| 12345678910111213141516171819202122232425262728293031323334353637383940414243444546474849505152535455565758596061626364656667686970717273747576777879808182838485868788899091929394959697989910010110210310410510610710810911011111211311411511611711811912012112212312412512612712812913013113213313413513613713813914014114214314414514614714814915015115215315415515615715815916016116216316416516616716816917017117217317417517617717817918018118218318418518618718818919019119219319419519619719819920020120220320420520620720820921021121221321421521621721821922022122222322422522622722822923023123223323423523623723823924024124224324424524624724824925025125225325425525625725825926026126226326426526626726826927027127227327427527627727827928028128228328428528628728828929029129229329429529629729829930030130230330430530630730830931031131231331431531631731831932032132232332432532632732832933033133233333433533633733833934034134234334434534634734834935035135235335435535635735835936036136236336436536636736836937037137237337437537637737837938038138238338438538638738838939039139239339439539639739839940040140240340440540640740840941041141241341441541641741841942042142242342442542642742842943043143243343443543643743843944044144244344444544644744844945045145245345445545645745845946046146246346446546646746846947047147247347447547647747847948048148248348448548648748848949049149249349449549649749849950050150250350450550650750850951051151251351451551651751851952052152252352452552652752852953053153253353453553653753853954054154254354454554654754854955055155255355455555655755855956056156256356456556656756856957057157257357457557657757857958058158258358458558658758858959059159259359459559659759859960060160260360460560660760860961061161261361461561661761861962062162262362462562662762862963063163263363463563663763863964064164264364464564664764864965065165265365465565665765865966066166266366466566666766866967067167267367467567667767867968068168268368468568668768868969069169269369469569669769869970070170270370470570670770870971071171271371471571671771871972072172272372472572672772872973073173273373473573673773873974074174274374474574674774874975075175275375475575675775875976076176276376476576676776876977077177277377477577677777877978078178278378478578678778878979079179279379479579679779879980080180280380480580680780880981081181281381481581681781881982082182282382482582682782882983083183283383483583683783883984084184284384484584684784884985085185285385485585685785885986086186286386486586686786886987087187287387487587687787887988088188288388488588688788888989089189289389489589689789889990090190290390490590690790890991091191291391491591691791891992092192292392492592692792892993093193293393493593693793893994094194294394494594694794894995095195295395495595695795895996096196296396496596696796896997097197297397497597697797897998098198298398498598698798898999099199299399499599699799899910001001100210031004100510061007100810091010101110121013101410151016101710181019102010211022102310241025102610271028102910301031103210331034103510361037103810391040104110421043104410451046104710481049105010511052105310541055105610571058105910601061106210631064106510661067106810691070107110721073107410751076107710781079108010811082108310841085108610871088108910901091109210931094109510961097109810991100110111021103110411051106110711081109111011111112111311141115111611171118111911201121112211231124112511261127112811291130113111321133113411351136113711381139114011411142114311441145114611471148114911501151115211531154115511561157115811591160116111621163116411651166116711681169117011711172117311741175117611771178117911801181118211831184118511861187118811891190119111921193119411951196119711981199120012011202120312041205120612071208120912101211121212131214121512161217121812191220122112221223122412251226122712281229123012311232123312341235123612371238123912401241124212431244124512461247124812491250125112521253125412551256125712581259126012611262126312641265126612671268126912701271127212731274127512761277127812791280128112821283128412851286128712881289129012911292129312941295129612971298129913001301130213031304130513061307130813091310131113121313131413151316131713181319132013211322132313241325132613271328132913301331133213331334133513361337133813391340134113421343134413451346134713481349135013511352135313541355135613571358135913601361136213631364136513661367136813691370137113721373137413751376137713781379138013811382138313841385138613871388138913901391139213931394139513961397139813991400140114021403140414051406140714081409141014111412141314141415141614171418141914201421142214231424142514261427142814291430143114321433143414351436143714381439144014411442144314441445144614471448144914501451145214531454145514561457145814591460146114621463146414651466146714681469147014711472147314741475147614771478147914801481148214831484148514861487148814891490149114921493149414951496149714981499150015011502150315041505150615071508150915101511151215131514151515161517151815191520152115221523152415251526152715281529153015311532153315341535153615371538153915401541154215431544154515461547154815491550155115521553155415551556155715581559156015611562156315641565156615671568156915701571157215731574157515761577157815791580158115821583158415851586158715881589159015911592159315941595159615971598159916001601160216031604160516061607160816091610161116121613161416151616161716181619162016211622162316241625162616271628162916301631163216331634163516361637163816391640164116421643164416451646164716481649165016511652165316541655165616571658165916601661166216631664166516661667166816691670167116721673167416751676167716781679168016811682168316841685168616871688168916901691169216931694169516961697169816991700170117021703170417051706170717081709171017111712171317141715171617171718171917201721172217231724172517261727172817291730173117321733173417351736173717381739174017411742174317441745174617471748174917501751175217531754175517561757175817591760176117621763176417651766176717681769177017711772177317741775177617771778177917801781178217831784178517861787178817891790179117921793179417951796179717981799180018011802180318041805180618071808180918101811181218131814181518161817181818191820182118221823182418251826182718281829183018311832183318341835183618371838183918401841184218431844184518461847184818491850185118521853185418551856185718581859186018611862186318641865186618671868186918701871187218731874187518761877187818791880188118821883188418851886188718881889189018911892189318941895189618971898189919001901190219031904190519061907190819091910191119121913191419151916191719181919192019211922192319241925192619271928192919301931193219331934193519361937193819391940194119421943194419451946194719481949195019511952195319541955195619571958195919601961196219631964196519661967196819691970197119721973197419751976197719781979198019811982198319841985198619871988198919901991199219931994199519961997199819992000200120022003200420052006200720082009201020112012201320142015201620172018201920202021202220232024202520262027202820292030203120322033203420352036203720382039204020412042204320442045204620472048204920502051205220532054205520562057205820592060206120622063206420652066206720682069207020712072207320742075207620772078207920802081208220832084208520862087208820892090209120922093209420952096209720982099210021012102210321042105210621072108210921102111211221132114211521162117211821192120212121222123212421252126212721282129213021312132213321342135213621372138213921402141214221432144214521462147214821492150215121522153215421552156215721582159216021612162216321642165216621672168216921702171217221732174217521762177217821792180218121822183218421852186218721882189219021912192219321942195219621972198219922002201220222032204220522062207220822092210221122122213221422152216221722182219222022212222222322242225222622272228222922302231223222332234223522362237223822392240224122422243224422452246224722482249225022512252225322542255225622572258225922602261226222632264226522662267226822692270227122722273227422752276227722782279228022812282228322842285228622872288228922902291229222932294229522962297229822992300230123022303230423052306230723082309231023112312231323142315231623172318231923202321232223232324232523262327232823292330233123322333233423352336233723382339234023412342234323442345234623472348234923502351235223532354235523562357235823592360236123622363236423652366236723682369237023712372237323742375237623772378237923802381238223832384238523862387238823892390239123922393239423952396239723982399240024012402240324042405240624072408240924102411241224132414241524162417241824192420242124222423242424252426242724282429243024312432243324342435243624372438243924402441244224432444244524462447244824492450245124522453245424552456245724582459246024612462246324642465246624672468246924702471247224732474247524762477247824792480248124822483248424852486248724882489249024912492249324942495249624972498249925002501250225032504250525062507250825092510251125122513251425152516251725182519252025212522252325242525252625272528252925302531253225332534253525362537253825392540254125422543254425452546254725482549255025512552255325542555255625572558255925602561256225632564256525662567256825692570257125722573257425752576257725782579258025812582258325842585258625872588258925902591259225932594259525962597259825992600260126022603260426052606260726082609261026112612261326142615261626172618261926202621262226232624262526262627262826292630263126322633263426352636263726382639264026412642264326442645264626472648264926502651265226532654265526562657265826592660266126622663266426652666266726682669267026712672267326742675267626772678267926802681268226832684268526862687268826892690269126922693269426952696269726982699270027012702270327042705270627072708270927102711271227132714271527162717271827192720272127222723272427252726272727282729273027312732273327342735273627372738273927402741274227432744274527462747274827492750275127522753275427552756275727582759276027612762276327642765276627672768276927702771277227732774277527762777277827792780278127822783278427852786278727882789279027912792279327942795279627972798279928002801280228032804280528062807280828092810281128122813281428152816281728182819282028212822282328242825282628272828282928302831283228332834283528362837283828392840284128422843284428452846284728482849285028512852285328542855285628572858285928602861286228632864286528662867286828692870287128722873287428752876287728782879288028812882288328842885288628872888288928902891289228932894289528962897289828992900290129022903290429052906290729082909291029112912291329142915291629172918291929202921292229232924292529262927292829292930293129322933293429352936293729382939294029412942294329442945294629472948294929502951295229532954295529562957295829592960296129622963296429652966296729682969297029712972297329742975297629772978297929802981298229832984298529862987298829892990299129922993299429952996299729982999300030013002300330043005300630073008300930103011301230133014301530163017301830193020302130223023302430253026302730283029303030313032303330343035303630373038303930403041304230433044304530463047304830493050305130523053305430553056305730583059306030613062306330643065306630673068306930703071307230733074307530763077307830793080308130823083308430853086308730883089309030913092309330943095309630973098309931003101310231033104310531063107310831093110311131123113311431153116311731183119312031213122312331243125312631273128312931303131313231333134313531363137313831393140314131423143314431453146314731483149315031513152315331543155315631573158315931603161316231633164316531663167316831693170317131723173317431753176317731783179318031813182318331843185318631873188318931903191319231933194319531963197319831993200320132023203320432053206320732083209321032113212321332143215321632173218321932203221322232233224322532263227322832293230323132323233323432353236323732383239324032413242324332443245324632473248324932503251325232533254325532563257325832593260326132623263326432653266326732683269327032713272327332743275327632773278327932803281328232833284328532863287328832893290329132923293329432953296329732983299330033013302330333043305330633073308330933103311331233133314331533163317331833193320332133223323332433253326332733283329333033313332333333343335333633373338333933403341334233433344334533463347334833493350335133523353335433553356335733583359336033613362336333643365336633673368336933703371337233733374337533763377337833793380338133823383338433853386338733883389339033913392339333943395339633973398339934003401340234033404340534063407340834093410341134123413341434153416341734183419342034213422342334243425342634273428342934303431343234333434343534363437343834393440344134423443344434453446344734483449345034513452345334543455345634573458345934603461346234633464346534663467346834693470347134723473347434753476347734783479348034813482348334843485348634873488348934903491349234933494349534963497349834993500350135023503350435053506350735083509351035113512351335143515351635173518351935203521352235233524352535263527352835293530353135323533353435353536353735383539354035413542354335443545354635473548354935503551355235533554355535563557355835593560356135623563356435653566356735683569357035713572357335743575357635773578357935803581358235833584358535863587358835893590359135923593359435953596359735983599360036013602360336043605360636073608360936103611361236133614361536163617361836193620362136223623362436253626362736283629363036313632363336343635363636373638363936403641364236433644364536463647364836493650365136523653365436553656365736583659366036613662366336643665366636673668366936703671367236733674367536763677367836793680368136823683368436853686368736883689369036913692369336943695369636973698369937003701370237033704370537063707370837093710371137123713371437153716371737183719372037213722372337243725372637273728372937303731373237333734373537363737373837393740374137423743374437453746374737483749375037513752375337543755375637573758375937603761376237633764376537663767376837693770377137723773377437753776377737783779378037813782378337843785378637873788378937903791379237933794379537963797379837993800380138023803380438053806380738083809381038113812381338143815381638173818381938203821382238233824382538263827382838293830383138323833383438353836383738383839384038413842384338443845384638473848384938503851385238533854385538563857385838593860386138623863386438653866386738683869387038713872387338743875387638773878387938803881388238833884388538863887388838893890389138923893389438953896389738983899390039013902390339043905390639073908390939103911391239133914391539163917391839193920392139223923392439253926392739283929393039313932393339343935393639373938393939403941394239433944394539463947394839493950395139523953395439553956395739583959396039613962396339643965396639673968396939703971397239733974397539763977397839793980398139823983398439853986398739883989399039913992399339943995399639973998399940004001400240034004400540064007400840094010401140124013401440154016401740184019402040214022402340244025402640274028402940304031403240334034403540364037403840394040404140424043404440454046404740484049405040514052405340544055405640574058405940604061406240634064406540664067406840694070407140724073407440754076407740784079408040814082408340844085408640874088408940904091409240934094409540964097409840994100410141024103410441054106410741084109411041114112411341144115411641174118411941204121412241234124412541264127412841294130413141324133413441354136413741384139414041414142414341444145414641474148414941504151415241534154415541564157415841594160416141624163416441654166416741684169417041714172417341744175417641774178417941804181418241834184418541864187418841894190419141924193419441954196419741984199420042014202420342044205420642074208420942104211421242134214421542164217421842194220422142224223422442254226422742284229423042314232423342344235423642374238423942404241424242434244424542464247424842494250425142524253425442554256425742584259426042614262426342644265426642674268426942704271427242734274427542764277427842794280428142824283428442854286428742884289429042914292429342944295429642974298429943004301430243034304430543064307430843094310431143124313431443154316431743184319432043214322432343244325432643274328432943304331433243334334433543364337433843394340434143424343434443454346434743484349435043514352435343544355435643574358435943604361436243634364436543664367436843694370437143724373437443754376437743784379438043814382438343844385438643874388438943904391439243934394439543964397439843994400440144024403440444054406440744084409441044114412441344144415441644174418441944204421442244234424442544264427442844294430443144324433443444354436443744384439444044414442444344444445444644474448444944504451445244534454445544564457445844594460446144624463446444654466446744684469447044714472447344744475447644774478447944804481448244834484448544864487448844894490449144924493449444954496449744984499450045014502450345044505450645074508450945104511451245134514451545164517451845194520452145224523452445254526452745284529453045314532453345344535453645374538453945404541454245434544454545464547454845494550455145524553455445554556455745584559456045614562456345644565456645674568456945704571457245734574457545764577457845794580458145824583458445854586458745884589459045914592459345944595459645974598459946004601460246034604460546064607460846094610461146124613461446154616461746184619462046214622462346244625462646274628462946304631463246334634463546364637463846394640464146424643464446454646464746484649465046514652465346544655465646574658465946604661466246634664466546664667466846694670467146724673467446754676467746784679468046814682468346844685468646874688468946904691469246934694469546964697469846994700470147024703470447054706470747084709471047114712471347144715471647174718471947204721472247234724472547264727472847294730473147324733473447354736473747384739474047414742474347444745474647474748474947504751475247534754475547564757475847594760476147624763476447654766476747684769477047714772477347744775477647774778477947804781478247834784478547864787478847894790479147924793479447954796479747984799480048014802480348044805480648074808480948104811481248134814481548164817481848194820482148224823482448254826482748284829483048314832483348344835483648374838483948404841484248434844484548464847484848494850485148524853485448554856485748584859486048614862486348644865486648674868486948704871487248734874487548764877487848794880488148824883488448854886488748884889489048914892489348944895489648974898489949004901490249034904490549064907490849094910491149124913491449154916491749184919492049214922492349244925492649274928492949304931493249334934493549364937493849394940494149424943494449454946494749484949495049514952495349544955495649574958495949604961496249634964496549664967496849694970497149724973497449754976497749784979498049814982498349844985498649874988498949904991499249934994499549964997499849995000500150025003500450055006500750085009501050115012501350145015501650175018501950205021502250235024502550265027502850295030503150325033503450355036503750385039504050415042504350445045504650475048504950505051505250535054505550565057505850595060506150625063506450655066506750685069507050715072507350745075507650775078507950805081508250835084508550865087508850895090509150925093509450955096509750985099510051015102510351045105510651075108510951105111511251135114511551165117511851195120512151225123512451255126512751285129513051315132513351345135513651375138513951405141514251435144514551465147514851495150515151525153515451555156515751585159516051615162516351645165516651675168516951705171517251735174517551765177517851795180518151825183518451855186518751885189519051915192519351945195519651975198519952005201520252035204520552065207520852095210521152125213521452155216521752185219522052215222522352245225522652275228522952305231523252335234523552365237523852395240524152425243524452455246524752485249525052515252525352545255525652575258525952605261526252635264526552665267526852695270527152725273527452755276527752785279528052815282528352845285528652875288528952905291529252935294529552965297529852995300530153025303530453055306530753085309531053115312531353145315531653175318531953205321532253235324532553265327532853295330533153325333533453355336533753385339534053415342534353445345534653475348534953505351535253535354535553565357535853595360536153625363536453655366536753685369537053715372537353745375537653775378537953805381538253835384538553865387538853895390539153925393539453955396539753985399540054015402540354045405540654075408540954105411541254135414541554165417541854195420542154225423542454255426542754285429543054315432543354345435543654375438543954405441544254435444544554465447544854495450545154525453545454555456545754585459546054615462546354645465546654675468546954705471547254735474547554765477547854795480548154825483548454855486548754885489549054915492549354945495549654975498549955005501550255035504550555065507550855095510551155125513551455155516551755185519552055215522552355245525552655275528552955305531553255335534553555365537553855395540554155425543554455455546554755485549555055515552555355545555555655575558555955605561556255635564556555665567556855695570557155725573557455755576557755785579558055815582558355845585558655875588558955905591559255935594559555965597559855995600560156025603560456055606560756085609561056115612561356145615561656175618561956205621562256235624562556265627562856295630563156325633563456355636563756385639564056415642564356445645564656475648564956505651565256535654565556565657565856595660566156625663566456655666566756685669567056715672567356745675567656775678567956805681568256835684568556865687568856895690569156925693569456955696569756985699570057015702570357045705570657075708570957105711571257135714571557165717571857195720572157225723572457255726572757285729573057315732573357345735573657375738573957405741574257435744574557465747574857495750575157525753575457555756575757585759576057615762576357645765576657675768576957705771577257735774577557765777577857795780578157825783578457855786578757885789579057915792579357945795579657975798579958005801580258035804580558065807580858095810581158125813581458155816581758185819582058215822582358245825582658275828582958305831583258335834583558365837583858395840584158425843584458455846584758485849585058515852585358545855585658575858585958605861586258635864586558665867586858695870587158725873587458755876587758785879588058815882588358845885588658875888588958905891589258935894589558965897589858995900590159025903590459055906590759085909591059115912591359145915591659175918591959205921592259235924592559265927592859295930593159325933593459355936593759385939594059415942594359445945594659475948594959505951595259535954595559565957595859595960596159625963596459655966596759685969597059715972597359745975597659775978597959805981598259835984598559865987598859895990599159925993599459955996599759985999600060016002600360046005600660076008600960106011601260136014601560166017601860196020602160226023602460256026602760286029603060316032603360346035603660376038603960406041604260436044604560466047604860496050605160526053605460556056605760586059606060616062606360646065606660676068606960706071607260736074607560766077607860796080608160826083608460856086608760886089609060916092609360946095609660976098609961006101610261036104610561066107610861096110611161126113611461156116611761186119612061216122612361246125612661276128612961306131613261336134613561366137613861396140614161426143614461456146614761486149615061516152615361546155615661576158615961606161616261636164616561666167616861696170617161726173617461756176617761786179618061816182618361846185618661876188618961906191619261936194619561966197619861996200620162026203620462056206620762086209621062116212621362146215621662176218621962206221622262236224622562266227622862296230623162326233623462356236623762386239624062416242624362446245624662476248624962506251625262536254625562566257625862596260626162626263626462656266626762686269627062716272627362746275627662776278627962806281628262836284628562866287628862896290629162926293629462956296629762986299630063016302630363046305630663076308630963106311631263136314631563166317631863196320632163226323632463256326632763286329633063316332633363346335633663376338633963406341634263436344634563466347634863496350635163526353635463556356635763586359636063616362636363646365636663676368636963706371637263736374637563766377637863796380638163826383638463856386638763886389639063916392639363946395639663976398639964006401640264036404640564066407640864096410641164126413641464156416641764186419642064216422642364246425642664276428642964306431643264336434643564366437643864396440644164426443644464456446644764486449645064516452645364546455645664576458645964606461646264636464646564666467646864696470647164726473647464756476647764786479648064816482648364846485648664876488648964906491649264936494649564966497649864996500650165026503650465056506650765086509651065116512651365146515651665176518651965206521652265236524652565266527652865296530653165326533653465356536653765386539654065416542654365446545654665476548654965506551655265536554655565566557655865596560656165626563656465656566656765686569657065716572657365746575657665776578657965806581658265836584658565866587658865896590659165926593659465956596659765986599660066016602660366046605660666076608660966106611661266136614661566166617661866196620662166226623662466256626662766286629663066316632663366346635663666376638663966406641664266436644664566466647664866496650665166526653665466556656665766586659666066616662666366646665666666676668666966706671667266736674667566766677667866796680668166826683668466856686668766886689669066916692669366946695669666976698669967006701670267036704670567066707670867096710671167126713671467156716671767186719672067216722672367246725672667276728672967306731673267336734673567366737673867396740674167426743674467456746674767486749675067516752675367546755675667576758675967606761676267636764676567666767676867696770677167726773677467756776677767786779678067816782678367846785678667876788678967906791679267936794679567966797679867996800680168026803680468056806680768086809681068116812681368146815681668176818681968206821682268236824682568266827682868296830683168326833683468356836683768386839684068416842684368446845684668476848684968506851685268536854685568566857685868596860686168626863686468656866686768686869687068716872687368746875687668776878687968806881688268836884688568866887688868896890689168926893689468956896689768986899690069016902690369046905690669076908690969106911691269136914691569166917691869196920692169226923692469256926692769286929693069316932693369346935693669376938693969406941694269436944694569466947694869496950695169526953695469556956695769586959696069616962696369646965696669676968696969706971697269736974697569766977697869796980698169826983698469856986698769886989699069916992699369946995699669976998699970007001700270037004700570067007700870097010701170127013701470157016701770187019702070217022702370247025702670277028702970307031703270337034703570367037703870397040704170427043704470457046704770487049705070517052705370547055705670577058705970607061706270637064706570667067706870697070707170727073707470757076707770787079708070817082708370847085708670877088708970907091709270937094709570967097709870997100710171027103710471057106710771087109711071117112711371147115711671177118711971207121712271237124712571267127712871297130713171327133713471357136713771387139714071417142714371447145714671477148714971507151715271537154715571567157715871597160716171627163716471657166716771687169717071717172717371747175717671777178717971807181718271837184718571867187718871897190719171927193719471957196719771987199720072017202720372047205720672077208720972107211721272137214721572167217721872197220722172227223722472257226722772287229723072317232723372347235723672377238723972407241724272437244724572467247724872497250725172527253725472557256725772587259726072617262726372647265726672677268726972707271727272737274727572767277727872797280728172827283728472857286728772887289729072917292729372947295729672977298729973007301730273037304730573067307730873097310731173127313731473157316731773187319732073217322732373247325732673277328732973307331733273337334733573367337733873397340734173427343734473457346734773487349735073517352735373547355735673577358735973607361736273637364736573667367736873697370737173727373737473757376737773787379738073817382738373847385738673877388738973907391739273937394739573967397739873997400740174027403740474057406740774087409741074117412741374147415741674177418741974207421742274237424742574267427742874297430743174327433743474357436743774387439744074417442744374447445744674477448744974507451745274537454745574567457745874597460746174627463746474657466746774687469747074717472747374747475747674777478747974807481748274837484748574867487748874897490749174927493749474957496749774987499750075017502750375047505750675077508750975107511751275137514751575167517751875197520752175227523752475257526752775287529753075317532753375347535753675377538753975407541754275437544754575467547754875497550755175527553755475557556755775587559756075617562756375647565756675677568756975707571757275737574757575767577757875797580758175827583758475857586758775887589759075917592759375947595759675977598759976007601760276037604760576067607760876097610761176127613761476157616761776187619762076217622762376247625762676277628762976307631763276337634763576367637763876397640764176427643764476457646764776487649765076517652765376547655765676577658765976607661766276637664766576667667766876697670767176727673767476757676767776787679768076817682768376847685768676877688768976907691769276937694769576967697769876997700770177027703770477057706770777087709771077117712771377147715771677177718771977207721772277237724772577267727772877297730773177327733773477357736773777387739774077417742774377447745774677477748774977507751775277537754775577567757775877597760776177627763776477657766776777687769777077717772777377747775777677777778777977807781778277837784778577867787778877897790779177927793779477957796779777987799780078017802780378047805780678077808780978107811781278137814781578167817781878197820782178227823782478257826782778287829783078317832783378347835783678377838783978407841784278437844784578467847784878497850785178527853785478557856785778587859786078617862786378647865786678677868786978707871787278737874787578767877787878797880788178827883788478857886788778887889789078917892789378947895789678977898789979007901790279037904790579067907790879097910791179127913791479157916791779187919792079217922792379247925792679277928792979307931793279337934793579367937793879397940794179427943794479457946794779487949795079517952795379547955795679577958795979607961796279637964796579667967796879697970797179727973797479757976797779787979798079817982798379847985798679877988798979907991799279937994799579967997799879998000800180028003800480058006800780088009801080118012801380148015801680178018801980208021802280238024802580268027802880298030803180328033803480358036803780388039804080418042804380448045804680478048804980508051805280538054805580568057805880598060806180628063806480658066806780688069807080718072807380748075807680778078807980808081808280838084808580868087808880898090809180928093809480958096809780988099810081018102810381048105810681078108810981108111811281138114811581168117811881198120812181228123812481258126812781288129813081318132813381348135813681378138813981408141814281438144814581468147814881498150815181528153815481558156815781588159816081618162816381648165816681678168816981708171817281738174817581768177817881798180818181828183818481858186818781888189819081918192819381948195819681978198819982008201820282038204820582068207820882098210821182128213821482158216821782188219822082218222822382248225822682278228822982308231823282338234823582368237823882398240824182428243824482458246824782488249825082518252825382548255825682578258825982608261826282638264826582668267826882698270827182728273827482758276827782788279828082818282828382848285828682878288828982908291829282938294829582968297829882998300830183028303830483058306830783088309831083118312831383148315831683178318831983208321832283238324832583268327832883298330833183328333833483358336833783388339834083418342834383448345834683478348834983508351835283538354835583568357835883598360836183628363836483658366836783688369837083718372837383748375837683778378837983808381838283838384838583868387838883898390839183928393839483958396839783988399840084018402840384048405840684078408840984108411841284138414841584168417841884198420842184228423842484258426842784288429843084318432843384348435843684378438843984408441844284438444844584468447844884498450845184528453845484558456845784588459846084618462846384648465846684678468846984708471847284738474847584768477847884798480848184828483848484858486848784888489849084918492849384948495849684978498849985008501850285038504850585068507850885098510851185128513851485158516851785188519852085218522852385248525852685278528852985308531853285338534853585368537853885398540854185428543854485458546854785488549855085518552855385548555855685578558855985608561856285638564856585668567856885698570857185728573857485758576857785788579858085818582858385848585858685878588858985908591859285938594859585968597859885998600860186028603860486058606860786088609861086118612861386148615861686178618861986208621862286238624862586268627862886298630863186328633863486358636863786388639864086418642864386448645864686478648864986508651865286538654865586568657865886598660866186628663866486658666866786688669867086718672867386748675867686778678867986808681868286838684868586868687868886898690869186928693869486958696869786988699870087018702870387048705870687078708870987108711871287138714871587168717871887198720872187228723872487258726872787288729873087318732873387348735873687378738873987408741874287438744874587468747874887498750875187528753875487558756875787588759876087618762876387648765876687678768876987708771877287738774877587768777877887798780878187828783878487858786878787888789879087918792879387948795879687978798879988008801880288038804880588068807880888098810881188128813881488158816881788188819882088218822882388248825882688278828882988308831883288338834883588368837883888398840884188428843884488458846884788488849885088518852885388548855885688578858885988608861886288638864886588668867886888698870887188728873887488758876887788788879888088818882888388848885888688878888888988908891889288938894889588968897889888998900890189028903890489058906890789088909891089118912891389148915891689178918891989208921892289238924892589268927892889298930893189328933893489358936893789388939894089418942894389448945894689478948894989508951895289538954895589568957895889598960896189628963896489658966896789688969897089718972897389748975897689778978897989808981898289838984898589868987898889898990899189928993899489958996899789988999900090019002900390049005900690079008900990109011901290139014901590169017901890199020902190229023902490259026902790289029903090319032903390349035903690379038903990409041904290439044904590469047904890499050905190529053905490559056905790589059906090619062906390649065906690679068906990709071907290739074907590769077907890799080908190829083908490859086908790889089909090919092909390949095909690979098909991009101910291039104910591069107910891099110911191129113911491159116911791189119912091219122912391249125912691279128912991309131913291339134913591369137913891399140914191429143914491459146914791489149915091519152915391549155915691579158915991609161916291639164916591669167916891699170917191729173917491759176917791789179918091819182918391849185918691879188918991909191919291939194919591969197919891999200920192029203920492059206920792089209921092119212921392149215921692179218921992209221922292239224922592269227922892299230923192329233923492359236923792389239924092419242924392449245924692479248924992509251925292539254925592569257925892599260926192629263926492659266926792689269927092719272927392749275927692779278927992809281928292839284928592869287928892899290929192929293929492959296929792989299930093019302930393049305930693079308930993109311931293139314931593169317931893199320932193229323932493259326932793289329933093319332933393349335933693379338933993409341934293439344934593469347934893499350935193529353935493559356935793589359936093619362936393649365936693679368936993709371937293739374937593769377937893799380938193829383938493859386938793889389939093919392939393949395939693979398939994009401940294039404940594069407940894099410941194129413941494159416941794189419942094219422942394249425942694279428942994309431943294339434943594369437943894399440944194429443944494459446944794489449945094519452945394549455945694579458945994609461946294639464946594669467946894699470947194729473947494759476947794789479948094819482948394849485948694879488948994909491949294939494949594969497949894999500950195029503950495059506950795089509951095119512951395149515951695179518951995209521952295239524952595269527952895299530953195329533953495359536953795389539954095419542954395449545954695479548954995509551955295539554955595569557955895599560956195629563956495659566956795689569957095719572957395749575957695779578957995809581958295839584958595869587958895899590959195929593959495959596959795989599960096019602960396049605960696079608960996109611961296139614961596169617961896199620962196229623962496259626962796289629963096319632963396349635963696379638963996409641964296439644964596469647964896499650965196529653965496559656965796589659966096619662966396649665966696679668966996709671967296739674967596769677967896799680968196829683968496859686968796889689969096919692969396949695969696979698969997009701970297039704970597069707970897099710971197129713971497159716971797189719972097219722972397249725972697279728972997309731973297339734973597369737973897399740974197429743974497459746974797489749975097519752975397549755975697579758975997609761976297639764976597669767976897699770977197729773977497759776977797789779978097819782978397849785978697879788978997909791979297939794979597969797979897999800980198029803980498059806980798089809981098119812981398149815981698179818981998209821982298239824982598269827982898299830983198329833983498359836983798389839984098419842984398449845984698479848984998509851985298539854985598569857985898599860986198629863986498659866986798689869987098719872987398749875987698779878987998809881988298839884988598869887988898899890989198929893989498959896989798989899990099019902990399049905990699079908990999109911991299139914991599169917991899199920992199229923992499259926992799289929993099319932993399349935993699379938993999409941994299439944994599469947994899499950995199529953995499559956995799589959996099619962996399649965996699679968996999709971997299739974997599769977997899799980998199829983998499859986998799889989999099919992999399949995999699979998999910000100011000210003100041000510006100071000810009100101001110012100131001410015100161001710018100191002010021100221002310024100251002610027100281002910030100311003210033100341003510036100371003810039100401004110042100431004410045100461004710048100491005010051100521005310054100551005610057100581005910060100611006210063100641006510066100671006810069100701007110072100731007410075100761007710078100791008010081100821008310084100851008610087100881008910090100911009210093100941009510096100971009810099101001010110102101031010410105101061010710108101091011010111101121011310114101151011610117101181011910120101211012210123101241012510126101271012810129101301013110132101331013410135101361013710138101391014010141101421014310144101451014610147101481014910150101511015210153101541015510156101571015810159101601016110162101631016410165101661016710168101691017010171101721017310174101751017610177101781017910180101811018210183101841018510186101871018810189101901019110192101931019410195101961019710198101991020010201102021020310204102051020610207102081020910210102111021210213102141021510216102171021810219102201022110222102231022410225102261022710228102291023010231102321023310234102351023610237102381023910240102411024210243102441024510246102471024810249102501025110252102531025410255102561025710258102591026010261102621026310264102651026610267102681026910270102711027210273102741027510276102771027810279102801028110282102831028410285102861028710288102891029010291102921029310294102951029610297102981029910300103011030210303103041030510306103071030810309103101031110312103131031410315103161031710318103191032010321103221032310324103251032610327103281032910330103311033210333103341033510336103371033810339103401034110342103431034410345103461034710348103491035010351103521035310354103551035610357103581035910360103611036210363103641036510366103671036810369103701037110372103731037410375103761037710378103791038010381103821038310384103851038610387103881038910390103911039210393103941039510396103971039810399104001040110402104031040410405104061040710408104091041010411104121041310414104151041610417104181041910420104211042210423104241042510426104271042810429104301043110432104331043410435104361043710438104391044010441104421044310444104451044610447104481044910450104511045210453104541045510456104571045810459104601046110462104631046410465104661046710468104691047010471104721047310474104751047610477104781047910480104811048210483104841048510486104871048810489104901049110492104931049410495104961049710498104991050010501105021050310504105051050610507105081050910510105111051210513105141051510516105171051810519105201052110522105231052410525105261052710528105291053010531105321053310534105351053610537105381053910540105411054210543105441054510546105471054810549105501055110552105531055410555105561055710558105591056010561105621056310564105651056610567105681056910570105711057210573105741057510576105771057810579105801058110582105831058410585105861058710588105891059010591105921059310594105951059610597105981059910600106011060210603106041060510606106071060810609106101061110612106131061410615106161061710618106191062010621106221062310624106251062610627106281062910630106311063210633106341063510636106371063810639106401064110642106431064410645106461064710648106491065010651106521065310654106551065610657106581065910660106611066210663106641066510666106671066810669106701067110672106731067410675106761067710678106791068010681106821068310684106851068610687106881068910690106911069210693106941069510696106971069810699107001070110702107031070410705107061070710708107091071010711107121071310714107151071610717107181071910720107211072210723107241072510726107271072810729107301073110732107331073410735107361073710738107391074010741107421074310744107451074610747107481074910750107511075210753107541075510756107571075810759107601076110762107631076410765107661076710768107691077010771107721077310774107751077610777107781077910780107811078210783107841078510786107871078810789107901079110792107931079410795107961079710798107991080010801108021080310804108051080610807108081080910810108111081210813108141081510816108171081810819108201082110822108231082410825108261082710828108291083010831108321083310834108351083610837108381083910840108411084210843108441084510846108471084810849108501085110852108531085410855108561085710858108591086010861108621086310864108651086610867108681086910870108711087210873108741087510876108771087810879108801088110882108831088410885108861088710888108891089010891108921089310894108951089610897108981089910900109011090210903109041090510906109071090810909109101091110912109131091410915109161091710918109191092010921109221092310924109251092610927109281092910930109311093210933109341093510936109371093810939109401094110942109431094410945109461094710948109491095010951109521095310954109551095610957109581095910960109611096210963109641096510966109671096810969109701097110972109731097410975109761097710978109791098010981109821098310984109851098610987109881098910990109911099210993109941099510996109971099810999110001100111002110031100411005110061100711008110091101011011110121101311014110151101611017110181101911020110211102211023110241102511026110271102811029110301103111032110331103411035110361103711038110391104011041110421104311044110451104611047110481104911050110511105211053110541105511056110571105811059110601106111062110631106411065110661106711068110691107011071110721107311074110751107611077110781107911080110811108211083110841108511086110871108811089110901109111092110931109411095110961109711098110991110011101111021110311104111051110611107111081110911110111111111211113111141111511116111171111811119111201112111122111231112411125111261112711128111291113011131111321113311134111351113611137111381113911140111411114211143111441114511146111471114811149111501115111152111531115411155111561115711158111591116011161111621116311164111651116611167111681116911170111711117211173111741117511176111771117811179111801118111182111831118411185111861118711188111891119011191111921119311194111951119611197111981119911200112011120211203112041120511206112071120811209112101121111212112131121411215112161121711218112191122011221112221122311224112251122611227112281122911230112311123211233112341123511236112371123811239112401124111242112431124411245112461124711248112491125011251112521125311254112551125611257112581125911260112611126211263112641126511266112671126811269112701127111272112731127411275112761127711278112791128011281112821128311284112851128611287112881128911290112911129211293112941129511296112971129811299113001130111302113031130411305113061130711308113091131011311113121131311314113151131611317113181131911320113211132211323113241132511326113271132811329113301133111332113331133411335113361133711338113391134011341113421134311344113451134611347113481134911350113511135211353113541135511356113571135811359113601136111362113631136411365113661136711368113691137011371113721137311374113751137611377113781137911380113811138211383113841138511386113871138811389113901139111392113931139411395113961139711398113991140011401114021140311404114051140611407114081140911410114111141211413114141141511416114171141811419114201142111422114231142411425114261142711428114291143011431114321143311434114351143611437114381143911440114411144211443114441144511446114471144811449114501145111452114531145411455114561145711458114591146011461114621146311464114651146611467114681146911470114711147211473114741147511476114771147811479114801148111482114831148411485114861148711488114891149011491114921149311494114951149611497114981149911500115011150211503115041150511506115071150811509115101151111512115131151411515115161151711518115191152011521115221152311524115251152611527115281152911530115311153211533115341153511536115371153811539115401154111542115431154411545115461154711548115491155011551115521155311554115551155611557115581155911560115611156211563115641156511566115671156811569115701157111572115731157411575115761157711578115791158011581115821158311584115851158611587115881158911590115911159211593115941159511596115971159811599116001160111602116031160411605116061160711608116091161011611116121161311614116151161611617116181161911620116211162211623116241162511626116271162811629116301163111632116331163411635116361163711638116391164011641116421164311644116451164611647116481164911650116511165211653116541165511656116571165811659116601166111662116631166411665116661166711668116691167011671116721167311674116751167611677116781167911680116811168211683116841168511686116871168811689116901169111692116931169411695116961169711698116991170011701117021170311704117051170611707117081170911710117111171211713117141171511716117171171811719117201172111722117231172411725117261172711728117291173011731117321173311734117351173611737117381173911740117411174211743117441174511746117471174811749117501175111752117531175411755117561175711758117591176011761117621176311764117651176611767117681176911770117711177211773117741177511776117771177811779117801178111782117831178411785117861178711788117891179011791117921179311794117951179611797117981179911800118011180211803118041180511806118071180811809118101181111812118131181411815118161181711818118191182011821118221182311824118251182611827118281182911830118311183211833118341183511836118371183811839118401184111842118431184411845118461184711848118491185011851118521185311854118551185611857118581185911860118611186211863118641186511866118671186811869118701187111872118731187411875118761187711878118791188011881118821188311884118851188611887118881188911890118911189211893118941189511896118971189811899119001190111902119031190411905119061190711908119091191011911119121191311914119151191611917119181191911920119211192211923119241192511926119271192811929119301193111932119331193411935119361193711938119391194011941119421194311944119451194611947119481194911950119511195211953119541195511956119571195811959119601196111962119631196411965119661196711968119691197011971119721197311974119751197611977119781197911980119811198211983119841198511986119871198811989119901199111992119931199411995119961199711998119991200012001120021200312004120051200612007120081200912010120111201212013120141201512016120171201812019120201202112022120231202412025120261202712028120291203012031120321203312034120351203612037120381203912040120411204212043120441204512046120471204812049120501205112052120531205412055120561205712058120591206012061120621206312064120651206612067120681206912070120711207212073120741207512076120771207812079120801208112082120831208412085120861208712088120891209012091120921209312094120951209612097120981209912100121011210212103121041210512106121071210812109121101211112112121131211412115121161211712118121191212012121121221212312124121251212612127121281212912130121311213212133121341213512136121371213812139121401214112142121431214412145121461214712148121491215012151121521215312154121551215612157121581215912160121611216212163121641216512166121671216812169121701217112172121731217412175121761217712178121791218012181121821218312184121851218612187121881218912190121911219212193121941219512196121971219812199122001220112202122031220412205122061220712208122091221012211122121221312214122151221612217122181221912220122211222212223122241222512226122271222812229122301223112232122331223412235122361223712238122391224012241122421224312244122451224612247122481224912250122511225212253122541225512256122571225812259122601226112262122631226412265122661226712268122691227012271122721227312274122751227612277122781227912280122811228212283122841228512286122871228812289122901229112292122931229412295122961229712298122991230012301123021230312304123051230612307123081230912310123111231212313123141231512316123171231812319123201232112322123231232412325123261232712328123291233012331123321233312334123351233612337123381233912340123411234212343123441234512346123471234812349123501235112352123531235412355123561235712358123591236012361123621236312364123651236612367123681236912370123711237212373123741237512376123771237812379123801238112382123831238412385123861238712388123891239012391123921239312394123951239612397123981239912400124011240212403124041240512406124071240812409124101241112412124131241412415124161241712418124191242012421124221242312424124251242612427124281242912430124311243212433124341243512436124371243812439124401244112442124431244412445124461244712448124491245012451124521245312454124551245612457124581245912460124611246212463124641246512466124671246812469124701247112472124731247412475124761247712478124791248012481124821248312484124851248612487124881248912490124911249212493124941249512496124971249812499125001250112502125031250412505125061250712508125091251012511125121251312514125151251612517125181251912520125211252212523125241252512526125271252812529125301253112532125331253412535125361253712538125391254012541125421254312544125451254612547125481254912550125511255212553125541255512556125571255812559125601256112562125631256412565125661256712568125691257012571125721257312574125751257612577125781257912580125811258212583125841258512586125871258812589125901259112592125931259412595125961259712598125991260012601126021260312604126051260612607126081260912610126111261212613126141261512616126171261812619126201262112622126231262412625126261262712628126291263012631126321263312634126351263612637126381263912640126411264212643126441264512646126471264812649126501265112652126531265412655126561265712658126591266012661126621266312664126651266612667126681266912670126711267212673126741267512676126771267812679126801268112682126831268412685126861268712688126891269012691126921269312694126951269612697126981269912700127011270212703127041270512706127071270812709127101271112712127131271412715127161271712718127191272012721127221272312724127251272612727127281272912730127311273212733127341273512736127371273812739127401274112742127431274412745127461274712748127491275012751127521275312754127551275612757127581275912760127611276212763127641276512766127671276812769127701277112772127731277412775127761277712778127791278012781127821278312784127851278612787127881278912790127911279212793127941279512796127971279812799128001280112802128031280412805128061280712808128091281012811128121281312814128151281612817128181281912820128211282212823128241282512826128271282812829128301283112832128331283412835128361283712838128391284012841128421284312844128451284612847128481284912850128511285212853128541285512856128571285812859128601286112862128631286412865128661286712868128691287012871128721287312874128751287612877128781287912880128811288212883128841288512886128871288812889128901289112892128931289412895128961289712898128991290012901129021290312904129051290612907129081290912910129111291212913129141291512916129171291812919129201292112922129231292412925129261292712928129291293012931129321293312934129351293612937129381293912940129411294212943129441294512946129471294812949129501295112952129531295412955129561295712958129591296012961129621296312964129651296612967129681296912970129711297212973129741297512976129771297812979129801298112982129831298412985129861298712988129891299012991129921299312994129951299612997129981299913000130011300213003130041300513006130071300813009130101301113012130131301413015130161301713018130191302013021130221302313024130251302613027130281302913030130311303213033130341303513036130371303813039130401304113042130431304413045130461304713048130491305013051130521305313054130551305613057130581305913060130611306213063130641306513066130671306813069130701307113072130731307413075130761307713078130791308013081130821308313084130851308613087130881308913090130911309213093130941309513096130971309813099131001310113102131031310413105131061310713108131091311013111131121311313114131151311613117131181311913120131211312213123131241312513126131271312813129131301313113132131331313413135131361313713138131391314013141131421314313144131451314613147131481314913150131511315213153131541315513156131571315813159131601316113162131631316413165131661316713168131691317013171131721317313174131751317613177131781317913180131811318213183131841318513186131871318813189131901319113192131931319413195131961319713198131991320013201132021320313204132051320613207132081320913210132111321213213132141321513216132171321813219132201322113222132231322413225132261322713228132291323013231132321323313234132351323613237132381323913240132411324213243132441324513246132471324813249132501325113252132531325413255132561325713258132591326013261132621326313264132651326613267132681326913270132711327213273132741327513276132771327813279132801328113282132831328413285132861328713288132891329013291132921329313294132951329613297132981329913300133011330213303133041330513306133071330813309133101331113312133131331413315133161331713318133191332013321133221332313324133251332613327133281332913330133311333213333133341333513336133371333813339133401334113342133431334413345133461334713348133491335013351133521335313354133551335613357133581335913360133611336213363133641336513366133671336813369133701337113372133731337413375133761337713378133791338013381133821338313384133851338613387133881338913390133911339213393133941339513396133971339813399134001340113402134031340413405134061340713408134091341013411134121341313414134151341613417134181341913420134211342213423134241342513426134271342813429134301343113432134331343413435134361343713438134391344013441134421344313444134451344613447134481344913450134511345213453134541345513456134571345813459134601346113462134631346413465134661346713468134691347013471134721347313474134751347613477134781347913480134811348213483134841348513486134871348813489134901349113492134931349413495134961349713498134991350013501135021350313504135051350613507135081350913510135111351213513135141351513516135171351813519135201352113522135231352413525135261352713528135291353013531135321353313534135351353613537135381353913540135411354213543135441354513546135471354813549135501355113552135531355413555135561355713558135591356013561135621356313564135651356613567135681356913570135711357213573135741357513576135771357813579135801358113582135831358413585135861358713588135891359013591135921359313594135951359613597135981359913600136011360213603136041360513606136071360813609136101361113612136131361413615136161361713618136191362013621136221362313624136251362613627136281362913630136311363213633136341363513636136371363813639136401364113642136431364413645136461364713648136491365013651136521365313654136551365613657136581365913660136611366213663136641366513666136671366813669136701367113672136731367413675136761367713678136791368013681136821368313684136851368613687136881368913690136911369213693136941369513696136971369813699137001370113702137031370413705137061370713708137091371013711137121371313714137151371613717137181371913720137211372213723137241372513726137271372813729137301373113732137331373413735137361373713738137391374013741137421374313744137451374613747137481374913750137511375213753137541375513756137571375813759137601376113762137631376413765137661376713768137691377013771137721377313774137751377613777137781377913780137811378213783137841378513786137871378813789137901379113792137931379413795137961379713798137991380013801138021380313804138051380613807138081380913810138111381213813138141381513816138171381813819138201382113822138231382413825138261382713828138291383013831138321383313834138351383613837138381383913840138411384213843138441384513846138471384813849138501385113852138531385413855138561385713858138591386013861138621386313864138651386613867138681386913870138711387213873138741387513876138771387813879138801388113882138831388413885138861388713888138891389013891138921389313894138951389613897138981389913900139011390213903139041390513906139071390813909139101391113912139131391413915139161391713918139191392013921139221392313924139251392613927139281392913930139311393213933139341393513936139371393813939139401394113942139431394413945139461394713948139491395013951139521395313954139551395613957139581395913960139611396213963139641396513966139671396813969139701397113972139731397413975139761397713978139791398013981139821398313984139851398613987139881398913990139911399213993139941399513996139971399813999140001400114002140031400414005140061400714008140091401014011140121401314014140151401614017140181401914020140211402214023140241402514026140271402814029140301403114032140331403414035140361403714038140391404014041140421404314044140451404614047140481404914050140511405214053140541405514056140571405814059140601406114062140631406414065140661406714068140691407014071140721407314074140751407614077140781407914080140811408214083140841408514086140871408814089140901409114092140931409414095140961409714098140991410014101141021410314104141051410614107141081410914110141111411214113141141411514116141171411814119141201412114122141231412414125141261412714128141291413014131141321413314134141351413614137141381413914140141411414214143141441414514146141471414814149141501415114152141531415414155141561415714158141591416014161141621416314164141651416614167141681416914170141711417214173141741417514176141771417814179141801418114182141831418414185141861418714188141891419014191141921419314194141951419614197141981419914200142011420214203142041420514206142071420814209142101421114212142131421414215142161421714218142191422014221142221422314224142251422614227142281422914230142311423214233142341423514236142371423814239142401424114242142431424414245142461424714248142491425014251142521425314254142551425614257142581425914260142611426214263142641426514266142671426814269142701427114272142731427414275142761427714278142791428014281142821428314284142851428614287142881428914290142911429214293142941429514296142971429814299143001430114302143031430414305143061430714308143091431014311143121431314314143151431614317143181431914320143211432214323143241432514326143271432814329143301433114332143331433414335143361433714338143391434014341143421434314344143451434614347143481434914350143511435214353143541435514356143571435814359143601436114362143631436414365143661436714368143691437014371143721437314374143751437614377143781437914380143811438214383143841438514386143871438814389143901439114392143931439414395143961439714398143991440014401144021440314404144051440614407144081440914410144111441214413144141441514416144171441814419144201442114422144231442414425144261442714428144291443014431144321443314434144351443614437144381443914440144411444214443144441444514446144471444814449144501445114452144531445414455144561445714458144591446014461144621446314464144651446614467144681446914470144711447214473144741447514476144771447814479144801448114482144831448414485144861448714488144891449014491144921449314494144951449614497144981449914500145011450214503145041450514506145071450814509145101451114512145131451414515145161451714518145191452014521145221452314524145251452614527145281452914530145311453214533145341453514536145371453814539145401454114542145431454414545145461454714548145491455014551145521455314554145551455614557145581455914560145611456214563145641456514566145671456814569145701457114572145731457414575145761457714578145791458014581145821458314584145851458614587145881458914590145911459214593145941459514596145971459814599146001460114602146031460414605146061460714608146091461014611146121461314614146151461614617146181461914620146211462214623146241462514626146271462814629146301463114632146331463414635146361463714638146391464014641146421464314644146451464614647146481464914650146511465214653146541465514656146571465814659146601466114662146631466414665146661466714668146691467014671146721467314674146751467614677146781467914680146811468214683146841468514686146871468814689146901469114692146931469414695146961469714698146991470014701147021470314704147051470614707147081470914710147111471214713147141471514716147171471814719147201472114722147231472414725147261472714728147291473014731147321473314734147351473614737147381473914740147411474214743147441474514746147471474814749147501475114752147531475414755147561475714758147591476014761147621476314764147651476614767147681476914770147711477214773147741477514776147771477814779147801478114782147831478414785147861478714788147891479014791147921479314794147951479614797147981479914800148011480214803148041480514806148071480814809148101481114812148131481414815148161481714818148191482014821148221482314824148251482614827148281482914830148311483214833148341483514836148371483814839148401484114842148431484414845148461484714848148491485014851148521485314854148551485614857148581485914860148611486214863148641486514866148671486814869148701487114872148731487414875148761487714878148791488014881148821488314884148851488614887148881488914890148911489214893148941489514896148971489814899149001490114902149031490414905149061490714908149091491014911149121491314914149151491614917149181491914920149211492214923149241492514926149271492814929149301493114932149331493414935149361493714938149391494014941149421494314944149451494614947149481494914950149511495214953149541495514956149571495814959149601496114962149631496414965149661496714968149691497014971149721497314974149751497614977149781497914980149811498214983149841498514986149871498814989149901499114992149931499414995149961499714998149991500015001150021500315004150051500615007150081500915010150111501215013150141501515016150171501815019150201502115022150231502415025150261502715028150291503015031150321503315034150351503615037150381503915040150411504215043150441504515046150471504815049150501505115052150531505415055150561505715058150591506015061150621506315064150651506615067150681506915070150711507215073150741507515076150771507815079150801508115082150831508415085150861508715088150891509015091150921509315094150951509615097150981509915100151011510215103151041510515106151071510815109151101511115112151131511415115151161511715118151191512015121151221512315124151251512615127151281512915130151311513215133151341513515136151371513815139151401514115142151431514415145151461514715148151491515015151151521515315154151551515615157151581515915160151611516215163151641516515166151671516815169151701517115172151731517415175151761517715178151791518015181151821518315184151851518615187151881518915190151911519215193151941519515196151971519815199152001520115202152031520415205152061520715208152091521015211152121521315214152151521615217152181521915220152211522215223152241522515226152271522815229152301523115232152331523415235152361523715238152391524015241152421524315244152451524615247152481524915250152511525215253152541525515256152571525815259152601526115262152631526415265152661526715268152691527015271152721527315274152751527615277152781527915280152811528215283152841528515286152871528815289152901529115292152931529415295152961529715298152991530015301153021530315304153051530615307153081530915310153111531215313153141531515316153171531815319153201532115322153231532415325153261532715328153291533015331153321533315334153351533615337153381533915340153411534215343153441534515346153471534815349153501535115352153531535415355153561535715358153591536015361153621536315364153651536615367153681536915370153711537215373153741537515376153771537815379153801538115382153831538415385153861538715388153891539015391153921539315394153951539615397153981539915400154011540215403154041540515406154071540815409154101541115412154131541415415154161541715418154191542015421154221542315424154251542615427154281542915430154311543215433154341543515436154371543815439154401544115442154431544415445154461544715448154491545015451154521545315454154551545615457154581545915460154611546215463154641546515466154671546815469154701547115472154731547415475154761547715478154791548015481154821548315484154851548615487154881548915490154911549215493154941549515496154971549815499155001550115502155031550415505155061550715508155091551015511155121551315514155151551615517155181551915520155211552215523155241552515526155271552815529155301553115532155331553415535155361553715538155391554015541155421554315544155451554615547155481554915550155511555215553155541555515556155571555815559155601556115562155631556415565155661556715568155691557015571155721557315574155751557615577155781557915580155811558215583155841558515586155871558815589155901559115592155931559415595155961559715598155991560015601156021560315604156051560615607156081560915610156111561215613156141561515616156171561815619156201562115622156231562415625156261562715628156291563015631156321563315634156351563615637156381563915640156411564215643156441564515646156471564815649156501565115652156531565415655156561565715658156591566015661156621566315664156651566615667156681566915670156711567215673156741567515676156771567815679156801568115682156831568415685156861568715688156891569015691156921569315694156951569615697156981569915700157011570215703157041570515706157071570815709157101571115712157131571415715157161571715718157191572015721157221572315724157251572615727157281572915730157311573215733157341573515736157371573815739157401574115742157431574415745157461574715748157491575015751157521575315754157551575615757157581575915760157611576215763157641576515766157671576815769157701577115772157731577415775157761577715778157791578015781157821578315784157851578615787157881578915790157911579215793157941579515796157971579815799158001580115802158031580415805158061580715808158091581015811158121581315814158151581615817158181581915820158211582215823158241582515826158271582815829158301583115832158331583415835158361583715838158391584015841158421584315844158451584615847158481584915850158511585215853158541585515856158571585815859158601586115862158631586415865158661586715868158691587015871158721587315874158751587615877158781587915880158811588215883158841588515886158871588815889158901589115892158931589415895158961589715898158991590015901159021590315904159051590615907159081590915910159111591215913159141591515916159171591815919159201592115922159231592415925159261592715928159291593015931159321593315934159351593615937159381593915940159411594215943159441594515946159471594815949159501595115952159531595415955159561595715958159591596015961159621596315964159651596615967159681596915970159711597215973159741597515976159771597815979159801598115982159831598415985159861598715988159891599015991159921599315994159951599615997159981599916000160011600216003160041600516006160071600816009160101601116012160131601416015160161601716018160191602016021160221602316024160251602616027160281602916030160311603216033160341603516036160371603816039160401604116042160431604416045160461604716048160491605016051160521605316054160551605616057160581605916060160611606216063160641606516066160671606816069160701607116072160731607416075160761607716078160791608016081160821608316084160851608616087160881608916090160911609216093160941609516096160971609816099161001610116102161031610416105161061610716108161091611016111161121611316114161151611616117161181611916120161211612216123161241612516126161271612816129161301613116132161331613416135161361613716138161391614016141161421614316144161451614616147161481614916150161511615216153161541615516156161571615816159161601616116162161631616416165161661616716168161691617016171161721617316174161751617616177161781617916180161811618216183161841618516186161871618816189161901619116192161931619416195161961619716198161991620016201162021620316204162051620616207162081620916210162111621216213162141621516216162171621816219162201622116222162231622416225162261622716228162291623016231162321623316234162351623616237162381623916240162411624216243162441624516246162471624816249162501625116252162531625416255162561625716258162591626016261162621626316264162651626616267162681626916270162711627216273162741627516276162771627816279162801628116282162831628416285162861628716288162891629016291162921629316294162951629616297162981629916300163011630216303163041630516306163071630816309163101631116312163131631416315163161631716318163191632016321163221632316324163251632616327163281632916330163311633216333163341633516336163371633816339163401634116342163431634416345163461634716348163491635016351163521635316354163551635616357163581635916360163611636216363163641636516366163671636816369163701637116372163731637416375163761637716378163791638016381163821638316384163851638616387163881638916390163911639216393163941639516396163971639816399164001640116402164031640416405164061640716408164091641016411164121641316414164151641616417164181641916420164211642216423164241642516426164271642816429164301643116432164331643416435164361643716438164391644016441164421644316444164451644616447164481644916450164511645216453164541645516456164571645816459164601646116462164631646416465164661646716468164691647016471164721647316474164751647616477164781647916480164811648216483164841648516486164871648816489164901649116492164931649416495164961649716498164991650016501165021650316504165051650616507165081650916510165111651216513165141651516516165171651816519165201652116522165231652416525165261652716528165291653016531165321653316534165351653616537165381653916540165411654216543165441654516546165471654816549165501655116552165531655416555165561655716558165591656016561165621656316564165651656616567165681656916570165711657216573165741657516576165771657816579165801658116582165831658416585165861658716588165891659016591165921659316594165951659616597165981659916600166011660216603166041660516606166071660816609166101661116612166131661416615166161661716618166191662016621166221662316624166251662616627166281662916630166311663216633166341663516636166371663816639166401664116642166431664416645166461664716648166491665016651166521665316654166551665616657166581665916660166611666216663166641666516666166671666816669166701667116672166731667416675166761667716678166791668016681166821668316684166851668616687166881668916690166911669216693166941669516696166971669816699167001670116702167031670416705167061670716708167091671016711167121671316714167151671616717167181671916720167211672216723167241672516726167271672816729167301673116732167331673416735167361673716738167391674016741167421674316744167451674616747167481674916750167511675216753167541675516756167571675816759167601676116762167631676416765167661676716768167691677016771167721677316774167751677616777167781677916780167811678216783167841678516786167871678816789167901679116792167931679416795167961679716798167991680016801168021680316804168051680616807168081680916810168111681216813168141681516816168171681816819168201682116822168231682416825168261682716828168291683016831168321683316834168351683616837168381683916840168411684216843168441684516846168471684816849168501685116852168531685416855168561685716858168591686016861168621686316864168651686616867168681686916870168711687216873168741687516876168771687816879168801688116882168831688416885168861688716888168891689016891168921689316894168951689616897168981689916900169011690216903169041690516906169071690816909169101691116912169131691416915169161691716918169191692016921169221692316924169251692616927169281692916930169311693216933169341693516936169371693816939169401694116942169431694416945169461694716948169491695016951169521695316954169551695616957169581695916960169611696216963169641696516966169671696816969169701697116972169731697416975169761697716978169791698016981169821698316984169851698616987169881698916990169911699216993169941699516996169971699816999170001700117002170031700417005170061700717008170091701017011170121701317014170151701617017170181701917020170211702217023170241702517026170271702817029170301703117032170331703417035170361703717038170391704017041170421704317044170451704617047170481704917050170511705217053170541705517056170571705817059170601706117062170631706417065170661706717068170691707017071170721707317074170751707617077170781707917080170811708217083170841708517086170871708817089170901709117092170931709417095170961709717098170991710017101171021710317104171051710617107171081710917110171111711217113171141711517116171171711817119171201712117122171231712417125171261712717128171291713017131171321713317134171351713617137171381713917140171411714217143171441714517146171471714817149171501715117152171531715417155171561715717158171591716017161171621716317164171651716617167171681716917170171711717217173171741717517176171771717817179171801718117182171831718417185171861718717188171891719017191171921719317194171951719617197171981719917200172011720217203172041720517206172071720817209172101721117212172131721417215172161721717218172191722017221172221722317224172251722617227172281722917230172311723217233172341723517236172371723817239172401724117242172431724417245172461724717248172491725017251172521725317254172551725617257172581725917260172611726217263172641726517266172671726817269172701727117272172731727417275172761727717278172791728017281172821728317284172851728617287172881728917290172911729217293172941729517296172971729817299173001730117302173031730417305173061730717308173091731017311173121731317314173151731617317173181731917320173211732217323173241732517326173271732817329173301733117332173331733417335173361733717338173391734017341173421734317344173451734617347173481734917350173511735217353173541735517356173571735817359173601736117362173631736417365173661736717368173691737017371173721737317374173751737617377173781737917380173811738217383173841738517386173871738817389173901739117392173931739417395173961739717398173991740017401174021740317404174051740617407174081740917410174111741217413174141741517416174171741817419174201742117422174231742417425174261742717428174291743017431174321743317434174351743617437174381743917440174411744217443174441744517446174471744817449174501745117452174531745417455174561745717458174591746017461174621746317464174651746617467174681746917470174711747217473174741747517476174771747817479174801748117482174831748417485174861748717488174891749017491174921749317494174951749617497174981749917500175011750217503175041750517506175071750817509175101751117512175131751417515175161751717518175191752017521175221752317524175251752617527175281752917530175311753217533175341753517536175371753817539175401754117542175431754417545175461754717548175491755017551175521755317554175551755617557175581755917560175611756217563175641756517566175671756817569175701757117572175731757417575175761757717578175791758017581175821758317584175851758617587175881758917590175911759217593175941759517596175971759817599176001760117602176031760417605176061760717608176091761017611176121761317614176151761617617176181761917620176211762217623176241762517626176271762817629176301763117632176331763417635176361763717638176391764017641176421764317644176451764617647176481764917650176511765217653176541765517656176571765817659176601766117662176631766417665176661766717668176691767017671176721767317674176751767617677176781767917680176811768217683176841768517686176871768817689176901769117692176931769417695176961769717698176991770017701177021770317704177051770617707177081770917710177111771217713177141771517716177171771817719177201772117722177231772417725177261772717728177291773017731177321773317734177351773617737177381773917740177411774217743177441774517746177471774817749177501775117752177531775417755177561775717758177591776017761177621776317764177651776617767177681776917770177711777217773177741777517776177771777817779177801778117782177831778417785177861778717788177891779017791177921779317794177951779617797177981779917800178011780217803178041780517806178071780817809178101781117812178131781417815178161781717818178191782017821178221782317824178251782617827178281782917830178311783217833178341783517836178371783817839178401784117842178431784417845178461784717848178491785017851178521785317854178551785617857178581785917860178611786217863178641786517866178671786817869178701787117872178731787417875178761787717878178791788017881178821788317884178851788617887178881788917890178911789217893178941789517896178971789817899179001790117902179031790417905179061790717908179091791017911179121791317914179151791617917179181791917920179211792217923179241792517926179271792817929179301793117932179331793417935179361793717938179391794017941179421794317944179451794617947179481794917950179511795217953179541795517956179571795817959179601796117962179631796417965179661796717968179691797017971179721797317974179751797617977179781797917980179811798217983179841798517986179871798817989179901799117992179931799417995179961799717998179991800018001180021800318004180051800618007180081800918010180111801218013180141801518016180171801818019180201802118022180231802418025180261802718028180291803018031180321803318034180351803618037180381803918040180411804218043180441804518046180471804818049180501805118052180531805418055180561805718058180591806018061180621806318064180651806618067180681806918070180711807218073180741807518076180771807818079180801808118082180831808418085180861808718088180891809018091180921809318094180951809618097180981809918100181011810218103181041810518106181071810818109181101811118112181131811418115181161811718118181191812018121181221812318124181251812618127181281812918130181311813218133181341813518136181371813818139181401814118142181431814418145181461814718148181491815018151181521815318154181551815618157181581815918160181611816218163181641816518166181671816818169181701817118172181731817418175181761817718178181791818018181181821818318184181851818618187181881818918190181911819218193181941819518196181971819818199182001820118202182031820418205182061820718208182091821018211182121821318214182151821618217182181821918220182211822218223182241822518226182271822818229182301823118232182331823418235182361823718238182391824018241182421824318244182451824618247182481824918250182511825218253182541825518256182571825818259182601826118262182631826418265182661826718268182691827018271182721827318274182751827618277182781827918280182811828218283182841828518286182871828818289182901829118292182931829418295182961829718298182991830018301183021830318304183051830618307183081830918310183111831218313183141831518316183171831818319183201832118322183231832418325183261832718328183291833018331183321833318334183351833618337183381833918340183411834218343183441834518346183471834818349183501835118352183531835418355183561835718358183591836018361183621836318364183651836618367183681836918370183711837218373183741837518376183771837818379183801838118382183831838418385183861838718388183891839018391183921839318394183951839618397183981839918400184011840218403184041840518406184071840818409184101841118412184131841418415184161841718418184191842018421184221842318424184251842618427184281842918430184311843218433184341843518436184371843818439184401844118442184431844418445184461844718448184491845018451184521845318454184551845618457184581845918460184611846218463184641846518466184671846818469184701847118472184731847418475184761847718478184791848018481184821848318484184851848618487184881848918490184911849218493184941849518496184971849818499185001850118502185031850418505185061850718508185091851018511185121851318514185151851618517185181851918520185211852218523185241852518526185271852818529185301853118532185331853418535185361853718538185391854018541185421854318544185451854618547185481854918550185511855218553185541855518556185571855818559185601856118562185631856418565185661856718568185691857018571185721857318574185751857618577185781857918580185811858218583185841858518586185871858818589185901859118592185931859418595185961859718598185991860018601186021860318604186051860618607186081860918610186111861218613186141861518616186171861818619186201862118622186231862418625186261862718628186291863018631186321863318634186351863618637186381863918640186411864218643186441864518646186471864818649186501865118652186531865418655186561865718658186591866018661186621866318664186651866618667186681866918670186711867218673186741867518676186771867818679186801868118682186831868418685186861868718688186891869018691186921869318694186951869618697186981869918700187011870218703187041870518706187071870818709187101871118712187131871418715187161871718718187191872018721187221872318724187251872618727187281872918730187311873218733187341873518736187371873818739187401874118742187431874418745187461874718748187491875018751187521875318754187551875618757187581875918760187611876218763187641876518766187671876818769187701877118772187731877418775187761877718778187791878018781187821878318784187851878618787187881878918790187911879218793187941879518796187971879818799188001880118802188031880418805188061880718808188091881018811188121881318814188151881618817188181881918820188211882218823188241882518826188271882818829188301883118832188331883418835188361883718838188391884018841188421884318844188451884618847188481884918850188511885218853188541885518856188571885818859188601886118862188631886418865188661886718868188691887018871188721887318874188751887618877188781887918880188811888218883188841888518886188871888818889188901889118892188931889418895188961889718898188991890018901189021890318904189051890618907189081890918910189111891218913189141891518916189171891818919189201892118922189231892418925189261892718928189291893018931189321893318934189351893618937189381893918940189411894218943189441894518946189471894818949189501895118952189531895418955189561895718958189591896018961189621896318964189651896618967189681896918970189711897218973189741897518976189771897818979189801898118982189831898418985189861898718988189891899018991189921899318994189951899618997189981899919000190011900219003190041900519006190071900819009190101901119012190131901419015190161901719018190191902019021190221902319024190251902619027190281902919030190311903219033190341903519036190371903819039190401904119042190431904419045190461904719048190491905019051190521905319054190551905619057190581905919060190611906219063190641906519066190671906819069190701907119072190731907419075190761907719078190791908019081190821908319084190851908619087190881908919090190911909219093190941909519096190971909819099191001910119102191031910419105191061910719108191091911019111191121911319114191151911619117191181911919120191211912219123191241912519126191271912819129191301913119132191331913419135191361913719138191391914019141191421914319144191451914619147191481914919150191511915219153191541915519156191571915819159191601916119162191631916419165191661916719168191691917019171191721917319174191751917619177191781917919180191811918219183191841918519186191871918819189191901919119192191931919419195191961919719198191991920019201192021920319204192051920619207192081920919210192111921219213192141921519216192171921819219192201922119222192231922419225192261922719228192291923019231192321923319234192351923619237192381923919240192411924219243192441924519246192471924819249192501925119252192531925419255192561925719258192591926019261192621926319264192651926619267192681926919270192711927219273192741927519276192771927819279192801928119282192831928419285192861928719288192891929019291192921929319294192951929619297192981929919300193011930219303193041930519306193071930819309193101931119312193131931419315193161931719318193191932019321193221932319324193251932619327193281932919330193311933219333193341933519336193371933819339193401934119342193431934419345193461934719348193491935019351193521935319354193551935619357193581935919360193611936219363193641936519366193671936819369193701937119372193731937419375193761937719378193791938019381193821938319384193851938619387193881938919390193911939219393193941939519396193971939819399194001940119402194031940419405194061940719408194091941019411194121941319414194151941619417194181941919420194211942219423194241942519426194271942819429194301943119432194331943419435194361943719438194391944019441194421944319444194451944619447194481944919450194511945219453194541945519456194571945819459194601946119462194631946419465194661946719468194691947019471194721947319474194751947619477194781947919480194811948219483194841948519486194871948819489194901949119492194931949419495194961949719498194991950019501195021950319504195051950619507195081950919510195111951219513195141951519516195171951819519195201952119522195231952419525195261952719528195291953019531195321953319534195351953619537195381953919540195411954219543195441954519546195471954819549195501955119552195531955419555195561955719558195591956019561195621956319564195651956619567195681956919570195711957219573195741957519576195771957819579195801958119582195831958419585195861958719588195891959019591195921959319594195951959619597195981959919600196011960219603196041960519606196071960819609196101961119612196131961419615196161961719618196191962019621196221962319624196251962619627196281962919630196311963219633196341963519636196371963819639196401964119642196431964419645196461964719648196491965019651196521965319654196551965619657196581965919660196611966219663196641966519666196671966819669196701967119672196731967419675196761967719678196791968019681196821968319684196851968619687196881968919690196911969219693196941969519696196971969819699197001970119702197031970419705197061970719708197091971019711197121971319714197151971619717197181971919720197211972219723197241972519726197271972819729197301973119732197331973419735197361973719738197391974019741197421974319744197451974619747197481974919750197511975219753197541975519756197571975819759197601976119762197631976419765197661976719768197691977019771197721977319774197751977619777197781977919780197811978219783197841978519786197871978819789197901979119792197931979419795197961979719798197991980019801198021980319804198051980619807198081980919810198111981219813198141981519816198171981819819198201982119822198231982419825198261982719828198291983019831198321983319834198351983619837198381983919840198411984219843198441984519846198471984819849198501985119852198531985419855198561985719858198591986019861198621986319864198651986619867198681986919870198711987219873198741987519876198771987819879198801988119882198831988419885198861988719888198891989019891198921989319894198951989619897198981989919900199011990219903199041990519906199071990819909199101991119912199131991419915199161991719918199191992019921199221992319924199251992619927199281992919930199311993219933199341993519936199371993819939199401994119942199431994419945199461994719948199491995019951199521995319954199551995619957199581995919960199611996219963199641996519966199671996819969199701997119972199731997419975199761997719978199791998019981199821998319984199851998619987199881998919990199911999219993199941999519996199971999819999200002000120002200032000420005200062000720008200092001020011200122001320014200152001620017200182001920020200212002220023200242002520026200272002820029200302003120032200332003420035200362003720038200392004020041200422004320044200452004620047200482004920050200512005220053200542005520056200572005820059200602006120062200632006420065200662006720068200692007020071200722007320074200752007620077200782007920080200812008220083200842008520086200872008820089200902009120092200932009420095200962009720098200992010020101201022010320104201052010620107201082010920110201112011220113201142011520116201172011820119201202012120122201232012420125201262012720128201292013020131201322013320134201352013620137201382013920140201412014220143201442014520146201472014820149201502015120152201532015420155201562015720158201592016020161201622016320164201652016620167201682016920170201712017220173201742017520176201772017820179201802018120182201832018420185201862018720188201892019020191201922019320194201952019620197201982019920200202012020220203202042020520206202072020820209202102021120212202132021420215202162021720218202192022020221202222022320224202252022620227202282022920230202312023220233202342023520236202372023820239202402024120242202432024420245202462024720248202492025020251202522025320254202552025620257202582025920260202612026220263202642026520266202672026820269202702027120272202732027420275202762027720278202792028020281202822028320284202852028620287202882028920290202912029220293202942029520296202972029820299203002030120302203032030420305203062030720308203092031020311203122031320314203152031620317203182031920320203212032220323203242032520326203272032820329203302033120332203332033420335203362033720338203392034020341203422034320344203452034620347203482034920350203512035220353203542035520356203572035820359203602036120362203632036420365203662036720368203692037020371203722037320374203752037620377203782037920380203812038220383203842038520386203872038820389203902039120392203932039420395203962039720398203992040020401204022040320404204052040620407204082040920410204112041220413204142041520416204172041820419204202042120422204232042420425204262042720428204292043020431204322043320434204352043620437204382043920440204412044220443204442044520446204472044820449204502045120452204532045420455204562045720458204592046020461204622046320464204652046620467204682046920470204712047220473204742047520476204772047820479204802048120482204832048420485204862048720488204892049020491204922049320494204952049620497204982049920500205012050220503205042050520506205072050820509205102051120512205132051420515205162051720518205192052020521205222052320524205252052620527205282052920530205312053220533205342053520536205372053820539205402054120542205432054420545205462054720548205492055020551205522055320554205552055620557205582055920560205612056220563205642056520566205672056820569205702057120572205732057420575205762057720578205792058020581205822058320584205852058620587205882058920590205912059220593205942059520596205972059820599206002060120602206032060420605206062060720608206092061020611206122061320614206152061620617206182061920620206212062220623206242062520626206272062820629206302063120632206332063420635206362063720638206392064020641206422064320644206452064620647206482064920650206512065220653206542065520656206572065820659206602066120662206632066420665206662066720668206692067020671206722067320674206752067620677206782067920680206812068220683206842068520686206872068820689206902069120692206932069420695206962069720698206992070020701207022070320704207052070620707207082070920710207112071220713207142071520716207172071820719207202072120722207232072420725207262072720728207292073020731207322073320734207352073620737207382073920740207412074220743207442074520746207472074820749207502075120752207532075420755207562075720758207592076020761207622076320764207652076620767207682076920770207712077220773207742077520776207772077820779207802078120782207832078420785207862078720788207892079020791207922079320794207952079620797207982079920800208012080220803208042080520806208072080820809208102081120812208132081420815208162081720818208192082020821208222082320824208252082620827208282082920830208312083220833208342083520836208372083820839208402084120842208432084420845208462084720848208492085020851208522085320854208552085620857208582085920860208612086220863208642086520866208672086820869208702087120872208732087420875208762087720878208792088020881208822088320884208852088620887208882088920890208912089220893208942089520896208972089820899209002090120902209032090420905209062090720908209092091020911209122091320914209152091620917209182091920920209212092220923209242092520926209272092820929209302093120932209332093420935209362093720938209392094020941209422094320944209452094620947209482094920950209512095220953209542095520956209572095820959209602096120962209632096420965209662096720968209692097020971209722097320974209752097620977209782097920980209812098220983209842098520986209872098820989209902099120992209932099420995209962099720998209992100021001210022100321004210052100621007210082100921010210112101221013210142101521016210172101821019210202102121022210232102421025210262102721028210292103021031210322103321034210352103621037210382103921040210412104221043210442104521046210472104821049210502105121052210532105421055210562105721058210592106021061210622106321064210652106621067210682106921070210712107221073210742107521076210772107821079210802108121082210832108421085210862108721088210892109021091210922109321094210952109621097210982109921100211012110221103211042110521106211072110821109211102111121112211132111421115211162111721118211192112021121211222112321124211252112621127211282112921130211312113221133211342113521136211372113821139211402114121142211432114421145211462114721148211492115021151211522115321154211552115621157211582115921160211612116221163211642116521166211672116821169211702117121172211732117421175211762117721178211792118021181211822118321184211852118621187211882118921190211912119221193211942119521196211972119821199212002120121202212032120421205212062120721208212092121021211212122121321214212152121621217212182121921220212212122221223212242122521226212272122821229212302123121232212332123421235212362123721238212392124021241212422124321244212452124621247212482124921250212512125221253212542125521256212572125821259212602126121262212632126421265212662126721268212692127021271212722127321274212752127621277212782127921280212812128221283212842128521286212872128821289212902129121292212932129421295212962129721298212992130021301213022130321304213052130621307213082130921310213112131221313213142131521316213172131821319213202132121322213232132421325213262132721328213292133021331213322133321334213352133621337213382133921340213412134221343213442134521346213472134821349213502135121352213532135421355213562135721358213592136021361213622136321364213652136621367213682136921370213712137221373213742137521376213772137821379213802138121382213832138421385213862138721388213892139021391213922139321394213952139621397213982139921400214012140221403214042140521406214072140821409214102141121412214132141421415214162141721418214192142021421214222142321424214252142621427214282142921430214312143221433214342143521436214372143821439214402144121442214432144421445214462144721448214492145021451214522145321454214552145621457214582145921460214612146221463214642146521466214672146821469214702147121472214732147421475214762147721478214792148021481214822148321484214852148621487214882148921490214912149221493214942149521496214972149821499215002150121502215032150421505215062150721508215092151021511215122151321514215152151621517215182151921520215212152221523215242152521526215272152821529215302153121532215332153421535215362153721538215392154021541215422154321544215452154621547215482154921550215512155221553215542155521556215572155821559215602156121562215632156421565215662156721568215692157021571215722157321574215752157621577215782157921580215812158221583215842158521586215872158821589215902159121592215932159421595215962159721598215992160021601216022160321604216052160621607216082160921610216112161221613216142161521616216172161821619216202162121622216232162421625216262162721628216292163021631216322163321634216352163621637216382163921640216412164221643216442164521646216472164821649216502165121652216532165421655216562165721658216592166021661216622166321664216652166621667216682166921670216712167221673216742167521676216772167821679216802168121682216832168421685216862168721688216892169021691216922169321694216952169621697216982169921700217012170221703217042170521706217072170821709217102171121712217132171421715217162171721718217192172021721217222172321724217252172621727217282172921730217312173221733217342173521736217372173821739217402174121742217432174421745217462174721748217492175021751217522175321754217552175621757217582175921760217612176221763217642176521766217672176821769217702177121772217732177421775217762177721778217792178021781217822178321784217852178621787217882178921790217912179221793217942179521796217972179821799218002180121802218032180421805218062180721808218092181021811218122181321814218152181621817218182181921820218212182221823218242182521826218272182821829218302183121832218332183421835218362183721838218392184021841218422184321844218452184621847218482184921850218512185221853218542185521856218572185821859218602186121862218632186421865218662186721868218692187021871218722187321874218752187621877218782187921880218812188221883218842188521886218872188821889218902189121892218932189421895218962189721898218992190021901219022190321904219052190621907219082190921910219112191221913219142191521916219172191821919219202192121922219232192421925219262192721928219292193021931219322193321934219352193621937219382193921940219412194221943219442194521946219472194821949219502195121952219532195421955219562195721958219592196021961219622196321964219652196621967219682196921970219712197221973219742197521976219772197821979219802198121982219832198421985219862198721988219892199021991219922199321994219952199621997219982199922000220012200222003220042200522006220072200822009220102201122012220132201422015220162201722018220192202022021220222202322024220252202622027220282202922030220312203222033220342203522036220372203822039220402204122042220432204422045220462204722048220492205022051220522205322054220552205622057220582205922060220612206222063220642206522066220672206822069220702207122072220732207422075220762207722078220792208022081220822208322084220852208622087220882208922090220912209222093220942209522096220972209822099221002210122102221032210422105221062210722108221092211022111221122211322114221152211622117221182211922120221212212222123221242212522126221272212822129221302213122132221332213422135221362213722138221392214022141221422214322144221452214622147221482214922150221512215222153221542215522156221572215822159221602216122162221632216422165221662216722168221692217022171221722217322174221752217622177221782217922180221812218222183221842218522186221872218822189221902219122192221932219422195221962219722198221992220022201222022220322204222052220622207222082220922210222112221222213222142221522216222172221822219222202222122222222232222422225222262222722228222292223022231222322223322234222352223622237222382223922240222412224222243222442224522246222472224822249222502225122252222532225422255222562225722258222592226022261222622226322264222652226622267222682226922270222712227222273222742227522276222772227822279222802228122282222832228422285222862228722288222892229022291222922229322294222952229622297222982229922300223012230222303223042230522306223072230822309223102231122312223132231422315223162231722318223192232022321223222232322324223252232622327223282232922330223312233222333223342233522336223372233822339223402234122342223432234422345223462234722348223492235022351223522235322354223552235622357223582235922360223612236222363223642236522366223672236822369223702237122372223732237422375223762237722378223792238022381223822238322384223852238622387223882238922390223912239222393223942239522396223972239822399224002240122402224032240422405224062240722408224092241022411224122241322414224152241622417224182241922420224212242222423224242242522426224272242822429224302243122432224332243422435224362243722438224392244022441224422244322444224452244622447224482244922450224512245222453224542245522456224572245822459224602246122462224632246422465224662246722468224692247022471224722247322474224752247622477224782247922480224812248222483224842248522486224872248822489224902249122492224932249422495224962249722498224992250022501225022250322504225052250622507225082250922510225112251222513225142251522516225172251822519225202252122522225232252422525225262252722528225292253022531225322253322534225352253622537225382253922540225412254222543225442254522546225472254822549225502255122552225532255422555225562255722558225592256022561225622256322564225652256622567225682256922570225712257222573225742257522576225772257822579225802258122582225832258422585225862258722588225892259022591225922259322594225952259622597225982259922600226012260222603226042260522606226072260822609226102261122612226132261422615226162261722618226192262022621226222262322624226252262622627226282262922630226312263222633226342263522636226372263822639226402264122642226432264422645226462264722648226492265022651226522265322654226552265622657226582265922660226612266222663226642266522666226672266822669226702267122672226732267422675226762267722678226792268022681226822268322684226852268622687226882268922690226912269222693226942269522696226972269822699227002270122702227032270422705227062270722708227092271022711227122271322714227152271622717227182271922720227212272222723227242272522726227272272822729227302273122732227332273422735227362273722738227392274022741227422274322744227452274622747227482274922750227512275222753227542275522756227572275822759227602276122762227632276422765227662276722768227692277022771227722277322774227752277622777227782277922780227812278222783227842278522786227872278822789227902279122792227932279422795227962279722798227992280022801228022280322804228052280622807228082280922810228112281222813228142281522816228172281822819228202282122822228232282422825228262282722828228292283022831228322283322834228352283622837228382283922840228412284222843228442284522846228472284822849228502285122852228532285422855228562285722858228592286022861228622286322864228652286622867228682286922870228712287222873228742287522876228772287822879228802288122882228832288422885228862288722888228892289022891228922289322894228952289622897228982289922900229012290222903229042290522906229072290822909229102291122912229132291422915229162291722918229192292022921229222292322924229252292622927229282292922930229312293222933229342293522936229372293822939229402294122942229432294422945229462294722948229492295022951229522295322954229552295622957229582295922960229612296222963229642296522966229672296822969229702297122972229732297422975229762297722978229792298022981229822298322984229852298622987229882298922990229912299222993229942299522996229972299822999230002300123002230032300423005230062300723008230092301023011230122301323014230152301623017230182301923020230212302223023230242302523026230272302823029230302303123032230332303423035230362303723038230392304023041230422304323044230452304623047230482304923050230512305223053230542305523056230572305823059230602306123062230632306423065230662306723068230692307023071230722307323074230752307623077230782307923080230812308223083230842308523086230872308823089230902309123092230932309423095230962309723098230992310023101231022310323104231052310623107231082310923110231112311223113231142311523116231172311823119231202312123122231232312423125231262312723128231292313023131231322313323134231352313623137231382313923140231412314223143231442314523146231472314823149231502315123152231532315423155231562315723158231592316023161231622316323164231652316623167231682316923170231712317223173231742317523176231772317823179231802318123182231832318423185231862318723188231892319023191231922319323194231952319623197231982319923200232012320223203232042320523206232072320823209232102321123212232132321423215232162321723218232192322023221232222322323224232252322623227232282322923230232312323223233232342323523236232372323823239232402324123242232432324423245232462324723248232492325023251232522325323254232552325623257232582325923260232612326223263232642326523266232672326823269232702327123272232732327423275232762327723278232792328023281232822328323284232852328623287232882328923290232912329223293232942329523296232972329823299233002330123302233032330423305233062330723308233092331023311233122331323314233152331623317233182331923320233212332223323233242332523326233272332823329233302333123332233332333423335233362333723338233392334023341233422334323344233452334623347233482334923350233512335223353233542335523356233572335823359233602336123362233632336423365233662336723368233692337023371233722337323374233752337623377233782337923380233812338223383233842338523386233872338823389233902339123392233932339423395233962339723398233992340023401234022340323404234052340623407234082340923410234112341223413234142341523416234172341823419234202342123422234232342423425234262342723428234292343023431234322343323434234352343623437234382343923440234412344223443234442344523446234472344823449234502345123452234532345423455234562345723458234592346023461234622346323464234652346623467234682346923470234712347223473234742347523476234772347823479234802348123482234832348423485234862348723488234892349023491234922349323494234952349623497234982349923500235012350223503235042350523506235072350823509235102351123512235132351423515235162351723518235192352023521235222352323524235252352623527235282352923530235312353223533235342353523536235372353823539235402354123542235432354423545235462354723548235492355023551235522355323554235552355623557235582355923560235612356223563235642356523566235672356823569235702357123572235732357423575235762357723578235792358023581235822358323584235852358623587235882358923590235912359223593235942359523596235972359823599236002360123602236032360423605236062360723608236092361023611236122361323614236152361623617236182361923620236212362223623236242362523626236272362823629236302363123632236332363423635236362363723638236392364023641236422364323644236452364623647236482364923650236512365223653236542365523656236572365823659236602366123662236632366423665236662366723668236692367023671236722367323674236752367623677236782367923680236812368223683236842368523686236872368823689236902369123692236932369423695236962369723698236992370023701237022370323704237052370623707237082370923710237112371223713237142371523716237172371823719237202372123722237232372423725237262372723728237292373023731237322373323734237352373623737237382373923740237412374223743237442374523746237472374823749237502375123752237532375423755237562375723758237592376023761237622376323764237652376623767237682376923770237712377223773237742377523776237772377823779237802378123782237832378423785237862378723788237892379023791237922379323794237952379623797237982379923800238012380223803238042380523806238072380823809238102381123812238132381423815238162381723818238192382023821238222382323824238252382623827238282382923830238312383223833238342383523836238372383823839238402384123842238432384423845238462384723848238492385023851238522385323854238552385623857238582385923860238612386223863238642386523866238672386823869238702387123872238732387423875238762387723878238792388023881238822388323884238852388623887238882388923890238912389223893238942389523896238972389823899239002390123902239032390423905239062390723908239092391023911239122391323914239152391623917239182391923920239212392223923239242392523926239272392823929239302393123932239332393423935239362393723938239392394023941239422394323944239452394623947239482394923950239512395223953239542395523956239572395823959239602396123962239632396423965239662396723968239692397023971239722397323974239752397623977239782397923980239812398223983239842398523986239872398823989239902399123992239932399423995239962399723998239992400024001240022400324004240052400624007240082400924010240112401224013240142401524016240172401824019240202402124022240232402424025240262402724028240292403024031240322403324034240352403624037240382403924040240412404224043240442404524046240472404824049240502405124052240532405424055240562405724058240592406024061240622406324064240652406624067240682406924070240712407224073240742407524076240772407824079240802408124082240832408424085240862408724088240892409024091240922409324094240952409624097240982409924100241012410224103241042410524106241072410824109241102411124112241132411424115241162411724118241192412024121241222412324124241252412624127241282412924130241312413224133241342413524136241372413824139241402414124142241432414424145241462414724148241492415024151241522415324154241552415624157241582415924160241612416224163241642416524166241672416824169241702417124172241732417424175241762417724178241792418024181241822418324184241852418624187241882418924190241912419224193241942419524196241972419824199242002420124202242032420424205242062420724208242092421024211242122421324214242152421624217242182421924220242212422224223242242422524226242272422824229242302423124232242332423424235242362423724238242392424024241242422424324244242452424624247242482424924250242512425224253242542425524256242572425824259242602426124262242632426424265242662426724268242692427024271242722427324274242752427624277242782427924280242812428224283242842428524286242872428824289242902429124292242932429424295242962429724298242992430024301243022430324304243052430624307243082430924310243112431224313243142431524316243172431824319243202432124322243232432424325243262432724328243292433024331243322433324334243352433624337243382433924340243412434224343243442434524346243472434824349243502435124352243532435424355243562435724358243592436024361243622436324364243652436624367243682436924370243712437224373243742437524376243772437824379243802438124382243832438424385243862438724388243892439024391243922439324394243952439624397243982439924400244012440224403244042440524406244072440824409244102441124412244132441424415244162441724418244192442024421244222442324424244252442624427244282442924430244312443224433244342443524436244372443824439244402444124442244432444424445244462444724448244492445024451244522445324454244552445624457244582445924460244612446224463244642446524466244672446824469244702447124472244732447424475244762447724478244792448024481244822448324484244852448624487244882448924490244912449224493244942449524496244972449824499245002450124502245032450424505245062450724508245092451024511245122451324514245152451624517245182451924520245212452224523245242452524526245272452824529245302453124532245332453424535245362453724538245392454024541245422454324544245452454624547245482454924550245512455224553245542455524556245572455824559245602456124562245632456424565245662456724568245692457024571245722457324574245752457624577245782457924580245812458224583245842458524586245872458824589245902459124592245932459424595245962459724598245992460024601246022460324604246052460624607246082460924610246112461224613246142461524616246172461824619246202462124622246232462424625246262462724628246292463024631246322463324634246352463624637246382463924640246412464224643246442464524646246472464824649246502465124652246532465424655246562465724658246592466024661246622466324664246652466624667246682466924670246712467224673246742467524676246772467824679246802468124682246832468424685246862468724688246892469024691246922469324694246952469624697246982469924700247012470224703247042470524706247072470824709247102471124712247132471424715247162471724718247192472024721247222472324724247252472624727247282472924730247312473224733247342473524736247372473824739247402474124742247432474424745247462474724748247492475024751247522475324754247552475624757247582475924760247612476224763247642476524766247672476824769247702477124772247732477424775247762477724778247792478024781247822478324784247852478624787247882478924790247912479224793247942479524796247972479824799248002480124802248032480424805248062480724808248092481024811248122481324814248152481624817248182481924820248212482224823248242482524826248272482824829248302483124832248332483424835248362483724838248392484024841248422484324844248452484624847248482484924850248512485224853248542485524856248572485824859248602486124862248632486424865248662486724868248692487024871248722487324874248752487624877248782487924880248812488224883248842488524886248872488824889248902489124892248932489424895248962489724898248992490024901249022490324904249052490624907249082490924910249112491224913249142491524916249172491824919249202492124922249232492424925249262492724928249292493024931249322493324934249352493624937249382493924940249412494224943249442494524946249472494824949249502495124952249532495424955249562495724958249592496024961249622496324964249652496624967249682496924970249712497224973249742497524976249772497824979249802498124982249832498424985249862498724988249892499024991249922499324994249952499624997249982499925000250012500225003250042500525006250072500825009250102501125012250132501425015250162501725018250192502025021250222502325024250252502625027250282502925030250312503225033250342503525036250372503825039250402504125042250432504425045250462504725048250492505025051250522505325054250552505625057250582505925060250612506225063250642506525066250672506825069250702507125072250732507425075250762507725078250792508025081250822508325084250852508625087250882508925090250912509225093250942509525096250972509825099251002510125102251032510425105251062510725108251092511025111251122511325114251152511625117251182511925120251212512225123251242512525126251272512825129251302513125132251332513425135251362513725138251392514025141251422514325144251452514625147251482514925150251512515225153251542515525156251572515825159251602516125162251632516425165251662516725168251692517025171251722517325174251752517625177251782517925180251812518225183251842518525186251872518825189251902519125192251932519425195251962519725198251992520025201252022520325204252052520625207252082520925210252112521225213252142521525216252172521825219252202522125222252232522425225252262522725228252292523025231252322523325234252352523625237252382523925240252412524225243252442524525246252472524825249252502525125252252532525425255252562525725258252592526025261252622526325264252652526625267252682526925270252712527225273252742527525276252772527825279252802528125282252832528425285252862528725288252892529025291252922529325294252952529625297252982529925300253012530225303253042530525306253072530825309253102531125312253132531425315253162531725318253192532025321253222532325324253252532625327253282532925330253312533225333253342533525336253372533825339253402534125342253432534425345253462534725348253492535025351253522535325354253552535625357253582535925360253612536225363253642536525366253672536825369253702537125372253732537425375253762537725378253792538025381253822538325384253852538625387253882538925390253912539225393253942539525396253972539825399254002540125402254032540425405254062540725408254092541025411254122541325414254152541625417254182541925420254212542225423254242542525426254272542825429254302543125432254332543425435254362543725438254392544025441254422544325444254452544625447254482544925450254512545225453254542545525456254572545825459254602546125462254632546425465254662546725468254692547025471254722547325474254752547625477254782547925480254812548225483254842548525486254872548825489254902549125492254932549425495254962549725498254992550025501255022550325504255052550625507255082550925510255112551225513255142551525516255172551825519255202552125522255232552425525255262552725528255292553025531255322553325534255352553625537255382553925540255412554225543255442554525546255472554825549255502555125552255532555425555255562555725558255592556025561255622556325564255652556625567255682556925570255712557225573255742557525576255772557825579255802558125582255832558425585255862558725588255892559025591255922559325594255952559625597255982559925600256012560225603256042560525606256072560825609256102561125612256132561425615256162561725618256192562025621256222562325624256252562625627256282562925630256312563225633256342563525636256372563825639256402564125642256432564425645256462564725648256492565025651256522565325654256552565625657256582565925660256612566225663256642566525666256672566825669256702567125672256732567425675256762567725678256792568025681256822568325684256852568625687256882568925690256912569225693256942569525696256972569825699257002570125702257032570425705257062570725708257092571025711257122571325714257152571625717257182571925720257212572225723257242572525726257272572825729257302573125732257332573425735257362573725738257392574025741257422574325744257452574625747257482574925750257512575225753257542575525756257572575825759257602576125762257632576425765257662576725768257692577025771257722577325774257752577625777257782577925780257812578225783257842578525786257872578825789257902579125792257932579425795257962579725798257992580025801258022580325804258052580625807258082580925810258112581225813258142581525816258172581825819258202582125822258232582425825258262582725828258292583025831258322583325834258352583625837258382583925840258412584225843258442584525846258472584825849258502585125852258532585425855258562585725858258592586025861258622586325864258652586625867258682586925870258712587225873258742587525876258772587825879258802588125882258832588425885258862588725888258892589025891258922589325894258952589625897258982589925900259012590225903259042590525906259072590825909259102591125912259132591425915259162591725918259192592025921259222592325924259252592625927259282592925930259312593225933259342593525936259372593825939259402594125942259432594425945259462594725948259492595025951259522595325954259552595625957259582595925960259612596225963259642596525966259672596825969259702597125972259732597425975259762597725978259792598025981259822598325984259852598625987259882598925990259912599225993259942599525996259972599825999260002600126002260032600426005260062600726008260092601026011260122601326014260152601626017260182601926020260212602226023260242602526026260272602826029260302603126032260332603426035260362603726038260392604026041260422604326044260452604626047260482604926050260512605226053260542605526056260572605826059260602606126062260632606426065260662606726068260692607026071260722607326074260752607626077260782607926080260812608226083260842608526086260872608826089260902609126092260932609426095260962609726098260992610026101261022610326104261052610626107261082610926110261112611226113261142611526116261172611826119261202612126122261232612426125261262612726128261292613026131261322613326134261352613626137261382613926140261412614226143261442614526146261472614826149261502615126152261532615426155261562615726158261592616026161261622616326164261652616626167261682616926170261712617226173261742617526176261772617826179261802618126182261832618426185261862618726188261892619026191261922619326194261952619626197261982619926200262012620226203262042620526206262072620826209262102621126212262132621426215262162621726218262192622026221262222622326224262252622626227262282622926230262312623226233262342623526236262372623826239262402624126242262432624426245262462624726248262492625026251262522625326254262552625626257262582625926260262612626226263262642626526266262672626826269262702627126272262732627426275262762627726278262792628026281262822628326284262852628626287262882628926290262912629226293262942629526296262972629826299263002630126302263032630426305263062630726308263092631026311263122631326314263152631626317263182631926320263212632226323263242632526326263272632826329263302633126332263332633426335263362633726338263392634026341263422634326344263452634626347263482634926350263512635226353263542635526356263572635826359263602636126362263632636426365263662636726368263692637026371263722637326374263752637626377263782637926380263812638226383263842638526386263872638826389263902639126392263932639426395263962639726398263992640026401264022640326404264052640626407264082640926410264112641226413264142641526416264172641826419264202642126422264232642426425264262642726428264292643026431264322643326434264352643626437264382643926440264412644226443264442644526446264472644826449264502645126452264532645426455264562645726458264592646026461264622646326464264652646626467264682646926470264712647226473264742647526476264772647826479264802648126482264832648426485264862648726488264892649026491264922649326494264952649626497264982649926500265012650226503265042650526506265072650826509265102651126512265132651426515265162651726518265192652026521265222652326524265252652626527265282652926530265312653226533265342653526536265372653826539265402654126542265432654426545265462654726548265492655026551265522655326554265552655626557265582655926560265612656226563265642656526566265672656826569265702657126572265732657426575265762657726578265792658026581265822658326584265852658626587265882658926590265912659226593265942659526596265972659826599266002660126602266032660426605266062660726608266092661026611266122661326614266152661626617266182661926620266212662226623266242662526626266272662826629266302663126632266332663426635266362663726638266392664026641266422664326644266452664626647266482664926650266512665226653266542665526656266572665826659266602666126662266632666426665266662666726668266692667026671266722667326674266752667626677266782667926680266812668226683266842668526686266872668826689266902669126692266932669426695266962669726698266992670026701267022670326704267052670626707267082670926710267112671226713267142671526716267172671826719267202672126722267232672426725267262672726728267292673026731267322673326734267352673626737267382673926740267412674226743267442674526746267472674826749267502675126752267532675426755267562675726758267592676026761267622676326764267652676626767267682676926770267712677226773267742677526776267772677826779267802678126782267832678426785267862678726788267892679026791267922679326794267952679626797267982679926800268012680226803268042680526806268072680826809268102681126812268132681426815268162681726818268192682026821268222682326824268252682626827268282682926830268312683226833268342683526836268372683826839268402684126842268432684426845268462684726848268492685026851268522685326854268552685626857268582685926860268612686226863268642686526866268672686826869268702687126872268732687426875268762687726878268792688026881268822688326884268852688626887268882688926890268912689226893268942689526896268972689826899269002690126902269032690426905269062690726908269092691026911269122691326914269152691626917269182691926920269212692226923269242692526926269272692826929269302693126932269332693426935269362693726938269392694026941269422694326944269452694626947269482694926950269512695226953269542695526956269572695826959269602696126962269632696426965269662696726968269692697026971269722697326974269752697626977269782697926980269812698226983269842698526986269872698826989269902699126992269932699426995269962699726998269992700027001270022700327004270052700627007270082700927010270112701227013270142701527016270172701827019270202702127022270232702427025270262702727028270292703027031270322703327034270352703627037270382703927040270412704227043270442704527046270472704827049270502705127052270532705427055270562705727058270592706027061270622706327064270652706627067270682706927070270712707227073270742707527076270772707827079270802708127082270832708427085270862708727088270892709027091270922709327094270952709627097270982709927100271012710227103271042710527106271072710827109271102711127112271132711427115271162711727118271192712027121271222712327124271252712627127271282712927130271312713227133271342713527136271372713827139271402714127142271432714427145271462714727148271492715027151271522715327154271552715627157271582715927160271612716227163271642716527166271672716827169271702717127172271732717427175271762717727178271792718027181271822718327184271852718627187271882718927190271912719227193271942719527196271972719827199272002720127202272032720427205272062720727208272092721027211272122721327214272152721627217272182721927220272212722227223272242722527226272272722827229272302723127232272332723427235272362723727238272392724027241272422724327244272452724627247272482724927250272512725227253272542725527256272572725827259272602726127262272632726427265272662726727268272692727027271272722727327274272752727627277272782727927280272812728227283272842728527286272872728827289272902729127292272932729427295272962729727298272992730027301273022730327304273052730627307273082730927310273112731227313273142731527316273172731827319273202732127322273232732427325273262732727328273292733027331273322733327334273352733627337273382733927340273412734227343273442734527346273472734827349273502735127352273532735427355273562735727358273592736027361273622736327364273652736627367273682736927370273712737227373273742737527376273772737827379273802738127382273832738427385273862738727388273892739027391273922739327394273952739627397273982739927400274012740227403274042740527406274072740827409274102741127412274132741427415274162741727418274192742027421274222742327424274252742627427274282742927430274312743227433274342743527436274372743827439274402744127442274432744427445274462744727448274492745027451274522745327454274552745627457274582745927460274612746227463274642746527466274672746827469274702747127472274732747427475274762747727478274792748027481274822748327484274852748627487274882748927490274912749227493274942749527496274972749827499275002750127502275032750427505275062750727508275092751027511275122751327514275152751627517275182751927520275212752227523275242752527526275272752827529275302753127532275332753427535275362753727538275392754027541275422754327544275452754627547275482754927550275512755227553275542755527556275572755827559275602756127562275632756427565275662756727568275692757027571275722757327574275752757627577275782757927580275812758227583275842758527586275872758827589275902759127592275932759427595275962759727598275992760027601276022760327604276052760627607276082760927610276112761227613276142761527616276172761827619276202762127622276232762427625276262762727628276292763027631276322763327634276352763627637276382763927640276412764227643276442764527646276472764827649276502765127652276532765427655276562765727658276592766027661276622766327664276652766627667276682766927670276712767227673276742767527676276772767827679276802768127682276832768427685276862768727688276892769027691276922769327694276952769627697276982769927700277012770227703277042770527706277072770827709277102771127712277132771427715277162771727718277192772027721277222772327724277252772627727277282772927730277312773227733277342773527736277372773827739277402774127742277432774427745277462774727748277492775027751277522775327754277552775627757277582775927760277612776227763277642776527766277672776827769277702777127772277732777427775277762777727778277792778027781277822778327784277852778627787277882778927790277912779227793277942779527796277972779827799278002780127802278032780427805 |
- <html>
- <head>
- <meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
- <title>Special Function Error Rates Report</title>
- <link rel="stylesheet" href="http://www.boost.org/doc/libs/1_58_0/doc/src/boostbook.css" type="text/css">
- <meta name="generator" content="DocBook XSL Stylesheets V1.77.1">
- <link rel="home" href="index.html" title="Special Function Error Rates Report">
- </head>
- <body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
- <table cellpadding="2" width="100%"><tr>
- <td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../boost.png"></td>
- <td align="center"><a href="../../../../../index.html">Home</a></td>
- <td align="center"><a href="../../../../../libs/libraries.htm">Libraries</a></td>
- <td align="center"><a href="http://www.boost.org/users/people.html">People</a></td>
- <td align="center"><a href="http://www.boost.org/users/faq.html">FAQ</a></td>
- <td align="center"><a href="../../../../../more/index.htm">More</a></td>
- </tr></table>
- <hr>
- <div class="spirit-nav"></div>
- <div class="article">
- <div class="titlepage">
- <div>
- <div><h2 class="title">
- <a name="special_function_error_rates_rep"></a>Special Function Error Rates Report</h2></div>
- <div><div class="legalnotice">
- <a name="special_function_error_rates_rep.legal"></a><p>
- Distributed under the Boost Software License, Version 1.0. (See accompanying
- file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
- </p>
- </div></div>
- </div>
- <hr>
- </div>
- <div class="toc">
- <p><b>Table of Contents</b></p>
- <dl>
- <dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_beta">beta</a></span></dt>
- <dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_beta_incomplete_">beta
- (incomplete)</a></span></dt>
- <dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_betac">betac</a></span></dt>
- <dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_binomial_coefficient">binomial_coefficient</a></span></dt>
- <dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_boost_math_powm1">boost::math::powm1</a></span></dt>
- <dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_cbrt">cbrt</a></span></dt>
- <dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_cos_pi">cos_pi</a></span></dt>
- <dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_cyl_bessel_i">cyl_bessel_i</a></span></dt>
- <dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_cyl_bessel_i_integer_orders_">cyl_bessel_i
- (integer orders)</a></span></dt>
- <dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_cyl_bessel_i_prime">cyl_bessel_i_prime</a></span></dt>
- <dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_cyl_bessel_i_prime_integer_orders_">cyl_bessel_i_prime
- (integer orders)</a></span></dt>
- <dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_cyl_bessel_j">cyl_bessel_j</a></span></dt>
- <dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_cyl_bessel_j_integer_orders_">cyl_bessel_j
- (integer orders)</a></span></dt>
- <dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_cyl_bessel_j_prime">cyl_bessel_j_prime</a></span></dt>
- <dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_cyl_bessel_j_prime_integer_orders_">cyl_bessel_j_prime
- (integer orders)</a></span></dt>
- <dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_cyl_bessel_k">cyl_bessel_k</a></span></dt>
- <dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_cyl_bessel_k_integer_orders_">cyl_bessel_k
- (integer orders)</a></span></dt>
- <dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_cyl_bessel_k_prime">cyl_bessel_k_prime</a></span></dt>
- <dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_cyl_bessel_k_prime_integer_orders_">cyl_bessel_k_prime
- (integer orders)</a></span></dt>
- <dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_cyl_neumann">cyl_neumann</a></span></dt>
- <dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_cyl_neumann_integer_orders_">cyl_neumann
- (integer orders)</a></span></dt>
- <dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_cyl_neumann_prime">cyl_neumann_prime</a></span></dt>
- <dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_cyl_neumann_prime_integer_orders_">cyl_neumann_prime
- (integer orders)</a></span></dt>
- <dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_digamma">digamma</a></span></dt>
- <dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_ellint_1">ellint_1</a></span></dt>
- <dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_ellint_1_complete_">ellint_1
- (complete)</a></span></dt>
- <dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_ellint_2">ellint_2</a></span></dt>
- <dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_ellint_2_complete_">ellint_2
- (complete)</a></span></dt>
- <dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_ellint_3">ellint_3</a></span></dt>
- <dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_ellint_3_complete_">ellint_3
- (complete)</a></span></dt>
- <dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_ellint_d">ellint_d</a></span></dt>
- <dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_ellint_d_complete_">ellint_d
- (complete)</a></span></dt>
- <dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_ellint_rc">ellint_rc</a></span></dt>
- <dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_ellint_rd">ellint_rd</a></span></dt>
- <dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_ellint_rf">ellint_rf</a></span></dt>
- <dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_ellint_rg">ellint_rg</a></span></dt>
- <dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_ellint_rj">ellint_rj</a></span></dt>
- <dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_erf">erf</a></span></dt>
- <dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_erf_inv">erf_inv</a></span></dt>
- <dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_erfc">erfc</a></span></dt>
- <dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_erfc_inv">erfc_inv</a></span></dt>
- <dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_expint_Ei_">expint
- (Ei)</a></span></dt>
- <dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_expint_En_">expint
- (En)</a></span></dt>
- <dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_expm1">expm1</a></span></dt>
- <dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_gamma_p">gamma_p</a></span></dt>
- <dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_gamma_p_inv">gamma_p_inv</a></span></dt>
- <dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_gamma_p_inva">gamma_p_inva</a></span></dt>
- <dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_gamma_q">gamma_q</a></span></dt>
- <dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_gamma_q_inv">gamma_q_inv</a></span></dt>
- <dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_gamma_q_inva">gamma_q_inva</a></span></dt>
- <dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_hermite">hermite</a></span></dt>
- <dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_heuman_lambda">heuman_lambda</a></span></dt>
- <dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_ibeta">ibeta</a></span></dt>
- <dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_ibeta_inv">ibeta_inv</a></span></dt>
- <dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_ibeta_inva">ibeta_inva</a></span></dt>
- <dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_ibeta_invb">ibeta_invb</a></span></dt>
- <dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_ibetac">ibetac</a></span></dt>
- <dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_ibetac_inv">ibetac_inv</a></span></dt>
- <dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_ibetac_inva">ibetac_inva</a></span></dt>
- <dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_ibetac_invb">ibetac_invb</a></span></dt>
- <dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_jacobi_cn">jacobi_cn</a></span></dt>
- <dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_jacobi_dn">jacobi_dn</a></span></dt>
- <dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_jacobi_sn">jacobi_sn</a></span></dt>
- <dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_jacobi_zeta">jacobi_zeta</a></span></dt>
- <dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_laguerre_n_m_x_">laguerre(n,
- m, x)</a></span></dt>
- <dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_laguerre_n_x_">laguerre(n,
- x)</a></span></dt>
- <dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_legendre_p">legendre_p</a></span></dt>
- <dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_legendre_p_associated_">legendre_p
- (associated)</a></span></dt>
- <dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_legendre_q">legendre_q</a></span></dt>
- <dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_lgamma">lgamma</a></span></dt>
- <dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_log1p">log1p</a></span></dt>
- <dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_non_central_beta_CDF">non
- central beta CDF</a></span></dt>
- <dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_non_central_beta_CDF_complement">non
- central beta CDF complement</a></span></dt>
- <dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_non_central_chi_squared_CDF">non
- central chi squared CDF</a></span></dt>
- <dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_non_central_chi_squared_CDF_complement">non
- central chi squared CDF complement</a></span></dt>
- <dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_non_central_t_CDF">non
- central t CDF</a></span></dt>
- <dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_non_central_t_CDF_complement">non
- central t CDF complement</a></span></dt>
- <dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_owens_t">owens_t</a></span></dt>
- <dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_polygamma">polygamma</a></span></dt>
- <dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_powm1">powm1</a></span></dt>
- <dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_sin_pi">sin_pi</a></span></dt>
- <dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_sph_bessel">sph_bessel</a></span></dt>
- <dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_sph_bessel_prime">sph_bessel_prime</a></span></dt>
- <dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_sph_neumann">sph_neumann</a></span></dt>
- <dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_sph_neumann_prime">sph_neumann_prime</a></span></dt>
- <dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_spherical_harmonic_i">spherical_harmonic_i</a></span></dt>
- <dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_spherical_harmonic_r">spherical_harmonic_r</a></span></dt>
- <dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_sqrt1pm1">sqrt1pm1</a></span></dt>
- <dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_tgamma">tgamma</a></span></dt>
- <dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_tgamma1pm1">tgamma1pm1</a></span></dt>
- <dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_tgamma_delta_ratio">tgamma_delta_ratio</a></span></dt>
- <dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_tgamma_incomplete_">tgamma
- (incomplete)</a></span></dt>
- <dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_tgamma_lower">tgamma_lower</a></span></dt>
- <dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_tgamma_ratio">tgamma_ratio</a></span></dt>
- <dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_trigamma">trigamma</a></span></dt>
- <dt><span class="section"><a href="index.html#special_function_error_rates_rep.section_zeta">zeta</a></span></dt>
- <dt><span class="section"><a href="index.html#special_function_error_rates_rep.error_logs">Error Logs</a></span></dt>
- <dt><span class="section"><a href="index.html#special_function_error_rates_rep.all_the_tables">Tables</a></span></dt>
- </dl>
- </div>
- <div class="section">
- <div class="titlepage"><div><div><h2 class="title" style="clear: both">
- <a name="special_function_error_rates_rep.section_beta"></a><a class="link" href="index.html#special_function_error_rates_rep.section_beta" title="beta">beta</a>
- </h2></div></div></div>
- <div class="table">
- <a name="special_function_error_rates_rep.section_beta.table_beta"></a><p class="title"><b>Table 1. Error rates for beta</b></p>
- <div class="table-contents"><table class="table" summary="Error rates for beta">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> double
- </p>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> long double
- </p>
- </th>
- <th>
- <p>
- Sun compiler version 0x5150<br> Sun Solaris<br> long double
- </p>
- </th>
- <th>
- <p>
- Microsoft Visual C++ version 14.1<br> Win32<br> double
- </p>
- </th>
- </tr></thead>
- <tbody>
- <tr>
- <td>
- <p>
- Beta Function: Small Values
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> <span class="red">Max = +INFε (Mean = +INFε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_beta_GSL_2_1_Beta_Function_Small_Values">And
- other failures.</a>)</span><br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
- Max = 1.14ε (Mean = 0.574ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 2.86ε (Mean = 1.22ε)</span><br> <br>
- (<span class="emphasis"><em><cmath>:</em></span> Max = 364ε (Mean = 76.2ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 2.86ε (Mean = 1.22ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 2.23ε (Mean = 1.14ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Beta Function: Medium Values
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.978ε (Mean = 0.0595ε)</span><br> <br>
- (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 1.18e+03ε (Mean = 238ε))<br>
- (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 1.09e+03ε (Mean = 265ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 61.4ε (Mean = 19.4ε)</span><br> <br>
- (<span class="emphasis"><em><cmath>:</em></span> Max = 1.07e+03ε (Mean = 264ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 107ε (Mean = 24.5ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 96.5ε (Mean = 22.4ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Beta Function: Divergent Values
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 12.1ε (Mean = 1.99ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
- Max = 176ε (Mean = 28ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 8.99ε (Mean = 2.44ε)</span><br> <br>
- (<span class="emphasis"><em><cmath>:</em></span> Max = 128ε (Mean = 23.8ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 18.8ε (Mean = 2.71ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 11.4ε (Mean = 2.19ε)</span>
- </p>
- </td>
- </tr>
- </tbody>
- </table></div>
- </div>
- <br class="table-break">
- </div>
- <div class="section">
- <div class="titlepage"><div><div><h2 class="title" style="clear: both">
- <a name="special_function_error_rates_rep.section_beta_incomplete_"></a><a class="link" href="index.html#special_function_error_rates_rep.section_beta_incomplete_" title="beta (incomplete)">beta
- (incomplete)</a>
- </h2></div></div></div>
- <div class="table">
- <a name="special_function_error_rates_rep.section_beta_incomplete_.table_beta_incomplete_"></a><p class="title"><b>Table 2. Error rates for beta (incomplete)</b></p>
- <div class="table-contents"><table class="table" summary="Error rates for beta (incomplete)">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> double
- </p>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> long double
- </p>
- </th>
- <th>
- <p>
- Sun compiler version 0x5150<br> Sun Solaris<br> long double
- </p>
- </th>
- <th>
- <p>
- Microsoft Visual C++ version 14.1<br> Win32<br> double
- </p>
- </th>
- </tr></thead>
- <tbody>
- <tr>
- <td>
- <p>
- Incomplete Beta Function: Small Values
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 11.1ε (Mean = 2.32ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 18.7ε (Mean = 3.19ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 9.94ε (Mean = 2.17ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Incomplete Beta Function: Medium Values
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.568ε (Mean = 0.0254ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 69.2ε (Mean = 13.4ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 174ε (Mean = 25ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 90ε (Mean = 12.7ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Incomplete Beta Function: Large and Diverse Values
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.999ε (Mean = 0.0325ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 6.84e+04ε (Mean = 2.76e+03ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 6.86e+04ε (Mean = 2.79e+03ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 633ε (Mean = 29.7ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Incomplete Beta Function: Small Integer Values
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.786ε (Mean = 0.0323ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 11.6ε (Mean = 3.6ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 51.8ε (Mean = 11ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 26ε (Mean = 6.28ε)</span>
- </p>
- </td>
- </tr>
- </tbody>
- </table></div>
- </div>
- <br class="table-break">
- </div>
- <div class="section">
- <div class="titlepage"><div><div><h2 class="title" style="clear: both">
- <a name="special_function_error_rates_rep.section_betac"></a><a class="link" href="index.html#special_function_error_rates_rep.section_betac" title="betac">betac</a>
- </h2></div></div></div>
- <div class="table">
- <a name="special_function_error_rates_rep.section_betac.table_betac"></a><p class="title"><b>Table 3. Error rates for betac</b></p>
- <div class="table-contents"><table class="table" summary="Error rates for betac">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> double
- </p>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> long double
- </p>
- </th>
- <th>
- <p>
- Sun compiler version 0x5150<br> Sun Solaris<br> long double
- </p>
- </th>
- <th>
- <p>
- Microsoft Visual C++ version 14.1<br> Win32<br> double
- </p>
- </th>
- </tr></thead>
- <tbody>
- <tr>
- <td>
- <p>
- Incomplete Beta Function: Small Values
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.676ε (Mean = 0.0302ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 9.92ε (Mean = 2.3ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 11.2ε (Mean = 2.94ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 8.94ε (Mean = 2.06ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Incomplete Beta Function: Medium Values
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.949ε (Mean = 0.098ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 63.5ε (Mean = 13.5ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 97.6ε (Mean = 24.3ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 90.6ε (Mean = 14.8ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Incomplete Beta Function: Large and Diverse Values
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.12ε (Mean = 0.0458ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.05e+05ε (Mean = 5.45e+03ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.04e+05ε (Mean = 5.46e+03ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 3.72e+03ε (Mean = 113ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Incomplete Beta Function: Small Integer Values
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.586ε (Mean = 0.0314ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 11.1ε (Mean = 3.65ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 103ε (Mean = 17.4ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 26.2ε (Mean = 6.36ε)</span>
- </p>
- </td>
- </tr>
- </tbody>
- </table></div>
- </div>
- <br class="table-break">
- </div>
- <div class="section">
- <div class="titlepage"><div><div><h2 class="title" style="clear: both">
- <a name="special_function_error_rates_rep.section_binomial_coefficient"></a><a class="link" href="index.html#special_function_error_rates_rep.section_binomial_coefficient" title="binomial_coefficient">binomial_coefficient</a>
- </h2></div></div></div>
- <div class="table">
- <a name="special_function_error_rates_rep.section_binomial_coefficient.table_binomial_coefficient"></a><p class="title"><b>Table 4. Error rates for binomial_coefficient</b></p>
- <div class="table-contents"><table class="table" summary="Error rates for binomial_coefficient">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> double
- </p>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> long double
- </p>
- </th>
- <th>
- <p>
- Sun compiler version 0x5150<br> Sun Solaris<br> long double
- </p>
- </th>
- <th>
- <p>
- Microsoft Visual C++ version 14.1<br> Win32<br> double
- </p>
- </th>
- </tr></thead>
- <tbody>
- <tr>
- <td>
- <p>
- Binomials: small arguments
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1ε (Mean = 0.369ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.5ε (Mean = 0.339ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.5ε (Mean = 0.339ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1ε (Mean = 0.369ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Binomials: large arguments
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.939ε (Mean = 0.314ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 26.6ε (Mean = 6.13ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 53.2ε (Mean = 10.8ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 37.2ε (Mean = 7.4ε)</span>
- </p>
- </td>
- </tr>
- </tbody>
- </table></div>
- </div>
- <br class="table-break">
- </div>
- <div class="section">
- <div class="titlepage"><div><div><h2 class="title" style="clear: both">
- <a name="special_function_error_rates_rep.section_boost_math_powm1"></a><a class="link" href="index.html#special_function_error_rates_rep.section_boost_math_powm1" title="boost::math::powm1">boost::math::powm1</a>
- </h2></div></div></div>
- <div class="table">
- <a name="special_function_error_rates_rep.section_boost_math_powm1.table_boost_math_powm1"></a><p class="title"><b>Table 5. Error rates for boost::math::powm1</b></p>
- <div class="table-contents"><table class="table" summary="Error rates for boost::math::powm1">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> long double
- </p>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> double
- </p>
- </th>
- <th>
- <p>
- Sun compiler version 0x5150<br> Sun Solaris<br> long double
- </p>
- </th>
- <th>
- <p>
- Microsoft Visual C++ version 14.1<br> Win32<br> double
- </p>
- </th>
- </tr></thead>
- <tbody><tr>
- <td>
- <p>
- powm1
- </p>
- </td>
- <td>
- <p>
- (<span class="emphasis"><em><math.h>:</em></span> Max = 2.04ε (Mean = 0.493ε))<br>
- <br> <span class="blue">Max = 2.04ε (Mean = 0.493ε)</span><br>
- <br> (<span class="emphasis"><em><cmath>:</em></span> Max = 2.04ε (Mean = 0.493ε))
- </p>
- </td>
- <td>
- <p>
- (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 1.06ε (Mean = 0.425ε))<br>
- <br> (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 1.06ε (Mean = 0.425ε))<br>
- <br> <span class="blue">Max = 1.06ε (Mean = 0.425ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.88ε (Mean = 0.49ε)</span><br> <br>
- (<span class="emphasis"><em><math.h>:</em></span> Max = 1.88ε (Mean = 0.49ε))
- </p>
- </td>
- <td>
- <p>
- (<span class="emphasis"><em><math.h>:</em></span> Max = 1.84ε (Mean = 0.486ε))<br>
- <br> <span class="blue">Max = 1.84ε (Mean = 0.486ε)</span>
- </p>
- </td>
- </tr></tbody>
- </table></div>
- </div>
- <br class="table-break">
- </div>
- <div class="section">
- <div class="titlepage"><div><div><h2 class="title" style="clear: both">
- <a name="special_function_error_rates_rep.section_cbrt"></a><a class="link" href="index.html#special_function_error_rates_rep.section_cbrt" title="cbrt">cbrt</a>
- </h2></div></div></div>
- <div class="table">
- <a name="special_function_error_rates_rep.section_cbrt.table_cbrt"></a><p class="title"><b>Table 6. Error rates for cbrt</b></p>
- <div class="table-contents"><table class="table" summary="Error rates for cbrt">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> double
- </p>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> long double
- </p>
- </th>
- <th>
- <p>
- Sun compiler version 0x5150<br> Sun Solaris<br> long double
- </p>
- </th>
- <th>
- <p>
- Microsoft Visual C++ version 14.1<br> Win32<br> double
- </p>
- </th>
- </tr></thead>
- <tbody><tr>
- <td>
- <p>
- cbrt Function
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.34ε (Mean = 0.471ε)</span><br> <br>
- (<span class="emphasis"><em><cmath>:</em></span> Max = 1.34ε (Mean = 0.471ε))<br>
- (<span class="emphasis"><em><math.h>:</em></span> Max = 1.34ε (Mean = 0.471ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.34ε (Mean = 0.471ε)</span><br> <br>
- (<span class="emphasis"><em><math.h>:</em></span> Max = 1.34ε (Mean = 0.471ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.7ε (Mean = 0.565ε)</span><br> <br>
- (<span class="emphasis"><em><math.h>:</em></span> Max = 1.7ε (Mean = 0.565ε))
- </p>
- </td>
- </tr></tbody>
- </table></div>
- </div>
- <br class="table-break">
- </div>
- <div class="section">
- <div class="titlepage"><div><div><h2 class="title" style="clear: both">
- <a name="special_function_error_rates_rep.section_cos_pi"></a><a class="link" href="index.html#special_function_error_rates_rep.section_cos_pi" title="cos_pi">cos_pi</a>
- </h2></div></div></div>
- <div class="table">
- <a name="special_function_error_rates_rep.section_cos_pi.table_cos_pi"></a><p class="title"><b>Table 7. Error rates for cos_pi</b></p>
- <div class="table-contents"><table class="table" summary="Error rates for cos_pi">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> double
- </p>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> long double
- </p>
- </th>
- <th>
- <p>
- Sun compiler version 0x5150<br> Sun Solaris<br> long double
- </p>
- </th>
- <th>
- <p>
- Microsoft Visual C++ version 14.1<br> Win32<br> double
- </p>
- </th>
- </tr></thead>
- <tbody>
- <tr>
- <td>
- <p>
- sin_pi and cos_pi
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.991ε (Mean = 0.302ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.991ε (Mean = 0.302ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.996ε (Mean = 0.284ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- sin_pi and cos_pi near integers and half integers
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.976ε (Mean = 0.28ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.976ε (Mean = 0.28ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.996ε (Mean = 0.298ε)</span>
- </p>
- </td>
- </tr>
- </tbody>
- </table></div>
- </div>
- <br class="table-break">
- </div>
- <div class="section">
- <div class="titlepage"><div><div><h2 class="title" style="clear: both">
- <a name="special_function_error_rates_rep.section_cyl_bessel_i"></a><a class="link" href="index.html#special_function_error_rates_rep.section_cyl_bessel_i" title="cyl_bessel_i">cyl_bessel_i</a>
- </h2></div></div></div>
- <div class="table">
- <a name="special_function_error_rates_rep.section_cyl_bessel_i.table_cyl_bessel_i"></a><p class="title"><b>Table 8. Error rates for cyl_bessel_i</b></p>
- <div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_i">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> double
- </p>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> long double
- </p>
- </th>
- <th>
- <p>
- Sun compiler version 0x5150<br> Sun Solaris<br> long double
- </p>
- </th>
- <th>
- <p>
- Microsoft Visual C++ version 14.1<br> Win32<br> double
- </p>
- </th>
- </tr></thead>
- <tbody>
- <tr>
- <td>
- <p>
- Bessel I0: Mathworld Data
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 270ε (Mean = 91.6ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_GSL_2_1_Bessel_I0_Mathworld_Data">And
- other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
- Max = 1.52ε (Mean = 0.622ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_Rmath_3_2_3_Bessel_I0_Mathworld_Data">And
- other failures.</a>)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.95ε (Mean = 0.738ε)</span><br> <br>
- (<span class="emphasis"><em><cmath>:</em></span> Max = 8.49ε (Mean = 3.46ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_i__cmath__Bessel_I0_Mathworld_Data">And
- other failures.</a>)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.95ε (Mean = 0.661ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.762ε (Mean = 0.329ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Bessel I1: Mathworld Data
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 128ε (Mean = 41ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_GSL_2_1_Bessel_I1_Mathworld_Data">And
- other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
- Max = 1.53ε (Mean = 0.483ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_Rmath_3_2_3_Bessel_I1_Mathworld_Data">And
- other failures.</a>)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.64ε (Mean = 0.202ε)</span><br> <br>
- (<span class="emphasis"><em><cmath>:</em></span> Max = 5ε (Mean = 2.15ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_i__cmath__Bessel_I1_Mathworld_Data">And
- other failures.</a>)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.64ε (Mean = 0.202ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.767ε (Mean = 0.398ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Bessel In: Mathworld Data
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 2.31ε (Mean = 0.838ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_GSL_2_1_Bessel_In_Mathworld_Data">And
- other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
- Max = 1.73ε (Mean = 0.601ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_Rmath_3_2_3_Bessel_In_Mathworld_Data">And
- other failures.</a>)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.8ε (Mean = 1.33ε)</span><br> <br>
- (<span class="emphasis"><em><cmath>:</em></span> Max = 430ε (Mean = 163ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_i__cmath__Bessel_In_Mathworld_Data">And
- other failures.</a>)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 463ε (Mean = 140ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 3.46ε (Mean = 1.32ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Bessel Iv: Mathworld Data
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 5.95ε (Mean = 2.08ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_GSL_2_1_Bessel_Iv_Mathworld_Data">And
- other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
- Max = 3.53ε (Mean = 1.39ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 4.12ε (Mean = 1.85ε)</span><br> <br>
- (<span class="emphasis"><em><cmath>:</em></span> Max = 616ε (Mean = 221ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_i__cmath__Bessel_Iv_Mathworld_Data">And
- other failures.</a>)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 4.12ε (Mean = 1.95ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 2.97ε (Mean = 1.24ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Bessel In: Random Data
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 261ε (Mean = 53.2ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_GSL_2_1_Bessel_In_Random_Data">And
- other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
- Max = 7.37ε (Mean = 2.4ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 4.62ε (Mean = 1.06ε)</span><br> <br>
- (<span class="emphasis"><em><cmath>:</em></span> Max = 645ε (Mean = 132ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 176ε (Mean = 39.1ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 9.67ε (Mean = 1.88ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Bessel Iv: Random Data
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.661ε (Mean = 0.0441ε)</span><br> <br>
- (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 6.18e+03ε (Mean = 1.55e+03ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_GSL_2_1_Bessel_Iv_Random_Data">And
- other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
- <span class="red">Max = 4.28e+08ε (Mean = 2.85e+07ε))</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 8.35ε (Mean = 1.62ε)</span><br> <br>
- (<span class="emphasis"><em><cmath>:</em></span> Max = 1.05e+03ε (Mean = 224ε)
- <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_i__cmath__Bessel_Iv_Random_Data">And
- other failures.</a>)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 283ε (Mean = 88.4ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 7.46ε (Mean = 1.71ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Bessel Iv: Mathworld Data (large values)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 37ε (Mean = 18ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_GSL_2_1_Bessel_Iv_Mathworld_Data_large_values_">And
- other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
- <span class="red">Max = 3.77e+168ε (Mean = 2.39e+168ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_Rmath_3_2_3_Bessel_Iv_Mathworld_Data_large_values_">And
- other failures.</a>)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 14.7ε (Mean = 6.66ε)</span><br> <br>
- (<span class="emphasis"><em><cmath>:</em></span> Max = 118ε (Mean = 57.2ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_i__cmath__Bessel_Iv_Mathworld_Data_large_values_">And
- other failures.</a>)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 14.7ε (Mean = 6.59ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 3.67ε (Mean = 1.64ε)</span>
- </p>
- </td>
- </tr>
- </tbody>
- </table></div>
- </div>
- <br class="table-break">
- </div>
- <div class="section">
- <div class="titlepage"><div><div><h2 class="title" style="clear: both">
- <a name="special_function_error_rates_rep.section_cyl_bessel_i_integer_orders_"></a><a class="link" href="index.html#special_function_error_rates_rep.section_cyl_bessel_i_integer_orders_" title="cyl_bessel_i (integer orders)">cyl_bessel_i
- (integer orders)</a>
- </h2></div></div></div>
- <div class="table">
- <a name="special_function_error_rates_rep.section_cyl_bessel_i_integer_orders_.table_cyl_bessel_i_integer_orders_"></a><p class="title"><b>Table 9. Error rates for cyl_bessel_i (integer orders)</b></p>
- <div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_i (integer orders)">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> double
- </p>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> long double
- </p>
- </th>
- <th>
- <p>
- Sun compiler version 0x5150<br> Sun Solaris<br> long double
- </p>
- </th>
- <th>
- <p>
- Microsoft Visual C++ version 14.1<br> Win32<br> double
- </p>
- </th>
- </tr></thead>
- <tbody>
- <tr>
- <td>
- <p>
- Bessel I0: Mathworld Data (Integer Version)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 0.79ε (Mean = 0.482ε))<br> (<span class="emphasis"><em>Rmath
- 3.2.3:</em></span> Max = 1.52ε (Mean = 0.622ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_integer_orders__Rmath_3_2_3_Bessel_I0_Mathworld_Data_Integer_Version_">And
- other failures.</a>)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.95ε (Mean = 0.738ε)</span><br> <br>
- (<span class="emphasis"><em><cmath>:</em></span> Max = 8.49ε (Mean = 3.46ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_i_integer_orders___cmath__Bessel_I0_Mathworld_Data_Integer_Version_">And
- other failures.</a>)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.95ε (Mean = 0.661ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.762ε (Mean = 0.329ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Bessel I1: Mathworld Data (Integer Version)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 0.82ε (Mean = 0.456ε))<br> (<span class="emphasis"><em>Rmath
- 3.2.3:</em></span> Max = 1.53ε (Mean = 0.483ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_integer_orders__Rmath_3_2_3_Bessel_I1_Mathworld_Data_Integer_Version_">And
- other failures.</a>)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.64ε (Mean = 0.202ε)</span><br> <br>
- (<span class="emphasis"><em><cmath>:</em></span> Max = 5ε (Mean = 2.15ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_i_integer_orders___cmath__Bessel_I1_Mathworld_Data_Integer_Version_">And
- other failures.</a>)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.64ε (Mean = 0.202ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.767ε (Mean = 0.398ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Bessel In: Mathworld Data (Integer Version)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 5.15ε (Mean = 2.13ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_integer_orders__GSL_2_1_Bessel_In_Mathworld_Data_Integer_Version_">And
- other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
- Max = 1.73ε (Mean = 0.601ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_integer_orders__Rmath_3_2_3_Bessel_In_Mathworld_Data_Integer_Version_">And
- other failures.</a>)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.8ε (Mean = 1.33ε)</span><br> <br>
- (<span class="emphasis"><em><cmath>:</em></span> Max = 430ε (Mean = 163ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_i_integer_orders___cmath__Bessel_In_Mathworld_Data_Integer_Version_">And
- other failures.</a>)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 463ε (Mean = 140ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 3.46ε (Mean = 1.32ε)</span>
- </p>
- </td>
- </tr>
- </tbody>
- </table></div>
- </div>
- <br class="table-break">
- </div>
- <div class="section">
- <div class="titlepage"><div><div><h2 class="title" style="clear: both">
- <a name="special_function_error_rates_rep.section_cyl_bessel_i_prime"></a><a class="link" href="index.html#special_function_error_rates_rep.section_cyl_bessel_i_prime" title="cyl_bessel_i_prime">cyl_bessel_i_prime</a>
- </h2></div></div></div>
- <div class="table">
- <a name="special_function_error_rates_rep.section_cyl_bessel_i_prime.table_cyl_bessel_i_prime"></a><p class="title"><b>Table 10. Error rates for cyl_bessel_i_prime</b></p>
- <div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_i_prime">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> double
- </p>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> long double
- </p>
- </th>
- <th>
- <p>
- Sun compiler version 0x5150<br> Sun Solaris<br> long double
- </p>
- </th>
- <th>
- <p>
- Microsoft Visual C++ version 14.1<br> Win32<br> double
- </p>
- </th>
- </tr></thead>
- <tbody>
- <tr>
- <td>
- <p>
- Bessel I'0: Mathworld Data
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.82ε (Mean = 0.259ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.82ε (Mean = 0.259ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.82ε (Mean = 0.354ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Bessel I'1: Mathworld Data
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.97ε (Mean = 0.757ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.97ε (Mean = 0.757ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.36ε (Mean = 0.782ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Bessel I'n: Mathworld Data
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 2.31ε (Mean = 1.41ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 701ε (Mean = 212ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 3.61ε (Mean = 1.22ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Bessel I'v: Mathworld Data
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.62ε (Mean = 0.512ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 2.89e+03ε (Mean = 914ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 2.89e+03ε (Mean = 914ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 3.76e+03ε (Mean = 1.19e+03ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Bessel I'n: Random Data
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 3.95ε (Mean = 1.06ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 195ε (Mean = 37.1ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 9.85ε (Mean = 1.82ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Bessel I'v: Random Data
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 14.1ε (Mean = 2.93ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 336ε (Mean = 68.5ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 14ε (Mean = 2.5ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Bessel I'v: Mathworld Data (large values)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 42.6ε (Mean = 20.2ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 42.6ε (Mean = 20.2ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 59.5ε (Mean = 26.6ε)</span>
- </p>
- </td>
- </tr>
- </tbody>
- </table></div>
- </div>
- <br class="table-break">
- </div>
- <div class="section">
- <div class="titlepage"><div><div><h2 class="title" style="clear: both">
- <a name="special_function_error_rates_rep.section_cyl_bessel_i_prime_integer_orders_"></a><a class="link" href="index.html#special_function_error_rates_rep.section_cyl_bessel_i_prime_integer_orders_" title="cyl_bessel_i_prime (integer orders)">cyl_bessel_i_prime
- (integer orders)</a>
- </h2></div></div></div>
- <div class="table">
- <a name="special_function_error_rates_rep.section_cyl_bessel_i_prime_integer_orders_.table_cyl_bessel_i_prime_integer_orders_"></a><p class="title"><b>Table 11. Error rates for cyl_bessel_i_prime (integer orders)</b></p>
- <div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_i_prime (integer orders)">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> double
- </p>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> long double
- </p>
- </th>
- <th>
- <p>
- Sun compiler version 0x5150<br> Sun Solaris<br> long double
- </p>
- </th>
- <th>
- <p>
- Microsoft Visual C++ version 14.1<br> Win32<br> double
- </p>
- </th>
- </tr></thead>
- <tbody>
- <tr>
- <td>
- <p>
- Bessel I'0: Mathworld Data (Integer Version)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.82ε (Mean = 0.259ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.82ε (Mean = 0.259ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.82ε (Mean = 0.354ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Bessel I'1: Mathworld Data (Integer Version)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.97ε (Mean = 0.757ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.97ε (Mean = 0.757ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.36ε (Mean = 0.782ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Bessel I'n: Mathworld Data (Integer Version)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 2.31ε (Mean = 1.41ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 701ε (Mean = 212ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 3.61ε (Mean = 1.22ε)</span>
- </p>
- </td>
- </tr>
- </tbody>
- </table></div>
- </div>
- <br class="table-break">
- </div>
- <div class="section">
- <div class="titlepage"><div><div><h2 class="title" style="clear: both">
- <a name="special_function_error_rates_rep.section_cyl_bessel_j"></a><a class="link" href="index.html#special_function_error_rates_rep.section_cyl_bessel_j" title="cyl_bessel_j">cyl_bessel_j</a>
- </h2></div></div></div>
- <div class="table">
- <a name="special_function_error_rates_rep.section_cyl_bessel_j.table_cyl_bessel_j"></a><p class="title"><b>Table 12. Error rates for cyl_bessel_j</b></p>
- <div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_j">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> long double
- </p>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> double
- </p>
- </th>
- <th>
- <p>
- Sun compiler version 0x5150<br> Sun Solaris<br> long double
- </p>
- </th>
- <th>
- <p>
- Microsoft Visual C++ version 14.1<br> Win32<br> double
- </p>
- </th>
- </tr></thead>
- <tbody>
- <tr>
- <td>
- <p>
- Bessel J0: Mathworld Data
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 6.55ε (Mean = 2.86ε)</span><br> <br>
- (<span class="emphasis"><em><cmath>:</em></span> Max = 5.04ε (Mean = 1.78ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_j__cmath__Bessel_J0_Mathworld_Data">And
- other failures.</a>)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 0.629ε (Mean = 0.223ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_GSL_2_1_Bessel_J0_Mathworld_Data">And
- other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
- Max = 0.629ε (Mean = 0.223ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_Rmath_3_2_3_Bessel_J0_Mathworld_Data">And
- other failures.</a>)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 6.55ε (Mean = 2.86ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 2.52ε (Mean = 1.2ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Bessel J0: Mathworld Data (Tricky cases)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.64e+08ε (Mean = 6.69e+07ε)</span><br>
- <br> (<span class="emphasis"><em><cmath>:</em></span> Max = 4.79e+08ε (Mean =
- 1.96e+08ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 8e+04ε (Mean = 3.27e+04ε)</span><br>
- <br> (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 6.5e+07ε (Mean = 2.66e+07ε))<br>
- (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 1.04e+07ε (Mean = 4.29e+06ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.64e+08ε (Mean = 6.69e+07ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1e+07ε (Mean = 4.09e+06ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Bessel J1: Mathworld Data
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 3.59ε (Mean = 1.33ε)</span><br> <br>
- (<span class="emphasis"><em><cmath>:</em></span> Max = 6.1ε (Mean = 2.95ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_j__cmath__Bessel_J1_Mathworld_Data">And
- other failures.</a>)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 6.62ε (Mean = 2.35ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_GSL_2_1_Bessel_J1_Mathworld_Data">And
- other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
- Max = 0.946ε (Mean = 0.39ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_Rmath_3_2_3_Bessel_J1_Mathworld_Data">And
- other failures.</a>)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.44ε (Mean = 0.637ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.73ε (Mean = 0.976ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Bessel J1: Mathworld Data (tricky cases)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 2.18e+05ε (Mean = 9.76e+04ε)</span><br>
- <br> (<span class="emphasis"><em><cmath>:</em></span> Max = 2.15e+06ε (Mean =
- 1.58e+06ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 106ε (Mean = 47.5ε)</span><br> <br>
- (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 8.75e+05ε (Mean = 5.32e+05ε))<br>
- (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 2.93e+06ε (Mean = 1.7e+06ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 2.18e+05ε (Mean = 9.76e+04ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 3.23e+04ε (Mean = 1.45e+04ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Bessel JN: Mathworld Data
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 6.85ε (Mean = 3.35ε)</span><br> <br>
- (<span class="emphasis"><em><cmath>:</em></span> <span class="red">Max = 2.13e+19ε (Mean
- = 5.16e+18ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_j__cmath__Bessel_JN_Mathworld_Data">And
- other failures.</a>)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 6.9e+05ε (Mean = 2.15e+05ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_GSL_2_1_Bessel_JN_Mathworld_Data">And
- other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
- <span class="red">Max = +INFε (Mean = +INFε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_Rmath_3_2_3_Bessel_JN_Mathworld_Data">And
- other failures.</a>)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 463ε (Mean = 112ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 14.7ε (Mean = 5.4ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Bessel J: Mathworld Data
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 14.7ε (Mean = 4.11ε)</span><br> <br>
- (<span class="emphasis"><em><cmath>:</em></span> Max = 3.49e+05ε (Mean = 8.09e+04ε)
- <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_j__cmath__Bessel_J_Mathworld_Data">And
- other failures.</a>)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 10ε (Mean = 2.24ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 2.39e+05ε (Mean = 5.37e+04ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_GSL_2_1_Bessel_J_Mathworld_Data">And
- other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
- <span class="red">Max = +INFε (Mean = +INFε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_Rmath_3_2_3_Bessel_J_Mathworld_Data">And
- other failures.</a>)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 14.7ε (Mean = 4.22ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 14.9ε (Mean = 3.89ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Bessel J: Mathworld Data (large values)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 607ε (Mean = 305ε)</span><br> <br> (<span class="emphasis"><em><cmath>:</em></span>
- Max = 34.9ε (Mean = 17.4ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_j__cmath__Bessel_J_Mathworld_Data_large_values_">And
- other failures.</a>)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.536ε (Mean = 0.268ε)</span><br> <br>
- (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 4.91e+03ε (Mean = 2.46e+03ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_GSL_2_1_Bessel_J_Mathworld_Data_large_values_">And
- other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
- Max = 5.9ε (Mean = 3.76ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 607ε (Mean = 305ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 9.31ε (Mean = 5.52ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Bessel JN: Random Data
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 50.8ε (Mean = 3.69ε)</span><br> <br>
- (<span class="emphasis"><em><cmath>:</em></span> Max = 1.12e+03ε (Mean = 88.7ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 75.7ε (Mean = 5.36ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
- Max = 3.93ε (Mean = 1.22ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 99.6ε (Mean = 22ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 17.5ε (Mean = 1.46ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Bessel J: Random Data
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 11.4ε (Mean = 1.68ε)</span><br> <br>
- (<span class="emphasis"><em><cmath>:</em></span> Max = 501ε (Mean = 52.3ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 15.5ε (Mean = 3.33ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_GSL_2_1_Bessel_J_Random_Data">And
- other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
- Max = 6.74ε (Mean = 1.3ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 260ε (Mean = 34ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 9.24ε (Mean = 1.17ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Bessel J: Random Data (Tricky large values)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 785ε (Mean = 94.2ε)</span><br> <br>
- (<span class="emphasis"><em><cmath>:</em></span> <span class="red">Max = 5.01e+17ε (Mean
- = 6.23e+16ε))</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 2.48e+05ε (Mean = 5.11e+04ε))<br> (<span class="emphasis"><em>Rmath
- 3.2.3:</em></span> Max = 71.6ε (Mean = 11.7ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 785ε (Mean = 97.4ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 59.2ε (Mean = 8.67ε)</span>
- </p>
- </td>
- </tr>
- </tbody>
- </table></div>
- </div>
- <br class="table-break">
- </div>
- <div class="section">
- <div class="titlepage"><div><div><h2 class="title" style="clear: both">
- <a name="special_function_error_rates_rep.section_cyl_bessel_j_integer_orders_"></a><a class="link" href="index.html#special_function_error_rates_rep.section_cyl_bessel_j_integer_orders_" title="cyl_bessel_j (integer orders)">cyl_bessel_j
- (integer orders)</a>
- </h2></div></div></div>
- <div class="table">
- <a name="special_function_error_rates_rep.section_cyl_bessel_j_integer_orders_.table_cyl_bessel_j_integer_orders_"></a><p class="title"><b>Table 13. Error rates for cyl_bessel_j (integer orders)</b></p>
- <div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_j (integer orders)">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> long double
- </p>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> double
- </p>
- </th>
- <th>
- <p>
- Sun compiler version 0x5150<br> Sun Solaris<br> long double
- </p>
- </th>
- <th>
- <p>
- Microsoft Visual C++ version 14.1<br> Win32<br> double
- </p>
- </th>
- </tr></thead>
- <tbody>
- <tr>
- <td>
- <p>
- Bessel J0: Mathworld Data (Integer Version)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 6.55ε (Mean = 2.86ε)</span><br> <br>
- (<span class="emphasis"><em><cmath>:</em></span> Max = 5.04ε (Mean = 1.78ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_j_integer_orders___cmath__Bessel_J0_Mathworld_Data_Integer_Version_">And
- other failures.</a>)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 1.12ε (Mean = 0.488ε))<br> (<span class="emphasis"><em>Rmath
- 3.2.3:</em></span> Max = 0.629ε (Mean = 0.223ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_integer_orders__Rmath_3_2_3_Bessel_J0_Mathworld_Data_Integer_Version_">And
- other failures.</a>)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 6.55ε (Mean = 2.86ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 2.52ε (Mean = 1.2ε)</span><br> <br>
- (<span class="emphasis"><em><math.h>:</em></span> Max = 1.89ε (Mean = 0.988ε))
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Bessel J0: Mathworld Data (Tricky cases) (Integer Version)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.64e+08ε (Mean = 6.69e+07ε)</span><br>
- <br> (<span class="emphasis"><em><cmath>:</em></span> Max = 4.79e+08ε (Mean =
- 1.96e+08ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 8e+04ε (Mean = 3.27e+04ε)</span><br>
- <br> (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 1e+07ε (Mean = 4.11e+06ε))<br>
- (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 1.04e+07ε (Mean = 4.29e+06ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.64e+08ε (Mean = 6.69e+07ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1e+07ε (Mean = 4.09e+06ε)</span><br>
- <br> (<span class="emphasis"><em><math.h>:</em></span> <span class="red">Max
- = 2.54e+08ε (Mean = 1.04e+08ε))</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Bessel J1: Mathworld Data (Integer Version)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 3.59ε (Mean = 1.33ε)</span><br> <br>
- (<span class="emphasis"><em><cmath>:</em></span> Max = 6.1ε (Mean = 2.95ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_j_integer_orders___cmath__Bessel_J1_Mathworld_Data_Integer_Version_">And
- other failures.</a>)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 1.89ε (Mean = 0.721ε))<br> (<span class="emphasis"><em>Rmath
- 3.2.3:</em></span> Max = 0.946ε (Mean = 0.39ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_integer_orders__Rmath_3_2_3_Bessel_J1_Mathworld_Data_Integer_Version_">And
- other failures.</a>)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.44ε (Mean = 0.637ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.73ε (Mean = 0.976ε)</span><br> <br>
- (<span class="emphasis"><em><math.h>:</em></span> Max = 11.4ε (Mean = 4.15ε))
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Bessel J1: Mathworld Data (tricky cases) (Integer Version)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 2.18e+05ε (Mean = 9.76e+04ε)</span><br>
- <br> (<span class="emphasis"><em><cmath>:</em></span> Max = 2.15e+06ε (Mean =
- 1.58e+06ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 106ε (Mean = 47.5ε)</span><br> <br>
- (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 1.26e+06ε (Mean = 6.28e+05ε))<br>
- (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 2.93e+06ε (Mean = 1.7e+06ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 2.18e+05ε (Mean = 9.76e+04ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 3.23e+04ε (Mean = 1.45e+04ε)</span><br>
- <br> (<span class="emphasis"><em><math.h>:</em></span> Max = 1.44e+07ε (Mean
- = 6.5e+06ε))
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Bessel JN: Mathworld Data (Integer Version)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 6.85ε (Mean = 3.35ε)</span><br> <br>
- (<span class="emphasis"><em><cmath>:</em></span> <span class="red">Max = 2.13e+19ε (Mean
- = 5.16e+18ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_j_integer_orders___cmath__Bessel_JN_Mathworld_Data_Integer_Version_">And
- other failures.</a>)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 6.9e+05ε (Mean = 2.53e+05ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_integer_orders__GSL_2_1_Bessel_JN_Mathworld_Data_Integer_Version_">And
- other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
- <span class="red">Max = +INFε (Mean = +INFε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_integer_orders__Rmath_3_2_3_Bessel_JN_Mathworld_Data_Integer_Version_">And
- other failures.</a>)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 463ε (Mean = 112ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 14.7ε (Mean = 5.4ε)</span><br> <br>
- (<span class="emphasis"><em><math.h>:</em></span> <span class="red">Max = +INFε (Mean
- = +INFε) <a class="link" href="index.html#errors_Microsoft_Visual_C_version_14_1_Win32_double_cyl_bessel_j_integer_orders___math_h__Bessel_JN_Mathworld_Data_Integer_Version_">And
- other failures.</a>)</span>
- </p>
- </td>
- </tr>
- </tbody>
- </table></div>
- </div>
- <br class="table-break">
- </div>
- <div class="section">
- <div class="titlepage"><div><div><h2 class="title" style="clear: both">
- <a name="special_function_error_rates_rep.section_cyl_bessel_j_prime"></a><a class="link" href="index.html#special_function_error_rates_rep.section_cyl_bessel_j_prime" title="cyl_bessel_j_prime">cyl_bessel_j_prime</a>
- </h2></div></div></div>
- <div class="table">
- <a name="special_function_error_rates_rep.section_cyl_bessel_j_prime.table_cyl_bessel_j_prime"></a><p class="title"><b>Table 14. Error rates for cyl_bessel_j_prime</b></p>
- <div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_j_prime">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> double
- </p>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> long double
- </p>
- </th>
- <th>
- <p>
- Sun compiler version 0x5150<br> Sun Solaris<br> long double
- </p>
- </th>
- <th>
- <p>
- Microsoft Visual C++ version 14.1<br> Win32<br> double
- </p>
- </th>
- </tr></thead>
- <tbody>
- <tr>
- <td>
- <p>
- Bessel J0': Mathworld Data
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 18.9ε (Mean = 6.82ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 18.9ε (Mean = 6.72ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 6.62ε (Mean = 2.55ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Bessel J0': Mathworld Data (Tricky cases)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 7.44ε (Mean = 3.34ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 7.44ε (Mean = 3.31ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 3.67ε (Mean = 1.74ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Bessel J1': Mathworld Data
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 7.9ε (Mean = 3.37ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 7.9ε (Mean = 3.37ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.999ε (Mean = 0.627ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Bessel J1': Mathworld Data (tricky cases)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 287ε (Mean = 129ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 5.88e+05ε (Mean = 2.63e+05ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 5.88e+05ε (Mean = 2.63e+05ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 288ε (Mean = 129ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Bessel JN': Mathworld Data
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.527ε (Mean = 0.128ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.29e+03ε (Mean = 312ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.29e+03ε (Mean = 355ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 14ε (Mean = 6.13ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Bessel J': Mathworld Data
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 21.5ε (Mean = 4.7ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 42.5ε (Mean = 9.31ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 42.5ε (Mean = 9.32ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 23.7ε (Mean = 8ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Bessel J': Mathworld Data (large values)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 989ε (Mean = 495ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 989ε (Mean = 495ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 2.9ε (Mean = 1.61ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Bessel JN': Random Data
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.593ε (Mean = 0.0396ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 11.3ε (Mean = 1.85ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 79.4ε (Mean = 16.2ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 6.34ε (Mean = 0.999ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Bessel J': Random Data
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.885ε (Mean = 0.033ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 139ε (Mean = 6.47ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 279ε (Mean = 27.2ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 176ε (Mean = 9.75ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Bessel J': Random Data (Tricky large values)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 474ε (Mean = 62.2ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 474ε (Mean = 64.5ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 379ε (Mean = 45.4ε)</span>
- </p>
- </td>
- </tr>
- </tbody>
- </table></div>
- </div>
- <br class="table-break">
- </div>
- <div class="section">
- <div class="titlepage"><div><div><h2 class="title" style="clear: both">
- <a name="special_function_error_rates_rep.section_cyl_bessel_j_prime_integer_orders_"></a><a class="link" href="index.html#special_function_error_rates_rep.section_cyl_bessel_j_prime_integer_orders_" title="cyl_bessel_j_prime (integer orders)">cyl_bessel_j_prime
- (integer orders)</a>
- </h2></div></div></div>
- <div class="table">
- <a name="special_function_error_rates_rep.section_cyl_bessel_j_prime_integer_orders_.table_cyl_bessel_j_prime_integer_orders_"></a><p class="title"><b>Table 15. Error rates for cyl_bessel_j_prime (integer orders)</b></p>
- <div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_j_prime (integer orders)">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> double
- </p>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> long double
- </p>
- </th>
- <th>
- <p>
- Sun compiler version 0x5150<br> Sun Solaris<br> long double
- </p>
- </th>
- <th>
- <p>
- Microsoft Visual C++ version 14.1<br> Win32<br> double
- </p>
- </th>
- </tr></thead>
- <tbody>
- <tr>
- <td>
- <p>
- Bessel J0': Mathworld Data (Integer Version)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 18.9ε (Mean = 6.82ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 18.9ε (Mean = 6.72ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 6.62ε (Mean = 2.55ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Bessel J0': Mathworld Data (Tricky cases) (Integer Version)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 7.44ε (Mean = 3.34ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 7.44ε (Mean = 3.31ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 3.67ε (Mean = 1.74ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Bessel J1': Mathworld Data (Integer Version)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 7.9ε (Mean = 3.37ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 7.9ε (Mean = 3.37ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.999ε (Mean = 0.627ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Bessel J1': Mathworld Data (tricky cases) (Integer Version)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 287ε (Mean = 129ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 5.88e+05ε (Mean = 2.63e+05ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 5.88e+05ε (Mean = 2.63e+05ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 288ε (Mean = 129ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Bessel JN': Mathworld Data (Integer Version)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.527ε (Mean = 0.128ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.29e+03ε (Mean = 312ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.29e+03ε (Mean = 355ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 14ε (Mean = 6.13ε)</span>
- </p>
- </td>
- </tr>
- </tbody>
- </table></div>
- </div>
- <br class="table-break">
- </div>
- <div class="section">
- <div class="titlepage"><div><div><h2 class="title" style="clear: both">
- <a name="special_function_error_rates_rep.section_cyl_bessel_k"></a><a class="link" href="index.html#special_function_error_rates_rep.section_cyl_bessel_k" title="cyl_bessel_k">cyl_bessel_k</a>
- </h2></div></div></div>
- <div class="table">
- <a name="special_function_error_rates_rep.section_cyl_bessel_k.table_cyl_bessel_k"></a><p class="title"><b>Table 16. Error rates for cyl_bessel_k</b></p>
- <div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_k">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> long double
- </p>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> double
- </p>
- </th>
- <th>
- <p>
- Sun compiler version 0x5150<br> Sun Solaris<br> long double
- </p>
- </th>
- <th>
- <p>
- Microsoft Visual C++ version 14.1<br> Win32<br> double
- </p>
- </th>
- </tr></thead>
- <tbody>
- <tr>
- <td>
- <p>
- Bessel K0: Mathworld Data
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.833ε (Mean = 0.436ε)</span><br> <br>
- (<span class="emphasis"><em><cmath>:</em></span> Max = 9.33ε (Mean = 3.25ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 6.04ε (Mean = 2.16ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
- Max = 0.833ε (Mean = 0.601ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.833ε (Mean = 0.436ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.833ε (Mean = 0.552ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Bessel K1: Mathworld Data
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.786ε (Mean = 0.329ε)</span><br> <br>
- (<span class="emphasis"><em><cmath>:</em></span> Max = 8.94ε (Mean = 3.19ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 6.26ε (Mean = 2.21ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
- Max = 0.894ε (Mean = 0.516ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.786ε (Mean = 0.329ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.786ε (Mean = 0.39ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Bessel Kn: Mathworld Data
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 2.6ε (Mean = 1.21ε)</span><br> <br>
- (<span class="emphasis"><em><cmath>:</em></span> Max = 12.9ε (Mean = 4.91ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_k__cmath__Bessel_Kn_Mathworld_Data">And
- other failures.</a>)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 3.36ε (Mean = 1.43ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_k_GSL_2_1_Bessel_Kn_Mathworld_Data">And
- other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
- Max = 8.48ε (Mean = 2.98ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 2.6ε (Mean = 1.21ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 3.63ε (Mean = 1.46ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Bessel Kv: Mathworld Data
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 3.58ε (Mean = 2.39ε)</span><br> <br>
- (<span class="emphasis"><em><cmath>:</em></span> Max = 13ε (Mean = 4.81ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_k__cmath__Bessel_Kv_Mathworld_Data">And
- other failures.</a>)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 5.47ε (Mean = 2.04ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_k_GSL_2_1_Bessel_Kv_Mathworld_Data">And
- other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
- Max = 3.15ε (Mean = 1.35ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 5.21ε (Mean = 2.53ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 4.78ε (Mean = 2.19ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Bessel Kv: Mathworld Data (large values)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 42.3ε (Mean = 21ε)</span><br> <br> (<span class="emphasis"><em><cmath>:</em></span>
- Max = 42.3ε (Mean = 19.8ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_k__cmath__Bessel_Kv_Mathworld_Data_large_values_">And
- other failures.</a>)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 308ε (Mean = 142ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_k_GSL_2_1_Bessel_Kv_Mathworld_Data_large_values_">And
- other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
- Max = 84.6ε (Mean = 37.8ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 42.3ε (Mean = 21ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 59.8ε (Mean = 26.9ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Bessel Kn: Random Data
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 4.55ε (Mean = 1.12ε)</span><br> <br>
- (<span class="emphasis"><em><cmath>:</em></span> Max = 13.9ε (Mean = 2.91ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.764ε (Mean = 0.0348ε)</span><br> <br>
- (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 8.71ε (Mean = 1.76ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_k_GSL_2_1_Bessel_Kn_Random_Data">And
- other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
- Max = 7.47ε (Mean = 1.34ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 4.55ε (Mean = 1.12ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 9.34ε (Mean = 1.7ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Bessel Kv: Random Data
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 7.88ε (Mean = 1.48ε)</span><br> <br>
- (<span class="emphasis"><em><cmath>:</em></span> Max = 13.6ε (Mean = 2.68ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_k__cmath__Bessel_Kv_Random_Data">And
- other failures.</a>)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.507ε (Mean = 0.0313ε)</span><br> <br>
- (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 9.71ε (Mean = 1.47ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_k_GSL_2_1_Bessel_Kv_Random_Data">And
- other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
- Max = 7.37ε (Mean = 1.49ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 7.88ε (Mean = 1.47ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 8.33ε (Mean = 1.62ε)</span>
- </p>
- </td>
- </tr>
- </tbody>
- </table></div>
- </div>
- <br class="table-break">
- </div>
- <div class="section">
- <div class="titlepage"><div><div><h2 class="title" style="clear: both">
- <a name="special_function_error_rates_rep.section_cyl_bessel_k_integer_orders_"></a><a class="link" href="index.html#special_function_error_rates_rep.section_cyl_bessel_k_integer_orders_" title="cyl_bessel_k (integer orders)">cyl_bessel_k
- (integer orders)</a>
- </h2></div></div></div>
- <div class="table">
- <a name="special_function_error_rates_rep.section_cyl_bessel_k_integer_orders_.table_cyl_bessel_k_integer_orders_"></a><p class="title"><b>Table 17. Error rates for cyl_bessel_k (integer orders)</b></p>
- <div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_k (integer orders)">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> long double
- </p>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> double
- </p>
- </th>
- <th>
- <p>
- Sun compiler version 0x5150<br> Sun Solaris<br> long double
- </p>
- </th>
- <th>
- <p>
- Microsoft Visual C++ version 14.1<br> Win32<br> double
- </p>
- </th>
- </tr></thead>
- <tbody>
- <tr>
- <td>
- <p>
- Bessel K0: Mathworld Data (Integer Version)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.833ε (Mean = 0.436ε)</span><br> <br>
- (<span class="emphasis"><em><cmath>:</em></span> Max = 9.33ε (Mean = 3.25ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 1.2ε (Mean = 0.733ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
- Max = 0.833ε (Mean = 0.601ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.833ε (Mean = 0.436ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.833ε (Mean = 0.552ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Bessel K1: Mathworld Data (Integer Version)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.786ε (Mean = 0.329ε)</span><br> <br>
- (<span class="emphasis"><em><cmath>:</em></span> Max = 8.94ε (Mean = 3.19ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 0.626ε (Mean = 0.333ε))<br> (<span class="emphasis"><em>Rmath
- 3.2.3:</em></span> Max = 0.894ε (Mean = 0.516ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.786ε (Mean = 0.329ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.786ε (Mean = 0.39ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Bessel Kn: Mathworld Data (Integer Version)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 2.6ε (Mean = 1.21ε)</span><br> <br>
- (<span class="emphasis"><em><cmath>:</em></span> Max = 12.9ε (Mean = 4.91ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_k_integer_orders___cmath__Bessel_Kn_Mathworld_Data_Integer_Version_">And
- other failures.</a>)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 168ε (Mean = 59.5ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
- Max = 8.48ε (Mean = 2.98ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 2.6ε (Mean = 1.21ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 3.63ε (Mean = 1.46ε)</span>
- </p>
- </td>
- </tr>
- </tbody>
- </table></div>
- </div>
- <br class="table-break">
- </div>
- <div class="section">
- <div class="titlepage"><div><div><h2 class="title" style="clear: both">
- <a name="special_function_error_rates_rep.section_cyl_bessel_k_prime"></a><a class="link" href="index.html#special_function_error_rates_rep.section_cyl_bessel_k_prime" title="cyl_bessel_k_prime">cyl_bessel_k_prime</a>
- </h2></div></div></div>
- <div class="table">
- <a name="special_function_error_rates_rep.section_cyl_bessel_k_prime.table_cyl_bessel_k_prime"></a><p class="title"><b>Table 18. Error rates for cyl_bessel_k_prime</b></p>
- <div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_k_prime">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> double
- </p>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> long double
- </p>
- </th>
- <th>
- <p>
- Sun compiler version 0x5150<br> Sun Solaris<br> long double
- </p>
- </th>
- <th>
- <p>
- Microsoft Visual C++ version 14.1<br> Win32<br> double
- </p>
- </th>
- </tr></thead>
- <tbody>
- <tr>
- <td>
- <p>
- Bessel K'0: Mathworld Data
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.786ε (Mean = 0.329ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.786ε (Mean = 0.329ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.786ε (Mean = 0.39ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Bessel K'1: Mathworld Data
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.736ε (Mean = 0.389ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.736ε (Mean = 0.389ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.761ε (Mean = 0.444ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Bessel K'n: Mathworld Data
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 2.16ε (Mean = 1.08ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 2.16ε (Mean = 1.08ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 4.17ε (Mean = 1.75ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Bessel K'v: Mathworld Data
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 3.94ε (Mean = 2.44ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 3.94ε (Mean = 2.34ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 3.94ε (Mean = 1.47ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Bessel K'v: Mathworld Data (large values)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 59.2ε (Mean = 42.9ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 58.7ε (Mean = 42.6ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 18.6ε (Mean = 11.8ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Bessel K'n: Random Data
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 4.45ε (Mean = 1.19ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 4.45ε (Mean = 1.19ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 9.67ε (Mean = 1.73ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Bessel K'v: Random Data
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 7.95ε (Mean = 1.53ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 7.95ε (Mean = 1.52ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 8.32ε (Mean = 1.65ε)</span>
- </p>
- </td>
- </tr>
- </tbody>
- </table></div>
- </div>
- <br class="table-break">
- </div>
- <div class="section">
- <div class="titlepage"><div><div><h2 class="title" style="clear: both">
- <a name="special_function_error_rates_rep.section_cyl_bessel_k_prime_integer_orders_"></a><a class="link" href="index.html#special_function_error_rates_rep.section_cyl_bessel_k_prime_integer_orders_" title="cyl_bessel_k_prime (integer orders)">cyl_bessel_k_prime
- (integer orders)</a>
- </h2></div></div></div>
- <div class="table">
- <a name="special_function_error_rates_rep.section_cyl_bessel_k_prime_integer_orders_.table_cyl_bessel_k_prime_integer_orders_"></a><p class="title"><b>Table 19. Error rates for cyl_bessel_k_prime (integer orders)</b></p>
- <div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_k_prime (integer orders)">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> double
- </p>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> long double
- </p>
- </th>
- <th>
- <p>
- Sun compiler version 0x5150<br> Sun Solaris<br> long double
- </p>
- </th>
- <th>
- <p>
- Microsoft Visual C++ version 14.1<br> Win32<br> double
- </p>
- </th>
- </tr></thead>
- <tbody>
- <tr>
- <td>
- <p>
- Bessel K'0: Mathworld Data (Integer Version)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.786ε (Mean = 0.329ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.786ε (Mean = 0.329ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.786ε (Mean = 0.39ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Bessel K'1: Mathworld Data (Integer Version)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.736ε (Mean = 0.389ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.736ε (Mean = 0.389ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.761ε (Mean = 0.444ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Bessel K'n: Mathworld Data (Integer Version)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 2.16ε (Mean = 1.08ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 2.16ε (Mean = 1.08ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 4.17ε (Mean = 1.75ε)</span>
- </p>
- </td>
- </tr>
- </tbody>
- </table></div>
- </div>
- <br class="table-break">
- </div>
- <div class="section">
- <div class="titlepage"><div><div><h2 class="title" style="clear: both">
- <a name="special_function_error_rates_rep.section_cyl_neumann"></a><a class="link" href="index.html#special_function_error_rates_rep.section_cyl_neumann" title="cyl_neumann">cyl_neumann</a>
- </h2></div></div></div>
- <div class="table">
- <a name="special_function_error_rates_rep.section_cyl_neumann.table_cyl_neumann"></a><p class="title"><b>Table 20. Error rates for cyl_neumann</b></p>
- <div class="table-contents"><table class="table" summary="Error rates for cyl_neumann">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> long double
- </p>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> double
- </p>
- </th>
- <th>
- <p>
- Sun compiler version 0x5150<br> Sun Solaris<br> long double
- </p>
- </th>
- <th>
- <p>
- Microsoft Visual C++ version 14.1<br> Win32<br> double
- </p>
- </th>
- </tr></thead>
- <tbody>
- <tr>
- <td>
- <p>
- Y0: Mathworld Data
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 5.53ε (Mean = 2.4ε)</span><br> <br>
- (<span class="emphasis"><em><cmath>:</em></span> Max = 2.05e+05ε (Mean = 6.87e+04ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 60.9ε (Mean = 20.4ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
- Max = 167ε (Mean = 56.5ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 5.53ε (Mean = 2.4ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 4.61ε (Mean = 2.29ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Y1: Mathworld Data
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 6.33ε (Mean = 2.25ε)</span><br> <br>
- (<span class="emphasis"><em><cmath>:</em></span> Max = 9.71e+03ε (Mean = 4.08e+03ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 23.4ε (Mean = 8.1ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
- Max = 193ε (Mean = 64.4ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 6.33ε (Mean = 2.29ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 4.75ε (Mean = 1.72ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Yn: Mathworld Data
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 55.2ε (Mean = 17.8ε)</span><br> <br>
- (<span class="emphasis"><em><cmath>:</em></span> <span class="red">Max = 2.2e+20ε (Mean
- = 6.97e+19ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_neumann__cmath__Yn_Mathworld_Data">And
- other failures.</a>)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.993ε (Mean = 0.314ε)</span><br> <br>
- (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 2.41e+05ε (Mean = 7.62e+04ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_neumann_GSL_2_1_Yn_Mathworld_Data">And
- other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
- Max = 1.24e+04ε (Mean = 4e+03ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 55.2ε (Mean = 17.8ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 35ε (Mean = 11.9ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Yv: Mathworld Data
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 10.7ε (Mean = 4.93ε)</span><br> <br>
- (<span class="emphasis"><em><cmath>:</em></span> <span class="red">Max = 3.49e+15ε (Mean
- = 1.05e+15ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_neumann__cmath__Yv_Mathworld_Data">And
- other failures.</a>)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 10ε (Mean = 3.02ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 1.07e+05ε (Mean = 3.22e+04ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_neumann_GSL_2_1_Yv_Mathworld_Data">And
- other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
- Max = 243ε (Mean = 73.9ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 10.7ε (Mean = 5.1ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 7.89ε (Mean = 3.27ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Yv: Mathworld Data (large values)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.7ε (Mean = 1.33ε)</span><br> <br>
- (<span class="emphasis"><em><cmath>:</em></span> Max = 43.2ε (Mean = 16.3ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_neumann__cmath__Yv_Mathworld_Data_large_values_">And
- other failures.</a>)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 60.8ε (Mean = 23ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_neumann_GSL_2_1_Yv_Mathworld_Data_large_values_">And
- other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
- Max = 0.682ε (Mean = 0.335ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.7ε (Mean = 1.33ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.682ε (Mean = 0.423ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Y0 and Y1: Random Data
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 10.8ε (Mean = 3.04ε)</span><br> <br>
- (<span class="emphasis"><em><cmath>:</em></span> Max = 2.59e+03ε (Mean = 500ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 34.4ε (Mean = 8.9ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
- Max = 83ε (Mean = 14.2ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 10.8ε (Mean = 3.04ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 4.17ε (Mean = 1.24ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Yn: Random Data
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 338ε (Mean = 27.5ε)</span><br> <br>
- (<span class="emphasis"><em><cmath>:</em></span> Max = 4.01e+03ε (Mean = 348ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 500ε (Mean = 47.8ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
- Max = 691ε (Mean = 67.9ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 338ε (Mean = 27.5ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 117ε (Mean = 10.2ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Yv: Random Data
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 2.08e+03ε (Mean = 149ε)</span><br> <br>
- (<span class="emphasis"><em><cmath>:</em></span> <span class="red">Max = +INFε (Mean
- = +INFε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_neumann__cmath__Yv_Random_Data">And
- other failures.</a>)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.53ε (Mean = 0.102ε)</span><br> <br>
- (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 1.41e+06ε (Mean = 7.67e+04ε))<br>
- (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 1.79e+05ε (Mean = 9.64e+03ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 2.08e+03ε (Mean = 149ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.23e+03ε (Mean = 69.9ε)</span>
- </p>
- </td>
- </tr>
- </tbody>
- </table></div>
- </div>
- <br class="table-break">
- </div>
- <div class="section">
- <div class="titlepage"><div><div><h2 class="title" style="clear: both">
- <a name="special_function_error_rates_rep.section_cyl_neumann_integer_orders_"></a><a class="link" href="index.html#special_function_error_rates_rep.section_cyl_neumann_integer_orders_" title="cyl_neumann (integer orders)">cyl_neumann
- (integer orders)</a>
- </h2></div></div></div>
- <div class="table">
- <a name="special_function_error_rates_rep.section_cyl_neumann_integer_orders_.table_cyl_neumann_integer_orders_"></a><p class="title"><b>Table 21. Error rates for cyl_neumann (integer orders)</b></p>
- <div class="table-contents"><table class="table" summary="Error rates for cyl_neumann (integer orders)">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> long double
- </p>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> double
- </p>
- </th>
- <th>
- <p>
- Sun compiler version 0x5150<br> Sun Solaris<br> long double
- </p>
- </th>
- <th>
- <p>
- Microsoft Visual C++ version 14.1<br> Win32<br> double
- </p>
- </th>
- </tr></thead>
- <tbody>
- <tr>
- <td>
- <p>
- Y0: Mathworld Data (Integer Version)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 5.53ε (Mean = 2.4ε)</span><br> <br>
- (<span class="emphasis"><em><cmath>:</em></span> Max = 2.05e+05ε (Mean = 6.87e+04ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 6.46ε (Mean = 2.38ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
- Max = 167ε (Mean = 56.5ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 5.53ε (Mean = 2.4ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 4.61ε (Mean = 2.29ε)</span><br> <br>
- (<span class="emphasis"><em><math.h>:</em></span> Max = 5.37e+03ε (Mean = 1.81e+03ε))
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Y1: Mathworld Data (Integer Version)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 6.33ε (Mean = 2.25ε)</span><br> <br>
- (<span class="emphasis"><em><cmath>:</em></span> Max = 9.71e+03ε (Mean = 4.08e+03ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 1.51ε (Mean = 0.839ε))<br> (<span class="emphasis"><em>Rmath
- 3.2.3:</em></span> Max = 193ε (Mean = 64.4ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 6.33ε (Mean = 2.29ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 4.75ε (Mean = 1.72ε)</span><br> <br>
- (<span class="emphasis"><em><math.h>:</em></span> Max = 1.86e+04ε (Mean = 6.2e+03ε))
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Yn: Mathworld Data (Integer Version)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 55.2ε (Mean = 17.8ε)</span><br> <br>
- (<span class="emphasis"><em><cmath>:</em></span> <span class="red">Max = 2.2e+20ε (Mean
- = 6.97e+19ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_neumann_integer_orders___cmath__Yn_Mathworld_Data_Integer_Version_">And
- other failures.</a>)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.993ε (Mean = 0.314ε)</span><br> <br>
- (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 2.41e+05ε (Mean = 7.62e+04ε))<br>
- (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 1.24e+04ε (Mean = 4e+03ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 55.2ε (Mean = 17.8ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 35ε (Mean = 11.9ε)</span><br> <br> (<span class="emphasis"><em><math.h>:</em></span>
- Max = 2.49e+05ε (Mean = 8.14e+04ε))
- </p>
- </td>
- </tr>
- </tbody>
- </table></div>
- </div>
- <br class="table-break">
- </div>
- <div class="section">
- <div class="titlepage"><div><div><h2 class="title" style="clear: both">
- <a name="special_function_error_rates_rep.section_cyl_neumann_prime"></a><a class="link" href="index.html#special_function_error_rates_rep.section_cyl_neumann_prime" title="cyl_neumann_prime">cyl_neumann_prime</a>
- </h2></div></div></div>
- <div class="table">
- <a name="special_function_error_rates_rep.section_cyl_neumann_prime.table_cyl_neumann_prime"></a><p class="title"><b>Table 22. Error rates for cyl_neumann_prime</b></p>
- <div class="table-contents"><table class="table" summary="Error rates for cyl_neumann_prime">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> double
- </p>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> long double
- </p>
- </th>
- <th>
- <p>
- Sun compiler version 0x5150<br> Sun Solaris<br> long double
- </p>
- </th>
- <th>
- <p>
- Microsoft Visual C++ version 14.1<br> Win32<br> double
- </p>
- </th>
- </tr></thead>
- <tbody>
- <tr>
- <td>
- <p>
- Y'0: Mathworld Data
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 6.33ε (Mean = 3.12ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 6.33ε (Mean = 3.14ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 4.75ε (Mean = 1.75ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Y'1: Mathworld Data
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.58ε (Mean = 0.193ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 37.1ε (Mean = 12.8ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 34ε (Mean = 11.8ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 3.08ε (Mean = 1.2ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Y'n: Mathworld Data
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 2.05ε (Mean = 0.677ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 56ε (Mean = 18.2ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 56ε (Mean = 21.3ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 563ε (Mean = 178ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Y'v: Mathworld Data
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 21.5ε (Mean = 6.49ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 42.5ε (Mean = 13.4ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 42.5ε (Mean = 13.6ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 23.7ε (Mean = 10.1ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Y'v: Mathworld Data (large values)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.57ε (Mean = 1.24ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.57ε (Mean = 1.24ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.627ε (Mean = 0.237ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Y'0 and Y'1: Random Data
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 23.8ε (Mean = 3.69ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 23.8ε (Mean = 3.69ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 5.95ε (Mean = 1.36ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Y'n: Random Data
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.53ε (Mean = 0.0885ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 2.35e+03ε (Mean = 136ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 2.35e+03ε (Mean = 136ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 621ε (Mean = 36ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Y'v: Random Data
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 56.8ε (Mean = 2.59ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.16e+05ε (Mean = 5.28e+03ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.16e+05ε (Mean = 5.28e+03ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 3.23e+04ε (Mean = 1.13e+03ε)</span>
- </p>
- </td>
- </tr>
- </tbody>
- </table></div>
- </div>
- <br class="table-break">
- </div>
- <div class="section">
- <div class="titlepage"><div><div><h2 class="title" style="clear: both">
- <a name="special_function_error_rates_rep.section_cyl_neumann_prime_integer_orders_"></a><a class="link" href="index.html#special_function_error_rates_rep.section_cyl_neumann_prime_integer_orders_" title="cyl_neumann_prime (integer orders)">cyl_neumann_prime
- (integer orders)</a>
- </h2></div></div></div>
- <div class="table">
- <a name="special_function_error_rates_rep.section_cyl_neumann_prime_integer_orders_.table_cyl_neumann_prime_integer_orders_"></a><p class="title"><b>Table 23. Error rates for cyl_neumann_prime (integer orders)</b></p>
- <div class="table-contents"><table class="table" summary="Error rates for cyl_neumann_prime (integer orders)">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> double
- </p>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> long double
- </p>
- </th>
- <th>
- <p>
- Sun compiler version 0x5150<br> Sun Solaris<br> long double
- </p>
- </th>
- <th>
- <p>
- Microsoft Visual C++ version 14.1<br> Win32<br> double
- </p>
- </th>
- </tr></thead>
- <tbody>
- <tr>
- <td>
- <p>
- Y'0: Mathworld Data (Integer Version)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 6.33ε (Mean = 3.12ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 6.33ε (Mean = 3.14ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 4.75ε (Mean = 1.75ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Y'1: Mathworld Data (Integer Version)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.58ε (Mean = 0.193ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 37.1ε (Mean = 12.8ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 34ε (Mean = 11.8ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 3.08ε (Mean = 1.2ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Y'n: Mathworld Data (Integer Version)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 2.05ε (Mean = 0.677ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 56ε (Mean = 18.2ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 56ε (Mean = 21.3ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 563ε (Mean = 178ε)</span>
- </p>
- </td>
- </tr>
- </tbody>
- </table></div>
- </div>
- <br class="table-break">
- </div>
- <div class="section">
- <div class="titlepage"><div><div><h2 class="title" style="clear: both">
- <a name="special_function_error_rates_rep.section_digamma"></a><a class="link" href="index.html#special_function_error_rates_rep.section_digamma" title="digamma">digamma</a>
- </h2></div></div></div>
- <div class="table">
- <a name="special_function_error_rates_rep.section_digamma.table_digamma"></a><p class="title"><b>Table 24. Error rates for digamma</b></p>
- <div class="table-contents"><table class="table" summary="Error rates for digamma">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> double
- </p>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> long double
- </p>
- </th>
- <th>
- <p>
- Sun compiler version 0x5150<br> Sun Solaris<br> long double
- </p>
- </th>
- <th>
- <p>
- Microsoft Visual C++ version 14.1<br> Win32<br> double
- </p>
- </th>
- </tr></thead>
- <tbody>
- <tr>
- <td>
- <p>
- Digamma Function: Large Values
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 1.84ε (Mean = 0.71ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
- Max = 1.18ε (Mean = 0.331ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.39ε (Mean = 0.413ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.39ε (Mean = 0.413ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.98ε (Mean = 0.369ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Digamma Function: Near the Positive Root
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.891ε (Mean = 0.0995ε)</span><br> <br>
- (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 135ε (Mean = 11.9ε))<br> (<span class="emphasis"><em>Rmath
- 3.2.3:</em></span> Max = 2.02e+03ε (Mean = 256ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.37ε (Mean = 0.477ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.31ε (Mean = 0.471ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.997ε (Mean = 0.527ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Digamma Function: Near Zero
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 0.953ε (Mean = 0.348ε))<br> (<span class="emphasis"><em>Rmath
- 3.2.3:</em></span> Max = 1.17ε (Mean = 0.564ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.984ε (Mean = 0.361ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.984ε (Mean = 0.361ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.953ε (Mean = 0.337ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Digamma Function: Negative Values
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 4.56e+04ε (Mean = 3.91e+03ε))<br> (<span class="emphasis"><em>Rmath
- 3.2.3:</em></span> Max = 4.6e+04ε (Mean = 3.94e+03ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 180ε (Mean = 13ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 180ε (Mean = 13ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 214ε (Mean = 16.1ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Digamma Function: Values near 0
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 0.866ε (Mean = 0.387ε))<br> (<span class="emphasis"><em>Rmath
- 3.2.3:</em></span> Max = 3.58e+05ε (Mean = 1.6e+05ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1ε (Mean = 0.592ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1ε (Mean = 0.592ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Digamma Function: Integer arguments
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.992ε (Mean = 0.215ε)</span><br> <br>
- (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 1.18ε (Mean = 0.607ε))<br> (<span class="emphasis"><em>Rmath
- 3.2.3:</em></span> Max = 4.33ε (Mean = 0.982ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.888ε (Mean = 0.403ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.888ε (Mean = 0.403ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.992ε (Mean = 0.452ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Digamma Function: Half integer arguments
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 1.09ε (Mean = 0.531ε))<br> (<span class="emphasis"><em>Rmath
- 3.2.3:</em></span> Max = 46.2ε (Mean = 7.24ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.906ε (Mean = 0.409ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.906ε (Mean = 0.409ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.78ε (Mean = 0.314ε)</span>
- </p>
- </td>
- </tr>
- </tbody>
- </table></div>
- </div>
- <br class="table-break">
- </div>
- <div class="section">
- <div class="titlepage"><div><div><h2 class="title" style="clear: both">
- <a name="special_function_error_rates_rep.section_ellint_1"></a><a class="link" href="index.html#special_function_error_rates_rep.section_ellint_1" title="ellint_1">ellint_1</a>
- </h2></div></div></div>
- <div class="table">
- <a name="special_function_error_rates_rep.section_ellint_1.table_ellint_1"></a><p class="title"><b>Table 25. Error rates for ellint_1</b></p>
- <div class="table-contents"><table class="table" summary="Error rates for ellint_1">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> long double
- </p>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> double
- </p>
- </th>
- <th>
- <p>
- Sun compiler version 0x5150<br> Sun Solaris<br> long double
- </p>
- </th>
- <th>
- <p>
- Microsoft Visual C++ version 14.1<br> Win32<br> double
- </p>
- </th>
- </tr></thead>
- <tbody>
- <tr>
- <td>
- <p>
- Elliptic Integral F: Mathworld Data
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.94ε (Mean = 0.509ε)</span><br> <br>
- (<span class="emphasis"><em><cmath>:</em></span> <span class="red">Max = +INFε (Mean
- = +INFε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_ellint_1__cmath__Elliptic_Integral_F_Mathworld_Data">And
- other failures.</a>)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 0.919ε (Mean = 0.544ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.94ε (Mean = 0.509ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.919ε (Mean = 0.542ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Elliptic Integral F: Random Data
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.57ε (Mean = 0.56ε)</span><br> <br>
- (<span class="emphasis"><em><cmath>:</em></span> Max = 2.56ε (Mean = 0.816ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 2.99ε (Mean = 0.797ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.57ε (Mean = 0.561ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 2.26ε (Mean = 0.631ε)</span>
- </p>
- </td>
- </tr>
- </tbody>
- </table></div>
- </div>
- <br class="table-break">
- </div>
- <div class="section">
- <div class="titlepage"><div><div><h2 class="title" style="clear: both">
- <a name="special_function_error_rates_rep.section_ellint_1_complete_"></a><a class="link" href="index.html#special_function_error_rates_rep.section_ellint_1_complete_" title="ellint_1 (complete)">ellint_1
- (complete)</a>
- </h2></div></div></div>
- <div class="table">
- <a name="special_function_error_rates_rep.section_ellint_1_complete_.table_ellint_1_complete_"></a><p class="title"><b>Table 26. Error rates for ellint_1 (complete)</b></p>
- <div class="table-contents"><table class="table" summary="Error rates for ellint_1 (complete)">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> long double
- </p>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> double
- </p>
- </th>
- <th>
- <p>
- Sun compiler version 0x5150<br> Sun Solaris<br> long double
- </p>
- </th>
- <th>
- <p>
- Microsoft Visual C++ version 14.1<br> Win32<br> double
- </p>
- </th>
- </tr></thead>
- <tbody>
- <tr>
- <td>
- <p>
- Elliptic Integral K: Mathworld Data
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.887ε (Mean = 0.296ε)</span><br> <br>
- (<span class="emphasis"><em><cmath>:</em></span> Max = 1.19ε (Mean = 0.765ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 0.623ε (Mean = 0.393ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.887ε (Mean = 0.296ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.915ε (Mean = 0.547ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Elliptic Integral K: Random Data
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.27ε (Mean = 0.473ε)</span><br> <br>
- (<span class="emphasis"><em><cmath>:</em></span> Max = 2.19ε (Mean = 0.694ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.851ε (Mean = 0.0851ε)</span><br> <br>
- (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 2.32ε (Mean = 0.688ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.27ε (Mean = 0.473ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.958ε (Mean = 0.408ε)</span>
- </p>
- </td>
- </tr>
- </tbody>
- </table></div>
- </div>
- <br class="table-break">
- </div>
- <div class="section">
- <div class="titlepage"><div><div><h2 class="title" style="clear: both">
- <a name="special_function_error_rates_rep.section_ellint_2"></a><a class="link" href="index.html#special_function_error_rates_rep.section_ellint_2" title="ellint_2">ellint_2</a>
- </h2></div></div></div>
- <div class="table">
- <a name="special_function_error_rates_rep.section_ellint_2.table_ellint_2"></a><p class="title"><b>Table 27. Error rates for ellint_2</b></p>
- <div class="table-contents"><table class="table" summary="Error rates for ellint_2">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> double
- </p>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> long double
- </p>
- </th>
- <th>
- <p>
- Sun compiler version 0x5150<br> Sun Solaris<br> long double
- </p>
- </th>
- <th>
- <p>
- Microsoft Visual C++ version 14.1<br> Win32<br> double
- </p>
- </th>
- </tr></thead>
- <tbody>
- <tr>
- <td>
- <p>
- Elliptic Integral E: Mathworld Data
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 0.63ε (Mean = 0.325ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.656ε (Mean = 0.317ε)</span><br> <br>
- (<span class="emphasis"><em><cmath>:</em></span> <span class="red">Max = +INFε (Mean
- = +INFε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_ellint_2__cmath__Elliptic_Integral_E_Mathworld_Data">And
- other failures.</a>)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.656ε (Mean = 0.317ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.31ε (Mean = 0.727ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Elliptic Integral E: Random Data
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 4.4ε (Mean = 1.16ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 2.05ε (Mean = 0.632ε)</span><br> <br>
- (<span class="emphasis"><em><cmath>:</em></span> Max = 3.08e+04ε (Mean = 3.84e+03ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 2.05ε (Mean = 0.632ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 2.23ε (Mean = 0.639ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Elliptic Integral E: Small Angles
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 0.5ε (Mean = 0.118ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1ε (Mean = 0.283ε)</span><br> <br> (<span class="emphasis"><em><cmath>:</em></span>
- Max = 2ε (Mean = 0.333ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1ε (Mean = 0.283ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1ε (Mean = 0.421ε)</span>
- </p>
- </td>
- </tr>
- </tbody>
- </table></div>
- </div>
- <br class="table-break">
- </div>
- <div class="section">
- <div class="titlepage"><div><div><h2 class="title" style="clear: both">
- <a name="special_function_error_rates_rep.section_ellint_2_complete_"></a><a class="link" href="index.html#special_function_error_rates_rep.section_ellint_2_complete_" title="ellint_2 (complete)">ellint_2
- (complete)</a>
- </h2></div></div></div>
- <div class="table">
- <a name="special_function_error_rates_rep.section_ellint_2_complete_.table_ellint_2_complete_"></a><p class="title"><b>Table 28. Error rates for ellint_2 (complete)</b></p>
- <div class="table-contents"><table class="table" summary="Error rates for ellint_2 (complete)">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> double
- </p>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> long double
- </p>
- </th>
- <th>
- <p>
- Sun compiler version 0x5150<br> Sun Solaris<br> long double
- </p>
- </th>
- <th>
- <p>
- Microsoft Visual C++ version 14.1<br> Win32<br> double
- </p>
- </th>
- </tr></thead>
- <tbody>
- <tr>
- <td>
- <p>
- Elliptic Integral E: Mathworld Data
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 3.09ε (Mean = 1.04ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_ellint_2_complete__GSL_2_1_Elliptic_Integral_E_Mathworld_Data">And
- other failures.</a>)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.836ε (Mean = 0.469ε)</span><br> <br>
- (<span class="emphasis"><em><cmath>:</em></span> Max = 170ε (Mean = 55.1ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.836ε (Mean = 0.469ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.3ε (Mean = 0.615ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Elliptic Integral E: Random Data
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 4.34ε (Mean = 1.18ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.97ε (Mean = 0.629ε)</span><br> <br>
- (<span class="emphasis"><em><cmath>:</em></span> Max = 2.49e+04ε (Mean = 3.39e+03ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.97ε (Mean = 0.629ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.71ε (Mean = 0.553ε)</span>
- </p>
- </td>
- </tr>
- </tbody>
- </table></div>
- </div>
- <br class="table-break">
- </div>
- <div class="section">
- <div class="titlepage"><div><div><h2 class="title" style="clear: both">
- <a name="special_function_error_rates_rep.section_ellint_3"></a><a class="link" href="index.html#special_function_error_rates_rep.section_ellint_3" title="ellint_3">ellint_3</a>
- </h2></div></div></div>
- <div class="table">
- <a name="special_function_error_rates_rep.section_ellint_3.table_ellint_3"></a><p class="title"><b>Table 29. Error rates for ellint_3</b></p>
- <div class="table-contents"><table class="table" summary="Error rates for ellint_3">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> long double
- </p>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> double
- </p>
- </th>
- <th>
- <p>
- Sun compiler version 0x5150<br> Sun Solaris<br> long double
- </p>
- </th>
- <th>
- <p>
- Microsoft Visual C++ version 14.1<br> Win32<br> double
- </p>
- </th>
- </tr></thead>
- <tbody>
- <tr>
- <td>
- <p>
- Elliptic Integral PI: Mathworld Data
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 475ε (Mean = 86.3ε)</span><br> <br>
- (<span class="emphasis"><em><cmath>:</em></span> <span class="red">Max = +INFε (Mean
- = +INFε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_ellint_3__cmath__Elliptic_Integral_PI_Mathworld_Data">And
- other failures.</a>)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 1.48e+05ε (Mean = 2.54e+04ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_ellint_3_GSL_2_1_Elliptic_Integral_PI_Mathworld_Data">And
- other failures.</a>)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 475ε (Mean = 86.3ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 565ε (Mean = 102ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Elliptic Integral PI: Random Data
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 4.54ε (Mean = 0.895ε)</span><br> <br>
- (<span class="emphasis"><em><cmath>:</em></span> <span class="red">Max = 3.37e+20ε (Mean
- = 3.47e+19ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_ellint_3__cmath__Elliptic_Integral_PI_Random_Data">And
- other failures.</a>)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 633ε (Mean = 50.1ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 4.49ε (Mean = 0.885ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 8.33ε (Mean = 0.971ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Elliptic Integral PI: Large Random Data
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 3.7ε (Mean = 0.893ε)</span><br> <br>
- (<span class="emphasis"><em><cmath>:</em></span> <span class="red">Max = 2.52e+18ε (Mean
- = 4.83e+17ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_ellint_3__cmath__Elliptic_Integral_PI_Large_Random_Data">And
- other failures.</a>)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.557ε (Mean = 0.0389ε)</span><br> <br>
- (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 40.1ε (Mean = 7.77ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 3.7ε (Mean = 0.892ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 2.86ε (Mean = 0.944ε)</span>
- </p>
- </td>
- </tr>
- </tbody>
- </table></div>
- </div>
- <br class="table-break">
- </div>
- <div class="section">
- <div class="titlepage"><div><div><h2 class="title" style="clear: both">
- <a name="special_function_error_rates_rep.section_ellint_3_complete_"></a><a class="link" href="index.html#special_function_error_rates_rep.section_ellint_3_complete_" title="ellint_3 (complete)">ellint_3
- (complete)</a>
- </h2></div></div></div>
- <div class="table">
- <a name="special_function_error_rates_rep.section_ellint_3_complete_.table_ellint_3_complete_"></a><p class="title"><b>Table 30. Error rates for ellint_3 (complete)</b></p>
- <div class="table-contents"><table class="table" summary="Error rates for ellint_3 (complete)">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> long double
- </p>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> double
- </p>
- </th>
- <th>
- <p>
- Sun compiler version 0x5150<br> Sun Solaris<br> long double
- </p>
- </th>
- <th>
- <p>
- Microsoft Visual C++ version 14.1<br> Win32<br> double
- </p>
- </th>
- </tr></thead>
- <tbody>
- <tr>
- <td>
- <p>
- Complete Elliptic Integral PI: Mathworld Data
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.4ε (Mean = 0.575ε)</span><br> <br>
- (<span class="emphasis"><em><cmath>:</em></span> <span class="red">Max = 6.31e+20ε (Mean
- = 1.53e+20ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_ellint_3_complete___cmath__Complete_Elliptic_Integral_PI_Mathworld_Data">And
- other failures.</a>)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 6.33e+04ε (Mean = 1.54e+04ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_ellint_3_complete__GSL_2_1_Complete_Elliptic_Integral_PI_Mathworld_Data">And
- other failures.</a>)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.4ε (Mean = 0.575ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.971ε (Mean = 0.464ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Complete Elliptic Integral PI: Random Data
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 2.45ε (Mean = 0.696ε)</span><br> <br>
- (<span class="emphasis"><em><cmath>:</em></span> <span class="red">Max = 8.78e+20ε (Mean
- = 1.02e+20ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_ellint_3_complete___cmath__Complete_Elliptic_Integral_PI_Random_Data">And
- other failures.</a>)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 24ε (Mean = 2.99ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 2.4ε (Mean = 0.677ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 2.46ε (Mean = 0.657ε)</span>
- </p>
- </td>
- </tr>
- </tbody>
- </table></div>
- </div>
- <br class="table-break">
- </div>
- <div class="section">
- <div class="titlepage"><div><div><h2 class="title" style="clear: both">
- <a name="special_function_error_rates_rep.section_ellint_d"></a><a class="link" href="index.html#special_function_error_rates_rep.section_ellint_d" title="ellint_d">ellint_d</a>
- </h2></div></div></div>
- <div class="table">
- <a name="special_function_error_rates_rep.section_ellint_d.table_ellint_d"></a><p class="title"><b>Table 31. Error rates for ellint_d</b></p>
- <div class="table-contents"><table class="table" summary="Error rates for ellint_d">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> double
- </p>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> long double
- </p>
- </th>
- <th>
- <p>
- Sun compiler version 0x5150<br> Sun Solaris<br> long double
- </p>
- </th>
- <th>
- <p>
- Microsoft Visual C++ version 14.1<br> Win32<br> double
- </p>
- </th>
- </tr></thead>
- <tbody>
- <tr>
- <td>
- <p>
- Elliptic Integral E: Mathworld Data
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 0.862ε (Mean = 0.568ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.3ε (Mean = 0.813ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.3ε (Mean = 0.813ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.862ε (Mean = 0.457ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Elliptic Integral D: Random Data
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 3.01ε (Mean = 0.928ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 2.51ε (Mean = 0.883ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 2.51ε (Mean = 0.883ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 2.87ε (Mean = 0.805ε)</span>
- </p>
- </td>
- </tr>
- </tbody>
- </table></div>
- </div>
- <br class="table-break">
- </div>
- <div class="section">
- <div class="titlepage"><div><div><h2 class="title" style="clear: both">
- <a name="special_function_error_rates_rep.section_ellint_d_complete_"></a><a class="link" href="index.html#special_function_error_rates_rep.section_ellint_d_complete_" title="ellint_d (complete)">ellint_d
- (complete)</a>
- </h2></div></div></div>
- <div class="table">
- <a name="special_function_error_rates_rep.section_ellint_d_complete_.table_ellint_d_complete_"></a><p class="title"><b>Table 32. Error rates for ellint_d (complete)</b></p>
- <div class="table-contents"><table class="table" summary="Error rates for ellint_d (complete)">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> double
- </p>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> long double
- </p>
- </th>
- <th>
- <p>
- Sun compiler version 0x5150<br> Sun Solaris<br> long double
- </p>
- </th>
- <th>
- <p>
- Microsoft Visual C++ version 14.1<br> Win32<br> double
- </p>
- </th>
- </tr></thead>
- <tbody>
- <tr>
- <td>
- <p>
- Elliptic Integral E: Mathworld Data
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.637ε (Mean = 0.368ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.27ε (Mean = 0.735ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.27ε (Mean = 0.735ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.637ε (Mean = 0.368ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Elliptic Integral D: Random Data
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.27ε (Mean = 0.334ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.27ε (Mean = 0.334ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.27ε (Mean = 0.355ε)</span>
- </p>
- </td>
- </tr>
- </tbody>
- </table></div>
- </div>
- <br class="table-break">
- </div>
- <div class="section">
- <div class="titlepage"><div><div><h2 class="title" style="clear: both">
- <a name="special_function_error_rates_rep.section_ellint_rc"></a><a class="link" href="index.html#special_function_error_rates_rep.section_ellint_rc" title="ellint_rc">ellint_rc</a>
- </h2></div></div></div>
- <div class="table">
- <a name="special_function_error_rates_rep.section_ellint_rc.table_ellint_rc"></a><p class="title"><b>Table 33. Error rates for ellint_rc</b></p>
- <div class="table-contents"><table class="table" summary="Error rates for ellint_rc">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> double
- </p>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> long double
- </p>
- </th>
- <th>
- <p>
- Microsoft Visual C++ version 14.1<br> Win32<br> double
- </p>
- </th>
- </tr></thead>
- <tbody><tr>
- <td>
- <p>
- RC: Random data
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 2.4ε (Mean = 0.624ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.995ε (Mean = 0.433ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.962ε (Mean = 0.407ε)</span>
- </p>
- </td>
- </tr></tbody>
- </table></div>
- </div>
- <br class="table-break">
- </div>
- <div class="section">
- <div class="titlepage"><div><div><h2 class="title" style="clear: both">
- <a name="special_function_error_rates_rep.section_ellint_rd"></a><a class="link" href="index.html#special_function_error_rates_rep.section_ellint_rd" title="ellint_rd">ellint_rd</a>
- </h2></div></div></div>
- <div class="table">
- <a name="special_function_error_rates_rep.section_ellint_rd.table_ellint_rd"></a><p class="title"><b>Table 34. Error rates for ellint_rd</b></p>
- <div class="table-contents"><table class="table" summary="Error rates for ellint_rd">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> double
- </p>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> long double
- </p>
- </th>
- <th>
- <p>
- Microsoft Visual C++ version 14.1<br> Win32<br> double
- </p>
- </th>
- </tr></thead>
- <tbody>
- <tr>
- <td>
- <p>
- RD: Random data
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 2.59ε (Mean = 0.878ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 2.73ε (Mean = 0.831ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 2.16ε (Mean = 0.803ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- RD: y = z
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.896ε (Mean = 0.022ε)</span><br> <br>
- (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 2.88ε (Mean = 0.839ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 2.65ε (Mean = 0.82ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 16.5ε (Mean = 0.843ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- RD: x = y
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.824ε (Mean = 0.0272ε)</span><br> <br>
- (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 3.74ε (Mean = 0.84ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 2.85ε (Mean = 0.865ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 3.51ε (Mean = 0.816ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- RD: x = 0, y = z
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 2ε (Mean = 0.656ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.19ε (Mean = 0.522ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.16ε (Mean = 0.497ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- RD: x = y = z
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 1.03ε (Mean = 0.418ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.998ε (Mean = 0.387ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.03ε (Mean = 0.418ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- RD: x = 0
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 2.85ε (Mean = 0.781ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 2.79ε (Mean = 0.883ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 2.64ε (Mean = 0.894ε)</span>
- </p>
- </td>
- </tr>
- </tbody>
- </table></div>
- </div>
- <br class="table-break">
- </div>
- <div class="section">
- <div class="titlepage"><div><div><h2 class="title" style="clear: both">
- <a name="special_function_error_rates_rep.section_ellint_rf"></a><a class="link" href="index.html#special_function_error_rates_rep.section_ellint_rf" title="ellint_rf">ellint_rf</a>
- </h2></div></div></div>
- <div class="table">
- <a name="special_function_error_rates_rep.section_ellint_rf.table_ellint_rf"></a><p class="title"><b>Table 35. Error rates for ellint_rf</b></p>
- <div class="table-contents"><table class="table" summary="Error rates for ellint_rf">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> double
- </p>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> long double
- </p>
- </th>
- <th>
- <p>
- Microsoft Visual C++ version 14.1<br> Win32<br> double
- </p>
- </th>
- </tr></thead>
- <tbody>
- <tr>
- <td>
- <p>
- RF: Random data
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 2.73ε (Mean = 0.804ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 2.54ε (Mean = 0.674ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 2.02ε (Mean = 0.677ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- RF: x = y = z
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 0.999ε (Mean = 0.34ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.991ε (Mean = 0.345ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.999ε (Mean = 0.34ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- RF: x = y or y = z or x = z
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.536ε (Mean = 0.00658ε)</span><br> <br>
- (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 2.89ε (Mean = 0.749ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.95ε (Mean = 0.418ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.21ε (Mean = 0.394ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- RF: x = 0, y = z
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 1.29ε (Mean = 0.527ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.894ε (Mean = 0.338ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.999ε (Mean = 0.407ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- RF: z = 0
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 2.54ε (Mean = 0.781ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.7ε (Mean = 0.539ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.89ε (Mean = 0.587ε)</span>
- </p>
- </td>
- </tr>
- </tbody>
- </table></div>
- </div>
- <br class="table-break">
- </div>
- <div class="section">
- <div class="titlepage"><div><div><h2 class="title" style="clear: both">
- <a name="special_function_error_rates_rep.section_ellint_rg"></a><a class="link" href="index.html#special_function_error_rates_rep.section_ellint_rg" title="ellint_rg">ellint_rg</a>
- </h2></div></div></div>
- <div class="table">
- <a name="special_function_error_rates_rep.section_ellint_rg.table_ellint_rg"></a><p class="title"><b>Table 36. Error rates for ellint_rg</b></p>
- <div class="table-contents"><table class="table" summary="Error rates for ellint_rg">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> double
- </p>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> long double
- </p>
- </th>
- <th>
- <p>
- Microsoft Visual C++ version 14.1<br> Win32<br> double
- </p>
- </th>
- </tr></thead>
- <tbody>
- <tr>
- <td>
- <p>
- RG: Random Data
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.983ε (Mean = 0.0172ε)</span><br> <br>
- (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 0.983ε (Mean = 0.0172ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 3.95ε (Mean = 0.951ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 3.65ε (Mean = 0.929ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- RG: two values 0
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 0ε (Mean = 0ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- RG: All values the same or zero
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 0ε (Mean = 0ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.992ε (Mean = 0.288ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.06ε (Mean = 0.348ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- RG: two values the same
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.594ε (Mean = 0.0103ε)</span><br> <br>
- (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 0.594ε (Mean = 0.0103ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.51ε (Mean = 0.404ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.96ε (Mean = 0.374ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- RG: one value zero
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 0ε (Mean = 0ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 2.14ε (Mean = 0.722ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.96ε (Mean = 0.674ε)</span>
- </p>
- </td>
- </tr>
- </tbody>
- </table></div>
- </div>
- <br class="table-break">
- </div>
- <div class="section">
- <div class="titlepage"><div><div><h2 class="title" style="clear: both">
- <a name="special_function_error_rates_rep.section_ellint_rj"></a><a class="link" href="index.html#special_function_error_rates_rep.section_ellint_rj" title="ellint_rj">ellint_rj</a>
- </h2></div></div></div>
- <div class="table">
- <a name="special_function_error_rates_rep.section_ellint_rj.table_ellint_rj"></a><p class="title"><b>Table 37. Error rates for ellint_rj</b></p>
- <div class="table-contents"><table class="table" summary="Error rates for ellint_rj">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> double
- </p>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> long double
- </p>
- </th>
- <th>
- <p>
- Microsoft Visual C++ version 14.1<br> Win32<br> double
- </p>
- </th>
- </tr></thead>
- <tbody>
- <tr>
- <td>
- <p>
- RJ: Random data
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.52ε (Mean = 0.0184ε)</span><br> <br>
- (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 3.57ε (Mean = 0.704ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_ellint_rj_GSL_2_1_RJ_Random_data">And
- other failures.</a>)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 186ε (Mean = 6.67ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 215ε (Mean = 7.66ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- RJ: 4 Equal Values
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 1.03ε (Mean = 0.418ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.998ε (Mean = 0.387ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.03ε (Mean = 0.418ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- RJ: 3 Equal Values
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 3.96ε (Mean = 1.06ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 20.8ε (Mean = 0.986ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 39.9ε (Mean = 1.17ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- RJ: 2 Equal Values
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.6ε (Mean = 0.0228ε)</span><br> <br>
- (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 2.57ε (Mean = 0.754ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 220ε (Mean = 6.64ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 214ε (Mean = 5.28ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- RJ: Equal z and p
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.742ε (Mean = 0.0166ε)</span><br> <br>
- (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 2.62ε (Mean = 0.699ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 17.2ε (Mean = 1.16ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 16.1ε (Mean = 1.14ε)</span>
- </p>
- </td>
- </tr>
- </tbody>
- </table></div>
- </div>
- <br class="table-break">
- </div>
- <div class="section">
- <div class="titlepage"><div><div><h2 class="title" style="clear: both">
- <a name="special_function_error_rates_rep.section_erf"></a><a class="link" href="index.html#special_function_error_rates_rep.section_erf" title="erf">erf</a>
- </h2></div></div></div>
- <div class="table">
- <a name="special_function_error_rates_rep.section_erf.table_erf"></a><p class="title"><b>Table 38. Error rates for erf</b></p>
- <div class="table-contents"><table class="table" summary="Error rates for erf">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> long double
- </p>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> double
- </p>
- </th>
- <th>
- <p>
- Sun compiler version 0x5150<br> Sun Solaris<br> long double
- </p>
- </th>
- <th>
- <p>
- Microsoft Visual C++ version 14.1<br> Win32<br> double
- </p>
- </th>
- </tr></thead>
- <tbody>
- <tr>
- <td>
- <p>
- Erf Function: Small Values
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.925ε (Mean = 0.193ε)</span><br> <br>
- (<span class="emphasis"><em><cmath>:</em></span> Max = 0.944ε (Mean = 0.191ε))<br>
- (<span class="emphasis"><em><math.h>:</em></span> Max = 0.944ε (Mean = 0.191ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.841ε (Mean = 0.0687ε)</span><br> <br>
- (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 2.06ε (Mean = 0.319ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.925ε (Mean = 0.193ε)</span><br> <br>
- (<span class="emphasis"><em><math.h>:</em></span> Max = 0.944ε (Mean = 0.194ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.996ε (Mean = 0.182ε)</span><br> <br>
- (<span class="emphasis"><em><math.h>:</em></span> Max = 1.57ε (Mean = 0.317ε))
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Erf Function: Medium Values
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.5ε (Mean = 0.193ε)</span><br> <br>
- (<span class="emphasis"><em><cmath>:</em></span> Max = 0.921ε (Mean = 0.0723ε))<br>
- (<span class="emphasis"><em><math.h>:</em></span> Max = 0.921ε (Mean = 0.0723ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1ε (Mean = 0.119ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 2.31ε (Mean = 0.368ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.5ε (Mean = 0.197ε)</span><br> <br>
- (<span class="emphasis"><em><math.h>:</em></span> Max = 0.921ε (Mean = 0.071ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1ε (Mean = 0.171ε)</span><br> <br> (<span class="emphasis"><em><math.h>:</em></span>
- Max = 1.19ε (Mean = 0.244ε))
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Erf Function: Large Values
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em><cmath>:</em></span>
- Max = 0ε (Mean = 0ε))<br> (<span class="emphasis"><em><math.h>:</em></span> Max
- = 0ε (Mean = 0ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 0ε (Mean = 0ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em><math.h>:</em></span>
- Max = 0ε (Mean = 0ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em><math.h>:</em></span>
- Max = 0ε (Mean = 0ε))
- </p>
- </td>
- </tr>
- </tbody>
- </table></div>
- </div>
- <br class="table-break">
- </div>
- <div class="section">
- <div class="titlepage"><div><div><h2 class="title" style="clear: both">
- <a name="special_function_error_rates_rep.section_erf_inv"></a><a class="link" href="index.html#special_function_error_rates_rep.section_erf_inv" title="erf_inv">erf_inv</a>
- </h2></div></div></div>
- <div class="table">
- <a name="special_function_error_rates_rep.section_erf_inv.table_erf_inv"></a><p class="title"><b>Table 39. Error rates for erf_inv</b></p>
- <div class="table-contents"><table class="table" summary="Error rates for erf_inv">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> double
- </p>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> long double
- </p>
- </th>
- <th>
- <p>
- Sun compiler version 0x5150<br> Sun Solaris<br> long double
- </p>
- </th>
- <th>
- <p>
- Microsoft Visual C++ version 14.1<br> Win32<br> double
- </p>
- </th>
- </tr></thead>
- <tbody><tr>
- <td>
- <p>
- Inverse Erf Function
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.996ε (Mean = 0.389ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.08ε (Mean = 0.395ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.09ε (Mean = 0.502ε)</span>
- </p>
- </td>
- </tr></tbody>
- </table></div>
- </div>
- <br class="table-break">
- </div>
- <div class="section">
- <div class="titlepage"><div><div><h2 class="title" style="clear: both">
- <a name="special_function_error_rates_rep.section_erfc"></a><a class="link" href="index.html#special_function_error_rates_rep.section_erfc" title="erfc">erfc</a>
- </h2></div></div></div>
- <div class="table">
- <a name="special_function_error_rates_rep.section_erfc.table_erfc"></a><p class="title"><b>Table 40. Error rates for erfc</b></p>
- <div class="table-contents"><table class="table" summary="Error rates for erfc">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> long double
- </p>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> double
- </p>
- </th>
- <th>
- <p>
- Sun compiler version 0x5150<br> Sun Solaris<br> long double
- </p>
- </th>
- <th>
- <p>
- Microsoft Visual C++ version 14.1<br> Win32<br> double
- </p>
- </th>
- </tr></thead>
- <tbody>
- <tr>
- <td>
- <p>
- Erf Function: Small Values
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em><cmath>:</em></span>
- Max = 0ε (Mean = 0ε))<br> (<span class="emphasis"><em><math.h>:</em></span> Max
- = 0ε (Mean = 0ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.658ε (Mean = 0.0537ε)</span><br> <br>
- (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 1.01ε (Mean = 0.485ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em><math.h>:</em></span>
- Max = 0ε (Mean = 0ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em><math.h>:</em></span>
- Max = 0ε (Mean = 0ε))
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Erf Function: Medium Values
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.76ε (Mean = 0.365ε)</span><br> <br>
- (<span class="emphasis"><em><cmath>:</em></span> Max = 1.35ε (Mean = 0.307ε))<br>
- (<span class="emphasis"><em><math.h>:</em></span> Max = 1.35ε (Mean = 0.307ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.983ε (Mean = 0.213ε)</span><br> <br>
- (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 2.64ε (Mean = 0.662ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.76ε (Mean = 0.38ε)</span><br> <br>
- (<span class="emphasis"><em><math.h>:</em></span> Max = 2.81ε (Mean = 0.739ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.65ε (Mean = 0.373ε)</span><br> <br>
- (<span class="emphasis"><em><math.h>:</em></span> Max = 2.36ε (Mean = 0.539ε))
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Erf Function: Large Values
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.57ε (Mean = 0.542ε)</span><br> <br>
- (<span class="emphasis"><em><cmath>:</em></span> Max = 1.26ε (Mean = 0.441ε))<br>
- (<span class="emphasis"><em><math.h>:</em></span> Max = 1.26ε (Mean = 0.441ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.868ε (Mean = 0.147ε)</span><br> <br>
- (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 3.9ε (Mean = 0.472ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.57ε (Mean = 0.564ε)</span><br> <br>
- (<span class="emphasis"><em><math.h>:</em></span> Max = 4.91ε (Mean = 1.54ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.14ε (Mean = 0.248ε)</span><br> <br>
- (<span class="emphasis"><em><math.h>:</em></span> Max = 1.84ε (Mean = 0.331ε))
- </p>
- </td>
- </tr>
- </tbody>
- </table></div>
- </div>
- <br class="table-break">
- </div>
- <div class="section">
- <div class="titlepage"><div><div><h2 class="title" style="clear: both">
- <a name="special_function_error_rates_rep.section_erfc_inv"></a><a class="link" href="index.html#special_function_error_rates_rep.section_erfc_inv" title="erfc_inv">erfc_inv</a>
- </h2></div></div></div>
- <div class="table">
- <a name="special_function_error_rates_rep.section_erfc_inv.table_erfc_inv"></a><p class="title"><b>Table 41. Error rates for erfc_inv</b></p>
- <div class="table-contents"><table class="table" summary="Error rates for erfc_inv">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> double
- </p>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> long double
- </p>
- </th>
- <th>
- <p>
- Sun compiler version 0x5150<br> Sun Solaris<br> long double
- </p>
- </th>
- <th>
- <p>
- Microsoft Visual C++ version 14.1<br> Win32<br> double
- </p>
- </th>
- </tr></thead>
- <tbody>
- <tr>
- <td>
- <p>
- Inverse Erfc Function
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.996ε (Mean = 0.397ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.08ε (Mean = 0.403ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1ε (Mean = 0.491ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Inverse Erfc Function: extreme values
- </p>
- </td>
- <td>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.62ε (Mean = 0.383ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.62ε (Mean = 0.383ε)</span>
- </p>
- </td>
- <td>
- </td>
- </tr>
- </tbody>
- </table></div>
- </div>
- <br class="table-break">
- </div>
- <div class="section">
- <div class="titlepage"><div><div><h2 class="title" style="clear: both">
- <a name="special_function_error_rates_rep.section_expint_Ei_"></a><a class="link" href="index.html#special_function_error_rates_rep.section_expint_Ei_" title="expint (Ei)">expint
- (Ei)</a>
- </h2></div></div></div>
- <div class="table">
- <a name="special_function_error_rates_rep.section_expint_Ei_.table_expint_Ei_"></a><p class="title"><b>Table 42. Error rates for expint (Ei)</b></p>
- <div class="table-contents"><table class="table" summary="Error rates for expint (Ei)">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> long double
- </p>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> double
- </p>
- </th>
- <th>
- <p>
- Sun compiler version 0x5150<br> Sun Solaris<br> long double
- </p>
- </th>
- <th>
- <p>
- Microsoft Visual C++ version 14.1<br> Win32<br> double
- </p>
- </th>
- </tr></thead>
- <tbody>
- <tr>
- <td>
- <p>
- Exponential Integral Ei
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 5.05ε (Mean = 0.821ε)</span><br> <br>
- (<span class="emphasis"><em><cmath>:</em></span> Max = 14.1ε (Mean = 2.43ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_expint_Ei___cmath__Exponential_Integral_Ei">And
- other failures.</a>)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.994ε (Mean = 0.142ε)</span><br> <br>
- (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 8.96ε (Mean = 0.703ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 5.05ε (Mean = 0.835ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.43ε (Mean = 0.54ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Exponential Integral Ei: double exponent range
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.72ε (Mean = 0.593ε)</span><br> <br>
- (<span class="emphasis"><em><cmath>:</em></span> Max = 3.11ε (Mean = 1.13ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.998ε (Mean = 0.156ε)</span><br> <br>
- (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 1.5ε (Mean = 0.612ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.72ε (Mean = 0.607ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.7ε (Mean = 0.66ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Exponential Integral Ei: long exponent range
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.98ε (Mean = 0.595ε)</span><br> <br>
- (<span class="emphasis"><em><cmath>:</em></span> Max = 1.93ε (Mean = 0.855ε))
- </p>
- </td>
- <td>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.98ε (Mean = 0.575ε)</span>
- </p>
- </td>
- <td>
- </td>
- </tr>
- </tbody>
- </table></div>
- </div>
- <br class="table-break">
- </div>
- <div class="section">
- <div class="titlepage"><div><div><h2 class="title" style="clear: both">
- <a name="special_function_error_rates_rep.section_expint_En_"></a><a class="link" href="index.html#special_function_error_rates_rep.section_expint_En_" title="expint (En)">expint
- (En)</a>
- </h2></div></div></div>
- <div class="table">
- <a name="special_function_error_rates_rep.section_expint_En_.table_expint_En_"></a><p class="title"><b>Table 43. Error rates for expint (En)</b></p>
- <div class="table-contents"><table class="table" summary="Error rates for expint (En)">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> double
- </p>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> long double
- </p>
- </th>
- <th>
- <p>
- Sun compiler version 0x5150<br> Sun Solaris<br> long double
- </p>
- </th>
- <th>
- <p>
- Microsoft Visual C++ version 14.1<br> Win32<br> double
- </p>
- </th>
- </tr></thead>
- <tbody>
- <tr>
- <td>
- <p>
- Exponential Integral En
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.589ε (Mean = 0.0331ε)</span><br> <br>
- (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 58.5ε (Mean = 17.1ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 9.97ε (Mean = 2.13ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 9.97ε (Mean = 2.13ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 7.16ε (Mean = 1.85ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Exponential Integral En: small z values
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 115ε (Mean = 23.6ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.99ε (Mean = 0.559ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.99ε (Mean = 0.559ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 2.62ε (Mean = 0.531ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Exponential Integral E1
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.556ε (Mean = 0.0625ε)</span><br> <br>
- (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 0.988ε (Mean = 0.469ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.965ε (Mean = 0.414ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.965ε (Mean = 0.408ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.988ε (Mean = 0.486ε)</span>
- </p>
- </td>
- </tr>
- </tbody>
- </table></div>
- </div>
- <br class="table-break">
- </div>
- <div class="section">
- <div class="titlepage"><div><div><h2 class="title" style="clear: both">
- <a name="special_function_error_rates_rep.section_expm1"></a><a class="link" href="index.html#special_function_error_rates_rep.section_expm1" title="expm1">expm1</a>
- </h2></div></div></div>
- <div class="table">
- <a name="special_function_error_rates_rep.section_expm1.table_expm1"></a><p class="title"><b>Table 44. Error rates for expm1</b></p>
- <div class="table-contents"><table class="table" summary="Error rates for expm1">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> long double
- </p>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> double
- </p>
- </th>
- <th>
- <p>
- Sun compiler version 0x5150<br> Sun Solaris<br> long double
- </p>
- </th>
- <th>
- <p>
- Microsoft Visual C++ version 14.1<br> Win32<br> double
- </p>
- </th>
- </tr></thead>
- <tbody><tr>
- <td>
- <p>
- Random test data
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.992ε (Mean = 0.402ε)</span><br> <br>
- (<span class="emphasis"><em><cmath>:</em></span> Max = 0.992ε (Mean = 0.402ε))<br>
- (<span class="emphasis"><em><math.h>:</em></span> Max = 0.992ε (Mean = 0.402ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.793ε (Mean = 0.126ε)</span><br> <br>
- (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 0.793ε (Mean = 0.126ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.31ε (Mean = 0.428ε)</span><br> <br>
- (<span class="emphasis"><em><math.h>:</em></span> Max = 0.996ε (Mean = 0.426ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.31ε (Mean = 0.496ε)</span><br> <br>
- (<span class="emphasis"><em><math.h>:</em></span> Max = 1.31ε (Mean = 0.496ε))
- </p>
- </td>
- </tr></tbody>
- </table></div>
- </div>
- <br class="table-break">
- </div>
- <div class="section">
- <div class="titlepage"><div><div><h2 class="title" style="clear: both">
- <a name="special_function_error_rates_rep.section_gamma_p"></a><a class="link" href="index.html#special_function_error_rates_rep.section_gamma_p" title="gamma_p">gamma_p</a>
- </h2></div></div></div>
- <div class="table">
- <a name="special_function_error_rates_rep.section_gamma_p.table_gamma_p"></a><p class="title"><b>Table 45. Error rates for gamma_p</b></p>
- <div class="table-contents"><table class="table" summary="Error rates for gamma_p">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> double
- </p>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> long double
- </p>
- </th>
- <th>
- <p>
- Sun compiler version 0x5150<br> Sun Solaris<br> long double
- </p>
- </th>
- <th>
- <p>
- Microsoft Visual C++ version 14.1<br> Win32<br> double
- </p>
- </th>
- </tr></thead>
- <tbody>
- <tr>
- <td>
- <p>
- tgamma(a, z) medium values
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.955ε (Mean = 0.05ε)</span><br> <br>
- (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 342ε (Mean = 45.8ε))<br> (<span class="emphasis"><em>Rmath
- 3.2.3:</em></span> Max = 389ε (Mean = 44ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 41.6ε (Mean = 8.09ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 239ε (Mean = 30.2ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 35.1ε (Mean = 6.98ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- tgamma(a, z) small values
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 4.82ε (Mean = 0.758ε))<br> (<span class="emphasis"><em>Rmath
- 3.2.3:</em></span> Max = 1.01ε (Mean = 0.306ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 2ε (Mean = 0.464ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 2ε (Mean = 0.461ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.54ε (Mean = 0.439ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- tgamma(a, z) large values
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 1.02e+03ε (Mean = 105ε))<br> (<span class="emphasis"><em>Rmath
- 3.2.3:</em></span> Max = 1.11e+03ε (Mean = 67.5ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 3.08e+04ε (Mean = 1.86e+03ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 3.02e+04ε (Mean = 1.91e+03ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 243ε (Mean = 20.2ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- tgamma(a, z) integer and half integer values
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 128ε (Mean = 22.6ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
- Max = 66.2ε (Mean = 12.2ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 11.8ε (Mean = 2.66ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 71.6ε (Mean = 9.47ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 13ε (Mean = 2.97ε)</span>
- </p>
- </td>
- </tr>
- </tbody>
- </table></div>
- </div>
- <br class="table-break">
- </div>
- <div class="section">
- <div class="titlepage"><div><div><h2 class="title" style="clear: both">
- <a name="special_function_error_rates_rep.section_gamma_p_inv"></a><a class="link" href="index.html#special_function_error_rates_rep.section_gamma_p_inv" title="gamma_p_inv">gamma_p_inv</a>
- </h2></div></div></div>
- <div class="table">
- <a name="special_function_error_rates_rep.section_gamma_p_inv.table_gamma_p_inv"></a><p class="title"><b>Table 46. Error rates for gamma_p_inv</b></p>
- <div class="table-contents"><table class="table" summary="Error rates for gamma_p_inv">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> double
- </p>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> long double
- </p>
- </th>
- <th>
- <p>
- Sun compiler version 0x5150<br> Sun Solaris<br> long double
- </p>
- </th>
- <th>
- <p>
- Microsoft Visual C++ version 14.1<br> Win32<br> double
- </p>
- </th>
- </tr></thead>
- <tbody>
- <tr>
- <td>
- <p>
- incomplete gamma inverse(a, z) medium values
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.993ε (Mean = 0.15ε)</span><br> <br>
- (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 4.88ε (Mean = 0.868ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.8ε (Mean = 0.406ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.89ε (Mean = 0.466ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.71ε (Mean = 0.34ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- incomplete gamma inverse(a, z) large values
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>Rmath
- 3.2.3:</em></span> Max = 0.816ε (Mean = 0.0874ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.509ε (Mean = 0.0447ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.509ε (Mean = 0.0447ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.924ε (Mean = 0.108ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- incomplete gamma inverse(a, z) small values
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 441ε (Mean = 53.9ε)</span><br> <br>
- (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 547ε (Mean = 61.6ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 9.17e+03ε (Mean = 1.45e+03ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.09e+04ε (Mean = 1.3e+03ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.1e+03ε (Mean = 131ε)</span>
- </p>
- </td>
- </tr>
- </tbody>
- </table></div>
- </div>
- <br class="table-break">
- </div>
- <div class="section">
- <div class="titlepage"><div><div><h2 class="title" style="clear: both">
- <a name="special_function_error_rates_rep.section_gamma_p_inva"></a><a class="link" href="index.html#special_function_error_rates_rep.section_gamma_p_inva" title="gamma_p_inva">gamma_p_inva</a>
- </h2></div></div></div>
- <div class="table">
- <a name="special_function_error_rates_rep.section_gamma_p_inva.table_gamma_p_inva"></a><p class="title"><b>Table 47. Error rates for gamma_p_inva</b></p>
- <div class="table-contents"><table class="table" summary="Error rates for gamma_p_inva">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> double
- </p>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> long double
- </p>
- </th>
- <th>
- <p>
- Sun compiler version 0x5150<br> Sun Solaris<br> long double
- </p>
- </th>
- <th>
- <p>
- Microsoft Visual C++ version 14.1<br> Win32<br> double
- </p>
- </th>
- </tr></thead>
- <tbody><tr>
- <td>
- <p>
- Incomplete gamma inverses.
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 7.87ε (Mean = 1.15ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 4.08ε (Mean = 1.12ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 4.92ε (Mean = 1.03ε)</span>
- </p>
- </td>
- </tr></tbody>
- </table></div>
- </div>
- <br class="table-break">
- </div>
- <div class="section">
- <div class="titlepage"><div><div><h2 class="title" style="clear: both">
- <a name="special_function_error_rates_rep.section_gamma_q"></a><a class="link" href="index.html#special_function_error_rates_rep.section_gamma_q" title="gamma_q">gamma_q</a>
- </h2></div></div></div>
- <div class="table">
- <a name="special_function_error_rates_rep.section_gamma_q.table_gamma_q"></a><p class="title"><b>Table 48. Error rates for gamma_q</b></p>
- <div class="table-contents"><table class="table" summary="Error rates for gamma_q">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> double
- </p>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> long double
- </p>
- </th>
- <th>
- <p>
- Sun compiler version 0x5150<br> Sun Solaris<br> long double
- </p>
- </th>
- <th>
- <p>
- Microsoft Visual C++ version 14.1<br> Win32<br> double
- </p>
- </th>
- </tr></thead>
- <tbody>
- <tr>
- <td>
- <p>
- tgamma(a, z) medium values
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.927ε (Mean = 0.035ε)</span><br> <br>
- (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 201ε (Mean = 13.5ε))<br> (<span class="emphasis"><em>Rmath
- 3.2.3:</em></span> Max = 131ε (Mean = 12.7ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 32.3ε (Mean = 6.61ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 199ε (Mean = 26.6ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 23.7ε (Mean = 4ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- tgamma(a, z) small values
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> <span class="red">Max = 1.38e+10ε (Mean = 1.05e+09ε))</span><br>
- (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 65.6ε (Mean = 11ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 2.45ε (Mean = 0.885ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 2.45ε (Mean = 0.819ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 2.26ε (Mean = 0.74ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- tgamma(a, z) large values
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 2.71e+04ε (Mean = 2.16e+03ε))<br> (<span class="emphasis"><em>Rmath
- 3.2.3:</em></span> Max = 1.02e+03ε (Mean = 62.7ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 6.82e+03ε (Mean = 414ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.15e+04ε (Mean = 733ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 469ε (Mean = 31.5ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- tgamma(a, z) integer and half integer values
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 118ε (Mean = 12.5ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
- Max = 138ε (Mean = 16.9ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 11.1ε (Mean = 2.07ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 54.7ε (Mean = 6.16ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 8.72ε (Mean = 1.48ε)</span>
- </p>
- </td>
- </tr>
- </tbody>
- </table></div>
- </div>
- <br class="table-break">
- </div>
- <div class="section">
- <div class="titlepage"><div><div><h2 class="title" style="clear: both">
- <a name="special_function_error_rates_rep.section_gamma_q_inv"></a><a class="link" href="index.html#special_function_error_rates_rep.section_gamma_q_inv" title="gamma_q_inv">gamma_q_inv</a>
- </h2></div></div></div>
- <div class="table">
- <a name="special_function_error_rates_rep.section_gamma_q_inv.table_gamma_q_inv"></a><p class="title"><b>Table 49. Error rates for gamma_q_inv</b></p>
- <div class="table-contents"><table class="table" summary="Error rates for gamma_q_inv">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> double
- </p>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> long double
- </p>
- </th>
- <th>
- <p>
- Sun compiler version 0x5150<br> Sun Solaris<br> long double
- </p>
- </th>
- <th>
- <p>
- Microsoft Visual C++ version 14.1<br> Win32<br> double
- </p>
- </th>
- </tr></thead>
- <tbody>
- <tr>
- <td>
- <p>
- incomplete gamma inverse(a, z) medium values
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.912ε (Mean = 0.154ε)</span><br> <br>
- (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 4.66ε (Mean = 0.792ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 6.2ε (Mean = 0.627ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 6.2ε (Mean = 0.683ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 2.88ε (Mean = 0.469ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- incomplete gamma inverse(a, z) large values
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.894ε (Mean = 0.0915ε)</span><br> <br>
- (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 0.894ε (Mean = 0.106ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.814ε (Mean = 0.0856ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- incomplete gamma inverse(a, z) small values
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 292ε (Mean = 36.4ε)</span><br> <br>
- (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 415ε (Mean = 48.7ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 8.28e+03ε (Mean = 1.09e+03ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 8.98e+03ε (Mean = 877ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 451ε (Mean = 64.7ε)</span>
- </p>
- </td>
- </tr>
- </tbody>
- </table></div>
- </div>
- <br class="table-break">
- </div>
- <div class="section">
- <div class="titlepage"><div><div><h2 class="title" style="clear: both">
- <a name="special_function_error_rates_rep.section_gamma_q_inva"></a><a class="link" href="index.html#special_function_error_rates_rep.section_gamma_q_inva" title="gamma_q_inva">gamma_q_inva</a>
- </h2></div></div></div>
- <div class="table">
- <a name="special_function_error_rates_rep.section_gamma_q_inva.table_gamma_q_inva"></a><p class="title"><b>Table 50. Error rates for gamma_q_inva</b></p>
- <div class="table-contents"><table class="table" summary="Error rates for gamma_q_inva">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> double
- </p>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> long double
- </p>
- </th>
- <th>
- <p>
- Sun compiler version 0x5150<br> Sun Solaris<br> long double
- </p>
- </th>
- <th>
- <p>
- Microsoft Visual C++ version 14.1<br> Win32<br> double
- </p>
- </th>
- </tr></thead>
- <tbody><tr>
- <td>
- <p>
- Incomplete gamma inverses.
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 8.42ε (Mean = 1.3ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 7.86ε (Mean = 1.24ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 5.05ε (Mean = 1.08ε)</span>
- </p>
- </td>
- </tr></tbody>
- </table></div>
- </div>
- <br class="table-break">
- </div>
- <div class="section">
- <div class="titlepage"><div><div><h2 class="title" style="clear: both">
- <a name="special_function_error_rates_rep.section_hermite"></a><a class="link" href="index.html#special_function_error_rates_rep.section_hermite" title="hermite">hermite</a>
- </h2></div></div></div>
- <div class="table">
- <a name="special_function_error_rates_rep.section_hermite.table_hermite"></a><p class="title"><b>Table 51. Error rates for hermite</b></p>
- <div class="table-contents"><table class="table" summary="Error rates for hermite">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> double
- </p>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> long double
- </p>
- </th>
- <th>
- <p>
- Sun compiler version 0x5150<br> Sun Solaris<br> long double
- </p>
- </th>
- <th>
- <p>
- Microsoft Visual C++ version 14.1<br> Win32<br> double
- </p>
- </th>
- </tr></thead>
- <tbody><tr>
- <td>
- <p>
- Hermite Polynomials
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 6.24ε (Mean = 2.07ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 6.24ε (Mean = 2.07ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 4.46ε (Mean = 1.41ε)</span>
- </p>
- </td>
- </tr></tbody>
- </table></div>
- </div>
- <br class="table-break">
- </div>
- <div class="section">
- <div class="titlepage"><div><div><h2 class="title" style="clear: both">
- <a name="special_function_error_rates_rep.section_heuman_lambda"></a><a class="link" href="index.html#special_function_error_rates_rep.section_heuman_lambda" title="heuman_lambda">heuman_lambda</a>
- </h2></div></div></div>
- <div class="table">
- <a name="special_function_error_rates_rep.section_heuman_lambda.table_heuman_lambda"></a><p class="title"><b>Table 52. Error rates for heuman_lambda</b></p>
- <div class="table-contents"><table class="table" summary="Error rates for heuman_lambda">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> double
- </p>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> long double
- </p>
- </th>
- <th>
- <p>
- Sun compiler version 0x5150<br> Sun Solaris<br> long double
- </p>
- </th>
- <th>
- <p>
- Microsoft Visual C++ version 14.1<br> Win32<br> double
- </p>
- </th>
- </tr></thead>
- <tbody>
- <tr>
- <td>
- <p>
- Elliptic Integral Jacobi Zeta: Mathworld Data
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.89ε (Mean = 0.887ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.89ε (Mean = 0.887ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.08ε (Mean = 0.734ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Elliptic Integral Heuman Lambda: Random Data
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 3.82ε (Mean = 0.609ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 3.82ε (Mean = 0.608ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 2.12ε (Mean = 0.588ε)</span>
- </p>
- </td>
- </tr>
- </tbody>
- </table></div>
- </div>
- <br class="table-break">
- </div>
- <div class="section">
- <div class="titlepage"><div><div><h2 class="title" style="clear: both">
- <a name="special_function_error_rates_rep.section_ibeta"></a><a class="link" href="index.html#special_function_error_rates_rep.section_ibeta" title="ibeta">ibeta</a>
- </h2></div></div></div>
- <div class="table">
- <a name="special_function_error_rates_rep.section_ibeta.table_ibeta"></a><p class="title"><b>Table 53. Error rates for ibeta</b></p>
- <div class="table-contents"><table class="table" summary="Error rates for ibeta">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> double
- </p>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> long double
- </p>
- </th>
- <th>
- <p>
- Sun compiler version 0x5150<br> Sun Solaris<br> long double
- </p>
- </th>
- <th>
- <p>
- Microsoft Visual C++ version 14.1<br> Win32<br> double
- </p>
- </th>
- </tr></thead>
- <tbody>
- <tr>
- <td>
- <p>
- Incomplete Beta Function: Small Values
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 682ε (Mean = 32.6ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
- Max = 22.9ε (Mean = 3.35ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 8.97ε (Mean = 2.09ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 21.3ε (Mean = 2.75ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 8.4ε (Mean = 1.93ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Incomplete Beta Function: Medium Values
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 690ε (Mean = 151ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
- Max = 232ε (Mean = 27.9ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 50ε (Mean = 12.1ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 124ε (Mean = 18.4ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 106ε (Mean = 16.3ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Incomplete Beta Function: Large and Diverse Values
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.26ε (Mean = 0.063ε)</span><br> <br>
- (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 3.9e+05ε (Mean = 1.82e+04ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_ibeta_GSL_2_1_Incomplete_Beta_Function_Large_and_Diverse_Values">And
- other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
- Max = 574ε (Mean = 49.4ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.96e+04ε (Mean = 997ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 4.98e+04ε (Mean = 2.07e+03ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.32e+03ε (Mean = 68.5ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Incomplete Beta Function: Small Integer Values
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 254ε (Mean = 50.9ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
- Max = 62.2ε (Mean = 8.95ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 4.45ε (Mean = 0.814ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 44.5ε (Mean = 10.1ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 3.85ε (Mean = 0.791ε)</span>
- </p>
- </td>
- </tr>
- </tbody>
- </table></div>
- </div>
- <br class="table-break">
- </div>
- <div class="section">
- <div class="titlepage"><div><div><h2 class="title" style="clear: both">
- <a name="special_function_error_rates_rep.section_ibeta_inv"></a><a class="link" href="index.html#special_function_error_rates_rep.section_ibeta_inv" title="ibeta_inv">ibeta_inv</a>
- </h2></div></div></div>
- <div class="table">
- <a name="special_function_error_rates_rep.section_ibeta_inv.table_ibeta_inv"></a><p class="title"><b>Table 54. Error rates for ibeta_inv</b></p>
- <div class="table-contents"><table class="table" summary="Error rates for ibeta_inv">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> double
- </p>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> long double
- </p>
- </th>
- <th>
- <p>
- Sun compiler version 0x5150<br> Sun Solaris<br> long double
- </p>
- </th>
- <th>
- <p>
- Microsoft Visual C++ version 14.1<br> Win32<br> double
- </p>
- </th>
- </tr></thead>
- <tbody><tr>
- <td>
- <p>
- Inverse incomplete beta
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 11ε (Mean = 0.345ε)</span><br> <br>
- (<span class="emphasis"><em>Rmath 3.2.3:</em></span> <span class="red">Max = 1.14e+121ε (Mean
- = 3.28e+119ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_ibeta_inv_Rmath_3_2_3_Inverse_incomplete_beta">And
- other failures.</a>)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 3.8e+04ε (Mean = 2.66e+03ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 4.07e+04ε (Mean = 2.86e+03ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 8.59e+03ε (Mean = 277ε)</span>
- </p>
- </td>
- </tr></tbody>
- </table></div>
- </div>
- <br class="table-break">
- </div>
- <div class="section">
- <div class="titlepage"><div><div><h2 class="title" style="clear: both">
- <a name="special_function_error_rates_rep.section_ibeta_inva"></a><a class="link" href="index.html#special_function_error_rates_rep.section_ibeta_inva" title="ibeta_inva">ibeta_inva</a>
- </h2></div></div></div>
- <div class="table">
- <a name="special_function_error_rates_rep.section_ibeta_inva.table_ibeta_inva"></a><p class="title"><b>Table 55. Error rates for ibeta_inva</b></p>
- <div class="table-contents"><table class="table" summary="Error rates for ibeta_inva">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> double
- </p>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> long double
- </p>
- </th>
- <th>
- <p>
- Sun compiler version 0x5150<br> Sun Solaris<br> long double
- </p>
- </th>
- <th>
- <p>
- Microsoft Visual C++ version 14.1<br> Win32<br> double
- </p>
- </th>
- </tr></thead>
- <tbody><tr>
- <td>
- <p>
- Inverse incomplete beta
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.602ε (Mean = 0.0239ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 377ε (Mean = 24.4ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 438ε (Mean = 31.3ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 242ε (Mean = 22.9ε)</span>
- </p>
- </td>
- </tr></tbody>
- </table></div>
- </div>
- <br class="table-break">
- </div>
- <div class="section">
- <div class="titlepage"><div><div><h2 class="title" style="clear: both">
- <a name="special_function_error_rates_rep.section_ibeta_invb"></a><a class="link" href="index.html#special_function_error_rates_rep.section_ibeta_invb" title="ibeta_invb">ibeta_invb</a>
- </h2></div></div></div>
- <div class="table">
- <a name="special_function_error_rates_rep.section_ibeta_invb.table_ibeta_invb"></a><p class="title"><b>Table 56. Error rates for ibeta_invb</b></p>
- <div class="table-contents"><table class="table" summary="Error rates for ibeta_invb">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> double
- </p>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> long double
- </p>
- </th>
- <th>
- <p>
- Sun compiler version 0x5150<br> Sun Solaris<br> long double
- </p>
- </th>
- <th>
- <p>
- Microsoft Visual C++ version 14.1<br> Win32<br> double
- </p>
- </th>
- </tr></thead>
- <tbody><tr>
- <td>
- <p>
- Inverse incomplete beta
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.765ε (Mean = 0.0422ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 407ε (Mean = 27.2ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 407ε (Mean = 24.4ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 409ε (Mean = 19.3ε)</span>
- </p>
- </td>
- </tr></tbody>
- </table></div>
- </div>
- <br class="table-break">
- </div>
- <div class="section">
- <div class="titlepage"><div><div><h2 class="title" style="clear: both">
- <a name="special_function_error_rates_rep.section_ibetac"></a><a class="link" href="index.html#special_function_error_rates_rep.section_ibetac" title="ibetac">ibetac</a>
- </h2></div></div></div>
- <div class="table">
- <a name="special_function_error_rates_rep.section_ibetac.table_ibetac"></a><p class="title"><b>Table 57. Error rates for ibetac</b></p>
- <div class="table-contents"><table class="table" summary="Error rates for ibetac">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> double
- </p>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> long double
- </p>
- </th>
- <th>
- <p>
- Sun compiler version 0x5150<br> Sun Solaris<br> long double
- </p>
- </th>
- <th>
- <p>
- Microsoft Visual C++ version 14.1<br> Win32<br> double
- </p>
- </th>
- </tr></thead>
- <tbody>
- <tr>
- <td>
- <p>
- Incomplete Beta Function: Small Values
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>Rmath
- 3.2.3:</em></span> Max = 22.4ε (Mean = 3.67ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 10.6ε (Mean = 2.22ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 13.8ε (Mean = 2.68ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 6.94ε (Mean = 1.71ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Incomplete Beta Function: Medium Values
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>Rmath
- 3.2.3:</em></span> Max = 204ε (Mean = 25.8ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 73.9ε (Mean = 11.2ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 132ε (Mean = 19.8ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 56.7ε (Mean = 14.3ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Incomplete Beta Function: Large and Diverse Values
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.981ε (Mean = 0.0573ε)</span><br> <br>
- (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 889ε (Mean = 68.4ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 3.45e+04ε (Mean = 1.32e+03ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 6.31e+04ε (Mean = 2.04e+03ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.88e+03ε (Mean = 82.7ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Incomplete Beta Function: Small Integer Values
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>Rmath
- 3.2.3:</em></span> Max = 84.6ε (Mean = 18ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 5.34ε (Mean = 1.11ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 107ε (Mean = 17.1ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 6.37ε (Mean = 1.03ε)</span>
- </p>
- </td>
- </tr>
- </tbody>
- </table></div>
- </div>
- <br class="table-break">
- </div>
- <div class="section">
- <div class="titlepage"><div><div><h2 class="title" style="clear: both">
- <a name="special_function_error_rates_rep.section_ibetac_inv"></a><a class="link" href="index.html#special_function_error_rates_rep.section_ibetac_inv" title="ibetac_inv">ibetac_inv</a>
- </h2></div></div></div>
- <div class="table">
- <a name="special_function_error_rates_rep.section_ibetac_inv.table_ibetac_inv"></a><p class="title"><b>Table 58. Error rates for ibetac_inv</b></p>
- <div class="table-contents"><table class="table" summary="Error rates for ibetac_inv">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> double
- </p>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> long double
- </p>
- </th>
- <th>
- <p>
- Sun compiler version 0x5150<br> Sun Solaris<br> long double
- </p>
- </th>
- <th>
- <p>
- Microsoft Visual C++ version 14.1<br> Win32<br> double
- </p>
- </th>
- </tr></thead>
- <tbody><tr>
- <td>
- <p>
- Inverse incomplete beta
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.977ε (Mean = 0.0976ε)</span><br> <br>
- (<span class="emphasis"><em>Rmath 3.2.3:</em></span> <span class="red">Max = 3.01e+132ε (Mean
- = 8.65e+130ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_ibetac_inv_Rmath_3_2_3_Inverse_incomplete_beta">And
- other failures.</a>)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 4.88e+04ε (Mean = 3.16e+03ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 5.05e+04ε (Mean = 3.33e+03ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 2.93e+03ε (Mean = 198ε)</span>
- </p>
- </td>
- </tr></tbody>
- </table></div>
- </div>
- <br class="table-break">
- </div>
- <div class="section">
- <div class="titlepage"><div><div><h2 class="title" style="clear: both">
- <a name="special_function_error_rates_rep.section_ibetac_inva"></a><a class="link" href="index.html#special_function_error_rates_rep.section_ibetac_inva" title="ibetac_inva">ibetac_inva</a>
- </h2></div></div></div>
- <div class="table">
- <a name="special_function_error_rates_rep.section_ibetac_inva.table_ibetac_inva"></a><p class="title"><b>Table 59. Error rates for ibetac_inva</b></p>
- <div class="table-contents"><table class="table" summary="Error rates for ibetac_inva">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> double
- </p>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> long double
- </p>
- </th>
- <th>
- <p>
- Sun compiler version 0x5150<br> Sun Solaris<br> long double
- </p>
- </th>
- <th>
- <p>
- Microsoft Visual C++ version 14.1<br> Win32<br> double
- </p>
- </th>
- </tr></thead>
- <tbody><tr>
- <td>
- <p>
- Inverse incomplete beta
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.683ε (Mean = 0.0314ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 382ε (Mean = 22.2ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 315ε (Mean = 23.7ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 408ε (Mean = 26.7ε)</span>
- </p>
- </td>
- </tr></tbody>
- </table></div>
- </div>
- <br class="table-break">
- </div>
- <div class="section">
- <div class="titlepage"><div><div><h2 class="title" style="clear: both">
- <a name="special_function_error_rates_rep.section_ibetac_invb"></a><a class="link" href="index.html#special_function_error_rates_rep.section_ibetac_invb" title="ibetac_invb">ibetac_invb</a>
- </h2></div></div></div>
- <div class="table">
- <a name="special_function_error_rates_rep.section_ibetac_invb.table_ibetac_invb"></a><p class="title"><b>Table 60. Error rates for ibetac_invb</b></p>
- <div class="table-contents"><table class="table" summary="Error rates for ibetac_invb">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> double
- </p>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> long double
- </p>
- </th>
- <th>
- <p>
- Sun compiler version 0x5150<br> Sun Solaris<br> long double
- </p>
- </th>
- <th>
- <p>
- Microsoft Visual C++ version 14.1<br> Win32<br> double
- </p>
- </th>
- </tr></thead>
- <tbody><tr>
- <td>
- <p>
- Inverse incomplete beta
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.724ε (Mean = 0.0303ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 317ε (Mean = 19.8ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 369ε (Mean = 22.6ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 271ε (Mean = 16.4ε)</span>
- </p>
- </td>
- </tr></tbody>
- </table></div>
- </div>
- <br class="table-break">
- </div>
- <div class="section">
- <div class="titlepage"><div><div><h2 class="title" style="clear: both">
- <a name="special_function_error_rates_rep.section_jacobi_cn"></a><a class="link" href="index.html#special_function_error_rates_rep.section_jacobi_cn" title="jacobi_cn">jacobi_cn</a>
- </h2></div></div></div>
- <div class="table">
- <a name="special_function_error_rates_rep.section_jacobi_cn.table_jacobi_cn"></a><p class="title"><b>Table 61. Error rates for jacobi_cn</b></p>
- <div class="table-contents"><table class="table" summary="Error rates for jacobi_cn">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> double
- </p>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> long double
- </p>
- </th>
- <th>
- <p>
- Sun compiler version 0x5150<br> Sun Solaris<br> long double
- </p>
- </th>
- <th>
- <p>
- Microsoft Visual C++ version 14.1<br> Win32<br> double
- </p>
- </th>
- </tr></thead>
- <tbody>
- <tr>
- <td>
- <p>
- Jacobi Elliptic: Mathworld Data
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 17.3ε (Mean = 4.29ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_jacobi_cn_GSL_2_1_Jacobi_Elliptic_Mathworld_Data">And
- other failures.</a>)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 71.6ε (Mean = 19.3ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 71.6ε (Mean = 19.4ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 45.8ε (Mean = 11.4ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Jacobi Elliptic: Random Data
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.816ε (Mean = 0.0563ε)</span><br> <br>
- (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 2.43ε (Mean = 0.803ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.68ε (Mean = 0.443ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.68ε (Mean = 0.454ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.83ε (Mean = 0.455ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Jacobi Elliptic: Random Small Values
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 55.2ε (Mean = 1.64ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_jacobi_cn_GSL_2_1_Jacobi_Elliptic_Random_Small_Values">And
- other failures.</a>)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 10.4ε (Mean = 0.594ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 10.4ε (Mean = 0.602ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 26.2ε (Mean = 1.17ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Jacobi Elliptic: Modulus near 1
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.919ε (Mean = 0.127ε)</span><br> <br>
- (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 0ε (Mean = 0ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_jacobi_cn_GSL_2_1_Jacobi_Elliptic_Modulus_near_1">And
- other failures.</a>)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 675ε (Mean = 87.1ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 675ε (Mean = 86.8ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 513ε (Mean = 126ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Jacobi Elliptic: Large Phi
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 14.2ε (Mean = 0.927ε)</span><br> <br>
- (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 5.92e+03ε (Mean = 477ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 2.97e+04ε (Mean = 1.9e+03ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 2.97e+04ε (Mean = 1.9e+03ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 3.27e+04ε (Mean = 1.93e+03ε)</span>
- </p>
- </td>
- </tr>
- </tbody>
- </table></div>
- </div>
- <br class="table-break">
- </div>
- <div class="section">
- <div class="titlepage"><div><div><h2 class="title" style="clear: both">
- <a name="special_function_error_rates_rep.section_jacobi_dn"></a><a class="link" href="index.html#special_function_error_rates_rep.section_jacobi_dn" title="jacobi_dn">jacobi_dn</a>
- </h2></div></div></div>
- <div class="table">
- <a name="special_function_error_rates_rep.section_jacobi_dn.table_jacobi_dn"></a><p class="title"><b>Table 62. Error rates for jacobi_dn</b></p>
- <div class="table-contents"><table class="table" summary="Error rates for jacobi_dn">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> double
- </p>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> long double
- </p>
- </th>
- <th>
- <p>
- Sun compiler version 0x5150<br> Sun Solaris<br> long double
- </p>
- </th>
- <th>
- <p>
- Microsoft Visual C++ version 14.1<br> Win32<br> double
- </p>
- </th>
- </tr></thead>
- <tbody>
- <tr>
- <td>
- <p>
- Jacobi Elliptic: Mathworld Data
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 2.82ε (Mean = 1.18ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_jacobi_dn_GSL_2_1_Jacobi_Elliptic_Mathworld_Data">And
- other failures.</a>)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 49ε (Mean = 14ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 49ε (Mean = 14ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 34.3ε (Mean = 8.71ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Jacobi Elliptic: Random Data
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 3ε (Mean = 0.61ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.53ε (Mean = 0.473ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.53ε (Mean = 0.481ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.52ε (Mean = 0.466ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Jacobi Elliptic: Random Small Values
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.5ε (Mean = 0.0122ε)</span><br> <br>
- (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 1.5ε (Mean = 0.391ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_jacobi_dn_GSL_2_1_Jacobi_Elliptic_Random_Small_Values">And
- other failures.</a>)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 22.4ε (Mean = 0.777ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 22.4ε (Mean = 0.763ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 16.1ε (Mean = 0.685ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Jacobi Elliptic: Modulus near 1
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 2.28ε (Mean = 0.194ε)</span><br> <br>
- (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 0ε (Mean = 0ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_jacobi_dn_GSL_2_1_Jacobi_Elliptic_Modulus_near_1">And
- other failures.</a>)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 3.75e+03ε (Mean = 293ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 3.75e+03ε (Mean = 293ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 6.24e+03ε (Mean = 482ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Jacobi Elliptic: Large Phi
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 14.1ε (Mean = 0.897ε)</span><br> <br>
- (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 121ε (Mean = 22ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 2.82e+04ε (Mean = 1.79e+03ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 2.82e+04ε (Mean = 1.79e+03ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.67e+04ε (Mean = 1e+03ε)</span>
- </p>
- </td>
- </tr>
- </tbody>
- </table></div>
- </div>
- <br class="table-break">
- </div>
- <div class="section">
- <div class="titlepage"><div><div><h2 class="title" style="clear: both">
- <a name="special_function_error_rates_rep.section_jacobi_sn"></a><a class="link" href="index.html#special_function_error_rates_rep.section_jacobi_sn" title="jacobi_sn">jacobi_sn</a>
- </h2></div></div></div>
- <div class="table">
- <a name="special_function_error_rates_rep.section_jacobi_sn.table_jacobi_sn"></a><p class="title"><b>Table 63. Error rates for jacobi_sn</b></p>
- <div class="table-contents"><table class="table" summary="Error rates for jacobi_sn">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> double
- </p>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> long double
- </p>
- </th>
- <th>
- <p>
- Sun compiler version 0x5150<br> Sun Solaris<br> long double
- </p>
- </th>
- <th>
- <p>
- Microsoft Visual C++ version 14.1<br> Win32<br> double
- </p>
- </th>
- </tr></thead>
- <tbody>
- <tr>
- <td>
- <p>
- Jacobi Elliptic: Mathworld Data
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 588ε (Mean = 146ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_jacobi_sn_GSL_2_1_Jacobi_Elliptic_Mathworld_Data">And
- other failures.</a>)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 341ε (Mean = 80.7ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 341ε (Mean = 80.7ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 481ε (Mean = 113ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Jacobi Elliptic: Random Data
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 4.02ε (Mean = 1.07ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 2.01ε (Mean = 0.584ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 2.01ε (Mean = 0.593ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.92ε (Mean = 0.567ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Jacobi Elliptic: Random Small Values
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 11.7ε (Mean = 1.65ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_jacobi_sn_GSL_2_1_Jacobi_Elliptic_Random_Small_Values">And
- other failures.</a>)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.99ε (Mean = 0.347ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.99ε (Mean = 0.347ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 2.11ε (Mean = 0.385ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Jacobi Elliptic: Modulus near 1
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 0ε (Mean = 0ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_jacobi_sn_GSL_2_1_Jacobi_Elliptic_Modulus_near_1">And
- other failures.</a>)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 109ε (Mean = 7.35ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 109ε (Mean = 7.38ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 23.2ε (Mean = 1.85ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Jacobi Elliptic: Large Phi
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 12ε (Mean = 0.771ε)</span><br> <br>
- (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 4.54e+04ε (Mean = 2.63e+03ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 2.45e+04ε (Mean = 1.51e+03ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 2.45e+04ε (Mean = 1.51e+03ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 4.36e+04ε (Mean = 2.54e+03ε)</span>
- </p>
- </td>
- </tr>
- </tbody>
- </table></div>
- </div>
- <br class="table-break">
- </div>
- <div class="section">
- <div class="titlepage"><div><div><h2 class="title" style="clear: both">
- <a name="special_function_error_rates_rep.section_jacobi_zeta"></a><a class="link" href="index.html#special_function_error_rates_rep.section_jacobi_zeta" title="jacobi_zeta">jacobi_zeta</a>
- </h2></div></div></div>
- <div class="table">
- <a name="special_function_error_rates_rep.section_jacobi_zeta.table_jacobi_zeta"></a><p class="title"><b>Table 64. Error rates for jacobi_zeta</b></p>
- <div class="table-contents"><table class="table" summary="Error rates for jacobi_zeta">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> double
- </p>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> long double
- </p>
- </th>
- <th>
- <p>
- Sun compiler version 0x5150<br> Sun Solaris<br> long double
- </p>
- </th>
- <th>
- <p>
- Microsoft Visual C++ version 14.1<br> Win32<br> double
- </p>
- </th>
- </tr></thead>
- <tbody>
- <tr>
- <td>
- <p>
- Elliptic Integral Jacobi Zeta: Mathworld Data
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.66ε (Mean = 0.48ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.66ε (Mean = 0.48ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.52ε (Mean = 0.357ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Elliptic Integral Jacobi Zeta: Random Data
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 2.99ε (Mean = 0.824ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 3.96ε (Mean = 1.06ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 3.89ε (Mean = 0.824ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Elliptic Integral Jacobi Zeta: Large Phi Values
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 2.92ε (Mean = 0.951ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 3.05ε (Mean = 1.13ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 2.52ε (Mean = 0.977ε)</span>
- </p>
- </td>
- </tr>
- </tbody>
- </table></div>
- </div>
- <br class="table-break">
- </div>
- <div class="section">
- <div class="titlepage"><div><div><h2 class="title" style="clear: both">
- <a name="special_function_error_rates_rep.section_laguerre_n_m_x_"></a><a class="link" href="index.html#special_function_error_rates_rep.section_laguerre_n_m_x_" title="laguerre(n, m, x)">laguerre(n,
- m, x)</a>
- </h2></div></div></div>
- <div class="table">
- <a name="special_function_error_rates_rep.section_laguerre_n_m_x_.table_laguerre_n_m_x_"></a><p class="title"><b>Table 65. Error rates for laguerre(n, m, x)</b></p>
- <div class="table-contents"><table class="table" summary="Error rates for laguerre(n, m, x)">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> double
- </p>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> long double
- </p>
- </th>
- <th>
- <p>
- Sun compiler version 0x5150<br> Sun Solaris<br> long double
- </p>
- </th>
- <th>
- <p>
- Microsoft Visual C++ version 14.1<br> Win32<br> double
- </p>
- </th>
- </tr></thead>
- <tbody><tr>
- <td>
- <p>
- Associated Laguerre Polynomials
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.84ε (Mean = 0.0358ε)</span><br> <br>
- (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 434ε (Mean = 10.7ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 167ε (Mean = 6.38ε)</span><br> <br>
- (<span class="emphasis"><em><cmath>:</em></span> Max = 206ε (Mean = 6.86ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 167ε (Mean = 6.38ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 434ε (Mean = 11.1ε)</span>
- </p>
- </td>
- </tr></tbody>
- </table></div>
- </div>
- <br class="table-break">
- </div>
- <div class="section">
- <div class="titlepage"><div><div><h2 class="title" style="clear: both">
- <a name="special_function_error_rates_rep.section_laguerre_n_x_"></a><a class="link" href="index.html#special_function_error_rates_rep.section_laguerre_n_x_" title="laguerre(n, x)">laguerre(n,
- x)</a>
- </h2></div></div></div>
- <div class="table">
- <a name="special_function_error_rates_rep.section_laguerre_n_x_.table_laguerre_n_x_"></a><p class="title"><b>Table 66. Error rates for laguerre(n, x)</b></p>
- <div class="table-contents"><table class="table" summary="Error rates for laguerre(n, x)">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> double
- </p>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> long double
- </p>
- </th>
- <th>
- <p>
- Sun compiler version 0x5150<br> Sun Solaris<br> long double
- </p>
- </th>
- <th>
- <p>
- Microsoft Visual C++ version 14.1<br> Win32<br> double
- </p>
- </th>
- </tr></thead>
- <tbody><tr>
- <td>
- <p>
- Laguerre Polynomials
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 6.82ε (Mean = 0.408ε)</span><br> <br>
- (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 3.1e+03ε (Mean = 185ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.39e+04ε (Mean = 828ε)</span><br> <br>
- (<span class="emphasis"><em><cmath>:</em></span> Max = 4.2e+03ε (Mean = 251ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.39e+04ε (Mean = 828ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 3.1e+03ε (Mean = 185ε)</span>
- </p>
- </td>
- </tr></tbody>
- </table></div>
- </div>
- <br class="table-break">
- </div>
- <div class="section">
- <div class="titlepage"><div><div><h2 class="title" style="clear: both">
- <a name="special_function_error_rates_rep.section_legendre_p"></a><a class="link" href="index.html#special_function_error_rates_rep.section_legendre_p" title="legendre_p">legendre_p</a>
- </h2></div></div></div>
- <div class="table">
- <a name="special_function_error_rates_rep.section_legendre_p.table_legendre_p"></a><p class="title"><b>Table 67. Error rates for legendre_p</b></p>
- <div class="table-contents"><table class="table" summary="Error rates for legendre_p">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> double
- </p>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> long double
- </p>
- </th>
- <th>
- <p>
- Sun compiler version 0x5150<br> Sun Solaris<br> long double
- </p>
- </th>
- <th>
- <p>
- Microsoft Visual C++ version 14.1<br> Win32<br> double
- </p>
- </th>
- </tr></thead>
- <tbody>
- <tr>
- <td>
- <p>
- Legendre Polynomials: Small Values
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.732ε (Mean = 0.0619ε)</span><br> <br>
- (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 211ε (Mean = 20.4ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 69.2ε (Mean = 9.58ε)</span><br> <br>
- (<span class="emphasis"><em><cmath>:</em></span> Max = 124ε (Mean = 13.2ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 69.2ε (Mean = 9.58ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 211ε (Mean = 20.4ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Legendre Polynomials: Large Values
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.632ε (Mean = 0.0693ε)</span><br> <br>
- (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 300ε (Mean = 33.2ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 699ε (Mean = 59.6ε)</span><br> <br>
- (<span class="emphasis"><em><cmath>:</em></span> Max = 343ε (Mean = 32.1ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 699ε (Mean = 59.6ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 300ε (Mean = 33.2ε)</span>
- </p>
- </td>
- </tr>
- </tbody>
- </table></div>
- </div>
- <br class="table-break">
- </div>
- <div class="section">
- <div class="titlepage"><div><div><h2 class="title" style="clear: both">
- <a name="special_function_error_rates_rep.section_legendre_p_associated_"></a><a class="link" href="index.html#special_function_error_rates_rep.section_legendre_p_associated_" title="legendre_p (associated)">legendre_p
- (associated)</a>
- </h2></div></div></div>
- <div class="table">
- <a name="special_function_error_rates_rep.section_legendre_p_associated_.table_legendre_p_associated_"></a><p class="title"><b>Table 68. Error rates for legendre_p (associated)</b></p>
- <div class="table-contents"><table class="table" summary="Error rates for legendre_p (associated)">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> double
- </p>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> long double
- </p>
- </th>
- <th>
- <p>
- Sun compiler version 0x5150<br> Sun Solaris<br> long double
- </p>
- </th>
- <th>
- <p>
- Microsoft Visual C++ version 14.1<br> Win32<br> double
- </p>
- </th>
- </tr></thead>
- <tbody><tr>
- <td>
- <p>
- Associated Legendre Polynomials: Small Values
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.999ε (Mean = 0.05ε)</span><br> <br>
- (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 121ε (Mean = 6.75ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_legendre_p_associated__GSL_2_1_Associated_Legendre_Polynomials_Small_Values">And
- other failures.</a>)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 175ε (Mean = 9.88ε)</span><br> <br>
- (<span class="emphasis"><em><cmath>:</em></span> Max = 175ε (Mean = 9.36ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_legendre_p_associated___cmath__Associated_Legendre_Polynomials_Small_Values">And
- other failures.</a>)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 77.7ε (Mean = 5.59ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 121ε (Mean = 7.14ε)</span>
- </p>
- </td>
- </tr></tbody>
- </table></div>
- </div>
- <br class="table-break">
- </div>
- <div class="section">
- <div class="titlepage"><div><div><h2 class="title" style="clear: both">
- <a name="special_function_error_rates_rep.section_legendre_q"></a><a class="link" href="index.html#special_function_error_rates_rep.section_legendre_q" title="legendre_q">legendre_q</a>
- </h2></div></div></div>
- <div class="table">
- <a name="special_function_error_rates_rep.section_legendre_q.table_legendre_q"></a><p class="title"><b>Table 69. Error rates for legendre_q</b></p>
- <div class="table-contents"><table class="table" summary="Error rates for legendre_q">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> double
- </p>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> long double
- </p>
- </th>
- <th>
- <p>
- Sun compiler version 0x5150<br> Sun Solaris<br> long double
- </p>
- </th>
- <th>
- <p>
- Microsoft Visual C++ version 14.1<br> Win32<br> double
- </p>
- </th>
- </tr></thead>
- <tbody>
- <tr>
- <td>
- <p>
- Legendre Polynomials: Small Values
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.612ε (Mean = 0.0517ε)</span><br> <br>
- (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 46.4ε (Mean = 7.46ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 50.9ε (Mean = 9ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 50.9ε (Mean = 8.98ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 46.4ε (Mean = 7.32ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Legendre Polynomials: Large Values
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 2.49ε (Mean = 0.202ε)</span><br> <br>
- (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 4.6e+03ε (Mean = 366ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 5.98e+03ε (Mean = 478ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 5.98e+03ε (Mean = 478ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 4.6e+03ε (Mean = 366ε)</span>
- </p>
- </td>
- </tr>
- </tbody>
- </table></div>
- </div>
- <br class="table-break">
- </div>
- <div class="section">
- <div class="titlepage"><div><div><h2 class="title" style="clear: both">
- <a name="special_function_error_rates_rep.section_lgamma"></a><a class="link" href="index.html#special_function_error_rates_rep.section_lgamma" title="lgamma">lgamma</a>
- </h2></div></div></div>
- <div class="table">
- <a name="special_function_error_rates_rep.section_lgamma.table_lgamma"></a><p class="title"><b>Table 70. Error rates for lgamma</b></p>
- <div class="table-contents"><table class="table" summary="Error rates for lgamma">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> double
- </p>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> long double
- </p>
- </th>
- <th>
- <p>
- Sun compiler version 0x5150<br> Sun Solaris<br> long double
- </p>
- </th>
- <th>
- <p>
- Microsoft Visual C++ version 14.1<br> Win32<br> double
- </p>
- </th>
- </tr></thead>
- <tbody>
- <tr>
- <td>
- <p>
- factorials
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 33.6ε (Mean = 2.78ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
- Max = 1.55ε (Mean = 0.592ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.991ε (Mean = 0.308ε)</span><br> <br>
- (<span class="emphasis"><em><cmath>:</em></span> Max = 1.67ε (Mean = 0.487ε))<br>
- (<span class="emphasis"><em><math.h>:</em></span> Max = 1.67ε (Mean = 0.487ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.991ε (Mean = 0.383ε)</span><br> <br>
- (<span class="emphasis"><em><math.h>:</em></span> Max = 1.36ε (Mean = 0.476ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.914ε (Mean = 0.175ε)</span><br> <br>
- (<span class="emphasis"><em><math.h>:</em></span> Max = 0.958ε (Mean = 0.38ε))
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- near 0
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 5.21ε (Mean = 1.57ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
- Max = 0ε (Mean = 0ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.42ε (Mean = 0.566ε)</span><br> <br>
- (<span class="emphasis"><em><cmath>:</em></span> Max = 0.964ε (Mean = 0.543ε))<br>
- (<span class="emphasis"><em><math.h>:</em></span> Max = 0.964ε (Mean = 0.543ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.42ε (Mean = 0.566ε)</span><br> <br>
- (<span class="emphasis"><em><math.h>:</em></span> Max = 0.964ε (Mean = 0.543ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.964ε (Mean = 0.462ε)</span><br> <br>
- (<span class="emphasis"><em><math.h>:</em></span> Max = 0.962ε (Mean = 0.372ε))
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- near 1
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 442ε (Mean = 88.8ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
- Max = 7.99e+04ε (Mean = 1.68e+04ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.948ε (Mean = 0.36ε)</span><br> <br>
- (<span class="emphasis"><em><cmath>:</em></span> Max = 0.615ε (Mean = 0.096ε))<br>
- (<span class="emphasis"><em><math.h>:</em></span> Max = 0.615ε (Mean = 0.096ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.948ε (Mean = 0.36ε)</span><br> <br>
- (<span class="emphasis"><em><math.h>:</em></span> Max = 1.71ε (Mean = 0.581ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.867ε (Mean = 0.468ε)</span><br> <br>
- (<span class="emphasis"><em><math.h>:</em></span> Max = 0.906ε (Mean = 0.565ε))
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- near 2
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 1.17e+03ε (Mean = 274ε))<br> (<span class="emphasis"><em>Rmath
- 3.2.3:</em></span> Max = 2.63e+05ε (Mean = 5.84e+04ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.878ε (Mean = 0.242ε)</span><br> <br>
- (<span class="emphasis"><em><cmath>:</em></span> Max = 0.741ε (Mean = 0.263ε))<br>
- (<span class="emphasis"><em><math.h>:</em></span> Max = 0.741ε (Mean = 0.263ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.878ε (Mean = 0.242ε)</span><br> <br>
- (<span class="emphasis"><em><math.h>:</em></span> Max = 0.598ε (Mean = 0.235ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.591ε (Mean = 0.159ε)</span><br> <br>
- (<span class="emphasis"><em><math.h>:</em></span> Max = 0.741ε (Mean = 0.473ε))
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- near -10
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 24.9ε (Mean = 4.6ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
- Max = 4.22ε (Mean = 1.26ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 3.81ε (Mean = 1.01ε)</span><br> <br>
- (<span class="emphasis"><em><cmath>:</em></span> Max = 0.997ε (Mean = 0.412ε))<br>
- (<span class="emphasis"><em><math.h>:</em></span> Max = 0.997ε (Mean = 0.412ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 3.81ε (Mean = 1.01ε)</span><br> <br>
- (<span class="emphasis"><em><math.h>:</em></span> Max = 3.04ε (Mean = 1.01ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 4.22ε (Mean = 1.33ε)</span><br> <br>
- (<span class="emphasis"><em><math.h>:</em></span> Max = 0.997ε (Mean = 0.444ε))
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- near -55
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 7.02ε (Mean = 1.47ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
- Max = 250ε (Mean = 60.9ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.821ε (Mean = 0.513ε)</span><br> <br>
- (<span class="emphasis"><em><cmath>:</em></span> Max = 1.58ε (Mean = 0.672ε))<br>
- (<span class="emphasis"><em><math.h>:</em></span> Max = 1.58ε (Mean = 0.672ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.59ε (Mean = 0.587ε)</span><br> <br>
- (<span class="emphasis"><em><math.h>:</em></span> Max = 0.821ε (Mean = 0.674ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.821ε (Mean = 0.419ε)</span><br> <br>
- (<span class="emphasis"><em><math.h>:</em></span> Max = 249ε (Mean = 43.1ε))
- </p>
- </td>
- </tr>
- </tbody>
- </table></div>
- </div>
- <br class="table-break">
- </div>
- <div class="section">
- <div class="titlepage"><div><div><h2 class="title" style="clear: both">
- <a name="special_function_error_rates_rep.section_log1p"></a><a class="link" href="index.html#special_function_error_rates_rep.section_log1p" title="log1p">log1p</a>
- </h2></div></div></div>
- <div class="table">
- <a name="special_function_error_rates_rep.section_log1p.table_log1p"></a><p class="title"><b>Table 71. Error rates for log1p</b></p>
- <div class="table-contents"><table class="table" summary="Error rates for log1p">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> long double
- </p>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> double
- </p>
- </th>
- <th>
- <p>
- Sun compiler version 0x5150<br> Sun Solaris<br> long double
- </p>
- </th>
- <th>
- <p>
- Microsoft Visual C++ version 14.1<br> Win32<br> double
- </p>
- </th>
- </tr></thead>
- <tbody><tr>
- <td>
- <p>
- Random test data
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.818ε (Mean = 0.227ε)</span><br> <br>
- (<span class="emphasis"><em><cmath>:</em></span> Max = 0.818ε (Mean = 0.227ε))<br>
- (<span class="emphasis"><em><math.h>:</em></span> Max = 0.818ε (Mean = 0.227ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.846ε (Mean = 0.153ε)</span><br> <br>
- (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 0.846ε (Mean = 0.153ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 2.3ε (Mean = 0.66ε)</span><br> <br>
- (<span class="emphasis"><em><math.h>:</em></span> Max = 0.818ε (Mean = 0.249ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.509ε (Mean = 0.057ε)</span><br> <br>
- (<span class="emphasis"><em><math.h>:</em></span> Max = 0.509ε (Mean = 0.057ε))
- </p>
- </td>
- </tr></tbody>
- </table></div>
- </div>
- <br class="table-break">
- </div>
- <div class="section">
- <div class="titlepage"><div><div><h2 class="title" style="clear: both">
- <a name="special_function_error_rates_rep.section_non_central_beta_CDF"></a><a class="link" href="index.html#special_function_error_rates_rep.section_non_central_beta_CDF" title="non central beta CDF">non
- central beta CDF</a>
- </h2></div></div></div>
- <div class="table">
- <a name="special_function_error_rates_rep.section_non_central_beta_CDF.table_non_central_beta_CDF"></a><p class="title"><b>Table 72. Error rates for non central beta CDF</b></p>
- <div class="table-contents"><table class="table" summary="Error rates for non central beta CDF">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> double
- </p>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> long double
- </p>
- </th>
- <th>
- <p>
- Sun compiler version 0x5150<br> Sun Solaris<br> long double
- </p>
- </th>
- <th>
- <p>
- Microsoft Visual C++ version 14.1<br> Win32<br> double
- </p>
- </th>
- </tr></thead>
- <tbody>
- <tr>
- <td>
- <p>
- Non Central Beta, medium parameters
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.998ε (Mean = 0.0649ε)</span><br> <br>
- (<span class="emphasis"><em>Rmath 3.2.3:</em></span> <span class="red">Max = 1.46e+26ε (Mean
- = 3.5e+24ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_non_central_beta_CDF_Rmath_3_2_3_Non_Central_Beta_medium_parameters">And
- other failures.</a>)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 824ε (Mean = 27.4ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 832ε (Mean = 38.1ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 242ε (Mean = 31ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Non Central Beta, large parameters
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.18ε (Mean = 0.175ε)</span><br> <br>
- (<span class="emphasis"><em>Rmath 3.2.3:</em></span> <span class="red">Max = 1.01e+36ε (Mean
- = 1.19e+35ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_non_central_beta_CDF_Rmath_3_2_3_Non_Central_Beta_large_parameters">And
- other failures.</a>)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 2.5e+04ε (Mean = 3.78e+03ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 2.57e+04ε (Mean = 4.45e+03ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 3.66e+03ε (Mean = 500ε)</span>
- </p>
- </td>
- </tr>
- </tbody>
- </table></div>
- </div>
- <br class="table-break">
- </div>
- <div class="section">
- <div class="titlepage"><div><div><h2 class="title" style="clear: both">
- <a name="special_function_error_rates_rep.section_non_central_beta_CDF_complement"></a><a class="link" href="index.html#special_function_error_rates_rep.section_non_central_beta_CDF_complement" title="non central beta CDF complement">non
- central beta CDF complement</a>
- </h2></div></div></div>
- <div class="table">
- <a name="special_function_error_rates_rep.section_non_central_beta_CDF_complement.table_non_central_beta_CDF_complement"></a><p class="title"><b>Table 73. Error rates for non central beta CDF complement</b></p>
- <div class="table-contents"><table class="table" summary="Error rates for non central beta CDF complement">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> double
- </p>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> long double
- </p>
- </th>
- <th>
- <p>
- Sun compiler version 0x5150<br> Sun Solaris<br> long double
- </p>
- </th>
- <th>
- <p>
- Microsoft Visual C++ version 14.1<br> Win32<br> double
- </p>
- </th>
- </tr></thead>
- <tbody>
- <tr>
- <td>
- <p>
- Non Central Beta, medium parameters
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.998ε (Mean = 0.0936ε)</span><br> <br>
- (<span class="emphasis"><em>Rmath 3.2.3:</em></span> <span class="red">Max = 7.5e+97ε (Mean
- = 1.37e+96ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_non_central_beta_CDF_complement_Rmath_3_2_3_Non_Central_Beta_medium_parameters">And
- other failures.</a>)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 396ε (Mean = 50.7ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 554ε (Mean = 57.2ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 624ε (Mean = 62.7ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Non Central Beta, large parameters
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.986ε (Mean = 0.188ε)</span><br> <br>
- (<span class="emphasis"><em>Rmath 3.2.3:</em></span> <span class="red">Max = +INFε (Mean
- = +INFε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_non_central_beta_CDF_complement_Rmath_3_2_3_Non_Central_Beta_large_parameters">And
- other failures.</a>)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 6.83e+03ε (Mean = 993ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 3.56e+03ε (Mean = 707ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.25e+04ε (Mean = 1.49e+03ε)</span>
- </p>
- </td>
- </tr>
- </tbody>
- </table></div>
- </div>
- <br class="table-break">
- </div>
- <div class="section">
- <div class="titlepage"><div><div><h2 class="title" style="clear: both">
- <a name="special_function_error_rates_rep.section_non_central_chi_squared_CDF"></a><a class="link" href="index.html#special_function_error_rates_rep.section_non_central_chi_squared_CDF" title="non central chi squared CDF">non
- central chi squared CDF</a>
- </h2></div></div></div>
- <div class="table">
- <a name="special_function_error_rates_rep.section_non_central_chi_squared_CDF.table_non_central_chi_squared_CDF"></a><p class="title"><b>Table 74. Error rates for non central chi squared CDF</b></p>
- <div class="table-contents"><table class="table" summary="Error rates for non central chi squared CDF">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> double
- </p>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> long double
- </p>
- </th>
- <th>
- <p>
- Sun compiler version 0x5150<br> Sun Solaris<br> long double
- </p>
- </th>
- <th>
- <p>
- Microsoft Visual C++ version 14.1<br> Win32<br> double
- </p>
- </th>
- </tr></thead>
- <tbody>
- <tr>
- <td>
- <p>
- Non Central Chi Squared, medium parameters
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.99ε (Mean = 0.0544ε)</span><br> <br>
- (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 727ε (Mean = 121ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 46.5ε (Mean = 10.3ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 115ε (Mean = 13.9ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 48.9ε (Mean = 10ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Non Central Chi Squared, large parameters
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.07ε (Mean = 0.102ε)</span><br> <br>
- (<span class="emphasis"><em>Rmath 3.2.3:</em></span> <span class="red">Max = 3.27e+08ε (Mean
- = 2.23e+07ε))</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 3.07e+03ε (Mean = 336ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 6.17e+03ε (Mean = 677ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 9.79e+03ε (Mean = 723ε)</span>
- </p>
- </td>
- </tr>
- </tbody>
- </table></div>
- </div>
- <br class="table-break">
- </div>
- <div class="section">
- <div class="titlepage"><div><div><h2 class="title" style="clear: both">
- <a name="special_function_error_rates_rep.section_non_central_chi_squared_CDF_complement"></a><a class="link" href="index.html#special_function_error_rates_rep.section_non_central_chi_squared_CDF_complement" title="non central chi squared CDF complement">non
- central chi squared CDF complement</a>
- </h2></div></div></div>
- <div class="table">
- <a name="special_function_error_rates_rep.section_non_central_chi_squared_CDF_complement.table_non_central_chi_squared_CDF_complement"></a><p class="title"><b>Table 75. Error rates for non central chi squared CDF complement</b></p>
- <div class="table-contents"><table class="table" summary="Error rates for non central chi squared CDF complement">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> double
- </p>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> long double
- </p>
- </th>
- <th>
- <p>
- Sun compiler version 0x5150<br> Sun Solaris<br> long double
- </p>
- </th>
- <th>
- <p>
- Microsoft Visual C++ version 14.1<br> Win32<br> double
- </p>
- </th>
- </tr></thead>
- <tbody>
- <tr>
- <td>
- <p>
- Non Central Chi Squared, medium parameters
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.96ε (Mean = 0.0635ε)</span><br> <br>
- (<span class="emphasis"><em>Rmath 3.2.3:</em></span> <span class="red">Max = +INFε (Mean
- = +INFε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_non_central_chi_squared_CDF_complement_Rmath_3_2_3_Non_Central_Chi_Squared_medium_parameters">And
- other failures.</a>)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 107ε (Mean = 17.2ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 171ε (Mean = 22.8ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 98.6ε (Mean = 15.8ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Non Central Chi Squared, large parameters
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 2.11ε (Mean = 0.278ε)</span><br> <br>
- (<span class="emphasis"><em>Rmath 3.2.3:</em></span> <span class="red">Max = +INFε (Mean
- = +INFε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_non_central_chi_squared_CDF_complement_Rmath_3_2_3_Non_Central_Chi_Squared_large_parameters">And
- other failures.</a>)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 5.02e+03ε (Mean = 630ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 5.1e+03ε (Mean = 577ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 5.43e+03ε (Mean = 705ε)</span>
- </p>
- </td>
- </tr>
- </tbody>
- </table></div>
- </div>
- <br class="table-break">
- </div>
- <div class="section">
- <div class="titlepage"><div><div><h2 class="title" style="clear: both">
- <a name="special_function_error_rates_rep.section_non_central_t_CDF"></a><a class="link" href="index.html#special_function_error_rates_rep.section_non_central_t_CDF" title="non central t CDF">non
- central t CDF</a>
- </h2></div></div></div>
- <div class="table">
- <a name="special_function_error_rates_rep.section_non_central_t_CDF.table_non_central_t_CDF"></a><p class="title"><b>Table 76. Error rates for non central t CDF</b></p>
- <div class="table-contents"><table class="table" summary="Error rates for non central t CDF">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> double
- </p>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> long double
- </p>
- </th>
- <th>
- <p>
- Sun compiler version 0x5150<br> Sun Solaris<br> long double
- </p>
- </th>
- <th>
- <p>
- Microsoft Visual C++ version 14.1<br> Win32<br> double
- </p>
- </th>
- </tr></thead>
- <tbody>
- <tr>
- <td>
- <p>
- Non Central T
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.796ε (Mean = 0.0691ε)</span><br> <br>
- (<span class="emphasis"><em>Rmath 3.2.3:</em></span> <span class="red">Max = 5.28e+15ε (Mean
- = 8.49e+14ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_non_central_t_CDF_Rmath_3_2_3_Non_Central_T">And
- other failures.</a>)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 139ε (Mean = 31ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 145ε (Mean = 30.9ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 135ε (Mean = 32.1ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Non Central T (small non-centrality)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>Rmath
- 3.2.3:</em></span> Max = 2.09e+03ε (Mean = 244ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 3.86ε (Mean = 1.4ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 9.15ε (Mean = 2.13ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 6.17ε (Mean = 1.45ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Non Central T (large parameters)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 257ε (Mean = 72.1ε)</span><br> <br>
- (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 2.46ε (Mean = 0.657ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 5.26e+05ε (Mean = 1.48e+05ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 5.24e+05ε (Mean = 1.47e+05ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 286ε (Mean = 62.8ε)</span>
- </p>
- </td>
- </tr>
- </tbody>
- </table></div>
- </div>
- <br class="table-break">
- </div>
- <div class="section">
- <div class="titlepage"><div><div><h2 class="title" style="clear: both">
- <a name="special_function_error_rates_rep.section_non_central_t_CDF_complement"></a><a class="link" href="index.html#special_function_error_rates_rep.section_non_central_t_CDF_complement" title="non central t CDF complement">non
- central t CDF complement</a>
- </h2></div></div></div>
- <div class="table">
- <a name="special_function_error_rates_rep.section_non_central_t_CDF_complement.table_non_central_t_CDF_complement"></a><p class="title"><b>Table 77. Error rates for non central t CDF complement</b></p>
- <div class="table-contents"><table class="table" summary="Error rates for non central t CDF complement">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> double
- </p>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> long double
- </p>
- </th>
- <th>
- <p>
- Sun compiler version 0x5150<br> Sun Solaris<br> long double
- </p>
- </th>
- <th>
- <p>
- Microsoft Visual C++ version 14.1<br> Win32<br> double
- </p>
- </th>
- </tr></thead>
- <tbody>
- <tr>
- <td>
- <p>
- Non Central T
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.707ε (Mean = 0.0497ε)</span><br> <br>
- (<span class="emphasis"><em>Rmath 3.2.3:</em></span> <span class="red">Max = 6.19e+15ε (Mean
- = 6.72e+14ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_non_central_t_CDF_complement_Rmath_3_2_3_Non_Central_T">And
- other failures.</a>)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 201ε (Mean = 31.7ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 340ε (Mean = 43.2ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 154ε (Mean = 32.1ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Non Central T (small non-centrality)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>Rmath
- 3.2.3:</em></span> Max = 1.87e+03ε (Mean = 263ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 10.5ε (Mean = 2.13ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 10.5ε (Mean = 2.39ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 4.6ε (Mean = 1.63ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Non Central T (large parameters)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 478ε (Mean = 96.3ε)</span><br> <br>
- (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 2.24ε (Mean = 0.945ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 9.79e+05ε (Mean = 1.97e+05ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 9.79e+05ε (Mean = 1.97e+05ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 227ε (Mean = 50.4ε)</span>
- </p>
- </td>
- </tr>
- </tbody>
- </table></div>
- </div>
- <br class="table-break">
- </div>
- <div class="section">
- <div class="titlepage"><div><div><h2 class="title" style="clear: both">
- <a name="special_function_error_rates_rep.section_owens_t"></a><a class="link" href="index.html#special_function_error_rates_rep.section_owens_t" title="owens_t">owens_t</a>
- </h2></div></div></div>
- <div class="table">
- <a name="special_function_error_rates_rep.section_owens_t.table_owens_t"></a><p class="title"><b>Table 78. Error rates for owens_t</b></p>
- <div class="table-contents"><table class="table" summary="Error rates for owens_t">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> double
- </p>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> long double
- </p>
- </th>
- <th>
- <p>
- Sun compiler version 0x5150<br> Sun Solaris<br> long double
- </p>
- </th>
- <th>
- <p>
- Microsoft Visual C++ version 14.1<br> Win32<br> double
- </p>
- </th>
- </tr></thead>
- <tbody>
- <tr>
- <td>
- <p>
- Owens T (medium small values)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 3.34ε (Mean = 0.944ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 3.34ε (Mean = 0.911ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 4.37ε (Mean = 0.98ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Owens T (large and diverse values)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 49ε (Mean = 2.16ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 24.5ε (Mean = 1.39ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 3.78ε (Mean = 0.621ε)</span>
- </p>
- </td>
- </tr>
- </tbody>
- </table></div>
- </div>
- <br class="table-break">
- </div>
- <div class="section">
- <div class="titlepage"><div><div><h2 class="title" style="clear: both">
- <a name="special_function_error_rates_rep.section_polygamma"></a><a class="link" href="index.html#special_function_error_rates_rep.section_polygamma" title="polygamma">polygamma</a>
- </h2></div></div></div>
- <div class="table">
- <a name="special_function_error_rates_rep.section_polygamma.table_polygamma"></a><p class="title"><b>Table 79. Error rates for polygamma</b></p>
- <div class="table-contents"><table class="table" summary="Error rates for polygamma">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> double
- </p>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> long double
- </p>
- </th>
- <th>
- <p>
- Sun compiler version 0x5150<br> Sun Solaris<br> long double
- </p>
- </th>
- <th>
- <p>
- Microsoft Visual C++ version 14.1<br> Win32<br> double
- </p>
- </th>
- </tr></thead>
- <tbody>
- <tr>
- <td>
- <p>
- Mathematica Data
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.824ε (Mean = 0.0574ε)</span><br> <br>
- (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 62.9ε (Mean = 12.8ε))<br> (<span class="emphasis"><em>Rmath
- 3.2.3:</em></span> Max = 108ε (Mean = 15.2ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 7.38ε (Mean = 1.84ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 34.3ε (Mean = 7.65ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 9.32ε (Mean = 1.95ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Mathematica Data - large arguments
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.998ε (Mean = 0.0592ε)</span><br> <br>
- (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 244ε (Mean = 32.8ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_polygamma_GSL_2_1_Mathematica_Data_large_arguments">And
- other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
- <span class="red">Max = 1.71e+56ε (Mean = 1.01e+55ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_polygamma_Rmath_3_2_3_Mathematica_Data_large_arguments">And
- other failures.</a>)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 2.23ε (Mean = 0.323ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 11.1ε (Mean = 0.848ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 150ε (Mean = 13.9ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Mathematica Data - negative arguments
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.516ε (Mean = 0.022ε)</span><br> <br>
- (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 36.6ε (Mean = 3.04ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_polygamma_GSL_2_1_Mathematica_Data_negative_arguments">And
- other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
- Max = 0ε (Mean = 0ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_polygamma_Rmath_3_2_3_Mathematica_Data_negative_arguments">And
- other failures.</a>)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 269ε (Mean = 87.7ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 269ε (Mean = 88.4ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 497ε (Mean = 129ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Mathematica Data - large negative arguments
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 1.79ε (Mean = 0.197ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_polygamma_GSL_2_1_Mathematica_Data_large_negative_arguments">And
- other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
- Max = 0ε (Mean = 0ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_polygamma_Rmath_3_2_3_Mathematica_Data_large_negative_arguments">And
- other failures.</a>)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 155ε (Mean = 96.4ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 155ε (Mean = 96.4ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 162ε (Mean = 101ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Mathematica Data - small arguments
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 15.2ε (Mean = 5.03ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
- Max = 106ε (Mean = 20ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 3.33ε (Mean = 0.75ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 3.33ε (Mean = 0.75ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 3ε (Mean = 0.496ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Mathematica Data - Large orders and other bug cases
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 151ε (Mean = 39.3ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_polygamma_GSL_2_1_Mathematica_Data_Large_orders_and_other_bug_cases">And
- other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
- <span class="red">Max = +INFε (Mean = +INFε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_polygamma_Rmath_3_2_3_Mathematica_Data_Large_orders_and_other_bug_cases">And
- other failures.</a>)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 54.5ε (Mean = 13.3ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 145ε (Mean = 55.9ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 200ε (Mean = 57.2ε)</span>
- </p>
- </td>
- </tr>
- </tbody>
- </table></div>
- </div>
- <br class="table-break">
- </div>
- <div class="section">
- <div class="titlepage"><div><div><h2 class="title" style="clear: both">
- <a name="special_function_error_rates_rep.section_powm1"></a><a class="link" href="index.html#special_function_error_rates_rep.section_powm1" title="powm1">powm1</a>
- </h2></div></div></div>
- <div class="table">
- <a name="special_function_error_rates_rep.section_powm1.table_powm1"></a><p class="title"><b>Table 80. Error rates for powm1</b></p>
- <div class="table-contents"><table class="table" summary="Error rates for powm1">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> double
- </p>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> long double
- </p>
- </th>
- <th>
- <p>
- Sun compiler version 0x5150<br> Sun Solaris<br> long double
- </p>
- </th>
- <th>
- <p>
- Microsoft Visual C++ version 14.1<br> Win32<br> double
- </p>
- </th>
- </tr></thead>
- <tbody><tr>
- <td>
- <p>
- powm1
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.06ε (Mean = 0.425ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 2.04ε (Mean = 0.493ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.88ε (Mean = 0.49ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.84ε (Mean = 0.486ε)</span>
- </p>
- </td>
- </tr></tbody>
- </table></div>
- </div>
- <br class="table-break">
- </div>
- <div class="section">
- <div class="titlepage"><div><div><h2 class="title" style="clear: both">
- <a name="special_function_error_rates_rep.section_sin_pi"></a><a class="link" href="index.html#special_function_error_rates_rep.section_sin_pi" title="sin_pi">sin_pi</a>
- </h2></div></div></div>
- <div class="table">
- <a name="special_function_error_rates_rep.section_sin_pi.table_sin_pi"></a><p class="title"><b>Table 81. Error rates for sin_pi</b></p>
- <div class="table-contents"><table class="table" summary="Error rates for sin_pi">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> double
- </p>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> long double
- </p>
- </th>
- <th>
- <p>
- Sun compiler version 0x5150<br> Sun Solaris<br> long double
- </p>
- </th>
- <th>
- <p>
- Microsoft Visual C++ version 14.1<br> Win32<br> double
- </p>
- </th>
- </tr></thead>
- <tbody>
- <tr>
- <td>
- <p>
- sin_pi and cos_pi
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.996ε (Mean = 0.335ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.996ε (Mean = 0.336ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.99ε (Mean = 0.328ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- sin_pi and cos_pi near integers and half integers
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.976ε (Mean = 0.293ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.976ε (Mean = 0.293ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.996ε (Mean = 0.343ε)</span>
- </p>
- </td>
- </tr>
- </tbody>
- </table></div>
- </div>
- <br class="table-break">
- </div>
- <div class="section">
- <div class="titlepage"><div><div><h2 class="title" style="clear: both">
- <a name="special_function_error_rates_rep.section_sph_bessel"></a><a class="link" href="index.html#special_function_error_rates_rep.section_sph_bessel" title="sph_bessel">sph_bessel</a>
- </h2></div></div></div>
- <div class="table">
- <a name="special_function_error_rates_rep.section_sph_bessel.table_sph_bessel"></a><p class="title"><b>Table 82. Error rates for sph_bessel</b></p>
- <div class="table-contents"><table class="table" summary="Error rates for sph_bessel">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> long double
- </p>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> double
- </p>
- </th>
- <th>
- <p>
- Sun compiler version 0x5150<br> Sun Solaris<br> long double
- </p>
- </th>
- <th>
- <p>
- Microsoft Visual C++ version 14.1<br> Win32<br> double
- </p>
- </th>
- </tr></thead>
- <tbody><tr>
- <td>
- <p>
- Bessel j: Random Data
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 243ε (Mean = 13.3ε)</span><br> <br>
- (<span class="emphasis"><em><cmath>:</em></span> Max = 1.91e+06ε (Mean = 1.09e+05ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.978ε (Mean = 0.0445ε)</span><br> <br>
- (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 1.79e+03ε (Mean = 107ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 243ε (Mean = 33.7ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 245ε (Mean = 16.3ε)</span>
- </p>
- </td>
- </tr></tbody>
- </table></div>
- </div>
- <br class="table-break">
- </div>
- <div class="section">
- <div class="titlepage"><div><div><h2 class="title" style="clear: both">
- <a name="special_function_error_rates_rep.section_sph_bessel_prime"></a><a class="link" href="index.html#special_function_error_rates_rep.section_sph_bessel_prime" title="sph_bessel_prime">sph_bessel_prime</a>
- </h2></div></div></div>
- <div class="table">
- <a name="special_function_error_rates_rep.section_sph_bessel_prime.table_sph_bessel_prime"></a><p class="title"><b>Table 83. Error rates for sph_bessel_prime</b></p>
- <div class="table-contents"><table class="table" summary="Error rates for sph_bessel_prime">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> double
- </p>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> long double
- </p>
- </th>
- <th>
- <p>
- Sun compiler version 0x5150<br> Sun Solaris<br> long double
- </p>
- </th>
- <th>
- <p>
- Microsoft Visual C++ version 14.1<br> Win32<br> double
- </p>
- </th>
- </tr></thead>
- <tbody><tr>
- <td>
- <p>
- Bessel j': Random Data
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.753ε (Mean = 0.0343ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 167ε (Mean = 12ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 167ε (Mean = 33.2ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 307ε (Mean = 25.2ε)</span>
- </p>
- </td>
- </tr></tbody>
- </table></div>
- </div>
- <br class="table-break">
- </div>
- <div class="section">
- <div class="titlepage"><div><div><h2 class="title" style="clear: both">
- <a name="special_function_error_rates_rep.section_sph_neumann"></a><a class="link" href="index.html#special_function_error_rates_rep.section_sph_neumann" title="sph_neumann">sph_neumann</a>
- </h2></div></div></div>
- <div class="table">
- <a name="special_function_error_rates_rep.section_sph_neumann.table_sph_neumann"></a><p class="title"><b>Table 84. Error rates for sph_neumann</b></p>
- <div class="table-contents"><table class="table" summary="Error rates for sph_neumann">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> long double
- </p>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> double
- </p>
- </th>
- <th>
- <p>
- Sun compiler version 0x5150<br> Sun Solaris<br> long double
- </p>
- </th>
- <th>
- <p>
- Microsoft Visual C++ version 14.1<br> Win32<br> double
- </p>
- </th>
- </tr></thead>
- <tbody><tr>
- <td>
- <p>
- y: Random Data
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 234ε (Mean = 19.5ε)</span><br> <br>
- (<span class="emphasis"><em><cmath>:</em></span> Max = 1.6e+06ε (Mean = 1.4e+05ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.995ε (Mean = 0.0665ε)</span><br> <br>
- (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 8.5e+04ε (Mean = 5.33e+03ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 234ε (Mean = 19.8ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 281ε (Mean = 31.1ε)</span>
- </p>
- </td>
- </tr></tbody>
- </table></div>
- </div>
- <br class="table-break">
- </div>
- <div class="section">
- <div class="titlepage"><div><div><h2 class="title" style="clear: both">
- <a name="special_function_error_rates_rep.section_sph_neumann_prime"></a><a class="link" href="index.html#special_function_error_rates_rep.section_sph_neumann_prime" title="sph_neumann_prime">sph_neumann_prime</a>
- </h2></div></div></div>
- <div class="table">
- <a name="special_function_error_rates_rep.section_sph_neumann_prime.table_sph_neumann_prime"></a><p class="title"><b>Table 85. Error rates for sph_neumann_prime</b></p>
- <div class="table-contents"><table class="table" summary="Error rates for sph_neumann_prime">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> double
- </p>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> long double
- </p>
- </th>
- <th>
- <p>
- Sun compiler version 0x5150<br> Sun Solaris<br> long double
- </p>
- </th>
- <th>
- <p>
- Microsoft Visual C++ version 14.1<br> Win32<br> double
- </p>
- </th>
- </tr></thead>
- <tbody><tr>
- <td>
- <p>
- y': Random Data
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.988ε (Mean = 0.0869ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 158ε (Mean = 18.8ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 158ε (Mean = 20.2ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 296ε (Mean = 25.6ε)</span>
- </p>
- </td>
- </tr></tbody>
- </table></div>
- </div>
- <br class="table-break">
- </div>
- <div class="section">
- <div class="titlepage"><div><div><h2 class="title" style="clear: both">
- <a name="special_function_error_rates_rep.section_spherical_harmonic_i"></a><a class="link" href="index.html#special_function_error_rates_rep.section_spherical_harmonic_i" title="spherical_harmonic_i">spherical_harmonic_i</a>
- </h2></div></div></div>
- <div class="table">
- <a name="special_function_error_rates_rep.section_spherical_harmonic_i.table_spherical_harmonic_i"></a><p class="title"><b>Table 86. Error rates for spherical_harmonic_i</b></p>
- <div class="table-contents"><table class="table" summary="Error rates for spherical_harmonic_i">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> double
- </p>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> long double
- </p>
- </th>
- <th>
- <p>
- Sun compiler version 0x5150<br> Sun Solaris<br> long double
- </p>
- </th>
- <th>
- <p>
- Microsoft Visual C++ version 14.1<br> Win32<br> double
- </p>
- </th>
- </tr></thead>
- <tbody><tr>
- <td>
- <p>
- Spherical Harmonics
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.36ε (Mean = 0.0765ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 2.89e+03ε (Mean = 108ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.03e+04ε (Mean = 327ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 2.27e+04ε (Mean = 725ε)</span>
- </p>
- </td>
- </tr></tbody>
- </table></div>
- </div>
- <br class="table-break">
- </div>
- <div class="section">
- <div class="titlepage"><div><div><h2 class="title" style="clear: both">
- <a name="special_function_error_rates_rep.section_spherical_harmonic_r"></a><a class="link" href="index.html#special_function_error_rates_rep.section_spherical_harmonic_r" title="spherical_harmonic_r">spherical_harmonic_r</a>
- </h2></div></div></div>
- <div class="table">
- <a name="special_function_error_rates_rep.section_spherical_harmonic_r.table_spherical_harmonic_r"></a><p class="title"><b>Table 87. Error rates for spherical_harmonic_r</b></p>
- <div class="table-contents"><table class="table" summary="Error rates for spherical_harmonic_r">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> double
- </p>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> long double
- </p>
- </th>
- <th>
- <p>
- Sun compiler version 0x5150<br> Sun Solaris<br> long double
- </p>
- </th>
- <th>
- <p>
- Microsoft Visual C++ version 14.1<br> Win32<br> double
- </p>
- </th>
- </tr></thead>
- <tbody><tr>
- <td>
- <p>
- Spherical Harmonics
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.58ε (Mean = 0.0707ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 2.89e+03ε (Mean = 108ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.03e+04ε (Mean = 327ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 2.27e+04ε (Mean = 725ε)</span>
- </p>
- </td>
- </tr></tbody>
- </table></div>
- </div>
- <br class="table-break">
- </div>
- <div class="section">
- <div class="titlepage"><div><div><h2 class="title" style="clear: both">
- <a name="special_function_error_rates_rep.section_sqrt1pm1"></a><a class="link" href="index.html#special_function_error_rates_rep.section_sqrt1pm1" title="sqrt1pm1">sqrt1pm1</a>
- </h2></div></div></div>
- <div class="table">
- <a name="special_function_error_rates_rep.section_sqrt1pm1.table_sqrt1pm1"></a><p class="title"><b>Table 88. Error rates for sqrt1pm1</b></p>
- <div class="table-contents"><table class="table" summary="Error rates for sqrt1pm1">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> double
- </p>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> long double
- </p>
- </th>
- <th>
- <p>
- Sun compiler version 0x5150<br> Sun Solaris<br> long double
- </p>
- </th>
- <th>
- <p>
- Microsoft Visual C++ version 14.1<br> Win32<br> double
- </p>
- </th>
- </tr></thead>
- <tbody><tr>
- <td>
- <p>
- sqrt1pm1
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.3ε (Mean = 0.404ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.33ε (Mean = 0.404ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.54ε (Mean = 0.563ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.35ε (Mean = 0.497ε)</span>
- </p>
- </td>
- </tr></tbody>
- </table></div>
- </div>
- <br class="table-break">
- </div>
- <div class="section">
- <div class="titlepage"><div><div><h2 class="title" style="clear: both">
- <a name="special_function_error_rates_rep.section_tgamma"></a><a class="link" href="index.html#special_function_error_rates_rep.section_tgamma" title="tgamma">tgamma</a>
- </h2></div></div></div>
- <div class="table">
- <a name="special_function_error_rates_rep.section_tgamma.table_tgamma"></a><p class="title"><b>Table 89. Error rates for tgamma</b></p>
- <div class="table-contents"><table class="table" summary="Error rates for tgamma">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> double
- </p>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> long double
- </p>
- </th>
- <th>
- <p>
- Sun compiler version 0x5150<br> Sun Solaris<br> long double
- </p>
- </th>
- <th>
- <p>
- Microsoft Visual C++ version 14.1<br> Win32<br> double
- </p>
- </th>
- </tr></thead>
- <tbody>
- <tr>
- <td>
- <p>
- factorials
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 3.95ε (Mean = 0.783ε))<br> (<span class="emphasis"><em>Rmath
- 3.2.3:</em></span> Max = 314ε (Mean = 93.4ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 2.67ε (Mean = 0.617ε)</span><br> <br>
- (<span class="emphasis"><em><cmath>:</em></span> Max = 1.66ε (Mean = 0.584ε))<br>
- (<span class="emphasis"><em><math.h>:</em></span> Max = 1.66ε (Mean = 0.584ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 172ε (Mean = 41ε)</span><br> <br> (<span class="emphasis"><em><math.h>:</em></span>
- Max = 0ε (Mean = 0ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.85ε (Mean = 0.566ε)</span><br> <br>
- (<span class="emphasis"><em><math.h>:</em></span> Max = 3.17ε (Mean = 0.928ε))
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- near 0
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 4.51ε (Mean = 1.92ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
- Max = 1ε (Mean = 0.335ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 2ε (Mean = 0.608ε)</span><br> <br> (<span class="emphasis"><em><cmath>:</em></span>
- Max = 1ε (Mean = 0.376ε))<br> (<span class="emphasis"><em><math.h>:</em></span>
- Max = 1ε (Mean = 0.376ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 2ε (Mean = 0.647ε)</span><br> <br> (<span class="emphasis"><em><math.h>:</em></span>
- Max = 0.5ε (Mean = 0.0791ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.5ε (Mean = 0.635ε)</span><br> <br>
- (<span class="emphasis"><em><math.h>:</em></span> Max = 1ε (Mean = 0.405ε))
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- near 1
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 4.41ε (Mean = 1.81ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
- Max = 1ε (Mean = 0.32ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 2.51ε (Mean = 1.02ε)</span><br> <br>
- (<span class="emphasis"><em><cmath>:</em></span> Max = 0.918ε (Mean = 0.203ε))<br>
- (<span class="emphasis"><em><math.h>:</em></span> Max = 0.918ε (Mean = 0.203ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 3.01ε (Mean = 1.06ε)</span><br> <br>
- (<span class="emphasis"><em><math.h>:</em></span> Max = 1ε (Mean = 0.175ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.1ε (Mean = 0.59ε)</span><br> <br>
- (<span class="emphasis"><em><math.h>:</em></span> Max = 1ε (Mean = 0.4ε))
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- near 2
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 7.95ε (Mean = 3.12ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
- Max = 1ε (Mean = 0.191ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 4.1ε (Mean = 1.55ε)</span><br> <br>
- (<span class="emphasis"><em><cmath>:</em></span> Max = 0.558ε (Mean = 0.298ε))<br>
- (<span class="emphasis"><em><math.h>:</em></span> Max = 0.558ε (Mean = 0.298ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 5.01ε (Mean = 1.89ε)</span><br> <br>
- (<span class="emphasis"><em><math.h>:</em></span> Max = 0ε (Mean = 0ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 2ε (Mean = 0.733ε)</span><br> <br> (<span class="emphasis"><em><math.h>:</em></span>
- Max = 0ε (Mean = 0ε))
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- near -10
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 2.6ε (Mean = 1.05ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
- Max = 34.9ε (Mean = 9.2ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.75ε (Mean = 0.895ε)</span><br> <br>
- (<span class="emphasis"><em><cmath>:</em></span> Max = 2.26ε (Mean = 1.08ε))<br>
- (<span class="emphasis"><em><math.h>:</em></span> Max = 2.26ε (Mean = 1.08ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.75ε (Mean = 0.819ε)</span><br> <br>
- (<span class="emphasis"><em><math.h>:</em></span> Max = 0ε (Mean = 0ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.86ε (Mean = 0.881ε)</span><br> <br>
- (<span class="emphasis"><em><math.h>:</em></span> Max = 0.866ε (Mean = 0.445ε))
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- near -55
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 1.8ε (Mean = 0.782ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
- Max = 3.89e+04ε (Mean = 9.52e+03ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 2.69ε (Mean = 1.09ε)</span><br> <br>
- (<span class="emphasis"><em><cmath>:</em></span> Max = 1.79ε (Mean = 0.75ε))<br>
- (<span class="emphasis"><em><math.h>:</em></span> Max = 1.79ε (Mean = 0.75ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 98.5ε (Mean = 53.4ε)</span><br> <br>
- (<span class="emphasis"><em><math.h>:</em></span> Max = 0ε (Mean = 0ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 2.7ε (Mean = 1.35ε)</span><br> <br>
- (<span class="emphasis"><em><math.h>:</em></span> Max = 3.87e+04ε (Mean = 6.71e+03ε))
- </p>
- </td>
- </tr>
- </tbody>
- </table></div>
- </div>
- <br class="table-break">
- </div>
- <div class="section">
- <div class="titlepage"><div><div><h2 class="title" style="clear: both">
- <a name="special_function_error_rates_rep.section_tgamma1pm1"></a><a class="link" href="index.html#special_function_error_rates_rep.section_tgamma1pm1" title="tgamma1pm1">tgamma1pm1</a>
- </h2></div></div></div>
- <div class="table">
- <a name="special_function_error_rates_rep.section_tgamma1pm1.table_tgamma1pm1"></a><p class="title"><b>Table 90. Error rates for tgamma1pm1</b></p>
- <div class="table-contents"><table class="table" summary="Error rates for tgamma1pm1">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> double
- </p>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> long double
- </p>
- </th>
- <th>
- <p>
- Sun compiler version 0x5150<br> Sun Solaris<br> long double
- </p>
- </th>
- <th>
- <p>
- Microsoft Visual C++ version 14.1<br> Win32<br> double
- </p>
- </th>
- </tr></thead>
- <tbody><tr>
- <td>
- <p>
- tgamma1pm1(dz)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.12ε (Mean = 0.49ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 6.61ε (Mean = 0.84ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 3.31ε (Mean = 0.517ε)</span>
- </p>
- </td>
- </tr></tbody>
- </table></div>
- </div>
- <br class="table-break">
- </div>
- <div class="section">
- <div class="titlepage"><div><div><h2 class="title" style="clear: both">
- <a name="special_function_error_rates_rep.section_tgamma_delta_ratio"></a><a class="link" href="index.html#special_function_error_rates_rep.section_tgamma_delta_ratio" title="tgamma_delta_ratio">tgamma_delta_ratio</a>
- </h2></div></div></div>
- <div class="table">
- <a name="special_function_error_rates_rep.section_tgamma_delta_ratio.table_tgamma_delta_ratio"></a><p class="title"><b>Table 91. Error rates for tgamma_delta_ratio</b></p>
- <div class="table-contents"><table class="table" summary="Error rates for tgamma_delta_ratio">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> double
- </p>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> long double
- </p>
- </th>
- <th>
- <p>
- Sun compiler version 0x5150<br> Sun Solaris<br> long double
- </p>
- </th>
- <th>
- <p>
- Microsoft Visual C++ version 14.1<br> Win32<br> double
- </p>
- </th>
- </tr></thead>
- <tbody>
- <tr>
- <td>
- <p>
- tgamma + small delta ratios
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 5.83ε (Mean = 1.3ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 15.4ε (Mean = 2.09ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 7.56ε (Mean = 1.31ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- tgamma + small delta ratios (negative delta)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 7.94ε (Mean = 1.4ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 18.3ε (Mean = 2.03ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 7.43ε (Mean = 1.42ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- tgamma + small integer ratios
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.96ε (Mean = 0.677ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.96ε (Mean = 0.677ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 2.74ε (Mean = 0.736ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- tgamma + small integer ratios (negative delta)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.62ε (Mean = 0.451ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.62ε (Mean = 0.451ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 2.15ε (Mean = 0.685ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- integer tgamma ratios
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.997ε (Mean = 0.4ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.997ε (Mean = 0.4ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.968ε (Mean = 0.386ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- integer tgamma ratios (negative delta)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.853ε (Mean = 0.176ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.853ε (Mean = 0.176ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.974ε (Mean = 0.175ε)</span>
- </p>
- </td>
- </tr>
- </tbody>
- </table></div>
- </div>
- <br class="table-break">
- </div>
- <div class="section">
- <div class="titlepage"><div><div><h2 class="title" style="clear: both">
- <a name="special_function_error_rates_rep.section_tgamma_incomplete_"></a><a class="link" href="index.html#special_function_error_rates_rep.section_tgamma_incomplete_" title="tgamma (incomplete)">tgamma
- (incomplete)</a>
- </h2></div></div></div>
- <div class="table">
- <a name="special_function_error_rates_rep.section_tgamma_incomplete_.table_tgamma_incomplete_"></a><p class="title"><b>Table 92. Error rates for tgamma (incomplete)</b></p>
- <div class="table-contents"><table class="table" summary="Error rates for tgamma (incomplete)">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> double
- </p>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> long double
- </p>
- </th>
- <th>
- <p>
- Sun compiler version 0x5150<br> Sun Solaris<br> long double
- </p>
- </th>
- <th>
- <p>
- Microsoft Visual C++ version 14.1<br> Win32<br> double
- </p>
- </th>
- </tr></thead>
- <tbody>
- <tr>
- <td>
- <p>
- tgamma(a, z) medium values
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 200ε (Mean = 13.3ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 8.47ε (Mean = 1.9ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 412ε (Mean = 95.5ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 8.14ε (Mean = 1.76ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- tgamma(a, z) small values
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.753ε (Mean = 0.0474ε)</span><br> <br>
- (<span class="emphasis"><em>GSL 2.1:</em></span> <span class="red">Max = 1.38e+10ε (Mean
- = 1.05e+09ε))</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 2.31ε (Mean = 0.775ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 2.13ε (Mean = 0.717ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 2.53ε (Mean = 0.66ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- tgamma(a, z) integer and half integer values
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 117ε (Mean = 12.5ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 5.52ε (Mean = 1.48ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 79.6ε (Mean = 20.9ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 5.16ε (Mean = 1.33ε)</span>
- </p>
- </td>
- </tr>
- </tbody>
- </table></div>
- </div>
- <br class="table-break">
- </div>
- <div class="section">
- <div class="titlepage"><div><div><h2 class="title" style="clear: both">
- <a name="special_function_error_rates_rep.section_tgamma_lower"></a><a class="link" href="index.html#special_function_error_rates_rep.section_tgamma_lower" title="tgamma_lower">tgamma_lower</a>
- </h2></div></div></div>
- <div class="table">
- <a name="special_function_error_rates_rep.section_tgamma_lower.table_tgamma_lower"></a><p class="title"><b>Table 93. Error rates for tgamma_lower</b></p>
- <div class="table-contents"><table class="table" summary="Error rates for tgamma_lower">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> double
- </p>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> long double
- </p>
- </th>
- <th>
- <p>
- Sun compiler version 0x5150<br> Sun Solaris<br> long double
- </p>
- </th>
- <th>
- <p>
- Microsoft Visual C++ version 14.1<br> Win32<br> double
- </p>
- </th>
- </tr></thead>
- <tbody>
- <tr>
- <td>
- <p>
- tgamma(a, z) medium values
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.833ε (Mean = 0.0315ε)</span><br> <br>
- (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 0.833ε (Mean = 0.0315ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 6.79ε (Mean = 1.46ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 363ε (Mean = 63.8ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 5.62ε (Mean = 1.49ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- tgamma(a, z) small values
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 0ε (Mean = 0ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.97ε (Mean = 0.555ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.97ε (Mean = 0.558ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.57ε (Mean = 0.525ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- tgamma(a, z) integer and half integer values
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 0ε (Mean = 0ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 4.83ε (Mean = 1.15ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 84.7ε (Mean = 17.5ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 2.69ε (Mean = 0.849ε)</span>
- </p>
- </td>
- </tr>
- </tbody>
- </table></div>
- </div>
- <br class="table-break">
- </div>
- <div class="section">
- <div class="titlepage"><div><div><h2 class="title" style="clear: both">
- <a name="special_function_error_rates_rep.section_tgamma_ratio"></a><a class="link" href="index.html#special_function_error_rates_rep.section_tgamma_ratio" title="tgamma_ratio">tgamma_ratio</a>
- </h2></div></div></div>
- <div class="table">
- <a name="special_function_error_rates_rep.section_tgamma_ratio.table_tgamma_ratio"></a><p class="title"><b>Table 94. Error rates for tgamma_ratio</b></p>
- <div class="table-contents"><table class="table" summary="Error rates for tgamma_ratio">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> double
- </p>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> long double
- </p>
- </th>
- <th>
- <p>
- Sun compiler version 0x5150<br> Sun Solaris<br> long double
- </p>
- </th>
- <th>
- <p>
- Microsoft Visual C++ version 14.1<br> Win32<br> double
- </p>
- </th>
- </tr></thead>
- <tbody><tr>
- <td>
- <p>
- tgamma ratios
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.694ε (Mean = 0.0347ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 2.99ε (Mean = 1.15ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 174ε (Mean = 61.2ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 3.28ε (Mean = 1.12ε)</span>
- </p>
- </td>
- </tr></tbody>
- </table></div>
- </div>
- <br class="table-break">
- </div>
- <div class="section">
- <div class="titlepage"><div><div><h2 class="title" style="clear: both">
- <a name="special_function_error_rates_rep.section_trigamma"></a><a class="link" href="index.html#special_function_error_rates_rep.section_trigamma" title="trigamma">trigamma</a>
- </h2></div></div></div>
- <div class="table">
- <a name="special_function_error_rates_rep.section_trigamma.table_trigamma"></a><p class="title"><b>Table 95. Error rates for trigamma</b></p>
- <div class="table-contents"><table class="table" summary="Error rates for trigamma">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> double
- </p>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> long double
- </p>
- </th>
- <th>
- <p>
- Sun compiler version 0x5150<br> Sun Solaris<br> long double
- </p>
- </th>
- <th>
- <p>
- Microsoft Visual C++ version 14.1<br> Win32<br> double
- </p>
- </th>
- </tr></thead>
- <tbody><tr>
- <td>
- <p>
- Mathematica Data
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.998ε (Mean = 0.105ε)</span><br> <br>
- (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 1.34e+04ε (Mean = 1.49e+03ε))<br>
- (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 1.34e+04ε (Mean = 1.51e+03ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.28ε (Mean = 0.449ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.28ε (Mean = 0.449ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1ε (Mean = 0.382ε)</span>
- </p>
- </td>
- </tr></tbody>
- </table></div>
- </div>
- <br class="table-break">
- </div>
- <div class="section">
- <div class="titlepage"><div><div><h2 class="title" style="clear: both">
- <a name="special_function_error_rates_rep.section_zeta"></a><a class="link" href="index.html#special_function_error_rates_rep.section_zeta" title="zeta">zeta</a>
- </h2></div></div></div>
- <div class="table">
- <a name="special_function_error_rates_rep.section_zeta.table_zeta"></a><p class="title"><b>Table 96. Error rates for zeta</b></p>
- <div class="table-contents"><table class="table" summary="Error rates for zeta">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> long double
- </p>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> double
- </p>
- </th>
- <th>
- <p>
- Sun compiler version 0x5150<br> Sun Solaris<br> long double
- </p>
- </th>
- <th>
- <p>
- Microsoft Visual C++ version 14.1<br> Win32<br> double
- </p>
- </th>
- </tr></thead>
- <tbody>
- <tr>
- <td>
- <p>
- Zeta: Random values greater than 1
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.846ε (Mean = 0.0833ε)</span><br> <br>
- (<span class="emphasis"><em><cmath>:</em></span> Max = 5.45ε (Mean = 1ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 8.69ε (Mean = 1.03ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.846ε (Mean = 0.0833ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.836ε (Mean = 0.093ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Zeta: Random values less than 1
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 7.03ε (Mean = 2.93ε)</span><br> <br>
- (<span class="emphasis"><em><cmath>:</em></span> Max = 538ε (Mean = 59.3ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 137ε (Mean = 13.8ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 70.1ε (Mean = 17.1ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 6.84ε (Mean = 3.12ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Zeta: Values close to and greater than 1
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.995ε (Mean = 0.5ε)</span><br> <br>
- (<span class="emphasis"><em><cmath>:</em></span> Max = 1.9e+06ε (Mean = 5.11e+05ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 7.73ε (Mean = 4.07ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.995ε (Mean = 0.5ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.994ε (Mean = 0.421ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Zeta: Values close to and less than 1
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.998ε (Mean = 0.508ε)</span><br> <br>
- (<span class="emphasis"><em><cmath>:</em></span> Max = 8.53e+06ε (Mean = 1.87e+06ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 0.991ε (Mean = 0.28ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.998ε (Mean = 0.508ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.991ε (Mean = 0.375ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Zeta: Integer arguments
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 9ε (Mean = 3.06ε)</span><br> <br> (<span class="emphasis"><em><cmath>:</em></span>
- Max = 70.3ε (Mean = 17.4ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 3.75ε (Mean = 1.1ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 28ε (Mean = 5.62ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 9ε (Mean = 3ε)</span>
- </p>
- </td>
- </tr>
- </tbody>
- </table></div>
- </div>
- <br class="table-break">
- </div>
- <div class="section">
- <div class="titlepage"><div><div><h2 class="title" style="clear: both">
- <a name="special_function_error_rates_rep.error_logs"></a><a class="link" href="index.html#special_function_error_rates_rep.error_logs" title="Error Logs">Error Logs</a>
- </h2></div></div></div>
- <h5>
- <a name="special_function_error_rates_rep.error_logs.h0"></a>
- <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_in"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_in">Error
- Output For cyl_bessel_j (integer orders) with compiler Microsoft Visual C++
- version 14.1 and library <math.h> and test data Bessel JN: Mathworld
- Data (Integer Version)</a>
- </h5>
- <p>
- <a name="errors_Microsoft_Visual_C_version_14_1_Win32_double_cyl_bessel_j_integer_orders___math_h__Bessel_JN_Mathworld_Data_Integer_Version_"></a>CAUTION:
- Found non-finite result, when a finite value was expected at entry 16<br>
- Found: -nan(ind) Expected 0 Error: 1.79769e+308<br> 10, 1e-100, 0<br> CAUTION:
- Gross error found at entry 16.<br> Found: -nan(ind) Expected 0 Error: 1.79769e+308<br>
- 10, 1e-100, 0<br>
- </p>
- <h5>
- <a name="special_function_error_rates_rep.error_logs.h1"></a>
- <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_legendre_p_asso"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_legendre_p_asso">Error
- Output For legendre_p (associated) with compiler GNU C++ version 7.1.0 and
- library GSL 2.1 and test data Associated Legendre Polynomials: Small Values</a>
- </h5>
- <p>
- <a name="errors_GNU_C_version_7_1_0_linux_double_legendre_p_associated__GSL_2_1_Associated_Legendre_Polynomials_Small_Values"></a>domain
- error<br> 3.75573, -3, 0.264719, 0.0186823<br> domain error<br> 3.75573,
- -3, 0.670017, 0.0085227<br> domain error<br> 3.75573, -3, 0.915014, 0.00136786<br>
- domain error<br> 3.75573, -3, 0.93539, 0.000921218<br> domain error<br>
- 3.75573, -2, -0.804919, -0.035427<br> domain error<br> 3.75573, -2, -0.623236,
- -0.0476446<br> domain error<br> 3.75573, -2, 0.629447, 0.0475072<br>
- domain error<br> 3.75573, -2, 0.929777, 0.0157498<br> domain error<br>
- 3.75573, -2, 0.985763, 0.0034837<br> domain error<br> 3.75573, -1, 0.093763,
- -0.118979<br> domain error<br> 4.28576, -4, 0.0944412, 0.00255792<br>
- domain error<br> 4.28576, -4, 0.670017, 0.000790849<br> domain error<br>
- 4.28576, -3, -0.746026, -0.00458957<br> domain error<br> 4.28576, -2, -0.623236,
- 0.0219016<br> domain error<br> 4.28576, -2, 0.629447, 0.0223081<br> domain
- error<br> 4.28576, -2, 0.93539, 0.0133504<br> domain error<br> 4.28576,
- -1, 0.915014, 0.132001<br> domain error<br> 4.28576, -1, 0.985763, 0.0787743<br>
- domain error<br> 4.43859, -4, 0.093763, 0.00255858<br> domain error<br>
- 4.43859, -4, 0.811584, 0.000303404<br> domain error<br> 4.43859, -4, 0.826752,
- 0.000260835<br> domain error<br> 4.43859, -4, 0.929777, 4.78235e-05<br>
- domain error<br> 4.43859, -3, -0.804919, -0.00350364<br> domain error<br>
- 4.43859, -3, -0.729046, -0.00487043<br> domain error<br> 4.43859, -3, -0.623236,
- -0.00620995<br> domain error<br> 4.43859, -3, 0.93539, 0.000861698<br>
- domain error<br> 4.43859, -2, -0.557932, 0.0169167<br> domain error<br>
- 4.43859, -2, -0.443004, 0.0062586<br> domain error<br> 4.43859, -2, 0.915014,
- 0.016481<br> domain error<br> 4.43859, -1, 0.629447, -0.0138523<br> domain
- error<br> 5.39088, -5, 0.0944412, 0.000254649<br> domain error<br> 5.39088,
- -5, 0.264719, 0.000217164<br> domain error<br> 5.39088, -5, 0.670017, 5.87083e-05<br>
- domain error<br> 5.39088, -5, 0.915014, 2.78273e-06<br> domain error<br>
- 5.39088, -3, 0.929777, 0.000880849<br> domain error<br> 5.39088, -2, 0.629447,
- 0.00448021<br> domain error<br> 5.39088, -2, 0.826752, 0.01718<br> domain
- error<br> 5.39088, -2, 0.937736, 0.011583<br> domain error<br> 5.39088,
- -1, -0.804919, 0.0276144<br> domain error<br> 5.39088, -1, -0.746026, -0.0119425<br>
- domain error<br> 5.39088, -1, -0.443004, -0.0525987<br> domain error<br>
- 5.39088, -1, 0.811584, 0.032475<br> domain error<br> 5.39088, -1, 0.985763,
- 0.0759289<br> domain error<br> 5.97861, -5, -0.729046, 3.91223e-05<br>
- domain error<br> 5.97861, -5, -0.383666, 0.000174899<br> domain error<br>
- 5.97861, -5, 0.93539, 1.43993e-06<br> domain error<br> 5.97861, -4, -0.623236,
- -0.000607048<br> domain error<br> 5.97861, -4, 0.264719, 0.00059614<br>
- domain error<br> 5.97861, -3, 0.629447, 0.00313497<br> domain error<br>
- 5.97861, -3, 0.670017, 0.00323895<br> domain error<br> 5.97861, -2, 0.915014,
- 0.0140705<br> domain error<br> 5.97861, -2, 0.992923, 0.00171356<br>
- domain error<br> 5.97861, -1, -0.746026, -0.0119425<br> domain error<br>
- 5.97861, -1, 0.937736, 0.106972<br> domain error<br> 7.01297, -6, -0.443004,
- -4.99177e-06<br> domain error<br> 7.01297, -6, 0.629447, 3.00689e-06<br>
- domain error<br> 7.01297, -6, 0.811584, 7.00407e-07<br> domain error<br>
- 7.01297, -6, 0.985763, 4.83431e-10<br> domain error<br> 7.01297, -3, 0.670017,
- 0.000233323<br> domain error<br> 7.01297, -2, -0.804919, -0.0027739<br>
- domain error<br> 7.01297, -1, -0.383666, 0.0397866<br> domain error<br>
- 7.01297, -1, 0.929777, 0.0544549<br> domain error<br> 7.54701, -7, 0.929777,
- 1.42008e-09<br> domain error<br> 7.54701, -6, 0.992923, 6.04622e-11<br>
- domain error<br> 7.54701, -5, -0.804919, 1.18502e-05<br> domain error<br>
- 7.54701, -5, -0.623236, 2.57049e-05<br> domain error<br> 7.54701, -5, -0.557932,
- 2.60266e-05<br> domain error<br> 7.54701, -5, 0.826752, 9.64276e-06<br>
- domain error<br> 7.54701, -4, -0.746026, -0.0001618<br> domain error<br>
- 7.54701, -3, 0.0944412, 0.000622493<br> domain error<br> 7.54701, -3, 0.985763,
- 9.14782e-05<br> domain error<br> 7.54701, -1, 0.811584, -0.0376184<br>
- domain error<br> 11.8439, -10, -0.557932, -2.32652e-11<br> domain error<br>
- 11.8439, -10, 0.811584, 1.01194e-12<br> domain error<br> 11.8439, -8, -0.746026,
- -1.34891e-09<br> domain error<br> 11.8439, -8, -0.729046, -1.5428e-09<br>
- domain error<br> 11.8439, -8, 0.985763, 5.90035e-14<br> domain error<br>
- 11.8439, -4, 0.629447, -1.44723e-05<br> domain error<br> 11.8439, -4, 0.929777,
- 1.98812e-05<br> domain error<br> 11.8439, -3, 0.670017, -4.58296e-05<br>
- domain error<br> 11.8439, -2, 0.826752, -0.00244759<br> domain error<br>
- 11.8439, -2, 0.992923, 0.00151458<br> domain error<br> 11.8439, -1, -0.383666,
- 0.00419108<br> domain error<br> 11.85, -11, 0.093763, 1.16526e-11<br>
- domain error<br> 11.85, -11, 0.929777, 2.05797e-16<br> domain error<br>
- 11.85, -11, 0.93539, 1.32249e-16<br> domain error<br> *** FURTHER CONTENT
- HAS BEEN TRUNCATED FOR BREVITY ***<br>
- </p>
- <h5>
- <a name="special_function_error_rates_rep.error_logs.h2"></a>
- <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_legendre_p_ass0"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_legendre_p_ass0">Error
- Output For legendre_p (associated) with compiler GNU C++ version 7.1.0 and
- library <cmath> and test data Associated Legendre Polynomials: Small
- Values</a>
- </h5>
- <p>
- <a name="errors_GNU_C_version_7_1_0_linux_long_double_legendre_p_associated___cmath__Associated_Legendre_Polynomials_Small_Values"></a>order
- parameters less than 0 not supported in TR1<br> 3.75573, -3, 0.264719, 0.0186823<br>
- order parameters less than 0 not supported in TR1<br> 3.75573, -3, 0.670017,
- 0.0085227<br> order parameters less than 0 not supported in TR1<br> 3.75573,
- -3, 0.915014, 0.00136786<br> order parameters less than 0 not supported in
- TR1<br> 3.75573, -3, 0.93539, 0.000921218<br> order parameters less than
- 0 not supported in TR1<br> 3.75573, -2, -0.804919, -0.035427<br> order
- parameters less than 0 not supported in TR1<br> 3.75573, -2, -0.623236, -0.0476446<br>
- order parameters less than 0 not supported in TR1<br> 3.75573, -2, 0.629447,
- 0.0475072<br> order parameters less than 0 not supported in TR1<br> 3.75573,
- -2, 0.929777, 0.0157498<br> order parameters less than 0 not supported in
- TR1<br> 3.75573, -2, 0.985763, 0.0034837<br> order parameters less than
- 0 not supported in TR1<br> 3.75573, -1, 0.093763, -0.118979<br> order parameters
- less than 0 not supported in TR1<br> 4.28576, -4, 0.0944412, 0.00255792<br>
- order parameters less than 0 not supported in TR1<br> 4.28576, -4, 0.670017,
- 0.000790849<br> order parameters less than 0 not supported in TR1<br> 4.28576,
- -3, -0.746026, -0.00458957<br> order parameters less than 0 not supported
- in TR1<br> 4.28576, -2, -0.623236, 0.0219016<br> order parameters less
- than 0 not supported in TR1<br> 4.28576, -2, 0.629447, 0.0223081<br> order
- parameters less than 0 not supported in TR1<br> 4.28576, -2, 0.93539, 0.0133504<br>
- order parameters less than 0 not supported in TR1<br> 4.28576, -1, 0.915014,
- 0.132001<br> order parameters less than 0 not supported in TR1<br> 4.28576,
- -1, 0.985763, 0.0787743<br> order parameters less than 0 not supported in
- TR1<br> 4.43859, -4, 0.093763, 0.00255858<br> order parameters less than
- 0 not supported in TR1<br> 4.43859, -4, 0.811584, 0.000303404<br> order
- parameters less than 0 not supported in TR1<br> 4.43859, -4, 0.826752, 0.000260835<br>
- order parameters less than 0 not supported in TR1<br> 4.43859, -4, 0.929777,
- 4.78235e-05<br> order parameters less than 0 not supported in TR1<br> 4.43859,
- -3, -0.804919, -0.00350364<br> order parameters less than 0 not supported
- in TR1<br> 4.43859, -3, -0.729046, -0.00487043<br> order parameters less
- than 0 not supported in TR1<br> 4.43859, -3, -0.623236, -0.00620995<br>
- order parameters less than 0 not supported in TR1<br> 4.43859, -3, 0.93539,
- 0.000861698<br> order parameters less than 0 not supported in TR1<br> 4.43859,
- -2, -0.557932, 0.0169167<br> order parameters less than 0 not supported in
- TR1<br> 4.43859, -2, -0.443004, 0.0062586<br> order parameters less than
- 0 not supported in TR1<br> 4.43859, -2, 0.915014, 0.016481<br> order parameters
- less than 0 not supported in TR1<br> 4.43859, -1, 0.629447, -0.0138523<br>
- order parameters less than 0 not supported in TR1<br> 5.39088, -5, 0.0944412,
- 0.000254649<br> order parameters less than 0 not supported in TR1<br> 5.39088,
- -5, 0.264719, 0.000217164<br> order parameters less than 0 not supported
- in TR1<br> 5.39088, -5, 0.670017, 5.87083e-05<br> order parameters less
- than 0 not supported in TR1<br> 5.39088, -5, 0.915014, 2.78273e-06<br>
- order parameters less than 0 not supported in TR1<br> 5.39088, -3, 0.929777,
- 0.000880849<br> order parameters less than 0 not supported in TR1<br> 5.39088,
- -2, 0.629447, 0.00448021<br> order parameters less than 0 not supported in
- TR1<br> 5.39088, -2, 0.826752, 0.01718<br> order parameters less than 0
- not supported in TR1<br> 5.39088, -2, 0.937736, 0.011583<br> order parameters
- less than 0 not supported in TR1<br> 5.39088, -1, -0.804919, 0.0276144<br>
- order parameters less than 0 not supported in TR1<br> 5.39088, -1, -0.746026,
- -0.0119425<br> order parameters less than 0 not supported in TR1<br> 5.39088,
- -1, -0.443004, -0.0525987<br> order parameters less than 0 not supported
- in TR1<br> 5.39088, -1, 0.811584, 0.032475<br> order parameters less than
- 0 not supported in TR1<br> 5.39088, -1, 0.985763, 0.0759289<br> order parameters
- less than 0 not supported in TR1<br> 5.97861, -5, -0.729046, 3.91223e-05<br>
- order parameters less than 0 not supported in TR1<br> 5.97861, -5, -0.383666,
- 0.000174899<br> order parameters less than 0 not supported in TR1<br> 5.97861,
- -5, 0.93539, 1.43993e-06<br> order parameters less than 0 not supported in
- TR1<br> 5.97861, -4, -0.623236, -0.000607048<br> order parameters less
- than 0 not supported in TR1<br> 5.97861, -4, 0.264719, 0.00059614<br> order
- parameters less than 0 not supported in TR1<br> 5.97861, -3, 0.629447, 0.00313497<br>
- *** FURTHER CONTENT HAS BEEN TRUNCATED FOR BREVITY ***<br>
- </p>
- <h5>
- <a name="special_function_error_rates_rep.error_logs.h3"></a>
- <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_wi"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_wi">Error
- Output For cyl_bessel_i with compiler GNU C++ version 7.1.0 and library Rmath
- 3.2.3 and test data Bessel Iv: Mathworld Data (large values)</a>
- </h5>
- <p>
- <a name="errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_Rmath_3_2_3_Bessel_Iv_Mathworld_Data_large_values_"></a>CAUTION:
- Gross error found at entry 0.<br> Found: 0 Expected 1.86459e-155 Error: 8.37988e+152<br>
- -1, 3.72917e-155, 1.86459e-155<br> CAUTION: Gross error found at entry 1.<br>
- Found: 0 Expected 1.86459e-155 Error: 8.37988e+152<br> 1, 3.72917e-155, 1.86459e-155<br>
- CAUTION: Gross error found at entry 3.<br> Found: 0 Expected 8.02269e-175
- Error: 3.60559e+133<br> 1.125, 3.72917e-155, 8.02269e-175<br>
- </p>
- <h5>
- <a name="special_function_error_rates_rep.error_logs.h4"></a>
- <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_in"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_in">Error
- Output For cyl_bessel_i (integer orders) with compiler GNU C++ version 7.1.0
- and library Rmath 3.2.3 and test data Bessel In: Mathworld Data (Integer Version)</a>
- </h5>
- <p>
- <a name="errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_integer_orders__Rmath_3_2_3_Bessel_In_Mathworld_Data_Integer_Version_"></a>Unsupported
- domain<br> -5, -1, -0.000271463<br> Unsupported domain<br> 10, -5, 0.00458004<br>
- Unsupported domain<br> -100, -200, 4.35275e+74<br>
- </p>
- <h5>
- <a name="special_function_error_rates_rep.error_logs.h5"></a>
- <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_i0"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_i0">Error
- Output For cyl_bessel_i (integer orders) with compiler GNU C++ version 7.1.0
- and library Rmath 3.2.3 and test data Bessel I1: Mathworld Data (Integer Version)</a>
- </h5>
- <p>
- <a name="errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_integer_orders__Rmath_3_2_3_Bessel_I1_Mathworld_Data_Integer_Version_"></a>Unsupported
- domain<br> 1, -2, -1.59064<br> Unsupported domain<br> 1, -8, -399.873<br>
- Unsupported domain<br> 1, -10, -2670.99<br>
- </p>
- <h5>
- <a name="special_function_error_rates_rep.error_logs.h6"></a>
- <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_i1"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_i1">Error
- Output For cyl_bessel_i (integer orders) with compiler GNU C++ version 7.1.0
- and library Rmath 3.2.3 and test data Bessel I0: Mathworld Data (Integer Version)</a>
- </h5>
- <p>
- <a name="errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_integer_orders__Rmath_3_2_3_Bessel_I0_Mathworld_Data_Integer_Version_"></a>Unsupported
- domain<br> 0, -2, 2.27959<br> Unsupported domain<br> 0, -7, 168.594<br>
- Unsupported domain<br> 0, -1, 1.26607<br>
- </p>
- <h5>
- <a name="special_function_error_rates_rep.error_logs.h7"></a>
- <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_w0"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_w0">Error
- Output For cyl_bessel_i with compiler GNU C++ version 7.1.0 and library Rmath
- 3.2.3 and test data Bessel In: Mathworld Data</a>
- </h5>
- <p>
- <a name="errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_Rmath_3_2_3_Bessel_In_Mathworld_Data"></a>Unsupported
- domain<br> -5, -1, -0.000271463<br> Unsupported domain<br> 10, -5, 0.00458004<br>
- Unsupported domain<br> -100, -200, 4.35275e+74<br>
- </p>
- <h5>
- <a name="special_function_error_rates_rep.error_logs.h8"></a>
- <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_w1"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_w1">Error
- Output For cyl_bessel_i with compiler GNU C++ version 7.1.0 and library Rmath
- 3.2.3 and test data Bessel I1: Mathworld Data</a>
- </h5>
- <p>
- <a name="errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_Rmath_3_2_3_Bessel_I1_Mathworld_Data"></a>Unsupported
- domain<br> 1, -2, -1.59064<br> Unsupported domain<br> 1, -8, -399.873<br>
- Unsupported domain<br> 1, -10, -2670.99<br>
- </p>
- <h5>
- <a name="special_function_error_rates_rep.error_logs.h9"></a>
- <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_w2"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_w2">Error
- Output For cyl_bessel_i with compiler GNU C++ version 7.1.0 and library Rmath
- 3.2.3 and test data Bessel I0: Mathworld Data</a>
- </h5>
- <p>
- <a name="errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_Rmath_3_2_3_Bessel_I0_Mathworld_Data"></a>Unsupported
- domain<br> 0, -2, 2.27959<br> Unsupported domain<br> 0, -7, 168.594<br>
- Unsupported domain<br> 0, -1, 1.26607<br>
- </p>
- <h5>
- <a name="special_function_error_rates_rep.error_logs.h10"></a>
- <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_wi"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_wi">Error
- Output For cyl_bessel_j with compiler GNU C++ version 7.1.0 and library Rmath
- 3.2.3 and test data Bessel J: Mathworld Data</a>
- </h5>
- <p>
- <a name="errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_Rmath_3_2_3_Bessel_J_Mathworld_Data"></a>CAUTION:
- Gross error found at entry 6.<br> Found: 0 Expected -0.000747424 Error: 3.3591e+304<br>
- 5.5, 1e+06, -0.000747424<br> CAUTION: Gross error found at entry 7.<br>
- Found: 0 Expected -0.0007766 Error: 3.49022e+304<br> 5.125, 1e+06, -0.0007766<br>
- CAUTION: Gross error found at entry 8.<br> Found: 0 Expected -0.000466323
- Error: 2.09576e+304<br> 5.875, 1e+06, -0.000466323<br>
- </p>
- <h5>
- <a name="special_function_error_rates_rep.error_logs.h11"></a>
- <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_i0"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_i0">Error
- Output For cyl_bessel_j (integer orders) with compiler GNU C++ version 7.1.0
- and library Rmath 3.2.3 and test data Bessel JN: Mathworld Data (Integer Version)</a>
- </h5>
- <p>
- <a name="errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_integer_orders__Rmath_3_2_3_Bessel_JN_Mathworld_Data_Integer_Version_"></a>Unsupported
- domain<br> 5, -10, 0.234062<br> CAUTION: Gross error found at entry 6.<br>
- Found: 0 Expected 0.000725964 Error: 3.26265e+304<br> -5, 1e+06, 0.000725964<br>
- CAUTION: Gross error found at entry 7.<br> Found: 0 Expected -0.000725964
- Error: 3.26265e+304<br> 5, 1e+06, -0.000725964<br> Unsupported domain<br>
- -5, -1, 0.000249758<br> Unsupported domain<br> 10, -10, 0.207486<br>
- Unsupported domain<br> 10, -5, 0.0014678<br> CAUTION: Gross error found
- at entry 12.<br> Found: 0 Expected -0.000331079 Error: 1.48795e+304<br>
- -10, 1e+06, -0.000331079<br> CAUTION: Gross error found at entry 13.<br>
- Found: 0 Expected -0.000331079 Error: 1.48795e+304<br> 10, 1e+06, -0.000331079<br>
- </p>
- <h5>
- <a name="special_function_error_rates_rep.error_logs.h12"></a>
- <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_i1"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_i1">Error
- Output For cyl_bessel_j (integer orders) with compiler GNU C++ version 7.1.0
- and library Rmath 3.2.3 and test data Bessel J1: Mathworld Data (Integer Version)</a>
- </h5>
- <p>
- <a name="errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_integer_orders__Rmath_3_2_3_Bessel_J1_Mathworld_Data_Integer_Version_"></a>Unsupported
- domain<br> 1, -2, -0.576725<br> Unsupported domain<br> 1, -8, -0.234636<br>
- Unsupported domain<br> 1, -10, -0.0434727<br>
- </p>
- <h5>
- <a name="special_function_error_rates_rep.error_logs.h13"></a>
- <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_i2"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_i2">Error
- Output For cyl_bessel_j (integer orders) with compiler GNU C++ version 7.1.0
- and library Rmath 3.2.3 and test data Bessel J0: Mathworld Data (Integer Version)</a>
- </h5>
- <p>
- <a name="errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_integer_orders__Rmath_3_2_3_Bessel_J0_Mathworld_Data_Integer_Version_"></a>Unsupported
- domain<br> 0, -2, 0.223891<br> Unsupported domain<br> 0, -8, 0.171651<br>
- Unsupported domain<br> 0, -10, -0.245936<br>
- </p>
- <h5>
- <a name="special_function_error_rates_rep.error_logs.h14"></a>
- <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_w0"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_w0">Error
- Output For cyl_bessel_j with compiler GNU C++ version 7.1.0 and library Rmath
- 3.2.3 and test data Bessel JN: Mathworld Data</a>
- </h5>
- <p>
- <a name="errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_Rmath_3_2_3_Bessel_JN_Mathworld_Data"></a>Unsupported
- domain<br> 5, -10, 0.234062<br> CAUTION: Gross error found at entry 6.<br>
- Found: 0 Expected 0.000725964 Error: 3.26265e+304<br> -5, 1e+06, 0.000725964<br>
- CAUTION: Gross error found at entry 7.<br> Found: 0 Expected -0.000725964
- Error: 3.26265e+304<br> 5, 1e+06, -0.000725964<br> Unsupported domain<br>
- -5, -1, 0.000249758<br> Unsupported domain<br> 10, -10, 0.207486<br>
- Unsupported domain<br> 10, -5, 0.0014678<br> CAUTION: Gross error found
- at entry 12.<br> Found: 0 Expected -0.000331079 Error: 1.48795e+304<br>
- -10, 1e+06, -0.000331079<br> CAUTION: Gross error found at entry 13.<br>
- Found: 0 Expected -0.000331079 Error: 1.48795e+304<br> 10, 1e+06, -0.000331079<br>
- </p>
- <h5>
- <a name="special_function_error_rates_rep.error_logs.h15"></a>
- <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_w1"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_w1">Error
- Output For cyl_bessel_j with compiler GNU C++ version 7.1.0 and library Rmath
- 3.2.3 and test data Bessel J1: Mathworld Data</a>
- </h5>
- <p>
- <a name="errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_Rmath_3_2_3_Bessel_J1_Mathworld_Data"></a>Unsupported
- domain<br> 1, -2, -0.576725<br> Unsupported domain<br> 1, -8, -0.234636<br>
- Unsupported domain<br> 1, -10, -0.0434727<br>
- </p>
- <h5>
- <a name="special_function_error_rates_rep.error_logs.h16"></a>
- <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_w2"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_w2">Error
- Output For cyl_bessel_j with compiler GNU C++ version 7.1.0 and library Rmath
- 3.2.3 and test data Bessel J0: Mathworld Data</a>
- </h5>
- <p>
- <a name="errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_Rmath_3_2_3_Bessel_J0_Mathworld_Data"></a>Unsupported
- domain<br> 0, -2, 0.223891<br> Unsupported domain<br> 0, -8, 0.171651<br>
- Unsupported domain<br> 0, -10, -0.245936<br>
- </p>
- <h5>
- <a name="special_function_error_rates_rep.error_logs.h17"></a>
- <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_ibetac_inv_with"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_ibetac_inv_with">Error
- Output For ibetac_inv with compiler GNU C++ version 7.1.0 and library Rmath
- 3.2.3 and test data Inverse incomplete beta</a>
- </h5>
- <p>
- <a name="errors_GNU_C_version_7_1_0_linux_double_ibetac_inv_Rmath_3_2_3_Inverse_incomplete_beta"></a>CAUTION:
- Gross error found at entry 7.<br> Found: 3.8247e-302 Expected 0 Error: 1.71891e+06<br>
- 1.38853e-05, 0.0497627, 0.632396, 0, 0<br> CAUTION: Gross error found at
- entry 71.<br> Found: 1.38362e-204 Expected 0 Error: 6.21832e+103<br> 3.77931e-05,
- 0.0150073, 0.835025, 0, 0<br> CAUTION: Gross error found at entry 90.<br>
- Found: 1.09275e-303 Expected 0 Error: 49109.6<br> 4.29383e-05, 0.0428761,
- 0.814742, 0, 0<br> CAUTION: Gross error found at entry 102.<br> Found:
- 3.8625e-304 Expected 0 Error: 17358<br> 4.80089e-05, 0.0296236, 0.913384,
- 0, 0<br> CAUTION: Gross error found at entry 115.<br> Found: 1.51774e-303
- Expected 0 Error: 68209.8<br> 0.000130387, 0.0404969, 0.814742, 0, 0<br>
- CAUTION: Gross error found at entry 123.<br> Found: 1.28036e-303 Expected
- 0 Error: 57541.4<br> 0.000149328, 0.0201182, 0.905801, 5.70765e-267, 0<br>
- CAUTION: Gross error found at entry 133.<br> Found: 1.96732e-302 Expected
- 0 Error: 884160<br> 0.000173563, 0.0301908, 0.913384, 4.21662e-213, 0<br>
- CAUTION: Gross error found at entry 159.<br> Found: 1.48697e-191 Expected
- 0 Error: 6.68279e+116<br> 0.000260723, 0.0252933, 0.632396, 0, 0<br> CAUTION:
- Gross error found at entry 256.<br> Found: 9.24166e-245 Expected 0 Error:
- 4.15342e+63<br> 0.00246975, 0.016063, 0.913384, 1, 0<br>
- </p>
- <h5>
- <a name="special_function_error_rates_rep.error_logs.h18"></a>
- <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_ibeta_inv_with_"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_ibeta_inv_with_">Error
- Output For ibeta_inv with compiler GNU C++ version 7.1.0 and library Rmath
- 3.2.3 and test data Inverse incomplete beta</a>
- </h5>
- <p>
- <a name="errors_GNU_C_version_7_1_0_linux_double_ibeta_inv_Rmath_3_2_3_Inverse_incomplete_beta"></a>CAUTION:
- Gross error found at entry 1.<br> Found: 1.90197e-247 Expected 0 Error: 8.54789e+60<br>
- 1.12733e-05, 0.022662, 0.135563, 0, 0<br> CAUTION: Gross error found at entry
- 30.<br> Found: 1.36217e-301 Expected 0 Error: 6.12191e+06<br> 2.10769e-05,
- 0.0448972, 0.221112, 0, 0<br> CAUTION: Gross error found at entry 152.<br>
- Found: 2.92621e-285 Expected 0 Error: 1.31511e+23<br> 0.000240381, 0.017982,
- 0.221112, 0, 0<br> CAUTION: Gross error found at entry 184.<br> Found:
- 5.63355e-203 Expected 0 Error: 2.53185e+105<br> 0.000348822, 0.0275467, 0.135563,
- 0, 1.88165e-166<br> CAUTION: Gross error found at entry 205.<br> Found:
- 5.52731e-303 Expected 0 Error: 248409<br> 0.000441212, 0.0313573, 0.127074,
- 0, 9.07221e-121<br>
- </p>
- <h5>
- <a name="special_function_error_rates_rep.error_logs.h19"></a>
- <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_non_central_bet"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_non_central_bet">Error
- Output For non central beta CDF complement with compiler GNU C++ version 7.1.0
- and library Rmath 3.2.3 and test data Non Central Beta, large parameters</a>
- </h5>
- <p>
- <a name="errors_GNU_C_version_7_1_0_linux_double_non_central_beta_CDF_complement_Rmath_3_2_3_Non_Central_Beta_large_parameters"></a>CAUTION:
- Gross error found at entry 10.<br> Found: 9.76918e-10 Expected 1.61248e-15
- Error: 605846<br> 290.682, 72.6705, 20005.4, 0.997663, 1, 1.61248e-15<br>
- CAUTION: Gross error found at entry 11.<br> Found: 9.94184e-10 Expected 3.0108e-42
- Error: 3.30205e+32<br> 290.682, 145.341, 53489.1, 0.998663, 1, 3.0108e-42<br>
- CAUTION: Gross error found at entry 16.<br> Found: 8.45406e-10 Expected 4.46652e-22
- Error: 1.89276e+12<br> 290.682, 1162.73, 2308.07, 0.656921, 1, 4.46652e-22<br>
- CAUTION: Gross error found at entry 17.<br> Found: 9.41971e-10 Expected 1.7241e-50
- Error: 5.46356e+40<br> 290.682, 1453.41, 8064.48, 0.832237, 1, 1.7241e-50<br>
- CAUTION: Gross error found at entry 18.<br> Found: 9.30663e-10 Expected 2.09803e-305
- Error: 4.43589e+295<br> 975.766, 731.824, 232.285, 0.919742, 1, 2.09803e-305<br>
- CAUTION: Gross error found at entry 27.<br> Found: 9.76918e-10 Expected 9.3474e-18
- Error: 1.04512e+08<br> 1879.05, 187.905, 20005.4, 0.992215, 1, 9.3474e-18<br>
- CAUTION: Gross error found at entry 28.<br> Found: 9.94184e-10 Expected 1.8122e-90
- Error: 5.48607e+80<br> 1879.05, 469.762, 53489.1, 0.994618, 1, 1.8122e-90<br>
- CAUTION: Gross error found at entry 32.<br> Found: 9.27224e-10 Expected 3.18255e-15
- Error: 291345<br> 1879.05, 3758.1, 1879.05, 0.480508, 1, 3.18255e-15<br>
- CAUTION: Gross error found at entry 33.<br> Found: 8.45406e-10 Expected 1.10218e-77
- Error: 7.67029e+67<br> 1879.05, 5637.15, 2308.07, 0.458181, 1, 1.10218e-77<br>
- CAUTION: Gross error found at entry 34.<br> Found: 9.30663e-10 Expected 0
- Error: 4.18262e+298<br> 2308.07, 1154.03, 232.285, 0.919371, 1, 0<br> CAUTION:
- Gross error found at entry 35.<br> Found: 8.93617e-10 Expected 0 Error: 4.01612e+298<br>
- 2308.07, 1731.05, 290.682, 0.917262, 1, 0<br> CAUTION: Gross error found
- at entry 43.<br> Found: 9.94184e-10 Expected 3.57283e-70 Error: 2.78262e+60<br>
- 8064.48, 806.448, 53489.1, 0.988678, 1, 3.57283e-70<br> CAUTION: Gross error
- found at entry 48.<br> Found: 8.45406e-10 Expected 8.78057e-74 Error: 9.62814e+63<br>
- 8064.48, 16129, 2308.07, 0.421531, 1, 8.78057e-74<br> CAUTION: Gross error
- found at entry 49.<br> Found: 9.30663e-10 Expected 0 Error: 4.18262e+298<br>
- 15674.4, 3918.59, 232.285, 0.933726, 1, 0<br> CAUTION: Gross error found
- at entry 50.<br> Found: 8.93617e-10 Expected 0 Error: 4.01612e+298<br>
- 15674.4, 7837.19, 290.682, 0.917179, 1, 0<br> CAUTION: Gross error found
- at entry 51.<br> Found: 8.9318e-10 Expected 0 Error: 4.01416e+298<br> 15674.4,
- 11755.8, 975.766, 0.915784, 1, 0<br> CAUTION: Gross error found at entry
- 63.<br> Found: 9.41971e-10 Expected 2.31296e-171 Error: 4.07258e+161<br>
- 20005.4, 40010.8, 8064.48, 0.432094, 1, 2.31296e-171<br> CAUTION: Gross error
- found at entry 64.<br> Found: 9.30663e-10 Expected 0 Error: 4.18262e+298<br>
- 53489.1, 5348.92, 232.285, 0.954635, 1, 0<br> CAUTION: Gross error found
- at entry 65.<br> Found: 8.93617e-10 Expected 0 Error: 4.01612e+298<br>
- 53489.1, 13372.3, 290.682, 0.933478, 1, 0<br> CAUTION: Gross error found
- at entry 66.<br> Found: 8.9318e-10 Expected 0 Error: 4.01416e+298<br> 53489.1,
- 26744.6, 975.766, 0.91717, 1, 0<br>
- </p>
- <h5>
- <a name="special_function_error_rates_rep.error_logs.h20"></a>
- <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_non_central_be0"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_non_central_be0">Error
- Output For non central beta CDF with compiler GNU C++ version 7.1.0 and library
- Rmath 3.2.3 and test data Non Central Beta, large parameters</a>
- </h5>
- <p>
- <a name="errors_GNU_C_version_7_1_0_linux_double_non_central_beta_CDF_Rmath_3_2_3_Non_Central_Beta_large_parameters"></a>CAUTION:
- Gross error found at entry 0.<br> Found: 9.1136e-209 Expected 5.82279e-200
- Error: 6.38913e+08<br> 232.285, 209.056, 232.285, 0.062486, 5.82279e-200,
- 1<br> CAUTION: Gross error found at entry 1.<br> Found: 4.08108e-115 Expected
- 2.37643e-112 Error: 581.304<br> 232.285, 229.962, 290.682, 0.155342, 2.37643e-112,
- 1<br> CAUTION: Gross error found at entry 2.<br> Found: 1.07549e-93 Expected
- 9.53431e-89 Error: 88650<br> 232.285, 232.052, 975.766, 0.378086, 9.53431e-89,
- 1<br> CAUTION: Gross error found at entry 3.<br> Found: 2.58402e-54 Expected
- 8.27353e-53 Error: 31.0181<br> 232.285, 232.285, 1879.05, 0.625865, 8.27353e-53,
- 1<br> CAUTION: Gross error found at entry 4.<br> Found: 1.93718e-19 Expected
- 6.64275e-16 Error: 3428.08<br> 232.285, 232.308, 2308.07, 0.770774, 6.64275e-16,
- 1<br> CAUTION: Gross error found at entry 21.<br> Found: 8.12962e-240 Expected
- 1.82294e-219 Error: 2.24234e+20<br> 975.766, 974.79, 1879.05, 0.331337, 1.82294e-219,
- 1<br> CAUTION: Gross error found at entry 22.<br> Found: 3.47274e-69 Expected
- 1.42183e-67 Error: 39.9426<br> 975.766, 975.766, 2308.07, 0.514323, 1.42183e-67,
- 1<br> CAUTION: Gross error found at entry 23.<br> Found: 5.86885e-50 Expected
- 1.27896e-47 Error: 216.923<br> 975.766, 975.863, 8064.48, 0.753209, 1.27896e-47,
- 1<br> CAUTION: Gross error found at entry 39.<br> Found: 4.82785e-230 Expected
- 1.25446e-213 Error: 2.59838e+16<br> 2308.07, 2308.07, 8064.48, 0.54983, 1.25446e-213,
- 1<br> CAUTION: Gross error found at entry 40.<br> Found: 1.22971e-87 Expected
- 1.82618e-85 Error: 147.505<br> 2308.07, 2308.3, 15674.4, 0.733174, 1.82618e-85,
- 1<br> CAUTION: Gross error found at entry 56.<br> Found: 2.97337e-127 Expected
- 2.56068e-124 Error: 860.205<br> 15674.4, 15675.9, 20005.4, 0.55883, 2.56068e-124,
- 1<br>
- </p>
- <h5>
- <a name="special_function_error_rates_rep.error_logs.h21"></a>
- <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_non_central_be1"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_non_central_be1">Error
- Output For non central beta CDF complement with compiler GNU C++ version 7.1.0
- and library Rmath 3.2.3 and test data Non Central Beta, medium parameters</a>
- </h5>
- <p>
- <a name="errors_GNU_C_version_7_1_0_linux_double_non_central_beta_CDF_complement_Rmath_3_2_3_Non_Central_Beta_medium_parameters"></a>CAUTION:
- Gross error found at entry 296.<br> Found: 9.44166e-10 Expected 6.22975e-10
- Error: 0.515577<br> 22.9367, 114.683, 19.5081, 0.480981, 1, 6.22975e-10<br>
- CAUTION: Gross error found at entry 369.<br> Found: 2.52234e-10 Expected
- 1.40246e-10 Error: 0.79851<br> 27.5277, 20.6457, 0.956697, 0.915111, 1, 1.40246e-10<br>
- CAUTION: Gross error found at entry 429.<br> Found: 1.18105e-09 Expected
- 7.45745e-10 Error: 0.58372<br> 28.8063, 21.6047, 60.3826, 0.946143, 1, 7.45745e-10<br>
- CAUTION: Gross error found at entry 430.<br> Found: 2.44435e-09 Expected
- 1.60695e-09 Error: 0.521115<br> 28.8063, 21.6047, 148.129, 0.965121, 1, 1.60695e-09<br>
- CAUTION: Gross error found at entry 477.<br> Found: 7.57435e-10 Expected
- 7.14133e-11 Error: 9.60635<br> 28.8063, 144.032, 42.3849, 0.504845, 1, 7.14133e-11<br>
- CAUTION: Gross error found at entry 489.<br> Found: 4.8561e-10 Expected 5.62991e-11
- Error: 7.62553<br> 31.9438, 23.9579, 44.2068, 0.93835, 1, 5.62991e-11<br>
- CAUTION: Gross error found at entry 490.<br> Found: 8.35187e-10 Expected
- 1.87483e-10 Error: 3.45473<br> 31.9438, 23.9579, 135.747, 0.961117, 1, 1.87483e-10<br>
- CAUTION: Gross error found at entry 491.<br> Found: 1.00174e-09 Expected
- 2.38491e-10 Error: 3.20032<br> 31.9438, 23.9579, 191.501, 0.968273, 1, 2.38491e-10<br>
- CAUTION: Gross error found at entry 537.<br> Found: 7.29746e-10 Expected
- 1.31223e-12 Error: 555.111<br> 31.9438, 159.719, 34.2373, 0.489796, 1, 1.31223e-12<br>
- CAUTION: Gross error found at entry 538.<br> Found: 2.49663e-09 Expected
- 1.54239e-09 Error: 0.618681<br> 31.9438, 159.719, 126.472, 0.581861, 1, 1.54239e-09<br>
- CAUTION: Gross error found at entry 549.<br> Found: 4.16125e-10 Expected
- 4.8536e-13 Error: 856.353<br> 38.0822, 28.5617, 34.773, 0.931853, 1, 4.8536e-13<br>
- CAUTION: Gross error found at entry 550.<br> Found: 9.69907e-10 Expected
- 2.87054e-12 Error: 336.883<br> 38.0822, 28.5617, 127.953, 0.956104, 1, 2.87054e-12<br>
- CAUTION: Gross error found at entry 551.<br> Found: 5.90132e-10 Expected
- 4.08361e-12 Error: 143.512<br> 38.0822, 28.5617, 183.147, 0.963764, 1, 4.08361e-12<br>
- CAUTION: Gross error found at entry 597.<br> Found: 4.67033e-10 Expected
- 9.82939e-16 Error: 475139<br> 38.0822, 190.411, 27.0954, 0.475419, 1, 9.82939e-16<br>
- CAUTION: Gross error found at entry 598.<br> Found: 9.33207e-10 Expected
- 4.03465e-12 Error: 230.298<br> 38.0822, 190.411, 100.733, 0.544491, 1, 4.03465e-12<br>
- CAUTION: Gross error found at entry 599.<br> Found: 7.4092e-10 Expected 9.53942e-11
- Error: 6.76693<br> 38.0822, 190.411, 169.826, 0.594614, 1, 9.53942e-11<br>
- CAUTION: Gross error found at entry 609.<br> Found: 5.71813e-10 Expected
- 1.17207e-14 Error: 48785.7<br> 42.7789, 32.0842, 28.3773, 0.927814, 1, 1.17207e-14<br>
- CAUTION: Gross error found at entry 610.<br> Found: 5.16834e-10 Expected
- 9.62679e-14 Error: 5367.71<br> 42.7789, 32.0842, 109.376, 0.950307, 1, 9.62679e-14<br>
- CAUTION: Gross error found at entry 611.<br> Found: 6.08012e-10 Expected
- 1.7454e-13 Error: 3482.51<br> 42.7789, 32.0842, 175.686, 0.960431, 1, 1.7454e-13<br>
- CAUTION: Gross error found at entry 657.<br> Found: 5.59489e-10 Expected
- 2.86344e-18 Error: 1.95391e+08<br> 42.7789, 213.895, 21.9724, 0.467166, 1,
- 2.86344e-18<br> CAUTION: Gross error found at entry 658.<br> Found: 5.14798e-10
- Expected 2.50972e-14 Error: 20511.2<br> 42.7789, 213.895, 84.4175, 0.522676,
- 1, 2.50972e-14<br> CAUTION: Gross error found at entry 659.<br> Found:
- 8.49991e-10 Expected 2.38005e-12 Error: 356.131<br> 42.7789, 213.895, 160.056,
- 0.576191, 1, 2.38005e-12<br> CAUTION: Gross error found at entry 671.<br>
- Found: 3.03281e-10 Expected 2.22036e-15 Error: 136590<br> 44.5963, 33.4472,
- 22.4929, 0.924976, 1, 2.22036e-15<br> CAUTION: Gross error found at entry
- 672.<br> Found: 8.40636e-10 Expected 2.22384e-14 Error: 37800.1<br> 44.5963,
- 33.4472, 94.9517, 0.946545, 1, 2.22384e-14<br> CAUTION: Gross error found
- at entry 673.<br> Found: 8.15021e-10 Expected 4.75974e-14 Error: 17122.2<br>
- 44.5963, 33.4472, 162.945, 0.95793, 1, 4.75974e-14<br> CAUTION: Gross error
- found at entry 716.<br> Found: 1.11988e-10 Expected 2.84965e-22 Error: 3.92989e+11<br>
- 44.5963, 222.981, 0.956697, 0.445432, 1, 2.84965e-22<br> CAUTION: Gross error
- found at entry 717.<br> Found: 7.99524e-10 Expected 3.04552e-15 Error: 262523<br>
- 44.5963, 222.981, 78.4454, 0.515267, 1, 3.04552e-15<br> CAUTION: Gross error
- found at entry 718.<br> Found: 8.0958e-10 Expected 5.89458e-13 Error: 1372.43<br>
- 44.5963, 222.981, 158.441, 0.57107, 1, 5.89458e-13<br> *** FURTHER CONTENT
- HAS BEEN TRUNCATED FOR BREVITY ***<br>
- </p>
- <h5>
- <a name="special_function_error_rates_rep.error_logs.h22"></a>
- <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_non_central_be2"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_non_central_be2">Error
- Output For non central beta CDF with compiler GNU C++ version 7.1.0 and library
- Rmath 3.2.3 and test data Non Central Beta, medium parameters</a>
- </h5>
- <p>
- <a name="errors_GNU_C_version_7_1_0_linux_double_non_central_beta_CDF_Rmath_3_2_3_Non_Central_Beta_medium_parameters"></a>CAUTION:
- Gross error found at entry 14.<br> Found: 4.64669e-35 Expected 7.14875e-33
- Error: 152.846<br> 1.45431, 1.30887, 158.441, 0.0983847, 7.14875e-33, 1<br>
- CAUTION: Gross error found at entry 15.<br> Found: 4.66674e-46 Expected 3.13332e-40
- Error: 671416<br> 1.45431, 1.30887, 196.222, 0.09869, 3.13332e-40, 1<br>
- CAUTION: Gross error found at entry 18.<br> Found: 5.84342e-28 Expected 3.61559e-27
- Error: 5.18745<br> 1.45431, 1.43976, 159.586, 0.245596, 3.61559e-27, 1<br>
- CAUTION: Gross error found at entry 19.<br> Found: 1.72833e-34 Expected 1.76943e-33
- Error: 9.2378<br> 1.45431, 1.43976, 198.576, 0.246444, 1.76943e-33, 1<br>
- CAUTION: Gross error found at entry 22.<br> Found: 1.76915e-19 Expected 3.69506e-18
- Error: 19.8861<br> 1.45431, 1.45285, 159.621, 0.491116, 3.69506e-18, 1<br>
- CAUTION: Gross error found at entry 23.<br> Found: 2.52007e-25 Expected 2.00482e-22
- Error: 794.544<br> 1.45431, 1.45285, 199.292, 0.492849, 2.00482e-22, 1<br>
- CAUTION: Gross error found at entry 73.<br> Found: 2.04477e-34 Expected 2.45287e-33
- Error: 10.9958<br> 7.62448, 6.86203, 148.129, 0.0921776, 2.45287e-33, 1<br>
- CAUTION: Gross error found at entry 74.<br> Found: 2.36587e-46 Expected 7.32638e-42
- Error: 30966<br> 7.62448, 6.86203, 193.539, 0.093784, 7.32638e-42, 1<br>
- CAUTION: Gross error found at entry 76.<br> Found: 3.29122e-26 Expected 7.418e-25
- Error: 21.5387<br> 7.62448, 7.54824, 148.626, 0.228717, 7.418e-25, 1<br>
- CAUTION: Gross error found at entry 77.<br> Found: 1.70126e-32 Expected 1.07666e-31
- Error: 5.32864<br> 7.62448, 7.54824, 193.774, 0.23303, 1.07666e-31, 1<br>
- CAUTION: Gross error found at entry 79.<br> Found: 1.3478e-15 Expected 4.21836e-15
- Error: 2.12982<br> 7.62448, 7.61686, 151.548, 0.457773, 4.21836e-15, 1<br>
- CAUTION: Gross error found at entry 80.<br> Found: 8.78487e-21 Expected 3.41238e-19
- Error: 37.8438<br> 7.62448, 7.61686, 194.119, 0.465826, 3.41238e-19, 1<br>
- CAUTION: Gross error found at entry 132.<br> Found: 3.85783e-23 Expected
- 1.54142e-22 Error: 2.99555<br> 19.9593, 17.9634, 44.2068, 0.0698905, 1.54142e-22,
- 1<br> CAUTION: Gross error found at entry 133.<br> Found: 8.6122e-39 Expected
- 3.94361e-38 Error: 3.5791<br> 19.9593, 17.9634, 135.747, 0.0829178, 3.94361e-38,
- 1<br> CAUTION: Gross error found at entry 134.<br> Found: 3.61781e-52 Expected
- 3.98669e-48 Error: 11018.6<br> 19.9593, 17.9634, 191.501, 0.0864897, 3.98669e-48,
- 1<br> CAUTION: Gross error found at entry 135.<br> Found: 2.07122e-15 Expected
- 7.08614e-15 Error: 2.42124<br> 19.9593, 19.7597, 55.6996, 0.176444, 7.08614e-15,
- 1<br> CAUTION: Gross error found at entry 136.<br> Found: 2.28223e-27 Expected
- 2.16759e-25 Error: 93.977<br> 19.9593, 19.7597, 136.272, 0.20393, 2.16759e-25,
- 1<br> CAUTION: Gross error found at entry 137.<br> Found: 6.4251e-34 Expected
- 4.0064e-33 Error: 5.23554<br> 19.9593, 19.7597, 191.898, 0.213398, 4.0064e-33,
- 1<br> CAUTION: Gross error found at entry 139.<br> Found: 2.1734e-14 Expected
- 4.65637e-14 Error: 1.14243<br> 19.9593, 19.9394, 145.168, 0.410858, 4.65637e-14,
- 1<br> CAUTION: Gross error found at entry 140.<br> Found: 2.18388e-19 Expected
- 5.1677e-18 Error: 22.663<br> 19.9593, 19.9394, 192.978, 0.426523, 5.1677e-18,
- 1<br> CAUTION: Gross error found at entry 192.<br> Found: 3.29537e-23 Expected
- 8.29996e-23 Error: 1.51867<br> 22.4174, 20.1757, 34.773, 0.0661999, 8.29996e-23,
- 1<br> CAUTION: Gross error found at entry 193.<br> Found: 7.86091e-39 Expected
- 2.77686e-38 Error: 2.5325<br> 22.4174, 20.1757, 127.953, 0.0809614, 2.77686e-38,
- 1<br> CAUTION: Gross error found at entry 194.<br> Found: 3.0161e-51 Expected
- 4.5396e-48 Error: 1504.12<br> 22.4174, 20.1757, 183.147, 0.0848857, 4.5396e-48,
- 1<br> CAUTION: Gross error found at entry 195.<br> Found: 3.08022e-14 Expected
- 1.42713e-13 Error: 3.6332<br> 22.4174, 22.1932, 37.6764, 0.162145, 1.42713e-13,
- 1<br> CAUTION: Gross error found at entry 196.<br> Found: 8.89935e-28 Expected
- 2.56187e-25 Error: 286.871<br> 22.4174, 22.1932, 131.096, 0.199361, 2.56187e-25,
- 1<br> CAUTION: Gross error found at entry 197.<br> Found: 9.34392e-34 Expected
- 6.14831e-33 Error: 5.58001<br> 22.4174, 22.1932, 186.799, 0.209601, 6.14831e-33,
- 1<br> CAUTION: Gross error found at entry 199.<br> Found: 2.79341e-13 Expected
- 4.79277e-13 Error: 0.71574<br> 22.4174, 22.395, 131.148, 0.398015, 4.79277e-13,
- 1<br> CAUTION: Gross error found at entry 200.<br> Found: 3.13989e-19 Expected
- 7.01608e-18 Error: 21.345<br> 22.4174, 22.395, 191.433, 0.419933, 7.01608e-18,
- 1<br> *** FURTHER CONTENT HAS BEEN TRUNCATED FOR BREVITY ***<br>
- </p>
- <h5>
- <a name="special_function_error_rates_rep.error_logs.h23"></a>
- <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_non_central_chi"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_non_central_chi">Error
- Output For non central chi squared CDF complement with compiler GNU C++ version
- 7.1.0 and library Rmath 3.2.3 and test data Non Central Chi Squared, large
- parameters</a>
- </h5>
- <p>
- <a name="errors_GNU_C_version_7_1_0_linux_double_non_central_chi_squared_CDF_complement_Rmath_3_2_3_Non_Central_Chi_Squared_large_parameters"></a>CAUTION:
- Gross error found at entry 12.<br> Found: 0 Expected 1.17655e-12 Error: 5.28771e+295<br>
- 101.815, 5236.73, 6406.25, 1, 1.17655e-12<br> CAUTION: Gross error found
- at entry 13.<br> Found: 0 Expected 1.79374e-44 Error: 8.06149e+263<br>
- 101.815, 9735.22, 12788.2, 1, 1.79374e-44<br> CAUTION: Gross error found
- at entry 35.<br> Found: 2.58682e-14 Expected 1.84404e-61 Error: 1.4028e+47<br>
- 107.623, 122.456, 920.317, 1, 1.84404e-61<br> CAUTION: Gross error found
- at entry 36.<br> Found: 0 Expected 2.30757e-102 Error: 1.03707e+206<br>
- 107.623, 156.292, 1319.58, 1, 2.30757e-102<br> CAUTION: Gross error found
- at entry 52.<br> Found: 0 Expected 6.40952e-24 Error: 2.88059e+284<br>
- 114.68, 417.884, 1065.13, 1, 6.40952e-24<br> CAUTION: Gross error found at
- entry 53.<br> Found: 0 Expected 1.02366e-98 Error: 4.60058e+209<br> 114.68,
- 669.781, 2353.38, 1, 1.02366e-98<br> CAUTION: Gross error found at entry
- 69.<br> Found: 0 Expected 6.55726e-39 Error: 2.94699e+269<br> 118.032,
- 3168.71, 4930.11, 1, 6.55726e-39<br> CAUTION: Gross error found at entry
- 85.<br> Found: 0 Expected 7.30688e-22 Error: 3.28388e+286<br> 163.004,
- 9735.22, 11877.9, 1, 7.30688e-22<br> CAUTION: Gross error found at entry
- 86.<br> Found: 0 Expected 1.17171e-111 Error: 5.26596e+196<br> 163.004,
- 25344.1, 33159.2, 1, 1.17171e-111<br> CAUTION: Gross error found at entry
- 108.<br> Found: 1.12355e-13 Expected 2.67349e-61 Error: 4.20255e+47<br>
- 256.292, 122.456, 1136.25, 1, 2.67349e-61<br> CAUTION: Gross error found
- at entry 109.<br> Found: 1.16462e-13 Expected 8.30595e-116 Error: 1.40216e+102<br>
- 256.292, 156.292, 1650.34, 1, 8.30595e-116<br> CAUTION: Gross error found
- at entry 124.<br> Found: 1.05804e-13 Expected 1.01672e-15 Error: 103.064<br>
- 517.884, 417.884, 1403.65, 1, 1.01672e-15<br> CAUTION: Gross error found
- at entry 125.<br> Found: 2.00728e-13 Expected 3.50192e-56 Error: 5.73194e+42<br>
- 517.884, 669.781, 2375.33, 1, 3.50192e-56<br> CAUTION: Gross error found
- at entry 141.<br> Found: 0 Expected 1.36924e-20 Error: 6.15368e+287<br>
- 769.781, 3168.71, 5120.04, 1, 1.36924e-20<br> CAUTION: Gross error found
- at entry 142.<br> Found: 0 Expected 3.19215e-72 Error: 1.43463e+236<br>
- 769.781, 5236.73, 9009.76, 1, 3.19215e-72<br> CAUTION: Gross error found
- at entry 157.<br> Found: 0 Expected 7.26231e-08 Error: 3.26385e+300<br>
- 1223.88, 9735.22, 12055, 1, 7.26231e-08<br> CAUTION: Gross error found at
- entry 158.<br> Found: 0 Expected 4.5906e-56 Error: 2.06312e+252<br> 1223.88,
- 25344.1, 31881.6, 1, 4.5906e-56<br> CAUTION: Gross error found at entry 194.<br>
- Found: 0 Expected 5.34714e-12 Error: 2.40313e+296<br> 9835.22, 122.456, 10953.4,
- 1, 5.34714e-12<br> CAUTION: Gross error found at entry 195.<br> Found:
- 0 Expected 4.84412e-40 Error: 2.17706e+268<br> 9835.22, 156.292, 11989.8,
- 1, 4.84412e-40<br> CAUTION: Gross error found at entry 196.<br> Found:
- 0 Expected 5.50199e-83 Error: 2.47272e+225<br> 9835.22, 417.884, 13329, 1,
- 5.50199e-83<br> CAUTION: Gross error found at entry 197.<br> Found: 0 Expected
- 1.28192e-205 Error: 5.76124e+102<br> 9835.22, 669.781, 15757.5, 1, 1.28192e-205<br>
- CAUTION: Gross error found at entry 211.<br> Found: 0 Expected 3.83272e-28
- Error: 1.72251e+280<br> 25444.1, 1123.88, 29224.8, 1, 3.83272e-28<br> CAUTION:
- Gross error found at entry 212.<br> Found: 0 Expected 1.69815e-101 Error:
- 7.63188e+206<br> 25444.1, 3168.71, 34335.4, 1, 1.69815e-101<br> CAUTION:
- Gross error found at entry 213.<br> Found: 0 Expected 1.09245e-217 Error:
- 4.90974e+90<br> 25444.1, 5236.73, 39885.1, 1, 1.09245e-217<br>
- </p>
- <h5>
- <a name="special_function_error_rates_rep.error_logs.h24"></a>
- <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_non_central_ch0"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_non_central_ch0">Error
- Output For non central chi squared CDF complement with compiler GNU C++ version
- 7.1.0 and library Rmath 3.2.3 and test data Non Central Chi Squared, medium
- parameters</a>
- </h5>
- <p>
- <a name="errors_GNU_C_version_7_1_0_linux_double_non_central_chi_squared_CDF_complement_Rmath_3_2_3_Non_Central_Chi_Squared_medium_parameters"></a>CAUTION:
- Gross error found at entry 36.<br> Found: 1.11022e-14 Expected 1.30043e-26
- Error: 8.53738e+11<br> 1.95191, 109.376, 445.313, 1, 1.30043e-26<br> CAUTION:
- Gross error found at entry 37.<br> Found: 0 Expected 1.45478e-39 Error: 6.53812e+268<br>
- 1.95191, 109.444, 556.98, 1, 1.45478e-39<br> CAUTION: Gross error found at
- entry 54.<br> Found: 2.91989e-14 Expected 4.25949e-21 Error: 6.85501e+06<br>
- 1.95191, 159.586, 484.613, 1, 4.25949e-21<br> CAUTION: Gross error found
- at entry 55.<br> Found: 0 Expected 1.33424e-37 Error: 5.99639e+270<br>
- 1.95191, 159.621, 646.292, 1, 1.33424e-37<br> CAUTION: Gross error found
- at entry 56.<br> Found: 1.25455e-14 Expected 1.95903e-56 Error: 6.40393e+41<br>
- 1.95191, 160.056, 810.04, 1, 1.95903e-56<br> CAUTION: Gross error found at
- entry 73.<br> Found: 0 Expected 4.34735e-25 Error: 1.9538e+283<br> 1.95191,
- 193.539, 586.473, 1, 4.34735e-25<br> CAUTION: Gross error found at entry
- 74.<br> Found: 0 Expected 4.66119e-45 Error: 2.09485e+263<br> 1.95191,
- 193.774, 782.902, 1, 4.66119e-45<br> CAUTION: Gross error found at entry
- 75.<br> Found: 4.77396e-15 Expected 8.92248e-68 Error: 5.35048e+52<br>
- 1.95191, 194.119, 980.352, 1, 8.92248e-68<br> CAUTION: Gross error found
- at entry 111.<br> Found: 0 Expected 3.1064e-15 Error: 1.39609e+293<br>
- 20.4105, 84.4175, 314.484, 1, 3.1064e-15<br> CAUTION: Gross error found at
- entry 112.<br> Found: 0 Expected 7.50903e-29 Error: 3.37473e+279<br> 20.4105,
- 94.9517, 461.449, 1, 7.50903e-29<br> CAUTION: Gross error found at entry
- 113.<br> Found: 3.77476e-15 Expected 1.74225e-43 Error: 2.1666e+28<br>
- 20.4105, 97.0751, 587.428, 1, 1.74225e-43<br> CAUTION: Gross error found
- at entry 130.<br> Found: 8.88178e-16 Expected 4.13277e-23 Error: 2.14911e+07<br>
- 20.4105, 151.548, 515.876, 1, 4.13277e-23<br> CAUTION: Gross error found
- at entry 131.<br> Found: 1.75415e-14 Expected 1.92146e-41 Error: 9.12928e+26<br>
- 20.4105, 152.75, 692.642, 1, 1.92146e-41<br> CAUTION: Gross error found at
- entry 132.<br> Found: 1.38778e-14 Expected 7.09864e-64 Error: 1.95499e+49<br>
- 20.4105, 158.441, 894.26, 1, 7.09864e-64<br> CAUTION: Gross error found at
- entry 149.<br> Found: 2.22045e-16 Expected 8.74501e-28 Error: 2.5391e+11<br>
- 20.4105, 191.433, 635.532, 1, 8.74501e-28<br> CAUTION: Gross error found
- at entry 150.<br> Found: 0 Expected 6.94227e-50 Error: 3.12002e+258<br>
- 20.4105, 191.501, 847.648, 1, 6.94227e-50<br> CAUTION: Gross error found
- at entry 151.<br> Found: 3.40838e-14 Expected 5.3889e-75 Error: 6.32482e+60<br>
- 20.4105, 191.898, 1061.55, 1, 5.3889e-75<br> CAUTION: Gross error found at
- entry 206.<br> Found: 5.88418e-15 Expected 2.69136e-22 Error: 2.18632e+07<br>
- 22.8625, 141.209, 492.215, 1, 2.69136e-22<br> CAUTION: Gross error found
- at entry 207.<br> Found: 3.60822e-14 Expected 1.64941e-40 Error: 2.18759e+26<br>
- 22.8625, 145.168, 672.121, 1, 1.64941e-40<br> CAUTION: Gross error found
- at entry 208.<br> Found: 3.73035e-14 Expected 1.6094e-61 Error: 2.31784e+47<br>
- 22.8625, 148.129, 854.96, 1, 1.6094e-61<br> CAUTION: Gross error found at
- entry 225.<br> Found: 0 Expected 3.73672e-27 Error: 1.67937e+281<br> 22.8625,
- 182.675, 616.613, 1, 3.73672e-27<br> CAUTION: Gross error found at entry
- 226.<br> Found: 0 Expected 8.85688e-49 Error: 3.98049e+259<br> 22.8625,
- 183.147, 824.038, 1, 8.85688e-49<br> CAUTION: Gross error found at entry
- 227.<br> Found: 0 Expected 2.29176e-74 Error: 1.02997e+234<br> 22.8625,
- 186.799, 1048.31, 1, 2.29176e-74<br> CAUTION: Gross error found at entry
- 282.<br> Found: 0 Expected 2.18831e-21 Error: 9.8348e+286<br> 23.3804,
- 132.721, 468.305, 1, 2.18831e-21<br> CAUTION: Gross error found at entry
- 283.<br> Found: 0 Expected 1.3071e-38 Error: 5.87439e+269<br> 23.3804,
- 135.747, 636.51, 1, 1.3071e-38<br> CAUTION: Gross error found at entry 284.<br>
- Found: 1.84297e-14 Expected 8.27843e-58 Error: 2.22623e+43<br> 23.3804, 136.272,
- 798.262, 1, 8.27843e-58<br> CAUTION: Gross error found at entry 301.<br>
- Found: 0 Expected 9.85282e-26 Error: 4.42808e+282<br> 23.3804, 169.826, 579.619,
- 1, 9.85282e-26<br> CAUTION: Gross error found at entry 302.<br> Found:
- 0 Expected 4.8094e-47 Error: 2.16145e+261<br> 23.3804, 174.486, 791.465,
- 1, 4.8094e-47<br> CAUTION: Gross error found at entry 303.<br> Found: 1.11022e-16
- Expected 6.70476e-71 Error: 1.65587e+54<br> 23.3804, 175.686, 995.333, 1,
- 6.70476e-71<br> CAUTION: Gross error found at entry 358.<br> Found: 0 Expected
- 3.9702e-21 Error: 1.7843e+287<br> 26.2704, 126.472, 458.227, 1, 3.9702e-21<br>
- CAUTION: Gross error found at entry 359.<br> *** FURTHER CONTENT HAS BEEN
- TRUNCATED FOR BREVITY ***<br>
- </p>
- <h5>
- <a name="special_function_error_rates_rep.error_logs.h25"></a>
- <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_non_central_t_c"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_non_central_t_c">Error
- Output For non central t CDF complement with compiler GNU C++ version 7.1.0
- and library Rmath 3.2.3 and test data Non Central T</a>
- </h5>
- <p>
- <a name="errors_GNU_C_version_7_1_0_linux_double_non_central_t_CDF_complement_Rmath_3_2_3_Non_Central_T"></a>CAUTION:
- Gross error found at entry 56.<br> Found: 0.000186411 Expected 7.85192e-05
- Error: 1.37408<br> 61.6335, 46.2251, 68.8608, 0.999921, 7.85192e-05<br>
- CAUTION: Gross error found at entry 75.<br> Found: 0.00011439 Expected 5.05344e-05
- Error: 1.26361<br> 80.8418, 60.6313, 86.1278, 0.999949, 5.05344e-05<br>
- CAUTION: Gross error found at entry 93.<br> Found: 0.000655162 Expected 0.000423927
- Error: 0.545458<br> 100.733, 50.3663, 65.7619, 0.999576, 0.000423927<br>
- CAUTION: Gross error found at entry 112.<br> Found: 0.000518249 Expected
- 0.00034473 Error: 0.503348<br> 127.953, 63.9764, 81.0824, 0.999655, 0.00034473<br>
- </p>
- <h5>
- <a name="special_function_error_rates_rep.error_logs.h26"></a>
- <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_non_central_t_0"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_non_central_t_0">Error
- Output For non central t CDF with compiler GNU C++ version 7.1.0 and library
- Rmath 3.2.3 and test data Non Central T</a>
- </h5>
- <p>
- <a name="errors_GNU_C_version_7_1_0_linux_double_non_central_t_CDF_Rmath_3_2_3_Non_Central_T"></a>CAUTION:
- Gross error found at entry 74.<br> Found: 0.000830062 Expected 0.000522858
- Error: 0.587549<br> 79.7478, -39.8739, -53.8066, 0.000522858, 0.999477<br>
- CAUTION: Gross error found at entry 94.<br> Found: 7.69292e-05 Expected 3.54024e-05
- Error: 1.17299<br> 101.191, -75.8936, -104.104, 3.54024e-05, 0.999965<br>
- CAUTION: Gross error found at entry 113.<br> Found: 5.07713e-05 Expected
- 2.4439e-05 Error: 1.07747<br> 128.792, -96.5942, -128.112, 2.4439e-05, 0.999976<br>
- CAUTION: Gross error found at entry 132.<br> Found: 4.08612e-05 Expected
- 2.01542e-05 Error: 1.02743<br> 146.56, -109.92, -143.392, 2.01542e-05, 0.99998<br>
- CAUTION: Gross error found at entry 151.<br> Found: 3.55146e-05 Expected
- 1.7803e-05 Error: 0.994869<br> 159.586, -119.689, -154.522, 1.7803e-05, 0.999982<br>
- CAUTION: Gross error found at entry 170.<br> Found: 3.03671e-05 Expected
- 1.55023e-05 Error: 0.958873<br> 175.686, -131.765, -168.211, 1.55023e-05,
- 0.999984<br> CAUTION: Gross error found at entry 189.<br> Found: 2.61339e-05
- Expected 1.3581e-05 Error: 0.924298<br> 192.978, -144.733, -182.834, 1.3581e-05,
- 0.999986<br>
- </p>
- <h5>
- <a name="special_function_error_rates_rep.error_logs.h27"></a>
- <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_polygamma_with_"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_polygamma_with_">Error
- Output For polygamma with compiler GNU C++ version 7.1.0 and library Rmath
- 3.2.3 and test data Mathematica Data - Large orders and other bug cases</a>
- </h5>
- <p>
- <a name="errors_GNU_C_version_7_1_0_linux_double_polygamma_Rmath_3_2_3_Mathematica_Data_Large_orders_and_other_bug_cases"></a>CAUTION:
- Found non-finite result, when a finite value was expected at entry 0<br>
- Found: -nan Expected 2.07309e+257 Error: 1.79769e+308<br> 171, 2, 2.07309e+257<br>
- CAUTION: Gross error found at entry 0.<br> Found: -nan Expected 2.07309e+257
- Error: 1.79769e+308<br> 171, 2, 2.07309e+257<br> CAUTION: Found non-finite
- result, when a finite value was expected at entry 1<br> Found: -nan Expected
- 7.42912e+188 Error: 1.79769e+308<br> 171, 5, 7.42912e+188<br> CAUTION:
- Gross error found at entry 1.<br> Found: -nan Expected 7.42912e+188 Error:
- 1.79769e+308<br> 171, 5, 7.42912e+188<br> CAUTION: Found non-finite result,
- when a finite value was expected at entry 2<br> Found: -nan Expected -4.81295e+247
- Error: 1.79769e+308<br> 166, 2, -4.81295e+247<br> CAUTION: Gross error
- found at entry 2.<br> Found: -nan Expected -4.81295e+247 Error: 1.79769e+308<br>
- 166, 2, -4.81295e+247<br> CAUTION: Found non-finite result, when a finite
- value was expected at entry 3<br> Found: -nan Expected -1.88439e+218 Error:
- 1.79769e+308<br> 166, 3, -1.88439e+218<br> CAUTION: Gross error found at
- entry 3.<br> Found: -nan Expected -1.88439e+218 Error: 1.79769e+308<br>
- 166, 3, -1.88439e+218<br> CAUTION: Found non-finite result, when a finite
- value was expected at entry 4<br> Found: -nan Expected 7.53144e+74 Error:
- 1.79769e+308<br> 171, 23, 7.53144e+74<br> CAUTION: Gross error found at
- entry 4.<br> Found: -nan Expected 7.53144e+74 Error: 1.79769e+308<br> 171,
- 23, 7.53144e+74<br> CAUTION: Found non-finite result, when a finite value
- was expected at entry 5<br> Found: -nan Expected -6.52661e-66 Error: 1.79769e+308<br>
- 168, 150, -6.52661e-66<br> CAUTION: Gross error found at entry 5.<br> Found:
- -nan Expected -6.52661e-66 Error: 1.79769e+308<br> 168, 150, -6.52661e-66<br>
- CAUTION: Found non-finite result, when a finite value was expected at entry
- 6<br> Found: -nan Expected 9.2734e-88 Error: 1.79769e+308<br> 169, 202,
- 9.2734e-88<br> CAUTION: Gross error found at entry 6.<br> Found: -nan Expected
- 9.2734e-88 Error: 1.79769e+308<br> 169, 202, 9.2734e-88<br> Outside supported
- domain<br> 20, -9.5, -0.00103076<br> Outside supported domain<br> 21,
- -9.5, 4.28582e+26<br> Outside supported domain<br> 22, -9.5, -0.00419144<br>
- Outside supported domain<br> 23, -9.5, 8.6745e+29<br> Outside supported
- domain<br> 24, -9.5, -0.0204825<br> Outside supported domain<br> 25,
- -9.5, 2.08188e+33<br> Outside supported domain<br> 26, -9.5, -0.118403<br>
- Outside supported domain<br> 27, -9.5, 5.84592e+36<br> Outside supported
- domain<br> 28, -9.5, -0.798969<br> Outside supported domain<br> 29, -9.5,
- 1.89875e+40<br> Outside supported domain<br> 30, -9.5, -6.22245<br>
- </p>
- <h5>
- <a name="special_function_error_rates_rep.error_logs.h28"></a>
- <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_polygamma_with0"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_polygamma_with0">Error
- Output For polygamma with compiler GNU C++ version 7.1.0 and library Rmath
- 3.2.3 and test data Mathematica Data - large negative arguments</a>
- </h5>
- <p>
- <a name="errors_GNU_C_version_7_1_0_linux_double_polygamma_Rmath_3_2_3_Mathematica_Data_large_negative_arguments"></a>Outside
- supported domain<br> 124, -1.5, 7.63705e+240<br> Outside supported domain<br>
- 124, -2.5, 7.63705e+240<br> Outside supported domain<br> 124, -3.5, 7.63705e+240<br>
- Outside supported domain<br> 124, -4.5, 7.63705e+240<br> Outside supported
- domain<br> 124, -5.5, 7.63705e+240<br> Outside supported domain<br> 124,
- -6.5, 7.63705e+240<br> Outside supported domain<br> 124, -7.5, 7.63705e+240<br>
- Outside supported domain<br> 124, -8.5, 7.63705e+240<br> Outside supported
- domain<br> 124, -9.5, 7.63705e+240<br> Outside supported domain<br> 124,
- -10.5, 7.63705e+240<br> Outside supported domain<br> 124, -11.5, 7.63705e+240<br>
- Outside supported domain<br> 124, -12.5, 7.63705e+240<br> Outside supported
- domain<br> 124, -13.5, 7.63705e+240<br> Outside supported domain<br>
- 124, -14.5, 7.63705e+240<br> Outside supported domain<br> 124, -15.5, 7.63705e+240<br>
- Outside supported domain<br> 124, -16.5, 7.63705e+240<br> Outside supported
- domain<br> 124, -17.5, 7.63705e+240<br> Outside supported domain<br>
- 124, -18.5, 7.63705e+240<br> Outside supported domain<br> 124, -19.5, 7.63705e+240<br>
- Outside supported domain<br> 124, -20.5, 7.63705e+240<br> Outside supported
- domain<br> 124, -1.5, -7.63705e+240<br> Outside supported domain<br>
- 124, -2.5, -7.63705e+240<br> Outside supported domain<br> 124, -3.5, -7.63705e+240<br>
- Outside supported domain<br> 124, -4.5, -7.63705e+240<br> Outside supported
- domain<br> 124, -5.5, -7.63705e+240<br> Outside supported domain<br>
- 124, -6.5, -7.63705e+240<br> Outside supported domain<br> 124, -7.5, -7.63705e+240<br>
- Outside supported domain<br> 124, -8.5, -7.63705e+240<br> Outside supported
- domain<br> 124, -9.5, -7.63705e+240<br> Outside supported domain<br>
- 124, -10.5, -7.63705e+240<br> Outside supported domain<br> 124, -11.5,
- -7.63705e+240<br> Outside supported domain<br> 124, -12.5, -7.63705e+240<br>
- Outside supported domain<br> 124, -13.5, -7.63705e+240<br> Outside supported
- domain<br> 124, -14.5, -7.63705e+240<br> Outside supported domain<br>
- 124, -15.5, -7.63705e+240<br> Outside supported domain<br> 124, -16.5,
- -7.63705e+240<br> Outside supported domain<br> 124, -17.5, -7.63705e+240<br>
- Outside supported domain<br> 124, -18.5, -7.63705e+240<br> Outside supported
- domain<br> 124, -19.5, -7.63705e+240<br> Outside supported domain<br>
- 124, -20.5, -7.63705e+240<br> Outside supported domain<br> 1, -0.5, 8.9348<br>
- Outside supported domain<br> 2, -0.5, -0.828797<br> Outside supported domain<br>
- 3, -0.5, 193.409<br> Outside supported domain<br> 4, -0.5, -3.47425<br>
- Outside supported domain<br> 5, -0.5, 15371.1<br> Outside supported domain<br>
- 6, -0.5, -43.4579<br> Outside supported domain<br> 7, -0.5, 2.58068e+06<br>
- Outside supported domain<br> 8, -0.5, -1059.96<br> Outside supported domain<br>
- 9, -0.5, 7.43185e+08<br> Outside supported domain<br> 10, -0.5, -42108.9<br>
- Outside supported domain<br> 11, -0.5, 3.26999e+11<br> Outside supported
- domain<br> 12, -0.5, -2.46448e+06<br> Outside supported domain<br> 13,
- -0.5, 2.04047e+14<br> Outside supported domain<br> 14, -0.5, -1.9918e+08<br>
- Outside supported domain<br> 15, -0.5, 1.71399e+17<br> Outside supported
- domain<br> 16, -0.5, -2.12394e+10<br> Outside supported domain<br> 17,
- -0.5, 1.86483e+20<br> Outside supported domain<br> 18, -0.5, -2.88824e+12<br>
- Outside supported domain<br> 19, -0.5, 2.55108e+23<br> Outside supported
- domain<br> 20, -0.5, -4.87773e+14<br> Outside supported domain<br> 21,
- -0.5, 4.28582e+26<br> Outside supported domain<br> 1, -0.5, 8.9348<br>
- Outside supported domain<br> 2, -0.5, -0.828843<br> Outside supported domain<br>
- 3, -0.5, 193.409<br> Outside supported domain<br> 4, -0.5, -3.47791<br>
- Outside supported domain<br> 5, -0.5, 15371.1<br> Outside supported domain<br>
- 6, -0.5, -44.0732<br> Outside supported domain<br> 7, -0.5, 2.58068e+06<br>
- Outside supported domain<br> 8, -0.5, -1237.15<br> Outside supported domain<br>
- 9, -0.5, 7.43185e+08<br> Outside supported domain<br> 10, -0.5, -120071<br>
- Outside supported domain<br> 11, -0.5, 3.26999e+11<br> Outside supported
- domain<br> 12, -0.5, -5.11131e+07<br> Outside supported domain<br> 13,
- -0.5, 2.04047e+14<br> Outside supported domain<br> 14, -0.5, -4.1064e+10<br>
- Outside supported domain<br> 15, -0.5, 1.71399e+17<br> Outside supported
- domain<br> 16, -0.5, -4.44822e+13<br> Outside supported domain<br> 17,
- -0.5, 1.86483e+20<br> Outside supported domain<br> 18, -0.5, -6.08254e+16<br>
- Outside supported domain<br> 19, -0.5, 2.55108e+23<br> Outside supported
- domain<br> 20, -0.5, -1.02182e+20<br> Outside supported domain<br> 21,
- -0.5, 4.28582e+26<br> Outside supported domain<br> 1, -0.5, 8.9348<br>
- Outside supported domain<br> 2, -0.5, -0.828751<br> Outside supported domain<br>
- 3, -0.5, 193.409<br> Outside supported domain<br> 4, -0.5, -3.47059<br>
- Outside supported domain<br> *** FURTHER CONTENT HAS BEEN TRUNCATED FOR BREVITY
- ***<br>
- </p>
- <h5>
- <a name="special_function_error_rates_rep.error_logs.h29"></a>
- <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_polygamma_with1"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_polygamma_with1">Error
- Output For polygamma with compiler GNU C++ version 7.1.0 and library Rmath
- 3.2.3 and test data Mathematica Data - negative arguments</a>
- </h5>
- <p>
- <a name="errors_GNU_C_version_7_1_0_linux_double_polygamma_Rmath_3_2_3_Mathematica_Data_negative_arguments"></a>Outside
- supported domain<br> 1, -12.75, 19.6638<br> Outside supported domain<br>
- 1, -12.25, 19.6608<br> Outside supported domain<br> 1, -11.75, 19.6576<br>
- Outside supported domain<br> 1, -11.25, 19.6542<br> Outside supported domain<br>
- 1, -10.75, 19.6504<br> Outside supported domain<br> 1, -10.25, 19.6463<br>
- Outside supported domain<br> 1, -9.75, 19.6417<br> Outside supported domain<br>
- 1, -9.25, 19.6367<br> Outside supported domain<br> 1, -8.75, 19.6312<br>
- Outside supported domain<br> 1, -8.25, 19.625<br> Outside supported domain<br>
- 1, -7.75, 19.6181<br> Outside supported domain<br> 1, -7.25, 19.6104<br>
- Outside supported domain<br> 1, -6.75, 19.6015<br> Outside supported domain<br>
- 1, -6.25, 19.5913<br> Outside supported domain<br> 1, -5.75, 19.5795<br>
- Outside supported domain<br> 1, -5.25, 19.5657<br> Outside supported domain<br>
- 1, -4.75, 19.5493<br> Outside supported domain<br> 1, -4.25, 19.5294<br>
- Outside supported domain<br> 1, -3.75, 19.505<br> Outside supported domain<br>
- 1, -3.25, 19.4741<br> Outside supported domain<br> 1, -2.75, 19.4339<br>
- Outside supported domain<br> 1, -2.25, 19.3794<br> Outside supported domain<br>
- 1, -1.75, 19.3016<br> Outside supported domain<br> 1, -1.25, 19.1819<br>
- Outside supported domain<br> 1, -0.75, 18.9751<br> Outside supported domain<br>
- 1, -0.25, 18.5419<br> Outside supported domain<br> 2, -12.75, -124.031<br>
- Outside supported domain<br> 2, -12.25, 124.019<br> Outside supported domain<br>
- 2, -11.75, -124.032<br> Outside supported domain<br> 2, -11.25, 124.018<br>
- Outside supported domain<br> 2, -10.75, -124.033<br> Outside supported
- domain<br> 2, -10.25, 124.016<br> Outside supported domain<br> 2, -9.75,
- -124.035<br> Outside supported domain<br> 2, -9.25, 124.015<br> Outside
- supported domain<br> 2, -8.75, -124.037<br> Outside supported domain<br>
- 2, -8.25, 124.012<br> Outside supported domain<br> 2, -7.75, -124.04<br>
- Outside supported domain<br> 2, -7.25, 124.009<br> Outside supported domain<br>
- 2, -6.75, -124.044<br> Outside supported domain<br> 2, -6.25, 124.003<br>
- Outside supported domain<br> 2, -5.75, -124.051<br> Outside supported domain<br>
- 2, -5.25, 123.995<br> Outside supported domain<br> 2, -4.75, -124.061<br>
- Outside supported domain<br> 2, -4.25, 123.981<br> Outside supported domain<br>
- 2, -3.75, -124.08<br> Outside supported domain<br> 2, -3.25, 123.955<br>
- Outside supported domain<br> 2, -2.75, -124.118<br> Outside supported domain<br>
- 2, -2.25, 123.897<br> Outside supported domain<br> 2, -1.75, -124.214<br>
- Outside supported domain<br> 2, -1.25, 123.721<br> Outside supported domain<br>
- 2, -0.75, -124.587<br> Outside supported domain<br> 2, -0.25, 122.697<br>
- Outside supported domain<br> 3, -12.75, 1558.54<br> Outside supported domain<br>
- 3, -12.25, 1558.54<br> Outside supported domain<br> 3, -11.75, 1558.54<br>
- Outside supported domain<br> 3, -11.25, 1558.54<br> Outside supported domain<br>
- 3, -10.75, 1558.54<br> Outside supported domain<br> 3, -10.25, 1558.54<br>
- Outside supported domain<br> 3, -9.75, 1558.54<br> Outside supported domain<br>
- 3, -9.25, 1558.54<br> Outside supported domain<br> 3, -8.75, 1558.54<br>
- Outside supported domain<br> 3, -8.25, 1558.54<br> Outside supported domain<br>
- 3, -7.75, 1558.54<br> Outside supported domain<br> 3, -7.25, 1558.54<br>
- Outside supported domain<br> 3, -6.75, 1558.54<br> Outside supported domain<br>
- 3, -6.25, 1558.54<br> Outside supported domain<br> 3, -5.75, 1558.54<br>
- Outside supported domain<br> 3, -5.25, 1558.54<br> Outside supported domain<br>
- 3, -4.75, 1558.53<br> Outside supported domain<br> 3, -4.25, 1558.53<br>
- Outside supported domain<br> 3, -3.75, 1558.52<br> Outside supported domain<br>
- 3, -3.25, 1558.51<br> Outside supported domain<br> 3, -2.75, 1558.49<br>
- Outside supported domain<br> 3, -2.25, 1558.46<br> Outside supported domain<br>
- 3, -1.75, 1558.38<br> Outside supported domain<br> 3, -1.25, 1558.22<br>
- Outside supported domain<br> 3, -0.75, 1557.75<br> Outside supported domain<br>
- 3, -0.25, 1555.76<br> Outside supported domain<br> 4, -12.75, -24481.6<br>
- Outside supported domain<br> 4, -12.25, 24481.6<br> Outside supported domain<br>
- 4, -11.75, -24481.6<br> Outside supported domain<br> 4, -11.25, 24481.6<br>
- Outside supported domain<br> 4, -10.75, -24481.6<br> Outside supported
- domain<br> 4, -10.25, 24481.6<br> Outside supported domain<br> 4, -9.75,
- -24481.6<br> Outside supported domain<br> 4, -9.25, 24481.6<br> Outside
- supported domain<br> 4, -8.75, -24481.6<br> Outside supported domain<br>
- 4, -8.25, 24481.6<br> Outside supported domain<br> 4, -7.75, -24481.6<br>
- Outside supported domain<br> 4, -7.25, 24481.6<br> Outside supported domain<br>
- 4, -6.75, -24481.6<br> Outside supported domain<br> 4, -6.25, 24481.6<br>
- Outside supported domain<br> 4, -5.75, -24481.6<br> Outside supported domain<br>
- 4, -5.25, 24481.6<br> Outside supported domain<br> *** FURTHER CONTENT
- HAS BEEN TRUNCATED FOR BREVITY ***<br>
- </p>
- <h5>
- <a name="special_function_error_rates_rep.error_logs.h30"></a>
- <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_polygamma_with2"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_polygamma_with2">Error
- Output For polygamma with compiler GNU C++ version 7.1.0 and library Rmath
- 3.2.3 and test data Mathematica Data - large arguments</a>
- </h5>
- <p>
- <a name="errors_GNU_C_version_7_1_0_linux_double_polygamma_Rmath_3_2_3_Mathematica_Data_large_arguments"></a>CAUTION:
- Gross error found at entry 211.<br> Found: -0 Expected -8.44974e-268 Error:
- 3.79751e+40<br> 30, 8.58993e+09, -8.44974e-268<br> CAUTION: Gross error
- found at entry 212.<br> Found: -0 Expected -7.86943e-277 Error: 3.5367e+31<br>
- 30, 1.71799e+10, -7.86943e-277<br> CAUTION: Gross error found at entry 213.<br>
- Found: -0 Expected -7.32898e-286 Error: 3.29381e+22<br> 30, 3.43597e+10,
- -7.32898e-286<br> CAUTION: Gross error found at entry 214.<br> Found: -0
- Expected -6.82564e-295 Error: 3.0676e+13<br> 30, 6.87195e+10, -6.82564e-295<br>
- CAUTION: Gross error found at entry 215.<br> Found: -0 Expected -6.35687e-304
- Error: 28568.3<br> 30, 1.37439e+11, -6.35687e-304<br>
- </p>
- <h5>
- <a name="special_function_error_rates_rep.error_logs.h31"></a>
- <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_w3"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_w3">Error
- Output For cyl_bessel_i with compiler GNU C++ version 7.1.0 and library GSL
- 2.1 and test data Bessel Iv: Mathworld Data (large values)</a>
- </h5>
- <p>
- <a name="errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_GSL_2_1_Bessel_Iv_Mathworld_Data_large_values_"></a>domain
- error<br> -1, 3.72917e-155, 1.86459e-155<br> domain error<br> -1.125,
- 3.72917e-155, -1.34964e+173<br>
- </p>
- <h5>
- <a name="special_function_error_rates_rep.error_logs.h32"></a>
- <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_w4"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_w4">Error
- Output For cyl_bessel_i with compiler GNU C++ version 7.1.0 and library GSL
- 2.1 and test data Bessel Iv: Random Data</a>
- </h5>
- <p>
- <a name="errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_GSL_2_1_Bessel_Iv_Random_Data"></a>domain
- error<br> -80.4919, 24.7501, 4.18698e+28<br> domain error<br> -80.4919,
- 63.7722, 2.03248e+06<br> domain error<br> -74.6026, 24.7501, 7.20977e+23<br>
- domain error<br> -74.6026, 63.7722, 8.7549e+08<br> domain error<br> -72.9046,
- 24.7501, 1.04535e+22<br> domain error<br> -72.9046, 63.7722, 4.7162e+09<br>
- domain error<br> -62.3236, 24.7501, 3.65147e+14<br> domain error<br>
- -62.3236, 63.7722, 8.56683e+13<br> domain error<br> -55.7932, 24.7501,
- -7.70364e+09<br> domain error<br> -55.7932, 63.7722, 1.95969e+16<br>
- domain error<br> -44.3004, 9.50706, 2.93478e+22<br> domain error<br>
- -44.3004, 24.7501, 640.568<br> domain error<br> -44.3004, 63.7722, 8.05557e+19<br>
- domain error<br> -38.3666, 5.11399, 2.89105e+27<br> domain error<br>
- -38.3666, 9.50706, 8.80632e+16<br> domain error<br> -38.3666, 24.7501,
- 0.389004<br> domain error<br> -38.3666, 63.7722, 3.06303e+21<br> underflow<br>
- 81.1584, 0.00177219, 0<br> underflow<br> 81.1584, 0.00221773, 0<br> underflow<br>
- 81.1584, 0.0074445, 6.08857e-319<br> underflow<br> 82.6752, 0.00177219,
- 0<br> underflow<br> 82.6752, 0.00221773, 0<br> underflow<br> 82.6752,
- 0.0074445, 0<br> underflow<br> 91.5014, 0.00177219, 0<br> underflow<br>
- 91.5014, 0.00221773, 0<br> underflow<br> 91.5014, 0.0074445, 0<br> underflow<br>
- 91.5014, 0.014336, 0<br> underflow<br> 91.5014, 0.0176092, 0<br> underflow<br>
- 92.9777, 0.00177219, 0<br> underflow<br> 92.9777, 0.00221773, 0<br> underflow<br>
- 92.9777, 0.0074445, 0<br> underflow<br> 92.9777, 0.014336, 0<br> underflow<br>
- 92.9777, 0.0176092, 0<br> underflow<br> 93.539, 0.00177219, 0<br> underflow<br>
- 93.539, 0.00221773, 0<br> underflow<br> 93.539, 0.0074445, 0<br> underflow<br>
- 93.539, 0.014336, 0<br> underflow<br> 93.539, 0.0176092, 0<br> underflow<br>
- 93.7736, 0.00177219, 0<br> underflow<br> 93.7736, 0.00221773, 0<br> underflow<br>
- 93.7736, 0.0074445, 0<br> underflow<br> 93.7736, 0.014336, 0<br> underflow<br>
- 93.7736, 0.0176092, 0<br> underflow<br> 98.5763, 0.00177219, 0<br> underflow<br>
- 98.5763, 0.00221773, 0<br> underflow<br> 98.5763, 0.0074445, 0<br> underflow<br>
- 98.5763, 0.014336, 0<br> underflow<br> 98.5763, 0.0176092, 0<br> underflow<br>
- 99.2923, 0.00177219, 0<br> underflow<br> 99.2923, 0.00221773, 0<br> underflow<br>
- 99.2923, 0.0074445, 0<br> underflow<br> 99.2923, 0.014336, 0<br> underflow<br>
- 99.2923, 0.0176092, 0<br>
- </p>
- <h5>
- <a name="special_function_error_rates_rep.error_logs.h33"></a>
- <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_w5"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_w5">Error
- Output For cyl_bessel_i with compiler GNU C++ version 7.1.0 and library GSL
- 2.1 and test data Bessel In: Random Data</a>
- </h5>
- <p>
- <a name="errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_GSL_2_1_Bessel_In_Random_Data"></a>underflow<br>
- 70, 0.00177219, 1.75887e-314<br> underflow<br> 73, 0.00177219, 0<br>
- underflow<br> 73, 0.00221773, 4.24896e-322<br> underflow<br> 76, 0.00177219,
- 0<br> underflow<br> 76, 0.00221773, 0<br> underflow<br> 79, 0.00177219,
- 0<br> underflow<br> 79, 0.00221773, 0<br> underflow<br> 79, 0.0074445,
- 1.38676e-309<br> underflow<br> 82, 0.00177219, 0<br> underflow<br>
- 82, 0.00221773, 0<br> underflow<br> 82, 0.0074445, 1.33398e-322<br> underflow<br>
- 85, 0.00177219, 0<br> underflow<br> 85, 0.00221773, 0<br> underflow<br>
- 85, 0.0074445, 0<br> underflow<br> 85, 0.014336, 1.81568e-311<br> underflow<br>
- 88, 0.00177219, 0<br> underflow<br> 88, 0.00221773, 0<br> underflow<br>
- 88, 0.0074445, 0<br> underflow<br> 88, 0.014336, 9.88131e-324<br> underflow<br>
- 88, 0.0176092, 7.34647e-316<br>
- </p>
- <h5>
- <a name="special_function_error_rates_rep.error_logs.h34"></a>
- <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_w6"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_w6">Error
- Output For cyl_bessel_i with compiler GNU C++ version 7.1.0 and library GSL
- 2.1 and test data Bessel Iv: Mathworld Data</a>
- </h5>
- <p>
- <a name="errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_GSL_2_1_Bessel_Iv_Mathworld_Data"></a>domain
- error<br> -4.99902, 2.125, 0.0267921<br> domain error<br> -5.5, 10, 597.578<br>
- domain error<br> -5.5, 100, 9.22363e+41<br> domain error<br> -10.0003,
- 0.000976562, 1.41474e+35<br> domain error<br> -10.0003, 50, 1.07153e+20<br>
- domain error<br> -141.4, 100, 2066.28<br>
- </p>
- <h5>
- <a name="special_function_error_rates_rep.error_logs.h35"></a>
- <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_i2"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_i2">Error
- Output For cyl_bessel_i (integer orders) with compiler GNU C++ version 7.1.0
- and library GSL 2.1 and test data Bessel In: Mathworld Data (Integer Version)</a>
- </h5>
- <p>
- <a name="errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_integer_orders__GSL_2_1_Bessel_In_Mathworld_Data_Integer_Version_"></a>underflow<br>
- 10, 1e-100, 0<br>
- </p>
- <h5>
- <a name="special_function_error_rates_rep.error_logs.h36"></a>
- <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_w7"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_w7">Error
- Output For cyl_bessel_i with compiler GNU C++ version 7.1.0 and library GSL
- 2.1 and test data Bessel In: Mathworld Data</a>
- </h5>
- <p>
- <a name="errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_GSL_2_1_Bessel_In_Mathworld_Data"></a>domain
- error<br> -2, 0, 0<br> domain error<br> -5, 100, 9.47009e+41<br> domain
- error<br> -5, -1, -0.000271463<br> domain error<br> 10, -5, 0.00458004<br>
- domain error<br> -100, -200, 4.35275e+74<br> underflow<br> 10, 1e-100,
- 0<br>
- </p>
- <h5>
- <a name="special_function_error_rates_rep.error_logs.h37"></a>
- <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_w8"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_w8">Error
- Output For cyl_bessel_i with compiler GNU C++ version 7.1.0 and library GSL
- 2.1 and test data Bessel I1: Mathworld Data</a>
- </h5>
- <p>
- <a name="errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_GSL_2_1_Bessel_I1_Mathworld_Data"></a>domain
- error<br> 1, -2, -1.59064<br> domain error<br> 1, -8, -399.873<br>
- domain error<br> 1, -10, -2670.99<br>
- </p>
- <h5>
- <a name="special_function_error_rates_rep.error_logs.h38"></a>
- <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_w9"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_w9">Error
- Output For cyl_bessel_i with compiler GNU C++ version 7.1.0 and library GSL
- 2.1 and test data Bessel I0: Mathworld Data</a>
- </h5>
- <p>
- <a name="errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_GSL_2_1_Bessel_I0_Mathworld_Data"></a>domain
- error<br> 0, -2, 2.27959<br> domain error<br> 0, -7, 168.594<br> domain
- error<br> 0, -1, 1.26607<br>
- </p>
- <h5>
- <a name="special_function_error_rates_rep.error_logs.h39"></a>
- <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_0"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_0">Error
- Output For cyl_bessel_i with compiler GNU C++ version 7.1.0 and library <cmath>
- and test data Bessel Iv: Mathworld Data (large values)</a>
- </h5>
- <p>
- <a name="errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_i__cmath__Bessel_Iv_Mathworld_Data_large_values_"></a>Bad
- argument in __cyl_bessel_i.<br> -1, 3.72917e-155, 1.86459e-155<br> Bad
- argument in __cyl_bessel_i.<br> -1.125, 3.72917e-155, -1.34964e+173<br>
- </p>
- <h5>
- <a name="special_function_error_rates_rep.error_logs.h40"></a>
- <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_1"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_1">Error
- Output For cyl_bessel_i with compiler GNU C++ version 7.1.0 and library <cmath>
- and test data Bessel Iv: Random Data</a>
- </h5>
- <p>
- <a name="errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_i__cmath__Bessel_Iv_Random_Data"></a>Bad
- argument in __cyl_bessel_i.<br> -80.4919, 24.7501, 4.18698e+28<br> Bad
- argument in __cyl_bessel_i.<br> -80.4919, 63.7722, 2.03248e+06<br> Bad
- argument in __cyl_bessel_i.<br> -74.6026, 24.7501, 7.20977e+23<br> Bad
- argument in __cyl_bessel_i.<br> -74.6026, 63.7722, 8.7549e+08<br> Bad argument
- in __cyl_bessel_i.<br> -72.9046, 24.7501, 1.04535e+22<br> Bad argument
- in __cyl_bessel_i.<br> -72.9046, 63.7722, 4.7162e+09<br> Bad argument in
- __cyl_bessel_i.<br> -62.3236, 24.7501, 3.65147e+14<br> Bad argument in
- __cyl_bessel_i.<br> -62.3236, 63.7722, 8.56683e+13<br> Bad argument in
- __cyl_bessel_i.<br> -55.7932, 24.7501, -7.70364e+09<br> Bad argument in
- __cyl_bessel_i.<br> -55.7932, 63.7722, 1.95969e+16<br> Bad argument in
- __cyl_bessel_i.<br> -44.3004, 9.50706, 2.93478e+22<br> Bad argument in
- __cyl_bessel_i.<br> -44.3004, 24.7501, 640.568<br> Bad argument in __cyl_bessel_i.<br>
- -44.3004, 63.7722, 8.05557e+19<br> Bad argument in __cyl_bessel_i.<br>
- -38.3666, 5.11399, 2.89105e+27<br> Bad argument in __cyl_bessel_i.<br>
- -38.3666, 9.50706, 8.80632e+16<br> Bad argument in __cyl_bessel_i.<br>
- -38.3666, 24.7501, 0.389004<br> Bad argument in __cyl_bessel_i.<br> -38.3666,
- 63.7722, 3.06303e+21<br>
- </p>
- <h5>
- <a name="special_function_error_rates_rep.error_logs.h41"></a>
- <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_2"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_2">Error
- Output For cyl_bessel_i with compiler GNU C++ version 7.1.0 and library <cmath>
- and test data Bessel Iv: Mathworld Data</a>
- </h5>
- <p>
- <a name="errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_i__cmath__Bessel_Iv_Mathworld_Data"></a>Bad
- argument in __cyl_bessel_i.<br> -4.99902, 2.125, 0.0267921<br> Bad argument
- in __cyl_bessel_i.<br> -5.5, 10, 597.578<br> Bad argument in __cyl_bessel_i.<br>
- -5.5, 100, 9.22363e+41<br> Bad argument in __cyl_bessel_i.<br> -10.0003,
- 0.000976562, 1.41474e+35<br> Bad argument in __cyl_bessel_i.<br> -10.0003,
- 50, 1.07153e+20<br> Bad argument in __cyl_bessel_i.<br> -141.4, 100, 2066.28<br>
- </p>
- <h5>
- <a name="special_function_error_rates_rep.error_logs.h42"></a>
- <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_i3"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_i3">Error
- Output For cyl_bessel_i (integer orders) with compiler GNU C++ version 7.1.0
- and library <cmath> and test data Bessel In: Mathworld Data (Integer
- Version)</a>
- </h5>
- <p>
- <a name="errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_i_integer_orders___cmath__Bessel_In_Mathworld_Data_Integer_Version_"></a>Bad
- argument in __cyl_bessel_i.<br> -2, 0, 0<br> Bad argument in __cyl_bessel_i.<br>
- -5, 100, 9.47009e+41<br> Bad argument in __cyl_bessel_i.<br> -5, -1, -0.000271463<br>
- Bad argument in __cyl_bessel_i.<br> 10, -5, 0.00458004<br> Bad argument
- in __cyl_bessel_i.<br> -100, -200, 4.35275e+74<br>
- </p>
- <h5>
- <a name="special_function_error_rates_rep.error_logs.h43"></a>
- <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_i4"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_i4">Error
- Output For cyl_bessel_i (integer orders) with compiler GNU C++ version 7.1.0
- and library <cmath> and test data Bessel I1: Mathworld Data (Integer
- Version)</a>
- </h5>
- <p>
- <a name="errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_i_integer_orders___cmath__Bessel_I1_Mathworld_Data_Integer_Version_"></a>Bad
- argument in __cyl_bessel_i.<br> 1, -2, -1.59064<br> Bad argument in __cyl_bessel_i.<br>
- 1, -8, -399.873<br> Bad argument in __cyl_bessel_i.<br> 1, -10, -2670.99<br>
- </p>
- <h5>
- <a name="special_function_error_rates_rep.error_logs.h44"></a>
- <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_i5"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_i5">Error
- Output For cyl_bessel_i (integer orders) with compiler GNU C++ version 7.1.0
- and library <cmath> and test data Bessel I0: Mathworld Data (Integer
- Version)</a>
- </h5>
- <p>
- <a name="errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_i_integer_orders___cmath__Bessel_I0_Mathworld_Data_Integer_Version_"></a>Bad
- argument in __cyl_bessel_i.<br> 0, -2, 2.27959<br> Bad argument in __cyl_bessel_i.<br>
- 0, -7, 168.594<br> Bad argument in __cyl_bessel_i.<br> 0, -1, 1.26607<br>
- </p>
- <h5>
- <a name="special_function_error_rates_rep.error_logs.h45"></a>
- <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_3"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_3">Error
- Output For cyl_bessel_i with compiler GNU C++ version 7.1.0 and library <cmath>
- and test data Bessel In: Mathworld Data</a>
- </h5>
- <p>
- <a name="errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_i__cmath__Bessel_In_Mathworld_Data"></a>Bad
- argument in __cyl_bessel_i.<br> -2, 0, 0<br> Bad argument in __cyl_bessel_i.<br>
- -5, 100, 9.47009e+41<br> Bad argument in __cyl_bessel_i.<br> -5, -1, -0.000271463<br>
- Bad argument in __cyl_bessel_i.<br> 10, -5, 0.00458004<br> Bad argument
- in __cyl_bessel_i.<br> -100, -200, 4.35275e+74<br>
- </p>
- <h5>
- <a name="special_function_error_rates_rep.error_logs.h46"></a>
- <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_4"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_4">Error
- Output For cyl_bessel_i with compiler GNU C++ version 7.1.0 and library <cmath>
- and test data Bessel I1: Mathworld Data</a>
- </h5>
- <p>
- <a name="errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_i__cmath__Bessel_I1_Mathworld_Data"></a>Bad
- argument in __cyl_bessel_i.<br> 1, -2, -1.59064<br> Bad argument in __cyl_bessel_i.<br>
- 1, -8, -399.873<br> Bad argument in __cyl_bessel_i.<br> 1, -10, -2670.99<br>
- </p>
- <h5>
- <a name="special_function_error_rates_rep.error_logs.h47"></a>
- <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_5"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_i_5">Error
- Output For cyl_bessel_i with compiler GNU C++ version 7.1.0 and library <cmath>
- and test data Bessel I0: Mathworld Data</a>
- </h5>
- <p>
- <a name="errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_i__cmath__Bessel_I0_Mathworld_Data"></a>Bad
- argument in __cyl_bessel_i.<br> 0, -2, 2.27959<br> Bad argument in __cyl_bessel_i.<br>
- 0, -7, 168.594<br> Bad argument in __cyl_bessel_i.<br> 0, -1, 1.26607<br>
- </p>
- <h5>
- <a name="special_function_error_rates_rep.error_logs.h48"></a>
- <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_w3"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_w3">Error
- Output For cyl_bessel_j with compiler GNU C++ version 7.1.0 and library GSL
- 2.1 and test data Bessel J: Random Data</a>
- </h5>
- <p>
- <a name="errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_GSL_2_1_Bessel_J_Random_Data"></a>underflow<br>
- 63.8868, 5.5381e-05, 0<br> underflow<br> 63.8868, 6.9304e-05, 0<br> underflow<br>
- 63.8868, 0.000232641, 0<br> underflow<br> 63.8868, 0.000448, 8.39912e-323<br>
- underflow<br> 63.8868, 0.000550287, 4.32897e-317<br>
- </p>
- <h5>
- <a name="special_function_error_rates_rep.error_logs.h49"></a>
- <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_w4"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_w4">Error
- Output For cyl_bessel_j with compiler GNU C++ version 7.1.0 and library GSL
- 2.1 and test data Bessel J: Mathworld Data (large values)</a>
- </h5>
- <p>
- <a name="errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_GSL_2_1_Bessel_J_Mathworld_Data_large_values_"></a>domain
- error<br> -0.5, 1.2459e-206, 7.14823e+102<br> domain error<br> -256,
- 8, 0<br> domain error<br> -2.5, 4, -0.0145679<br>
- </p>
- <h5>
- <a name="special_function_error_rates_rep.error_logs.h50"></a>
- <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_w5"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_w5">Error
- Output For cyl_bessel_j with compiler GNU C++ version 7.1.0 and library GSL
- 2.1 and test data Bessel J: Mathworld Data</a>
- </h5>
- <p>
- <a name="errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_GSL_2_1_Bessel_J_Mathworld_Data"></a>domain
- error<br> -5.5, 3.1416, -2.5582<br> domain error<br> -5.5, 10000, 0.00244984<br>
- domain error<br> -5.5, 10000, 0.00244984<br> domain error<br> -5.5, 1e+06,
- 0.000279243<br> domain error<br> -0.5, 101, 0.0708185<br> domain error<br>
- -10.0003, 0.000976562, 1.41474e+35<br> domain error<br> -10.0003, 15, -0.0902239<br>
- domain error<br> -10.0003, 100, -0.0547614<br> domain error<br> -10.0003,
- 20000, -0.00556869<br> domain error<br> -8.5, 12.5664, -0.257087<br>
- </p>
- <h5>
- <a name="special_function_error_rates_rep.error_logs.h51"></a>
- <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_i3"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_i3">Error
- Output For cyl_bessel_j (integer orders) with compiler GNU C++ version 7.1.0
- and library GSL 2.1 and test data Bessel JN: Mathworld Data (Integer Version)</a>
- </h5>
- <p>
- <a name="errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_integer_orders__GSL_2_1_Bessel_JN_Mathworld_Data_Integer_Version_"></a>underflow<br>
- 10, 1e-100, 0<br>
- </p>
- <h5>
- <a name="special_function_error_rates_rep.error_logs.h52"></a>
- <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_w6"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_w6">Error
- Output For cyl_bessel_j with compiler GNU C++ version 7.1.0 and library GSL
- 2.1 and test data Bessel JN: Mathworld Data</a>
- </h5>
- <p>
- <a name="errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_GSL_2_1_Bessel_JN_Mathworld_Data"></a>domain
- error<br> -1, 1.25, -0.510623<br> domain error<br> -2, 0, 0<br> domain
- error<br> 5, -10, 0.234062<br> domain error<br> -5, 1e+06, 0.000725964<br>
- domain error<br> -5, -1, 0.000249758<br> domain error<br> 10, -10, 0.207486<br>
- domain error<br> 10, -5, 0.0014678<br> domain error<br> -10, 1e+06, -0.000331079<br>
- underflow<br> 10, 1e-100, 0<br>
- </p>
- <h5>
- <a name="special_function_error_rates_rep.error_logs.h53"></a>
- <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_w7"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_w7">Error
- Output For cyl_bessel_j with compiler GNU C++ version 7.1.0 and library GSL
- 2.1 and test data Bessel J1: Mathworld Data</a>
- </h5>
- <p>
- <a name="errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_GSL_2_1_Bessel_J1_Mathworld_Data"></a>domain
- error<br> 1, -2, -0.576725<br> domain error<br> 1, -8, -0.234636<br>
- domain error<br> 1, -10, -0.0434727<br>
- </p>
- <h5>
- <a name="special_function_error_rates_rep.error_logs.h54"></a>
- <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_w8"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_w8">Error
- Output For cyl_bessel_j with compiler GNU C++ version 7.1.0 and library GSL
- 2.1 and test data Bessel J0: Mathworld Data</a>
- </h5>
- <p>
- <a name="errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_GSL_2_1_Bessel_J0_Mathworld_Data"></a>domain
- error<br> 0, -2, 0.223891<br> domain error<br> 0, -8, 0.171651<br>
- domain error<br> 0, -10, -0.245936<br>
- </p>
- <h5>
- <a name="special_function_error_rates_rep.error_logs.h55"></a>
- <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_w9"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_w9">Error
- Output For cyl_bessel_j with compiler GNU C++ version 7.1.0 and library <cmath>
- and test data Bessel J: Mathworld Data (large values)</a>
- </h5>
- <p>
- <a name="errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_j__cmath__Bessel_J_Mathworld_Data_large_values_"></a>Bad
- argument in __cyl_bessel_j.<br> -0.5, 1.2459e-206, 7.14823e+102<br> Bad
- argument in __cyl_bessel_j.<br> -256, 8, 1.46866e-353<br> Bad argument
- in __cyl_bessel_j.<br> -2.5, 4, -0.0145679<br>
- </p>
- <h5>
- <a name="special_function_error_rates_rep.error_logs.h56"></a>
- <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_0"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_0">Error
- Output For cyl_bessel_j with compiler GNU C++ version 7.1.0 and library <cmath>
- and test data Bessel J: Mathworld Data</a>
- </h5>
- <p>
- <a name="errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_j__cmath__Bessel_J_Mathworld_Data"></a>Bad
- argument in __cyl_bessel_j.<br> -5.5, 3.1416, -2.5582<br> Bad argument
- in __cyl_bessel_j.<br> -5.5, 10000, 0.00244984<br> Bad argument in __cyl_bessel_j.<br>
- -5.5, 10000, 0.00244984<br> Bad argument in __cyl_bessel_j.<br> -5.5, 1e+06,
- 0.000279243<br> Bad argument in __cyl_bessel_j.<br> -0.5, 101, 0.0708185<br>
- Bad argument in __cyl_bessel_j.<br> -10.0003, 0.000976562, 1.41474e+35<br>
- Bad argument in __cyl_bessel_j.<br> -10.0003, 15, -0.0902239<br> Bad argument
- in __cyl_bessel_j.<br> -10.0003, 100, -0.0547614<br> Bad argument in __cyl_bessel_j.<br>
- -10.0003, 20000, -0.00556869<br> Bad argument in __cyl_bessel_j.<br> -8.5,
- 12.5664, -0.257087<br>
- </p>
- <h5>
- <a name="special_function_error_rates_rep.error_logs.h57"></a>
- <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_i4"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_i4">Error
- Output For cyl_bessel_j (integer orders) with compiler GNU C++ version 7.1.0
- and library <cmath> and test data Bessel JN: Mathworld Data (Integer
- Version)</a>
- </h5>
- <p>
- <a name="errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_j_integer_orders___cmath__Bessel_JN_Mathworld_Data_Integer_Version_"></a>Bad
- argument in __cyl_bessel_j.<br> -1, 1.25, -0.510623<br> Bad argument in
- __cyl_bessel_j.<br> -2, 0, 0<br> Bad argument in __cyl_bessel_j.<br>
- 5, -10, 0.234062<br> Bad argument in __cyl_bessel_j.<br> -5, 1e+06, 0.000725964<br>
- Bad argument in __cyl_bessel_j.<br> -5, -1, 0.000249758<br> Bad argument
- in __cyl_bessel_j.<br> 10, -10, 0.207486<br> Bad argument in __cyl_bessel_j.<br>
- 10, -5, 0.0014678<br> Bad argument in __cyl_bessel_j.<br> -10, 1e+06, -0.000331079<br>
- CAUTION: Gross error found at entry 15.<br> Found: 0.0042409 Expected 0.00128318
- Error: 2.305<br> 1000, 100000, 0.00128318<br>
- </p>
- <h5>
- <a name="special_function_error_rates_rep.error_logs.h58"></a>
- <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_i5"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_i5">Error
- Output For cyl_bessel_j (integer orders) with compiler GNU C++ version 7.1.0
- and library <cmath> and test data Bessel J1: Mathworld Data (Integer
- Version)</a>
- </h5>
- <p>
- <a name="errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_j_integer_orders___cmath__Bessel_J1_Mathworld_Data_Integer_Version_"></a>Bad
- argument in __cyl_bessel_j.<br> 1, -2, -0.576725<br> Bad argument in __cyl_bessel_j.<br>
- 1, -8, -0.234636<br> Bad argument in __cyl_bessel_j.<br> 1, -10, -0.0434727<br>
- </p>
- <h5>
- <a name="special_function_error_rates_rep.error_logs.h59"></a>
- <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_i6"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_i6">Error
- Output For cyl_bessel_j (integer orders) with compiler GNU C++ version 7.1.0
- and library <cmath> and test data Bessel J0: Mathworld Data (Integer
- Version)</a>
- </h5>
- <p>
- <a name="errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_j_integer_orders___cmath__Bessel_J0_Mathworld_Data_Integer_Version_"></a>Bad
- argument in __cyl_bessel_j.<br> 0, -2, 0.223891<br> Bad argument in __cyl_bessel_j.<br>
- 0, -8, 0.171651<br> Bad argument in __cyl_bessel_j.<br> 0, -10, -0.245936<br>
- </p>
- <h5>
- <a name="special_function_error_rates_rep.error_logs.h60"></a>
- <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_1"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_1">Error
- Output For cyl_bessel_j with compiler GNU C++ version 7.1.0 and library <cmath>
- and test data Bessel JN: Mathworld Data</a>
- </h5>
- <p>
- <a name="errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_j__cmath__Bessel_JN_Mathworld_Data"></a>Bad
- argument in __cyl_bessel_j.<br> -1, 1.25, -0.510623<br> Bad argument in
- __cyl_bessel_j.<br> -2, 0, 0<br> Bad argument in __cyl_bessel_j.<br>
- 5, -10, 0.234062<br> Bad argument in __cyl_bessel_j.<br> -5, 1e+06, 0.000725964<br>
- Bad argument in __cyl_bessel_j.<br> -5, -1, 0.000249758<br> Bad argument
- in __cyl_bessel_j.<br> 10, -10, 0.207486<br> Bad argument in __cyl_bessel_j.<br>
- 10, -5, 0.0014678<br> Bad argument in __cyl_bessel_j.<br> -10, 1e+06, -0.000331079<br>
- CAUTION: Gross error found at entry 15.<br> Found: 0.0042409 Expected 0.00128318
- Error: 2.305<br> 1000, 100000, 0.00128318<br>
- </p>
- <h5>
- <a name="special_function_error_rates_rep.error_logs.h61"></a>
- <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_2"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_2">Error
- Output For cyl_bessel_j with compiler GNU C++ version 7.1.0 and library <cmath>
- and test data Bessel J1: Mathworld Data</a>
- </h5>
- <p>
- <a name="errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_j__cmath__Bessel_J1_Mathworld_Data"></a>Bad
- argument in __cyl_bessel_j.<br> 1, -2, -0.576725<br> Bad argument in __cyl_bessel_j.<br>
- 1, -8, -0.234636<br> Bad argument in __cyl_bessel_j.<br> 1, -10, -0.0434727<br>
- </p>
- <h5>
- <a name="special_function_error_rates_rep.error_logs.h62"></a>
- <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_3"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_j_3">Error
- Output For cyl_bessel_j with compiler GNU C++ version 7.1.0 and library <cmath>
- and test data Bessel J0: Mathworld Data</a>
- </h5>
- <p>
- <a name="errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_j__cmath__Bessel_J0_Mathworld_Data"></a>Bad
- argument in __cyl_bessel_j.<br> 0, -2, 0.223891<br> Bad argument in __cyl_bessel_j.<br>
- 0, -8, 0.171651<br> Bad argument in __cyl_bessel_j.<br> 0, -10, -0.245936<br>
- </p>
- <h5>
- <a name="special_function_error_rates_rep.error_logs.h63"></a>
- <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_k_wi"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_k_wi">Error
- Output For cyl_bessel_k with compiler GNU C++ version 7.1.0 and library GSL
- 2.1 and test data Bessel Kv: Random Data</a>
- </h5>
- <p>
- <a name="errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_k_GSL_2_1_Bessel_Kv_Random_Data"></a>domain
- error<br> -80.4919, 24.7501, 6.57902e+28<br> domain error<br> -80.4919,
- 63.7722, 2.39552e-09<br> domain error<br> -80.4919, 125.28, 3.06904e-45<br>
- domain error<br> -80.4919, 255.547, 2.30343e-107<br> domain error<br>
- -80.4919, 503.011, 1.20315e-217<br> domain error<br> -80.4919, 1007.46,
- 0<br> domain error<br> -80.4919, 1185.4, 0<br> domain error<br> -80.4919,
- 3534.52, 0<br> domain error<br> -80.4919, 8071.55, 0<br> domain error<br>
- -80.4919, 16229.2, 0<br> domain error<br> -80.4919, 32066.2, 0<br> domain
- error<br> -80.4919, 36367.9, 0<br> domain error<br> -74.6026, 24.7501,
- 1.19405e+24<br> domain error<br> -74.6026, 63.7722, 5.81897e-12<br> domain
- error<br> -74.6026, 125.28, 9.89214e-47<br> domain error<br> -74.6026,
- 255.547, 3.9726e-108<br> domain error<br> -74.6026, 503.011, 4.87462e-218<br>
- domain error<br> -74.6026, 1007.46, 0<br> domain error<br> -74.6026,
- 1185.4, 0<br> domain error<br> -74.6026, 3534.52, 0<br> domain error<br>
- -74.6026, 8071.55, 0<br> domain error<br> -74.6026, 16229.2, 0<br> domain
- error<br> -74.6026, 32066.2, 0<br> domain error<br> -74.6026, 36367.9,
- 0<br> domain error<br> -72.9046, 24.7501, 5.5618e+22<br> domain error<br>
- -72.9046, 63.7722, 1.09452e-12<br> domain error<br> -72.9046, 125.28, 3.8393e-47<br>
- domain error<br> -72.9046, 255.547, 2.45173e-108<br> domain error<br>
- -72.9046, 503.011, 3.80454e-218<br> domain error<br> -72.9046, 1007.46,
- 0<br> domain error<br> -72.9046, 1185.4, 0<br> domain error<br> -72.9046,
- 3534.52, 0<br> domain error<br> -72.9046, 8071.55, 0<br> domain error<br>
- -72.9046, 16229.2, 0<br> domain error<br> -72.9046, 32066.2, 0<br> domain
- error<br> -72.9046, 36367.9, 0<br> domain error<br> -62.3236, 24.7501,
- 6.74518e+14<br> domain error<br> -62.3236, 63.7722, 6.54531e-17<br> domain
- error<br> -62.3236, 125.28, 1.65653e-49<br> domain error<br> -62.3236,
- 255.547, 1.54767e-109<br> domain error<br> -62.3236, 503.011, 9.22721e-219<br>
- domain error<br> -62.3236, 1007.46, 0<br> domain error<br> -62.3236,
- 1185.4, 0<br> domain error<br> -62.3236, 3534.52, 0<br> domain error<br>
- -62.3236, 8071.55, 0<br> domain error<br> -62.3236, 16229.2, 0<br> domain
- error<br> -62.3236, 32066.2, 0<br> domain error<br> -62.3236, 36367.9,
- 0<br> domain error<br> -55.7932, 24.7501, 2.00028e+10<br> domain error<br>
- -55.7932, 63.7722, 3.01107e-19<br> domain error<br> -55.7932, 125.28, 8.54693e-51<br>
- domain error<br> -55.7932, 255.547, 3.47666e-110<br> domain error<br>
- -55.7932, 503.011, 4.29705e-219<br> domain error<br> -55.7932, 1007.46,
- 0<br> domain error<br> -55.7932, 1185.4, 0<br> domain error<br> -55.7932,
- 3534.52, 0<br> domain error<br> -55.7932, 8071.55, 0<br> domain error<br>
- -55.7932, 16229.2, 0<br> domain error<br> -55.7932, 32066.2, 0<br> domain
- error<br> -55.7932, 36367.9, 0<br> domain error<br> -44.3004, 9.50706,
- 5.6936e+22<br> domain error<br> -44.3004, 24.7501, 1242.73<br> domain
- error<br> -44.3004, 63.7722, 7.99341e-23<br> domain error<br> -44.3004,
- 125.28, 9.88149e-53<br> domain error<br> -44.3004, 255.547, 3.73007e-111<br>
- domain error<br> -44.3004, 503.011, 1.37367e-219<br> domain error<br>
- -44.3004, 1007.46, 0<br> domain error<br> -44.3004, 1185.4, 0<br> domain
- error<br> -44.3004, 3534.52, 0<br> domain error<br> -44.3004, 8071.55,
- 0<br> domain error<br> -44.3004, 16229.2, 0<br> domain error<br> -44.3004,
- 32066.2, 0<br> domain error<br> -44.3004, 36367.9, 0<br> domain error<br>
- -38.3666, 5.11399, 4.97154e+27<br> domain error<br> -38.3666, 9.50706,
- 1.51436e+17<br> domain error<br> -38.3666, 24.7501, 0.639495<br> domain
- error<br> -38.3666, 63.7722, 2.19334e-24<br> domain error<br> -38.3666,
- 125.28, 1.45351e-53<br> domain error<br> -38.3666, 255.547, 1.43713e-111<br>
- domain error<br> -38.3666, 503.011, 8.44445e-220<br> domain error<br>
- -38.3666, 1007.46, 0<br> domain error<br> -38.3666, 1185.4, 0<br> domain
- error<br> -38.3666, 3534.52, 0<br> domain error<br> -38.3666, 8071.55,
- 0<br> domain error<br> -38.3666, 16229.2, 0<br> domain error<br> -38.3666,
- 32066.2, 0<br> domain error<br> -38.3666, 36367.9, 0<br> underflow<br>
- 9.3763, 1007.46, 0<br> underflow<br> 9.3763, 1185.4, 0<br> underflow<br>
- 9.3763, 3534.52, 0<br> underflow<br> 9.3763, 8071.55, 0<br> underflow<br>
- 9.3763, 16229.2, 0<br> underflow<br> 9.3763, 32066.2, 0<br> underflow<br>
- 9.3763, 36367.9, 0<br> underflow<br> 9.44412, 1007.46, 0<br> underflow<br>
- 9.44412, 1185.4, 0<br> underflow<br> 9.44412, 3534.52, 0<br> underflow<br>
- 9.44412, 8071.55, 0<br> underflow<br> 9.44412, 16229.2, 0<br> underflow<br>
- 9.44412, 32066.2, 0<br> underflow<br> 9.44412, 36367.9, 0<br> underflow<br>
- 26.4719, 1007.46, 0<br> underflow<br> 26.4719, 1185.4, 0<br> underflow<br>
- 26.4719, 3534.52, 0<br> underflow<br> 26.4719, 8071.55, 0<br> underflow<br>
- 26.4719, 16229.2, 0<br> underflow<br> 26.4719, 32066.2, 0<br> underflow<br>
- 26.4719, 36367.9, 0<br> underflow<br> 62.9447, 1007.46, 0<br> underflow<br>
- 62.9447, 1185.4, 0<br> underflow<br> 62.9447, 3534.52, 0<br> underflow<br>
- 62.9447, 8071.55, 0<br> underflow<br> 62.9447, 16229.2, 0<br> underflow<br>
- *** FURTHER CONTENT HAS BEEN TRUNCATED FOR BREVITY ***<br>
- </p>
- <h5>
- <a name="special_function_error_rates_rep.error_logs.h64"></a>
- <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_k_w0"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_k_w0">Error
- Output For cyl_bessel_k with compiler GNU C++ version 7.1.0 and library GSL
- 2.1 and test data Bessel Kn: Random Data</a>
- </h5>
- <p>
- <a name="errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_k_GSL_2_1_Bessel_Kn_Random_Data"></a>underflow<br>
- 0, 1007.46, 0<br> underflow<br> 0, 1185.4, 0<br> underflow<br> 0, 3534.52,
- 0<br> underflow<br> 0, 8071.55, 0<br> underflow<br> 0, 16229.2, 0<br>
- underflow<br> 0, 32066.2, 0<br> underflow<br> 0, 36367.9, 0<br> underflow<br>
- 1, 1007.46, 0<br> underflow<br> 1, 1185.4, 0<br> underflow<br> 1, 3534.52,
- 0<br> underflow<br> 1, 8071.55, 0<br> underflow<br> 1, 16229.2, 0<br>
- underflow<br> 1, 32066.2, 0<br> underflow<br> 1, 36367.9, 0<br> underflow<br>
- 4, 1007.46, 0<br> underflow<br> 4, 1185.4, 0<br> underflow<br> 4, 3534.52,
- 0<br> underflow<br> 4, 8071.55, 0<br> underflow<br> 4, 16229.2, 0<br>
- underflow<br> 4, 32066.2, 0<br> underflow<br> 4, 36367.9, 0<br> underflow<br>
- 7, 1007.46, 0<br> underflow<br> 7, 1185.4, 0<br> underflow<br> 7, 3534.52,
- 0<br> underflow<br> 7, 8071.55, 0<br> underflow<br> 7, 16229.2, 0<br>
- underflow<br> 7, 32066.2, 0<br> underflow<br> 7, 36367.9, 0<br> underflow<br>
- 10, 1007.46, 0<br> underflow<br> 10, 1185.4, 0<br> underflow<br> 10,
- 3534.52, 0<br> underflow<br> 10, 8071.55, 0<br> underflow<br> 10, 16229.2,
- 0<br> underflow<br> 10, 32066.2, 0<br> underflow<br> 10, 36367.9, 0<br>
- underflow<br> 13, 1007.46, 0<br> underflow<br> 13, 1185.4, 0<br> underflow<br>
- 13, 3534.52, 0<br> underflow<br> 13, 8071.55, 0<br> underflow<br> 13,
- 16229.2, 0<br> underflow<br> 13, 32066.2, 0<br> underflow<br> 13, 36367.9,
- 0<br> underflow<br> 16, 1007.46, 0<br> underflow<br> 16, 1185.4, 0<br>
- underflow<br> 16, 3534.52, 0<br> underflow<br> 16, 8071.55, 0<br> underflow<br>
- 16, 16229.2, 0<br> underflow<br> 16, 32066.2, 0<br> underflow<br> 16,
- 36367.9, 0<br> underflow<br> 19, 1007.46, 0<br> underflow<br> 19, 1185.4,
- 0<br> underflow<br> 19, 3534.52, 0<br> underflow<br> 19, 8071.55, 0<br>
- underflow<br> 19, 16229.2, 0<br> underflow<br> 19, 32066.2, 0<br> underflow<br>
- 19, 36367.9, 0<br> underflow<br> 22, 1007.46, 0<br> underflow<br> 22,
- 1185.4, 0<br> underflow<br> 22, 3534.52, 0<br> underflow<br> 22, 8071.55,
- 0<br> underflow<br> 22, 16229.2, 0<br> underflow<br> 22, 32066.2, 0<br>
- underflow<br> 22, 36367.9, 0<br> underflow<br> 25, 1007.46, 0<br> underflow<br>
- 25, 1185.4, 0<br> underflow<br> 25, 3534.52, 0<br> underflow<br> 25,
- 8071.55, 0<br> underflow<br> 25, 16229.2, 0<br> underflow<br> 25, 32066.2,
- 0<br> underflow<br> 25, 36367.9, 0<br> underflow<br> 28, 1007.46, 0<br>
- underflow<br> 28, 1185.4, 0<br> underflow<br> 28, 3534.52, 0<br> underflow<br>
- 28, 8071.55, 0<br> underflow<br> 28, 16229.2, 0<br> underflow<br> 28,
- 32066.2, 0<br> underflow<br> 28, 36367.9, 0<br> underflow<br> 31, 1007.46,
- 0<br> underflow<br> 31, 1185.4, 0<br> underflow<br> 31, 3534.52, 0<br>
- underflow<br> 31, 8071.55, 0<br> underflow<br> 31, 16229.2, 0<br> underflow<br>
- 31, 32066.2, 0<br> underflow<br> 31, 36367.9, 0<br> underflow<br> 34,
- 1007.46, 0<br> underflow<br> 34, 1185.4, 0<br> underflow<br> 34, 3534.52,
- 0<br> underflow<br> 34, 8071.55, 0<br> underflow<br> 34, 16229.2, 0<br>
- underflow<br> 34, 32066.2, 0<br> underflow<br> 34, 36367.9, 0<br> underflow<br>
- 37, 1007.46, 0<br> underflow<br> 37, 1185.4, 0<br> underflow<br> 37,
- 3534.52, 0<br> underflow<br> 37, 8071.55, 0<br> underflow<br> 37, 16229.2,
- 0<br> underflow<br> 37, 32066.2, 0<br> underflow<br> 37, 36367.9, 0<br>
- underflow<br> 40, 1007.46, 0<br> underflow<br> 40, 1185.4, 0<br> underflow<br>
- 40, 3534.52, 0<br> underflow<br> 40, 8071.55, 0<br> underflow<br> 40,
- 16229.2, 0<br> underflow<br> 40, 32066.2, 0<br> underflow<br> 40, 36367.9,
- 0<br> underflow<br> 43, 1007.46, 0<br> underflow<br> 43, 1185.4, 0<br>
- underflow<br> 43, 3534.52, 0<br> underflow<br> 43, 8071.55, 0<br> underflow<br>
- 43, 16229.2, 0<br> underflow<br> 43, 32066.2, 0<br> underflow<br> 43,
- 36367.9, 0<br> underflow<br> 46, 1007.46, 0<br> underflow<br> 46, 1185.4,
- 0<br> underflow<br> 46, 3534.52, 0<br> underflow<br> 46, 8071.55, 0<br>
- underflow<br> 46, 16229.2, 0<br> underflow<br> 46, 32066.2, 0<br> underflow<br>
- 46, 36367.9, 0<br> underflow<br> 49, 1007.46, 0<br> underflow<br> 49,
- 1185.4, 0<br> underflow<br> 49, 3534.52, 0<br> underflow<br> 49, 8071.55,
- 0<br> underflow<br> 49, 16229.2, 0<br> underflow<br> 49, 32066.2, 0<br>
- underflow<br> 49, 36367.9, 0<br> underflow<br> 52, 1007.46, 0<br> underflow<br>
- 52, 1185.4, 0<br> underflow<br> 52, 3534.52, 0<br> underflow<br> 52,
- 8071.55, 0<br> underflow<br> 52, 16229.2, 0<br> underflow<br> 52, 32066.2,
- 0<br> underflow<br> 52, 36367.9, 0<br> underflow<br> 55, 1007.46, 0<br>
- underflow<br> 55, 1185.4, 0<br> underflow<br> 55, 3534.52, 0<br> underflow<br>
- 55, 8071.55, 0<br> underflow<br> 55, 16229.2, 0<br> underflow<br> 55,
- 32066.2, 0<br> underflow<br> 55, 36367.9, 0<br> underflow<br> 58, 1007.46,
- 0<br> underflow<br> 58, 1185.4, 0<br> underflow<br> 58, 3534.52, 0<br>
- underflow<br> 58, 8071.55, 0<br> underflow<br> 58, 16229.2, 0<br> underflow<br>
- 58, 32066.2, 0<br> underflow<br> 58, 36367.9, 0<br> underflow<br> 61,
- 1007.46, 0<br> underflow<br> 61, 1185.4, 0<br> underflow<br> 61, 3534.52,
- 0<br> underflow<br> 61, 8071.55, 0<br> underflow<br> 61, 16229.2, 0<br>
- underflow<br> 61, 32066.2, 0<br> underflow<br> 61, 36367.9, 0<br> underflow<br>
- 64, 1007.46, 0<br> underflow<br> 64, 1185.4, 0<br> underflow<br> 64,
- 3534.52, 0<br> underflow<br> 64, 8071.55, 0<br> underflow<br> 64, 16229.2,
- 0<br> underflow<br> 64, 32066.2, 0<br> underflow<br> 64, 36367.9, 0<br>
- underflow<br> 67, 1007.46, 0<br> underflow<br> 67, 1185.4, 0<br> underflow<br>
- 67, 3534.52, 0<br> underflow<br> 67, 8071.55, 0<br> underflow<br> 67,
- 16229.2, 0<br> *** FURTHER CONTENT HAS BEEN TRUNCATED FOR BREVITY ***<br>
- </p>
- <h5>
- <a name="special_function_error_rates_rep.error_logs.h65"></a>
- <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_k_w1"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_k_w1">Error
- Output For cyl_bessel_k with compiler GNU C++ version 7.1.0 and library GSL
- 2.1 and test data Bessel Kv: Mathworld Data (large values)</a>
- </h5>
- <p>
- <a name="errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_k_GSL_2_1_Bessel_Kv_Mathworld_Data_large_values_"></a>domain
- error<br> -1, 3.72917e-155, 2.68156e+154<br> domain error<br> -1.125,
- 3.72917e-155, 5.53984e+173<br>
- </p>
- <h5>
- <a name="special_function_error_rates_rep.error_logs.h66"></a>
- <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_k_w2"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_k_w2">Error
- Output For cyl_bessel_k with compiler GNU C++ version 7.1.0 and library GSL
- 2.1 and test data Bessel Kv: Mathworld Data</a>
- </h5>
- <p>
- <a name="errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_k_GSL_2_1_Bessel_Kv_Mathworld_Data"></a>domain
- error<br> -5.5, 10, 7.33045e-05<br> domain error<br> -5.5, 100, 5.41275e-45<br>
- domain error<br> -141.399, 50, 1.30185e+42<br>
- </p>
- <h5>
- <a name="special_function_error_rates_rep.error_logs.h67"></a>
- <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_k_w3"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_k_w3">Error
- Output For cyl_bessel_k with compiler GNU C++ version 7.1.0 and library GSL
- 2.1 and test data Bessel Kn: Mathworld Data</a>
- </h5>
- <p>
- <a name="errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_k_GSL_2_1_Bessel_Kn_Mathworld_Data"></a>domain
- error<br> -5, 100, 5.27326e-45<br> domain error<br> -10, 1, 1.80713e+08<br>
- domain error<br> -1000, 700, 6.51562e-31<br>
- </p>
- <h5>
- <a name="special_function_error_rates_rep.error_logs.h68"></a>
- <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_k_w4"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_k_w4">Error
- Output For cyl_bessel_k with compiler GNU C++ version 7.1.0 and library <cmath>
- and test data Bessel Kv: Random Data</a>
- </h5>
- <p>
- <a name="errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_k__cmath__Bessel_Kv_Random_Data"></a>Bad
- argument in __cyl_bessel_k.<br> -80.4919, 24.7501, 6.57902e+28<br> Bad
- argument in __cyl_bessel_k.<br> -80.4919, 63.7722, 2.39552e-09<br> Bad
- argument in __cyl_bessel_k.<br> -80.4919, 125.28, 3.06904e-45<br> Bad argument
- in __cyl_bessel_k.<br> -80.4919, 255.547, 2.30343e-107<br> Bad argument
- in __cyl_bessel_k.<br> -80.4919, 503.011, 1.20315e-217<br> Bad argument
- in __cyl_bessel_k.<br> -80.4919, 1007.46, 2.86537e-438<br> Bad argument
- in __cyl_bessel_k.<br> -80.4919, 1185.4, 8.63263e-516<br> Bad argument
- in __cyl_bessel_k.<br> -80.4919, 3534.52, 5.01367e-1537<br> Bad argument
- in __cyl_bessel_k.<br> -80.4919, 8071.55, 7.76555e-3508<br> Bad argument
- in __cyl_bessel_k.<br> -80.4919, 16229.2, 0<br> Bad argument in __cyl_bessel_k.<br>
- -80.4919, 32066.2, 0<br> Bad argument in __cyl_bessel_k.<br> -80.4919,
- 36367.9, 0<br> Bad argument in __cyl_bessel_k.<br> -74.6026, 24.7501, 1.19405e+24<br>
- Bad argument in __cyl_bessel_k.<br> -74.6026, 63.7722, 5.81897e-12<br>
- Bad argument in __cyl_bessel_k.<br> -74.6026, 125.28, 9.89214e-47<br> Bad
- argument in __cyl_bessel_k.<br> -74.6026, 255.547, 3.9726e-108<br> Bad
- argument in __cyl_bessel_k.<br> -74.6026, 503.011, 4.87462e-218<br> Bad
- argument in __cyl_bessel_k.<br> -74.6026, 1007.46, 1.82221e-438<br> Bad
- argument in __cyl_bessel_k.<br> -74.6026, 1185.4, 5.87506e-516<br> Bad
- argument in __cyl_bessel_k.<br> -74.6026, 3534.52, 4.40608e-1537<br> Bad
- argument in __cyl_bessel_k.<br> -74.6026, 8071.55, 7.3384e-3508<br> Bad
- argument in __cyl_bessel_k.<br> -74.6026, 16229.2, 0<br> Bad argument in
- __cyl_bessel_k.<br> -74.6026, 32066.2, 0<br> Bad argument in __cyl_bessel_k.<br>
- -74.6026, 36367.9, 0<br> Bad argument in __cyl_bessel_k.<br> -72.9046,
- 24.7501, 5.5618e+22<br> Bad argument in __cyl_bessel_k.<br> -72.9046, 63.7722,
- 1.09452e-12<br> Bad argument in __cyl_bessel_k.<br> -72.9046, 125.28, 3.8393e-47<br>
- Bad argument in __cyl_bessel_k.<br> -72.9046, 255.547, 2.45173e-108<br>
- Bad argument in __cyl_bessel_k.<br> -72.9046, 503.011, 3.80454e-218<br>
- Bad argument in __cyl_bessel_k.<br> -72.9046, 1007.46, 1.60949e-438<br>
- Bad argument in __cyl_bessel_k.<br> -72.9046, 1185.4, 5.28662e-516<br>
- Bad argument in __cyl_bessel_k.<br> -72.9046, 3534.52, 4.25273e-1537<br>
- Bad argument in __cyl_bessel_k.<br> -72.9046, 8071.55, 7.22542e-3508<br>
- Bad argument in __cyl_bessel_k.<br> -72.9046, 16229.2, 0<br> Bad argument
- in __cyl_bessel_k.<br> -72.9046, 32066.2, 0<br> Bad argument in __cyl_bessel_k.<br>
- -72.9046, 36367.9, 0<br> Bad argument in __cyl_bessel_k.<br> -62.3236,
- 24.7501, 6.74518e+14<br> Bad argument in __cyl_bessel_k.<br> -62.3236,
- 63.7722, 6.54531e-17<br> Bad argument in __cyl_bessel_k.<br> -62.3236,
- 125.28, 1.65653e-49<br> Bad argument in __cyl_bessel_k.<br> -62.3236, 255.547,
- 1.54767e-109<br> Bad argument in __cyl_bessel_k.<br> -62.3236, 503.011,
- 9.22721e-219<br> Bad argument in __cyl_bessel_k.<br> -62.3236, 1007.46,
- 7.91894e-439<br> Bad argument in __cyl_bessel_k.<br> -62.3236, 1185.4,
- 2.89281e-516<br> Bad argument in __cyl_bessel_k.<br> -62.3236, 3534.52,
- 3.4736e-1537<br> Bad argument in __cyl_bessel_k.<br> -62.3236, 8071.55,
- 6.6126e-3508<br> Bad argument in __cyl_bessel_k.<br> -62.3236, 16229.2,
- 0<br> Bad argument in __cyl_bessel_k.<br> -62.3236, 32066.2, 0<br> Bad
- argument in __cyl_bessel_k.<br> -62.3236, 36367.9, 0<br> Bad argument in
- __cyl_bessel_k.<br> -55.7932, 24.7501, 2.00028e+10<br> Bad argument in
- __cyl_bessel_k.<br> -55.7932, 63.7722, 3.01107e-19<br> Bad argument in
- __cyl_bessel_k.<br> -55.7932, 125.28, 8.54693e-51<br> Bad argument in __cyl_bessel_k.<br>
- -55.7932, 255.547, 3.47666e-110<br> Bad argument in __cyl_bessel_k.<br>
- -55.7932, 503.011, 4.29705e-219<br> Bad argument in __cyl_bessel_k.<br>
- -55.7932, 1007.46, 5.40242e-439<br> Bad argument in __cyl_bessel_k.<br>
- -55.7932, 1185.4, 2.08996e-516<br> Bad argument in __cyl_bessel_k.<br>
- -55.7932, 3534.52, 3.11458e-1537<br> Bad argument in __cyl_bessel_k.<br>
- -55.7932, 8071.55, 6.30409e-3508<br> Bad argument in __cyl_bessel_k.<br>
- -55.7932, 16229.2, 0<br> Bad argument in __cyl_bessel_k.<br> -55.7932,
- 32066.2, 0<br> Bad argument in __cyl_bessel_k.<br> -55.7932, 36367.9, 0<br>
- Bad argument in __cyl_bessel_k.<br> -44.3004, 9.50706, 5.6936e+22<br> Bad
- argument in __cyl_bessel_k.<br> -44.3004, 24.7501, 1242.73<br> Bad argument
- in __cyl_bessel_k.<br> -44.3004, 63.7722, 7.99341e-23<br> Bad argument
- in __cyl_bessel_k.<br> -44.3004, 125.28, 9.88149e-53<br> Bad argument in
- __cyl_bessel_k.<br> -44.3004, 255.547, 3.73007e-111<br> Bad argument in
- __cyl_bessel_k.<br> -44.3004, 503.011, 1.37367e-219<br> Bad argument in
- __cyl_bessel_k.<br> -44.3004, 1007.46, 3.05398e-439<br> Bad argument in
- __cyl_bessel_k.<br> *** FURTHER CONTENT HAS BEEN TRUNCATED FOR BREVITY ***<br>
- </p>
- <h5>
- <a name="special_function_error_rates_rep.error_logs.h69"></a>
- <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_k_w5"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_k_w5">Error
- Output For cyl_bessel_k with compiler GNU C++ version 7.1.0 and library <cmath>
- and test data Bessel Kv: Mathworld Data (large values)</a>
- </h5>
- <p>
- <a name="errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_k__cmath__Bessel_Kv_Mathworld_Data_large_values_"></a>Bad
- argument in __cyl_bessel_k.<br> -1, 3.72917e-155, 2.68156e+154<br> Bad
- argument in __cyl_bessel_k.<br> -1.125, 3.72917e-155, 5.53984e+173<br>
- </p>
- <h5>
- <a name="special_function_error_rates_rep.error_logs.h70"></a>
- <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_k_w6"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_k_w6">Error
- Output For cyl_bessel_k with compiler GNU C++ version 7.1.0 and library <cmath>
- and test data Bessel Kv: Mathworld Data</a>
- </h5>
- <p>
- <a name="errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_k__cmath__Bessel_Kv_Mathworld_Data"></a>Bad
- argument in __cyl_bessel_k.<br> -5.5, 10, 7.33045e-05<br> Bad argument
- in __cyl_bessel_k.<br> -5.5, 100, 5.41275e-45<br> Bad argument in __cyl_bessel_k.<br>
- -141.399, 50, 1.30185e+42<br>
- </p>
- <h5>
- <a name="special_function_error_rates_rep.error_logs.h71"></a>
- <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_k_in"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_k_in">Error
- Output For cyl_bessel_k (integer orders) with compiler GNU C++ version 7.1.0
- and library <cmath> and test data Bessel Kn: Mathworld Data (Integer
- Version)</a>
- </h5>
- <p>
- <a name="errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_k_integer_orders___cmath__Bessel_Kn_Mathworld_Data_Integer_Version_"></a>Bad
- argument in __cyl_bessel_k.<br> -5, 100, 5.27326e-45<br> Bad argument in
- __cyl_bessel_k.<br> -10, 1, 1.80713e+08<br> Bad argument in __cyl_bessel_k.<br>
- -1000, 700, 6.51562e-31<br>
- </p>
- <h5>
- <a name="special_function_error_rates_rep.error_logs.h72"></a>
- <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_k_w7"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_bessel_k_w7">Error
- Output For cyl_bessel_k with compiler GNU C++ version 7.1.0 and library <cmath>
- and test data Bessel Kn: Mathworld Data</a>
- </h5>
- <p>
- <a name="errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_k__cmath__Bessel_Kn_Mathworld_Data"></a>Bad
- argument in __cyl_bessel_k.<br> -5, 100, 5.27326e-45<br> Bad argument in
- __cyl_bessel_k.<br> -10, 1, 1.80713e+08<br> Bad argument in __cyl_bessel_k.<br>
- -1000, 700, 6.51562e-31<br>
- </p>
- <h5>
- <a name="special_function_error_rates_rep.error_logs.h73"></a>
- <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_neumann_wit"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_neumann_wit">Error
- Output For cyl_neumann with compiler GNU C++ version 7.1.0 and library GSL
- 2.1 and test data Yv: Mathworld Data (large values)</a>
- </h5>
- <p>
- <a name="errors_GNU_C_version_7_1_0_linux_double_cyl_neumann_GSL_2_1_Yv_Mathworld_Data_large_values_"></a>domain
- error<br> -0.5, 1.2459e-206, 8.90598e-104<br>
- </p>
- <h5>
- <a name="special_function_error_rates_rep.error_logs.h74"></a>
- <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_neumann_wi0"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_neumann_wi0">Error
- Output For cyl_neumann with compiler GNU C++ version 7.1.0 and library GSL
- 2.1 and test data Yv: Mathworld Data</a>
- </h5>
- <p>
- <a name="errors_GNU_C_version_7_1_0_linux_double_cyl_neumann_GSL_2_1_Yv_Mathworld_Data"></a>domain
- error<br> -5.5, 3.125, -0.0274994<br> domain error<br> -5.5, 10000, -0.00759344<br>
- domain error<br> -10.0003, 0.000976562, -1.50382e+38<br> domain error<br>
- -10.0003, 100, 0.0583042<br> domain error<br> -141.75, 100, -3.8101e+09<br>
- domain error<br> -8.5, 12.5664, 0.0436808<br>
- </p>
- <h5>
- <a name="special_function_error_rates_rep.error_logs.h75"></a>
- <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_neumann_wi1"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_neumann_wi1">Error
- Output For cyl_neumann with compiler GNU C++ version 7.1.0 and library GSL
- 2.1 and test data Yn: Mathworld Data</a>
- </h5>
- <p>
- <a name="errors_GNU_C_version_7_1_0_linux_double_cyl_neumann_GSL_2_1_Yn_Mathworld_Data"></a>domain
- error<br> -5, 1e+06, 0.000331052<br> domain error<br> -10, 1e+06, 0.000725952<br>
- domain error<br> -1000, 700, -1.88753e+77<br> domain error<br> -25, 8,
- 3.45114e+08<br>
- </p>
- <h5>
- <a name="special_function_error_rates_rep.error_logs.h76"></a>
- <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_neumann_wi2"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_neumann_wi2">Error
- Output For cyl_neumann with compiler GNU C++ version 7.1.0 and library <cmath>
- and test data Yv: Random Data</a>
- </h5>
- <p>
- <a name="errors_GNU_C_version_7_1_0_linux_long_double_cyl_neumann__cmath__Yv_Random_Data"></a>CAUTION:
- Gross error found at entry 394.<br> Found: -3.29903 Expected 0.0192842 Error:
- 1.18973e+4932<br> 125.28, 1007.46, 0.0192842<br> CAUTION: Gross error found
- at entry 395.<br> Found: 1.13543 Expected 0.0230358 Error: 48.2897<br>
- 125.28, 1185.4, 0.0230358<br> CAUTION: Gross error found at entry 396.<br>
- Found: 0.00119445 Expected 0.00460223 Error: 2.85302<br> 125.28, 3534.52,
- 0.00460223<br> CAUTION: Gross error found at entry 403.<br> Found: 1068
- Expected -0.00270959 Error: 1.18973e+4932<br> 255.547, 1007.46, -0.00270959<br>
- CAUTION: Gross error found at entry 404.<br> Found: -395.006 Expected 0.00738845
- Error: 1.18973e+4932<br> 255.547, 1185.4, 0.00738845<br> CAUTION: Gross
- error found at entry 405.<br> Found: 1.08701 Expected -0.000407036 Error:
- 1.18973e+4932<br> 255.547, 3534.52, -0.000407036<br> CAUTION: Gross error
- found at entry 406.<br> Found: 0.0232211 Expected 0.00886946 Error: 1.61809<br>
- 255.547, 8071.55, 0.00886946<br> CAUTION: Gross error found at entry 411.<br>
- Found: 65895.7 Expected -0.0158467 Error: 1.18973e+4932<br> 503.011, 1007.46,
- -0.0158467<br> CAUTION: Gross error found at entry 412.<br> Found: -123316
- Expected 0.00594357 Error: 1.18973e+4932<br> 503.011, 1185.4, 0.00594357<br>
- CAUTION: Gross error found at entry 413.<br> Found: -706.209 Expected 0.010151
- Error: 1.18973e+4932<br> 503.011, 3534.52, 0.010151<br> CAUTION: Gross
- error found at entry 414.<br> Found: -21.2081 Expected 0.00888375 Error:
- 1.18973e+4932<br> 503.011, 8071.55, 0.00888375<br> CAUTION: Gross error
- found at entry 415.<br> Found: 0.0272835 Expected 0.00552287 Error: 3.94008<br>
- 503.011, 16229.2, 0.00552287<br> CAUTION: Gross error found at entry 416.<br>
- Found: 0.0103324 Expected 0.00445559 Error: 1.31898<br> 503.011, 32066.2,
- 0.00445559<br> CAUTION: Gross error found at entry 417.<br> Found: 0.00540788
- Expected -0.00384344 Error: 1.18973e+4932<br> 503.011, 36367.9, -0.00384344<br>
- CAUTION: Gross error found at entry 418.<br> Found: 5.43091e+07 Expected
- -0.0772843 Error: 1.18973e+4932<br> 1007.46, 1007.46, -0.0772843<br> CAUTION:
- Gross error found at entry 419.<br> Found: -2.84383e+07 Expected 0.0304312
- Error: 1.18973e+4932<br> 1007.46, 1185.4, 0.0304312<br> CAUTION: Gross
- error found at entry 420.<br> Found: -61440.2 Expected -0.00474217 Error:
- 1.29562e+07<br> 1007.46, 3534.52, -0.00474217<br> CAUTION: Gross error
- found at entry 421.<br> Found: -4126.89 Expected -0.0074205 Error: 556146<br>
- 1007.46, 8071.55, -0.0074205<br> CAUTION: Gross error found at entry 422.<br>
- Found: -69.2831 Expected -0.00179572 Error: 38581.4<br> 1007.46, 16229.2,
- -0.00179572<br> CAUTION: Gross error found at entry 423.<br> Found: 2.32048
- Expected 0.000750053 Error: 3092.76<br> 1007.46, 32066.2, 0.000750053<br>
- CAUTION: Gross error found at entry 424.<br> Found: 3.90724 Expected 0.00305125
- Error: 1279.54<br> 1007.46, 36367.9, 0.00305125<br> CAUTION: Gross error
- found at entry 425.<br> Found: -1.83374e+08 Expected -7.25176e+28 Error:
- 3.95463e+20<br> 1185.4, 1007.46, -7.25176e+28<br> CAUTION: Gross error
- found at entry 426.<br> Found: 1.09822e+08 Expected -0.0732059 Error: 1.18973e+4932<br>
- 1185.4, 1185.4, -0.0732059<br> CAUTION: Gross error found at entry 427.<br>
- Found: 315632 Expected 0.000479585 Error: 6.58136e+08<br> 1185.4, 3534.52,
- 0.000479585<br> CAUTION: Gross error found at entry 428.<br> Found: 16815.6
- Expected 0.00174909 Error: 9.61391e+06<br> 1185.4, 8071.55, 0.00174909<br>
- CAUTION: Gross error found at entry 429.<br> Found: 133.356 Expected 0.00416288
- Error: 32033.6<br> 1185.4, 16229.2, 0.00416288<br> CAUTION: Gross error
- found at entry 430.<br> Found: -1.38401 Expected -0.000320056 Error: 4323.27<br>
- 1185.4, 32066.2, -0.000320056<br> CAUTION: Gross error found at entry 431.<br>
- Found: -17.7085 Expected -0.00417656 Error: 4238.96<br> 1185.4, 36367.9,
- -0.00417656<br>
- </p>
- <h5>
- <a name="special_function_error_rates_rep.error_logs.h77"></a>
- <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_neumann_wi3"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_neumann_wi3">Error
- Output For cyl_neumann with compiler GNU C++ version 7.1.0 and library <cmath>
- and test data Yv: Mathworld Data (large values)</a>
- </h5>
- <p>
- <a name="errors_GNU_C_version_7_1_0_linux_long_double_cyl_neumann__cmath__Yv_Mathworld_Data_large_values_"></a>Bad
- argument in __cyl_neumann_n.<br> -0.5, 1.2459e-206, 8.90598e-104<br>
- </p>
- <h5>
- <a name="special_function_error_rates_rep.error_logs.h78"></a>
- <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_neumann_wi4"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_neumann_wi4">Error
- Output For cyl_neumann with compiler GNU C++ version 7.1.0 and library <cmath>
- and test data Yv: Mathworld Data</a>
- </h5>
- <p>
- <a name="errors_GNU_C_version_7_1_0_linux_long_double_cyl_neumann__cmath__Yv_Mathworld_Data"></a>Bad
- argument in __cyl_neumann_n.<br> -5.5, 3.125, -0.0274994<br> Bad argument
- in __cyl_neumann_n.<br> -5.5, 10000, -0.00759344<br> Bad argument in __cyl_neumann_n.<br>
- -10.0003, 0.000976562, -1.50382e+38<br> Bad argument in __cyl_neumann_n.<br>
- -10.0003, 100, 0.0583042<br> Bad argument in __cyl_neumann_n.<br> -141.75,
- 100, -3.8101e+09<br> Bad argument in __cyl_neumann_n.<br> -8.5, 12.5664,
- 0.0436808<br>
- </p>
- <h5>
- <a name="special_function_error_rates_rep.error_logs.h79"></a>
- <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_neumann_int"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_neumann_int">Error
- Output For cyl_neumann (integer orders) with compiler GNU C++ version 7.1.0
- and library <cmath> and test data Yn: Mathworld Data (Integer Version)</a>
- </h5>
- <p>
- <a name="errors_GNU_C_version_7_1_0_linux_long_double_cyl_neumann_integer_orders___cmath__Yn_Mathworld_Data_Integer_Version_"></a>Bad
- argument in __cyl_neumann_n.<br> -5, 1e+06, 0.000331052<br> Bad argument
- in __cyl_neumann_n.<br> -10, 1e+06, 0.000725952<br> CAUTION: Gross error
- found at entry 7.<br> Found: 0.0540745 Expected 0.00217255 Error: 23.8899<br>
- 1000, 100000, 0.00217255<br> Bad argument in __cyl_neumann_n.<br> -1000,
- 700, -1.88753e+77<br> Bad argument in __cyl_neumann_n.<br> -25, 8, 3.45114e+08<br>
- </p>
- <h5>
- <a name="special_function_error_rates_rep.error_logs.h80"></a>
- <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_cyl_neumann_wi5"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_cyl_neumann_wi5">Error
- Output For cyl_neumann with compiler GNU C++ version 7.1.0 and library <cmath>
- and test data Yn: Mathworld Data</a>
- </h5>
- <p>
- <a name="errors_GNU_C_version_7_1_0_linux_long_double_cyl_neumann__cmath__Yn_Mathworld_Data"></a>Bad
- argument in __cyl_neumann_n.<br> -5, 1e+06, 0.000331052<br> Bad argument
- in __cyl_neumann_n.<br> -10, 1e+06, 0.000725952<br> CAUTION: Gross error
- found at entry 7.<br> Found: 0.0540745 Expected 0.00217255 Error: 23.8899<br>
- 1000, 100000, 0.00217255<br> Bad argument in __cyl_neumann_n.<br> -1000,
- 700, -1.88753e+77<br> Bad argument in __cyl_neumann_n.<br> -25, 8, 3.45114e+08<br>
- </p>
- <h5>
- <a name="special_function_error_rates_rep.error_logs.h81"></a>
- <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_beta_with_compi"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_beta_with_compi">Error
- Output For beta with compiler GNU C++ version 7.1.0 and library GSL 2.1 and
- test data Beta Function: Small Values</a>
- </h5>
- <p>
- <a name="errors_GNU_C_version_7_1_0_linux_double_beta_GSL_2_1_Beta_Function_Small_Values"></a>CAUTION:
- Found non-finite result, when a finite value was expected at entry 22<br>
- Found: inf Expected 5.69832e+154 Error: 1.79769e+308<br> 2.98334e-154, 1.86459e-155,
- 5.69832e+154<br> CAUTION: Gross error found at entry 22.<br> Found: inf
- Expected 5.69832e+154 Error: 1.79769e+308<br> 2.98334e-154, 1.86459e-155,
- 5.69832e+154<br>
- </p>
- <h5>
- <a name="special_function_error_rates_rep.error_logs.h82"></a>
- <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_ellint_rj_with_"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_ellint_rj_with_">Error
- Output For ellint_rj with compiler GNU C++ version 7.1.0 and library GSL 2.1
- and test data RJ: Random data</a>
- </h5>
- <p>
- <a name="errors_GNU_C_version_7_1_0_linux_double_ellint_rj_GSL_2_1_RJ_Random_data"></a>domain
- error<br> 1.77787e-31, 1.40657e+18, 10.046, -4.8298e-10, -2.51795e-10<br>
- domain error<br> 3.37448e-31, 4.65772e+22, 0.469831, -4.33756e-09, -2.95865e-11<br>
- domain error<br> 5.25297e-31, 5.85483e+25, 2.02482e-15, -1.87347e-28, 3.36445e+07<br>
- domain error<br> 6.22216e-31, 3.43401e+23, 0.673005, -2.7626e-13, -7.58898e-12<br>
- domain error<br> 6.26875e-31, 2.62568e-13, 1.06394e+24, -1.36451e+14, -6.70372e-25<br>
- domain error<br> 6.84599e-31, 3.57666e-29, 1.82191e+11, -3.63292e+08, -8.35235e-13<br>
- domain error<br> 8.90482e-31, 1.97093e-28, 1.14939e-31, -1.26424e-12, -6.39454e+26<br>
- domain error<br> 1.07374e-30, 1.70005e-12, 1.88773e-25, -1.16558e-29, 4.31668e+32<br>
- domain error<br> 1.17141e-30, 24.2523, 3.67522e+21, -4.79065e-22, 2.2702e-05<br>
- domain error<br> 1.64143e-30, 2.01978e-22, 2.58942e+12, -8.52649e-12, -2.82629e+06<br>
- domain error<br> 1.85141e-30, 0.0386712, 2.37846e-13, -1.57357e+15, -1.38574e-13<br>
- domain error<br> 2.70034e-30, 4.43896e-24, 7.54576e+16, -1.1436e-14, -1.10082e+07<br>
- domain error<br> 4.01162e-30, 2.73343e+23, 1.32333e+13, -1.86032e-07, -4.16626e-25<br>
- domain error<br> 4.13665e-30, 1.08034e-30, 3.13547e-16, -5.58099e-08, -5.14643e+16<br>
- domain error<br> 4.3728e-30, 7.79812e+12, 8.58894e+21, -4.58312e-24, 5.28901e-09<br>
- domain error<br> 5.6397e-30, 1.64768e+23, 9.64423e-15, -1.82207e+20, -1.62886e-30<br>
- domain error<br> 9.89841e-30, 9.69731e+10, 1.03263e+21, -0.00343967, -9.62714e-22<br>
- domain error<br> 1.3797e-29, 6.03357e+08, 5.62497e-15, -5.87235e+16, -5.80287e-20<br>
- domain error<br> 1.96963e-29, 3.22384e-25, 2.92187e+23, -3.80643e+27, -8.2513e-38<br>
- domain error<br> 2.00927e-29, 5.6976e-05, 1.16219e+25, -1.64129e-22, 0.00318397<br>
- domain error<br> 7.29506e-29, 5904.94, 9.93922e+10, -19.528, -1.60795e-09<br>
- domain error<br> 1.19698e-28, 1.66816e-22, 28472, -1.21137e-19, -5.84699e+17<br>
- domain error<br> 1.64095e-28, 2.13421e-21, 7.8914e-15, -1.77584e-07, -1.70156e+15<br>
- domain error<br> 2.03475e-28, 4.40987e+15, 28739.1, -9624.5, -1.29418e-12<br>
- domain error<br> 2.73113e-28, 1.08457e+19, 4.00674e+08, -5.70043e-11, 1.092e-17<br>
- domain error<br> 5.52633e-28, 1.45707e-17, 1.29411e-27, -1.67255e-15, -5.84881e+24<br>
- domain error<br> 5.61278e-28, 9.22881e-12, 8.64222e-13, -5.6282e+23, -4.57782e-18<br>
- domain error<br> 6.08465e-28, 1.32249e+26, 1.25536e-30, -1.89097e-14, -223.246<br>
- domain error<br> 9.50943e-28, 2.49682e-18, 0.000904584, -3.1419e-12, -2.44954e+14<br>
- domain error<br> 1.20779e-27, 35383.2, 1.35533e-15, -4.67834e-24, 3.20581e+15<br>
- domain error<br> 2.29822e-27, 3.35258e-16, 2.60689e+08, -9.99161e-20, -5.4924e+11<br>
- domain error<br> 3.0926e-27, 3.11839e-13, 3.37883e-23, -1.94349e+26, -3.55191e-19<br>
- domain error<br> 3.12803e-27, 1.15118e+16, 1.52495e+10, -4.2399e+13, -3.07515e-21<br>
- domain error<br> 4.49747e-27, 716.685, 1.69018e-23, -1.32558e-14, -9.2291e+13<br>
- domain error<br> 4.84575e-27, 3.44028e-27, 3.42665e+09, -812.399, -2.12767e-06<br>
- domain error<br> 5.81424e-27, 3.70845e-15, 3.69338e+11, -4.15794e+06, -2.95944e-11<br>
- domain error<br> 6.08654e-27, 1.23742e+08, 1.09124e-26, -2.19946e+16, -4.90896e-19<br>
- domain error<br> 7.71967e-27, 9.46115e-26, 1.24324e+25, -522800, -5.83203e-17<br>
- domain error<br> 9.20037e-27, 207550, 2.45782e-17, -6.06901e+29, -2.88945e-31<br>
- domain error<br> 1.75502e-26, 5.81507e+16, 8.83063e+21, -1.11214e-21, 1.57697e-11<br>
- domain error<br> 2.29965e-26, 2.9716e-21, 1.81059e-25, -5.23972e-08, -6.23302e+18<br>
- domain error<br> 2.32628e-26, 0.0655133, 1.62901e-21, -7.15441e-17, -9.88586e+17<br>
- domain error<br> 3.49194e-26, 2.53343e+14, 756.217, -1.3359e+10, -1.275e-16<br>
- domain error<br> 1.009e-25, 0.0694304, 1.20267e-14, -1.55746e-22, 2.10701e+17<br>
- domain error<br> 3.54771e-25, 1.67999e-27, 2.3917e+24, -9.98754e+25, -1.11704e-36<br>
- domain error<br> 6.31714e-25, 3.4594e-28, 6.37951e-24, -1.25529e-24, -9.56292e+35<br>
- domain error<br> 6.74086e-25, 2.47169e+12, 1.32962e+23, -6.78845e+06, -3.32861e-24<br>
- domain error<br> 1.8099e-24, 4.5215e-06, 8.66937e-11, -3.70795e-08, -1.41893e+11<br>
- domain error<br> 2.29798e-24, 9.30454e-30, 6.56584e-17, -9890.38, -373149<br>
- domain error<br> 2.88161e-24, 8.82377e-05, 1.57747e+21, -4.25068e-24, 2260.61<br>
- domain error<br> 3.25991e-24, 1.92923e+29, 3.09752e-05, -1.00986e+11, -1.25485e-24<br>
- domain error<br> 6.36705e-24, 2.8074e+22, 1.75569e-13, -1.53152e+24, -4.89823e-34<br>
- domain error<br> 7.90772e-24, 2.11611e-30, 1.42682e-07, -0.00296297, -5.38814e+07<br>
- domain error<br> 1.05302e-23, 4.83473e+26, 4.43149e-30, -1.56818e+13, -3.6836e-25<br>
- *** FURTHER CONTENT HAS BEEN TRUNCATED FOR BREVITY ***<br>
- </p>
- <h5>
- <a name="special_function_error_rates_rep.error_logs.h83"></a>
- <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_ellint_1_with_c"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_ellint_1_with_c">Error
- Output For ellint_1 with compiler GNU C++ version 7.1.0 and library <cmath>
- and test data Elliptic Integral F: Mathworld Data</a>
- </h5>
- <p>
- <a name="errors_GNU_C_version_7_1_0_linux_long_double_ellint_1__cmath__Elliptic_Integral_F_Mathworld_Data"></a>CAUTION:
- Gross error found at entry 9.<br> Found: -7.02862e+09 Expected 1.04181e+20
- Error: 1.18973e+4932<br> 1e+20, 0.390625, 1.04181e+20<br> CAUTION: Gross
- error found at entry 10.<br> Found: -9.3866e+09 Expected 1.39133e+50 Error:
- 1.18973e+4932<br> 1e+50, 0.875, 1.39133e+50<br>
- </p>
- <h5>
- <a name="special_function_error_rates_rep.error_logs.h84"></a>
- <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_ellint_2_comple"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_ellint_2_comple">Error
- Output For ellint_2 (complete) with compiler GNU C++ version 7.1.0 and library
- GSL 2.1 and test data Elliptic Integral E: Mathworld Data</a>
- </h5>
- <p>
- <a name="errors_GNU_C_version_7_1_0_linux_double_ellint_2_complete__GSL_2_1_Elliptic_Integral_E_Mathworld_Data"></a>domain
- error<br> -1, 1<br>
- </p>
- <h5>
- <a name="special_function_error_rates_rep.error_logs.h85"></a>
- <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_ellint_2_with_c"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_ellint_2_with_c">Error
- Output For ellint_2 with compiler GNU C++ version 7.1.0 and library <cmath>
- and test data Elliptic Integral E: Mathworld Data</a>
- </h5>
- <p>
- <a name="errors_GNU_C_version_7_1_0_linux_long_double_ellint_2__cmath__Elliptic_Integral_E_Mathworld_Data"></a>CAUTION:
- Gross error found at entry 7.<br> Found: -6.3027e+09 Expected 9.34215e+09
- Error: 1.18973e+4932<br> 1e+10, -0.5, 9.34215e+09<br> CAUTION: Gross error
- found at entry 8.<br> Found: -6.48129e+09 Expected 7.08861e+19 Error: 1.18973e+4932<br>
- 7.3787e+19, 0.390625, 7.08861e+19<br> CAUTION: Gross error found at entry
- 9.<br> Found: -5.13973e+09 Expected 7.1259e+49 Error: 1.18973e+4932<br>
- 9.35361e+49, 0.878906, 7.1259e+49<br>
- </p>
- <h5>
- <a name="special_function_error_rates_rep.error_logs.h86"></a>
- <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_ellint_3_comple"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_ellint_3_comple">Error
- Output For ellint_3 (complete) with compiler GNU C++ version 7.1.0 and library
- GSL 2.1 and test data Complete Elliptic Integral PI: Mathworld Data</a>
- </h5>
- <p>
- <a name="errors_GNU_C_version_7_1_0_linux_double_ellint_3_complete__GSL_2_1_Complete_Elliptic_Integral_PI_Mathworld_Data"></a>domain
- error<br> -4.14952e+180, 0.5, 7.71119e-91<br>
- </p>
- <h5>
- <a name="special_function_error_rates_rep.error_logs.h87"></a>
- <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_ellint_3_with_c"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_ellint_3_with_c">Error
- Output For ellint_3 with compiler GNU C++ version 7.1.0 and library GSL 2.1
- and test data Elliptic Integral PI: Mathworld Data</a>
- </h5>
- <p>
- <a name="errors_GNU_C_version_7_1_0_linux_double_ellint_3_GSL_2_1_Elliptic_Integral_PI_Mathworld_Data"></a>domain
- error<br> 1.125, 10, 0.25, 0.662468<br> domain error<br> 1.125, 3, 0.25,
- -0.142697<br> domain error<br> 1.00391, 21.5, 0.125, -0.535406<br> domain
- error<br> 1, 2, 0.5, -2.87535<br> domain error<br> 1, -2, 0.5, 2.87535<br>
- domain error<br> 1, 2, 6.22302e-61, -2.18504<br> domain error<br> 1,
- -2, 6.22302e-61, 2.18504<br> domain error<br> 20, 3.14257, 0.5, 0.000975941<br>
- domain error<br> 20, -3.14257, 0.5, -0.000975941<br> domain error<br>
- 1.01562, 1.6958, 0.5, -27.1647<br> domain error<br> 1.01562, -1.6958, 0.5,
- 27.1647<br>
- </p>
- <h5>
- <a name="special_function_error_rates_rep.error_logs.h88"></a>
- <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_ellint_3_compl0"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_ellint_3_compl0">Error
- Output For ellint_3 (complete) with compiler GNU C++ version 7.1.0 and library
- <cmath> and test data Complete Elliptic Integral PI: Random Data</a>
- </h5>
- <p>
- <a name="errors_GNU_C_version_7_1_0_linux_long_double_ellint_3_complete___cmath__Complete_Elliptic_Integral_PI_Random_Data"></a>Argument
- too small in __ellint_rj<br> -87.1743, 0.126987, 0.167413<br> Argument
- too small in __ellint_rj<br> -87.1743, 0.135477, 0.167431<br> Argument
- too small in __ellint_rj<br> -87.1743, 0.221034, 0.167683<br> Argument
- too small in __ellint_rj<br> -87.1743, 0.308167, 0.168078<br> Argument
- too small in __ellint_rj<br> -87.1743, 0.632359, 0.17122<br> Argument too
- small in __ellint_rj<br> -87.1743, 0.814724, 0.175341<br> Argument too
- small in __ellint_rj<br> -87.1743, 0.835009, 0.176056<br> Argument too
- small in __ellint_rj<br> -87.1743, 0.905792, 0.179501<br> Argument too
- small in __ellint_rj<br> -87.1743, 0.913376, 0.180014<br> Argument too
- small in __ellint_rj<br> -87.1743, 0.968868, 0.186162<br> Argument too
- small in __ellint_rj<br> -86.3168, 0.126987, 0.168233<br> Argument too
- small in __ellint_rj<br> -86.3168, 0.135477, 0.168252<br> Argument too
- small in __ellint_rj<br> -86.3168, 0.221034, 0.168506<br> Argument too
- small in __ellint_rj<br> -86.3168, 0.308167, 0.168905<br> Argument too
- small in __ellint_rj<br> -86.3168, 0.632359, 0.172077<br> Argument too
- small in __ellint_rj<br> -86.3168, 0.814724, 0.176237<br> Argument too
- small in __ellint_rj<br> -86.3168, 0.835009, 0.176958<br> Argument too
- small in __ellint_rj<br> -86.3168, 0.905792, 0.180437<br> Argument too
- small in __ellint_rj<br> -86.3168, 0.913376, 0.180955<br> Argument too
- small in __ellint_rj<br> -86.3168, 0.968868, 0.187163<br> Argument too
- small in __ellint_rj<br> -77.6756, 0.126987, 0.177238<br> Argument too
- small in __ellint_rj<br> -77.6756, 0.135477, 0.177258<br> Argument too
- small in __ellint_rj<br> -77.6756, 0.221034, 0.17754<br> Argument too small
- in __ellint_rj<br> -77.6756, 0.308167, 0.17798<br> Argument too small in
- __ellint_rj<br> -77.6756, 0.632359, 0.181485<br> Argument too small in
- __ellint_rj<br> -77.6756, 0.814724, 0.186089<br> Argument too small in
- __ellint_rj<br> -77.6756, 0.835009, 0.186888<br> Argument too small in
- __ellint_rj<br> -77.6756, 0.905792, 0.190742<br> Argument too small in
- __ellint_rj<br> -77.6756, 0.913376, 0.191315<br> Argument too small in
- __ellint_rj<br> -77.6756, 0.968868, 0.1982<br> Argument too small in __ellint_rj<br>
- -68.8751, 0.126987, 0.188077<br> Argument too small in __ellint_rj<br>
- -68.8751, 0.135477, 0.188099<br> Argument too small in __ellint_rj<br>
- -68.8751, 0.221034, 0.188414<br> Argument too small in __ellint_rj<br>
- -68.8751, 0.308167, 0.188907<br> Argument too small in __ellint_rj<br>
- -68.8751, 0.632359, 0.192834<br> Argument too small in __ellint_rj<br>
- -68.8751, 0.814724, 0.198<br> Argument too small in __ellint_rj<br> -68.8751,
- 0.835009, 0.198896<br> Argument too small in __ellint_rj<br> -68.8751,
- 0.905792, 0.203226<br> Argument too small in __ellint_rj<br> -68.8751,
- 0.913376, 0.203871<br> Argument too small in __ellint_rj<br> -68.8751,
- 0.968868, 0.211615<br> Argument too small in __ellint_rj<br> -36.1317,
- 0.126987, 0.258074<br> Argument too small in __ellint_rj<br> -36.1317,
- 0.135477, 0.258115<br> Argument too small in __ellint_rj<br> -36.1317,
- 0.221034, 0.258686<br> Argument too small in __ellint_rj<br> -36.1317,
- 0.308167, 0.259579<br> Argument too small in __ellint_rj<br> -36.1317,
- 0.632359, 0.266738<br> Argument too small in __ellint_rj<br> -36.1317,
- 0.814724, 0.276242<br> Argument too small in __ellint_rj<br> -36.1317,
- 0.835009, 0.2779<br> Argument too small in __ellint_rj<br> -36.1317, 0.905792,
- 0.285938<br> Argument too small in __ellint_rj<br> -36.1317, 0.913376,
- 0.287139<br> Argument too small in __ellint_rj<br> -36.1317, 0.968868,
- 0.301608<br> Argument too small in __ellint_rj<br> -17.7129, 0.126987,
- 0.363673<br> Argument too small in __ellint_rj<br> -17.7129, 0.135477,
- 0.36375<br> Argument too small in __ellint_rj<br> -17.7129, 0.221034, 0.364822<br>
- Argument too small in __ellint_rj<br> -17.7129, 0.308167, 0.366503<br>
- Argument too small in __ellint_rj<br> -17.7129, 0.632359, 0.380066<br>
- Argument too small in __ellint_rj<br> -17.7129, 0.814724, 0.398311<br>
- Argument too small in __ellint_rj<br> -17.7129, 0.835009, 0.401518<br>
- Argument too small in __ellint_rj<br> -17.7129, 0.905792, 0.417145<br>
- Argument too small in __ellint_rj<br> -17.7129, 0.913376, 0.41949<br> Argument
- too small in __ellint_rj<br> -17.7129, 0.968868, 0.447893<br> Argument
- too small in __ellint_rj<br> -15.6641, 0.126987, 0.385409<br> Argument
- too small in __ellint_rj<br> -15.6641, 0.135477, 0.385495<br> Argument
- too small in __ellint_rj<br> -15.6641, 0.221034, 0.386686<br> Argument
- too small in __ellint_rj<br> -15.6641, 0.308167, 0.388553<br> Argument
- too small in __ellint_rj<br> -15.6641, 0.632359, 0.403643<br> Argument
- too small in __ellint_rj<br> *** FURTHER CONTENT HAS BEEN TRUNCATED FOR BREVITY
- ***<br>
- </p>
- <h5>
- <a name="special_function_error_rates_rep.error_logs.h89"></a>
- <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_ellint_3_compl1"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_ellint_3_compl1">Error
- Output For ellint_3 (complete) with compiler GNU C++ version 7.1.0 and library
- <cmath> and test data Complete Elliptic Integral PI: Mathworld Data</a>
- </h5>
- <p>
- <a name="errors_GNU_C_version_7_1_0_linux_long_double_ellint_3_complete___cmath__Complete_Elliptic_Integral_PI_Mathworld_Data"></a>CAUTION:
- Gross error found at entry 3.<br> Found: 1.28255 Expected 2.22144 Error:
- 0.732051<br> 0.5, 0, 2.22144<br> Argument too small in __ellint_rj<br>
- -4, 0.3, 0.712709<br> Argument too small in __ellint_rj<br> -100000, -0.5,
- 0.00496945<br> Argument too small in __ellint_rj<br> -1e+10, -0.75, 1.5708e-05<br>
- CAUTION: Gross error found at entry 8.<br> Found: 1.45615 Expected 101.045
- Error: 68.3919<br> 0.999023, -0.875, 101.045<br> Argument too small in
- __ellint_rj<br> -4.14952e+180, 0.5, 7.71119e-91<br>
- </p>
- <h5>
- <a name="special_function_error_rates_rep.error_logs.h90"></a>
- <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_ellint_3_with_0"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_ellint_3_with_0">Error
- Output For ellint_3 with compiler GNU C++ version 7.1.0 and library <cmath>
- and test data Elliptic Integral PI: Large Random Data</a>
- </h5>
- <p>
- <a name="errors_GNU_C_version_7_1_0_linux_long_double_ellint_3__cmath__Elliptic_Integral_PI_Large_Random_Data"></a>Argument
- too small in __ellint_rj<br> -88.2952, -8.04919, 0.814724, -0.874724<br>
- Argument too small in __ellint_rj<br> -88.2952, -7.46026, 0.135477, -0.827189<br>
- Argument too small in __ellint_rj<br> -88.2952, -7.29046, 0.905792, -0.877476<br>
- Argument too small in __ellint_rj<br> -88.2952, -6.23236, 0.835009, -0.652152<br>
- Argument too small in __ellint_rj<br> -88.2952, -5.57932, 0.126987, -0.512276<br>
- Argument too small in __ellint_rj<br> -88.2952, -4.43004, 0.968868, -0.543324<br>
- Argument too small in __ellint_rj<br> -88.2952, -3.83666, 0.913376, -0.513389<br>
- Argument too small in __ellint_rj<br> -88.2952, 0.93763, 0.221034, 0.158243<br>
- Argument too small in __ellint_rj<br> -88.2952, 0.944412, 0.632359, 0.160101<br>
- Argument too small in __ellint_rj<br> -88.2952, 2.64719, 0.308167, 0.188127<br>
- Argument too small in __ellint_rj<br> -88.2952, 6.29447, 0.0975404, 0.676465<br>
- Argument too small in __ellint_rj<br> -88.2952, 6.70017, 0.547221, 0.817785<br>
- Argument too small in __ellint_rj<br> -88.2952, 8.11584, 0.278498, 0.837452<br>
- Argument too small in __ellint_rj<br> -88.2952, 8.26752, 0.188382, 0.837571<br>
- Argument too small in __ellint_rj<br> -88.2952, 9.15014, 0.546881, 0.885365<br>
- Argument too small in __ellint_rj<br> -88.2952, 9.29777, 0.992881, 1.06701<br>
- Argument too small in __ellint_rj<br> -88.2952, 9.3539, 0.957507, 1.03573<br>
- Argument too small in __ellint_rj<br> -88.2952, 9.37736, 0.996461, 1.13933<br>
- Argument too small in __ellint_rj<br> -88.2952, 9.85763, 0.964889, 1.24906<br>
- Argument too small in __ellint_rj<br> -88.2952, 9.92923, 0.967695, 1.25621<br>
- Argument too small in __ellint_rj<br> -86.8166, -8.04919, 0.157613, -0.841405<br>
- Argument too small in __ellint_rj<br> -86.8166, -7.46026, 0.725839, -0.859877<br>
- Argument too small in __ellint_rj<br> -86.8166, -7.29046, 0.970593, -0.914439<br>
- Argument too small in __ellint_rj<br> -86.8166, -6.23236, 0.98111, -0.710627<br>
- Argument too small in __ellint_rj<br> -86.8166, -5.57932, 0.957167, -0.58106<br>
- Argument too small in __ellint_rj<br> -86.8166, -4.43004, 0.109862, -0.499839<br>
- Argument too small in __ellint_rj<br> -86.8166, -3.83666, 0.485376, -0.494286<br>
- Argument too small in __ellint_rj<br> -86.8166, 0.93763, 0.798106, 0.162644<br>
- Argument too small in __ellint_rj<br> -86.8166, 0.944412, 0.80028, 0.16282<br>
- Argument too small in __ellint_rj<br> -86.8166, 2.64719, 0.297029, 0.18978<br>
- Argument too small in __ellint_rj<br> -86.8166, 6.29447, 0.141886, 0.682392<br>
- Argument too small in __ellint_rj<br> -86.8166, 6.70017, 0.00478348, 0.812885<br>
- Argument too small in __ellint_rj<br> -86.8166, 8.11584, 0.421761, 0.849249<br>
- Argument too small in __ellint_rj<br> -86.8166, 8.26752, 0.112465, 0.843648<br>
- Argument too small in __ellint_rj<br> -86.8166, 9.15014, 0.915736, 0.953733<br>
- Argument too small in __ellint_rj<br> -86.8166, 9.29777, 0.639763, 0.936743<br>
- Argument too small in __ellint_rj<br> -86.8166, 9.3539, 0.792207, 0.987359<br>
- Argument too small in __ellint_rj<br> -86.8166, 9.37736, 0.878431, 1.02525<br>
- Argument too small in __ellint_rj<br> -86.8166, 9.85763, 0.959492, 1.25508<br>
- Argument too small in __ellint_rj<br> -86.8166, 9.92923, 0.503663, 1.16735<br>
- Argument too small in __ellint_rj<br> -84.7616, -8.04919, 0.655741, -0.873305<br>
- Argument too small in __ellint_rj<br> -84.7616, -7.46026, 0.797929, -0.879044<br>
- Argument too small in __ellint_rj<br> -84.7616, -7.29046, 0.0357117, -0.840785<br>
- Argument too small in __ellint_rj<br> -84.7616, -6.23236, 0.361294, -0.635502<br>
- Argument too small in __ellint_rj<br> -84.7616, -5.57932, 0.849129, -0.558231<br>
- Argument too small in __ellint_rj<br> -84.7616, -4.43004, 0.211924, -0.506533<br>
- Argument too small in __ellint_rj<br> -84.7616, -3.83666, 0.933993, -0.527681<br>
- Argument too small in __ellint_rj<br> -84.7616, 0.93763, 0.68136, 0.163458<br>
- Argument too small in __ellint_rj<br> -84.7616, 0.944412, 0.678735, 0.163582<br>
- Argument too small in __ellint_rj<br> -84.7616, 2.64719, 0.398739, 0.193458<br>
- Argument too small in __ellint_rj<br> -84.7616, 6.29447, 0.75774, 0.716086<br>
- Argument too small in __ellint_rj<br> -84.7616, 6.70017, 0.740647, 0.847849<br>
- Argument too small in __ellint_rj<br> -84.7616, 8.11584, 0.743132, 0.883827<br>
- Argument too small in __ellint_rj<br> -84.7616, 8.26752, 0.474759, 0.864181<br>
- Argument too small in __ellint_rj<br> -84.7616, 9.15014, 0.392227, 0.895646<br>
- Argument too small in __ellint_rj<br> -84.7616, 9.29777, 0.422088, 0.933423<br>
- Argument too small in __ellint_rj<br> *** FURTHER CONTENT HAS BEEN TRUNCATED
- FOR BREVITY ***<br>
- </p>
- <h5>
- <a name="special_function_error_rates_rep.error_logs.h91"></a>
- <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_ellint_3_with_1"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_ellint_3_with_1">Error
- Output For ellint_3 with compiler GNU C++ version 7.1.0 and library <cmath>
- and test data Elliptic Integral PI: Random Data</a>
- </h5>
- <p>
- <a name="errors_GNU_C_version_7_1_0_linux_long_double_ellint_3__cmath__Elliptic_Integral_PI_Random_Data"></a>CAUTION:
- Gross error found at entry 150.<br> Found: 1.09748 Expected 1.76311 Error:
- 0.606506<br> 0.546881, 1.27977, 0.349984, 1.76311<br> CAUTION: Gross error
- found at entry 151.<br> Found: 1.39529 Expected 2.4686 Error: 0.769232<br>
- 0.546881, 1.31163, 0.907365, 2.4686<br> CAUTION: Gross error found at entry
- 152.<br> Found: 1.17627 Expected 2.03097 Error: 0.726615<br> 0.546881,
- 1.42281, 0.196595, 2.03097<br> CAUTION: Gross error found at entry 153.<br>
- Found: 1.47192 Expected 2.76894 Error: 0.881179<br> 0.546881, 1.43473, 0.848468,
- 2.76894<br> CAUTION: Gross error found at entry 154.<br> Found: 1.23674
- Expected 2.22733 Error: 0.800966<br> 0.546881, 1.50405, 0.251084, 2.22733<br>
- CAUTION: Gross error found at entry 155.<br> Found: 1.87704 Expected 3.98415
- Error: 1.12257<br> 0.546881, 1.51564, 0.955018, 3.98415<br> CAUTION: Gross
- error found at entry 156.<br> Found: 1.35817 Expected 2.53989 Error: 0.870091<br>
- 0.546881, 1.52005, 0.616045, 2.53989<br> CAUTION: Gross error found at entry
- 157.<br> Found: 1.48427 Expected 2.87082 Error: 0.934166<br> 0.546881,
- 1.52189, 0.778898, 2.87082<br> CAUTION: Gross error found at entry 158.<br>
- Found: 1.32687 Expected 2.48679 Error: 0.874176<br> 0.546881, 1.55961, 0.473289,
- 2.48679<br> CAUTION: Gross error found at entry 159.<br> Found: 2.37485
- Expected 5.58805 Error: 1.35301<br> 0.546881, 1.56524, 0.98746, 5.58805<br>
- CAUTION: Gross error found at entry 170.<br> Found: 1.08889 Expected 1.74565
- Error: 0.603142<br> 0.547221, 1.27977, 0.285839, 1.74565<br> CAUTION: Gross
- error found at entry 171.<br> Found: 1.21346 Expected 2.03956 Error: 0.680778<br>
- 0.547221, 1.31163, 0.67982, 2.03956<br> CAUTION: Gross error found at entry
- 172.<br> Found: 1.36407 Expected 2.48392 Error: 0.820965<br> 0.547221,
- 1.42281, 0.7572, 2.48392<br> CAUTION: Gross error found at entry 173.<br>
- Found: 1.21442 Expected 2.12881 Error: 0.752947<br> 0.547221, 1.43473, 0.39232,
- 2.12881<br> CAUTION: Gross error found at entry 174.<br> Found: 1.4409
- Expected 2.74399 Error: 0.904352<br> 0.547221, 1.50405, 0.753729, 2.74399<br>
- CAUTION: Gross error found at entry 175.<br> Found: 1.32796 Expected 2.46156
- Error: 0.853642<br> 0.547221, 1.51564, 0.561557, 2.46156<br> CAUTION: Gross
- error found at entry 176.<br> Found: 1.27163 Expected 2.32413 Error: 0.82767<br>
- 0.547221, 1.52005, 0.380446, 2.32413<br> CAUTION: Gross error found at entry
- 177.<br> Found: 1.24298 Expected 2.25511 Error: 0.814274<br> 0.547221,
- 1.52189, 0.208068, 2.25511<br> CAUTION: Gross error found at entry 178.<br>
- Found: 1.36528 Expected 2.58635 Error: 0.894379<br> 0.547221, 1.55961, 0.567822,
- 2.58635<br> CAUTION: Gross error found at entry 179.<br> Found: 1.35151
- Expected 2.55463 Error: 0.890206<br> 0.547221, 1.56524, 0.527371, 2.55463<br>
- CAUTION: Gross error found at entry 189.<br> Found: 1.01047 Expected 1.52344
- Error: 0.507658<br> 0.632359, 0.993308, 0.964966, 1.52344<br> CAUTION:
- Gross error found at entry 190.<br> Found: 1.05231 Expected 1.84135 Error:
- 0.749817<br> 0.632359, 1.27977, 0.129906, 1.84135<br> CAUTION: Gross error
- found at entry 191.<br> Found: 1.07393 Expected 1.92224 Error: 0.789918<br>
- 0.632359, 1.31163, 0.154438, 1.92224<br> CAUTION: Gross error found at entry
- 192.<br> Found: 1.22616 Expected 2.43657 Error: 0.987156<br> 0.632359,
- 1.42281, 0.568824, 2.43657<br> CAUTION: Gross error found at entry 193.<br>
- Found: 1.18462 Expected 2.33142 Error: 0.968083<br> 0.632359, 1.43473, 0.394908,
- 2.33142<br> CAUTION: Gross error found at entry 194.<br> Found: 1.25094
- Expected 2.59169 Error: 1.0718<br> 0.632359, 1.50405, 0.469391, 2.59169<br>
- CAUTION: Gross error found at entry 195.<br> Found: 1.23693 Expected 2.56158
- Error: 1.07091<br> 0.632359, 1.51564, 0.387296, 2.56158<br> CAUTION: Gross
- error found at entry 196.<br> Found: 1.19839 Expected 2.45293 Error: 1.04685<br>
- 0.632359, 1.52005, 0.0119021, 2.45293<br> CAUTION: Gross error found at entry
- 197.<br> Found: 1.39415 Expected 3.05228 Error: 1.18935<br> 0.632359, 1.52189,
- 0.726955, 3.05228<br> CAUTION: Gross error found at entry 198.<br> Found:
- 1.25489 Expected 2.6569 Error: 1.11723<br> 0.632359, 1.55961, 0.337123, 2.6569<br>
- CAUTION: Gross error found at entry 199.<br> Found: 1.27021 Expected 2.70857
- Error: 1.13237<br> 0.632359, 1.56524, 0.38857, 2.70857<br> CAUTION: Gross
- error found at entry 209.<br> Found: 0.83304 Expected 1.35947 Error: 0.631944<br>
- 0.814724, 0.993308, 0.119547, 1.35947<br> CAUTION: Gross error found at entry
- 210.<br> Found: 1.07764 Expected 2.50291 Error: 1.32258<br> *** FURTHER
- CONTENT HAS BEEN TRUNCATED FOR BREVITY ***<br>
- </p>
- <h5>
- <a name="special_function_error_rates_rep.error_logs.h92"></a>
- <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_ellint_3_with_2"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_ellint_3_with_2">Error
- Output For ellint_3 with compiler GNU C++ version 7.1.0 and library <cmath>
- and test data Elliptic Integral PI: Mathworld Data</a>
- </h5>
- <p>
- <a name="errors_GNU_C_version_7_1_0_linux_long_double_ellint_3__cmath__Elliptic_Integral_PI_Mathworld_Data"></a>CAUTION:
- Gross error found at entry 0.<br> Found: -0.809353 Expected -1.55741 Error:
- 0.924263<br> 1, -1, 0, -1.55741<br> CAUTION: Gross error found at entry
- 11.<br> Found: 1.07555 Expected 13.2822 Error: 11.3492<br> 0.999023, 1.5,
- 0, 13.2822<br> CAUTION: Gross error found at entry 13.<br> Found: -5.86896e+09
- Expected 1.53659e+10 Error: 1.18973e+4932<br> 0.5, 1e+10, 0.5, 1.53659e+10<br>
- Argument too small in __ellint_rj<br> -100000, 10, 0.75, 0.0347926<br>
- Argument too small in __ellint_rj<br> -1e+10, 10, 0.875, 0.000109956<br>
- Argument too small in __ellint_rj<br> -1e+10, 1e+20, 0.875, 1.00001e+15<br>
- Argument too small in __ellint_rj<br> -1e+10, 1.57031, 0.875, 1.57081e-05<br>
- CAUTION: Gross error found at entry 18.<br> Found: -6.25413e+09 Expected
- 6.43274e+21 Error: 1.18973e+4932<br> 0.999023, 1e+20, 0.875, 6.43274e+21<br>
- CAUTION: Gross error found at entry 19.<br> Found: 0.102424 Expected 0.196321
- Error: 0.916748<br> 50, 0.125, 0.25, 0.196321<br> CAUTION: Gross error
- found at entry 20.<br> Found: 0.798807 Expected 1.773 Error: 1.21956<br>
- 1.125, 1, 0.25, 1.773<br> CAUTION: Gross error found at entry 21.<br> Found:
- 7.07138 Expected 0.662468 Error: 9.6743<br> 1.125, 10, 0.25, 0.662468<br>
- CAUTION: Gross error found at entry 22.<br> Found: 2.04288 Expected -0.142697
- Error: 1.18973e+4932<br> 1.125, 3, 0.25, -0.142697<br> CAUTION: Gross error
- found at entry 23.<br> Found: 1.07762 Expected 22.2699 Error: 19.6659<br>
- 1.00391, 1.5, 0.125, 22.2699<br> CAUTION: Gross error found at entry 24.<br>
- Found: 15.1275 Expected -0.535406 Error: 1.18973e+4932<br> 1.00391, 21.5,
- 0.125, -0.535406<br> CAUTION: Gross error found at entry 41.<br> Found:
- 1.57454 Expected 3.0338 Error: 0.926787<br> 0.5, 2, 0, 3.0338<br> CAUTION:
- Gross error found at entry 42.<br> Found: 3.0338 Expected 1.57454 Error:
- 0.926787<br> -0.5, 2, 0, 1.57454<br> CAUTION: Gross error found at entry
- 43.<br> Found: -1.57454 Expected -3.0338 Error: 0.926787<br> 0.5, -2, 0,
- -3.0338<br> CAUTION: Gross error found at entry 44.<br> Found: -3.0338
- Expected -1.57454 Error: 0.926787<br> -0.5, -2, 0, -1.57454<br> CAUTION:
- Found non-finite result, when a finite value was expected at entry 51<br>
- Found: inf Expected -2.87535 Error: 1.18973e+4932<br> 1, 2, 0.5, -2.87535<br>
- CAUTION: Gross error found at entry 51.<br> Found: inf Expected -2.87535
- Error: 1.18973e+4932<br> 1, 2, 0.5, -2.87535<br> CAUTION: Found non-finite
- result, when a finite value was expected at entry 52<br> Found: -inf Expected
- 2.87535 Error: 1.18973e+4932<br> 1, -2, 0.5, 2.87535<br> CAUTION: Gross
- error found at entry 52.<br> Found: -inf Expected 2.87535 Error: 1.18973e+4932<br>
- 1, -2, 0.5, 2.87535<br> CAUTION: Found non-finite result, when a finite value
- was expected at entry 53<br> Found: inf Expected -2.18504 Error: 1.18973e+4932<br>
- 1, 2, 6.22302e-61, -2.18504<br> CAUTION: Gross error found at entry 53.<br>
- Found: inf Expected -2.18504 Error: 1.18973e+4932<br> 1, 2, 6.22302e-61,
- -2.18504<br> CAUTION: Found non-finite result, when a finite value was expected
- at entry 54<br> Found: -inf Expected 2.18504 Error: 1.18973e+4932<br> 1,
- -2, 6.22302e-61, 2.18504<br> CAUTION: Gross error found at entry 54.<br>
- Found: -inf Expected 2.18504 Error: 1.18973e+4932<br> 1, -2, 6.22302e-61,
- 2.18504<br> CAUTION: Gross error found at entry 57.<br> Found: 0.703907
- Expected 0.000975941 Error: 720.259<br> 20, 3.14257, 0.5, 0.000975941<br>
- CAUTION: Gross error found at entry 58.<br> Found: -0.703907 Expected -0.000975941
- Error: 720.259<br> 20, -3.14257, 0.5, -0.000975941<br> CAUTION: Gross error
- found at entry 59.<br> Found: 1.24445 Expected -27.1647 Error: 1.18973e+4932<br>
- 1.01562, 1.6958, 0.5, -27.1647<br> CAUTION: Gross error found at entry 60.<br>
- Found: -1.24445 Expected 27.1647 Error: 1.18973e+4932<br> 1.01562, -1.6958,
- 0.5, 27.1647<br>
- </p>
- <h5>
- <a name="special_function_error_rates_rep.error_logs.h93"></a>
- <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_expint_ei_with_"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_expint_ei_with_">Error
- Output For expint (Ei) with compiler GNU C++ version 7.1.0 and library <cmath>
- and test data Exponential Integral Ei</a>
- </h5>
- <p>
- <a name="errors_GNU_C_version_7_1_0_linux_long_double_expint_Ei___cmath__Exponential_Integral_Ei"></a>Continued
- fraction failed in __expint_En_cont_frac.<br> -1.30539, -0.134326<br>
- </p>
- <h5>
- <a name="special_function_error_rates_rep.error_logs.h94"></a>
- <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_ibeta_with_comp"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_ibeta_with_comp">Error
- Output For ibeta with compiler GNU C++ version 7.1.0 and library GSL 2.1 and
- test data Incomplete Beta Function: Large and Diverse Values</a>
- </h5>
- <p>
- <a name="errors_GNU_C_version_7_1_0_linux_double_ibeta_GSL_2_1_Incomplete_Beta_Function_Large_and_Diverse_Values"></a>underflow<br>
- 1.04761e-05, 39078.2, 0.913384, 95444.4, 0, 1, 0<br> underflow<br> 1.2158e-05,
- 24110.5, 0.135563, 82239.7, 0, 1, 0<br> underflow<br> 1.30342e-05, 26168.3,
- 0.127074, 76710.7, 0, 1, 0<br> underflow<br> 1.51962e-05, 16177.5, 0.814742,
- 65795.4, 0, 1, 0<br> underflow<br> 1.64873e-05, 470997, 0.127074, 60639.1,
- 0, 1, 0<br> underflow<br> 1.66259e-05, 147819, 0.632396, 60134.5, 0, 1,
- 0<br> underflow<br> 1.78638e-05, 439.387, 0.835025, 55972.4, 0, 1, 0<br>
- underflow<br> 2.00434e-05, 482.007, 0.905801, 49885.1, 0, 1, 0<br> underflow<br>
- 2.05189e-05, 236088, 0.835025, 48722.7, 0, 1, 0<br> underflow<br> 2.14336e-05,
- 3719.28, 0.814742, 46647, 0, 1, 0<br> underflow<br> 2.24486e-05, 445071,
- 0.221112, 44532.6, 0, 1, 0<br> underflow<br> 2.34849e-05, 25542.8, 0.968871,
- 42569.8, 0, 1, 0<br> underflow<br> 2.39993e-05, 462.946, 0.814742, 41661.1,
- 0, 1, 0<br> underflow<br> 2.52178e-05, 1832.27, 0.913384, 39646.4, 0, 1,
- 0<br> underflow<br> 2.87756e-05, 25491.8, 0.905801, 34740.9, 0, 1, 0<br>
- underflow<br> 2.89316e-05, 494.984, 0.968871, 34557.6, 0, 1, 0<br> underflow<br>
- 3.11413e-05, 348144, 0.308236, 32098.3, 0, 1, 0<br> underflow<br> 3.12319e-05,
- 33713, 0.221112, 32007.5, 0, 1, 0<br> underflow<br> 3.19889e-05, 3931.19,
- 0.308236, 31251.9, 0, 1, 0<br> underflow<br> 3.27129e-05, 3109.49, 0.968871,
- 30560.4, 0, 1, 0<br> underflow<br> 3.27529e-05, 25796.3, 0.835025, 30520.9,
- 0, 1, 0<br> underflow<br> 3.34106e-05, 3378.01, 0.221112, 29922, 0, 1,
- 0<br> underflow<br> 3.40793e-05, 288783, 0.814742, 29330.2, 0, 1, 0<br>
- underflow<br> 3.46418e-05, 411.559, 0.913384, 28860.3, 0, 1, 0<br> underflow<br>
- 3.61632e-05, 311937, 0.905801, 27639.2, 0, 1, 0<br> underflow<br> 3.75686e-05,
- 386440, 0.913384, 26604.5, 0, 1, 0<br> underflow<br> 3.99261e-05, 495352,
- 0.968871, 25032.6, 0, 1, 0<br> underflow<br> 4.01492e-05, 3246.23, 0.905801,
- 24898.5, 0, 1, 0<br> underflow<br> 4.0288e-05, 2569.28, 0.835025, 24812.9,
- 0, 1, 0<br> underflow<br> 4.11667e-05, 24253.8, 0.308236, 24280.8, 0, 1,
- 0<br> underflow<br> 4.17714e-05, 274447, 0.135563, 23926.7, 0, 1, 0<br>
- underflow<br> 4.66877e-05, 3780.93, 0.632396, 21410.1, 0, 1, 0<br> underflow<br>
- 4.73604e-05, 48598.7, 0.632396, 21103.3, 0, 1, 0<br> underflow<br> 0.00013245,
- 251.768, 0.968871, 7543.9, 0, 1, 0<br> underflow<br> 0.000168283, 195801,
- 0.905801, 5929.61, 0, 1, 0<br> underflow<br> 0.000177906, 276489, 0.814742,
- 5607.86, 0, 1, 0<br> underflow<br> 0.000183097, 316055, 0.127074, 5448.36,
- 0, 1, 0<br> underflow<br> 0.000190369, 159132, 0.835025, 5240.42, 0, 1,
- 0<br> underflow<br> 0.000191066, 419861, 0.913384, 5220.29, 0, 1, 0<br>
- underflow<br> 0.000192195, 177798, 0.308236, 5190.39, 0, 1, 0<br> underflow<br>
- 0.000220499, 107380, 0.135563, 4523.03, 0, 1, 0<br> underflow<br> 0.00022254,
- 1432.25, 0.814742, 4485.74, 0, 1, 0<br> underflow<br> 0.000240291, 49604.4,
- 0.632396, 4150.25, 0, 1, 0<br> underflow<br> 0.000251444, 15605.8, 0.135563,
- 3966.81, 0, 1, 0<br> underflow<br> 0.000274279, 289206, 0.968871, 3632.79,
- 0, 1, 0<br> underflow<br> 0.000274343, 2954.47, 0.308236, 3636.51, 0, 1,
- 0<br> underflow<br> 0.000278714, 4023.16, 0.632396, 3579.05, 0, 1, 0<br>
- underflow<br> 0.000288369, 460073, 0.221112, 3454.19, 0, 1, 0<br> underflow<br>
- 0.000294717, 4642.26, 0.221112, 3384.08, 0, 1, 0<br> underflow<br> 0.000303403,
- 2574.36, 0.835025, 3287.52, 0, 1, 0<br> underflow<br> 0.000304309, 4480.75,
- 0.905801, 3277.17, 0, 1, 0<br> underflow<br> 0.00031313, 47957, 0.308236,
- 3182.22, 0, 1, 0<br> underflow<br> 0.000320063, 25544.6, 0.905801, 3113.68,
- 0, 1, 0<br> underflow<br> 0.000334818, 29065.5, 0.968871, 2975.86, 0, 1,
- 0<br> underflow<br> 0.00034899, 41187.6, 0.913384, 2854.23, 0, 1, 0<br>
- underflow<br> 0.000350247, 426.308, 0.905801, 2848.5, 0, 1, 0<br> underflow<br>
- 0.000357727, 31752.2, 0.127074, 2784.5, 0, 1, 0<br> underflow<br> 0.000412091,
- 367.714, 0.913384, 2420.17, 0, 1, 0<br> underflow<br> 0.000417933, 4668.47,
- 0.968871, 2383.72, 0, 1, 0<br> underflow<br> 0.000424632, 17994.9, 0.221112,
- 2344.63, 0, 1, 0<br> underflow<br> 0.000427051, 2443.44, 0.913384, 2333.28,
- 0, 1, 0<br> underflow<br> 0.000437724, 454399, 0.632396, 2270.98, 0, 1,
- 0<br> underflow<br> 0.000450377, 10660.8, 0.835025, 2210.53, 0, 1, 0<br>
- underflow<br> 0.000475601, 19603, 0.814742, 2092.17, 0, 1, 0<br> underflow<br>
- 0.00116972, 4487.22, 0.221112, 845.964, 0, 1, 0<br> underflow<br> 0.00124188,
- 211066, 0.632396, 792.493, 0, 1, 0<br> underflow<br> 0.00128578, 4738.41,
- 0.308236, 768.75, 0, 1, 0<br> underflow<br> 0.00133388, 46277.8, 0.913384,
- 738.46, 0, 1, 0<br> underflow<br> 0.00138692, 2158.76, 0.814742, 712.816,
- 0, 1, 0<br> underflow<br> 0.00153268, 13060.2, 0.968871, 642.474, 0, 1,
- 0<br> underflow<br> 0.00159946, 1780.43, 0.968871, 617.202, 0, 1, 0<br>
- *** FURTHER CONTENT HAS BEEN TRUNCATED FOR BREVITY ***<br>
- </p>
- <h5>
- <a name="special_function_error_rates_rep.error_logs.h95"></a>
- <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_jacobi_dn_with_"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_jacobi_dn_with_">Error
- Output For jacobi_dn with compiler GNU C++ version 7.1.0 and library GSL 2.1
- and test data Jacobi Elliptic: Modulus near 1</a>
- </h5>
- <p>
- <a name="errors_GNU_C_version_7_1_0_linux_double_jacobi_dn_GSL_2_1_Jacobi_Elliptic_Modulus_near_1"></a>|m|
- > 1.0<br> -4.0246, 1, -0.999361, 0.0357365, 0.0357231<br> |m| > 1.0<br>
- -4.0246, 1, -0.999361, 0.0357497, 0.0357097<br> |m| > 1.0<br> -4.0246,
- 1, -0.99936, 0.0357762, 0.0356829<br> |m| > 1.0<br> -4.0246, 1, -0.999359,
- 0.0357895, 0.0356695<br> |m| > 1.0<br> -4.0246, 1.00001, -0.999354,
- 0.0359354, 0.0355222<br> |m| > 1.0<br> -4.0246, 1.00003, -0.999347,
- 0.0361343, 0.0353212<br> |m| > 1.0<br> -4.0246, 1.00004, -0.999343,
- 0.036247, 0.0352073<br> |m| > 1.0<br> -4.0246, 1.0001, -0.999311, 0.0371157,
- 0.0343296<br> |m| > 1.0<br> -4.0246, 1.00016, -0.99928, 0.0379513, 0.0334851<br>
- |m| > 1.0<br> -4.0246, 1.00027, -0.999221, 0.0394571, 0.0319634<br>
- |m| > 1.0<br> -4.0246, 1.00076, -0.99893, 0.0462407, 0.0251046<br> |m|
- > 1.0<br> -4.0246, 1.00125, -0.998589, 0.0531109, 0.0181532<br> |m|
- > 1.0<br> -4.0246, 1.00232, -0.99768, 0.0680761, 0.0029944<br> |m| >
- 1.0<br> -4.0246, 1.00604, -0.992752, 0.120179, -0.049966<br> |m| > 1.0<br>
- -4.0246, 1.01557, -0.967356, 0.25342, -0.186698<br> |m| > 1.0<br> -4.0246,
- 1.03059, -0.890373, 0.455232, -0.397492<br> |m| > 1.0<br> -4.0246, 1.06239,
- -0.607191, 0.794556, -0.76412<br> |m| > 1.0<br> -3.73013, 1, -0.998849,
- 0.0479567, 0.0479467<br> |m| > 1.0<br> -3.73013, 1, -0.998849, 0.0479665,
- 0.0479367<br> |m| > 1.0<br> -3.73013, 1, -0.998848, 0.0479862, 0.0479167<br>
- |m| > 1.0<br> -3.73013, 1, -0.998848, 0.047996, 0.0479067<br> |m| >
- 1.0<br> -3.73013, 1.00001, -0.998842, 0.0481042, 0.0477966<br> |m| >
- 1.0<br> -3.73013, 1.00003, -0.998835, 0.0482517, 0.0476465<br> |m| >
- 1.0<br> -3.73013, 1.00004, -0.998831, 0.0483354, 0.0475615<br> |m| >
- 1.0<br> -3.73013, 1.0001, -0.9988, 0.0489797, 0.0469059<br> |m| > 1.0<br>
- -3.73013, 1.00016, -0.998769, 0.0495995, 0.0462752<br> |m| > 1.0<br>
- -3.73013, 1.00027, -0.998713, 0.0507164, 0.0451386<br> |m| > 1.0<br>
- -3.73013, 1.00076, -0.998445, 0.0557477, 0.0400164<br> |m| > 1.0<br>
- -3.73013, 1.00125, -0.998147, 0.0608429, 0.0348257<br> |m| > 1.0<br>
- -3.73013, 1.00232, -0.997409, 0.0719406, 0.0235071<br> |m| > 1.0<br>
- -3.73013, 1.00604, -0.993866, 0.110593, -0.016048<br> |m| > 1.0<br>
- -3.73013, 1.01557, -0.977708, 0.209971, -0.118704<br> |m| > 1.0<br>
- -3.73013, 1.03059, -0.931162, 0.364606, -0.281224<br> |m| > 1.0<br>
- -3.73013, 1.06239, -0.753495, 0.657453, -0.599326<br> |m| > 1.0<br>
- -3.64523, 1, -0.998637, 0.0521997, 0.0521906<br> |m| > 1.0<br> -3.64523,
- 1, -0.998636, 0.0522087, 0.0521814<br> |m| > 1.0<br> -3.64523, 1, -0.998635,
- 0.0522268, 0.052163<br> |m| > 1.0<br> -3.64523, 1, -0.998635, 0.0522358,
- 0.0521538<br> |m| > 1.0<br> -3.64523, 1.00001, -0.99863, 0.052335, 0.0520526<br>
- |m| > 1.0<br> -3.64523, 1.00003, -0.998622, 0.0524703, 0.0519145<br>
- |m| > 1.0<br> -3.64523, 1.00004, -0.998618, 0.052547, 0.0518363<br>
- |m| > 1.0<br> -3.64523, 1.0001, -0.998587, 0.0531379, 0.0512335<br>
- |m| > 1.0<br> -3.64523, 1.00016, -0.998557, 0.0537063, 0.0506536<br>
- |m| > 1.0<br> -3.64523, 1.00027, -0.998501, 0.0547305, 0.0496084<br>
- |m| > 1.0<br> -3.64523, 1.00076, -0.998238, 0.0593443, 0.0448986<br>
- |m| > 1.0<br> -3.64523, 1.00125, -0.997949, 0.0640165, 0.0401258<br>
- |m| > 1.0<br> -3.64523, 1.00232, -0.997244, 0.0741927, 0.0297191<br>
- |m| > 1.0<br> -3.64523, 1.00604, -0.993972, 0.109636, -0.00664888<br>
- |m| > 1.0<br> -3.64523, 1.01557, -0.979623, 0.200844, -0.101111<br>
- |m| > 1.0<br> -3.64523, 1.03059, -0.939163, 0.343472, -0.251382<br>
- |m| > 1.0<br> -3.64523, 1.06239, -0.784719, 0.619852, -0.552253<br>
- |m| > 1.0<br> -3.11618, 1, -0.996078, 0.0884811, 0.0884757<br> |m| >
- 1.0<br> -3.11618, 1, -0.996077, 0.0884863, 0.0884702<br> |m| > 1.0<br>
- -3.11618, 1, -0.996076, 0.0884967, 0.0884593<br> |m| > 1.0<br> -3.11618,
- 1, -0.996076, 0.0885019, 0.0884538<br> |m| > 1.0<br> -3.11618, 1.00001,
- -0.996071, 0.0885593, 0.0883936<br> |m| > 1.0<br> -3.11618, 1.00003,
- -0.996064, 0.0886376, 0.0883114<br> |m| > 1.0<br> -3.11618, 1.00004,
- -0.99606, 0.0886819, 0.0882648<br> |m| > 1.0<br> -3.11618, 1.0001, -0.99603,
- 0.0890236, 0.0879059<br> |m| > 1.0<br> -3.11618, 1.00016, -0.996, 0.0893523,
- 0.0875607<br> |m| > 1.0<br> -3.11618, 1.00027, -0.995947, 0.0899445,
- 0.0869386<br> |m| > 1.0<br> -3.11618, 1.00076, -0.995702, 0.092612,
- 0.0841353<br> |m| > 1.0<br> -3.11618, 1.00125, -0.995447, 0.0953126,
- 0.0812953<br> |m| > 1.0<br> -3.11618, 1.00232, -0.994867, 0.101193,
- 0.0751049<br> |m| > 1.0<br> -3.11618, 1.00604, -0.992571, 0.121667,
- 0.0534858<br> |m| > 1.0<br> -3.11618, 1.01557, -0.984666, 0.174451,
- -0.00273723<br> |m| > 1.0<br> -3.11618, 1.03059, -0.966077, 0.258253,
- -0.0934336<br> |m| > 1.0<br> -3.11618, 1.06239, -0.901067, 0.433681,
- -0.289151<br> |m| > 1.0<br> -2.78966, 1, -0.992478, 0.122424, 0.12242<br>
- |m| > 1.0<br> -2.78966, 1, -0.992477, 0.122428, 0.122416<br> *** FURTHER
- CONTENT HAS BEEN TRUNCATED FOR BREVITY ***<br>
- </p>
- <h5>
- <a name="special_function_error_rates_rep.error_logs.h96"></a>
- <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_jacobi_cn_with_"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_jacobi_cn_with_">Error
- Output For jacobi_cn with compiler GNU C++ version 7.1.0 and library GSL 2.1
- and test data Jacobi Elliptic: Modulus near 1</a>
- </h5>
- <p>
- <a name="errors_GNU_C_version_7_1_0_linux_double_jacobi_cn_GSL_2_1_Jacobi_Elliptic_Modulus_near_1"></a>|m|
- > 1.0<br> -4.0246, 1, -0.999361, 0.0357365, 0.0357231<br> |m| > 1.0<br>
- -4.0246, 1, -0.999361, 0.0357497, 0.0357097<br> |m| > 1.0<br> -4.0246,
- 1, -0.99936, 0.0357762, 0.0356829<br> |m| > 1.0<br> -4.0246, 1, -0.999359,
- 0.0357895, 0.0356695<br> |m| > 1.0<br> -4.0246, 1.00001, -0.999354,
- 0.0359354, 0.0355222<br> |m| > 1.0<br> -4.0246, 1.00003, -0.999347,
- 0.0361343, 0.0353212<br> |m| > 1.0<br> -4.0246, 1.00004, -0.999343,
- 0.036247, 0.0352073<br> |m| > 1.0<br> -4.0246, 1.0001, -0.999311, 0.0371157,
- 0.0343296<br> |m| > 1.0<br> -4.0246, 1.00016, -0.99928, 0.0379513, 0.0334851<br>
- |m| > 1.0<br> -4.0246, 1.00027, -0.999221, 0.0394571, 0.0319634<br>
- |m| > 1.0<br> -4.0246, 1.00076, -0.99893, 0.0462407, 0.0251046<br> |m|
- > 1.0<br> -4.0246, 1.00125, -0.998589, 0.0531109, 0.0181532<br> |m|
- > 1.0<br> -4.0246, 1.00232, -0.99768, 0.0680761, 0.0029944<br> |m| >
- 1.0<br> -4.0246, 1.00604, -0.992752, 0.120179, -0.049966<br> |m| > 1.0<br>
- -4.0246, 1.01557, -0.967356, 0.25342, -0.186698<br> |m| > 1.0<br> -4.0246,
- 1.03059, -0.890373, 0.455232, -0.397492<br> |m| > 1.0<br> -4.0246, 1.06239,
- -0.607191, 0.794556, -0.76412<br> |m| > 1.0<br> -3.73013, 1, -0.998849,
- 0.0479567, 0.0479467<br> |m| > 1.0<br> -3.73013, 1, -0.998849, 0.0479665,
- 0.0479367<br> |m| > 1.0<br> -3.73013, 1, -0.998848, 0.0479862, 0.0479167<br>
- |m| > 1.0<br> -3.73013, 1, -0.998848, 0.047996, 0.0479067<br> |m| >
- 1.0<br> -3.73013, 1.00001, -0.998842, 0.0481042, 0.0477966<br> |m| >
- 1.0<br> -3.73013, 1.00003, -0.998835, 0.0482517, 0.0476465<br> |m| >
- 1.0<br> -3.73013, 1.00004, -0.998831, 0.0483354, 0.0475615<br> |m| >
- 1.0<br> -3.73013, 1.0001, -0.9988, 0.0489797, 0.0469059<br> |m| > 1.0<br>
- -3.73013, 1.00016, -0.998769, 0.0495995, 0.0462752<br> |m| > 1.0<br>
- -3.73013, 1.00027, -0.998713, 0.0507164, 0.0451386<br> |m| > 1.0<br>
- -3.73013, 1.00076, -0.998445, 0.0557477, 0.0400164<br> |m| > 1.0<br>
- -3.73013, 1.00125, -0.998147, 0.0608429, 0.0348257<br> |m| > 1.0<br>
- -3.73013, 1.00232, -0.997409, 0.0719406, 0.0235071<br> |m| > 1.0<br>
- -3.73013, 1.00604, -0.993866, 0.110593, -0.016048<br> |m| > 1.0<br>
- -3.73013, 1.01557, -0.977708, 0.209971, -0.118704<br> |m| > 1.0<br>
- -3.73013, 1.03059, -0.931162, 0.364606, -0.281224<br> |m| > 1.0<br>
- -3.73013, 1.06239, -0.753495, 0.657453, -0.599326<br> |m| > 1.0<br>
- -3.64523, 1, -0.998637, 0.0521997, 0.0521906<br> |m| > 1.0<br> -3.64523,
- 1, -0.998636, 0.0522087, 0.0521814<br> |m| > 1.0<br> -3.64523, 1, -0.998635,
- 0.0522268, 0.052163<br> |m| > 1.0<br> -3.64523, 1, -0.998635, 0.0522358,
- 0.0521538<br> |m| > 1.0<br> -3.64523, 1.00001, -0.99863, 0.052335, 0.0520526<br>
- |m| > 1.0<br> -3.64523, 1.00003, -0.998622, 0.0524703, 0.0519145<br>
- |m| > 1.0<br> -3.64523, 1.00004, -0.998618, 0.052547, 0.0518363<br>
- |m| > 1.0<br> -3.64523, 1.0001, -0.998587, 0.0531379, 0.0512335<br>
- |m| > 1.0<br> -3.64523, 1.00016, -0.998557, 0.0537063, 0.0506536<br>
- |m| > 1.0<br> -3.64523, 1.00027, -0.998501, 0.0547305, 0.0496084<br>
- |m| > 1.0<br> -3.64523, 1.00076, -0.998238, 0.0593443, 0.0448986<br>
- |m| > 1.0<br> -3.64523, 1.00125, -0.997949, 0.0640165, 0.0401258<br>
- |m| > 1.0<br> -3.64523, 1.00232, -0.997244, 0.0741927, 0.0297191<br>
- |m| > 1.0<br> -3.64523, 1.00604, -0.993972, 0.109636, -0.00664888<br>
- |m| > 1.0<br> -3.64523, 1.01557, -0.979623, 0.200844, -0.101111<br>
- |m| > 1.0<br> -3.64523, 1.03059, -0.939163, 0.343472, -0.251382<br>
- |m| > 1.0<br> -3.64523, 1.06239, -0.784719, 0.619852, -0.552253<br>
- |m| > 1.0<br> -3.11618, 1, -0.996078, 0.0884811, 0.0884757<br> |m| >
- 1.0<br> -3.11618, 1, -0.996077, 0.0884863, 0.0884702<br> |m| > 1.0<br>
- -3.11618, 1, -0.996076, 0.0884967, 0.0884593<br> |m| > 1.0<br> -3.11618,
- 1, -0.996076, 0.0885019, 0.0884538<br> |m| > 1.0<br> -3.11618, 1.00001,
- -0.996071, 0.0885593, 0.0883936<br> |m| > 1.0<br> -3.11618, 1.00003,
- -0.996064, 0.0886376, 0.0883114<br> |m| > 1.0<br> -3.11618, 1.00004,
- -0.99606, 0.0886819, 0.0882648<br> |m| > 1.0<br> -3.11618, 1.0001, -0.99603,
- 0.0890236, 0.0879059<br> |m| > 1.0<br> -3.11618, 1.00016, -0.996, 0.0893523,
- 0.0875607<br> |m| > 1.0<br> -3.11618, 1.00027, -0.995947, 0.0899445,
- 0.0869386<br> |m| > 1.0<br> -3.11618, 1.00076, -0.995702, 0.092612,
- 0.0841353<br> |m| > 1.0<br> -3.11618, 1.00125, -0.995447, 0.0953126,
- 0.0812953<br> |m| > 1.0<br> -3.11618, 1.00232, -0.994867, 0.101193,
- 0.0751049<br> |m| > 1.0<br> -3.11618, 1.00604, -0.992571, 0.121667,
- 0.0534858<br> |m| > 1.0<br> -3.11618, 1.01557, -0.984666, 0.174451,
- -0.00273723<br> |m| > 1.0<br> -3.11618, 1.03059, -0.966077, 0.258253,
- -0.0934336<br> |m| > 1.0<br> -3.11618, 1.06239, -0.901067, 0.433681,
- -0.289151<br> |m| > 1.0<br> -2.78966, 1, -0.992478, 0.122424, 0.12242<br>
- |m| > 1.0<br> -2.78966, 1, -0.992477, 0.122428, 0.122416<br> *** FURTHER
- CONTENT HAS BEEN TRUNCATED FOR BREVITY ***<br>
- </p>
- <h5>
- <a name="special_function_error_rates_rep.error_logs.h97"></a>
- <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_jacobi_sn_with_"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_jacobi_sn_with_">Error
- Output For jacobi_sn with compiler GNU C++ version 7.1.0 and library GSL 2.1
- and test data Jacobi Elliptic: Modulus near 1</a>
- </h5>
- <p>
- <a name="errors_GNU_C_version_7_1_0_linux_double_jacobi_sn_GSL_2_1_Jacobi_Elliptic_Modulus_near_1"></a>|m|
- > 1.0<br> -4.0246, 1, -0.999361, 0.0357365, 0.0357231<br> |m| > 1.0<br>
- -4.0246, 1, -0.999361, 0.0357497, 0.0357097<br> |m| > 1.0<br> -4.0246,
- 1, -0.99936, 0.0357762, 0.0356829<br> |m| > 1.0<br> -4.0246, 1, -0.999359,
- 0.0357895, 0.0356695<br> |m| > 1.0<br> -4.0246, 1.00001, -0.999354,
- 0.0359354, 0.0355222<br> |m| > 1.0<br> -4.0246, 1.00003, -0.999347,
- 0.0361343, 0.0353212<br> |m| > 1.0<br> -4.0246, 1.00004, -0.999343,
- 0.036247, 0.0352073<br> |m| > 1.0<br> -4.0246, 1.0001, -0.999311, 0.0371157,
- 0.0343296<br> |m| > 1.0<br> -4.0246, 1.00016, -0.99928, 0.0379513, 0.0334851<br>
- |m| > 1.0<br> -4.0246, 1.00027, -0.999221, 0.0394571, 0.0319634<br>
- |m| > 1.0<br> -4.0246, 1.00076, -0.99893, 0.0462407, 0.0251046<br> |m|
- > 1.0<br> -4.0246, 1.00125, -0.998589, 0.0531109, 0.0181532<br> |m|
- > 1.0<br> -4.0246, 1.00232, -0.99768, 0.0680761, 0.0029944<br> |m| >
- 1.0<br> -4.0246, 1.00604, -0.992752, 0.120179, -0.049966<br> |m| > 1.0<br>
- -4.0246, 1.01557, -0.967356, 0.25342, -0.186698<br> |m| > 1.0<br> -4.0246,
- 1.03059, -0.890373, 0.455232, -0.397492<br> |m| > 1.0<br> -4.0246, 1.06239,
- -0.607191, 0.794556, -0.76412<br> |m| > 1.0<br> -3.73013, 1, -0.998849,
- 0.0479567, 0.0479467<br> |m| > 1.0<br> -3.73013, 1, -0.998849, 0.0479665,
- 0.0479367<br> |m| > 1.0<br> -3.73013, 1, -0.998848, 0.0479862, 0.0479167<br>
- |m| > 1.0<br> -3.73013, 1, -0.998848, 0.047996, 0.0479067<br> |m| >
- 1.0<br> -3.73013, 1.00001, -0.998842, 0.0481042, 0.0477966<br> |m| >
- 1.0<br> -3.73013, 1.00003, -0.998835, 0.0482517, 0.0476465<br> |m| >
- 1.0<br> -3.73013, 1.00004, -0.998831, 0.0483354, 0.0475615<br> |m| >
- 1.0<br> -3.73013, 1.0001, -0.9988, 0.0489797, 0.0469059<br> |m| > 1.0<br>
- -3.73013, 1.00016, -0.998769, 0.0495995, 0.0462752<br> |m| > 1.0<br>
- -3.73013, 1.00027, -0.998713, 0.0507164, 0.0451386<br> |m| > 1.0<br>
- -3.73013, 1.00076, -0.998445, 0.0557477, 0.0400164<br> |m| > 1.0<br>
- -3.73013, 1.00125, -0.998147, 0.0608429, 0.0348257<br> |m| > 1.0<br>
- -3.73013, 1.00232, -0.997409, 0.0719406, 0.0235071<br> |m| > 1.0<br>
- -3.73013, 1.00604, -0.993866, 0.110593, -0.016048<br> |m| > 1.0<br>
- -3.73013, 1.01557, -0.977708, 0.209971, -0.118704<br> |m| > 1.0<br>
- -3.73013, 1.03059, -0.931162, 0.364606, -0.281224<br> |m| > 1.0<br>
- -3.73013, 1.06239, -0.753495, 0.657453, -0.599326<br> |m| > 1.0<br>
- -3.64523, 1, -0.998637, 0.0521997, 0.0521906<br> |m| > 1.0<br> -3.64523,
- 1, -0.998636, 0.0522087, 0.0521814<br> |m| > 1.0<br> -3.64523, 1, -0.998635,
- 0.0522268, 0.052163<br> |m| > 1.0<br> -3.64523, 1, -0.998635, 0.0522358,
- 0.0521538<br> |m| > 1.0<br> -3.64523, 1.00001, -0.99863, 0.052335, 0.0520526<br>
- |m| > 1.0<br> -3.64523, 1.00003, -0.998622, 0.0524703, 0.0519145<br>
- |m| > 1.0<br> -3.64523, 1.00004, -0.998618, 0.052547, 0.0518363<br>
- |m| > 1.0<br> -3.64523, 1.0001, -0.998587, 0.0531379, 0.0512335<br>
- |m| > 1.0<br> -3.64523, 1.00016, -0.998557, 0.0537063, 0.0506536<br>
- |m| > 1.0<br> -3.64523, 1.00027, -0.998501, 0.0547305, 0.0496084<br>
- |m| > 1.0<br> -3.64523, 1.00076, -0.998238, 0.0593443, 0.0448986<br>
- |m| > 1.0<br> -3.64523, 1.00125, -0.997949, 0.0640165, 0.0401258<br>
- |m| > 1.0<br> -3.64523, 1.00232, -0.997244, 0.0741927, 0.0297191<br>
- |m| > 1.0<br> -3.64523, 1.00604, -0.993972, 0.109636, -0.00664888<br>
- |m| > 1.0<br> -3.64523, 1.01557, -0.979623, 0.200844, -0.101111<br>
- |m| > 1.0<br> -3.64523, 1.03059, -0.939163, 0.343472, -0.251382<br>
- |m| > 1.0<br> -3.64523, 1.06239, -0.784719, 0.619852, -0.552253<br>
- |m| > 1.0<br> -3.11618, 1, -0.996078, 0.0884811, 0.0884757<br> |m| >
- 1.0<br> -3.11618, 1, -0.996077, 0.0884863, 0.0884702<br> |m| > 1.0<br>
- -3.11618, 1, -0.996076, 0.0884967, 0.0884593<br> |m| > 1.0<br> -3.11618,
- 1, -0.996076, 0.0885019, 0.0884538<br> |m| > 1.0<br> -3.11618, 1.00001,
- -0.996071, 0.0885593, 0.0883936<br> |m| > 1.0<br> -3.11618, 1.00003,
- -0.996064, 0.0886376, 0.0883114<br> |m| > 1.0<br> -3.11618, 1.00004,
- -0.99606, 0.0886819, 0.0882648<br> |m| > 1.0<br> -3.11618, 1.0001, -0.99603,
- 0.0890236, 0.0879059<br> |m| > 1.0<br> -3.11618, 1.00016, -0.996, 0.0893523,
- 0.0875607<br> |m| > 1.0<br> -3.11618, 1.00027, -0.995947, 0.0899445,
- 0.0869386<br> |m| > 1.0<br> -3.11618, 1.00076, -0.995702, 0.092612,
- 0.0841353<br> |m| > 1.0<br> -3.11618, 1.00125, -0.995447, 0.0953126,
- 0.0812953<br> |m| > 1.0<br> -3.11618, 1.00232, -0.994867, 0.101193,
- 0.0751049<br> |m| > 1.0<br> -3.11618, 1.00604, -0.992571, 0.121667,
- 0.0534858<br> |m| > 1.0<br> -3.11618, 1.01557, -0.984666, 0.174451,
- -0.00273723<br> |m| > 1.0<br> -3.11618, 1.03059, -0.966077, 0.258253,
- -0.0934336<br> |m| > 1.0<br> -3.11618, 1.06239, -0.901067, 0.433681,
- -0.289151<br> |m| > 1.0<br> -2.78966, 1, -0.992478, 0.122424, 0.12242<br>
- |m| > 1.0<br> -2.78966, 1, -0.992477, 0.122428, 0.122416<br> *** FURTHER
- CONTENT HAS BEEN TRUNCATED FOR BREVITY ***<br>
- </p>
- <h5>
- <a name="special_function_error_rates_rep.error_logs.h98"></a>
- <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_jacobi_dn_with0"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_jacobi_dn_with0">Error
- Output For jacobi_dn with compiler GNU C++ version 7.1.0 and library GSL 2.1
- and test data Jacobi Elliptic: Random Small Values</a>
- </h5>
- <p>
- <a name="errors_GNU_C_version_7_1_0_linux_double_jacobi_dn_GSL_2_1_Jacobi_Elliptic_Random_Small_Values"></a>|m|
- > 1.0<br> 1.65048e-12, 1.65574, 1.65048e-12, 1, 1<br> |m| > 1.0<br>
- 2.06542e-12, 1.65574, 2.06542e-12, 1, 1<br> |m| > 1.0<br> 6.93323e-12,
- 1.65574, 6.93323e-12, 1, 1<br> |m| > 1.0<br> 1.33514e-11, 1.65574, 1.33514e-11,
- 1, 1<br> |m| > 1.0<br> 1.63998e-11, 1.65574, 1.63998e-11, 1, 1<br>
- |m| > 1.0<br> 5.73016e-11, 1.65574, 5.73016e-11, 1, 1<br> |m| > 1.0<br>
- 1.11373e-10, 1.65574, 1.11373e-10, 1, 1<br> |m| > 1.0<br> 1.42147e-10,
- 1.65574, 1.42147e-10, 1, 1<br> |m| > 1.0<br> 3.80063e-10, 1.65574, 3.80063e-10,
- 1, 1<br> |m| > 1.0<br> 6.09163e-10, 1.65574, 6.09163e-10, 1, 1<br>
- |m| > 1.0<br> 1.02216e-09, 1.65574, 1.02216e-09, 1, 1<br> |m| > 1.0<br>
- 2.88192e-09, 1.65574, 2.88192e-09, 1, 1<br> |m| > 1.0<br> 4.76278e-09,
- 1.65574, 4.76278e-09, 1, 1<br> |m| > 1.0<br> 8.85413e-09, 1.65574, 8.85413e-09,
- 1, 1<br> |m| > 1.0<br> 2.30503e-08, 1.65574, 2.30503e-08, 1, 1<br>
- |m| > 1.0<br> 5.93925e-08, 1.65574, 5.93925e-08, 1, 1<br> |m| > 1.0<br>
- 1.16676e-07, 1.65574, 1.16676e-07, 1, 1<br> |m| > 1.0<br> 2.37997e-07,
- 1.65574, 2.37997e-07, 1, 1<br> |m| > 1.0<br> 4.68466e-07, 1.65574, 4.68466e-07,
- 1, 1<br> |m| > 1.0<br> 9.3827e-07, 1.65574, 9.3827e-07, 1, 1<br> |m|
- > 1.0<br> 1.10399e-06, 1.65574, 1.10399e-06, 1, 1<br> |m| > 1.0<br>
- 3.29178e-06, 1.65574, 3.29178e-06, 1, 1<br> |m| > 1.0<br> 7.51721e-06,
- 1.65574, 7.51721e-06, 1, 1<br> |m| > 1.0<br> 1.51147e-05, 1.65574, 1.51147e-05,
- 1, 1<br> |m| > 1.0<br> 2.9864e-05, 1.65574, 2.9864e-05, 1, 1<br> |m|
- > 1.0<br> 3.38703e-05, 1.65574, 3.38703e-05, 1, 1<br> |m| > 1.0<br>
- 9.06601e-05, 1.65574, 9.06601e-05, 1, 1<br> |m| > 1.0<br> 0.000219495,
- 1.65574, 0.000219495, 1, 1<br> |m| > 1.0<br> 0.000439522, 1.65574, 0.000439521,
- 1, 1<br> |m| > 1.0<br> 0.000633315, 1.65574, 0.000633315, 1, 0.999999<br>
- |m| > 1.0<br> 0.00111512, 1.65574, 0.00111512, 0.999999, 0.999998<br>
- |m| > 1.0<br> 0.00196247, 1.65574, 0.00196246, 0.999998, 0.999995<br>
- |m| > 1.0<br> 0.00555375, 1.65574, 0.00555365, 0.999985, 0.999958<br>
- |m| > 1.0<br> 0.00869113, 1.65574, 0.00869072, 0.999962, 0.999896<br>
- |m| > 1.0<br> 0.0299334, 1.65574, 0.0299166, 0.999552, 0.998772<br>
- |m| > 1.0<br> 0.0512426, 1.65574, 0.0511588, 0.998691, 0.996406<br>
- |m| > 1.0<br> 0.112013, 1.65574, 0.111143, 0.993804, 0.982922<br> |m|
- > 1.0<br> 0.234804, 1.65574, 0.227, 0.973895, 0.926679<br> |m| >
- 1.0<br> 0.489873, 1.65574, 0.425971, 0.904737, 0.708912<br> |m| > 1.0<br>
- 0.751831, 1.65574, 0.553446, 0.832885, 0.400346<br> |m| > 1.0<br> 1.65574,
- 1.65574, 0.408154, 0.912913, -0.737088<br>
- </p>
- <h5>
- <a name="special_function_error_rates_rep.error_logs.h99"></a>
- <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_jacobi_cn_with0"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_jacobi_cn_with0">Error
- Output For jacobi_cn with compiler GNU C++ version 7.1.0 and library GSL 2.1
- and test data Jacobi Elliptic: Random Small Values</a>
- </h5>
- <p>
- <a name="errors_GNU_C_version_7_1_0_linux_double_jacobi_cn_GSL_2_1_Jacobi_Elliptic_Random_Small_Values"></a>|m|
- > 1.0<br> 1.65048e-12, 1.65574, 1.65048e-12, 1, 1<br> |m| > 1.0<br>
- 2.06542e-12, 1.65574, 2.06542e-12, 1, 1<br> |m| > 1.0<br> 6.93323e-12,
- 1.65574, 6.93323e-12, 1, 1<br> |m| > 1.0<br> 1.33514e-11, 1.65574, 1.33514e-11,
- 1, 1<br> |m| > 1.0<br> 1.63998e-11, 1.65574, 1.63998e-11, 1, 1<br>
- |m| > 1.0<br> 5.73016e-11, 1.65574, 5.73016e-11, 1, 1<br> |m| > 1.0<br>
- 1.11373e-10, 1.65574, 1.11373e-10, 1, 1<br> |m| > 1.0<br> 1.42147e-10,
- 1.65574, 1.42147e-10, 1, 1<br> |m| > 1.0<br> 3.80063e-10, 1.65574, 3.80063e-10,
- 1, 1<br> |m| > 1.0<br> 6.09163e-10, 1.65574, 6.09163e-10, 1, 1<br>
- |m| > 1.0<br> 1.02216e-09, 1.65574, 1.02216e-09, 1, 1<br> |m| > 1.0<br>
- 2.88192e-09, 1.65574, 2.88192e-09, 1, 1<br> |m| > 1.0<br> 4.76278e-09,
- 1.65574, 4.76278e-09, 1, 1<br> |m| > 1.0<br> 8.85413e-09, 1.65574, 8.85413e-09,
- 1, 1<br> |m| > 1.0<br> 2.30503e-08, 1.65574, 2.30503e-08, 1, 1<br>
- |m| > 1.0<br> 5.93925e-08, 1.65574, 5.93925e-08, 1, 1<br> |m| > 1.0<br>
- 1.16676e-07, 1.65574, 1.16676e-07, 1, 1<br> |m| > 1.0<br> 2.37997e-07,
- 1.65574, 2.37997e-07, 1, 1<br> |m| > 1.0<br> 4.68466e-07, 1.65574, 4.68466e-07,
- 1, 1<br> |m| > 1.0<br> 9.3827e-07, 1.65574, 9.3827e-07, 1, 1<br> |m|
- > 1.0<br> 1.10399e-06, 1.65574, 1.10399e-06, 1, 1<br> |m| > 1.0<br>
- 3.29178e-06, 1.65574, 3.29178e-06, 1, 1<br> |m| > 1.0<br> 7.51721e-06,
- 1.65574, 7.51721e-06, 1, 1<br> |m| > 1.0<br> 1.51147e-05, 1.65574, 1.51147e-05,
- 1, 1<br> |m| > 1.0<br> 2.9864e-05, 1.65574, 2.9864e-05, 1, 1<br> |m|
- > 1.0<br> 3.38703e-05, 1.65574, 3.38703e-05, 1, 1<br> |m| > 1.0<br>
- 9.06601e-05, 1.65574, 9.06601e-05, 1, 1<br> |m| > 1.0<br> 0.000219495,
- 1.65574, 0.000219495, 1, 1<br> |m| > 1.0<br> 0.000439522, 1.65574, 0.000439521,
- 1, 1<br> |m| > 1.0<br> 0.000633315, 1.65574, 0.000633315, 1, 0.999999<br>
- |m| > 1.0<br> 0.00111512, 1.65574, 0.00111512, 0.999999, 0.999998<br>
- |m| > 1.0<br> 0.00196247, 1.65574, 0.00196246, 0.999998, 0.999995<br>
- |m| > 1.0<br> 0.00555375, 1.65574, 0.00555365, 0.999985, 0.999958<br>
- |m| > 1.0<br> 0.00869113, 1.65574, 0.00869072, 0.999962, 0.999896<br>
- |m| > 1.0<br> 0.0299334, 1.65574, 0.0299166, 0.999552, 0.998772<br>
- |m| > 1.0<br> 0.0512426, 1.65574, 0.0511588, 0.998691, 0.996406<br>
- |m| > 1.0<br> 0.112013, 1.65574, 0.111143, 0.993804, 0.982922<br> |m|
- > 1.0<br> 0.234804, 1.65574, 0.227, 0.973895, 0.926679<br> |m| >
- 1.0<br> 0.489873, 1.65574, 0.425971, 0.904737, 0.708912<br> |m| > 1.0<br>
- 0.751831, 1.65574, 0.553446, 0.832885, 0.400346<br> |m| > 1.0<br> 1.65574,
- 1.65574, 0.408154, 0.912913, -0.737088<br>
- </p>
- <h5>
- <a name="special_function_error_rates_rep.error_logs.h100"></a>
- <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_jacobi_sn_with0"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_jacobi_sn_with0">Error
- Output For jacobi_sn with compiler GNU C++ version 7.1.0 and library GSL 2.1
- and test data Jacobi Elliptic: Random Small Values</a>
- </h5>
- <p>
- <a name="errors_GNU_C_version_7_1_0_linux_double_jacobi_sn_GSL_2_1_Jacobi_Elliptic_Random_Small_Values"></a>|m|
- > 1.0<br> 1.65048e-12, 1.65574, 1.65048e-12, 1, 1<br> |m| > 1.0<br>
- 2.06542e-12, 1.65574, 2.06542e-12, 1, 1<br> |m| > 1.0<br> 6.93323e-12,
- 1.65574, 6.93323e-12, 1, 1<br> |m| > 1.0<br> 1.33514e-11, 1.65574, 1.33514e-11,
- 1, 1<br> |m| > 1.0<br> 1.63998e-11, 1.65574, 1.63998e-11, 1, 1<br>
- |m| > 1.0<br> 5.73016e-11, 1.65574, 5.73016e-11, 1, 1<br> |m| > 1.0<br>
- 1.11373e-10, 1.65574, 1.11373e-10, 1, 1<br> |m| > 1.0<br> 1.42147e-10,
- 1.65574, 1.42147e-10, 1, 1<br> |m| > 1.0<br> 3.80063e-10, 1.65574, 3.80063e-10,
- 1, 1<br> |m| > 1.0<br> 6.09163e-10, 1.65574, 6.09163e-10, 1, 1<br>
- |m| > 1.0<br> 1.02216e-09, 1.65574, 1.02216e-09, 1, 1<br> |m| > 1.0<br>
- 2.88192e-09, 1.65574, 2.88192e-09, 1, 1<br> |m| > 1.0<br> 4.76278e-09,
- 1.65574, 4.76278e-09, 1, 1<br> |m| > 1.0<br> 8.85413e-09, 1.65574, 8.85413e-09,
- 1, 1<br> |m| > 1.0<br> 2.30503e-08, 1.65574, 2.30503e-08, 1, 1<br>
- |m| > 1.0<br> 5.93925e-08, 1.65574, 5.93925e-08, 1, 1<br> |m| > 1.0<br>
- 1.16676e-07, 1.65574, 1.16676e-07, 1, 1<br> |m| > 1.0<br> 2.37997e-07,
- 1.65574, 2.37997e-07, 1, 1<br> |m| > 1.0<br> 4.68466e-07, 1.65574, 4.68466e-07,
- 1, 1<br> |m| > 1.0<br> 9.3827e-07, 1.65574, 9.3827e-07, 1, 1<br> |m|
- > 1.0<br> 1.10399e-06, 1.65574, 1.10399e-06, 1, 1<br> |m| > 1.0<br>
- 3.29178e-06, 1.65574, 3.29178e-06, 1, 1<br> |m| > 1.0<br> 7.51721e-06,
- 1.65574, 7.51721e-06, 1, 1<br> |m| > 1.0<br> 1.51147e-05, 1.65574, 1.51147e-05,
- 1, 1<br> |m| > 1.0<br> 2.9864e-05, 1.65574, 2.9864e-05, 1, 1<br> |m|
- > 1.0<br> 3.38703e-05, 1.65574, 3.38703e-05, 1, 1<br> |m| > 1.0<br>
- 9.06601e-05, 1.65574, 9.06601e-05, 1, 1<br> |m| > 1.0<br> 0.000219495,
- 1.65574, 0.000219495, 1, 1<br> |m| > 1.0<br> 0.000439522, 1.65574, 0.000439521,
- 1, 1<br> |m| > 1.0<br> 0.000633315, 1.65574, 0.000633315, 1, 0.999999<br>
- |m| > 1.0<br> 0.00111512, 1.65574, 0.00111512, 0.999999, 0.999998<br>
- |m| > 1.0<br> 0.00196247, 1.65574, 0.00196246, 0.999998, 0.999995<br>
- |m| > 1.0<br> 0.00555375, 1.65574, 0.00555365, 0.999985, 0.999958<br>
- |m| > 1.0<br> 0.00869113, 1.65574, 0.00869072, 0.999962, 0.999896<br>
- |m| > 1.0<br> 0.0299334, 1.65574, 0.0299166, 0.999552, 0.998772<br>
- |m| > 1.0<br> 0.0512426, 1.65574, 0.0511588, 0.998691, 0.996406<br>
- |m| > 1.0<br> 0.112013, 1.65574, 0.111143, 0.993804, 0.982922<br> |m|
- > 1.0<br> 0.234804, 1.65574, 0.227, 0.973895, 0.926679<br> |m| >
- 1.0<br> 0.489873, 1.65574, 0.425971, 0.904737, 0.708912<br> |m| > 1.0<br>
- 0.751831, 1.65574, 0.553446, 0.832885, 0.400346<br> |m| > 1.0<br> 1.65574,
- 1.65574, 0.408154, 0.912913, -0.737088<br>
- </p>
- <h5>
- <a name="special_function_error_rates_rep.error_logs.h101"></a>
- <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_jacobi_dn_with1"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_jacobi_dn_with1">Error
- Output For jacobi_dn with compiler GNU C++ version 7.1.0 and library GSL 2.1
- and test data Jacobi Elliptic: Mathworld Data</a>
- </h5>
- <p>
- <a name="errors_GNU_C_version_7_1_0_linux_double_jacobi_dn_GSL_2_1_Jacobi_Elliptic_Mathworld_Data"></a>|m|
- > 1.0<br> 2.98023e-08, 1.5, 2.98023e-08, 1, 1<br> |m| > 1.0<br>
- -2.98023e-08, 1.5, -2.98023e-08, 1, 1<br> |m| > 1.0<br> 0.25, 1.5, 0.24183,
- 0.970319, 0.931888<br> |m| > 1.0<br> -0.25, 1.5, -0.24183, 0.970319,
- 0.931888<br> |m| > 1.0<br> 1.25, 1.5, 0.665876, 0.746063, -0.0486921<br>
- |m| > 1.0<br> -1.25, 1.5, -0.665876, 0.746063, -0.0486921<br> |m| >
- 1.0<br> 25, 1.5, 0.618665, 0.785655, 0.372585<br> |m| > 1.0<br> -25,
- 1.5, -0.618665, 0.785655, 0.372585<br>
- </p>
- <h5>
- <a name="special_function_error_rates_rep.error_logs.h102"></a>
- <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_jacobi_cn_with1"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_jacobi_cn_with1">Error
- Output For jacobi_cn with compiler GNU C++ version 7.1.0 and library GSL 2.1
- and test data Jacobi Elliptic: Mathworld Data</a>
- </h5>
- <p>
- <a name="errors_GNU_C_version_7_1_0_linux_double_jacobi_cn_GSL_2_1_Jacobi_Elliptic_Mathworld_Data"></a>|m|
- > 1.0<br> 2.98023e-08, 1.5, 2.98023e-08, 1, 1<br> |m| > 1.0<br>
- -2.98023e-08, 1.5, -2.98023e-08, 1, 1<br> |m| > 1.0<br> 0.25, 1.5, 0.24183,
- 0.970319, 0.931888<br> |m| > 1.0<br> -0.25, 1.5, -0.24183, 0.970319,
- 0.931888<br> |m| > 1.0<br> 1.25, 1.5, 0.665876, 0.746063, -0.0486921<br>
- |m| > 1.0<br> -1.25, 1.5, -0.665876, 0.746063, -0.0486921<br> |m| >
- 1.0<br> 25, 1.5, 0.618665, 0.785655, 0.372585<br> |m| > 1.0<br> -25,
- 1.5, -0.618665, 0.785655, 0.372585<br>
- </p>
- <h5>
- <a name="special_function_error_rates_rep.error_logs.h103"></a>
- <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_jacobi_sn_with1"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_jacobi_sn_with1">Error
- Output For jacobi_sn with compiler GNU C++ version 7.1.0 and library GSL 2.1
- and test data Jacobi Elliptic: Mathworld Data</a>
- </h5>
- <p>
- <a name="errors_GNU_C_version_7_1_0_linux_double_jacobi_sn_GSL_2_1_Jacobi_Elliptic_Mathworld_Data"></a>|m|
- > 1.0<br> 2.98023e-08, 1.5, 2.98023e-08, 1, 1<br> |m| > 1.0<br>
- -2.98023e-08, 1.5, -2.98023e-08, 1, 1<br> |m| > 1.0<br> 0.25, 1.5, 0.24183,
- 0.970319, 0.931888<br> |m| > 1.0<br> -0.25, 1.5, -0.24183, 0.970319,
- 0.931888<br> |m| > 1.0<br> 1.25, 1.5, 0.665876, 0.746063, -0.0486921<br>
- |m| > 1.0<br> -1.25, 1.5, -0.665876, 0.746063, -0.0486921<br> |m| >
- 1.0<br> 25, 1.5, 0.618665, 0.785655, 0.372585<br> |m| > 1.0<br> -25,
- 1.5, -0.618665, 0.785655, 0.372585<br>
- </p>
- <h5>
- <a name="special_function_error_rates_rep.error_logs.h104"></a>
- <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_polygamma_with3"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_polygamma_with3">Error
- Output For polygamma with compiler GNU C++ version 7.1.0 and library GSL 2.1
- and test data Mathematica Data - Large orders and other bug cases</a>
- </h5>
- <p>
- <a name="errors_GNU_C_version_7_1_0_linux_double_polygamma_GSL_2_1_Mathematica_Data_Large_orders_and_other_bug_cases"></a>underflow<br>
- 168, 150, -6.52661e-66<br> underflow<br> 169, 202, 9.2734e-88<br> domain
- error<br> 20, -9.5, -0.00103076<br> domain error<br> 21, -9.5, 4.28582e+26<br>
- domain error<br> 22, -9.5, -0.00419144<br> domain error<br> 23, -9.5,
- 8.6745e+29<br> domain error<br> 24, -9.5, -0.0204825<br> domain error<br>
- 25, -9.5, 2.08188e+33<br> domain error<br> 26, -9.5, -0.118403<br> domain
- error<br> 27, -9.5, 5.84592e+36<br> domain error<br> 28, -9.5, -0.798969<br>
- domain error<br> 29, -9.5, 1.89875e+40<br> domain error<br> 30, -9.5,
- -6.22245<br> underflow<br> 10, 1.32923e+36, -0<br> underflow<br> 15,
- 1.32923e+36, 0<br>
- </p>
- <h5>
- <a name="special_function_error_rates_rep.error_logs.h105"></a>
- <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_polygamma_with4"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_polygamma_with4">Error
- Output For polygamma with compiler GNU C++ version 7.1.0 and library GSL 2.1
- and test data Mathematica Data - large negative arguments</a>
- </h5>
- <p>
- <a name="errors_GNU_C_version_7_1_0_linux_double_polygamma_GSL_2_1_Mathematica_Data_large_negative_arguments"></a>domain
- error<br> 124, -1.5, 7.63705e+240<br> domain error<br> 124, -2.5, 7.63705e+240<br>
- domain error<br> 124, -3.5, 7.63705e+240<br> domain error<br> 124, -4.5,
- 7.63705e+240<br> domain error<br> 124, -5.5, 7.63705e+240<br> domain
- error<br> 124, -6.5, 7.63705e+240<br> domain error<br> 124, -7.5, 7.63705e+240<br>
- domain error<br> 124, -8.5, 7.63705e+240<br> domain error<br> 124, -9.5,
- 7.63705e+240<br> domain error<br> 124, -10.5, 7.63705e+240<br> domain
- error<br> 124, -11.5, 7.63705e+240<br> domain error<br> 124, -12.5, 7.63705e+240<br>
- domain error<br> 124, -13.5, 7.63705e+240<br> domain error<br> 124, -14.5,
- 7.63705e+240<br> domain error<br> 124, -15.5, 7.63705e+240<br> domain
- error<br> 124, -16.5, 7.63705e+240<br> domain error<br> 124, -17.5, 7.63705e+240<br>
- domain error<br> 124, -18.5, 7.63705e+240<br> domain error<br> 124, -19.5,
- 7.63705e+240<br> domain error<br> 124, -20.5, 7.63705e+240<br> domain
- error<br> 124, -1.5, -7.63705e+240<br> domain error<br> 124, -2.5, -7.63705e+240<br>
- domain error<br> 124, -3.5, -7.63705e+240<br> domain error<br> 124, -4.5,
- -7.63705e+240<br> domain error<br> 124, -5.5, -7.63705e+240<br> domain
- error<br> 124, -6.5, -7.63705e+240<br> domain error<br> 124, -7.5, -7.63705e+240<br>
- domain error<br> 124, -8.5, -7.63705e+240<br> domain error<br> 124, -9.5,
- -7.63705e+240<br> domain error<br> 124, -10.5, -7.63705e+240<br> domain
- error<br> 124, -11.5, -7.63705e+240<br> domain error<br> 124, -12.5,
- -7.63705e+240<br> domain error<br> 124, -13.5, -7.63705e+240<br> domain
- error<br> 124, -14.5, -7.63705e+240<br> domain error<br> 124, -15.5,
- -7.63705e+240<br> domain error<br> 124, -16.5, -7.63705e+240<br> domain
- error<br> 124, -17.5, -7.63705e+240<br> domain error<br> 124, -18.5,
- -7.63705e+240<br> domain error<br> 124, -19.5, -7.63705e+240<br> domain
- error<br> 124, -20.5, -7.63705e+240<br> domain error<br> 2, -0.5, -0.828797<br>
- domain error<br> 3, -0.5, 193.409<br> domain error<br> 4, -0.5, -3.47425<br>
- domain error<br> 5, -0.5, 15371.1<br> domain error<br> 6, -0.5, -43.4579<br>
- domain error<br> 7, -0.5, 2.58068e+06<br> domain error<br> 8, -0.5, -1059.96<br>
- domain error<br> 9, -0.5, 7.43185e+08<br> domain error<br> 10, -0.5,
- -42108.9<br> domain error<br> 11, -0.5, 3.26999e+11<br> domain error<br>
- 12, -0.5, -2.46448e+06<br> domain error<br> 13, -0.5, 2.04047e+14<br>
- domain error<br> 14, -0.5, -1.9918e+08<br> domain error<br> 15, -0.5,
- 1.71399e+17<br> domain error<br> 16, -0.5, -2.12394e+10<br> domain error<br>
- 17, -0.5, 1.86483e+20<br> domain error<br> 18, -0.5, -2.88824e+12<br>
- domain error<br> 19, -0.5, 2.55108e+23<br> domain error<br> 20, -0.5,
- -4.87773e+14<br> domain error<br> 21, -0.5, 4.28582e+26<br> domain error<br>
- 2, -0.5, -0.828843<br> domain error<br> 3, -0.5, 193.409<br> domain error<br>
- 4, -0.5, -3.47791<br> domain error<br> 5, -0.5, 15371.1<br> domain error<br>
- 6, -0.5, -44.0732<br> domain error<br> 7, -0.5, 2.58068e+06<br> domain
- error<br> 8, -0.5, -1237.15<br> domain error<br> 9, -0.5, 7.43185e+08<br>
- domain error<br> 10, -0.5, -120071<br> domain error<br> 11, -0.5, 3.26999e+11<br>
- domain error<br> 12, -0.5, -5.11131e+07<br> domain error<br> 13, -0.5,
- 2.04047e+14<br> domain error<br> 14, -0.5, -4.1064e+10<br> domain error<br>
- 15, -0.5, 1.71399e+17<br> domain error<br> 16, -0.5, -4.44822e+13<br>
- domain error<br> 17, -0.5, 1.86483e+20<br> domain error<br> 18, -0.5,
- -6.08254e+16<br> domain error<br> 19, -0.5, 2.55108e+23<br> domain error<br>
- 20, -0.5, -1.02182e+20<br> domain error<br> 21, -0.5, 4.28582e+26<br>
- domain error<br> 2, -0.5, -0.828751<br> domain error<br> 3, -0.5, 193.409<br>
- domain error<br> 4, -0.5, -3.47059<br> domain error<br> 5, -0.5, 15371.1<br>
- domain error<br> 6, -0.5, -42.8426<br> domain error<br> 7, -0.5, 2.58068e+06<br>
- domain error<br> 8, -0.5, -882.773<br> domain error<br> 9, -0.5, 7.43185e+08<br>
- domain error<br> 10, -0.5, 35853.7<br> domain error<br> 11, -0.5, 3.26999e+11<br>
- domain error<br> 12, -0.5, 4.61841e+07<br> domain error<br> 13, -0.5,
- 2.04047e+14<br> domain error<br> 14, -0.5, 4.06656e+10<br> domain error<br>
- 15, -0.5, 1.71399e+17<br> domain error<br> 16, -0.5, 4.44397e+13<br>
- domain error<br> 17, -0.5, 1.86483e+20<br> domain error<br> 18, -0.5,
- 6.08197e+16<br> domain error<br> 19, -0.5, 2.55108e+23<br> domain error<br>
- 20, -0.5, 1.02181e+20<br> domain error<br> 21, -0.5, 4.28582e+26<br>
- </p>
- <h5>
- <a name="special_function_error_rates_rep.error_logs.h106"></a>
- <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_polygamma_with5"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_polygamma_with5">Error
- Output For polygamma with compiler GNU C++ version 7.1.0 and library GSL 2.1
- and test data Mathematica Data - negative arguments</a>
- </h5>
- <p>
- <a name="errors_GNU_C_version_7_1_0_linux_double_polygamma_GSL_2_1_Mathematica_Data_negative_arguments"></a>domain
- error<br> 2, -12.75, -124.031<br> domain error<br> 2, -12.25, 124.019<br>
- domain error<br> 2, -11.75, -124.032<br> domain error<br> 2, -11.25,
- 124.018<br> domain error<br> 2, -10.75, -124.033<br> domain error<br>
- 2, -10.25, 124.016<br> domain error<br> 2, -9.75, -124.035<br> domain
- error<br> 2, -9.25, 124.015<br> domain error<br> 2, -8.75, -124.037<br>
- domain error<br> 2, -8.25, 124.012<br> domain error<br> 2, -7.75, -124.04<br>
- domain error<br> 2, -7.25, 124.009<br> domain error<br> 2, -6.75, -124.044<br>
- domain error<br> 2, -6.25, 124.003<br> domain error<br> 2, -5.75, -124.051<br>
- domain error<br> 2, -5.25, 123.995<br> domain error<br> 2, -4.75, -124.061<br>
- domain error<br> 2, -4.25, 123.981<br> domain error<br> 2, -3.75, -124.08<br>
- domain error<br> 2, -3.25, 123.955<br> domain error<br> 2, -2.75, -124.118<br>
- domain error<br> 2, -2.25, 123.897<br> domain error<br> 2, -1.75, -124.214<br>
- domain error<br> 2, -1.25, 123.721<br> domain error<br> 2, -0.75, -124.587<br>
- domain error<br> 2, -0.25, 122.697<br> domain error<br> 3, -12.75, 1558.54<br>
- domain error<br> 3, -12.25, 1558.54<br> domain error<br> 3, -11.75, 1558.54<br>
- domain error<br> 3, -11.25, 1558.54<br> domain error<br> 3, -10.75, 1558.54<br>
- domain error<br> 3, -10.25, 1558.54<br> domain error<br> 3, -9.75, 1558.54<br>
- domain error<br> 3, -9.25, 1558.54<br> domain error<br> 3, -8.75, 1558.54<br>
- domain error<br> 3, -8.25, 1558.54<br> domain error<br> 3, -7.75, 1558.54<br>
- domain error<br> 3, -7.25, 1558.54<br> domain error<br> 3, -6.75, 1558.54<br>
- domain error<br> 3, -6.25, 1558.54<br> domain error<br> 3, -5.75, 1558.54<br>
- domain error<br> 3, -5.25, 1558.54<br> domain error<br> 3, -4.75, 1558.53<br>
- domain error<br> 3, -4.25, 1558.53<br> domain error<br> 3, -3.75, 1558.52<br>
- domain error<br> 3, -3.25, 1558.51<br> domain error<br> 3, -2.75, 1558.49<br>
- domain error<br> 3, -2.25, 1558.46<br> domain error<br> 3, -1.75, 1558.38<br>
- domain error<br> 3, -1.25, 1558.22<br> domain error<br> 3, -0.75, 1557.75<br>
- domain error<br> 3, -0.25, 1555.76<br> domain error<br> 4, -12.75, -24481.6<br>
- domain error<br> 4, -12.25, 24481.6<br> domain error<br> 4, -11.75, -24481.6<br>
- domain error<br> 4, -11.25, 24481.6<br> domain error<br> 4, -10.75, -24481.6<br>
- domain error<br> 4, -10.25, 24481.6<br> domain error<br> 4, -9.75, -24481.6<br>
- domain error<br> 4, -9.25, 24481.6<br> domain error<br> 4, -8.75, -24481.6<br>
- domain error<br> 4, -8.25, 24481.6<br> domain error<br> 4, -7.75, -24481.6<br>
- domain error<br> 4, -7.25, 24481.6<br> domain error<br> 4, -6.75, -24481.6<br>
- domain error<br> 4, -6.25, 24481.6<br> domain error<br> 4, -5.75, -24481.6<br>
- domain error<br> 4, -5.25, 24481.6<br> domain error<br> 4, -4.75, -24481.6<br>
- domain error<br> 4, -4.25, 24481.6<br> domain error<br> 4, -3.75, -24481.6<br>
- domain error<br> 4, -3.25, 24481.5<br> domain error<br> 4, -2.75, -24481.6<br>
- domain error<br> 4, -2.25, 24481.5<br> domain error<br> 4, -1.75, -24481.8<br>
- domain error<br> 4, -1.25, 24481.1<br> domain error<br> 4, -0.75, -24483.2<br>
- domain error<br> 4, -0.25, 24473.2<br> domain error<br> 5, -12.75, 492231<br>
- domain error<br> 5, -12.25, 492231<br> domain error<br> 5, -11.75, 492231<br>
- domain error<br> 5, -11.25, 492231<br> domain error<br> 5, -10.75, 492231<br>
- domain error<br> 5, -10.25, 492231<br> domain error<br> 5, -9.75, 492231<br>
- domain error<br> 5, -9.25, 492231<br> domain error<br> 5, -8.75, 492231<br>
- domain error<br> 5, -8.25, 492231<br> domain error<br> 5, -7.75, 492231<br>
- domain error<br> 5, -7.25, 492231<br> domain error<br> 5, -6.75, 492231<br>
- domain error<br> 5, -6.25, 492231<br> domain error<br> 5, -5.75, 492231<br>
- domain error<br> 5, -5.25, 492231<br> domain error<br> 5, -4.75, 492231<br>
- domain error<br> 5, -4.25, 492231<br> domain error<br> 5, -3.75, 492231<br>
- domain error<br> 5, -3.25, 492231<br> domain error<br> 5, -2.75, 492231<br>
- domain error<br> 5, -2.25, 492231<br> domain error<br> 5, -1.75, 492231<br>
- domain error<br> 5, -1.25, 492230<br> domain error<br> 5, -0.75, 492227<br>
- domain error<br> 5, -0.25, 492199<br> domain error<br> 6, -12.75, -1.17912e+07<br>
- domain error<br> 6, -12.25, 1.17912e+07<br> domain error<br> 6, -11.75,
- -1.17912e+07<br> domain error<br> 6, -11.25, 1.17912e+07<br> domain error<br>
- 6, -10.75, -1.17912e+07<br> domain error<br> 6, -10.25, 1.17912e+07<br>
- domain error<br> 6, -9.75, -1.17912e+07<br> domain error<br> 6, -9.25,
- 1.17912e+07<br> domain error<br> 6, -8.75, -1.17912e+07<br> domain error<br>
- 6, -8.25, 1.17912e+07<br> domain error<br> 6, -7.75, -1.17912e+07<br>
- domain error<br> 6, -7.25, 1.17912e+07<br> domain error<br> 6, -6.75,
- -1.17912e+07<br> domain error<br> 6, -6.25, 1.17912e+07<br> domain error<br>
- 6, -5.75, -1.17912e+07<br> domain error<br> 6, -5.25, 1.17912e+07<br>
- domain error<br> 6, -4.75, -1.17912e+07<br> domain error<br> 6, -4.25,
- 1.17912e+07<br> domain error<br> 6, -3.75, -1.17912e+07<br> domain error<br>
- 6, -3.25, 1.17912e+07<br> domain error<br> 6, -2.75, -1.17912e+07<br>
- domain error<br> 6, -2.25, 1.17912e+07<br> domain error<br> 6, -1.75,
- -1.17912e+07<br> domain error<br> 6, -1.25, 1.17912e+07<br> *** FURTHER
- CONTENT HAS BEEN TRUNCATED FOR BREVITY ***<br>
- </p>
- <h5>
- <a name="special_function_error_rates_rep.error_logs.h107"></a>
- <span class="phrase"><a name="special_function_error_rates_rep.error_logs.error_output_for_polygamma_with6"></a></span><a class="link" href="index.html#special_function_error_rates_rep.error_logs.error_output_for_polygamma_with6">Error
- Output For polygamma with compiler GNU C++ version 7.1.0 and library GSL 2.1
- and test data Mathematica Data - large arguments</a>
- </h5>
- <p>
- <a name="errors_GNU_C_version_7_1_0_linux_double_polygamma_GSL_2_1_Mathematica_Data_large_arguments"></a>underflow<br>
- 30, 8.58993e+09, -8.44974e-268<br> underflow<br> 30, 1.71799e+10, -7.86943e-277<br>
- underflow<br> 30, 3.43597e+10, -7.32898e-286<br> underflow<br> 30, 6.87195e+10,
- -6.82564e-295<br> underflow<br> 30, 1.37439e+11, -6.35687e-304<br> underflow<br>
- 30, 2.74878e+11, -5.9203e-313<br> underflow<br> 30, 5.49756e+11, -5.53354e-322<br>
- underflow<br> 30, 1.09951e+12, -0<br> underflow<br> 30, 2.19902e+12,
- -0<br> underflow<br> 30, 4.39805e+12, -0<br> underflow<br> 30, 8.79609e+12,
- -0<br> underflow<br> 30, 1.75922e+13, -0<br> underflow<br> 30, 3.51844e+13,
- -0<br> underflow<br> 30, 7.03687e+13, -0<br> underflow<br> 30, 1.40737e+14,
- -0<br> underflow<br> 30, 2.81475e+14, -0<br> underflow<br> 30, 5.6295e+14,
- -0<br> underflow<br> 30, 1.1259e+15, -0<br> underflow<br> 30, 2.2518e+15,
- -0<br> underflow<br> 30, 4.5036e+15, -0<br> underflow<br> 30, 9.0072e+15,
- -0<br> underflow<br> 30, 1.80144e+16, -0<br> underflow<br> 30, 3.60288e+16,
- -0<br> underflow<br> 30, 7.20576e+16, -0<br> underflow<br> 30, 1.44115e+17,
- -0<br> underflow<br> 30, 2.8823e+17, -0<br> underflow<br> 30, 5.76461e+17,
- -0<br> underflow<br> 30, 1.15292e+18, -0<br> underflow<br> 30, 2.30584e+18,
- -0<br> underflow<br> 30, 4.61169e+18, -0<br> underflow<br> 30, 9.22337e+18,
- -0<br> underflow<br> 30, 1.84467e+19, -0<br> underflow<br> 30, 3.68935e+19,
- -0<br> underflow<br> 30, 7.3787e+19, -0<br> underflow<br> 30, 1.47574e+20,
- -0<br> underflow<br> 30, 2.95148e+20, -0<br> underflow<br> 30, 5.90296e+20,
- -0<br> underflow<br> 30, 1.18059e+21, -0<br> underflow<br> 30, 2.36118e+21,
- -0<br> underflow<br> 30, 4.72237e+21, -0<br> underflow<br> 30, 9.44473e+21,
- -0<br> underflow<br> 30, 1.88895e+22, -0<br> underflow<br> 30, 3.77789e+22,
- -0<br> underflow<br> 30, 7.55579e+22, -0<br> underflow<br> 30, 1.51116e+23,
- -0<br> underflow<br> 30, 3.02231e+23, -0<br> underflow<br> 30, 6.04463e+23,
- -0<br> underflow<br> 30, 1.20893e+24, -0<br> underflow<br> 30, 2.41785e+24,
- -0<br> underflow<br> 30, 4.8357e+24, -0<br> underflow<br> 30, 9.67141e+24,
- -0<br> underflow<br> 30, 1.93428e+25, -0<br> underflow<br> 30, 3.86856e+25,
- -0<br> underflow<br> 30, 7.73713e+25, -0<br> underflow<br> 30, 1.54743e+26,
- -0<br> underflow<br> 30, 3.09485e+26, -0<br> underflow<br> 30, 6.1897e+26,
- -0<br> underflow<br> 30, 1.23794e+27, -0<br> underflow<br> 30, 2.47588e+27,
- -0<br> underflow<br> 30, 4.95176e+27, -0<br> underflow<br> 30, 9.90352e+27,
- -0<br> underflow<br> 30, 1.9807e+28, -0<br> underflow<br> 30, 3.96141e+28,
- -0<br> underflow<br> 30, 7.92282e+28, -0<br> underflow<br> 30, 1.58456e+29,
- -0<br> underflow<br> 30, 3.16913e+29, -0<br> underflow<br> 30, 6.33825e+29,
- -0<br> underflow<br> 30, 1.26765e+30, -0<br>
- </p>
- </div>
- <div class="section">
- <div class="titlepage"><div><div><h2 class="title" style="clear: both">
- <a name="special_function_error_rates_rep.all_the_tables"></a><a class="link" href="index.html#special_function_error_rates_rep.all_the_tables" title="Tables">Tables</a>
- </h2></div></div></div>
- <div class="table">
- <a name="special_function_error_rates_rep.all_the_tables.table_beta"></a><p class="title"><b>Table 97. Error rates for beta</b></p>
- <div class="table-contents"><table class="table" summary="Error rates for beta">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> double
- </p>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> long double
- </p>
- </th>
- <th>
- <p>
- Sun compiler version 0x5150<br> Sun Solaris<br> long double
- </p>
- </th>
- <th>
- <p>
- Microsoft Visual C++ version 14.1<br> Win32<br> double
- </p>
- </th>
- </tr></thead>
- <tbody>
- <tr>
- <td>
- <p>
- Beta Function: Small Values
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> <span class="red">Max = +INFε (Mean = +INFε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_beta_GSL_2_1_Beta_Function_Small_Values">And
- other failures.</a>)</span><br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
- Max = 1.14ε (Mean = 0.574ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 2.86ε (Mean = 1.22ε)</span><br> <br>
- (<span class="emphasis"><em><cmath>:</em></span> Max = 364ε (Mean = 76.2ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 2.86ε (Mean = 1.22ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 2.23ε (Mean = 1.14ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Beta Function: Medium Values
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.978ε (Mean = 0.0595ε)</span><br> <br>
- (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 1.18e+03ε (Mean = 238ε))<br>
- (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 1.09e+03ε (Mean = 265ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 61.4ε (Mean = 19.4ε)</span><br> <br>
- (<span class="emphasis"><em><cmath>:</em></span> Max = 1.07e+03ε (Mean = 264ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 107ε (Mean = 24.5ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 96.5ε (Mean = 22.4ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Beta Function: Divergent Values
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 12.1ε (Mean = 1.99ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
- Max = 176ε (Mean = 28ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 8.99ε (Mean = 2.44ε)</span><br> <br>
- (<span class="emphasis"><em><cmath>:</em></span> Max = 128ε (Mean = 23.8ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 18.8ε (Mean = 2.71ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 11.4ε (Mean = 2.19ε)</span>
- </p>
- </td>
- </tr>
- </tbody>
- </table></div>
- </div>
- <br class="table-break"><div class="table">
- <a name="special_function_error_rates_rep.all_the_tables.table_beta_incomplete_"></a><p class="title"><b>Table 98. Error rates for beta (incomplete)</b></p>
- <div class="table-contents"><table class="table" summary="Error rates for beta (incomplete)">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> double
- </p>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> long double
- </p>
- </th>
- <th>
- <p>
- Sun compiler version 0x5150<br> Sun Solaris<br> long double
- </p>
- </th>
- <th>
- <p>
- Microsoft Visual C++ version 14.1<br> Win32<br> double
- </p>
- </th>
- </tr></thead>
- <tbody>
- <tr>
- <td>
- <p>
- Incomplete Beta Function: Small Values
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 11.1ε (Mean = 2.32ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 18.7ε (Mean = 3.19ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 9.94ε (Mean = 2.17ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Incomplete Beta Function: Medium Values
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.568ε (Mean = 0.0254ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 69.2ε (Mean = 13.4ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 174ε (Mean = 25ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 90ε (Mean = 12.7ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Incomplete Beta Function: Large and Diverse Values
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.999ε (Mean = 0.0325ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 6.84e+04ε (Mean = 2.76e+03ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 6.86e+04ε (Mean = 2.79e+03ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 633ε (Mean = 29.7ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Incomplete Beta Function: Small Integer Values
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.786ε (Mean = 0.0323ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 11.6ε (Mean = 3.6ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 51.8ε (Mean = 11ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 26ε (Mean = 6.28ε)</span>
- </p>
- </td>
- </tr>
- </tbody>
- </table></div>
- </div>
- <br class="table-break"><div class="table">
- <a name="special_function_error_rates_rep.all_the_tables.table_betac"></a><p class="title"><b>Table 99. Error rates for betac</b></p>
- <div class="table-contents"><table class="table" summary="Error rates for betac">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> double
- </p>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> long double
- </p>
- </th>
- <th>
- <p>
- Sun compiler version 0x5150<br> Sun Solaris<br> long double
- </p>
- </th>
- <th>
- <p>
- Microsoft Visual C++ version 14.1<br> Win32<br> double
- </p>
- </th>
- </tr></thead>
- <tbody>
- <tr>
- <td>
- <p>
- Incomplete Beta Function: Small Values
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.676ε (Mean = 0.0302ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 9.92ε (Mean = 2.3ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 11.2ε (Mean = 2.94ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 8.94ε (Mean = 2.06ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Incomplete Beta Function: Medium Values
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.949ε (Mean = 0.098ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 63.5ε (Mean = 13.5ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 97.6ε (Mean = 24.3ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 90.6ε (Mean = 14.8ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Incomplete Beta Function: Large and Diverse Values
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.12ε (Mean = 0.0458ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.05e+05ε (Mean = 5.45e+03ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.04e+05ε (Mean = 5.46e+03ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 3.72e+03ε (Mean = 113ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Incomplete Beta Function: Small Integer Values
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.586ε (Mean = 0.0314ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 11.1ε (Mean = 3.65ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 103ε (Mean = 17.4ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 26.2ε (Mean = 6.36ε)</span>
- </p>
- </td>
- </tr>
- </tbody>
- </table></div>
- </div>
- <br class="table-break"><div class="table">
- <a name="special_function_error_rates_rep.all_the_tables.table_binomial_coefficient"></a><p class="title"><b>Table 100. Error rates for binomial_coefficient</b></p>
- <div class="table-contents"><table class="table" summary="Error rates for binomial_coefficient">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> double
- </p>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> long double
- </p>
- </th>
- <th>
- <p>
- Sun compiler version 0x5150<br> Sun Solaris<br> long double
- </p>
- </th>
- <th>
- <p>
- Microsoft Visual C++ version 14.1<br> Win32<br> double
- </p>
- </th>
- </tr></thead>
- <tbody>
- <tr>
- <td>
- <p>
- Binomials: small arguments
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1ε (Mean = 0.369ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.5ε (Mean = 0.339ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.5ε (Mean = 0.339ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1ε (Mean = 0.369ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Binomials: large arguments
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.939ε (Mean = 0.314ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 26.6ε (Mean = 6.13ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 53.2ε (Mean = 10.8ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 37.2ε (Mean = 7.4ε)</span>
- </p>
- </td>
- </tr>
- </tbody>
- </table></div>
- </div>
- <br class="table-break"><div class="table">
- <a name="special_function_error_rates_rep.all_the_tables.table_boost_math_powm1"></a><p class="title"><b>Table 101. Error rates for boost::math::powm1</b></p>
- <div class="table-contents"><table class="table" summary="Error rates for boost::math::powm1">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> long double
- </p>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> double
- </p>
- </th>
- <th>
- <p>
- Sun compiler version 0x5150<br> Sun Solaris<br> long double
- </p>
- </th>
- <th>
- <p>
- Microsoft Visual C++ version 14.1<br> Win32<br> double
- </p>
- </th>
- </tr></thead>
- <tbody><tr>
- <td>
- <p>
- powm1
- </p>
- </td>
- <td>
- <p>
- (<span class="emphasis"><em><math.h>:</em></span> Max = 2.04ε (Mean = 0.493ε))<br>
- <br> <span class="blue">Max = 2.04ε (Mean = 0.493ε)</span><br>
- <br> (<span class="emphasis"><em><cmath>:</em></span> Max = 2.04ε (Mean = 0.493ε))
- </p>
- </td>
- <td>
- <p>
- (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 1.06ε (Mean = 0.425ε))<br>
- <br> (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 1.06ε (Mean = 0.425ε))<br>
- <br> <span class="blue">Max = 1.06ε (Mean = 0.425ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.88ε (Mean = 0.49ε)</span><br> <br>
- (<span class="emphasis"><em><math.h>:</em></span> Max = 1.88ε (Mean = 0.49ε))
- </p>
- </td>
- <td>
- <p>
- (<span class="emphasis"><em><math.h>:</em></span> Max = 1.84ε (Mean = 0.486ε))<br>
- <br> <span class="blue">Max = 1.84ε (Mean = 0.486ε)</span>
- </p>
- </td>
- </tr></tbody>
- </table></div>
- </div>
- <br class="table-break"><div class="table">
- <a name="special_function_error_rates_rep.all_the_tables.table_cbrt"></a><p class="title"><b>Table 102. Error rates for cbrt</b></p>
- <div class="table-contents"><table class="table" summary="Error rates for cbrt">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> double
- </p>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> long double
- </p>
- </th>
- <th>
- <p>
- Sun compiler version 0x5150<br> Sun Solaris<br> long double
- </p>
- </th>
- <th>
- <p>
- Microsoft Visual C++ version 14.1<br> Win32<br> double
- </p>
- </th>
- </tr></thead>
- <tbody><tr>
- <td>
- <p>
- cbrt Function
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.34ε (Mean = 0.471ε)</span><br> <br>
- (<span class="emphasis"><em><cmath>:</em></span> Max = 1.34ε (Mean = 0.471ε))<br>
- (<span class="emphasis"><em><math.h>:</em></span> Max = 1.34ε (Mean = 0.471ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.34ε (Mean = 0.471ε)</span><br> <br>
- (<span class="emphasis"><em><math.h>:</em></span> Max = 1.34ε (Mean = 0.471ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.7ε (Mean = 0.565ε)</span><br> <br>
- (<span class="emphasis"><em><math.h>:</em></span> Max = 1.7ε (Mean = 0.565ε))
- </p>
- </td>
- </tr></tbody>
- </table></div>
- </div>
- <br class="table-break"><div class="table">
- <a name="special_function_error_rates_rep.all_the_tables.table_cos_pi"></a><p class="title"><b>Table 103. Error rates for cos_pi</b></p>
- <div class="table-contents"><table class="table" summary="Error rates for cos_pi">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> double
- </p>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> long double
- </p>
- </th>
- <th>
- <p>
- Sun compiler version 0x5150<br> Sun Solaris<br> long double
- </p>
- </th>
- <th>
- <p>
- Microsoft Visual C++ version 14.1<br> Win32<br> double
- </p>
- </th>
- </tr></thead>
- <tbody>
- <tr>
- <td>
- <p>
- sin_pi and cos_pi
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.991ε (Mean = 0.302ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.991ε (Mean = 0.302ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.996ε (Mean = 0.284ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- sin_pi and cos_pi near integers and half integers
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.976ε (Mean = 0.28ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.976ε (Mean = 0.28ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.996ε (Mean = 0.298ε)</span>
- </p>
- </td>
- </tr>
- </tbody>
- </table></div>
- </div>
- <br class="table-break"><div class="table">
- <a name="special_function_error_rates_rep.all_the_tables.table_cyl_bessel_i"></a><p class="title"><b>Table 104. Error rates for cyl_bessel_i</b></p>
- <div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_i">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> double
- </p>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> long double
- </p>
- </th>
- <th>
- <p>
- Sun compiler version 0x5150<br> Sun Solaris<br> long double
- </p>
- </th>
- <th>
- <p>
- Microsoft Visual C++ version 14.1<br> Win32<br> double
- </p>
- </th>
- </tr></thead>
- <tbody>
- <tr>
- <td>
- <p>
- Bessel I0: Mathworld Data
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 270ε (Mean = 91.6ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_GSL_2_1_Bessel_I0_Mathworld_Data">And
- other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
- Max = 1.52ε (Mean = 0.622ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_Rmath_3_2_3_Bessel_I0_Mathworld_Data">And
- other failures.</a>)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.95ε (Mean = 0.738ε)</span><br> <br>
- (<span class="emphasis"><em><cmath>:</em></span> Max = 8.49ε (Mean = 3.46ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_i__cmath__Bessel_I0_Mathworld_Data">And
- other failures.</a>)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.95ε (Mean = 0.661ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.762ε (Mean = 0.329ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Bessel I1: Mathworld Data
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 128ε (Mean = 41ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_GSL_2_1_Bessel_I1_Mathworld_Data">And
- other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
- Max = 1.53ε (Mean = 0.483ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_Rmath_3_2_3_Bessel_I1_Mathworld_Data">And
- other failures.</a>)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.64ε (Mean = 0.202ε)</span><br> <br>
- (<span class="emphasis"><em><cmath>:</em></span> Max = 5ε (Mean = 2.15ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_i__cmath__Bessel_I1_Mathworld_Data">And
- other failures.</a>)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.64ε (Mean = 0.202ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.767ε (Mean = 0.398ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Bessel In: Mathworld Data
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 2.31ε (Mean = 0.838ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_GSL_2_1_Bessel_In_Mathworld_Data">And
- other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
- Max = 1.73ε (Mean = 0.601ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_Rmath_3_2_3_Bessel_In_Mathworld_Data">And
- other failures.</a>)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.8ε (Mean = 1.33ε)</span><br> <br>
- (<span class="emphasis"><em><cmath>:</em></span> Max = 430ε (Mean = 163ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_i__cmath__Bessel_In_Mathworld_Data">And
- other failures.</a>)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 463ε (Mean = 140ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 3.46ε (Mean = 1.32ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Bessel Iv: Mathworld Data
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 5.95ε (Mean = 2.08ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_GSL_2_1_Bessel_Iv_Mathworld_Data">And
- other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
- Max = 3.53ε (Mean = 1.39ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 4.12ε (Mean = 1.85ε)</span><br> <br>
- (<span class="emphasis"><em><cmath>:</em></span> Max = 616ε (Mean = 221ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_i__cmath__Bessel_Iv_Mathworld_Data">And
- other failures.</a>)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 4.12ε (Mean = 1.95ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 2.97ε (Mean = 1.24ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Bessel In: Random Data
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 261ε (Mean = 53.2ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_GSL_2_1_Bessel_In_Random_Data">And
- other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
- Max = 7.37ε (Mean = 2.4ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 4.62ε (Mean = 1.06ε)</span><br> <br>
- (<span class="emphasis"><em><cmath>:</em></span> Max = 645ε (Mean = 132ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 176ε (Mean = 39.1ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 9.67ε (Mean = 1.88ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Bessel Iv: Random Data
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.661ε (Mean = 0.0441ε)</span><br> <br>
- (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 6.18e+03ε (Mean = 1.55e+03ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_GSL_2_1_Bessel_Iv_Random_Data">And
- other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
- <span class="red">Max = 4.28e+08ε (Mean = 2.85e+07ε))</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 8.35ε (Mean = 1.62ε)</span><br> <br>
- (<span class="emphasis"><em><cmath>:</em></span> Max = 1.05e+03ε (Mean = 224ε)
- <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_i__cmath__Bessel_Iv_Random_Data">And
- other failures.</a>)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 283ε (Mean = 88.4ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 7.46ε (Mean = 1.71ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Bessel Iv: Mathworld Data (large values)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 37ε (Mean = 18ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_GSL_2_1_Bessel_Iv_Mathworld_Data_large_values_">And
- other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
- <span class="red">Max = 3.77e+168ε (Mean = 2.39e+168ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_Rmath_3_2_3_Bessel_Iv_Mathworld_Data_large_values_">And
- other failures.</a>)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 14.7ε (Mean = 6.66ε)</span><br> <br>
- (<span class="emphasis"><em><cmath>:</em></span> Max = 118ε (Mean = 57.2ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_i__cmath__Bessel_Iv_Mathworld_Data_large_values_">And
- other failures.</a>)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 14.7ε (Mean = 6.59ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 3.67ε (Mean = 1.64ε)</span>
- </p>
- </td>
- </tr>
- </tbody>
- </table></div>
- </div>
- <br class="table-break"><div class="table">
- <a name="special_function_error_rates_rep.all_the_tables.table_cyl_bessel_i_integer_orders_"></a><p class="title"><b>Table 105. Error rates for cyl_bessel_i (integer orders)</b></p>
- <div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_i (integer orders)">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> double
- </p>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> long double
- </p>
- </th>
- <th>
- <p>
- Sun compiler version 0x5150<br> Sun Solaris<br> long double
- </p>
- </th>
- <th>
- <p>
- Microsoft Visual C++ version 14.1<br> Win32<br> double
- </p>
- </th>
- </tr></thead>
- <tbody>
- <tr>
- <td>
- <p>
- Bessel I0: Mathworld Data (Integer Version)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 0.79ε (Mean = 0.482ε))<br> (<span class="emphasis"><em>Rmath
- 3.2.3:</em></span> Max = 1.52ε (Mean = 0.622ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_integer_orders__Rmath_3_2_3_Bessel_I0_Mathworld_Data_Integer_Version_">And
- other failures.</a>)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.95ε (Mean = 0.738ε)</span><br> <br>
- (<span class="emphasis"><em><cmath>:</em></span> Max = 8.49ε (Mean = 3.46ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_i_integer_orders___cmath__Bessel_I0_Mathworld_Data_Integer_Version_">And
- other failures.</a>)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.95ε (Mean = 0.661ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.762ε (Mean = 0.329ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Bessel I1: Mathworld Data (Integer Version)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 0.82ε (Mean = 0.456ε))<br> (<span class="emphasis"><em>Rmath
- 3.2.3:</em></span> Max = 1.53ε (Mean = 0.483ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_integer_orders__Rmath_3_2_3_Bessel_I1_Mathworld_Data_Integer_Version_">And
- other failures.</a>)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.64ε (Mean = 0.202ε)</span><br> <br>
- (<span class="emphasis"><em><cmath>:</em></span> Max = 5ε (Mean = 2.15ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_i_integer_orders___cmath__Bessel_I1_Mathworld_Data_Integer_Version_">And
- other failures.</a>)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.64ε (Mean = 0.202ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.767ε (Mean = 0.398ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Bessel In: Mathworld Data (Integer Version)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 5.15ε (Mean = 2.13ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_integer_orders__GSL_2_1_Bessel_In_Mathworld_Data_Integer_Version_">And
- other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
- Max = 1.73ε (Mean = 0.601ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_i_integer_orders__Rmath_3_2_3_Bessel_In_Mathworld_Data_Integer_Version_">And
- other failures.</a>)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.8ε (Mean = 1.33ε)</span><br> <br>
- (<span class="emphasis"><em><cmath>:</em></span> Max = 430ε (Mean = 163ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_i_integer_orders___cmath__Bessel_In_Mathworld_Data_Integer_Version_">And
- other failures.</a>)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 463ε (Mean = 140ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 3.46ε (Mean = 1.32ε)</span>
- </p>
- </td>
- </tr>
- </tbody>
- </table></div>
- </div>
- <br class="table-break"><div class="table">
- <a name="special_function_error_rates_rep.all_the_tables.table_cyl_bessel_i_prime"></a><p class="title"><b>Table 106. Error rates for cyl_bessel_i_prime</b></p>
- <div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_i_prime">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> double
- </p>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> long double
- </p>
- </th>
- <th>
- <p>
- Sun compiler version 0x5150<br> Sun Solaris<br> long double
- </p>
- </th>
- <th>
- <p>
- Microsoft Visual C++ version 14.1<br> Win32<br> double
- </p>
- </th>
- </tr></thead>
- <tbody>
- <tr>
- <td>
- <p>
- Bessel I'0: Mathworld Data
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.82ε (Mean = 0.259ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.82ε (Mean = 0.259ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.82ε (Mean = 0.354ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Bessel I'1: Mathworld Data
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.97ε (Mean = 0.757ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.97ε (Mean = 0.757ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.36ε (Mean = 0.782ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Bessel I'n: Mathworld Data
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 2.31ε (Mean = 1.41ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 701ε (Mean = 212ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 3.61ε (Mean = 1.22ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Bessel I'v: Mathworld Data
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.62ε (Mean = 0.512ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 2.89e+03ε (Mean = 914ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 2.89e+03ε (Mean = 914ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 3.76e+03ε (Mean = 1.19e+03ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Bessel I'n: Random Data
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 3.95ε (Mean = 1.06ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 195ε (Mean = 37.1ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 9.85ε (Mean = 1.82ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Bessel I'v: Random Data
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 14.1ε (Mean = 2.93ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 336ε (Mean = 68.5ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 14ε (Mean = 2.5ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Bessel I'v: Mathworld Data (large values)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 42.6ε (Mean = 20.2ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 42.6ε (Mean = 20.2ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 59.5ε (Mean = 26.6ε)</span>
- </p>
- </td>
- </tr>
- </tbody>
- </table></div>
- </div>
- <br class="table-break"><div class="table">
- <a name="special_function_error_rates_rep.all_the_tables.table_cyl_bessel_i_prime_integer_orders_"></a><p class="title"><b>Table 107. Error rates for cyl_bessel_i_prime (integer orders)</b></p>
- <div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_i_prime (integer orders)">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> double
- </p>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> long double
- </p>
- </th>
- <th>
- <p>
- Sun compiler version 0x5150<br> Sun Solaris<br> long double
- </p>
- </th>
- <th>
- <p>
- Microsoft Visual C++ version 14.1<br> Win32<br> double
- </p>
- </th>
- </tr></thead>
- <tbody>
- <tr>
- <td>
- <p>
- Bessel I'0: Mathworld Data (Integer Version)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.82ε (Mean = 0.259ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.82ε (Mean = 0.259ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.82ε (Mean = 0.354ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Bessel I'1: Mathworld Data (Integer Version)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.97ε (Mean = 0.757ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.97ε (Mean = 0.757ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.36ε (Mean = 0.782ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Bessel I'n: Mathworld Data (Integer Version)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 2.31ε (Mean = 1.41ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 701ε (Mean = 212ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 3.61ε (Mean = 1.22ε)</span>
- </p>
- </td>
- </tr>
- </tbody>
- </table></div>
- </div>
- <br class="table-break"><div class="table">
- <a name="special_function_error_rates_rep.all_the_tables.table_cyl_bessel_j"></a><p class="title"><b>Table 108. Error rates for cyl_bessel_j</b></p>
- <div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_j">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> long double
- </p>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> double
- </p>
- </th>
- <th>
- <p>
- Sun compiler version 0x5150<br> Sun Solaris<br> long double
- </p>
- </th>
- <th>
- <p>
- Microsoft Visual C++ version 14.1<br> Win32<br> double
- </p>
- </th>
- </tr></thead>
- <tbody>
- <tr>
- <td>
- <p>
- Bessel J0: Mathworld Data
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 6.55ε (Mean = 2.86ε)</span><br> <br>
- (<span class="emphasis"><em><cmath>:</em></span> Max = 5.04ε (Mean = 1.78ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_j__cmath__Bessel_J0_Mathworld_Data">And
- other failures.</a>)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 0.629ε (Mean = 0.223ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_GSL_2_1_Bessel_J0_Mathworld_Data">And
- other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
- Max = 0.629ε (Mean = 0.223ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_Rmath_3_2_3_Bessel_J0_Mathworld_Data">And
- other failures.</a>)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 6.55ε (Mean = 2.86ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 2.52ε (Mean = 1.2ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Bessel J0: Mathworld Data (Tricky cases)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.64e+08ε (Mean = 6.69e+07ε)</span><br>
- <br> (<span class="emphasis"><em><cmath>:</em></span> Max = 4.79e+08ε (Mean =
- 1.96e+08ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 8e+04ε (Mean = 3.27e+04ε)</span><br>
- <br> (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 6.5e+07ε (Mean = 2.66e+07ε))<br>
- (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 1.04e+07ε (Mean = 4.29e+06ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.64e+08ε (Mean = 6.69e+07ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1e+07ε (Mean = 4.09e+06ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Bessel J1: Mathworld Data
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 3.59ε (Mean = 1.33ε)</span><br> <br>
- (<span class="emphasis"><em><cmath>:</em></span> Max = 6.1ε (Mean = 2.95ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_j__cmath__Bessel_J1_Mathworld_Data">And
- other failures.</a>)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 6.62ε (Mean = 2.35ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_GSL_2_1_Bessel_J1_Mathworld_Data">And
- other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
- Max = 0.946ε (Mean = 0.39ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_Rmath_3_2_3_Bessel_J1_Mathworld_Data">And
- other failures.</a>)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.44ε (Mean = 0.637ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.73ε (Mean = 0.976ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Bessel J1: Mathworld Data (tricky cases)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 2.18e+05ε (Mean = 9.76e+04ε)</span><br>
- <br> (<span class="emphasis"><em><cmath>:</em></span> Max = 2.15e+06ε (Mean =
- 1.58e+06ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 106ε (Mean = 47.5ε)</span><br> <br>
- (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 8.75e+05ε (Mean = 5.32e+05ε))<br>
- (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 2.93e+06ε (Mean = 1.7e+06ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 2.18e+05ε (Mean = 9.76e+04ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 3.23e+04ε (Mean = 1.45e+04ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Bessel JN: Mathworld Data
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 6.85ε (Mean = 3.35ε)</span><br> <br>
- (<span class="emphasis"><em><cmath>:</em></span> <span class="red">Max = 2.13e+19ε (Mean
- = 5.16e+18ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_j__cmath__Bessel_JN_Mathworld_Data">And
- other failures.</a>)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 6.9e+05ε (Mean = 2.15e+05ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_GSL_2_1_Bessel_JN_Mathworld_Data">And
- other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
- <span class="red">Max = +INFε (Mean = +INFε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_Rmath_3_2_3_Bessel_JN_Mathworld_Data">And
- other failures.</a>)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 463ε (Mean = 112ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 14.7ε (Mean = 5.4ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Bessel J: Mathworld Data
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 14.7ε (Mean = 4.11ε)</span><br> <br>
- (<span class="emphasis"><em><cmath>:</em></span> Max = 3.49e+05ε (Mean = 8.09e+04ε)
- <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_j__cmath__Bessel_J_Mathworld_Data">And
- other failures.</a>)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 10ε (Mean = 2.24ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 2.39e+05ε (Mean = 5.37e+04ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_GSL_2_1_Bessel_J_Mathworld_Data">And
- other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
- <span class="red">Max = +INFε (Mean = +INFε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_Rmath_3_2_3_Bessel_J_Mathworld_Data">And
- other failures.</a>)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 14.7ε (Mean = 4.22ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 14.9ε (Mean = 3.89ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Bessel J: Mathworld Data (large values)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 607ε (Mean = 305ε)</span><br> <br> (<span class="emphasis"><em><cmath>:</em></span>
- Max = 34.9ε (Mean = 17.4ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_j__cmath__Bessel_J_Mathworld_Data_large_values_">And
- other failures.</a>)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.536ε (Mean = 0.268ε)</span><br> <br>
- (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 4.91e+03ε (Mean = 2.46e+03ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_GSL_2_1_Bessel_J_Mathworld_Data_large_values_">And
- other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
- Max = 5.9ε (Mean = 3.76ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 607ε (Mean = 305ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 9.31ε (Mean = 5.52ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Bessel JN: Random Data
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 50.8ε (Mean = 3.69ε)</span><br> <br>
- (<span class="emphasis"><em><cmath>:</em></span> Max = 1.12e+03ε (Mean = 88.7ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 75.7ε (Mean = 5.36ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
- Max = 3.93ε (Mean = 1.22ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 99.6ε (Mean = 22ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 17.5ε (Mean = 1.46ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Bessel J: Random Data
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 11.4ε (Mean = 1.68ε)</span><br> <br>
- (<span class="emphasis"><em><cmath>:</em></span> Max = 501ε (Mean = 52.3ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 15.5ε (Mean = 3.33ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_GSL_2_1_Bessel_J_Random_Data">And
- other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
- Max = 6.74ε (Mean = 1.3ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 260ε (Mean = 34ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 9.24ε (Mean = 1.17ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Bessel J: Random Data (Tricky large values)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 785ε (Mean = 94.2ε)</span><br> <br>
- (<span class="emphasis"><em><cmath>:</em></span> <span class="red">Max = 5.01e+17ε (Mean
- = 6.23e+16ε))</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 2.48e+05ε (Mean = 5.11e+04ε))<br> (<span class="emphasis"><em>Rmath
- 3.2.3:</em></span> Max = 71.6ε (Mean = 11.7ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 785ε (Mean = 97.4ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 59.2ε (Mean = 8.67ε)</span>
- </p>
- </td>
- </tr>
- </tbody>
- </table></div>
- </div>
- <br class="table-break"><div class="table">
- <a name="special_function_error_rates_rep.all_the_tables.table_cyl_bessel_j_integer_orders_"></a><p class="title"><b>Table 109. Error rates for cyl_bessel_j (integer orders)</b></p>
- <div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_j (integer orders)">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> long double
- </p>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> double
- </p>
- </th>
- <th>
- <p>
- Sun compiler version 0x5150<br> Sun Solaris<br> long double
- </p>
- </th>
- <th>
- <p>
- Microsoft Visual C++ version 14.1<br> Win32<br> double
- </p>
- </th>
- </tr></thead>
- <tbody>
- <tr>
- <td>
- <p>
- Bessel J0: Mathworld Data (Integer Version)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 6.55ε (Mean = 2.86ε)</span><br> <br>
- (<span class="emphasis"><em><cmath>:</em></span> Max = 5.04ε (Mean = 1.78ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_j_integer_orders___cmath__Bessel_J0_Mathworld_Data_Integer_Version_">And
- other failures.</a>)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 1.12ε (Mean = 0.488ε))<br> (<span class="emphasis"><em>Rmath
- 3.2.3:</em></span> Max = 0.629ε (Mean = 0.223ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_integer_orders__Rmath_3_2_3_Bessel_J0_Mathworld_Data_Integer_Version_">And
- other failures.</a>)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 6.55ε (Mean = 2.86ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 2.52ε (Mean = 1.2ε)</span><br> <br>
- (<span class="emphasis"><em><math.h>:</em></span> Max = 1.89ε (Mean = 0.988ε))
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Bessel J0: Mathworld Data (Tricky cases) (Integer Version)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.64e+08ε (Mean = 6.69e+07ε)</span><br>
- <br> (<span class="emphasis"><em><cmath>:</em></span> Max = 4.79e+08ε (Mean =
- 1.96e+08ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 8e+04ε (Mean = 3.27e+04ε)</span><br>
- <br> (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 1e+07ε (Mean = 4.11e+06ε))<br>
- (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 1.04e+07ε (Mean = 4.29e+06ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.64e+08ε (Mean = 6.69e+07ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1e+07ε (Mean = 4.09e+06ε)</span><br>
- <br> (<span class="emphasis"><em><math.h>:</em></span> <span class="red">Max
- = 2.54e+08ε (Mean = 1.04e+08ε))</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Bessel J1: Mathworld Data (Integer Version)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 3.59ε (Mean = 1.33ε)</span><br> <br>
- (<span class="emphasis"><em><cmath>:</em></span> Max = 6.1ε (Mean = 2.95ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_j_integer_orders___cmath__Bessel_J1_Mathworld_Data_Integer_Version_">And
- other failures.</a>)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 1.89ε (Mean = 0.721ε))<br> (<span class="emphasis"><em>Rmath
- 3.2.3:</em></span> Max = 0.946ε (Mean = 0.39ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_integer_orders__Rmath_3_2_3_Bessel_J1_Mathworld_Data_Integer_Version_">And
- other failures.</a>)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.44ε (Mean = 0.637ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.73ε (Mean = 0.976ε)</span><br> <br>
- (<span class="emphasis"><em><math.h>:</em></span> Max = 11.4ε (Mean = 4.15ε))
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Bessel J1: Mathworld Data (tricky cases) (Integer Version)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 2.18e+05ε (Mean = 9.76e+04ε)</span><br>
- <br> (<span class="emphasis"><em><cmath>:</em></span> Max = 2.15e+06ε (Mean =
- 1.58e+06ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 106ε (Mean = 47.5ε)</span><br> <br>
- (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 1.26e+06ε (Mean = 6.28e+05ε))<br>
- (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 2.93e+06ε (Mean = 1.7e+06ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 2.18e+05ε (Mean = 9.76e+04ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 3.23e+04ε (Mean = 1.45e+04ε)</span><br>
- <br> (<span class="emphasis"><em><math.h>:</em></span> Max = 1.44e+07ε (Mean
- = 6.5e+06ε))
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Bessel JN: Mathworld Data (Integer Version)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 6.85ε (Mean = 3.35ε)</span><br> <br>
- (<span class="emphasis"><em><cmath>:</em></span> <span class="red">Max = 2.13e+19ε (Mean
- = 5.16e+18ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_j_integer_orders___cmath__Bessel_JN_Mathworld_Data_Integer_Version_">And
- other failures.</a>)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 6.9e+05ε (Mean = 2.53e+05ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_integer_orders__GSL_2_1_Bessel_JN_Mathworld_Data_Integer_Version_">And
- other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
- <span class="red">Max = +INFε (Mean = +INFε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_j_integer_orders__Rmath_3_2_3_Bessel_JN_Mathworld_Data_Integer_Version_">And
- other failures.</a>)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 463ε (Mean = 112ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 14.7ε (Mean = 5.4ε)</span><br> <br>
- (<span class="emphasis"><em><math.h>:</em></span> <span class="red">Max = +INFε (Mean
- = +INFε) <a class="link" href="index.html#errors_Microsoft_Visual_C_version_14_1_Win32_double_cyl_bessel_j_integer_orders___math_h__Bessel_JN_Mathworld_Data_Integer_Version_">And
- other failures.</a>)</span>
- </p>
- </td>
- </tr>
- </tbody>
- </table></div>
- </div>
- <br class="table-break"><div class="table">
- <a name="special_function_error_rates_rep.all_the_tables.table_cyl_bessel_j_prime"></a><p class="title"><b>Table 110. Error rates for cyl_bessel_j_prime</b></p>
- <div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_j_prime">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> double
- </p>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> long double
- </p>
- </th>
- <th>
- <p>
- Sun compiler version 0x5150<br> Sun Solaris<br> long double
- </p>
- </th>
- <th>
- <p>
- Microsoft Visual C++ version 14.1<br> Win32<br> double
- </p>
- </th>
- </tr></thead>
- <tbody>
- <tr>
- <td>
- <p>
- Bessel J0': Mathworld Data
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 18.9ε (Mean = 6.82ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 18.9ε (Mean = 6.72ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 6.62ε (Mean = 2.55ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Bessel J0': Mathworld Data (Tricky cases)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 7.44ε (Mean = 3.34ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 7.44ε (Mean = 3.31ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 3.67ε (Mean = 1.74ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Bessel J1': Mathworld Data
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 7.9ε (Mean = 3.37ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 7.9ε (Mean = 3.37ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.999ε (Mean = 0.627ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Bessel J1': Mathworld Data (tricky cases)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 287ε (Mean = 129ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 5.88e+05ε (Mean = 2.63e+05ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 5.88e+05ε (Mean = 2.63e+05ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 288ε (Mean = 129ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Bessel JN': Mathworld Data
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.527ε (Mean = 0.128ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.29e+03ε (Mean = 312ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.29e+03ε (Mean = 355ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 14ε (Mean = 6.13ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Bessel J': Mathworld Data
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 21.5ε (Mean = 4.7ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 42.5ε (Mean = 9.31ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 42.5ε (Mean = 9.32ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 23.7ε (Mean = 8ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Bessel J': Mathworld Data (large values)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 989ε (Mean = 495ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 989ε (Mean = 495ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 2.9ε (Mean = 1.61ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Bessel JN': Random Data
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.593ε (Mean = 0.0396ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 11.3ε (Mean = 1.85ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 79.4ε (Mean = 16.2ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 6.34ε (Mean = 0.999ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Bessel J': Random Data
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.885ε (Mean = 0.033ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 139ε (Mean = 6.47ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 279ε (Mean = 27.2ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 176ε (Mean = 9.75ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Bessel J': Random Data (Tricky large values)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 474ε (Mean = 62.2ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 474ε (Mean = 64.5ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 379ε (Mean = 45.4ε)</span>
- </p>
- </td>
- </tr>
- </tbody>
- </table></div>
- </div>
- <br class="table-break"><div class="table">
- <a name="special_function_error_rates_rep.all_the_tables.table_cyl_bessel_j_prime_integer_orders_"></a><p class="title"><b>Table 111. Error rates for cyl_bessel_j_prime (integer orders)</b></p>
- <div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_j_prime (integer orders)">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> double
- </p>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> long double
- </p>
- </th>
- <th>
- <p>
- Sun compiler version 0x5150<br> Sun Solaris<br> long double
- </p>
- </th>
- <th>
- <p>
- Microsoft Visual C++ version 14.1<br> Win32<br> double
- </p>
- </th>
- </tr></thead>
- <tbody>
- <tr>
- <td>
- <p>
- Bessel J0': Mathworld Data (Integer Version)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 18.9ε (Mean = 6.82ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 18.9ε (Mean = 6.72ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 6.62ε (Mean = 2.55ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Bessel J0': Mathworld Data (Tricky cases) (Integer Version)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 7.44ε (Mean = 3.34ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 7.44ε (Mean = 3.31ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 3.67ε (Mean = 1.74ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Bessel J1': Mathworld Data (Integer Version)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 7.9ε (Mean = 3.37ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 7.9ε (Mean = 3.37ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.999ε (Mean = 0.627ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Bessel J1': Mathworld Data (tricky cases) (Integer Version)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 287ε (Mean = 129ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 5.88e+05ε (Mean = 2.63e+05ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 5.88e+05ε (Mean = 2.63e+05ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 288ε (Mean = 129ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Bessel JN': Mathworld Data (Integer Version)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.527ε (Mean = 0.128ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.29e+03ε (Mean = 312ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.29e+03ε (Mean = 355ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 14ε (Mean = 6.13ε)</span>
- </p>
- </td>
- </tr>
- </tbody>
- </table></div>
- </div>
- <br class="table-break"><div class="table">
- <a name="special_function_error_rates_rep.all_the_tables.table_cyl_bessel_k"></a><p class="title"><b>Table 112. Error rates for cyl_bessel_k</b></p>
- <div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_k">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> long double
- </p>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> double
- </p>
- </th>
- <th>
- <p>
- Sun compiler version 0x5150<br> Sun Solaris<br> long double
- </p>
- </th>
- <th>
- <p>
- Microsoft Visual C++ version 14.1<br> Win32<br> double
- </p>
- </th>
- </tr></thead>
- <tbody>
- <tr>
- <td>
- <p>
- Bessel K0: Mathworld Data
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.833ε (Mean = 0.436ε)</span><br> <br>
- (<span class="emphasis"><em><cmath>:</em></span> Max = 9.33ε (Mean = 3.25ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 6.04ε (Mean = 2.16ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
- Max = 0.833ε (Mean = 0.601ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.833ε (Mean = 0.436ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.833ε (Mean = 0.552ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Bessel K1: Mathworld Data
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.786ε (Mean = 0.329ε)</span><br> <br>
- (<span class="emphasis"><em><cmath>:</em></span> Max = 8.94ε (Mean = 3.19ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 6.26ε (Mean = 2.21ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
- Max = 0.894ε (Mean = 0.516ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.786ε (Mean = 0.329ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.786ε (Mean = 0.39ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Bessel Kn: Mathworld Data
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 2.6ε (Mean = 1.21ε)</span><br> <br>
- (<span class="emphasis"><em><cmath>:</em></span> Max = 12.9ε (Mean = 4.91ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_k__cmath__Bessel_Kn_Mathworld_Data">And
- other failures.</a>)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 3.36ε (Mean = 1.43ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_k_GSL_2_1_Bessel_Kn_Mathworld_Data">And
- other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
- Max = 8.48ε (Mean = 2.98ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 2.6ε (Mean = 1.21ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 3.63ε (Mean = 1.46ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Bessel Kv: Mathworld Data
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 3.58ε (Mean = 2.39ε)</span><br> <br>
- (<span class="emphasis"><em><cmath>:</em></span> Max = 13ε (Mean = 4.81ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_k__cmath__Bessel_Kv_Mathworld_Data">And
- other failures.</a>)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 5.47ε (Mean = 2.04ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_k_GSL_2_1_Bessel_Kv_Mathworld_Data">And
- other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
- Max = 3.15ε (Mean = 1.35ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 5.21ε (Mean = 2.53ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 4.78ε (Mean = 2.19ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Bessel Kv: Mathworld Data (large values)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 42.3ε (Mean = 21ε)</span><br> <br> (<span class="emphasis"><em><cmath>:</em></span>
- Max = 42.3ε (Mean = 19.8ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_k__cmath__Bessel_Kv_Mathworld_Data_large_values_">And
- other failures.</a>)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 308ε (Mean = 142ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_k_GSL_2_1_Bessel_Kv_Mathworld_Data_large_values_">And
- other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
- Max = 84.6ε (Mean = 37.8ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 42.3ε (Mean = 21ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 59.8ε (Mean = 26.9ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Bessel Kn: Random Data
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 4.55ε (Mean = 1.12ε)</span><br> <br>
- (<span class="emphasis"><em><cmath>:</em></span> Max = 13.9ε (Mean = 2.91ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.764ε (Mean = 0.0348ε)</span><br> <br>
- (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 8.71ε (Mean = 1.76ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_k_GSL_2_1_Bessel_Kn_Random_Data">And
- other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
- Max = 7.47ε (Mean = 1.34ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 4.55ε (Mean = 1.12ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 9.34ε (Mean = 1.7ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Bessel Kv: Random Data
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 7.88ε (Mean = 1.48ε)</span><br> <br>
- (<span class="emphasis"><em><cmath>:</em></span> Max = 13.6ε (Mean = 2.68ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_k__cmath__Bessel_Kv_Random_Data">And
- other failures.</a>)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.507ε (Mean = 0.0313ε)</span><br> <br>
- (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 9.71ε (Mean = 1.47ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_bessel_k_GSL_2_1_Bessel_Kv_Random_Data">And
- other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
- Max = 7.37ε (Mean = 1.49ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 7.88ε (Mean = 1.47ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 8.33ε (Mean = 1.62ε)</span>
- </p>
- </td>
- </tr>
- </tbody>
- </table></div>
- </div>
- <br class="table-break"><div class="table">
- <a name="special_function_error_rates_rep.all_the_tables.table_cyl_bessel_k_integer_orders_"></a><p class="title"><b>Table 113. Error rates for cyl_bessel_k (integer orders)</b></p>
- <div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_k (integer orders)">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> long double
- </p>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> double
- </p>
- </th>
- <th>
- <p>
- Sun compiler version 0x5150<br> Sun Solaris<br> long double
- </p>
- </th>
- <th>
- <p>
- Microsoft Visual C++ version 14.1<br> Win32<br> double
- </p>
- </th>
- </tr></thead>
- <tbody>
- <tr>
- <td>
- <p>
- Bessel K0: Mathworld Data (Integer Version)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.833ε (Mean = 0.436ε)</span><br> <br>
- (<span class="emphasis"><em><cmath>:</em></span> Max = 9.33ε (Mean = 3.25ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 1.2ε (Mean = 0.733ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
- Max = 0.833ε (Mean = 0.601ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.833ε (Mean = 0.436ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.833ε (Mean = 0.552ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Bessel K1: Mathworld Data (Integer Version)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.786ε (Mean = 0.329ε)</span><br> <br>
- (<span class="emphasis"><em><cmath>:</em></span> Max = 8.94ε (Mean = 3.19ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 0.626ε (Mean = 0.333ε))<br> (<span class="emphasis"><em>Rmath
- 3.2.3:</em></span> Max = 0.894ε (Mean = 0.516ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.786ε (Mean = 0.329ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.786ε (Mean = 0.39ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Bessel Kn: Mathworld Data (Integer Version)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 2.6ε (Mean = 1.21ε)</span><br> <br>
- (<span class="emphasis"><em><cmath>:</em></span> Max = 12.9ε (Mean = 4.91ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_bessel_k_integer_orders___cmath__Bessel_Kn_Mathworld_Data_Integer_Version_">And
- other failures.</a>)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 168ε (Mean = 59.5ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
- Max = 8.48ε (Mean = 2.98ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 2.6ε (Mean = 1.21ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 3.63ε (Mean = 1.46ε)</span>
- </p>
- </td>
- </tr>
- </tbody>
- </table></div>
- </div>
- <br class="table-break"><div class="table">
- <a name="special_function_error_rates_rep.all_the_tables.table_cyl_bessel_k_prime"></a><p class="title"><b>Table 114. Error rates for cyl_bessel_k_prime</b></p>
- <div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_k_prime">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> double
- </p>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> long double
- </p>
- </th>
- <th>
- <p>
- Sun compiler version 0x5150<br> Sun Solaris<br> long double
- </p>
- </th>
- <th>
- <p>
- Microsoft Visual C++ version 14.1<br> Win32<br> double
- </p>
- </th>
- </tr></thead>
- <tbody>
- <tr>
- <td>
- <p>
- Bessel K'0: Mathworld Data
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.786ε (Mean = 0.329ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.786ε (Mean = 0.329ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.786ε (Mean = 0.39ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Bessel K'1: Mathworld Data
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.736ε (Mean = 0.389ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.736ε (Mean = 0.389ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.761ε (Mean = 0.444ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Bessel K'n: Mathworld Data
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 2.16ε (Mean = 1.08ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 2.16ε (Mean = 1.08ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 4.17ε (Mean = 1.75ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Bessel K'v: Mathworld Data
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 3.94ε (Mean = 2.44ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 3.94ε (Mean = 2.34ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 3.94ε (Mean = 1.47ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Bessel K'v: Mathworld Data (large values)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 59.2ε (Mean = 42.9ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 58.7ε (Mean = 42.6ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 18.6ε (Mean = 11.8ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Bessel K'n: Random Data
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 4.45ε (Mean = 1.19ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 4.45ε (Mean = 1.19ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 9.67ε (Mean = 1.73ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Bessel K'v: Random Data
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 7.95ε (Mean = 1.53ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 7.95ε (Mean = 1.52ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 8.32ε (Mean = 1.65ε)</span>
- </p>
- </td>
- </tr>
- </tbody>
- </table></div>
- </div>
- <br class="table-break"><div class="table">
- <a name="special_function_error_rates_rep.all_the_tables.table_cyl_bessel_k_prime_integer_orders_"></a><p class="title"><b>Table 115. Error rates for cyl_bessel_k_prime (integer orders)</b></p>
- <div class="table-contents"><table class="table" summary="Error rates for cyl_bessel_k_prime (integer orders)">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> double
- </p>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> long double
- </p>
- </th>
- <th>
- <p>
- Sun compiler version 0x5150<br> Sun Solaris<br> long double
- </p>
- </th>
- <th>
- <p>
- Microsoft Visual C++ version 14.1<br> Win32<br> double
- </p>
- </th>
- </tr></thead>
- <tbody>
- <tr>
- <td>
- <p>
- Bessel K'0: Mathworld Data (Integer Version)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.786ε (Mean = 0.329ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.786ε (Mean = 0.329ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.786ε (Mean = 0.39ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Bessel K'1: Mathworld Data (Integer Version)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.736ε (Mean = 0.389ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.736ε (Mean = 0.389ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.761ε (Mean = 0.444ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Bessel K'n: Mathworld Data (Integer Version)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 2.16ε (Mean = 1.08ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 2.16ε (Mean = 1.08ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 4.17ε (Mean = 1.75ε)</span>
- </p>
- </td>
- </tr>
- </tbody>
- </table></div>
- </div>
- <br class="table-break"><div class="table">
- <a name="special_function_error_rates_rep.all_the_tables.table_cyl_neumann"></a><p class="title"><b>Table 116. Error rates for cyl_neumann</b></p>
- <div class="table-contents"><table class="table" summary="Error rates for cyl_neumann">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> long double
- </p>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> double
- </p>
- </th>
- <th>
- <p>
- Sun compiler version 0x5150<br> Sun Solaris<br> long double
- </p>
- </th>
- <th>
- <p>
- Microsoft Visual C++ version 14.1<br> Win32<br> double
- </p>
- </th>
- </tr></thead>
- <tbody>
- <tr>
- <td>
- <p>
- Y0: Mathworld Data
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 5.53ε (Mean = 2.4ε)</span><br> <br>
- (<span class="emphasis"><em><cmath>:</em></span> Max = 2.05e+05ε (Mean = 6.87e+04ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 60.9ε (Mean = 20.4ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
- Max = 167ε (Mean = 56.5ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 5.53ε (Mean = 2.4ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 4.61ε (Mean = 2.29ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Y1: Mathworld Data
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 6.33ε (Mean = 2.25ε)</span><br> <br>
- (<span class="emphasis"><em><cmath>:</em></span> Max = 9.71e+03ε (Mean = 4.08e+03ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 23.4ε (Mean = 8.1ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
- Max = 193ε (Mean = 64.4ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 6.33ε (Mean = 2.29ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 4.75ε (Mean = 1.72ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Yn: Mathworld Data
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 55.2ε (Mean = 17.8ε)</span><br> <br>
- (<span class="emphasis"><em><cmath>:</em></span> <span class="red">Max = 2.2e+20ε (Mean
- = 6.97e+19ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_neumann__cmath__Yn_Mathworld_Data">And
- other failures.</a>)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.993ε (Mean = 0.314ε)</span><br> <br>
- (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 2.41e+05ε (Mean = 7.62e+04ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_neumann_GSL_2_1_Yn_Mathworld_Data">And
- other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
- Max = 1.24e+04ε (Mean = 4e+03ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 55.2ε (Mean = 17.8ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 35ε (Mean = 11.9ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Yv: Mathworld Data
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 10.7ε (Mean = 4.93ε)</span><br> <br>
- (<span class="emphasis"><em><cmath>:</em></span> <span class="red">Max = 3.49e+15ε (Mean
- = 1.05e+15ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_neumann__cmath__Yv_Mathworld_Data">And
- other failures.</a>)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 10ε (Mean = 3.02ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 1.07e+05ε (Mean = 3.22e+04ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_neumann_GSL_2_1_Yv_Mathworld_Data">And
- other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
- Max = 243ε (Mean = 73.9ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 10.7ε (Mean = 5.1ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 7.89ε (Mean = 3.27ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Yv: Mathworld Data (large values)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.7ε (Mean = 1.33ε)</span><br> <br>
- (<span class="emphasis"><em><cmath>:</em></span> Max = 43.2ε (Mean = 16.3ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_neumann__cmath__Yv_Mathworld_Data_large_values_">And
- other failures.</a>)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 60.8ε (Mean = 23ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_cyl_neumann_GSL_2_1_Yv_Mathworld_Data_large_values_">And
- other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
- Max = 0.682ε (Mean = 0.335ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.7ε (Mean = 1.33ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.682ε (Mean = 0.423ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Y0 and Y1: Random Data
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 10.8ε (Mean = 3.04ε)</span><br> <br>
- (<span class="emphasis"><em><cmath>:</em></span> Max = 2.59e+03ε (Mean = 500ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 34.4ε (Mean = 8.9ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
- Max = 83ε (Mean = 14.2ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 10.8ε (Mean = 3.04ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 4.17ε (Mean = 1.24ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Yn: Random Data
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 338ε (Mean = 27.5ε)</span><br> <br>
- (<span class="emphasis"><em><cmath>:</em></span> Max = 4.01e+03ε (Mean = 348ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 500ε (Mean = 47.8ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
- Max = 691ε (Mean = 67.9ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 338ε (Mean = 27.5ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 117ε (Mean = 10.2ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Yv: Random Data
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 2.08e+03ε (Mean = 149ε)</span><br> <br>
- (<span class="emphasis"><em><cmath>:</em></span> <span class="red">Max = +INFε (Mean
- = +INFε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_neumann__cmath__Yv_Random_Data">And
- other failures.</a>)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.53ε (Mean = 0.102ε)</span><br> <br>
- (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 1.41e+06ε (Mean = 7.67e+04ε))<br>
- (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 1.79e+05ε (Mean = 9.64e+03ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 2.08e+03ε (Mean = 149ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.23e+03ε (Mean = 69.9ε)</span>
- </p>
- </td>
- </tr>
- </tbody>
- </table></div>
- </div>
- <br class="table-break"><div class="table">
- <a name="special_function_error_rates_rep.all_the_tables.table_cyl_neumann_integer_orders_"></a><p class="title"><b>Table 117. Error rates for cyl_neumann (integer orders)</b></p>
- <div class="table-contents"><table class="table" summary="Error rates for cyl_neumann (integer orders)">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> long double
- </p>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> double
- </p>
- </th>
- <th>
- <p>
- Sun compiler version 0x5150<br> Sun Solaris<br> long double
- </p>
- </th>
- <th>
- <p>
- Microsoft Visual C++ version 14.1<br> Win32<br> double
- </p>
- </th>
- </tr></thead>
- <tbody>
- <tr>
- <td>
- <p>
- Y0: Mathworld Data (Integer Version)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 5.53ε (Mean = 2.4ε)</span><br> <br>
- (<span class="emphasis"><em><cmath>:</em></span> Max = 2.05e+05ε (Mean = 6.87e+04ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 6.46ε (Mean = 2.38ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
- Max = 167ε (Mean = 56.5ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 5.53ε (Mean = 2.4ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 4.61ε (Mean = 2.29ε)</span><br> <br>
- (<span class="emphasis"><em><math.h>:</em></span> Max = 5.37e+03ε (Mean = 1.81e+03ε))
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Y1: Mathworld Data (Integer Version)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 6.33ε (Mean = 2.25ε)</span><br> <br>
- (<span class="emphasis"><em><cmath>:</em></span> Max = 9.71e+03ε (Mean = 4.08e+03ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 1.51ε (Mean = 0.839ε))<br> (<span class="emphasis"><em>Rmath
- 3.2.3:</em></span> Max = 193ε (Mean = 64.4ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 6.33ε (Mean = 2.29ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 4.75ε (Mean = 1.72ε)</span><br> <br>
- (<span class="emphasis"><em><math.h>:</em></span> Max = 1.86e+04ε (Mean = 6.2e+03ε))
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Yn: Mathworld Data (Integer Version)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 55.2ε (Mean = 17.8ε)</span><br> <br>
- (<span class="emphasis"><em><cmath>:</em></span> <span class="red">Max = 2.2e+20ε (Mean
- = 6.97e+19ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_cyl_neumann_integer_orders___cmath__Yn_Mathworld_Data_Integer_Version_">And
- other failures.</a>)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.993ε (Mean = 0.314ε)</span><br> <br>
- (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 2.41e+05ε (Mean = 7.62e+04ε))<br>
- (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 1.24e+04ε (Mean = 4e+03ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 55.2ε (Mean = 17.8ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 35ε (Mean = 11.9ε)</span><br> <br> (<span class="emphasis"><em><math.h>:</em></span>
- Max = 2.49e+05ε (Mean = 8.14e+04ε))
- </p>
- </td>
- </tr>
- </tbody>
- </table></div>
- </div>
- <br class="table-break"><div class="table">
- <a name="special_function_error_rates_rep.all_the_tables.table_cyl_neumann_prime"></a><p class="title"><b>Table 118. Error rates for cyl_neumann_prime</b></p>
- <div class="table-contents"><table class="table" summary="Error rates for cyl_neumann_prime">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> double
- </p>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> long double
- </p>
- </th>
- <th>
- <p>
- Sun compiler version 0x5150<br> Sun Solaris<br> long double
- </p>
- </th>
- <th>
- <p>
- Microsoft Visual C++ version 14.1<br> Win32<br> double
- </p>
- </th>
- </tr></thead>
- <tbody>
- <tr>
- <td>
- <p>
- Y'0: Mathworld Data
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 6.33ε (Mean = 3.12ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 6.33ε (Mean = 3.14ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 4.75ε (Mean = 1.75ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Y'1: Mathworld Data
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.58ε (Mean = 0.193ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 37.1ε (Mean = 12.8ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 34ε (Mean = 11.8ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 3.08ε (Mean = 1.2ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Y'n: Mathworld Data
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 2.05ε (Mean = 0.677ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 56ε (Mean = 18.2ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 56ε (Mean = 21.3ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 563ε (Mean = 178ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Y'v: Mathworld Data
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 21.5ε (Mean = 6.49ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 42.5ε (Mean = 13.4ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 42.5ε (Mean = 13.6ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 23.7ε (Mean = 10.1ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Y'v: Mathworld Data (large values)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.57ε (Mean = 1.24ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.57ε (Mean = 1.24ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.627ε (Mean = 0.237ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Y'0 and Y'1: Random Data
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 23.8ε (Mean = 3.69ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 23.8ε (Mean = 3.69ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 5.95ε (Mean = 1.36ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Y'n: Random Data
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.53ε (Mean = 0.0885ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 2.35e+03ε (Mean = 136ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 2.35e+03ε (Mean = 136ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 621ε (Mean = 36ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Y'v: Random Data
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 56.8ε (Mean = 2.59ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.16e+05ε (Mean = 5.28e+03ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.16e+05ε (Mean = 5.28e+03ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 3.23e+04ε (Mean = 1.13e+03ε)</span>
- </p>
- </td>
- </tr>
- </tbody>
- </table></div>
- </div>
- <br class="table-break"><div class="table">
- <a name="special_function_error_rates_rep.all_the_tables.table_cyl_neumann_prime_integer_orders_"></a><p class="title"><b>Table 119. Error rates for cyl_neumann_prime (integer orders)</b></p>
- <div class="table-contents"><table class="table" summary="Error rates for cyl_neumann_prime (integer orders)">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> double
- </p>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> long double
- </p>
- </th>
- <th>
- <p>
- Sun compiler version 0x5150<br> Sun Solaris<br> long double
- </p>
- </th>
- <th>
- <p>
- Microsoft Visual C++ version 14.1<br> Win32<br> double
- </p>
- </th>
- </tr></thead>
- <tbody>
- <tr>
- <td>
- <p>
- Y'0: Mathworld Data (Integer Version)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 6.33ε (Mean = 3.12ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 6.33ε (Mean = 3.14ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 4.75ε (Mean = 1.75ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Y'1: Mathworld Data (Integer Version)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.58ε (Mean = 0.193ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 37.1ε (Mean = 12.8ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 34ε (Mean = 11.8ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 3.08ε (Mean = 1.2ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Y'n: Mathworld Data (Integer Version)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 2.05ε (Mean = 0.677ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 56ε (Mean = 18.2ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 56ε (Mean = 21.3ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 563ε (Mean = 178ε)</span>
- </p>
- </td>
- </tr>
- </tbody>
- </table></div>
- </div>
- <br class="table-break"><div class="table">
- <a name="special_function_error_rates_rep.all_the_tables.table_digamma"></a><p class="title"><b>Table 120. Error rates for digamma</b></p>
- <div class="table-contents"><table class="table" summary="Error rates for digamma">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> double
- </p>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> long double
- </p>
- </th>
- <th>
- <p>
- Sun compiler version 0x5150<br> Sun Solaris<br> long double
- </p>
- </th>
- <th>
- <p>
- Microsoft Visual C++ version 14.1<br> Win32<br> double
- </p>
- </th>
- </tr></thead>
- <tbody>
- <tr>
- <td>
- <p>
- Digamma Function: Large Values
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 1.84ε (Mean = 0.71ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
- Max = 1.18ε (Mean = 0.331ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.39ε (Mean = 0.413ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.39ε (Mean = 0.413ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.98ε (Mean = 0.369ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Digamma Function: Near the Positive Root
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.891ε (Mean = 0.0995ε)</span><br> <br>
- (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 135ε (Mean = 11.9ε))<br> (<span class="emphasis"><em>Rmath
- 3.2.3:</em></span> Max = 2.02e+03ε (Mean = 256ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.37ε (Mean = 0.477ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.31ε (Mean = 0.471ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.997ε (Mean = 0.527ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Digamma Function: Near Zero
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 0.953ε (Mean = 0.348ε))<br> (<span class="emphasis"><em>Rmath
- 3.2.3:</em></span> Max = 1.17ε (Mean = 0.564ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.984ε (Mean = 0.361ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.984ε (Mean = 0.361ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.953ε (Mean = 0.337ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Digamma Function: Negative Values
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 4.56e+04ε (Mean = 3.91e+03ε))<br> (<span class="emphasis"><em>Rmath
- 3.2.3:</em></span> Max = 4.6e+04ε (Mean = 3.94e+03ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 180ε (Mean = 13ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 180ε (Mean = 13ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 214ε (Mean = 16.1ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Digamma Function: Values near 0
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 0.866ε (Mean = 0.387ε))<br> (<span class="emphasis"><em>Rmath
- 3.2.3:</em></span> Max = 3.58e+05ε (Mean = 1.6e+05ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1ε (Mean = 0.592ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1ε (Mean = 0.592ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Digamma Function: Integer arguments
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.992ε (Mean = 0.215ε)</span><br> <br>
- (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 1.18ε (Mean = 0.607ε))<br> (<span class="emphasis"><em>Rmath
- 3.2.3:</em></span> Max = 4.33ε (Mean = 0.982ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.888ε (Mean = 0.403ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.888ε (Mean = 0.403ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.992ε (Mean = 0.452ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Digamma Function: Half integer arguments
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 1.09ε (Mean = 0.531ε))<br> (<span class="emphasis"><em>Rmath
- 3.2.3:</em></span> Max = 46.2ε (Mean = 7.24ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.906ε (Mean = 0.409ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.906ε (Mean = 0.409ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.78ε (Mean = 0.314ε)</span>
- </p>
- </td>
- </tr>
- </tbody>
- </table></div>
- </div>
- <br class="table-break"><div class="table">
- <a name="special_function_error_rates_rep.all_the_tables.table_ellint_1"></a><p class="title"><b>Table 121. Error rates for ellint_1</b></p>
- <div class="table-contents"><table class="table" summary="Error rates for ellint_1">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> long double
- </p>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> double
- </p>
- </th>
- <th>
- <p>
- Sun compiler version 0x5150<br> Sun Solaris<br> long double
- </p>
- </th>
- <th>
- <p>
- Microsoft Visual C++ version 14.1<br> Win32<br> double
- </p>
- </th>
- </tr></thead>
- <tbody>
- <tr>
- <td>
- <p>
- Elliptic Integral F: Mathworld Data
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.94ε (Mean = 0.509ε)</span><br> <br>
- (<span class="emphasis"><em><cmath>:</em></span> <span class="red">Max = +INFε (Mean
- = +INFε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_ellint_1__cmath__Elliptic_Integral_F_Mathworld_Data">And
- other failures.</a>)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 0.919ε (Mean = 0.544ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.94ε (Mean = 0.509ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.919ε (Mean = 0.542ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Elliptic Integral F: Random Data
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.57ε (Mean = 0.56ε)</span><br> <br>
- (<span class="emphasis"><em><cmath>:</em></span> Max = 2.56ε (Mean = 0.816ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 2.99ε (Mean = 0.797ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.57ε (Mean = 0.561ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 2.26ε (Mean = 0.631ε)</span>
- </p>
- </td>
- </tr>
- </tbody>
- </table></div>
- </div>
- <br class="table-break"><div class="table">
- <a name="special_function_error_rates_rep.all_the_tables.table_ellint_1_complete_"></a><p class="title"><b>Table 122. Error rates for ellint_1 (complete)</b></p>
- <div class="table-contents"><table class="table" summary="Error rates for ellint_1 (complete)">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> long double
- </p>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> double
- </p>
- </th>
- <th>
- <p>
- Sun compiler version 0x5150<br> Sun Solaris<br> long double
- </p>
- </th>
- <th>
- <p>
- Microsoft Visual C++ version 14.1<br> Win32<br> double
- </p>
- </th>
- </tr></thead>
- <tbody>
- <tr>
- <td>
- <p>
- Elliptic Integral K: Mathworld Data
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.887ε (Mean = 0.296ε)</span><br> <br>
- (<span class="emphasis"><em><cmath>:</em></span> Max = 1.19ε (Mean = 0.765ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 0.623ε (Mean = 0.393ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.887ε (Mean = 0.296ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.915ε (Mean = 0.547ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Elliptic Integral K: Random Data
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.27ε (Mean = 0.473ε)</span><br> <br>
- (<span class="emphasis"><em><cmath>:</em></span> Max = 2.19ε (Mean = 0.694ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.851ε (Mean = 0.0851ε)</span><br> <br>
- (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 2.32ε (Mean = 0.688ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.27ε (Mean = 0.473ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.958ε (Mean = 0.408ε)</span>
- </p>
- </td>
- </tr>
- </tbody>
- </table></div>
- </div>
- <br class="table-break"><div class="table">
- <a name="special_function_error_rates_rep.all_the_tables.table_ellint_2"></a><p class="title"><b>Table 123. Error rates for ellint_2</b></p>
- <div class="table-contents"><table class="table" summary="Error rates for ellint_2">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> double
- </p>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> long double
- </p>
- </th>
- <th>
- <p>
- Sun compiler version 0x5150<br> Sun Solaris<br> long double
- </p>
- </th>
- <th>
- <p>
- Microsoft Visual C++ version 14.1<br> Win32<br> double
- </p>
- </th>
- </tr></thead>
- <tbody>
- <tr>
- <td>
- <p>
- Elliptic Integral E: Mathworld Data
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 0.63ε (Mean = 0.325ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.656ε (Mean = 0.317ε)</span><br> <br>
- (<span class="emphasis"><em><cmath>:</em></span> <span class="red">Max = +INFε (Mean
- = +INFε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_ellint_2__cmath__Elliptic_Integral_E_Mathworld_Data">And
- other failures.</a>)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.656ε (Mean = 0.317ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.31ε (Mean = 0.727ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Elliptic Integral E: Random Data
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 4.4ε (Mean = 1.16ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 2.05ε (Mean = 0.632ε)</span><br> <br>
- (<span class="emphasis"><em><cmath>:</em></span> Max = 3.08e+04ε (Mean = 3.84e+03ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 2.05ε (Mean = 0.632ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 2.23ε (Mean = 0.639ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Elliptic Integral E: Small Angles
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 0.5ε (Mean = 0.118ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1ε (Mean = 0.283ε)</span><br> <br> (<span class="emphasis"><em><cmath>:</em></span>
- Max = 2ε (Mean = 0.333ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1ε (Mean = 0.283ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1ε (Mean = 0.421ε)</span>
- </p>
- </td>
- </tr>
- </tbody>
- </table></div>
- </div>
- <br class="table-break"><div class="table">
- <a name="special_function_error_rates_rep.all_the_tables.table_ellint_2_complete_"></a><p class="title"><b>Table 124. Error rates for ellint_2 (complete)</b></p>
- <div class="table-contents"><table class="table" summary="Error rates for ellint_2 (complete)">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> double
- </p>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> long double
- </p>
- </th>
- <th>
- <p>
- Sun compiler version 0x5150<br> Sun Solaris<br> long double
- </p>
- </th>
- <th>
- <p>
- Microsoft Visual C++ version 14.1<br> Win32<br> double
- </p>
- </th>
- </tr></thead>
- <tbody>
- <tr>
- <td>
- <p>
- Elliptic Integral E: Mathworld Data
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 3.09ε (Mean = 1.04ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_ellint_2_complete__GSL_2_1_Elliptic_Integral_E_Mathworld_Data">And
- other failures.</a>)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.836ε (Mean = 0.469ε)</span><br> <br>
- (<span class="emphasis"><em><cmath>:</em></span> Max = 170ε (Mean = 55.1ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.836ε (Mean = 0.469ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.3ε (Mean = 0.615ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Elliptic Integral E: Random Data
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 4.34ε (Mean = 1.18ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.97ε (Mean = 0.629ε)</span><br> <br>
- (<span class="emphasis"><em><cmath>:</em></span> Max = 2.49e+04ε (Mean = 3.39e+03ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.97ε (Mean = 0.629ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.71ε (Mean = 0.553ε)</span>
- </p>
- </td>
- </tr>
- </tbody>
- </table></div>
- </div>
- <br class="table-break"><div class="table">
- <a name="special_function_error_rates_rep.all_the_tables.table_ellint_3"></a><p class="title"><b>Table 125. Error rates for ellint_3</b></p>
- <div class="table-contents"><table class="table" summary="Error rates for ellint_3">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> long double
- </p>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> double
- </p>
- </th>
- <th>
- <p>
- Sun compiler version 0x5150<br> Sun Solaris<br> long double
- </p>
- </th>
- <th>
- <p>
- Microsoft Visual C++ version 14.1<br> Win32<br> double
- </p>
- </th>
- </tr></thead>
- <tbody>
- <tr>
- <td>
- <p>
- Elliptic Integral PI: Mathworld Data
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 475ε (Mean = 86.3ε)</span><br> <br>
- (<span class="emphasis"><em><cmath>:</em></span> <span class="red">Max = +INFε (Mean
- = +INFε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_ellint_3__cmath__Elliptic_Integral_PI_Mathworld_Data">And
- other failures.</a>)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 1.48e+05ε (Mean = 2.54e+04ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_ellint_3_GSL_2_1_Elliptic_Integral_PI_Mathworld_Data">And
- other failures.</a>)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 475ε (Mean = 86.3ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 565ε (Mean = 102ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Elliptic Integral PI: Random Data
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 4.54ε (Mean = 0.895ε)</span><br> <br>
- (<span class="emphasis"><em><cmath>:</em></span> <span class="red">Max = 3.37e+20ε (Mean
- = 3.47e+19ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_ellint_3__cmath__Elliptic_Integral_PI_Random_Data">And
- other failures.</a>)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 633ε (Mean = 50.1ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 4.49ε (Mean = 0.885ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 8.33ε (Mean = 0.971ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Elliptic Integral PI: Large Random Data
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 3.7ε (Mean = 0.893ε)</span><br> <br>
- (<span class="emphasis"><em><cmath>:</em></span> <span class="red">Max = 2.52e+18ε (Mean
- = 4.83e+17ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_ellint_3__cmath__Elliptic_Integral_PI_Large_Random_Data">And
- other failures.</a>)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.557ε (Mean = 0.0389ε)</span><br> <br>
- (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 40.1ε (Mean = 7.77ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 3.7ε (Mean = 0.892ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 2.86ε (Mean = 0.944ε)</span>
- </p>
- </td>
- </tr>
- </tbody>
- </table></div>
- </div>
- <br class="table-break"><div class="table">
- <a name="special_function_error_rates_rep.all_the_tables.table_ellint_3_complete_"></a><p class="title"><b>Table 126. Error rates for ellint_3 (complete)</b></p>
- <div class="table-contents"><table class="table" summary="Error rates for ellint_3 (complete)">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> long double
- </p>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> double
- </p>
- </th>
- <th>
- <p>
- Sun compiler version 0x5150<br> Sun Solaris<br> long double
- </p>
- </th>
- <th>
- <p>
- Microsoft Visual C++ version 14.1<br> Win32<br> double
- </p>
- </th>
- </tr></thead>
- <tbody>
- <tr>
- <td>
- <p>
- Complete Elliptic Integral PI: Mathworld Data
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.4ε (Mean = 0.575ε)</span><br> <br>
- (<span class="emphasis"><em><cmath>:</em></span> <span class="red">Max = 6.31e+20ε (Mean
- = 1.53e+20ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_ellint_3_complete___cmath__Complete_Elliptic_Integral_PI_Mathworld_Data">And
- other failures.</a>)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 6.33e+04ε (Mean = 1.54e+04ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_ellint_3_complete__GSL_2_1_Complete_Elliptic_Integral_PI_Mathworld_Data">And
- other failures.</a>)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.4ε (Mean = 0.575ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.971ε (Mean = 0.464ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Complete Elliptic Integral PI: Random Data
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 2.45ε (Mean = 0.696ε)</span><br> <br>
- (<span class="emphasis"><em><cmath>:</em></span> <span class="red">Max = 8.78e+20ε (Mean
- = 1.02e+20ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_ellint_3_complete___cmath__Complete_Elliptic_Integral_PI_Random_Data">And
- other failures.</a>)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 24ε (Mean = 2.99ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 2.4ε (Mean = 0.677ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 2.46ε (Mean = 0.657ε)</span>
- </p>
- </td>
- </tr>
- </tbody>
- </table></div>
- </div>
- <br class="table-break"><div class="table">
- <a name="special_function_error_rates_rep.all_the_tables.table_ellint_d"></a><p class="title"><b>Table 127. Error rates for ellint_d</b></p>
- <div class="table-contents"><table class="table" summary="Error rates for ellint_d">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> double
- </p>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> long double
- </p>
- </th>
- <th>
- <p>
- Sun compiler version 0x5150<br> Sun Solaris<br> long double
- </p>
- </th>
- <th>
- <p>
- Microsoft Visual C++ version 14.1<br> Win32<br> double
- </p>
- </th>
- </tr></thead>
- <tbody>
- <tr>
- <td>
- <p>
- Elliptic Integral E: Mathworld Data
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 0.862ε (Mean = 0.568ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.3ε (Mean = 0.813ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.3ε (Mean = 0.813ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.862ε (Mean = 0.457ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Elliptic Integral D: Random Data
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 3.01ε (Mean = 0.928ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 2.51ε (Mean = 0.883ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 2.51ε (Mean = 0.883ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 2.87ε (Mean = 0.805ε)</span>
- </p>
- </td>
- </tr>
- </tbody>
- </table></div>
- </div>
- <br class="table-break"><div class="table">
- <a name="special_function_error_rates_rep.all_the_tables.table_ellint_d_complete_"></a><p class="title"><b>Table 128. Error rates for ellint_d (complete)</b></p>
- <div class="table-contents"><table class="table" summary="Error rates for ellint_d (complete)">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> double
- </p>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> long double
- </p>
- </th>
- <th>
- <p>
- Sun compiler version 0x5150<br> Sun Solaris<br> long double
- </p>
- </th>
- <th>
- <p>
- Microsoft Visual C++ version 14.1<br> Win32<br> double
- </p>
- </th>
- </tr></thead>
- <tbody>
- <tr>
- <td>
- <p>
- Elliptic Integral E: Mathworld Data
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.637ε (Mean = 0.368ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.27ε (Mean = 0.735ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.27ε (Mean = 0.735ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.637ε (Mean = 0.368ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Elliptic Integral D: Random Data
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.27ε (Mean = 0.334ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.27ε (Mean = 0.334ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.27ε (Mean = 0.355ε)</span>
- </p>
- </td>
- </tr>
- </tbody>
- </table></div>
- </div>
- <br class="table-break"><div class="table">
- <a name="special_function_error_rates_rep.all_the_tables.table_ellint_rc"></a><p class="title"><b>Table 129. Error rates for ellint_rc</b></p>
- <div class="table-contents"><table class="table" summary="Error rates for ellint_rc">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> double
- </p>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> long double
- </p>
- </th>
- <th>
- <p>
- Microsoft Visual C++ version 14.1<br> Win32<br> double
- </p>
- </th>
- </tr></thead>
- <tbody><tr>
- <td>
- <p>
- RC: Random data
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 2.4ε (Mean = 0.624ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.995ε (Mean = 0.433ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.962ε (Mean = 0.407ε)</span>
- </p>
- </td>
- </tr></tbody>
- </table></div>
- </div>
- <br class="table-break"><div class="table">
- <a name="special_function_error_rates_rep.all_the_tables.table_ellint_rd"></a><p class="title"><b>Table 130. Error rates for ellint_rd</b></p>
- <div class="table-contents"><table class="table" summary="Error rates for ellint_rd">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> double
- </p>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> long double
- </p>
- </th>
- <th>
- <p>
- Microsoft Visual C++ version 14.1<br> Win32<br> double
- </p>
- </th>
- </tr></thead>
- <tbody>
- <tr>
- <td>
- <p>
- RD: Random data
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 2.59ε (Mean = 0.878ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 2.73ε (Mean = 0.831ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 2.16ε (Mean = 0.803ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- RD: y = z
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.896ε (Mean = 0.022ε)</span><br> <br>
- (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 2.88ε (Mean = 0.839ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 2.65ε (Mean = 0.82ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 16.5ε (Mean = 0.843ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- RD: x = y
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.824ε (Mean = 0.0272ε)</span><br> <br>
- (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 3.74ε (Mean = 0.84ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 2.85ε (Mean = 0.865ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 3.51ε (Mean = 0.816ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- RD: x = 0, y = z
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 2ε (Mean = 0.656ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.19ε (Mean = 0.522ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.16ε (Mean = 0.497ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- RD: x = y = z
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 1.03ε (Mean = 0.418ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.998ε (Mean = 0.387ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.03ε (Mean = 0.418ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- RD: x = 0
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 2.85ε (Mean = 0.781ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 2.79ε (Mean = 0.883ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 2.64ε (Mean = 0.894ε)</span>
- </p>
- </td>
- </tr>
- </tbody>
- </table></div>
- </div>
- <br class="table-break"><div class="table">
- <a name="special_function_error_rates_rep.all_the_tables.table_ellint_rf"></a><p class="title"><b>Table 131. Error rates for ellint_rf</b></p>
- <div class="table-contents"><table class="table" summary="Error rates for ellint_rf">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> double
- </p>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> long double
- </p>
- </th>
- <th>
- <p>
- Microsoft Visual C++ version 14.1<br> Win32<br> double
- </p>
- </th>
- </tr></thead>
- <tbody>
- <tr>
- <td>
- <p>
- RF: Random data
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 2.73ε (Mean = 0.804ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 2.54ε (Mean = 0.674ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 2.02ε (Mean = 0.677ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- RF: x = y = z
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 0.999ε (Mean = 0.34ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.991ε (Mean = 0.345ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.999ε (Mean = 0.34ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- RF: x = y or y = z or x = z
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.536ε (Mean = 0.00658ε)</span><br> <br>
- (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 2.89ε (Mean = 0.749ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.95ε (Mean = 0.418ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.21ε (Mean = 0.394ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- RF: x = 0, y = z
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 1.29ε (Mean = 0.527ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.894ε (Mean = 0.338ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.999ε (Mean = 0.407ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- RF: z = 0
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 2.54ε (Mean = 0.781ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.7ε (Mean = 0.539ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.89ε (Mean = 0.587ε)</span>
- </p>
- </td>
- </tr>
- </tbody>
- </table></div>
- </div>
- <br class="table-break"><div class="table">
- <a name="special_function_error_rates_rep.all_the_tables.table_ellint_rg"></a><p class="title"><b>Table 132. Error rates for ellint_rg</b></p>
- <div class="table-contents"><table class="table" summary="Error rates for ellint_rg">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> double
- </p>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> long double
- </p>
- </th>
- <th>
- <p>
- Microsoft Visual C++ version 14.1<br> Win32<br> double
- </p>
- </th>
- </tr></thead>
- <tbody>
- <tr>
- <td>
- <p>
- RG: Random Data
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.983ε (Mean = 0.0172ε)</span><br> <br>
- (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 0.983ε (Mean = 0.0172ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 3.95ε (Mean = 0.951ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 3.65ε (Mean = 0.929ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- RG: two values 0
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 0ε (Mean = 0ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- RG: All values the same or zero
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 0ε (Mean = 0ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.992ε (Mean = 0.288ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.06ε (Mean = 0.348ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- RG: two values the same
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.594ε (Mean = 0.0103ε)</span><br> <br>
- (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 0.594ε (Mean = 0.0103ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.51ε (Mean = 0.404ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.96ε (Mean = 0.374ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- RG: one value zero
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 0ε (Mean = 0ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 2.14ε (Mean = 0.722ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.96ε (Mean = 0.674ε)</span>
- </p>
- </td>
- </tr>
- </tbody>
- </table></div>
- </div>
- <br class="table-break"><div class="table">
- <a name="special_function_error_rates_rep.all_the_tables.table_ellint_rj"></a><p class="title"><b>Table 133. Error rates for ellint_rj</b></p>
- <div class="table-contents"><table class="table" summary="Error rates for ellint_rj">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> double
- </p>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> long double
- </p>
- </th>
- <th>
- <p>
- Microsoft Visual C++ version 14.1<br> Win32<br> double
- </p>
- </th>
- </tr></thead>
- <tbody>
- <tr>
- <td>
- <p>
- RJ: Random data
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.52ε (Mean = 0.0184ε)</span><br> <br>
- (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 3.57ε (Mean = 0.704ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_ellint_rj_GSL_2_1_RJ_Random_data">And
- other failures.</a>)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 186ε (Mean = 6.67ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 215ε (Mean = 7.66ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- RJ: 4 Equal Values
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 1.03ε (Mean = 0.418ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.998ε (Mean = 0.387ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.03ε (Mean = 0.418ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- RJ: 3 Equal Values
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 3.96ε (Mean = 1.06ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 20.8ε (Mean = 0.986ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 39.9ε (Mean = 1.17ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- RJ: 2 Equal Values
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.6ε (Mean = 0.0228ε)</span><br> <br>
- (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 2.57ε (Mean = 0.754ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 220ε (Mean = 6.64ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 214ε (Mean = 5.28ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- RJ: Equal z and p
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.742ε (Mean = 0.0166ε)</span><br> <br>
- (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 2.62ε (Mean = 0.699ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 17.2ε (Mean = 1.16ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 16.1ε (Mean = 1.14ε)</span>
- </p>
- </td>
- </tr>
- </tbody>
- </table></div>
- </div>
- <br class="table-break"><div class="table">
- <a name="special_function_error_rates_rep.all_the_tables.table_erf"></a><p class="title"><b>Table 134. Error rates for erf</b></p>
- <div class="table-contents"><table class="table" summary="Error rates for erf">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> long double
- </p>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> double
- </p>
- </th>
- <th>
- <p>
- Sun compiler version 0x5150<br> Sun Solaris<br> long double
- </p>
- </th>
- <th>
- <p>
- Microsoft Visual C++ version 14.1<br> Win32<br> double
- </p>
- </th>
- </tr></thead>
- <tbody>
- <tr>
- <td>
- <p>
- Erf Function: Small Values
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.925ε (Mean = 0.193ε)</span><br> <br>
- (<span class="emphasis"><em><cmath>:</em></span> Max = 0.944ε (Mean = 0.191ε))<br>
- (<span class="emphasis"><em><math.h>:</em></span> Max = 0.944ε (Mean = 0.191ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.841ε (Mean = 0.0687ε)</span><br> <br>
- (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 2.06ε (Mean = 0.319ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.925ε (Mean = 0.193ε)</span><br> <br>
- (<span class="emphasis"><em><math.h>:</em></span> Max = 0.944ε (Mean = 0.194ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.996ε (Mean = 0.182ε)</span><br> <br>
- (<span class="emphasis"><em><math.h>:</em></span> Max = 1.57ε (Mean = 0.317ε))
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Erf Function: Medium Values
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.5ε (Mean = 0.193ε)</span><br> <br>
- (<span class="emphasis"><em><cmath>:</em></span> Max = 0.921ε (Mean = 0.0723ε))<br>
- (<span class="emphasis"><em><math.h>:</em></span> Max = 0.921ε (Mean = 0.0723ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1ε (Mean = 0.119ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 2.31ε (Mean = 0.368ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.5ε (Mean = 0.197ε)</span><br> <br>
- (<span class="emphasis"><em><math.h>:</em></span> Max = 0.921ε (Mean = 0.071ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1ε (Mean = 0.171ε)</span><br> <br> (<span class="emphasis"><em><math.h>:</em></span>
- Max = 1.19ε (Mean = 0.244ε))
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Erf Function: Large Values
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em><cmath>:</em></span>
- Max = 0ε (Mean = 0ε))<br> (<span class="emphasis"><em><math.h>:</em></span> Max
- = 0ε (Mean = 0ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 0ε (Mean = 0ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em><math.h>:</em></span>
- Max = 0ε (Mean = 0ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em><math.h>:</em></span>
- Max = 0ε (Mean = 0ε))
- </p>
- </td>
- </tr>
- </tbody>
- </table></div>
- </div>
- <br class="table-break"><div class="table">
- <a name="special_function_error_rates_rep.all_the_tables.table_erf_inv"></a><p class="title"><b>Table 135. Error rates for erf_inv</b></p>
- <div class="table-contents"><table class="table" summary="Error rates for erf_inv">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> double
- </p>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> long double
- </p>
- </th>
- <th>
- <p>
- Sun compiler version 0x5150<br> Sun Solaris<br> long double
- </p>
- </th>
- <th>
- <p>
- Microsoft Visual C++ version 14.1<br> Win32<br> double
- </p>
- </th>
- </tr></thead>
- <tbody><tr>
- <td>
- <p>
- Inverse Erf Function
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.996ε (Mean = 0.389ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.08ε (Mean = 0.395ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.09ε (Mean = 0.502ε)</span>
- </p>
- </td>
- </tr></tbody>
- </table></div>
- </div>
- <br class="table-break"><div class="table">
- <a name="special_function_error_rates_rep.all_the_tables.table_erfc"></a><p class="title"><b>Table 136. Error rates for erfc</b></p>
- <div class="table-contents"><table class="table" summary="Error rates for erfc">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> long double
- </p>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> double
- </p>
- </th>
- <th>
- <p>
- Sun compiler version 0x5150<br> Sun Solaris<br> long double
- </p>
- </th>
- <th>
- <p>
- Microsoft Visual C++ version 14.1<br> Win32<br> double
- </p>
- </th>
- </tr></thead>
- <tbody>
- <tr>
- <td>
- <p>
- Erf Function: Small Values
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em><cmath>:</em></span>
- Max = 0ε (Mean = 0ε))<br> (<span class="emphasis"><em><math.h>:</em></span> Max
- = 0ε (Mean = 0ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.658ε (Mean = 0.0537ε)</span><br> <br>
- (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 1.01ε (Mean = 0.485ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em><math.h>:</em></span>
- Max = 0ε (Mean = 0ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em><math.h>:</em></span>
- Max = 0ε (Mean = 0ε))
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Erf Function: Medium Values
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.76ε (Mean = 0.365ε)</span><br> <br>
- (<span class="emphasis"><em><cmath>:</em></span> Max = 1.35ε (Mean = 0.307ε))<br>
- (<span class="emphasis"><em><math.h>:</em></span> Max = 1.35ε (Mean = 0.307ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.983ε (Mean = 0.213ε)</span><br> <br>
- (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 2.64ε (Mean = 0.662ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.76ε (Mean = 0.38ε)</span><br> <br>
- (<span class="emphasis"><em><math.h>:</em></span> Max = 2.81ε (Mean = 0.739ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.65ε (Mean = 0.373ε)</span><br> <br>
- (<span class="emphasis"><em><math.h>:</em></span> Max = 2.36ε (Mean = 0.539ε))
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Erf Function: Large Values
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.57ε (Mean = 0.542ε)</span><br> <br>
- (<span class="emphasis"><em><cmath>:</em></span> Max = 1.26ε (Mean = 0.441ε))<br>
- (<span class="emphasis"><em><math.h>:</em></span> Max = 1.26ε (Mean = 0.441ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.868ε (Mean = 0.147ε)</span><br> <br>
- (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 3.9ε (Mean = 0.472ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.57ε (Mean = 0.564ε)</span><br> <br>
- (<span class="emphasis"><em><math.h>:</em></span> Max = 4.91ε (Mean = 1.54ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.14ε (Mean = 0.248ε)</span><br> <br>
- (<span class="emphasis"><em><math.h>:</em></span> Max = 1.84ε (Mean = 0.331ε))
- </p>
- </td>
- </tr>
- </tbody>
- </table></div>
- </div>
- <br class="table-break"><div class="table">
- <a name="special_function_error_rates_rep.all_the_tables.table_erfc_inv"></a><p class="title"><b>Table 137. Error rates for erfc_inv</b></p>
- <div class="table-contents"><table class="table" summary="Error rates for erfc_inv">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> double
- </p>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> long double
- </p>
- </th>
- <th>
- <p>
- Sun compiler version 0x5150<br> Sun Solaris<br> long double
- </p>
- </th>
- <th>
- <p>
- Microsoft Visual C++ version 14.1<br> Win32<br> double
- </p>
- </th>
- </tr></thead>
- <tbody>
- <tr>
- <td>
- <p>
- Inverse Erfc Function
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.996ε (Mean = 0.397ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.08ε (Mean = 0.403ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1ε (Mean = 0.491ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Inverse Erfc Function: extreme values
- </p>
- </td>
- <td>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.62ε (Mean = 0.383ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.62ε (Mean = 0.383ε)</span>
- </p>
- </td>
- <td>
- </td>
- </tr>
- </tbody>
- </table></div>
- </div>
- <br class="table-break"><div class="table">
- <a name="special_function_error_rates_rep.all_the_tables.table_expint_Ei_"></a><p class="title"><b>Table 138. Error rates for expint (Ei)</b></p>
- <div class="table-contents"><table class="table" summary="Error rates for expint (Ei)">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> long double
- </p>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> double
- </p>
- </th>
- <th>
- <p>
- Sun compiler version 0x5150<br> Sun Solaris<br> long double
- </p>
- </th>
- <th>
- <p>
- Microsoft Visual C++ version 14.1<br> Win32<br> double
- </p>
- </th>
- </tr></thead>
- <tbody>
- <tr>
- <td>
- <p>
- Exponential Integral Ei
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 5.05ε (Mean = 0.821ε)</span><br> <br>
- (<span class="emphasis"><em><cmath>:</em></span> Max = 14.1ε (Mean = 2.43ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_expint_Ei___cmath__Exponential_Integral_Ei">And
- other failures.</a>)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.994ε (Mean = 0.142ε)</span><br> <br>
- (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 8.96ε (Mean = 0.703ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 5.05ε (Mean = 0.835ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.43ε (Mean = 0.54ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Exponential Integral Ei: double exponent range
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.72ε (Mean = 0.593ε)</span><br> <br>
- (<span class="emphasis"><em><cmath>:</em></span> Max = 3.11ε (Mean = 1.13ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.998ε (Mean = 0.156ε)</span><br> <br>
- (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 1.5ε (Mean = 0.612ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.72ε (Mean = 0.607ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.7ε (Mean = 0.66ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Exponential Integral Ei: long exponent range
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.98ε (Mean = 0.595ε)</span><br> <br>
- (<span class="emphasis"><em><cmath>:</em></span> Max = 1.93ε (Mean = 0.855ε))
- </p>
- </td>
- <td>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.98ε (Mean = 0.575ε)</span>
- </p>
- </td>
- <td>
- </td>
- </tr>
- </tbody>
- </table></div>
- </div>
- <br class="table-break"><div class="table">
- <a name="special_function_error_rates_rep.all_the_tables.table_expint_En_"></a><p class="title"><b>Table 139. Error rates for expint (En)</b></p>
- <div class="table-contents"><table class="table" summary="Error rates for expint (En)">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> double
- </p>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> long double
- </p>
- </th>
- <th>
- <p>
- Sun compiler version 0x5150<br> Sun Solaris<br> long double
- </p>
- </th>
- <th>
- <p>
- Microsoft Visual C++ version 14.1<br> Win32<br> double
- </p>
- </th>
- </tr></thead>
- <tbody>
- <tr>
- <td>
- <p>
- Exponential Integral En
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.589ε (Mean = 0.0331ε)</span><br> <br>
- (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 58.5ε (Mean = 17.1ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 9.97ε (Mean = 2.13ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 9.97ε (Mean = 2.13ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 7.16ε (Mean = 1.85ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Exponential Integral En: small z values
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 115ε (Mean = 23.6ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.99ε (Mean = 0.559ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.99ε (Mean = 0.559ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 2.62ε (Mean = 0.531ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Exponential Integral E1
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.556ε (Mean = 0.0625ε)</span><br> <br>
- (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 0.988ε (Mean = 0.469ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.965ε (Mean = 0.414ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.965ε (Mean = 0.408ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.988ε (Mean = 0.486ε)</span>
- </p>
- </td>
- </tr>
- </tbody>
- </table></div>
- </div>
- <br class="table-break"><div class="table">
- <a name="special_function_error_rates_rep.all_the_tables.table_expm1"></a><p class="title"><b>Table 140. Error rates for expm1</b></p>
- <div class="table-contents"><table class="table" summary="Error rates for expm1">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> long double
- </p>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> double
- </p>
- </th>
- <th>
- <p>
- Sun compiler version 0x5150<br> Sun Solaris<br> long double
- </p>
- </th>
- <th>
- <p>
- Microsoft Visual C++ version 14.1<br> Win32<br> double
- </p>
- </th>
- </tr></thead>
- <tbody><tr>
- <td>
- <p>
- Random test data
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.992ε (Mean = 0.402ε)</span><br> <br>
- (<span class="emphasis"><em><cmath>:</em></span> Max = 0.992ε (Mean = 0.402ε))<br>
- (<span class="emphasis"><em><math.h>:</em></span> Max = 0.992ε (Mean = 0.402ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.793ε (Mean = 0.126ε)</span><br> <br>
- (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 0.793ε (Mean = 0.126ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.31ε (Mean = 0.428ε)</span><br> <br>
- (<span class="emphasis"><em><math.h>:</em></span> Max = 0.996ε (Mean = 0.426ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.31ε (Mean = 0.496ε)</span><br> <br>
- (<span class="emphasis"><em><math.h>:</em></span> Max = 1.31ε (Mean = 0.496ε))
- </p>
- </td>
- </tr></tbody>
- </table></div>
- </div>
- <br class="table-break"><div class="table">
- <a name="special_function_error_rates_rep.all_the_tables.table_gamma_p"></a><p class="title"><b>Table 141. Error rates for gamma_p</b></p>
- <div class="table-contents"><table class="table" summary="Error rates for gamma_p">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> double
- </p>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> long double
- </p>
- </th>
- <th>
- <p>
- Sun compiler version 0x5150<br> Sun Solaris<br> long double
- </p>
- </th>
- <th>
- <p>
- Microsoft Visual C++ version 14.1<br> Win32<br> double
- </p>
- </th>
- </tr></thead>
- <tbody>
- <tr>
- <td>
- <p>
- tgamma(a, z) medium values
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.955ε (Mean = 0.05ε)</span><br> <br>
- (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 342ε (Mean = 45.8ε))<br> (<span class="emphasis"><em>Rmath
- 3.2.3:</em></span> Max = 389ε (Mean = 44ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 41.6ε (Mean = 8.09ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 239ε (Mean = 30.2ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 35.1ε (Mean = 6.98ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- tgamma(a, z) small values
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 4.82ε (Mean = 0.758ε))<br> (<span class="emphasis"><em>Rmath
- 3.2.3:</em></span> Max = 1.01ε (Mean = 0.306ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 2ε (Mean = 0.464ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 2ε (Mean = 0.461ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.54ε (Mean = 0.439ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- tgamma(a, z) large values
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 1.02e+03ε (Mean = 105ε))<br> (<span class="emphasis"><em>Rmath
- 3.2.3:</em></span> Max = 1.11e+03ε (Mean = 67.5ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 3.08e+04ε (Mean = 1.86e+03ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 3.02e+04ε (Mean = 1.91e+03ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 243ε (Mean = 20.2ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- tgamma(a, z) integer and half integer values
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 128ε (Mean = 22.6ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
- Max = 66.2ε (Mean = 12.2ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 11.8ε (Mean = 2.66ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 71.6ε (Mean = 9.47ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 13ε (Mean = 2.97ε)</span>
- </p>
- </td>
- </tr>
- </tbody>
- </table></div>
- </div>
- <br class="table-break"><div class="table">
- <a name="special_function_error_rates_rep.all_the_tables.table_gamma_p_inv"></a><p class="title"><b>Table 142. Error rates for gamma_p_inv</b></p>
- <div class="table-contents"><table class="table" summary="Error rates for gamma_p_inv">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> double
- </p>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> long double
- </p>
- </th>
- <th>
- <p>
- Sun compiler version 0x5150<br> Sun Solaris<br> long double
- </p>
- </th>
- <th>
- <p>
- Microsoft Visual C++ version 14.1<br> Win32<br> double
- </p>
- </th>
- </tr></thead>
- <tbody>
- <tr>
- <td>
- <p>
- incomplete gamma inverse(a, z) medium values
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.993ε (Mean = 0.15ε)</span><br> <br>
- (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 4.88ε (Mean = 0.868ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.8ε (Mean = 0.406ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.89ε (Mean = 0.466ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.71ε (Mean = 0.34ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- incomplete gamma inverse(a, z) large values
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>Rmath
- 3.2.3:</em></span> Max = 0.816ε (Mean = 0.0874ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.509ε (Mean = 0.0447ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.509ε (Mean = 0.0447ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.924ε (Mean = 0.108ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- incomplete gamma inverse(a, z) small values
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 441ε (Mean = 53.9ε)</span><br> <br>
- (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 547ε (Mean = 61.6ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 9.17e+03ε (Mean = 1.45e+03ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.09e+04ε (Mean = 1.3e+03ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.1e+03ε (Mean = 131ε)</span>
- </p>
- </td>
- </tr>
- </tbody>
- </table></div>
- </div>
- <br class="table-break"><div class="table">
- <a name="special_function_error_rates_rep.all_the_tables.table_gamma_p_inva"></a><p class="title"><b>Table 143. Error rates for gamma_p_inva</b></p>
- <div class="table-contents"><table class="table" summary="Error rates for gamma_p_inva">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> double
- </p>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> long double
- </p>
- </th>
- <th>
- <p>
- Sun compiler version 0x5150<br> Sun Solaris<br> long double
- </p>
- </th>
- <th>
- <p>
- Microsoft Visual C++ version 14.1<br> Win32<br> double
- </p>
- </th>
- </tr></thead>
- <tbody><tr>
- <td>
- <p>
- Incomplete gamma inverses.
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 7.87ε (Mean = 1.15ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 4.08ε (Mean = 1.12ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 4.92ε (Mean = 1.03ε)</span>
- </p>
- </td>
- </tr></tbody>
- </table></div>
- </div>
- <br class="table-break"><div class="table">
- <a name="special_function_error_rates_rep.all_the_tables.table_gamma_q"></a><p class="title"><b>Table 144. Error rates for gamma_q</b></p>
- <div class="table-contents"><table class="table" summary="Error rates for gamma_q">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> double
- </p>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> long double
- </p>
- </th>
- <th>
- <p>
- Sun compiler version 0x5150<br> Sun Solaris<br> long double
- </p>
- </th>
- <th>
- <p>
- Microsoft Visual C++ version 14.1<br> Win32<br> double
- </p>
- </th>
- </tr></thead>
- <tbody>
- <tr>
- <td>
- <p>
- tgamma(a, z) medium values
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.927ε (Mean = 0.035ε)</span><br> <br>
- (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 201ε (Mean = 13.5ε))<br> (<span class="emphasis"><em>Rmath
- 3.2.3:</em></span> Max = 131ε (Mean = 12.7ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 32.3ε (Mean = 6.61ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 199ε (Mean = 26.6ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 23.7ε (Mean = 4ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- tgamma(a, z) small values
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> <span class="red">Max = 1.38e+10ε (Mean = 1.05e+09ε))</span><br>
- (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 65.6ε (Mean = 11ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 2.45ε (Mean = 0.885ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 2.45ε (Mean = 0.819ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 2.26ε (Mean = 0.74ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- tgamma(a, z) large values
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 2.71e+04ε (Mean = 2.16e+03ε))<br> (<span class="emphasis"><em>Rmath
- 3.2.3:</em></span> Max = 1.02e+03ε (Mean = 62.7ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 6.82e+03ε (Mean = 414ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.15e+04ε (Mean = 733ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 469ε (Mean = 31.5ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- tgamma(a, z) integer and half integer values
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 118ε (Mean = 12.5ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
- Max = 138ε (Mean = 16.9ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 11.1ε (Mean = 2.07ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 54.7ε (Mean = 6.16ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 8.72ε (Mean = 1.48ε)</span>
- </p>
- </td>
- </tr>
- </tbody>
- </table></div>
- </div>
- <br class="table-break"><div class="table">
- <a name="special_function_error_rates_rep.all_the_tables.table_gamma_q_inv"></a><p class="title"><b>Table 145. Error rates for gamma_q_inv</b></p>
- <div class="table-contents"><table class="table" summary="Error rates for gamma_q_inv">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> double
- </p>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> long double
- </p>
- </th>
- <th>
- <p>
- Sun compiler version 0x5150<br> Sun Solaris<br> long double
- </p>
- </th>
- <th>
- <p>
- Microsoft Visual C++ version 14.1<br> Win32<br> double
- </p>
- </th>
- </tr></thead>
- <tbody>
- <tr>
- <td>
- <p>
- incomplete gamma inverse(a, z) medium values
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.912ε (Mean = 0.154ε)</span><br> <br>
- (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 4.66ε (Mean = 0.792ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 6.2ε (Mean = 0.627ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 6.2ε (Mean = 0.683ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 2.88ε (Mean = 0.469ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- incomplete gamma inverse(a, z) large values
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.894ε (Mean = 0.0915ε)</span><br> <br>
- (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 0.894ε (Mean = 0.106ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.814ε (Mean = 0.0856ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- incomplete gamma inverse(a, z) small values
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 292ε (Mean = 36.4ε)</span><br> <br>
- (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 415ε (Mean = 48.7ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 8.28e+03ε (Mean = 1.09e+03ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 8.98e+03ε (Mean = 877ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 451ε (Mean = 64.7ε)</span>
- </p>
- </td>
- </tr>
- </tbody>
- </table></div>
- </div>
- <br class="table-break"><div class="table">
- <a name="special_function_error_rates_rep.all_the_tables.table_gamma_q_inva"></a><p class="title"><b>Table 146. Error rates for gamma_q_inva</b></p>
- <div class="table-contents"><table class="table" summary="Error rates for gamma_q_inva">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> double
- </p>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> long double
- </p>
- </th>
- <th>
- <p>
- Sun compiler version 0x5150<br> Sun Solaris<br> long double
- </p>
- </th>
- <th>
- <p>
- Microsoft Visual C++ version 14.1<br> Win32<br> double
- </p>
- </th>
- </tr></thead>
- <tbody><tr>
- <td>
- <p>
- Incomplete gamma inverses.
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 8.42ε (Mean = 1.3ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 7.86ε (Mean = 1.24ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 5.05ε (Mean = 1.08ε)</span>
- </p>
- </td>
- </tr></tbody>
- </table></div>
- </div>
- <br class="table-break"><div class="table">
- <a name="special_function_error_rates_rep.all_the_tables.table_hermite"></a><p class="title"><b>Table 147. Error rates for hermite</b></p>
- <div class="table-contents"><table class="table" summary="Error rates for hermite">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> double
- </p>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> long double
- </p>
- </th>
- <th>
- <p>
- Sun compiler version 0x5150<br> Sun Solaris<br> long double
- </p>
- </th>
- <th>
- <p>
- Microsoft Visual C++ version 14.1<br> Win32<br> double
- </p>
- </th>
- </tr></thead>
- <tbody><tr>
- <td>
- <p>
- Hermite Polynomials
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 6.24ε (Mean = 2.07ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 6.24ε (Mean = 2.07ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 4.46ε (Mean = 1.41ε)</span>
- </p>
- </td>
- </tr></tbody>
- </table></div>
- </div>
- <br class="table-break"><div class="table">
- <a name="special_function_error_rates_rep.all_the_tables.table_heuman_lambda"></a><p class="title"><b>Table 148. Error rates for heuman_lambda</b></p>
- <div class="table-contents"><table class="table" summary="Error rates for heuman_lambda">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> double
- </p>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> long double
- </p>
- </th>
- <th>
- <p>
- Sun compiler version 0x5150<br> Sun Solaris<br> long double
- </p>
- </th>
- <th>
- <p>
- Microsoft Visual C++ version 14.1<br> Win32<br> double
- </p>
- </th>
- </tr></thead>
- <tbody>
- <tr>
- <td>
- <p>
- Elliptic Integral Jacobi Zeta: Mathworld Data
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.89ε (Mean = 0.887ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.89ε (Mean = 0.887ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.08ε (Mean = 0.734ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Elliptic Integral Heuman Lambda: Random Data
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 3.82ε (Mean = 0.609ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 3.82ε (Mean = 0.608ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 2.12ε (Mean = 0.588ε)</span>
- </p>
- </td>
- </tr>
- </tbody>
- </table></div>
- </div>
- <br class="table-break"><div class="table">
- <a name="special_function_error_rates_rep.all_the_tables.table_ibeta"></a><p class="title"><b>Table 149. Error rates for ibeta</b></p>
- <div class="table-contents"><table class="table" summary="Error rates for ibeta">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> double
- </p>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> long double
- </p>
- </th>
- <th>
- <p>
- Sun compiler version 0x5150<br> Sun Solaris<br> long double
- </p>
- </th>
- <th>
- <p>
- Microsoft Visual C++ version 14.1<br> Win32<br> double
- </p>
- </th>
- </tr></thead>
- <tbody>
- <tr>
- <td>
- <p>
- Incomplete Beta Function: Small Values
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 682ε (Mean = 32.6ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
- Max = 22.9ε (Mean = 3.35ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 8.97ε (Mean = 2.09ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 21.3ε (Mean = 2.75ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 8.4ε (Mean = 1.93ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Incomplete Beta Function: Medium Values
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 690ε (Mean = 151ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
- Max = 232ε (Mean = 27.9ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 50ε (Mean = 12.1ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 124ε (Mean = 18.4ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 106ε (Mean = 16.3ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Incomplete Beta Function: Large and Diverse Values
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.26ε (Mean = 0.063ε)</span><br> <br>
- (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 3.9e+05ε (Mean = 1.82e+04ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_ibeta_GSL_2_1_Incomplete_Beta_Function_Large_and_Diverse_Values">And
- other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
- Max = 574ε (Mean = 49.4ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.96e+04ε (Mean = 997ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 4.98e+04ε (Mean = 2.07e+03ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.32e+03ε (Mean = 68.5ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Incomplete Beta Function: Small Integer Values
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 254ε (Mean = 50.9ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
- Max = 62.2ε (Mean = 8.95ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 4.45ε (Mean = 0.814ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 44.5ε (Mean = 10.1ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 3.85ε (Mean = 0.791ε)</span>
- </p>
- </td>
- </tr>
- </tbody>
- </table></div>
- </div>
- <br class="table-break"><div class="table">
- <a name="special_function_error_rates_rep.all_the_tables.table_ibeta_inv"></a><p class="title"><b>Table 150. Error rates for ibeta_inv</b></p>
- <div class="table-contents"><table class="table" summary="Error rates for ibeta_inv">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> double
- </p>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> long double
- </p>
- </th>
- <th>
- <p>
- Sun compiler version 0x5150<br> Sun Solaris<br> long double
- </p>
- </th>
- <th>
- <p>
- Microsoft Visual C++ version 14.1<br> Win32<br> double
- </p>
- </th>
- </tr></thead>
- <tbody><tr>
- <td>
- <p>
- Inverse incomplete beta
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 11ε (Mean = 0.345ε)</span><br> <br>
- (<span class="emphasis"><em>Rmath 3.2.3:</em></span> <span class="red">Max = 1.14e+121ε (Mean
- = 3.28e+119ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_ibeta_inv_Rmath_3_2_3_Inverse_incomplete_beta">And
- other failures.</a>)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 3.8e+04ε (Mean = 2.66e+03ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 4.07e+04ε (Mean = 2.86e+03ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 8.59e+03ε (Mean = 277ε)</span>
- </p>
- </td>
- </tr></tbody>
- </table></div>
- </div>
- <br class="table-break"><div class="table">
- <a name="special_function_error_rates_rep.all_the_tables.table_ibeta_inva"></a><p class="title"><b>Table 151. Error rates for ibeta_inva</b></p>
- <div class="table-contents"><table class="table" summary="Error rates for ibeta_inva">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> double
- </p>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> long double
- </p>
- </th>
- <th>
- <p>
- Sun compiler version 0x5150<br> Sun Solaris<br> long double
- </p>
- </th>
- <th>
- <p>
- Microsoft Visual C++ version 14.1<br> Win32<br> double
- </p>
- </th>
- </tr></thead>
- <tbody><tr>
- <td>
- <p>
- Inverse incomplete beta
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.602ε (Mean = 0.0239ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 377ε (Mean = 24.4ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 438ε (Mean = 31.3ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 242ε (Mean = 22.9ε)</span>
- </p>
- </td>
- </tr></tbody>
- </table></div>
- </div>
- <br class="table-break"><div class="table">
- <a name="special_function_error_rates_rep.all_the_tables.table_ibeta_invb"></a><p class="title"><b>Table 152. Error rates for ibeta_invb</b></p>
- <div class="table-contents"><table class="table" summary="Error rates for ibeta_invb">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> double
- </p>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> long double
- </p>
- </th>
- <th>
- <p>
- Sun compiler version 0x5150<br> Sun Solaris<br> long double
- </p>
- </th>
- <th>
- <p>
- Microsoft Visual C++ version 14.1<br> Win32<br> double
- </p>
- </th>
- </tr></thead>
- <tbody><tr>
- <td>
- <p>
- Inverse incomplete beta
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.765ε (Mean = 0.0422ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 407ε (Mean = 27.2ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 407ε (Mean = 24.4ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 409ε (Mean = 19.3ε)</span>
- </p>
- </td>
- </tr></tbody>
- </table></div>
- </div>
- <br class="table-break"><div class="table">
- <a name="special_function_error_rates_rep.all_the_tables.table_ibetac"></a><p class="title"><b>Table 153. Error rates for ibetac</b></p>
- <div class="table-contents"><table class="table" summary="Error rates for ibetac">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> double
- </p>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> long double
- </p>
- </th>
- <th>
- <p>
- Sun compiler version 0x5150<br> Sun Solaris<br> long double
- </p>
- </th>
- <th>
- <p>
- Microsoft Visual C++ version 14.1<br> Win32<br> double
- </p>
- </th>
- </tr></thead>
- <tbody>
- <tr>
- <td>
- <p>
- Incomplete Beta Function: Small Values
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>Rmath
- 3.2.3:</em></span> Max = 22.4ε (Mean = 3.67ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 10.6ε (Mean = 2.22ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 13.8ε (Mean = 2.68ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 6.94ε (Mean = 1.71ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Incomplete Beta Function: Medium Values
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>Rmath
- 3.2.3:</em></span> Max = 204ε (Mean = 25.8ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 73.9ε (Mean = 11.2ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 132ε (Mean = 19.8ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 56.7ε (Mean = 14.3ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Incomplete Beta Function: Large and Diverse Values
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.981ε (Mean = 0.0573ε)</span><br> <br>
- (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 889ε (Mean = 68.4ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 3.45e+04ε (Mean = 1.32e+03ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 6.31e+04ε (Mean = 2.04e+03ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.88e+03ε (Mean = 82.7ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Incomplete Beta Function: Small Integer Values
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>Rmath
- 3.2.3:</em></span> Max = 84.6ε (Mean = 18ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 5.34ε (Mean = 1.11ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 107ε (Mean = 17.1ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 6.37ε (Mean = 1.03ε)</span>
- </p>
- </td>
- </tr>
- </tbody>
- </table></div>
- </div>
- <br class="table-break"><div class="table">
- <a name="special_function_error_rates_rep.all_the_tables.table_ibetac_inv"></a><p class="title"><b>Table 154. Error rates for ibetac_inv</b></p>
- <div class="table-contents"><table class="table" summary="Error rates for ibetac_inv">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> double
- </p>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> long double
- </p>
- </th>
- <th>
- <p>
- Sun compiler version 0x5150<br> Sun Solaris<br> long double
- </p>
- </th>
- <th>
- <p>
- Microsoft Visual C++ version 14.1<br> Win32<br> double
- </p>
- </th>
- </tr></thead>
- <tbody><tr>
- <td>
- <p>
- Inverse incomplete beta
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.977ε (Mean = 0.0976ε)</span><br> <br>
- (<span class="emphasis"><em>Rmath 3.2.3:</em></span> <span class="red">Max = 3.01e+132ε (Mean
- = 8.65e+130ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_ibetac_inv_Rmath_3_2_3_Inverse_incomplete_beta">And
- other failures.</a>)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 4.88e+04ε (Mean = 3.16e+03ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 5.05e+04ε (Mean = 3.33e+03ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 2.93e+03ε (Mean = 198ε)</span>
- </p>
- </td>
- </tr></tbody>
- </table></div>
- </div>
- <br class="table-break"><div class="table">
- <a name="special_function_error_rates_rep.all_the_tables.table_ibetac_inva"></a><p class="title"><b>Table 155. Error rates for ibetac_inva</b></p>
- <div class="table-contents"><table class="table" summary="Error rates for ibetac_inva">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> double
- </p>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> long double
- </p>
- </th>
- <th>
- <p>
- Sun compiler version 0x5150<br> Sun Solaris<br> long double
- </p>
- </th>
- <th>
- <p>
- Microsoft Visual C++ version 14.1<br> Win32<br> double
- </p>
- </th>
- </tr></thead>
- <tbody><tr>
- <td>
- <p>
- Inverse incomplete beta
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.683ε (Mean = 0.0314ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 382ε (Mean = 22.2ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 315ε (Mean = 23.7ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 408ε (Mean = 26.7ε)</span>
- </p>
- </td>
- </tr></tbody>
- </table></div>
- </div>
- <br class="table-break"><div class="table">
- <a name="special_function_error_rates_rep.all_the_tables.table_ibetac_invb"></a><p class="title"><b>Table 156. Error rates for ibetac_invb</b></p>
- <div class="table-contents"><table class="table" summary="Error rates for ibetac_invb">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> double
- </p>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> long double
- </p>
- </th>
- <th>
- <p>
- Sun compiler version 0x5150<br> Sun Solaris<br> long double
- </p>
- </th>
- <th>
- <p>
- Microsoft Visual C++ version 14.1<br> Win32<br> double
- </p>
- </th>
- </tr></thead>
- <tbody><tr>
- <td>
- <p>
- Inverse incomplete beta
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.724ε (Mean = 0.0303ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 317ε (Mean = 19.8ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 369ε (Mean = 22.6ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 271ε (Mean = 16.4ε)</span>
- </p>
- </td>
- </tr></tbody>
- </table></div>
- </div>
- <br class="table-break"><div class="table">
- <a name="special_function_error_rates_rep.all_the_tables.table_jacobi_cn"></a><p class="title"><b>Table 157. Error rates for jacobi_cn</b></p>
- <div class="table-contents"><table class="table" summary="Error rates for jacobi_cn">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> double
- </p>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> long double
- </p>
- </th>
- <th>
- <p>
- Sun compiler version 0x5150<br> Sun Solaris<br> long double
- </p>
- </th>
- <th>
- <p>
- Microsoft Visual C++ version 14.1<br> Win32<br> double
- </p>
- </th>
- </tr></thead>
- <tbody>
- <tr>
- <td>
- <p>
- Jacobi Elliptic: Mathworld Data
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 17.3ε (Mean = 4.29ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_jacobi_cn_GSL_2_1_Jacobi_Elliptic_Mathworld_Data">And
- other failures.</a>)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 71.6ε (Mean = 19.3ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 71.6ε (Mean = 19.4ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 45.8ε (Mean = 11.4ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Jacobi Elliptic: Random Data
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.816ε (Mean = 0.0563ε)</span><br> <br>
- (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 2.43ε (Mean = 0.803ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.68ε (Mean = 0.443ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.68ε (Mean = 0.454ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.83ε (Mean = 0.455ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Jacobi Elliptic: Random Small Values
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 55.2ε (Mean = 1.64ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_jacobi_cn_GSL_2_1_Jacobi_Elliptic_Random_Small_Values">And
- other failures.</a>)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 10.4ε (Mean = 0.594ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 10.4ε (Mean = 0.602ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 26.2ε (Mean = 1.17ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Jacobi Elliptic: Modulus near 1
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.919ε (Mean = 0.127ε)</span><br> <br>
- (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 0ε (Mean = 0ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_jacobi_cn_GSL_2_1_Jacobi_Elliptic_Modulus_near_1">And
- other failures.</a>)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 675ε (Mean = 87.1ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 675ε (Mean = 86.8ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 513ε (Mean = 126ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Jacobi Elliptic: Large Phi
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 14.2ε (Mean = 0.927ε)</span><br> <br>
- (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 5.92e+03ε (Mean = 477ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 2.97e+04ε (Mean = 1.9e+03ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 2.97e+04ε (Mean = 1.9e+03ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 3.27e+04ε (Mean = 1.93e+03ε)</span>
- </p>
- </td>
- </tr>
- </tbody>
- </table></div>
- </div>
- <br class="table-break"><div class="table">
- <a name="special_function_error_rates_rep.all_the_tables.table_jacobi_dn"></a><p class="title"><b>Table 158. Error rates for jacobi_dn</b></p>
- <div class="table-contents"><table class="table" summary="Error rates for jacobi_dn">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> double
- </p>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> long double
- </p>
- </th>
- <th>
- <p>
- Sun compiler version 0x5150<br> Sun Solaris<br> long double
- </p>
- </th>
- <th>
- <p>
- Microsoft Visual C++ version 14.1<br> Win32<br> double
- </p>
- </th>
- </tr></thead>
- <tbody>
- <tr>
- <td>
- <p>
- Jacobi Elliptic: Mathworld Data
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 2.82ε (Mean = 1.18ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_jacobi_dn_GSL_2_1_Jacobi_Elliptic_Mathworld_Data">And
- other failures.</a>)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 49ε (Mean = 14ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 49ε (Mean = 14ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 34.3ε (Mean = 8.71ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Jacobi Elliptic: Random Data
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 3ε (Mean = 0.61ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.53ε (Mean = 0.473ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.53ε (Mean = 0.481ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.52ε (Mean = 0.466ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Jacobi Elliptic: Random Small Values
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.5ε (Mean = 0.0122ε)</span><br> <br>
- (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 1.5ε (Mean = 0.391ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_jacobi_dn_GSL_2_1_Jacobi_Elliptic_Random_Small_Values">And
- other failures.</a>)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 22.4ε (Mean = 0.777ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 22.4ε (Mean = 0.763ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 16.1ε (Mean = 0.685ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Jacobi Elliptic: Modulus near 1
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 2.28ε (Mean = 0.194ε)</span><br> <br>
- (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 0ε (Mean = 0ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_jacobi_dn_GSL_2_1_Jacobi_Elliptic_Modulus_near_1">And
- other failures.</a>)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 3.75e+03ε (Mean = 293ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 3.75e+03ε (Mean = 293ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 6.24e+03ε (Mean = 482ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Jacobi Elliptic: Large Phi
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 14.1ε (Mean = 0.897ε)</span><br> <br>
- (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 121ε (Mean = 22ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 2.82e+04ε (Mean = 1.79e+03ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 2.82e+04ε (Mean = 1.79e+03ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.67e+04ε (Mean = 1e+03ε)</span>
- </p>
- </td>
- </tr>
- </tbody>
- </table></div>
- </div>
- <br class="table-break"><div class="table">
- <a name="special_function_error_rates_rep.all_the_tables.table_jacobi_sn"></a><p class="title"><b>Table 159. Error rates for jacobi_sn</b></p>
- <div class="table-contents"><table class="table" summary="Error rates for jacobi_sn">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> double
- </p>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> long double
- </p>
- </th>
- <th>
- <p>
- Sun compiler version 0x5150<br> Sun Solaris<br> long double
- </p>
- </th>
- <th>
- <p>
- Microsoft Visual C++ version 14.1<br> Win32<br> double
- </p>
- </th>
- </tr></thead>
- <tbody>
- <tr>
- <td>
- <p>
- Jacobi Elliptic: Mathworld Data
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 588ε (Mean = 146ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_jacobi_sn_GSL_2_1_Jacobi_Elliptic_Mathworld_Data">And
- other failures.</a>)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 341ε (Mean = 80.7ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 341ε (Mean = 80.7ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 481ε (Mean = 113ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Jacobi Elliptic: Random Data
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 4.02ε (Mean = 1.07ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 2.01ε (Mean = 0.584ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 2.01ε (Mean = 0.593ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.92ε (Mean = 0.567ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Jacobi Elliptic: Random Small Values
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 11.7ε (Mean = 1.65ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_jacobi_sn_GSL_2_1_Jacobi_Elliptic_Random_Small_Values">And
- other failures.</a>)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.99ε (Mean = 0.347ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.99ε (Mean = 0.347ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 2.11ε (Mean = 0.385ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Jacobi Elliptic: Modulus near 1
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 0ε (Mean = 0ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_jacobi_sn_GSL_2_1_Jacobi_Elliptic_Modulus_near_1">And
- other failures.</a>)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 109ε (Mean = 7.35ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 109ε (Mean = 7.38ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 23.2ε (Mean = 1.85ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Jacobi Elliptic: Large Phi
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 12ε (Mean = 0.771ε)</span><br> <br>
- (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 4.54e+04ε (Mean = 2.63e+03ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 2.45e+04ε (Mean = 1.51e+03ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 2.45e+04ε (Mean = 1.51e+03ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 4.36e+04ε (Mean = 2.54e+03ε)</span>
- </p>
- </td>
- </tr>
- </tbody>
- </table></div>
- </div>
- <br class="table-break"><div class="table">
- <a name="special_function_error_rates_rep.all_the_tables.table_jacobi_zeta"></a><p class="title"><b>Table 160. Error rates for jacobi_zeta</b></p>
- <div class="table-contents"><table class="table" summary="Error rates for jacobi_zeta">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> double
- </p>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> long double
- </p>
- </th>
- <th>
- <p>
- Sun compiler version 0x5150<br> Sun Solaris<br> long double
- </p>
- </th>
- <th>
- <p>
- Microsoft Visual C++ version 14.1<br> Win32<br> double
- </p>
- </th>
- </tr></thead>
- <tbody>
- <tr>
- <td>
- <p>
- Elliptic Integral Jacobi Zeta: Mathworld Data
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.66ε (Mean = 0.48ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.66ε (Mean = 0.48ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.52ε (Mean = 0.357ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Elliptic Integral Jacobi Zeta: Random Data
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 2.99ε (Mean = 0.824ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 3.96ε (Mean = 1.06ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 3.89ε (Mean = 0.824ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Elliptic Integral Jacobi Zeta: Large Phi Values
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 2.92ε (Mean = 0.951ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 3.05ε (Mean = 1.13ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 2.52ε (Mean = 0.977ε)</span>
- </p>
- </td>
- </tr>
- </tbody>
- </table></div>
- </div>
- <br class="table-break"><div class="table">
- <a name="special_function_error_rates_rep.all_the_tables.table_laguerre_n_m_x_"></a><p class="title"><b>Table 161. Error rates for laguerre(n, m, x)</b></p>
- <div class="table-contents"><table class="table" summary="Error rates for laguerre(n, m, x)">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> double
- </p>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> long double
- </p>
- </th>
- <th>
- <p>
- Sun compiler version 0x5150<br> Sun Solaris<br> long double
- </p>
- </th>
- <th>
- <p>
- Microsoft Visual C++ version 14.1<br> Win32<br> double
- </p>
- </th>
- </tr></thead>
- <tbody><tr>
- <td>
- <p>
- Associated Laguerre Polynomials
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.84ε (Mean = 0.0358ε)</span><br> <br>
- (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 434ε (Mean = 10.7ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 167ε (Mean = 6.38ε)</span><br> <br>
- (<span class="emphasis"><em><cmath>:</em></span> Max = 206ε (Mean = 6.86ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 167ε (Mean = 6.38ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 434ε (Mean = 11.1ε)</span>
- </p>
- </td>
- </tr></tbody>
- </table></div>
- </div>
- <br class="table-break"><div class="table">
- <a name="special_function_error_rates_rep.all_the_tables.table_laguerre_n_x_"></a><p class="title"><b>Table 162. Error rates for laguerre(n, x)</b></p>
- <div class="table-contents"><table class="table" summary="Error rates for laguerre(n, x)">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> double
- </p>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> long double
- </p>
- </th>
- <th>
- <p>
- Sun compiler version 0x5150<br> Sun Solaris<br> long double
- </p>
- </th>
- <th>
- <p>
- Microsoft Visual C++ version 14.1<br> Win32<br> double
- </p>
- </th>
- </tr></thead>
- <tbody><tr>
- <td>
- <p>
- Laguerre Polynomials
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 6.82ε (Mean = 0.408ε)</span><br> <br>
- (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 3.1e+03ε (Mean = 185ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.39e+04ε (Mean = 828ε)</span><br> <br>
- (<span class="emphasis"><em><cmath>:</em></span> Max = 4.2e+03ε (Mean = 251ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.39e+04ε (Mean = 828ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 3.1e+03ε (Mean = 185ε)</span>
- </p>
- </td>
- </tr></tbody>
- </table></div>
- </div>
- <br class="table-break"><div class="table">
- <a name="special_function_error_rates_rep.all_the_tables.table_legendre_p"></a><p class="title"><b>Table 163. Error rates for legendre_p</b></p>
- <div class="table-contents"><table class="table" summary="Error rates for legendre_p">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> double
- </p>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> long double
- </p>
- </th>
- <th>
- <p>
- Sun compiler version 0x5150<br> Sun Solaris<br> long double
- </p>
- </th>
- <th>
- <p>
- Microsoft Visual C++ version 14.1<br> Win32<br> double
- </p>
- </th>
- </tr></thead>
- <tbody>
- <tr>
- <td>
- <p>
- Legendre Polynomials: Small Values
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.732ε (Mean = 0.0619ε)</span><br> <br>
- (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 211ε (Mean = 20.4ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 69.2ε (Mean = 9.58ε)</span><br> <br>
- (<span class="emphasis"><em><cmath>:</em></span> Max = 124ε (Mean = 13.2ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 69.2ε (Mean = 9.58ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 211ε (Mean = 20.4ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Legendre Polynomials: Large Values
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.632ε (Mean = 0.0693ε)</span><br> <br>
- (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 300ε (Mean = 33.2ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 699ε (Mean = 59.6ε)</span><br> <br>
- (<span class="emphasis"><em><cmath>:</em></span> Max = 343ε (Mean = 32.1ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 699ε (Mean = 59.6ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 300ε (Mean = 33.2ε)</span>
- </p>
- </td>
- </tr>
- </tbody>
- </table></div>
- </div>
- <br class="table-break"><div class="table">
- <a name="special_function_error_rates_rep.all_the_tables.table_legendre_p_associated_"></a><p class="title"><b>Table 164. Error rates for legendre_p (associated)</b></p>
- <div class="table-contents"><table class="table" summary="Error rates for legendre_p (associated)">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> double
- </p>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> long double
- </p>
- </th>
- <th>
- <p>
- Sun compiler version 0x5150<br> Sun Solaris<br> long double
- </p>
- </th>
- <th>
- <p>
- Microsoft Visual C++ version 14.1<br> Win32<br> double
- </p>
- </th>
- </tr></thead>
- <tbody><tr>
- <td>
- <p>
- Associated Legendre Polynomials: Small Values
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.999ε (Mean = 0.05ε)</span><br> <br>
- (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 121ε (Mean = 6.75ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_legendre_p_associated__GSL_2_1_Associated_Legendre_Polynomials_Small_Values">And
- other failures.</a>)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 175ε (Mean = 9.88ε)</span><br> <br>
- (<span class="emphasis"><em><cmath>:</em></span> Max = 175ε (Mean = 9.36ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_long_double_legendre_p_associated___cmath__Associated_Legendre_Polynomials_Small_Values">And
- other failures.</a>)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 77.7ε (Mean = 5.59ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 121ε (Mean = 7.14ε)</span>
- </p>
- </td>
- </tr></tbody>
- </table></div>
- </div>
- <br class="table-break"><div class="table">
- <a name="special_function_error_rates_rep.all_the_tables.table_legendre_q"></a><p class="title"><b>Table 165. Error rates for legendre_q</b></p>
- <div class="table-contents"><table class="table" summary="Error rates for legendre_q">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> double
- </p>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> long double
- </p>
- </th>
- <th>
- <p>
- Sun compiler version 0x5150<br> Sun Solaris<br> long double
- </p>
- </th>
- <th>
- <p>
- Microsoft Visual C++ version 14.1<br> Win32<br> double
- </p>
- </th>
- </tr></thead>
- <tbody>
- <tr>
- <td>
- <p>
- Legendre Polynomials: Small Values
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.612ε (Mean = 0.0517ε)</span><br> <br>
- (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 46.4ε (Mean = 7.46ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 50.9ε (Mean = 9ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 50.9ε (Mean = 8.98ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 46.4ε (Mean = 7.32ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Legendre Polynomials: Large Values
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 2.49ε (Mean = 0.202ε)</span><br> <br>
- (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 4.6e+03ε (Mean = 366ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 5.98e+03ε (Mean = 478ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 5.98e+03ε (Mean = 478ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 4.6e+03ε (Mean = 366ε)</span>
- </p>
- </td>
- </tr>
- </tbody>
- </table></div>
- </div>
- <br class="table-break"><div class="table">
- <a name="special_function_error_rates_rep.all_the_tables.table_lgamma"></a><p class="title"><b>Table 166. Error rates for lgamma</b></p>
- <div class="table-contents"><table class="table" summary="Error rates for lgamma">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> double
- </p>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> long double
- </p>
- </th>
- <th>
- <p>
- Sun compiler version 0x5150<br> Sun Solaris<br> long double
- </p>
- </th>
- <th>
- <p>
- Microsoft Visual C++ version 14.1<br> Win32<br> double
- </p>
- </th>
- </tr></thead>
- <tbody>
- <tr>
- <td>
- <p>
- factorials
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 33.6ε (Mean = 2.78ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
- Max = 1.55ε (Mean = 0.592ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.991ε (Mean = 0.308ε)</span><br> <br>
- (<span class="emphasis"><em><cmath>:</em></span> Max = 1.67ε (Mean = 0.487ε))<br>
- (<span class="emphasis"><em><math.h>:</em></span> Max = 1.67ε (Mean = 0.487ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.991ε (Mean = 0.383ε)</span><br> <br>
- (<span class="emphasis"><em><math.h>:</em></span> Max = 1.36ε (Mean = 0.476ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.914ε (Mean = 0.175ε)</span><br> <br>
- (<span class="emphasis"><em><math.h>:</em></span> Max = 0.958ε (Mean = 0.38ε))
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- near 0
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 5.21ε (Mean = 1.57ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
- Max = 0ε (Mean = 0ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.42ε (Mean = 0.566ε)</span><br> <br>
- (<span class="emphasis"><em><cmath>:</em></span> Max = 0.964ε (Mean = 0.543ε))<br>
- (<span class="emphasis"><em><math.h>:</em></span> Max = 0.964ε (Mean = 0.543ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.42ε (Mean = 0.566ε)</span><br> <br>
- (<span class="emphasis"><em><math.h>:</em></span> Max = 0.964ε (Mean = 0.543ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.964ε (Mean = 0.462ε)</span><br> <br>
- (<span class="emphasis"><em><math.h>:</em></span> Max = 0.962ε (Mean = 0.372ε))
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- near 1
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 442ε (Mean = 88.8ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
- Max = 7.99e+04ε (Mean = 1.68e+04ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.948ε (Mean = 0.36ε)</span><br> <br>
- (<span class="emphasis"><em><cmath>:</em></span> Max = 0.615ε (Mean = 0.096ε))<br>
- (<span class="emphasis"><em><math.h>:</em></span> Max = 0.615ε (Mean = 0.096ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.948ε (Mean = 0.36ε)</span><br> <br>
- (<span class="emphasis"><em><math.h>:</em></span> Max = 1.71ε (Mean = 0.581ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.867ε (Mean = 0.468ε)</span><br> <br>
- (<span class="emphasis"><em><math.h>:</em></span> Max = 0.906ε (Mean = 0.565ε))
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- near 2
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 1.17e+03ε (Mean = 274ε))<br> (<span class="emphasis"><em>Rmath
- 3.2.3:</em></span> Max = 2.63e+05ε (Mean = 5.84e+04ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.878ε (Mean = 0.242ε)</span><br> <br>
- (<span class="emphasis"><em><cmath>:</em></span> Max = 0.741ε (Mean = 0.263ε))<br>
- (<span class="emphasis"><em><math.h>:</em></span> Max = 0.741ε (Mean = 0.263ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.878ε (Mean = 0.242ε)</span><br> <br>
- (<span class="emphasis"><em><math.h>:</em></span> Max = 0.598ε (Mean = 0.235ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.591ε (Mean = 0.159ε)</span><br> <br>
- (<span class="emphasis"><em><math.h>:</em></span> Max = 0.741ε (Mean = 0.473ε))
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- near -10
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 24.9ε (Mean = 4.6ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
- Max = 4.22ε (Mean = 1.26ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 3.81ε (Mean = 1.01ε)</span><br> <br>
- (<span class="emphasis"><em><cmath>:</em></span> Max = 0.997ε (Mean = 0.412ε))<br>
- (<span class="emphasis"><em><math.h>:</em></span> Max = 0.997ε (Mean = 0.412ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 3.81ε (Mean = 1.01ε)</span><br> <br>
- (<span class="emphasis"><em><math.h>:</em></span> Max = 3.04ε (Mean = 1.01ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 4.22ε (Mean = 1.33ε)</span><br> <br>
- (<span class="emphasis"><em><math.h>:</em></span> Max = 0.997ε (Mean = 0.444ε))
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- near -55
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 7.02ε (Mean = 1.47ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
- Max = 250ε (Mean = 60.9ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.821ε (Mean = 0.513ε)</span><br> <br>
- (<span class="emphasis"><em><cmath>:</em></span> Max = 1.58ε (Mean = 0.672ε))<br>
- (<span class="emphasis"><em><math.h>:</em></span> Max = 1.58ε (Mean = 0.672ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.59ε (Mean = 0.587ε)</span><br> <br>
- (<span class="emphasis"><em><math.h>:</em></span> Max = 0.821ε (Mean = 0.674ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.821ε (Mean = 0.419ε)</span><br> <br>
- (<span class="emphasis"><em><math.h>:</em></span> Max = 249ε (Mean = 43.1ε))
- </p>
- </td>
- </tr>
- </tbody>
- </table></div>
- </div>
- <br class="table-break"><div class="table">
- <a name="special_function_error_rates_rep.all_the_tables.table_log1p"></a><p class="title"><b>Table 167. Error rates for log1p</b></p>
- <div class="table-contents"><table class="table" summary="Error rates for log1p">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> long double
- </p>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> double
- </p>
- </th>
- <th>
- <p>
- Sun compiler version 0x5150<br> Sun Solaris<br> long double
- </p>
- </th>
- <th>
- <p>
- Microsoft Visual C++ version 14.1<br> Win32<br> double
- </p>
- </th>
- </tr></thead>
- <tbody><tr>
- <td>
- <p>
- Random test data
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.818ε (Mean = 0.227ε)</span><br> <br>
- (<span class="emphasis"><em><cmath>:</em></span> Max = 0.818ε (Mean = 0.227ε))<br>
- (<span class="emphasis"><em><math.h>:</em></span> Max = 0.818ε (Mean = 0.227ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.846ε (Mean = 0.153ε)</span><br> <br>
- (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 0.846ε (Mean = 0.153ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 2.3ε (Mean = 0.66ε)</span><br> <br>
- (<span class="emphasis"><em><math.h>:</em></span> Max = 0.818ε (Mean = 0.249ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.509ε (Mean = 0.057ε)</span><br> <br>
- (<span class="emphasis"><em><math.h>:</em></span> Max = 0.509ε (Mean = 0.057ε))
- </p>
- </td>
- </tr></tbody>
- </table></div>
- </div>
- <br class="table-break"><div class="table">
- <a name="special_function_error_rates_rep.all_the_tables.table_non_central_beta_CDF"></a><p class="title"><b>Table 168. Error rates for non central beta CDF</b></p>
- <div class="table-contents"><table class="table" summary="Error rates for non central beta CDF">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> double
- </p>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> long double
- </p>
- </th>
- <th>
- <p>
- Sun compiler version 0x5150<br> Sun Solaris<br> long double
- </p>
- </th>
- <th>
- <p>
- Microsoft Visual C++ version 14.1<br> Win32<br> double
- </p>
- </th>
- </tr></thead>
- <tbody>
- <tr>
- <td>
- <p>
- Non Central Beta, medium parameters
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.998ε (Mean = 0.0649ε)</span><br> <br>
- (<span class="emphasis"><em>Rmath 3.2.3:</em></span> <span class="red">Max = 1.46e+26ε (Mean
- = 3.5e+24ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_non_central_beta_CDF_Rmath_3_2_3_Non_Central_Beta_medium_parameters">And
- other failures.</a>)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 824ε (Mean = 27.4ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 832ε (Mean = 38.1ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 242ε (Mean = 31ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Non Central Beta, large parameters
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.18ε (Mean = 0.175ε)</span><br> <br>
- (<span class="emphasis"><em>Rmath 3.2.3:</em></span> <span class="red">Max = 1.01e+36ε (Mean
- = 1.19e+35ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_non_central_beta_CDF_Rmath_3_2_3_Non_Central_Beta_large_parameters">And
- other failures.</a>)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 2.5e+04ε (Mean = 3.78e+03ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 2.57e+04ε (Mean = 4.45e+03ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 3.66e+03ε (Mean = 500ε)</span>
- </p>
- </td>
- </tr>
- </tbody>
- </table></div>
- </div>
- <br class="table-break"><div class="table">
- <a name="special_function_error_rates_rep.all_the_tables.table_non_central_beta_CDF_complement"></a><p class="title"><b>Table 169. Error rates for non central beta CDF complement</b></p>
- <div class="table-contents"><table class="table" summary="Error rates for non central beta CDF complement">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> double
- </p>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> long double
- </p>
- </th>
- <th>
- <p>
- Sun compiler version 0x5150<br> Sun Solaris<br> long double
- </p>
- </th>
- <th>
- <p>
- Microsoft Visual C++ version 14.1<br> Win32<br> double
- </p>
- </th>
- </tr></thead>
- <tbody>
- <tr>
- <td>
- <p>
- Non Central Beta, medium parameters
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.998ε (Mean = 0.0936ε)</span><br> <br>
- (<span class="emphasis"><em>Rmath 3.2.3:</em></span> <span class="red">Max = 7.5e+97ε (Mean
- = 1.37e+96ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_non_central_beta_CDF_complement_Rmath_3_2_3_Non_Central_Beta_medium_parameters">And
- other failures.</a>)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 396ε (Mean = 50.7ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 554ε (Mean = 57.2ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 624ε (Mean = 62.7ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Non Central Beta, large parameters
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.986ε (Mean = 0.188ε)</span><br> <br>
- (<span class="emphasis"><em>Rmath 3.2.3:</em></span> <span class="red">Max = +INFε (Mean
- = +INFε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_non_central_beta_CDF_complement_Rmath_3_2_3_Non_Central_Beta_large_parameters">And
- other failures.</a>)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 6.83e+03ε (Mean = 993ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 3.56e+03ε (Mean = 707ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.25e+04ε (Mean = 1.49e+03ε)</span>
- </p>
- </td>
- </tr>
- </tbody>
- </table></div>
- </div>
- <br class="table-break"><div class="table">
- <a name="special_function_error_rates_rep.all_the_tables.table_non_central_chi_squared_CDF"></a><p class="title"><b>Table 170. Error rates for non central chi squared CDF</b></p>
- <div class="table-contents"><table class="table" summary="Error rates for non central chi squared CDF">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> double
- </p>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> long double
- </p>
- </th>
- <th>
- <p>
- Sun compiler version 0x5150<br> Sun Solaris<br> long double
- </p>
- </th>
- <th>
- <p>
- Microsoft Visual C++ version 14.1<br> Win32<br> double
- </p>
- </th>
- </tr></thead>
- <tbody>
- <tr>
- <td>
- <p>
- Non Central Chi Squared, medium parameters
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.99ε (Mean = 0.0544ε)</span><br> <br>
- (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 727ε (Mean = 121ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 46.5ε (Mean = 10.3ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 115ε (Mean = 13.9ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 48.9ε (Mean = 10ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Non Central Chi Squared, large parameters
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.07ε (Mean = 0.102ε)</span><br> <br>
- (<span class="emphasis"><em>Rmath 3.2.3:</em></span> <span class="red">Max = 3.27e+08ε (Mean
- = 2.23e+07ε))</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 3.07e+03ε (Mean = 336ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 6.17e+03ε (Mean = 677ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 9.79e+03ε (Mean = 723ε)</span>
- </p>
- </td>
- </tr>
- </tbody>
- </table></div>
- </div>
- <br class="table-break"><div class="table">
- <a name="special_function_error_rates_rep.all_the_tables.table_non_central_chi_squared_CDF_complement"></a><p class="title"><b>Table 171. Error rates for non central chi squared CDF complement</b></p>
- <div class="table-contents"><table class="table" summary="Error rates for non central chi squared CDF complement">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> double
- </p>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> long double
- </p>
- </th>
- <th>
- <p>
- Sun compiler version 0x5150<br> Sun Solaris<br> long double
- </p>
- </th>
- <th>
- <p>
- Microsoft Visual C++ version 14.1<br> Win32<br> double
- </p>
- </th>
- </tr></thead>
- <tbody>
- <tr>
- <td>
- <p>
- Non Central Chi Squared, medium parameters
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.96ε (Mean = 0.0635ε)</span><br> <br>
- (<span class="emphasis"><em>Rmath 3.2.3:</em></span> <span class="red">Max = +INFε (Mean
- = +INFε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_non_central_chi_squared_CDF_complement_Rmath_3_2_3_Non_Central_Chi_Squared_medium_parameters">And
- other failures.</a>)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 107ε (Mean = 17.2ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 171ε (Mean = 22.8ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 98.6ε (Mean = 15.8ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Non Central Chi Squared, large parameters
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 2.11ε (Mean = 0.278ε)</span><br> <br>
- (<span class="emphasis"><em>Rmath 3.2.3:</em></span> <span class="red">Max = +INFε (Mean
- = +INFε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_non_central_chi_squared_CDF_complement_Rmath_3_2_3_Non_Central_Chi_Squared_large_parameters">And
- other failures.</a>)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 5.02e+03ε (Mean = 630ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 5.1e+03ε (Mean = 577ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 5.43e+03ε (Mean = 705ε)</span>
- </p>
- </td>
- </tr>
- </tbody>
- </table></div>
- </div>
- <br class="table-break"><div class="table">
- <a name="special_function_error_rates_rep.all_the_tables.table_non_central_t_CDF"></a><p class="title"><b>Table 172. Error rates for non central t CDF</b></p>
- <div class="table-contents"><table class="table" summary="Error rates for non central t CDF">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> double
- </p>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> long double
- </p>
- </th>
- <th>
- <p>
- Sun compiler version 0x5150<br> Sun Solaris<br> long double
- </p>
- </th>
- <th>
- <p>
- Microsoft Visual C++ version 14.1<br> Win32<br> double
- </p>
- </th>
- </tr></thead>
- <tbody>
- <tr>
- <td>
- <p>
- Non Central T
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.796ε (Mean = 0.0691ε)</span><br> <br>
- (<span class="emphasis"><em>Rmath 3.2.3:</em></span> <span class="red">Max = 5.28e+15ε (Mean
- = 8.49e+14ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_non_central_t_CDF_Rmath_3_2_3_Non_Central_T">And
- other failures.</a>)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 139ε (Mean = 31ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 145ε (Mean = 30.9ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 135ε (Mean = 32.1ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Non Central T (small non-centrality)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>Rmath
- 3.2.3:</em></span> Max = 2.09e+03ε (Mean = 244ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 3.86ε (Mean = 1.4ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 9.15ε (Mean = 2.13ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 6.17ε (Mean = 1.45ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Non Central T (large parameters)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 257ε (Mean = 72.1ε)</span><br> <br>
- (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 2.46ε (Mean = 0.657ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 5.26e+05ε (Mean = 1.48e+05ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 5.24e+05ε (Mean = 1.47e+05ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 286ε (Mean = 62.8ε)</span>
- </p>
- </td>
- </tr>
- </tbody>
- </table></div>
- </div>
- <br class="table-break"><div class="table">
- <a name="special_function_error_rates_rep.all_the_tables.table_non_central_t_CDF_complement"></a><p class="title"><b>Table 173. Error rates for non central t CDF complement</b></p>
- <div class="table-contents"><table class="table" summary="Error rates for non central t CDF complement">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> double
- </p>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> long double
- </p>
- </th>
- <th>
- <p>
- Sun compiler version 0x5150<br> Sun Solaris<br> long double
- </p>
- </th>
- <th>
- <p>
- Microsoft Visual C++ version 14.1<br> Win32<br> double
- </p>
- </th>
- </tr></thead>
- <tbody>
- <tr>
- <td>
- <p>
- Non Central T
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.707ε (Mean = 0.0497ε)</span><br> <br>
- (<span class="emphasis"><em>Rmath 3.2.3:</em></span> <span class="red">Max = 6.19e+15ε (Mean
- = 6.72e+14ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_non_central_t_CDF_complement_Rmath_3_2_3_Non_Central_T">And
- other failures.</a>)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 201ε (Mean = 31.7ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 340ε (Mean = 43.2ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 154ε (Mean = 32.1ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Non Central T (small non-centrality)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>Rmath
- 3.2.3:</em></span> Max = 1.87e+03ε (Mean = 263ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 10.5ε (Mean = 2.13ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 10.5ε (Mean = 2.39ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 4.6ε (Mean = 1.63ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Non Central T (large parameters)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 478ε (Mean = 96.3ε)</span><br> <br>
- (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 2.24ε (Mean = 0.945ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 9.79e+05ε (Mean = 1.97e+05ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 9.79e+05ε (Mean = 1.97e+05ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 227ε (Mean = 50.4ε)</span>
- </p>
- </td>
- </tr>
- </tbody>
- </table></div>
- </div>
- <br class="table-break"><div class="table">
- <a name="special_function_error_rates_rep.all_the_tables.table_owens_t"></a><p class="title"><b>Table 174. Error rates for owens_t</b></p>
- <div class="table-contents"><table class="table" summary="Error rates for owens_t">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> double
- </p>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> long double
- </p>
- </th>
- <th>
- <p>
- Sun compiler version 0x5150<br> Sun Solaris<br> long double
- </p>
- </th>
- <th>
- <p>
- Microsoft Visual C++ version 14.1<br> Win32<br> double
- </p>
- </th>
- </tr></thead>
- <tbody>
- <tr>
- <td>
- <p>
- Owens T (medium small values)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 3.34ε (Mean = 0.944ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 3.34ε (Mean = 0.911ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 4.37ε (Mean = 0.98ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Owens T (large and diverse values)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 49ε (Mean = 2.16ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 24.5ε (Mean = 1.39ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 3.78ε (Mean = 0.621ε)</span>
- </p>
- </td>
- </tr>
- </tbody>
- </table></div>
- </div>
- <br class="table-break"><div class="table">
- <a name="special_function_error_rates_rep.all_the_tables.table_polygamma"></a><p class="title"><b>Table 175. Error rates for polygamma</b></p>
- <div class="table-contents"><table class="table" summary="Error rates for polygamma">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> double
- </p>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> long double
- </p>
- </th>
- <th>
- <p>
- Sun compiler version 0x5150<br> Sun Solaris<br> long double
- </p>
- </th>
- <th>
- <p>
- Microsoft Visual C++ version 14.1<br> Win32<br> double
- </p>
- </th>
- </tr></thead>
- <tbody>
- <tr>
- <td>
- <p>
- Mathematica Data
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.824ε (Mean = 0.0574ε)</span><br> <br>
- (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 62.9ε (Mean = 12.8ε))<br> (<span class="emphasis"><em>Rmath
- 3.2.3:</em></span> Max = 108ε (Mean = 15.2ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 7.38ε (Mean = 1.84ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 34.3ε (Mean = 7.65ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 9.32ε (Mean = 1.95ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Mathematica Data - large arguments
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.998ε (Mean = 0.0592ε)</span><br> <br>
- (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 244ε (Mean = 32.8ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_polygamma_GSL_2_1_Mathematica_Data_large_arguments">And
- other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
- <span class="red">Max = 1.71e+56ε (Mean = 1.01e+55ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_polygamma_Rmath_3_2_3_Mathematica_Data_large_arguments">And
- other failures.</a>)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 2.23ε (Mean = 0.323ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 11.1ε (Mean = 0.848ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 150ε (Mean = 13.9ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Mathematica Data - negative arguments
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.516ε (Mean = 0.022ε)</span><br> <br>
- (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 36.6ε (Mean = 3.04ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_polygamma_GSL_2_1_Mathematica_Data_negative_arguments">And
- other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
- Max = 0ε (Mean = 0ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_polygamma_Rmath_3_2_3_Mathematica_Data_negative_arguments">And
- other failures.</a>)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 269ε (Mean = 87.7ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 269ε (Mean = 88.4ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 497ε (Mean = 129ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Mathematica Data - large negative arguments
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 1.79ε (Mean = 0.197ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_polygamma_GSL_2_1_Mathematica_Data_large_negative_arguments">And
- other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
- Max = 0ε (Mean = 0ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_polygamma_Rmath_3_2_3_Mathematica_Data_large_negative_arguments">And
- other failures.</a>)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 155ε (Mean = 96.4ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 155ε (Mean = 96.4ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 162ε (Mean = 101ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Mathematica Data - small arguments
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 15.2ε (Mean = 5.03ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
- Max = 106ε (Mean = 20ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 3.33ε (Mean = 0.75ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 3.33ε (Mean = 0.75ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 3ε (Mean = 0.496ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Mathematica Data - Large orders and other bug cases
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 151ε (Mean = 39.3ε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_polygamma_GSL_2_1_Mathematica_Data_Large_orders_and_other_bug_cases">And
- other failures.</a>)<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
- <span class="red">Max = +INFε (Mean = +INFε) <a class="link" href="index.html#errors_GNU_C_version_7_1_0_linux_double_polygamma_Rmath_3_2_3_Mathematica_Data_Large_orders_and_other_bug_cases">And
- other failures.</a>)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 54.5ε (Mean = 13.3ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 145ε (Mean = 55.9ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 200ε (Mean = 57.2ε)</span>
- </p>
- </td>
- </tr>
- </tbody>
- </table></div>
- </div>
- <br class="table-break"><div class="table">
- <a name="special_function_error_rates_rep.all_the_tables.table_powm1"></a><p class="title"><b>Table 176. Error rates for powm1</b></p>
- <div class="table-contents"><table class="table" summary="Error rates for powm1">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> double
- </p>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> long double
- </p>
- </th>
- <th>
- <p>
- Sun compiler version 0x5150<br> Sun Solaris<br> long double
- </p>
- </th>
- <th>
- <p>
- Microsoft Visual C++ version 14.1<br> Win32<br> double
- </p>
- </th>
- </tr></thead>
- <tbody><tr>
- <td>
- <p>
- powm1
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.06ε (Mean = 0.425ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 2.04ε (Mean = 0.493ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.88ε (Mean = 0.49ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.84ε (Mean = 0.486ε)</span>
- </p>
- </td>
- </tr></tbody>
- </table></div>
- </div>
- <br class="table-break"><div class="table">
- <a name="special_function_error_rates_rep.all_the_tables.table_sin_pi"></a><p class="title"><b>Table 177. Error rates for sin_pi</b></p>
- <div class="table-contents"><table class="table" summary="Error rates for sin_pi">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> double
- </p>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> long double
- </p>
- </th>
- <th>
- <p>
- Sun compiler version 0x5150<br> Sun Solaris<br> long double
- </p>
- </th>
- <th>
- <p>
- Microsoft Visual C++ version 14.1<br> Win32<br> double
- </p>
- </th>
- </tr></thead>
- <tbody>
- <tr>
- <td>
- <p>
- sin_pi and cos_pi
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.996ε (Mean = 0.335ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.996ε (Mean = 0.336ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.99ε (Mean = 0.328ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- sin_pi and cos_pi near integers and half integers
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.976ε (Mean = 0.293ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.976ε (Mean = 0.293ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.996ε (Mean = 0.343ε)</span>
- </p>
- </td>
- </tr>
- </tbody>
- </table></div>
- </div>
- <br class="table-break"><div class="table">
- <a name="special_function_error_rates_rep.all_the_tables.table_sph_bessel"></a><p class="title"><b>Table 178. Error rates for sph_bessel</b></p>
- <div class="table-contents"><table class="table" summary="Error rates for sph_bessel">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> long double
- </p>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> double
- </p>
- </th>
- <th>
- <p>
- Sun compiler version 0x5150<br> Sun Solaris<br> long double
- </p>
- </th>
- <th>
- <p>
- Microsoft Visual C++ version 14.1<br> Win32<br> double
- </p>
- </th>
- </tr></thead>
- <tbody><tr>
- <td>
- <p>
- Bessel j: Random Data
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 243ε (Mean = 13.3ε)</span><br> <br>
- (<span class="emphasis"><em><cmath>:</em></span> Max = 1.91e+06ε (Mean = 1.09e+05ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.978ε (Mean = 0.0445ε)</span><br> <br>
- (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 1.79e+03ε (Mean = 107ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 243ε (Mean = 33.7ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 245ε (Mean = 16.3ε)</span>
- </p>
- </td>
- </tr></tbody>
- </table></div>
- </div>
- <br class="table-break"><div class="table">
- <a name="special_function_error_rates_rep.all_the_tables.table_sph_bessel_prime"></a><p class="title"><b>Table 179. Error rates for sph_bessel_prime</b></p>
- <div class="table-contents"><table class="table" summary="Error rates for sph_bessel_prime">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> double
- </p>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> long double
- </p>
- </th>
- <th>
- <p>
- Sun compiler version 0x5150<br> Sun Solaris<br> long double
- </p>
- </th>
- <th>
- <p>
- Microsoft Visual C++ version 14.1<br> Win32<br> double
- </p>
- </th>
- </tr></thead>
- <tbody><tr>
- <td>
- <p>
- Bessel j': Random Data
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.753ε (Mean = 0.0343ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 167ε (Mean = 12ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 167ε (Mean = 33.2ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 307ε (Mean = 25.2ε)</span>
- </p>
- </td>
- </tr></tbody>
- </table></div>
- </div>
- <br class="table-break"><div class="table">
- <a name="special_function_error_rates_rep.all_the_tables.table_sph_neumann"></a><p class="title"><b>Table 180. Error rates for sph_neumann</b></p>
- <div class="table-contents"><table class="table" summary="Error rates for sph_neumann">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> long double
- </p>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> double
- </p>
- </th>
- <th>
- <p>
- Sun compiler version 0x5150<br> Sun Solaris<br> long double
- </p>
- </th>
- <th>
- <p>
- Microsoft Visual C++ version 14.1<br> Win32<br> double
- </p>
- </th>
- </tr></thead>
- <tbody><tr>
- <td>
- <p>
- y: Random Data
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 234ε (Mean = 19.5ε)</span><br> <br>
- (<span class="emphasis"><em><cmath>:</em></span> Max = 1.6e+06ε (Mean = 1.4e+05ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.995ε (Mean = 0.0665ε)</span><br> <br>
- (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 8.5e+04ε (Mean = 5.33e+03ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 234ε (Mean = 19.8ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 281ε (Mean = 31.1ε)</span>
- </p>
- </td>
- </tr></tbody>
- </table></div>
- </div>
- <br class="table-break"><div class="table">
- <a name="special_function_error_rates_rep.all_the_tables.table_sph_neumann_prime"></a><p class="title"><b>Table 181. Error rates for sph_neumann_prime</b></p>
- <div class="table-contents"><table class="table" summary="Error rates for sph_neumann_prime">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> double
- </p>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> long double
- </p>
- </th>
- <th>
- <p>
- Sun compiler version 0x5150<br> Sun Solaris<br> long double
- </p>
- </th>
- <th>
- <p>
- Microsoft Visual C++ version 14.1<br> Win32<br> double
- </p>
- </th>
- </tr></thead>
- <tbody><tr>
- <td>
- <p>
- y': Random Data
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.988ε (Mean = 0.0869ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 158ε (Mean = 18.8ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 158ε (Mean = 20.2ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 296ε (Mean = 25.6ε)</span>
- </p>
- </td>
- </tr></tbody>
- </table></div>
- </div>
- <br class="table-break"><div class="table">
- <a name="special_function_error_rates_rep.all_the_tables.table_spherical_harmonic_i"></a><p class="title"><b>Table 182. Error rates for spherical_harmonic_i</b></p>
- <div class="table-contents"><table class="table" summary="Error rates for spherical_harmonic_i">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> double
- </p>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> long double
- </p>
- </th>
- <th>
- <p>
- Sun compiler version 0x5150<br> Sun Solaris<br> long double
- </p>
- </th>
- <th>
- <p>
- Microsoft Visual C++ version 14.1<br> Win32<br> double
- </p>
- </th>
- </tr></thead>
- <tbody><tr>
- <td>
- <p>
- Spherical Harmonics
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.36ε (Mean = 0.0765ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 2.89e+03ε (Mean = 108ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.03e+04ε (Mean = 327ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 2.27e+04ε (Mean = 725ε)</span>
- </p>
- </td>
- </tr></tbody>
- </table></div>
- </div>
- <br class="table-break"><div class="table">
- <a name="special_function_error_rates_rep.all_the_tables.table_spherical_harmonic_r"></a><p class="title"><b>Table 183. Error rates for spherical_harmonic_r</b></p>
- <div class="table-contents"><table class="table" summary="Error rates for spherical_harmonic_r">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> double
- </p>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> long double
- </p>
- </th>
- <th>
- <p>
- Sun compiler version 0x5150<br> Sun Solaris<br> long double
- </p>
- </th>
- <th>
- <p>
- Microsoft Visual C++ version 14.1<br> Win32<br> double
- </p>
- </th>
- </tr></thead>
- <tbody><tr>
- <td>
- <p>
- Spherical Harmonics
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.58ε (Mean = 0.0707ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 2.89e+03ε (Mean = 108ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.03e+04ε (Mean = 327ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 2.27e+04ε (Mean = 725ε)</span>
- </p>
- </td>
- </tr></tbody>
- </table></div>
- </div>
- <br class="table-break"><div class="table">
- <a name="special_function_error_rates_rep.all_the_tables.table_sqrt1pm1"></a><p class="title"><b>Table 184. Error rates for sqrt1pm1</b></p>
- <div class="table-contents"><table class="table" summary="Error rates for sqrt1pm1">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> double
- </p>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> long double
- </p>
- </th>
- <th>
- <p>
- Sun compiler version 0x5150<br> Sun Solaris<br> long double
- </p>
- </th>
- <th>
- <p>
- Microsoft Visual C++ version 14.1<br> Win32<br> double
- </p>
- </th>
- </tr></thead>
- <tbody><tr>
- <td>
- <p>
- sqrt1pm1
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.3ε (Mean = 0.404ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.33ε (Mean = 0.404ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.54ε (Mean = 0.563ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.35ε (Mean = 0.497ε)</span>
- </p>
- </td>
- </tr></tbody>
- </table></div>
- </div>
- <br class="table-break"><div class="table">
- <a name="special_function_error_rates_rep.all_the_tables.table_tgamma"></a><p class="title"><b>Table 185. Error rates for tgamma</b></p>
- <div class="table-contents"><table class="table" summary="Error rates for tgamma">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> double
- </p>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> long double
- </p>
- </th>
- <th>
- <p>
- Sun compiler version 0x5150<br> Sun Solaris<br> long double
- </p>
- </th>
- <th>
- <p>
- Microsoft Visual C++ version 14.1<br> Win32<br> double
- </p>
- </th>
- </tr></thead>
- <tbody>
- <tr>
- <td>
- <p>
- factorials
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 3.95ε (Mean = 0.783ε))<br> (<span class="emphasis"><em>Rmath
- 3.2.3:</em></span> Max = 314ε (Mean = 93.4ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 2.67ε (Mean = 0.617ε)</span><br> <br>
- (<span class="emphasis"><em><cmath>:</em></span> Max = 1.66ε (Mean = 0.584ε))<br>
- (<span class="emphasis"><em><math.h>:</em></span> Max = 1.66ε (Mean = 0.584ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 172ε (Mean = 41ε)</span><br> <br> (<span class="emphasis"><em><math.h>:</em></span>
- Max = 0ε (Mean = 0ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.85ε (Mean = 0.566ε)</span><br> <br>
- (<span class="emphasis"><em><math.h>:</em></span> Max = 3.17ε (Mean = 0.928ε))
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- near 0
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 4.51ε (Mean = 1.92ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
- Max = 1ε (Mean = 0.335ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 2ε (Mean = 0.608ε)</span><br> <br> (<span class="emphasis"><em><cmath>:</em></span>
- Max = 1ε (Mean = 0.376ε))<br> (<span class="emphasis"><em><math.h>:</em></span>
- Max = 1ε (Mean = 0.376ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 2ε (Mean = 0.647ε)</span><br> <br> (<span class="emphasis"><em><math.h>:</em></span>
- Max = 0.5ε (Mean = 0.0791ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.5ε (Mean = 0.635ε)</span><br> <br>
- (<span class="emphasis"><em><math.h>:</em></span> Max = 1ε (Mean = 0.405ε))
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- near 1
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 4.41ε (Mean = 1.81ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
- Max = 1ε (Mean = 0.32ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 2.51ε (Mean = 1.02ε)</span><br> <br>
- (<span class="emphasis"><em><cmath>:</em></span> Max = 0.918ε (Mean = 0.203ε))<br>
- (<span class="emphasis"><em><math.h>:</em></span> Max = 0.918ε (Mean = 0.203ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 3.01ε (Mean = 1.06ε)</span><br> <br>
- (<span class="emphasis"><em><math.h>:</em></span> Max = 1ε (Mean = 0.175ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.1ε (Mean = 0.59ε)</span><br> <br>
- (<span class="emphasis"><em><math.h>:</em></span> Max = 1ε (Mean = 0.4ε))
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- near 2
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 7.95ε (Mean = 3.12ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
- Max = 1ε (Mean = 0.191ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 4.1ε (Mean = 1.55ε)</span><br> <br>
- (<span class="emphasis"><em><cmath>:</em></span> Max = 0.558ε (Mean = 0.298ε))<br>
- (<span class="emphasis"><em><math.h>:</em></span> Max = 0.558ε (Mean = 0.298ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 5.01ε (Mean = 1.89ε)</span><br> <br>
- (<span class="emphasis"><em><math.h>:</em></span> Max = 0ε (Mean = 0ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 2ε (Mean = 0.733ε)</span><br> <br> (<span class="emphasis"><em><math.h>:</em></span>
- Max = 0ε (Mean = 0ε))
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- near -10
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 2.6ε (Mean = 1.05ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
- Max = 34.9ε (Mean = 9.2ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.75ε (Mean = 0.895ε)</span><br> <br>
- (<span class="emphasis"><em><cmath>:</em></span> Max = 2.26ε (Mean = 1.08ε))<br>
- (<span class="emphasis"><em><math.h>:</em></span> Max = 2.26ε (Mean = 1.08ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.75ε (Mean = 0.819ε)</span><br> <br>
- (<span class="emphasis"><em><math.h>:</em></span> Max = 0ε (Mean = 0ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.86ε (Mean = 0.881ε)</span><br> <br>
- (<span class="emphasis"><em><math.h>:</em></span> Max = 0.866ε (Mean = 0.445ε))
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- near -55
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 1.8ε (Mean = 0.782ε))<br> (<span class="emphasis"><em>Rmath 3.2.3:</em></span>
- Max = 3.89e+04ε (Mean = 9.52e+03ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 2.69ε (Mean = 1.09ε)</span><br> <br>
- (<span class="emphasis"><em><cmath>:</em></span> Max = 1.79ε (Mean = 0.75ε))<br>
- (<span class="emphasis"><em><math.h>:</em></span> Max = 1.79ε (Mean = 0.75ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 98.5ε (Mean = 53.4ε)</span><br> <br>
- (<span class="emphasis"><em><math.h>:</em></span> Max = 0ε (Mean = 0ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 2.7ε (Mean = 1.35ε)</span><br> <br>
- (<span class="emphasis"><em><math.h>:</em></span> Max = 3.87e+04ε (Mean = 6.71e+03ε))
- </p>
- </td>
- </tr>
- </tbody>
- </table></div>
- </div>
- <br class="table-break"><div class="table">
- <a name="special_function_error_rates_rep.all_the_tables.table_tgamma1pm1"></a><p class="title"><b>Table 186. Error rates for tgamma1pm1</b></p>
- <div class="table-contents"><table class="table" summary="Error rates for tgamma1pm1">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> double
- </p>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> long double
- </p>
- </th>
- <th>
- <p>
- Sun compiler version 0x5150<br> Sun Solaris<br> long double
- </p>
- </th>
- <th>
- <p>
- Microsoft Visual C++ version 14.1<br> Win32<br> double
- </p>
- </th>
- </tr></thead>
- <tbody><tr>
- <td>
- <p>
- tgamma1pm1(dz)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.12ε (Mean = 0.49ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 6.61ε (Mean = 0.84ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 3.31ε (Mean = 0.517ε)</span>
- </p>
- </td>
- </tr></tbody>
- </table></div>
- </div>
- <br class="table-break"><div class="table">
- <a name="special_function_error_rates_rep.all_the_tables.table_tgamma_delta_ratio"></a><p class="title"><b>Table 187. Error rates for tgamma_delta_ratio</b></p>
- <div class="table-contents"><table class="table" summary="Error rates for tgamma_delta_ratio">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> double
- </p>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> long double
- </p>
- </th>
- <th>
- <p>
- Sun compiler version 0x5150<br> Sun Solaris<br> long double
- </p>
- </th>
- <th>
- <p>
- Microsoft Visual C++ version 14.1<br> Win32<br> double
- </p>
- </th>
- </tr></thead>
- <tbody>
- <tr>
- <td>
- <p>
- tgamma + small delta ratios
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 5.83ε (Mean = 1.3ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 15.4ε (Mean = 2.09ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 7.56ε (Mean = 1.31ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- tgamma + small delta ratios (negative delta)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 7.94ε (Mean = 1.4ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 18.3ε (Mean = 2.03ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 7.43ε (Mean = 1.42ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- tgamma + small integer ratios
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.96ε (Mean = 0.677ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.96ε (Mean = 0.677ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 2.74ε (Mean = 0.736ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- tgamma + small integer ratios (negative delta)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.62ε (Mean = 0.451ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.62ε (Mean = 0.451ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 2.15ε (Mean = 0.685ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- integer tgamma ratios
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.997ε (Mean = 0.4ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.997ε (Mean = 0.4ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.968ε (Mean = 0.386ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- integer tgamma ratios (negative delta)
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.853ε (Mean = 0.176ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.853ε (Mean = 0.176ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.974ε (Mean = 0.175ε)</span>
- </p>
- </td>
- </tr>
- </tbody>
- </table></div>
- </div>
- <br class="table-break"><div class="table">
- <a name="special_function_error_rates_rep.all_the_tables.table_tgamma_incomplete_"></a><p class="title"><b>Table 188. Error rates for tgamma (incomplete)</b></p>
- <div class="table-contents"><table class="table" summary="Error rates for tgamma (incomplete)">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> double
- </p>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> long double
- </p>
- </th>
- <th>
- <p>
- Sun compiler version 0x5150<br> Sun Solaris<br> long double
- </p>
- </th>
- <th>
- <p>
- Microsoft Visual C++ version 14.1<br> Win32<br> double
- </p>
- </th>
- </tr></thead>
- <tbody>
- <tr>
- <td>
- <p>
- tgamma(a, z) medium values
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 200ε (Mean = 13.3ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 8.47ε (Mean = 1.9ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 412ε (Mean = 95.5ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 8.14ε (Mean = 1.76ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- tgamma(a, z) small values
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.753ε (Mean = 0.0474ε)</span><br> <br>
- (<span class="emphasis"><em>GSL 2.1:</em></span> <span class="red">Max = 1.38e+10ε (Mean
- = 1.05e+09ε))</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 2.31ε (Mean = 0.775ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 2.13ε (Mean = 0.717ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 2.53ε (Mean = 0.66ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- tgamma(a, z) integer and half integer values
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 117ε (Mean = 12.5ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 5.52ε (Mean = 1.48ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 79.6ε (Mean = 20.9ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 5.16ε (Mean = 1.33ε)</span>
- </p>
- </td>
- </tr>
- </tbody>
- </table></div>
- </div>
- <br class="table-break"><div class="table">
- <a name="special_function_error_rates_rep.all_the_tables.table_tgamma_lower"></a><p class="title"><b>Table 189. Error rates for tgamma_lower</b></p>
- <div class="table-contents"><table class="table" summary="Error rates for tgamma_lower">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> double
- </p>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> long double
- </p>
- </th>
- <th>
- <p>
- Sun compiler version 0x5150<br> Sun Solaris<br> long double
- </p>
- </th>
- <th>
- <p>
- Microsoft Visual C++ version 14.1<br> Win32<br> double
- </p>
- </th>
- </tr></thead>
- <tbody>
- <tr>
- <td>
- <p>
- tgamma(a, z) medium values
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.833ε (Mean = 0.0315ε)</span><br> <br>
- (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 0.833ε (Mean = 0.0315ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 6.79ε (Mean = 1.46ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 363ε (Mean = 63.8ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 5.62ε (Mean = 1.49ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- tgamma(a, z) small values
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 0ε (Mean = 0ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.97ε (Mean = 0.555ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.97ε (Mean = 0.558ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.57ε (Mean = 0.525ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- tgamma(a, z) integer and half integer values
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 0ε (Mean = 0ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 4.83ε (Mean = 1.15ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 84.7ε (Mean = 17.5ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 2.69ε (Mean = 0.849ε)</span>
- </p>
- </td>
- </tr>
- </tbody>
- </table></div>
- </div>
- <br class="table-break"><div class="table">
- <a name="special_function_error_rates_rep.all_the_tables.table_tgamma_ratio"></a><p class="title"><b>Table 190. Error rates for tgamma_ratio</b></p>
- <div class="table-contents"><table class="table" summary="Error rates for tgamma_ratio">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> double
- </p>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> long double
- </p>
- </th>
- <th>
- <p>
- Sun compiler version 0x5150<br> Sun Solaris<br> long double
- </p>
- </th>
- <th>
- <p>
- Microsoft Visual C++ version 14.1<br> Win32<br> double
- </p>
- </th>
- </tr></thead>
- <tbody><tr>
- <td>
- <p>
- tgamma ratios
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.694ε (Mean = 0.0347ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 2.99ε (Mean = 1.15ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 174ε (Mean = 61.2ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 3.28ε (Mean = 1.12ε)</span>
- </p>
- </td>
- </tr></tbody>
- </table></div>
- </div>
- <br class="table-break"><div class="table">
- <a name="special_function_error_rates_rep.all_the_tables.table_trigamma"></a><p class="title"><b>Table 191. Error rates for trigamma</b></p>
- <div class="table-contents"><table class="table" summary="Error rates for trigamma">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> double
- </p>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> long double
- </p>
- </th>
- <th>
- <p>
- Sun compiler version 0x5150<br> Sun Solaris<br> long double
- </p>
- </th>
- <th>
- <p>
- Microsoft Visual C++ version 14.1<br> Win32<br> double
- </p>
- </th>
- </tr></thead>
- <tbody><tr>
- <td>
- <p>
- Mathematica Data
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.998ε (Mean = 0.105ε)</span><br> <br>
- (<span class="emphasis"><em>GSL 2.1:</em></span> Max = 1.34e+04ε (Mean = 1.49e+03ε))<br>
- (<span class="emphasis"><em>Rmath 3.2.3:</em></span> Max = 1.34e+04ε (Mean = 1.51e+03ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.28ε (Mean = 0.449ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1.28ε (Mean = 0.449ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 1ε (Mean = 0.382ε)</span>
- </p>
- </td>
- </tr></tbody>
- </table></div>
- </div>
- <br class="table-break"><div class="table">
- <a name="special_function_error_rates_rep.all_the_tables.table_zeta"></a><p class="title"><b>Table 192. Error rates for zeta</b></p>
- <div class="table-contents"><table class="table" summary="Error rates for zeta">
- <colgroup>
- <col>
- <col>
- <col>
- <col>
- <col>
- </colgroup>
- <thead><tr>
- <th>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> long double
- </p>
- </th>
- <th>
- <p>
- GNU C++ version 7.1.0<br> linux<br> double
- </p>
- </th>
- <th>
- <p>
- Sun compiler version 0x5150<br> Sun Solaris<br> long double
- </p>
- </th>
- <th>
- <p>
- Microsoft Visual C++ version 14.1<br> Win32<br> double
- </p>
- </th>
- </tr></thead>
- <tbody>
- <tr>
- <td>
- <p>
- Zeta: Random values greater than 1
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.846ε (Mean = 0.0833ε)</span><br> <br>
- (<span class="emphasis"><em><cmath>:</em></span> Max = 5.45ε (Mean = 1ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 8.69ε (Mean = 1.03ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.846ε (Mean = 0.0833ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.836ε (Mean = 0.093ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Zeta: Random values less than 1
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 7.03ε (Mean = 2.93ε)</span><br> <br>
- (<span class="emphasis"><em><cmath>:</em></span> Max = 538ε (Mean = 59.3ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 137ε (Mean = 13.8ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 70.1ε (Mean = 17.1ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 6.84ε (Mean = 3.12ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Zeta: Values close to and greater than 1
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.995ε (Mean = 0.5ε)</span><br> <br>
- (<span class="emphasis"><em><cmath>:</em></span> Max = 1.9e+06ε (Mean = 5.11e+05ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 7.73ε (Mean = 4.07ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.995ε (Mean = 0.5ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.994ε (Mean = 0.421ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Zeta: Values close to and less than 1
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.998ε (Mean = 0.508ε)</span><br> <br>
- (<span class="emphasis"><em><cmath>:</em></span> Max = 8.53e+06ε (Mean = 1.87e+06ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 0.991ε (Mean = 0.28ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.998ε (Mean = 0.508ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0.991ε (Mean = 0.375ε)</span>
- </p>
- </td>
- </tr>
- <tr>
- <td>
- <p>
- Zeta: Integer arguments
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 9ε (Mean = 3.06ε)</span><br> <br> (<span class="emphasis"><em><cmath>:</em></span>
- Max = 70.3ε (Mean = 17.4ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 0ε (Mean = 0ε)</span><br> <br> (<span class="emphasis"><em>GSL
- 2.1:</em></span> Max = 3.75ε (Mean = 1.1ε))
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 28ε (Mean = 5.62ε)</span>
- </p>
- </td>
- <td>
- <p>
- <span class="blue">Max = 9ε (Mean = 3ε)</span>
- </p>
- </td>
- </tr>
- </tbody>
- </table></div>
- </div>
- <br class="table-break">
- </div>
- </div>
- <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
- <td align="left"><p><small>Last revised: March 09, 2018 at 13:43:44 GMT</small></p></td>
- <td align="right"><div class="copyright-footer"></div></td>
- </tr></table>
- <hr>
- <div class="spirit-nav"></div>
- </body>
- </html>
|
