ntl_rr_lanczos.hpp

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

         boost::lexical_cast<T>("283.8099337545793198947620951499958085157"),
         boost::lexical_cast<T>("-49.36969067101255103452092297769364837753"),
         boost::lexical_cast<T>("6.743492833270653628580811118017061581404"),
         boost::lexical_cast<T>("-0.7121578704864048548351804794951487823626"),
         boost::lexical_cast<T>("0.0570092738016915476694118877057948681298"),
         boost::lexical_cast<T>("-0.003373485297696102660302960722607722438643"),
         boost::lexical_cast<T>("0.0001429128843527532859999752593761934089751"),
         boost::lexical_cast<T>("-0.41595867130858508233493767243236888636e-5"),
         boost::lexical_cast<T>("0.7883284669307241040059778207492255409785e-7"),
         boost::lexical_cast<T>("-0.905786322462384670803148223703187214379e-9"),
         boost::lexical_cast<T>("0.5722790216999820323272452464661250331451e-11"),
         boost::lexical_cast<T>("-0.1731510870832349779315841757234562309727e-13"),
         boost::lexical_cast<T>("0.2043890314358438601429048378015983874378e-16"),
         boost::lexical_cast<T>("-0.6810185176079344204740000170500311171065e-20"),
         boost::lexical_cast<T>("0.3665567641131713928114853776588342403919e-24"),
         boost::lexical_cast<T>("-0.1060655106553177007425710511436497259484e-29"),
      };
      T result = 0;
      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);
      }
      return result;
   }

   static double g(){ return 32.08066999999999779902282170951366424561; }
};

//
// Lanczos Coefficients for N=61 G=63.192152
// Max experimental error (with 1000-bit precision arithmetic) 3.740e-113
// Generated with compiler: Microsoft Visual C++ version 8.0 on Win32 at Mar 12 2006
//
struct lanczos61UDT
{
   template <class T>
   static T lanczos_sum(const T& z)
   {
      using namespace boost;
      static const T d[61] = {
         boost::lexical_cast<T>("2.50662827463100050241576528481104525300698674060993831662992357634229365460784197494659584"),
         boost::lexical_cast<T>("13349415823254323512107320481.3495396037261649201426994438803767191136434970492309775123879"),
         boost::lexical_cast<T>("-300542621510568204264185787475.230003734889859348050696493467253861933279360152095861484548"),
         boost::lexical_cast<T>("3273919938390136737194044982676.40271056035622723775417608127544182097346526115858803376474"),
         boost::lexical_cast<T>("-22989594065095806099337396006399.5874206181563663855129141706748733174902067950115092492439"),
         boost::lexical_cast<T>("116970582893952893160414263796102.542775878583510989850142808618916073286745084692189044738"),
         boost::lexical_cast<T>("-459561969036479455224850813196807.283291532483532558959779434457349912822256480548436066098"),
         boost::lexical_cast<T>("1450959909778264914956547227964788.89797179379520834974601372820249784303794436366366810477"),
         boost::lexical_cast<T>("-3782846865486775046285288437885921.41537699732805465141128848354901016102326190612528503251"),
         boost::lexical_cast<T>("8305043213936355459145388670886540.09976337905520168067329932809302445437208115570138102767"),
         boost::lexical_cast<T>("-15580988484396722546934484726970745.4927787160273626078250810989811865283255762028143642311"),
         boost::lexical_cast<T>("25262722284076250779006793435537600.0822901485517345545978818780090308947301031347345640449"),
         boost::lexical_cast<T>("-35714428027687018805443603728757116.5304655170478705341887572982734901197345415291580897698"),
         boost::lexical_cast<T>("44334726194692443174715432419157343.2294160783772787096321009453791271387235388689346602833"),
         boost::lexical_cast<T>("-48599573547617297831555162417695106.187829304963846482633791012658974681648157963911491985"),
         boost::lexical_cast<T>("47258466493366798944386359199482189.0753349196625125615316002614813737880755896979754845101"),
         boost::lexical_cast<T>("-40913448215392412059728312039233342.142914753896559359297977982314043378636755884088383226"),
         boost::lexical_cast<T>("31626312914486892948769164616982902.7262756989418188077611392594232674722318027323102462687"),
         boost::lexical_cast<T>("-21878079174441332123064991795834438.4699982361692990285700077902601657354101259411789722708"),
         boost::lexical_cast<T>("13567268503974326527361474986354265.3136632133935430378937191911532112778452274286122946396"),
         boost::lexical_cast<T>("-7551494211746723529747611556474669.62996644923557605747803028485900789337467673523741066527"),
         boost::lexical_cast<T>("3775516572689476384052312341432597.70584966904950490541958869730702790312581801585742038997"),
         boost::lexical_cast<T>("-1696271471453637244930364711513292.79902955514107737992185368006225264329876265486853482449"),
         boost::lexical_cast<T>("684857608019352767999083000986166.20765273693720041519286231015176745354062413008561259139"),
         boost::lexical_cast<T>("-248397566275708464679881624417990.410438107634139924805871051723444048539177890346227250473"),
         boost::lexical_cast<T>("80880368999557992138783568858556.1512378233079327986518410244522800950609595592170022878937"),
         boost::lexical_cast<T>("-23618197945394013802495450485616.9025005749893350650829964098117490779655546610665927669729"),
         boost::lexical_cast<T>("6176884636893816103087134481332.06708966653493024119556843727320635285468825056891248447124"),
         boost::lexical_cast<T>("-1444348683723439589948246285262.64080678953468490544615312565485170860503207005915261691108"),
         boost::lexical_cast<T>("301342031656979076702313946827.961658905182634508217626783081241074250132289461989777865387"),
         boost::lexical_cast<T>("-55959656587719766738301589651.3940625826610668990368881615587469329021742236397809951765678"),
         boost::lexical_cast<T>("9223339169004064297247180402.36227016155682738556103138196079389248843082157924368301293963"),
         boost::lexical_cast<T>("-1344882881571942601385730283.42710150182526891377514071881534880944872423492272147871101373"),
         boost::lexical_cast<T>("172841913316760599352601139.54409257740173055624405575900164401527761357324625574736896079"),
         boost::lexical_cast<T>("-19496120443876233531343952.3802212016691702737346568192063937387825469602063310488794471653"),
         boost::lexical_cast<T>("1920907372583710284097959.44121420322495784420169085871802458519363819782779653621724219067"),
         boost::lexical_cast<T>("-164429314798240461613359.399597503536657962383155875723527581699785846599051112719962464604"),
         boost::lexical_cast<T>("12154026644351189572525.1452249886865981747374191977801688548318519692423556934568426042152"),
         boost::lexical_cast<T>("-770443988366210815096.519382051977221101156336663806705367929328924137169970381042234329058"),
         boost::lexical_cast<T>("41558909851418707920.4696085656889424895313728719601503526476333404973280596225722152966128"),
         boost::lexical_cast<T>("-1890879946549708819.24562220042687554209318172044783707920086716716717574156283898330017796"),
         boost::lexical_cast<T>("71844996557297623.9583461685535340440524052492427928388171299145330229958643439878608673403"),
         boost::lexical_cast<T>("-2253785109518255.55600197759875781765803818232939130127735487613049577235879610065545755637"),
         boost::lexical_cast<T>("57616883849355.997562563968344493719962252675875692642406455612671495250543228005045106721"),
         boost::lexical_cast<T>("-1182495730353.08218118278997948852215670614084013289033222774171548915344541249351599628436"),
         boost::lexical_cast<T>("19148649358.6196967288062261380599423925174178776792840639099120170800869284300966978300613"),
         boost::lexical_cast<T>("-239779605.891370259668403359614360511661030470269478602533200704639655585967442891496784613"),
         boost::lexical_cast<T>("2267583.00284368310957842936892685032434505866445291643236133553754152047677944820353796872"),
         boost::lexical_cast<T>("-15749.490806784673108773558070497383604733010677027764233749920147549999361110299643477893"),
         boost::lexical_cast<T>("77.7059495149052727171505425584459982871343274332635726864135949842508025564999785370162956"),
         boost::lexical_cast<T>("-0.261619987273930331397625130282851629108569607193781378836014468617185550622160348688297247"),
         boost::lexical_cast<T>("0.000572252321659691600529444769356185993188551770817110673186068921175991328434642504616377475"),
         boost::lexical_cast<T>("-0.765167220661540041663007112207436426423746402583423562585653954743978584117929356523307954e-6"),
         boost::lexical_cast<T>("0.579179571056209077507916813937971472839851499147582627425979879366849876944438724610663401e-9"),
         boost::lexical_cast<T>("-0.224804733043915149719206760378355636826808754704148660354494460792713189958510735070096991e-12"),
         boost::lexical_cast<T>("0.392711975389579343321746945135488409914483448652884894759297584020979857734289645857714768e-16"),
         boost::lexical_cast<T>("-0.258603588346412049542768766878162221817684639789901440429511261589010049357907537684380983e-20"),
         boost::lexical_cast<T>("0.499992460848751668441190360024540741752242879565548017176883304716370989218399797418478685e-25"),
         boost::lexical_cast<T>("-0.196211614533318174187346267877390498735734213905206562766348625767919122511096089367364025e-30"),
         boost::lexical_cast<T>("0.874722648949676363732094858062907290148733370978226751462386623191111439121706262759209573e-37"),
         boost::lexical_cast<T>("-0.163907874717737848669759890242660846846105433791283903651924563157080252845636658802930428e-44"),
      };
      T result = d[0];
      for(int k = 1; k < sizeof(d)/sizeof(d[0]); ++k)
      {
         result += d[k]/(z+(k-1));
      }
      return result;
   }

   template <class T>
   static T lanczos_sum_expG_scaled(const T& z)
   {
      using namespace boost;
      static const T d[61] = {
         boost::lexical_cast<T>("0.901751806425638853077358552989167785490911341809902155556127108480303870921448984935411583e-27"),
         boost::lexical_cast<T>("4.80241125306810017699523302110401965428995345115391817406006361151407344955277298373661032"),
         boost::lexical_cast<T>("-108.119283021710869401330097315436214587270846871451487282117128515476478251641970487922552"),
         boost::lexical_cast<T>("1177.78262074811362219818923738088833932279000985161077740440010901595132448469513438139561"),
         boost::lexical_cast<T>("-8270.43570321334374279057432173814835581983913167617217749736484999327758232081395983082867"),
         boost::lexical_cast<T>("42079.807161997077661752306902088979258826568702655699995911391774839958572703348502730394"),
         boost::lexical_cast<T>("-165326.003834443330215001219988296482004968548294447320869281647211603153902436231468280089"),
         boost::lexical_cast<T>("521978.361504895300685499370463597042533432134369277742485307843747923127933979566742421213"),
         boost::lexical_cast<T>("-1360867.51629992863544553419296636395576666570468519805449755596254912681418267100657262281"),
         boost::lexical_cast<T>("2987713.73338656161102517003716335104823650191612448011720936412226357385029800040631754755"),
         boost::lexical_cast<T>("-5605212.64915921452169919008770165304171481697939254152852673009005154549681704553438450709"),
         boost::lexical_cast<T>("9088186.58332916818449459635132673652700922052988327069535513580836143146727832380184335474"),
         boost::lexical_cast<T>("-12848155.5543636394746355365819800465364996596310467415907815393346205151090486190421959769"),
         boost::lexical_cast<T>("15949281.2867656960575878805158849857756293807220033618942867694361569866468996967761600898"),
         boost::lexical_cast<T>("-17483546.9948295433308250581770557182576171673272450149400973735206019559576269174369907171"),
         boost::lexical_cast<T>("17001087.8599749419660906448951424280111036786456594738278573653160553115681287326064596964"),
         boost::lexical_cast<T>("-14718487.0643665950346574802384331125115747311674609017568623694516187494204567579595827859"),
         boost::lexical_cast<T>("11377468.7255609717716845971105161298889777425898291183866813269222281486121330837791392732"),
         boost::lexical_cast<T>("-7870571.64253038587947746661946939286858490057774448573157856145556080330153403858747655263"),
         boost::lexical_cast<T>("4880783.08440908743641723492059912671377140680710345996273343885045364205895751515063844239"),
         boost::lexical_cast<T>("-2716626.7992639625103140035635916455652302249897918893040695025407382316653674141983775542"),
         boost::lexical_cast<T>("1358230.46602865696544327299659410214201327791319846880787515156343361311278133805428800255"),
         boost::lexical_cast<T>("-610228.440751458395860905749312275043435828322076830117123636938979942213530882048883969802"),
         boost::lexical_cast<T>("246375.416501158654327780901087115642493055617468601787093268312234390446439555559050129729"),
         boost::lexical_cast<T>("-89360.2599028475206119333931211015869139511677735549267100272095432140508089207221096740632"),
         boost::lexical_cast<T>("29096.4637987498328341260960356772198979319790332957125131055960448759586930781530063775634"),
         boost::lexical_cast<T>("-8496.57401431514433694413130585404918350686834939156759654375188338156288564260152505382438"),
         boost::lexical_cast<T>("2222.11523574301594407443285016240908726891841242444092960094015874546135316534057865883047"),
         boost::lexical_cast<T>("-519.599993280949289705514822058693289933461756514489674453254304308040888101533569480646682"),
         boost::lexical_cast<T>("108.406868361306987817730701109400305482972790224573776407166683184990131682003417239181112"),
         boost::lexical_cast<T>("-20.1313142142558596796857948064047373605439974799116521459977609253211918146595346493447238"),
         boost::lexical_cast<T>("3.31806787671783168020012913552384112429614503798293169239082032849759155847394955909684383"),
         boost::lexical_cast<T>("-0.483817477111537877685595212919784447924875428848331771524426361483392903320495411973587861"),
         boost::lexical_cast<T>("0.0621793463102927384924303843912913542297042029136293808338022462765755471002366206711862637"),
         boost::lexical_cast<T>("-0.00701366932085103924241526535768453911099671087892444015581511551813219720807206445462785293"),
         boost::lexical_cast<T>("0.000691040514756294308758606917671220770856269030526647010461217455799229645004351524024364997"),
         boost::lexical_cast<T>("-0.591529398871361458428147660822525365922497109038495896497692806150033516658042357799869656e-4"),
         boost::lexical_cast<T>("0.437237367535177689875119370170434437030440227275583289093139147244747901678407875809020739e-5"),
         boost::lexical_cast<T>("-0.277164853397051135996651958345647824709602266382721185838782221179129726200661453504250697e-6"),
         boost::lexical_cast<T>("0.149506899012035980148891401548317536032574502641368034781671941165064546410613201579653674e-7"),
         boost::lexical_cast<T>("-0.68023824066463262779882895193964639544061678698791279217407325790147925675797085217462974e-9"),
         boost::lexical_cast<T>("0.258460163734186329938721529982859244969655253624066115559707985878606277800329299821882688e-10"),
         boost::lexical_cast<T>("-0.810792256024669306744649981276512583535251727474303382740940985102669076169168931092026491e-12"),
         boost::lexical_cast<T>("0.207274966207031327521921078048021807442500113231320959236850963529304158700096495799022922e-13"),
         boost::lexical_cast<T>("-0.425399199286327802950259994834798737777721414442095221716122926637623478450472871269742436e-15"),
         boost::lexical_cast<T>("0.688866766744198529064607574117697940084548375790020728788313274612845280173338912495478431e-17"),
         boost::lexical_cast<T>("-0.862599751805643281578607291655858333628582704771553874199104377131082877406179933909898885e-19"),
         boost::lexical_cast<T>("0.815756005678735657200275584442908437977926312650210429668619446123450972547018343768177988e-21"),
         boost::lexical_cast<T>("-0.566583084099007858124915716926967268295318152203932871370429534546567151650626184750291695e-23"),
         boost::lexical_cast<T>("0.279544761599725082805446124351997692260093135930731230328454667675190245860598623539891708e-25"),
         boost::lexical_cast<T>("-0.941169851584987983984201821679114408126982142904386301937192011680047611188837432096199601e-28"),
         boost::lexical_cast<T>("0.205866011331040736302780507155525142187875191518455173304638008169488993406425201915370746e-30"),
         boost::lexical_cast<T>("-0.27526655245712584371295491216289353976964567057707464008951584303679019796521332324352501e-33"),
         boost::lexical_cast<T>("0.208358067979444305082929004102609366169534624348056112144990933897581971394396210379638792e-36"),
         boost::lexical_cast<T>("-0.808728107661779323263133007119729988596844663194254976820030366188579170595441991680169012e-40"),
         boost::lexical_cast<T>("0.141276924383478964519776436955079978012672985961918248012931336621229652792338950573694356e-43"),
         boost::lexical_cast<T>("-0.930318449287651389310440021745842417218125582685428432576258687100661462527604238849332053e-48"),
         boost::lexical_cast<T>("0.179870748819321661641184169834635133045197146966203370650788171790610563029431722308057539e-52"),
         boost::lexical_cast<T>("-0.705865243912790337263229413370018392321238639017433365017168104310561824133229343750737083e-58"),
         boost::lexical_cast<T>("0.3146787805734405996448268100558028857930560442377698646099945108125281507396722995748398e-64"),
         boost::lexical_cast<T>("-0.589653534231618730406843260601322236697428143603814281282790370329151249078338470962782338e-72"),
      };
      T result = d[0];
      for(int k = 1; k < sizeof(d)/sizeof(d[0]); ++k)
      {