ntl_rr_lanczos.hpp

Boost provides free peer-reviewed portable C++ source libraries. We emphasize libraries that work

         result += d[k]/(z+(k-1));
      }
      return result;
   }

   template<class T>
   static T lanczos_sum_near_1(const T& dz)
   {
      using namespace boost;
      static const T d[60] = {
         boost::lexical_cast<T>("23.2463658527729692390378860713647146932236940604550445351214987229819352880524561852919518"),
         boost::lexical_cast<T>("-523.358012551815715084547614110229469295755088686612838322817729744722233637819564673967396"),
         boost::lexical_cast<T>("5701.12892340421080714956066268650092612647620400476183901625272640935853188559347587495571"),
         boost::lexical_cast<T>("-40033.5506451901904954336453419007623117537868026994808919201793803506999271787018654246699"),
         boost::lexical_cast<T>("203689.884259074923009439144410340256983393397995558814367995938668111650624499963153485034"),
         boost::lexical_cast<T>("-800270.648969745331278757692597096167418585957703057412758177038340791380011708874081291202"),
         boost::lexical_cast<T>("2526668.23380061659863999395867315313385499515711742092815402701950519696944982260718031476"),
         boost::lexical_cast<T>("-6587362.57559198722630391278043503867973853468105110382293763174847657538179665571836023631"),
         boost::lexical_cast<T>("14462211.3454541602975917764900442754186801975533106565506542322063393991552960595701762805"),
         boost::lexical_cast<T>("-27132375.1879227404375395522940895789625516798992585980380939378508607160857820002128106898"),
         boost::lexical_cast<T>("43991923.8735251977856804364757478459275087361742168436524951824945035673768875988985478116"),
         boost::lexical_cast<T>("-62192284.0030124679010201921841372967696262036115679150017649233887633598058364494608060812"),
         boost::lexical_cast<T>("77203473.0770033513405070667417251568915937590689150831268228886281254637715669678358204991"),
         boost::lexical_cast<T>("-84630180.2217173903516348977915150565994784278120192219937728967986198118628659866582594874"),
         boost::lexical_cast<T>("82294807.2253549409847505891112074804416229757832871133388349982640444405470371147991706317"),
         boost::lexical_cast<T>("-71245738.2484649177928765605893043553453557808557887270209768163561363857395639001251515788"),
         boost::lexical_cast<T>("55073334.3180266913441333534260714059077572215147571872597651029894142803987981342430068594"),
         boost::lexical_cast<T>("-38097984.1648990787690036742690550656061009857688125101191167768314179751258568264424911474"),
         boost::lexical_cast<T>("23625729.5032184580395130592017474282828236643586203914515183078852982915252442161768527976"),
         boost::lexical_cast<T>("-13149998.4348054726172055622442157883429575511528431835657668083088902165366619827169829685"),
         boost::lexical_cast<T>("6574597.77221556423683199818131482663205682902023554728024972161230111356285973623550338976"),
         boost::lexical_cast<T>("-2953848.1483469149918109110050192571921018042012905892107136410603990336401921230407043408"),
         boost::lexical_cast<T>("1192595.29584357246380113611351829515963605337523874715861849584306265512819543347806085356"),
         boost::lexical_cast<T>("-432553.812019608638388918135375154289816441900572658692369491476137741687213006403648722272"),
         boost::lexical_cast<T>("140843.215385933866391177743292449477205328233960902455943995092958295858485718885800427129"),
         boost::lexical_cast<T>("-41128.186992679630058614841985110676526199977321524879849001760603476646382839182691529968"),
         boost::lexical_cast<T>("10756.2849191854701631989789887757784944313743544315113894758328432005767448056040879337769"),
         boost::lexical_cast<T>("-2515.15559672041299884426826962296210458052543246529646213159169885444118227871246315458787"),
         boost::lexical_cast<T>("524.750087004805200600237632074908875763734578390662349666321453103782638818305404274166951"),
         boost::lexical_cast<T>("-97.4468596421732493988298219295878130651986131393383646674144877163795143930682205035917965"),
         boost::lexical_cast<T>("16.0613108128210806736384551896802799172445298357754547684100294231532127326987175444453058"),
         boost::lexical_cast<T>("-2.34194813526540240672426202485306862230641838409943369059203455578340880900483887447559874"),
         boost::lexical_cast<T>("0.300982934748016059399829007219431333744032924923669397318820178988611410275964499475465815"),
         boost::lexical_cast<T>("-0.033950095985367909789000959795708551814461844488183964432565731809399824963680858993718525"),
         boost::lexical_cast<T>("0.00334502394288921146242772614150438404658527112198421937945605441697314216921393987758378122"),
         boost::lexical_cast<T>("-0.000286333429067523984607730553301991502191011265745476190940771685897687956262049750683013485"),
         boost::lexical_cast<T>("0.211647426149364947402896718485536530479491688838087899435991994237067890628274492042231115e-4"),
         boost::lexical_cast<T>("-0.134163345121302758109675190598169832775248626443483098532368562186356128620805552609175683e-5"),
         boost::lexical_cast<T>("0.723697303042715085329782938306424498336642078597508935450663080894255773653328980495047891e-7"),
         boost::lexical_cast<T>("-0.329273487343139063533251321553223583999676337945788660475231347828772272134656322947906888e-8"),
         boost::lexical_cast<T>("0.12510922551028971731767784013117088894558604838820475961392154031378891971216135267744134e-9"),
         boost::lexical_cast<T>("-0.392468958215589939603666430583400537413757786057185505426804034745840192914621891690369903e-11"),
         boost::lexical_cast<T>("0.100332717101049934370760667782927946803279422001380028508200697081188326364078428184546051e-12"),
         boost::lexical_cast<T>("-0.205917088291197705194762747639836655808855850989058813560983717575008725393428497910009756e-14"),
         boost::lexical_cast<T>("0.333450178247893143608439314203175490705783992567107481617660357577257627854979230819461489e-16"),
         boost::lexical_cast<T>("-0.417546693906616047110563550428133589051498362676394888715581845170969319500638944065594319e-18"),
         boost::lexical_cast<T>("0.394871691642184410859178529844325390739857256666676534513661579365702353214518478078730801e-20"),
         boost::lexical_cast<T>("-0.274258012587811199757875927548699264063511843669070634471054184977334027224611843434000922e-22"),
         boost::lexical_cast<T>("0.135315354265459854889496635967343027244391821142592599244505313738163473730636430399785048e-24"),
         boost::lexical_cast<T>("-0.455579032003288910408487905303223613382276173706542364543918076752861628464036586507967767e-27"),
         boost::lexical_cast<T>("0.99650703862462739161520123768147312466695159780582506041370833824093136783202694548427718e-30"),
         boost::lexical_cast<T>("-0.1332444609228706921659395801935919548447859029572115502899861345555006827214220195650058e-32"),
         boost::lexical_cast<T>("0.100856999148765307000182397631280249632761913433008379786888200467467364474581430670889392e-35"),
         boost::lexical_cast<T>("-0.39146979455613683472384690509165395074425354524713697428673406058157887065953366609738731e-39"),
         boost::lexical_cast<T>("0.683859606707931248105140296850112494069265272540298100341919970496564103098283709868586478e-43"),
         boost::lexical_cast<T>("-0.450326344248604222735147147805963966503893913752040066400766411031387063854141246972061792e-47"),
         boost::lexical_cast<T>("0.870675378039492904184581895322153006461319724931909799151743284769901586333730037761678891e-52"),
         boost::lexical_cast<T>("-0.341678395249272265744518787745356400350877656459401143889000625280131819505857966769964401e-57"),
         boost::lexical_cast<T>("0.152322191370871666358069530949353871960316638394428595988162174042653299702098929238880862e-63"),
         boost::lexical_cast<T>("-0.285425405297633795767452984791738825078111150078605004958179057245980222485147999495352632e-71"),
      };
      T result = 0;
      for(int k = 1; k <= sizeof(d)/sizeof(d[0]); ++k)
      {
         result += (-d[k-1]*dz)/(k*dz + k*k);
      }
      return result;
   }

   template<class T>
   static T lanczos_sum_near_2(const T& dz)
   {
      using namespace boost;
      static const T d[60] = {
         boost::lexical_cast<T>("557.56438192770795764344217888434355281097193198928944200046501607026919782564033547346298"),
         boost::lexical_cast<T>("-12552.748616427645475141433405567201788681683808077269330800392600825597799119572762385222"),
         boost::lexical_cast<T>("136741.650054039199076788077149441364242294724343897779563222338447737802381279007988884806"),
         boost::lexical_cast<T>("-960205.223613240309942047656967301131022760634321049075674684679438471862998829007639437133"),
         boost::lexical_cast<T>("4885504.47588736223774859617054275229642041717942140469884121916073195308537421162982679289"),
         boost::lexical_cast<T>("-19194501.738192166918904824982935279260356575935661514109550613809352009246483412530545583"),
         boost::lexical_cast<T>("60602169.8633537742937457094837494059849674261357199218329545854990149896822944801504450843"),
         boost::lexical_cast<T>("-157997975.522506767297528502540724511908584668874487506510120462561270100749019845014382885"),
         boost::lexical_cast<T>("346876323.86092543685419723290495817330608574729543216092477261152247521712190505658568876"),
         boost::lexical_cast<T>("-650770365.471136883718747607976242475416651908858429752332176373467422603953536408709972919"),
         boost::lexical_cast<T>("1055146856.05909309330903130910708372830487315684258450293308627289334336871273080305128138"),
         boost::lexical_cast<T>("-1491682726.25614447429071368736790697283307005456720192465860871846879804207692411263924608"),
         boost::lexical_cast<T>("1851726287.94866167094858600116562210167031458934987154557042242638980748286188183300900268"),
         boost::lexical_cast<T>("-2029855953.68334371445800569238095379629407314338521720558391277508374519526853827142679839"),
         boost::lexical_cast<T>("1973842002.53354868177824629525448788555435194808657489238517523691040148611221295436287925"),
         boost::lexical_cast<T>("-1708829941.98209573247426625323314413060108441455314880934710595647408841619484540679859098"),
         boost::lexical_cast<T>("1320934627.12433688699625456833930317624783222321555050330381730035733198249283009357314954"),
         boost::lexical_cast<T>("-913780636.858542526294419197161614811332299249415125108737474024007693329922089123296358727"),
         boost::lexical_cast<T>("566663423.929632170286007468016419798879660054391183200464733820209439185545886930103546787"),
         boost::lexical_cast<T>("-315402880.436816230388857961460509181823167373029384218959199936902955049832392362044305869"),
         boost::lexical_cast<T>("157691811.550465734461741500275930418786875005567018699867961482249002625886064187146134966"),
         boost::lexical_cast<T>("-70848085.5705405970640618473551954585013808128304384354476488268600720054598122945113512731"),
         boost::lexical_cast<T>("28604413.4050137708444142264980840059788755325900041515286382001704951527733220637586013815"),
         boost::lexical_cast<T>("-10374808.7067303054787164054055989420809074792801592763124972441820101840292558840131568633"),
         boost::lexical_cast<T>("3378126.32016207486657791623723515804931231041318964254116390764473281291389374196880720069"),
         boost::lexical_cast<T>("-986460.090390653140964189383080344920103075349535669020623874668558777188889544398718979744"),
         boost::lexical_cast<T>("257989.631187387317948158483575125380011593209850756066176921901006833159795100137743395985"),
         boost::lexical_cast<T>("-60326.0391159227288325790327830741260824763549807922845004854215660451399733578621565837087"),
         boost::lexical_cast<T>("12586.1375399649496159880821645216260841794563919652590583420570326276086323953958907053394"),
         boost::lexical_cast<T>("-2337.26417330316922535871922886167444795452055677161063205953141105726549966801856628447293"),
         boost::lexical_cast<T>("385.230745012608736644117458716226876976056390433401632749144285378123105481506733917763829"),
         boost::lexical_cast<T>("-56.1716559403731491675970177460841997333796694857076749852739159067307309470690838101179615"),
         boost::lexical_cast<T>("7.21907953468550196348585224042498727840087634483369357697580053424523903859773769748599575"),
         boost::lexical_cast<T>("-0.814293485887386870805786409956942772883474224091975496298369877683530509729332902182019049"),
         boost::lexical_cast<T>("0.0802304419995150047616460464220884371214157889148846405799324851793571580868840034085001373"),
         boost::lexical_cast<T>("-0.00686771095380619535195996193943858680694970000948742557733102777115482017857981277171196115"),
         boost::lexical_cast<T>("0.000507636621977556438232617777542864427109623356049335590894564220687567763620803789858345916"),
         boost::lexical_cast<T>("-0.32179095465362720747836116655088181481893063531138957363431280817392443948706754917605911e-4"),
         boost::lexical_cast<T>("0.173578890579848508947329833426585354230744194615295570820295052665075101971588563893718407e-5"),
         boost::lexical_cast<T>("-0.789762880006288893888161070734302768702358633525134582027140158619195373770299678322596835e-7"),
         boost::lexical_cast<T>("0.300074637200885066788470310738617992259402710843493097610337134266720909870967550606601658e-8"),
         boost::lexical_cast<T>("-0.941337297619721713151110244242536308266701344868601679868536153775533330272973088246835359e-10"),
         boost::lexical_cast<T>("0.24064815013182536657310186836079333949814111498828401548170442715552017773994482539471456e-11"),
         boost::lexical_cast<T>("-0.493892399304811910466345686492277504628763169549384435563232052965821874553923373100791477e-13"),
         boost::lexical_cast<T>("0.799780678476644196901221989475355609743387528732994566453160178199295104357319723742820593e-15"),
         boost::lexical_cast<T>("-0.100148627870893347527249092785257443532967736956154251497569191947184705954310833302770086e-16"),
         boost::lexical_cast<T>("0.947100256812658897084619699699028861352615460106539259289295071616221848196411749449858071e-19"),
         boost::lexical_cast<T>("-0.657808193528898116367845405906343884364280888644748907819280236995018351085371701094007759e-21"),
         boost::lexical_cast<T>("0.324554050057463845012469010247790763753999056976705084126950591088538742509983426730851614e-23"),
         boost::lexical_cast<T>("-0.10927068902162908990029309141242256163212535730975970310918370355165185052827948996110107e-25"),
         boost::lexical_cast<T>("0.239012340507870646690121104637467232366271566488184795459093215303237974655782634371712486e-28"),
         boost::lexical_cast<T>("-0.31958700972990573259359660326375143524864710953063781494908314884519046349402409667329667e-31"),
         boost::lexical_cast<T>("0.241905641292988284384362036555782113275737930713192053073501265726048089991747342247551645e-34"),
         boost::lexical_cast<T>("-0.93894080230619233745797029179332447129464915420290457418429337322820997038069119047864035e-38"),
         boost::lexical_cast<T>("0.164023814025085488413251990798690797467351995518990067783355251949198292596815470576539877e-41"),
         boost::lexical_cast<T>("-0.108010831192689925518484618970761942019888832176355541674171850211917230280206410356465451e-45"),
         boost::lexical_cast<T>("0.208831600642796805563854019033577205240227465154130766898180386564934443551840379116390645e-50"),
         boost::lexical_cast<T>("-0.819516067465171848863933747691434138146789031214932473898084756489529673230665363014007306e-56"),
         boost::lexical_cast<T>("0.365344970579318347488211604761724311582675708113250505307342682118101409913523622073678179e-62"),
         boost::lexical_cast<T>("-0.684593199208628857931267904308244537968349564351534581234005234847904343404822808648361291e-70"),
      };
      T result = 0;
      T z = dz + 2;
      for(int k = 1; k <= sizeof(d)/sizeof(d[0]); ++k)
      {
         result += (-d[k-1]*dz)/(z + k*z + k*k - 1);
      }
      return result;
   }

   static double g(){ return 63.19215200000000010049916454590857028961181640625; }
};

namespace boost{ namespace math{ namespace lanczos{

template<class Policy>
struct lanczos<boost::math::ntl::RR, Policy>
{
#ifdef L13
   typedef lanczos13UDT type;
#elif defined(L22)
   typedef lanczos22UDT type;
#elif defined(L31)
   typedef lanczos31UDT type;
#else
   typedef lanczos61UDT type;
#endif
};

}}}

#endif