>("1531345"),
         59*boost::lexical_cast<T>("1770"),
         60*boost::lexical_cast<T>("1")
      };
   static const double g = 63.192152;

   T zgh = x + g - 0.5;

   T result = (x - 0.5) / zgh;
   result += log(zgh);
   result += tools::evaluate_polynomial(PD, x) / tools::evaluate_polynomial(P, x);
   result -= tools::evaluate_polynomial(QD, x) / tools::evaluate_polynomial(Q, x);
   result -= 1;

   return result;
}

template <class T>
T big_digamma(T x)
{
   BOOST_MATH_STD_USING
   if(x < 0)
   {
      return big_digamma_helper(static_cast<T>(1-x)) + constants::pi<T>() / tan(constants::pi<T>() * (1-x));
   }
   return big_digamma_helper(x);
}

}}}

#endif // include guard
Commit	Line	Data
7c673cae FG	1	// (C) Copyright John Maddock 2006-8.
	2	// Use, modification and distribution are subject to the
	3	// Boost Software License, Version 1.0. (See accompanying file
	4	// LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
	5
	6	#ifndef BOOST_MATH_NTL_DIGAMMA
	7	#define BOOST_MATH_NTL_DIGAMMA
	8
	9	#include <boost/math/tools/rational.hpp>
	10	#include <boost/math/policies/error_handling.hpp>
	11	#include <boost/math/constants/constants.hpp>
	12	#include <boost/lexical_cast.hpp>
	13
	14	namespace boost{ namespace math{ namespace detail{
	15
	16	template <class T>
	17	T big_digamma_helper(T x)
	18	{
	19	static const T P[61] = {
	20	boost::lexical_cast<T>("0.6660133691143982067148122682345055274952e81"),
	21	boost::lexical_cast<T>("0.6365271516829242456324234577164675383137e81"),
	22	boost::lexical_cast<T>("0.2991038873096202943405966144203628966976e81"),
	23	boost::lexical_cast<T>("0.9211116495503170498076013367421231351115e80"),
	24	boost::lexical_cast<T>("0.2090792764676090716286400360584443891749e80"),
	25	boost::lexical_cast<T>("0.3730037777359591428226035156377978092809e79"),
	26	boost::lexical_cast<T>("0.5446396536956682043376492370432031543834e78"),
	27	boost::lexical_cast<T>("0.6692523966335177847425047827449069256345e77"),
	28	boost::lexical_cast<T>("0.7062543624100864681625612653756619116848e76"),
	29	boost::lexical_cast<T>("0.6499914905966283735005256964443226879158e75"),
	30	boost::lexical_cast<T>("0.5280364564853225211197557708655426736091e74"),
	31	boost::lexical_cast<T>("0.3823205608981176913075543599005095206953e73"),
	32	boost::lexical_cast<T>("0.2486733714214237704739129972671154532415e72"),
	33	boost::lexical_cast<T>("0.1462562139602039577983434547171318011675e71"),
	34	boost::lexical_cast<T>("0.7821169065036815012381267259559910324285e69"),
	35	boost::lexical_cast<T>("0.3820552182348155468636157988764435365078e68"),
	36	boost::lexical_cast<T>("0.1711618296983598244658239925535632505062e67"),
	37	boost::lexical_cast<T>("0.7056661618357643731419080738521475204245e65"),
	38	boost::lexical_cast<T>("0.2685246896473614017356264531791459936036e64"),
	39	boost::lexical_cast<T>("0.9455168125599643085283071944864977592391e62"),
	40	boost::lexical_cast<T>("0.3087541626972538362237309145177486236219e61"),
	41	boost::lexical_cast<T>("0.9367928873352980208052601301625005737407e59"),
	42	boost::lexical_cast<T>("0.2645306130689794942883818547314327466007e58"),
	43	boost::lexical_cast<T>("0.6961815141171454309161007351079576190079e56"),
	44	boost::lexical_cast<T>("0.1709637824471794552313802669803885946843e55"),
	45	boost::lexical_cast<T>("0.3921553258481531526663112728778759311158e53"),
	46	boost::lexical_cast<T>("0.8409006354449988687714450897575728228696e51"),
	47	boost::lexical_cast<T>("0.1686755204461325935742097669030363344927e50"),
	48	boost::lexical_cast<T>("0.3166653542877070999007425197729038754254e48"),
	49	boost::lexical_cast<T>("0.5566029092358215049069560272835654229637e46"),
	50	boost::lexical_cast<T>("0.9161766287916328133080586672953875116242e44"),
	51	boost::lexical_cast<T>("1412317772330871298317974693514430627922000"),
	52	boost::lexical_cast<T>("20387991986727877473732570146112459874790"),
	53	boost::lexical_cast<T>("275557928713904105182512535678580359839.3"),
	54	boost::lexical_cast<T>("3485719851040516559072031256589598330.723"),
	55	boost::lexical_cast<T>("41247046743564028399938106707656877.40859"),
	56	boost::lexical_cast<T>("456274078125709314602601667471879.0147312"),
	57	boost::lexical_cast<T>("4714450683242899367025707077155.310613012"),
	58	boost::lexical_cast<T>("45453933537925041680009544258.75073849996"),
	59	boost::lexical_cast<T>("408437900487067278846361972.302331241052"),
	60	boost::lexical_cast<T>("3415719344386166273085838.705771571751035"),
	61	boost::lexical_cast<T>("26541502879185876562320.93134691487351145"),
	62	boost::lexical_cast<T>("191261415065918713661.1571433274648417668"),
	63	boost::lexical_cast<T>("1275349770108718421.645275944284937551702"),
	64	boost::lexical_cast<T>("7849171120971773.318910987434906905704272"),
65	boost::lexical_cast<T>("44455946386549.80866460312682983576538056"),
66	boost::lexical_cast<T>("230920362395.3198137186361608905136598046"),
67	boost::lexical_cast<T>("1095700096.240863858624279930600654130254"),
68	boost::lexical_cast<T>("4727085.467506050153744334085516289728134"),
69	boost::lexical_cast<T>("18440.75118859447173303252421991479005424"),
70	boost::lexical_cast<T>("64.62515887799460295677071749181651317052"),
71	boost::lexical_cast<T>("0.201851568864688406206528472883512147547"),
72	boost::lexical_cast<T>("0.0005565091674187978029138500039504078098143"),
73	boost::lexical_cast<T>("0.1338097668312907986354698683493366559613e-5"),
74	boost::lexical_cast<T>("0.276308225077464312820179030238305271638e-8"),
75	boost::lexical_cast<T>("0.4801582970473168520375942100071070575043e-11"),
76	boost::lexical_cast<T>("0.6829184144212920949740376186058541800175e-14"),
77	boost::lexical_cast<T>("0.7634080076358511276617829524639455399182e-17"),
78	boost::lexical_cast<T>("0.6290035083727140966418512608156646142409e-20"),
79	boost::lexical_cast<T>("0.339652245667538733044036638506893821352e-23"),
80	boost::lexical_cast<T>("0.9017518064256388530773585529891677854909e-27")
81	};
82	static const T Q[61] = {
83	boost::lexical_cast<T>("0"),
84	boost::lexical_cast<T>("0.1386831185456898357379390197203894063459e81"),
85	boost::lexical_cast<T>("0.6467076379487574703291056110838151259438e81"),
86	boost::lexical_cast<T>("0.1394967823848615838336194279565285465161e82"),
87	boost::lexical_cast<T>("0.1872927317344192945218570366455046340458e82"),
88	boost::lexical_cast<T>("0.1772461045338946243584650759986310355937e82"),
89	boost::lexical_cast<T>("0.1267294892200258648315971144069595555118e82"),
90	boost::lexical_cast<T>("0.7157764838362416821508872117623058626589e81"),
91	boost::lexical_cast<T>("0.329447266909948668265277828268378274513e81"),
92	boost::lexical_cast<T>("0.1264376077317689779509250183194342571207e81"),
93	boost::lexical_cast<T>("0.4118230304191980787640446056583623228873e80"),
94	boost::lexical_cast<T>("0.1154393529762694616405952270558316515261e80"),
95	boost::lexical_cast<T>("0.281655612889423906125295485693696744275e79"),
96	boost::lexical_cast<T>("0.6037483524928743102724159846414025482077e78"),
97	boost::lexical_cast<T>("0.1145927995397835468123576831800276999614e78"),
98	boost::lexical_cast<T>("0.1938624296151985600348534009382865995154e77"),
99	boost::lexical_cast<T>("0.293980925856227626211879961219188406675e76"),
100	boost::lexical_cast<T>("0.4015574518216966910319562902099567437832e75"),
101	boost::lexical_cast<T>("0.4961475457509727343545565970423431880907e74"),
102	boost::lexical_cast<T>("0.5565482348278933960215521991000378896338e73"),
103	boost::lexical_cast<T>("0.5686112924615820754631098622770303094938e72"),
104	boost::lexical_cast<T>("0.5305988545844796293285410303747469932856e71"),
105	boost::lexical_cast<T>("0.4533363413802585060568537458067343491358e70"),
106	boost::lexical_cast<T>("0.3553932059473516064068322757331575565718e69"),
107	boost::lexical_cast<T>("0.2561198565218704414618802902533972354203e68"),
108	boost::lexical_cast<T>("0.1699519313292900324098102065697454295572e67"),
109	boost::lexical_cast<T>("0.1039830160862334505389615281373574959236e66"),
110	boost::lexical_cast<T>("0.5873082967977428281000961954715372504986e64"),
111	boost::lexical_cast<T>("0.3065255179030575882202133042549783442446e63"),
112	boost::lexical_cast<T>("0.1479494813481364701208655943688307245459e62"),
113	boost::lexical_cast<T>("0.6608150467921598615495180659808895663164e60"),
114	boost::lexical_cast<T>("0.2732535313770902021791888953487787496976e59"),
115	boost::lexical_cast<T>("0.1046402297662493314531194338414508049069e58"),
116	boost::lexical_cast<T>("0.3711375077192882936085049147920021549622e56"),
117	boost::lexical_cast<T>("0.1219154482883895482637944309702972234576e55"),
118	boost::lexical_cast<T>("0.3708359374149458741391374452286837880162e53"),
119	boost::lexical_cast<T>("0.1044095509971707189716913168889769471468e52"),
120	boost::lexical_cast<T>("0.271951506225063286130946773813524945052e50"),
121	boost::lexical_cast<T>("0.6548016291215163843464133978454065823866e48"),
122	boost::lexical_cast<T>("0.1456062447610542135403751730809295219344e47"),
123	boost::lexical_cast<T>("0.2986690175077969760978388356833006028929e45"),
124	boost::lexical_cast<T>("5643149706574013350061247429006443326844000"),
125	boost::lexical_cast<T>("98047545414467090421964387960743688053480"),
126	boost::lexical_cast<T>("1563378767746846395507385099301468978550"),
127	boost::lexical_cast<T>("22823360528584500077862274918382796495"),
128	boost::lexical_cast<T>("304215527004115213046601295970388750"),
129	boost::lexical_cast<T>("3690289075895685793844344966820325"),
130	boost::lexical_cast<T>("40584512015702371433911456606050"),
131	boost::lexical_cast<T>("402834190897282802772754873905"),
132	boost::lexical_cast<T>("3589522158493606918146495750"),
133	boost::lexical_cast<T>("28530557707503483723634725"),
134	boost::lexical_cast<T>("200714561335055753000730"),
135	boost::lexical_cast<T>("1237953783437761888641"),
136	boost::lexical_cast<T>("6614698701445762950"),
137	boost::lexical_cast<T>("30155495647727505"),
138	boost::lexical_cast<T>("114953256021450"),
139	boost::lexical_cast<T>("356398020013"),
140	boost::lexical_cast<T>("863113950"),
141	boost::lexical_cast<T>("1531345"),
142	boost::lexical_cast<T>("1770"),
143	boost::lexical_cast<T>("1")
144	};
145	static const T PD[60] = {
146	boost::lexical_cast<T>("0.6365271516829242456324234577164675383137e81"),
147	2*boost::lexical_cast<T>("0.2991038873096202943405966144203628966976e81"),
148	3*boost::lexical_cast<T>("0.9211116495503170498076013367421231351115e80"),
149	4*boost::lexical_cast<T>("0.2090792764676090716286400360584443891749e80"),
150	5*boost::lexical_cast<T>("0.3730037777359591428226035156377978092809e79"),
151	6*boost::lexical_cast<T>("0.5446396536956682043376492370432031543834e78"),
152	7*boost::lexical_cast<T>("0.6692523966335177847425047827449069256345e77"),
153	8*boost::lexical_cast<T>("0.7062543624100864681625612653756619116848e76"),
154	9*boost::lexical_cast<T>("0.6499914905966283735005256964443226879158e75"),
155	10*boost::lexical_cast<T>("0.5280364564853225211197557708655426736091e74"),
156	11*boost::lexical_cast<T>("0.3823205608981176913075543599005095206953e73"),
157	12*boost::lexical_cast<T>("0.2486733714214237704739129972671154532415e72"),
158	13*boost::lexical_cast<T>("0.1462562139602039577983434547171318011675e71"),
159	14*boost::lexical_cast<T>("0.7821169065036815012381267259559910324285e69"),
160	15*boost::lexical_cast<T>("0.3820552182348155468636157988764435365078e68"),
161	16*boost::lexical_cast<T>("0.1711618296983598244658239925535632505062e67"),
162	17*boost::lexical_cast<T>("0.7056661618357643731419080738521475204245e65"),
163	18*boost::lexical_cast<T>("0.2685246896473614017356264531791459936036e64"),
164	19*boost::lexical_cast<T>("0.9455168125599643085283071944864977592391e62"),
165	20*boost::lexical_cast<T>("0.3087541626972538362237309145177486236219e61"),
166	21*boost::lexical_cast<T>("0.9367928873352980208052601301625005737407e59"),
167	22*boost::lexical_cast<T>("0.2645306130689794942883818547314327466007e58"),
168	23*boost::lexical_cast<T>("0.6961815141171454309161007351079576190079e56"),
169	24*boost::lexical_cast<T>("0.1709637824471794552313802669803885946843e55"),
170	25*boost::lexical_cast<T>("0.3921553258481531526663112728778759311158e53"),
171	26*boost::lexical_cast<T>("0.8409006354449988687714450897575728228696e51"),
172	27*boost::lexical_cast<T>("0.1686755204461325935742097669030363344927e50"),
173	28*boost::lexical_cast<T>("0.3166653542877070999007425197729038754254e48"),
174	29*boost::lexical_cast<T>("0.5566029092358215049069560272835654229637e46"),
175	30*boost::lexical_cast<T>("0.9161766287916328133080586672953875116242e44"),
176	31*boost::lexical_cast<T>("1412317772330871298317974693514430627922000"),
177	32*boost::lexical_cast<T>("20387991986727877473732570146112459874790"),
178	33*boost::lexical_cast<T>("275557928713904105182512535678580359839.3"),
179	34*boost::lexical_cast<T>("3485719851040516559072031256589598330.723"),
180	35*boost::lexical_cast<T>("41247046743564028399938106707656877.40859"),
181	36*boost::lexical_cast<T>("456274078125709314602601667471879.0147312"),
182	37*boost::lexical_cast<T>("4714450683242899367025707077155.310613012"),
183	38*boost::lexical_cast<T>("45453933537925041680009544258.75073849996"),
184	39*boost::lexical_cast<T>("408437900487067278846361972.302331241052"),
185	40*boost::lexical_cast<T>("3415719344386166273085838.705771571751035"),
186	41*boost::lexical_cast<T>("26541502879185876562320.93134691487351145"),
187	42*boost::lexical_cast<T>("191261415065918713661.1571433274648417668"),
188	43*boost::lexical_cast<T>("1275349770108718421.645275944284937551702"),
189	44*boost::lexical_cast<T>("7849171120971773.318910987434906905704272"),
190	45*boost::lexical_cast<T>("44455946386549.80866460312682983576538056"),
191	46*boost::lexical_cast<T>("230920362395.3198137186361608905136598046"),
192	47*boost::lexical_cast<T>("1095700096.240863858624279930600654130254"),
193	48*boost::lexical_cast<T>("4727085.467506050153744334085516289728134"),
194	49*boost::lexical_cast<T>("18440.75118859447173303252421991479005424"),
195	50*boost::lexical_cast<T>("64.62515887799460295677071749181651317052"),
196	51*boost::lexical_cast<T>("0.201851568864688406206528472883512147547"),
197	52*boost::lexical_cast<T>("0.0005565091674187978029138500039504078098143"),
198	53*boost::lexical_cast<T>("0.1338097668312907986354698683493366559613e-5"),
199	54*boost::lexical_cast<T>("0.276308225077464312820179030238305271638e-8"),
200	55*boost::lexical_cast<T>("0.4801582970473168520375942100071070575043e-11"),
201	56*boost::lexical_cast<T>("0.6829184144212920949740376186058541800175e-14"),
202	57*boost::lexical_cast<T>("0.7634080076358511276617829524639455399182e-17"),
203	58*boost::lexical_cast<T>("0.6290035083727140966418512608156646142409e-20"),
204	59*boost::lexical_cast<T>("0.339652245667538733044036638506893821352e-23"),
205	60*boost::lexical_cast<T>("0.9017518064256388530773585529891677854909e-27")
206	};
207	static const T QD[60] = {
208	boost::lexical_cast<T>("0.1386831185456898357379390197203894063459e81"),
209	2*boost::lexical_cast<T>("0.6467076379487574703291056110838151259438e81"),
210	3*boost::lexical_cast<T>("0.1394967823848615838336194279565285465161e82"),
211	4*boost::lexical_cast<T>("0.1872927317344192945218570366455046340458e82"),
212	5*boost::lexical_cast<T>("0.1772461045338946243584650759986310355937e82"),
213	6*boost::lexical_cast<T>("0.1267294892200258648315971144069595555118e82"),
214	7*boost::lexical_cast<T>("0.7157764838362416821508872117623058626589e81"),
215	8*boost::lexical_cast<T>("0.329447266909948668265277828268378274513e81"),
216	9*boost::lexical_cast<T>("0.1264376077317689779509250183194342571207e81"),
217	10*boost::lexical_cast<T>("0.4118230304191980787640446056583623228873e80"),
218	11*boost::lexical_cast<T>("0.1154393529762694616405952270558316515261e80"),
219	12*boost::lexical_cast<T>("0.281655612889423906125295485693696744275e79"),
220	13*boost::lexical_cast<T>("0.6037483524928743102724159846414025482077e78"),
221	14*boost::lexical_cast<T>("0.1145927995397835468123576831800276999614e78"),
222	15*boost::lexical_cast<T>("0.1938624296151985600348534009382865995154e77"),
223	16*boost::lexical_cast<T>("0.293980925856227626211879961219188406675e76"),
224	17*boost::lexical_cast<T>("0.4015574518216966910319562902099567437832e75"),
225	18*boost::lexical_cast<T>("0.4961475457509727343545565970423431880907e74"),
226	19*boost::lexical_cast<T>("0.5565482348278933960215521991000378896338e73"),
227	20*boost::lexical_cast<T>("0.5686112924615820754631098622770303094938e72"),
228	21*boost::lexical_cast<T>("0.5305988545844796293285410303747469932856e71"),
229	22*boost::lexical_cast<T>("0.4533363413802585060568537458067343491358e70"),
230	23*boost::lexical_cast<T>("0.3553932059473516064068322757331575565718e69"),
231	24*boost::lexical_cast<T>("0.2561198565218704414618802902533972354203e68"),
232	25*boost::lexical_cast<T>("0.1699519313292900324098102065697454295572e67"),
233	26*boost::lexical_cast<T>("0.1039830160862334505389615281373574959236e66"),
234	27*boost::lexical_cast<T>("0.5873082967977428281000961954715372504986e64"),
235	28*boost::lexical_cast<T>("0.3065255179030575882202133042549783442446e63"),
236	29*boost::lexical_cast<T>("0.1479494813481364701208655943688307245459e62"),
237	30*boost::lexical_cast<T>("0.6608150467921598615495180659808895663164e60"),
238	31*boost::lexical_cast<T>("0.2732535313770902021791888953487787496976e59"),
239	32*boost::lexical_cast<T>("0.1046402297662493314531194338414508049069e58"),
240	33*boost::lexical_cast<T>("0.3711375077192882936085049147920021549622e56"),
241	34*boost::lexical_cast<T>("0.1219154482883895482637944309702972234576e55"),
242	35*boost::lexical_cast<T>("0.3708359374149458741391374452286837880162e53"),
243	36*boost::lexical_cast<T>("0.1044095509971707189716913168889769471468e52"),
244	37*boost::lexical_cast<T>("0.271951506225063286130946773813524945052e50"),
245	38*boost::lexical_cast<T>("0.6548016291215163843464133978454065823866e48"),
246	39*boost::lexical_cast<T>("0.1456062447610542135403751730809295219344e47"),
247	40*boost::lexical_cast<T>("0.2986690175077969760978388356833006028929e45"),
248	41*boost::lexical_cast<T>("5643149706574013350061247429006443326844000"),
249	42*boost::lexical_cast<T>("98047545414467090421964387960743688053480"),
250	43*boost::lexical_cast<T>("1563378767746846395507385099301468978550"),
251	44*boost::lexical_cast<T>("22823360528584500077862274918382796495"),
252	45*boost::lexical_cast<T>("304215527004115213046601295970388750"),
253	46*boost::lexical_cast<T>("3690289075895685793844344966820325"),
254	47*boost::lexical_cast<T>("40584512015702371433911456606050"),
255	48*boost::lexical_cast<T>("402834190897282802772754873905"),
256	49*boost::lexical_cast<T>("3589522158493606918146495750"),
257	50*boost::lexical_cast<T>("28530557707503483723634725"),
258	51*boost::lexical_cast<T>("200714561335055753000730"),
259	52*boost::lexical_cast<T>("1237953783437761888641"),
260	53*boost::lexical_cast<T>("6614698701445762950"),
261	54*boost::lexical_cast<T>("30155495647727505"),
262	55*boost::lexical_cast<T>("114953256021450"),
263	56*boost::lexical_cast<T>("356398020013"),
264	57*boost::lexical_cast<T>("863113950"),
265	58*boost::lexical_cast<T>("1531345"),
266	59*boost::lexical_cast<T>("1770"),
267	60*boost::lexical_cast<T>("1")
268	};
269	static const double g = 63.192152;
270
271	T zgh = x + g - 0.5;
272
273	T result = (x - 0.5) / zgh;
274	result += log(zgh);
275	result += tools::evaluate_polynomial(PD, x) / tools::evaluate_polynomial(P, x);
276	result -= tools::evaluate_polynomial(QD, x) / tools::evaluate_polynomial(Q, x);
277	result -= 1;
278
279	return result;
280	}
281
282	template <class T>
283	T big_digamma(T x)
284	{
285	BOOST_MATH_STD_USING
286	if(x < 0)
287	{
288	return big_digamma_helper(static_cast<T>(1-x)) + constants::pi<T>() / tan(constants::pi<T>() * (1-x));
289	}
290	return big_digamma_helper(x);
291	}
292
293	}}}
294
295	#endif // include guard