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Rebuilt after edits to quiet nags.

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[SVN r79834]
This commit is contained in:
Paul A. Bristow
2012-08-01 16:32:48 +00:00
parent 45fd99988d
commit 69ba66929d
8 changed files with 3686 additions and 3649 deletions
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805
test/jacobi_elliptic.ipp
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@@ -1,406 +1,413 @@
// Copyright John Maddock 2012.
// Use, modification and distribution are subject to the
// Boost Software License, Version 1.0.
// (See accompanying file LICENSE_1_0.txt
// or copy at http://www.boost.org/LICENSE_1_0.txt)
#ifndef SC_
# define SC_(x) static_cast<T>(BOOST_JOIN(x, L))
#endif
static const boost::array<boost::array<T, 5>, 400> jacobi_elliptic = {{
{{ SC_(9.7540378570556640625000000000000000000000000000000000000000000000000000000000000000000000000000000000e-02), SC_(9.7540378570556640625000000000000000000000000000000000000000000000000000000000000000000000000000000000e-02), SC_(9.7384321813508780300050309993112921610348339609531096226291156957843807163438391463300771570266454611e-02), SC_(9.9524685071841496279438927849850673342525676921414792528840427410727111940782381944976305408868157855e-01), SC_(9.9995488439733316729114394585903874689886199946693440341361736436672692239264636048488084336908171547e-01) }},
{{ SC_(9.7540378570556640625000000000000000000000000000000000000000000000000000000000000000000000000000000000e-02), SC_(1.2698680162429809570312500000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(9.7383306026428126815811673852101862643417212675894886262329096942831342806175591481538515201116435095e-02), SC_(9.9524695011206291426731901545274769005867525867705503210833924341584688692109569818882782443312019870e-01), SC_(9.9992353321916073154296514614318371763529995049379965142148455053362169878708374701587696243287582131e-01) }},
{{ SC_(9.7540378570556640625000000000000000000000000000000000000000000000000000000000000000000000000000000000e-02), SC_(1.3547700643539428710937500000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(9.7382963663268679354766311462039914384149178492941126840831062817834448292082576674044335924290112792e-02), SC_(9.9524698361168545268757042933526662768772514619668023376490370653166168736869277815425438301697322693e-01), SC_(9.9991296657753407444565165371686075323189094367991128619066744668429579140503359966446931860569605749e-01) }},
{{ SC_(9.7540378570556640625000000000000000000000000000000000000000000000000000000000000000000000000000000000e-02), SC_(1.8838196992874145507812500000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(9.7380331287488173017819681812505333548000401340832607031998520409371778408842832201970632399407455377e-02), SC_(9.9524724118097360944629737689090579536626111956092105184429209919209960381948277540779135011872980164e-01), SC_(9.9983172185713251267253025953154802657840786163407200767760200375372426265381549093953869220602182213e-01) }},
{{ SC_(9.7540378570556640625000000000000000000000000000000000000000000000000000000000000000000000000000000000e-02), SC_(2.2103404998779296875000000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(9.7378277454797060918439287025630752988524259325176347053163180340804501139998370882347991305783292950e-02), SC_(9.9524744213684697238369251137951559191374873239697065458847170083807556278595809556474002748294261664e-01), SC_(9.9976833370589598055738289274893465677056797771478451409770833086130339040015264801585644093126658918e-01) }},
{{ SC_(9.7540378570556640625000000000000000000000000000000000000000000000000000000000000000000000000000000000e-02), SC_(2.7849817276000976562500000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(9.7373867428466078827183319249605829662038878958674322241785141561706308176062148140500575389736858636e-02), SC_(9.9524787361843859046684503694959443606213073331077397309037690642929126741546581484860725317608308903e-01), SC_(9.9963222736499384529570421859460465646281312249068720158613197297025393833765853405888603462853042983e-01) }},
{{ SC_(9.7540378570556640625000000000000000000000000000000000000000000000000000000000000000000000000000000000e-02), SC_(3.0816698074340820312500000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(9.7371193424879810007588652514672604171038551577576512840133215162813719206019907024377008226545048940e-02), SC_(9.9524813523614031580155154272347701177066765446592058958809789667054121097494545539509044453284397477e-01), SC_(9.9954970099303609847458849068667534444745484953685258900209171332658289031259888119908884757012452532e-01) }},
{{ SC_(9.7540378570556640625000000000000000000000000000000000000000000000000000000000000000000000000000000000e-02), SC_(5.4688143730163574218750000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(9.7339839179579928018704143000418077269746964304983646252493319558842047662986337736134976401214155303e-02), SC_(9.9525120231451793830985245843366966203733236112111860397852232906222180662225991758767056042339001978e-01), SC_(9.9858209994199781278941437194680143132324188699653873991712233555081338659514668305299268048007246328e-01) }},
{{ SC_(9.7540378570556640625000000000000000000000000000000000000000000000000000000000000000000000000000000000e-02), SC_(5.4722046852111816406250000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(9.7339782204735098983141505623993711911459001259399602837752570540694687172295574882766475269842999767e-02), SC_(9.9525120788690065078512180252804658575870883738949865086421010712034580246577640951605540994760241665e-01), SC_(9.9858034179693371185530389839478102909306909444244139828444148460849700760700112751223062617432481898e-01) }},
{{ SC_(9.7540378570556640625000000000000000000000000000000000000000000000000000000000000000000000000000000000e-02), SC_(6.3235926628112792968750000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(9.7324357382337915060878514538001614103127959113855749132567239992517451675127438717163091023277436887e-02), SC_(9.9525271637916917939363212827434662588809382803755724970123962674618546815060076204600270615937503766e-01), SC_(9.9810437384215507531192865121492102169160078954931664380383811419406897938852089977538372535612829971e-01) }},
{{ SC_(9.7540378570556640625000000000000000000000000000000000000000000000000000000000000000000000000000000000e-02), SC_(8.1472349166870117187500000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(9.7283832207787332968350504435429144214762136106042661009244142576287985290132328716551768340406726525e-02), SC_(9.9525667844580027212519964525662529454780451004601160492220566958669619783126116364988358493401101876e-01), SC_(9.9685402331179302384119860067365790061187418556554456085008029417476701630546266620873973439295183575e-01) }},
{{ SC_(9.7540378570556640625000000000000000000000000000000000000000000000000000000000000000000000000000000000e-02), SC_(8.3500838279724121093750000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(9.7278693925629101473730435341228310212032309563196883073408404976412708107672325578164629264874000079e-02), SC_(9.9525718068654182996379555937806239819599280949500315783758413223431440712177599882842080674201603958e-01), SC_(9.9669550352317052980773857626559666269204531893591114427801701253901312521428606453243059354958930545e-01) }},
{{ SC_(9.7540378570556640625000000000000000000000000000000000000000000000000000000000000000000000000000000000e-02), SC_(9.0579175949096679687500000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(9.7259775696151969231560088118671897900432100312079923769575924893086166745621797945635252162042457459e-02), SC_(9.9525902961567457799459980362930626346578307070578660454715450064990786754293178291486280639555469960e-01), SC_(9.9611189149631570780194584866472514410147478802889450853381129958809506344781648993683324004393139400e-01) }},
{{ SC_(9.7540378570556640625000000000000000000000000000000000000000000000000000000000000000000000000000000000e-02), SC_(9.1337585449218750000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(9.7257657583072734398564817378715512213597927085867646425816327114748354915967246517590740628001648382e-02), SC_(9.9525923660192864077140433651715283184822491030430309366345862602952814976707227038950564349076111474e-01), SC_(9.9604655229407085613020817827545499990274574505860169796764685614255261186781008745763895029260399934e-01) }},
{{ SC_(9.7540378570556640625000000000000000000000000000000000000000000000000000000000000000000000000000000000e-02), SC_(9.5750665664672851562500000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(9.7244982770042818904024531685011575954627230233210286803989361976045451794730571449048456332621323951e-02), SC_(9.9526047511495907655064681291117857597207801050777388462844588407020878200858505148516677103386126487e-01), SC_(9.9565557382340077224630623621638890196227919522504229996558938083078176693734660018540050675794907254e-01) }},
{{ SC_(9.7540378570556640625000000000000000000000000000000000000000000000000000000000000000000000000000000000e-02), SC_(9.6488833427429199218750000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(9.7242804401238330394641034407571773598415791334970660265829118621816630813903078372035638501402854060e-02), SC_(9.9526068795676969770830147652098548970870591187020705631353682973051952503866517509360167878496802699e-01), SC_(9.9558838001891729294499891780505516968777413390971340214047171239353816575095609120301571391073133445e-01) }},
{{ SC_(9.7540378570556640625000000000000000000000000000000000000000000000000000000000000000000000000000000000e-02), SC_(9.6769475936889648437500000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(9.7241971830040626580775446834986136249520903646682302901559733248423563672355475550286992004247011330e-02), SC_(9.9526076930350549471991585281853568963609976679114746406156151825336912211360294679020458186631077546e-01), SC_(9.9556269875012748079193459899059614648026964684907523159920139031085488131527377860967239854162520648e-01) }},
{{ SC_(9.7540378570556640625000000000000000000000000000000000000000000000000000000000000000000000000000000000e-02), SC_(9.6886777877807617187500000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(9.7241623119621507768675533305231494633519052635102622629454283243024320020666848207623354683904466225e-02), SC_(9.9526080337420175720684817572609318291152213025067248310909549916814881246189911074085103017210067969e-01), SC_(9.9555194254819173899689090341202623861942977239356687223773368135903981199872362824922639858352857970e-01) }},
{{ SC_(9.7540378570556640625000000000000000000000000000000000000000000000000000000000000000000000000000000000e-02), SC_(9.9288129806518554687500000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(9.7234391800827738968992450665433357666742411135127401009733638701177282347102378993477236969678654384e-02), SC_(9.9526150988125885796360273996610273175186092020643789825948701988318876024022145047763437281682892141e-01), SC_(9.9532889129818059354033929751614120883992975273268479379992266644335702830351636902588795874617070406e-01) }},
{{ SC_(9.7540378570556640625000000000000000000000000000000000000000000000000000000000000000000000000000000000e-02), SC_(9.9646115303039550781250000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(9.7233298644478973403186335285900151115960047949746687839215967221911192031090096952634390287961810058e-02), SC_(9.9526161667910893238555566309439694986630762455664353906763841267218133910312675011879044026031301748e-01), SC_(9.9529517329166101513341571318056995313554164948688445541889776316051021077409476762097381272562596493e-01) }},
{{ SC_(1.2698680162429809570312500000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(9.7540378570556640625000000000000000000000000000000000000000000000000000000000000000000000000000000000e-02), SC_(1.2664257541417004306368951282691748727550124386720100600608750546318698226257203720501683038955900435e-01), SC_(9.9194841503601700817490236765031671061294384597914801836296273830499788073745688271122867056931693804e-01), SC_(9.9992370169081134090096139778728212576933539830520415345599126533770335253944052333509204238907245252e-01) }},
{{ SC_(1.2698680162429809570312500000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(1.2698680162429809570312500000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(1.2664034438368367615558599657163363971530646734795711968270194977547712684218447066591858350732790914e-01), SC_(9.9194869987030175974065452521412422683585122017884833703172127477318391160839598306916141357487061604e-01), SC_(9.9987068186822403724749028083081518011247091434035237209533262760757214065053721683798188881413986251e-01) }},
{{ SC_(1.2698680162429809570312500000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(1.3547700643539428710937500000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(1.2663959243421258905813608345822828017922530244400625498512136982817465216522876223180316746892978949e-01), SC_(9.9194879587007742159475715284033058520863291944391982961636532662432995118718631907184665515795900253e-01), SC_(9.9985281208317985060971531909892334434677570476838685775408615707510438112357380797799157313711172762e-01) }},
{{ SC_(1.2698680162429809570312500000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(1.8838196992874145507812500000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(1.2663381084916491805090059492100784238269531877861315216778816447532202573932684348672955289435329564e-01), SC_(9.9194953397328531710160500722460026622655952036103040094265110799584619676852721018077456040008038541e-01), SC_(9.9971541642789849558372993501158595197975574212963933886048158773290926889665199945423225402810274253e-01) }},
{{ SC_(1.2698680162429809570312500000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(2.2103404998779296875000000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(1.2662929998242081571139218814069795892923025976302653342009659020548480739650785177125529517333216777e-01), SC_(9.9195010982708302717556304478333609322185594815599681184080622604103482677714560248637311499973443224e-01), SC_(9.9960822036141720568423059443779597670253897270187040517610329946323987386528311228454125508327135443e-01) }},
{{ SC_(1.2698680162429809570312500000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(2.7849817276000976562500000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(1.2661961429460418896967396810246571405727207422895958972385864065275488877136482238636675755124590557e-01), SC_(9.9195134622414100866733580145832318164333662539872220791472939170731476462823729405537088602256531729e-01), SC_(9.9937805532816590734549896953199729957319400587793257255984019593010016180390682729079027380693079026e-01) }},
{{ SC_(1.2698680162429809570312500000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(3.0816698074340820312500000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(1.2661374149642430498275814078314106907940053959163726876931088942592173877800165066908556638658111681e-01), SC_(9.9195209585154697731347941628428426390274881177960013587295374143129739974658168687491437531765414110e-01), SC_(9.9923850109148547626583577239570508951580732513750278611967550553394336805805481340265773352381893379e-01) }},
{{ SC_(1.2698680162429809570312500000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(5.4688143730163574218750000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(1.2654488424423158028146538144364661933525780622463738133669996961977781584193025131615978691374736521e-01), SC_(9.9196088243015612875932298709053672424734467141780120825856707350305433097042525294321552164863047109e-01), SC_(9.9760245654598811811584699102546894291904546191886429980627001499665291127151607954102898970245409851e-01) }},
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{{ SC_(1.2698680162429809570312500000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(6.3235926628112792968750000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(1.2651088778028249529681324961472643930079008980008330443355801794393510519029990510797116683182423634e-01), SC_(9.9196521878191110759219578926460974418887553288384632411906981490130493843683671418532806952146307632e-01), SC_(9.9679483689080146267036555206087036941264673152290486533337176224825544066841611926466991550562261874e-01) }},
{{ SC_(1.2698680162429809570312500000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(8.1472349166870117187500000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(1.2642190862830527580721215526505229730209030323519852184974507764030465101007745564782832625354258426e-01), SC_(9.9197656273662858755859536262180938253203297732542725317281233590840843833734141008855041566100980432e-01), SC_(9.9468147004035723310154343069206567712485541810261085505258701220192600870722139834124181369745440365e-01) }},
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{{ SC_(9.9646115303039550781250000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(1.2698680162429809570312500000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(8.3836846976079144894023795726943708541833389995672584811366755923228253071174017567635353431121846609e-01), SC_(5.4510394321720780766887536717356250054610572085005960031610835416626521365025255202834856505988398552e-01), SC_(9.9431680058555042048560821892288124889668236747200833373307558342592799237570669113081508646858944123e-01) }},
{{ SC_(9.9646115303039550781250000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(1.3547700643539428710937500000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(8.3820441560966632694840359993609916279790205370061844267576841794174497598281495713485622976344391591e-01), SC_(5.4535617503834845711324861801153301842141480493596794361183694684559717959677144037999716529712971962e-01), SC_(9.9353143444262221939465586259809215783089086048975947684621927841892919843078927555582450058279233656e-01) }},
{{ SC_(9.9646115303039550781250000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(1.8838196992874145507812500000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(8.3694080839939330368414271429214551959961793583075530257748487453202093020709691019075041846416360706e-01), SC_(5.4729341603546632401734901252585114956817351177725909693254699621320094637152673766320203739840879612e-01), SC_(9.8749272761250703526071418423335735642830175784158270003092854064131945258173428320458022832662895698e-01) }},
{{ SC_(9.9646115303039550781250000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(2.2103404998779296875000000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(8.3595219488333541745953223658793448369279376370877659139211318590602107483272687491384205103621224117e-01), SC_(5.4880226664048500692879221583078985251740360874646904338195445074557839493958187702092044696804312843e-01), SC_(9.8278105708386568298282282875597998137429996085178472000521847835028605762176132021719290137727508239e-01) }},
{{ SC_(9.9646115303039550781250000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(2.7849817276000976562500000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(8.3382140916514258364057514275189395234076096015656622904743683896148751450562302576019453974647090151e-01), SC_(5.5203429025546581114852096977818457319004303981372761755614161259277270015439079181206829579325032785e-01), SC_(9.7266382772180763980428823267587850291886472907988601665506049159784515142450655743912151433457442980e-01) }},
{{ SC_(9.9646115303039550781250000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(3.0816698074340820312500000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(8.3252411677796080099984218005465406247603158092900382879848475335969228461284474294838346745658610338e-01), SC_(5.5398880402321876447537992744785992051147320066434509696867298206540346295080549987859520437777915381e-01), SC_(9.6652925010955620940395542670963601024004192923501024067547444076347996257852171861223080733972851268e-01) }},
{{ SC_(9.9646115303039550781250000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(5.4688143730163574218750000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(8.1702126153451325670867681664834862284442900110619845692881310008319720517769069946797733509893494105e-01), SC_(5.7660754261503767522810562864064328455649166811864815390603109965795766966575540449279700563129428370e-01), SC_(8.9462699615741016868034408689337159403352108892081501750962490910797925647981891785415699133208532444e-01) }},
{{ SC_(9.9646115303039550781250000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(5.4722046852111816406250000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(8.1699261272360843718094896717933608151745983515066309372984104102996139405622722607210355081833891513e-01), SC_(5.7664813426824850966137934301882037328247242522271394061105905414771445854256739255757146117096354987e-01), SC_(8.9449643518753563454611035039011276118628076201799942256582642209492573307351767556846756787034337047e-01) }},
{{ SC_(9.9646115303039550781250000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(6.3235926628112792968750000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(8.0917470232222200804623180098129133036872476212345687946408231027401224355414186080302191412417315445e-01), SC_(5.8756812466448807626035048020623505899237385118588318521559957175811892777170782847243623726402163039e-01), SC_(8.5917067186634159636297999262881680727474209461119658335870527906879501356002165645327808755884914641e-01) }},
{{ SC_(9.9646115303039550781250000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(8.1472349166870117187500000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(7.8807119444979816800923969304385287292785209340565035630430040254664427368175755115143127657804319275e-01), SC_(6.1558410674616056493571795007635947841655775384258519636348871522168706473724532307349806008226940840e-01), SC_(7.6665429525726110361447413684552291171054174846338591438308890401356527577849589856356276150225732188e-01) }},
{{ SC_(9.9646115303039550781250000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(8.3500838279724121093750000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(7.8533974060861189062248546305583049909685081062975650698710874051826667020351572955065423608667621888e-01), SC_(6.1906501421159166628343674250361648671913040974698965825105617076167069374238270072189557585460007272e-01), SC_(7.5496484350046113300800020039074081961933680785286101512645919124096025389484980045855949751906931482e-01) }},
{{ SC_(9.9646115303039550781250000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(9.0579175949096679687500000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(7.7518052347000925314010007943527768455040920946345973339627012081381376695222757183254277030896944957e-01), SC_(6.3173978506404235602086192410695037495356623570300207001965408561482576560706910009779017218552967902e-01), SC_(7.1202695591348996943901212719172676293237917080282599202090818283760895203386224684127468737115722039e-01) }},
{{ SC_(9.9646115303039550781250000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(9.1337585449218750000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(7.7403326959640178723563496098403563126044877288657909026716436291016997542128873110698916026557616324e-01), SC_(6.3314492618823376986676740088221455887438346847232176226658849048417517890369368618344349029048271542e-01), SC_(7.0723024179015572507350410631921738029759560477969903360400060435126461530726016656465837852310688792e-01) }},
{{ SC_(9.9646115303039550781250000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(9.5750665664672851562500000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(7.6712800823285619471798123561258913583803638220534736201364708009370629428320353958750416444955694982e-01), SC_(6.4149405218185064504992339458407016741795699167416304441730489787216690117110750201301703730190120252e-01), SC_(6.7857602589593721337697403304549699145452424462317392210364305668406670401778150852638680470506706518e-01) }},
{{ SC_(9.9646115303039550781250000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(9.6488833427429199218750000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(7.6593441813020686107904272195284976164911143038148978940760933715399917785398101606027733051459971132e-01), SC_(6.4291870957652293482277601636810697919275457997668849096935959115861162055784408260876292546568984644e-01), SC_(6.7366024601538257589655742562219072544530334312218911862590121331700593411003613779831508617892420325e-01) }},
{{ SC_(9.9646115303039550781250000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(9.6769475936889648437500000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(7.6547770865632652104311857431350648982519639693036504351701283181609474922881977308885338563907679349e-01), SC_(6.4346241347126103408603307544875846579869659656475523368458255827578551435308991733382243465986469958e-01), SC_(6.7178215521760534606784911003038819524570089099102635584446923804691272196126068898352982615576142014e-01) }},
{{ SC_(9.9646115303039550781250000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(9.6886777877807617187500000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(7.6528633729797841460176785222203390514942625072618331938529597075420681577693034777030027274670865291e-01), SC_(6.4369000454026378494764961458275300252507916799112249356864558832261907901572939091058344628185994802e-01), SC_(6.7099566282750678306967995163385198199449520575839393027024329721293501791261343629006364525136879702e-01) }},
{{ SC_(9.9646115303039550781250000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(9.9288129806518554687500000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(7.6130656170513378346158650596006841065509926127276492299715158864622868192915634720105938405478654273e-01), SC_(6.4839210290125166440291833468322114687478245067783826919074500661090573579759551799996853065323027448e-01), SC_(6.5470204815482800802602415811048971704607358039770120289884409108362609917793951796905679822441221683e-01) }},
{{ SC_(9.9646115303039550781250000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(9.9646115303039550781250000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(7.6070308834386404159049681239553434730978977615881969147142722819631969635063229458010769940901615571e-01), SC_(6.4910000106617422443762696869434170692368988825415526998433303308325407487195203453870690819261137407e-01), SC_(6.5224167903128336698276201258993391810194122946207851950380395682119994293224476046299862066823494348e-01) }}
}};
//#undef SC_

3367
test/jacobi_elliptic_small.ipp
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605
test/jacobi_large_phi.ipp
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@@ -1,306 +1,313 @@
// Copyright John Maddock 2012.
// Use, modification and distribution are subject to the
// Boost Software License, Version 1.0.
// (See accompanying file LICENSE_1_0.txt
// or copy at http://www.boost.org/LICENSE_1_0.txt)
#ifndef SC_
# define SC_(x) static_cast<T>(BOOST_JOIN(x, L))
#endif
static const boost::array<boost::array<T, 5>, 300> jacobi_large_phi = {{
{{ SC_(-1.6098388671875000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+02), SC_(1.2698680162429809570312500000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(1.1058797357690320086682997888107252211628291495151688601393407863373061954395848396257429511756176811e-01), SC_(-9.9386633915238026812869743952282655015178929533806734450981604274006648191113417152643248132020074274e-01), SC_(9.9990138922139577345821742312959843927086669798900631576940452344894647029651168866543336495621319962e-01) }},
{{ SC_(-1.6098388671875000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+02), SC_(1.3547700643539428710937500000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(1.9796027195728077189442848498661232305049387865637023002287165495702857395230146075769449539819678763e-02), SC_(-9.9980403945336507845151345500450800737097833473134761034812701539547907788852267602747381881654129683e-01), SC_(9.9999640368228571150326548705630160155372276544820513372782759452847671460675392468118278515564642670e-01) }},
{{ SC_(-1.6098388671875000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+02), SC_(2.2103404998779296875000000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(-9.4524463054363015830543554229266024611315133648646726829860103132985305860006657410579310878453671719e-01), SC_(-3.2636266396209619739852328880763978392918068940083223909131243802010656037702645968281828914985898722e-01), SC_(9.7793033147839850499560648584765033296353170435094191917820984988398156187728059208365609303718763468e-01) }},
{{ SC_(-1.6098388671875000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+02), SC_(3.0816698074340820312500000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(3.8467092829206275416395221453254971947309775360749050985209931262282264520459122402381792953068010283e-02), SC_(9.9925986748656589242807594841179280186636858779886436718703277243900358292074844422479042190466225049e-01), SC_(9.9992973546117087872258976240789404601766963067622683679015332787486976781350082685530756477017893531e-01) }},
{{ SC_(-1.6098388671875000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+02), SC_(6.3235926628112792968750000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(8.1828487869642382837142082205368890409594444563859603885036504087100530651689815737374300479572152806e-01), SC_(-5.7481288894454945115324043802657481607935129579981996144467071525751961910351319915758240211691782206e-01), SC_(8.5571342814553735162229894739444873282853333740663537333659164564589208017713251914590680386027272809e-01) }},
{{ SC_(-1.6098388671875000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+02), SC_(8.1472349166870117187500000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(8.0342555778181684908553725700040860110642531214149151205515131896190048290879021057059409802362096946e-01), SC_(5.9540521756445540531188114127706021212880690887199697020660799772318324844598317460087416642725615927e-01), SC_(7.5600167963587697285196939810169457229824831904454088987922148028116675585554507425145383067593756070e-01) }},
{{ SC_(-1.6098388671875000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+02), SC_(8.3500838279724121093750000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(-5.2923808769191278344096906576129452977508979277324972114028585485897292732749175191104387817153243622e-01), SC_(-8.4847336230208620189522999730668948980498026956351676759653713074643763505826560196595716137493813219e-01), SC_(8.9705533240946393665356057247371866574922627996248245980741140274917656623741748929349898927165638735e-01) }},
{{ SC_(-1.6098388671875000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+02), SC_(9.0579175949096679687500000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(-4.3588329433998778344118299461470119260462800471832395414994779852496041561445544177910644873466410470e-01), SC_(-9.0000319650283441310099684480078605946721143546738341042331933310537915309970277408204072796535470377e-01), SC_(9.1875870906845118047635806822648200063819834288643294354356983053626866318919800547192402870664676236e-01) }},
{{ SC_(-1.6098388671875000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+02), SC_(9.1337585449218750000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(-9.5600856122085672092800268968580894468432579079804656774052584258946328842723868281852714693291460848e-01), SC_(2.9333876469438444648579701071867907567539764964724421796135027276816072964646665290023055039395020032e-01), SC_(4.8737075577081420166881282500675564846609614724320216534645035828942396447404446035830276248915799790e-01) }},
{{ SC_(-1.6098388671875000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+02), SC_(9.6886777877807617187500000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(-9.7736452897241769061181430418007365494795330898556587924749704567000625360724157676092701517939511727e-01), SC_(-2.1156223081288422793211063644770138572453563413600394268502697586678182945457777132434950354231163677e-01), SC_(3.2141922402480394843964588019150294350276272721151544568588531146246464930473505445135251473893910091e-01) }},
{{ SC_(-1.5605529785156250000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+02), SC_(1.2698680162429809570312500000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(9.9634594511488441239446124536812458462568892642529680265004423990558267843732051305555937342925952892e-01), SC_(-8.5409353428812105256571523319257903922757730296962059795625764794071278796936359904999417711418506963e-02), SC_(9.9196370140536661517806007451248913316445364776565729227577579281057604045077901201671022992954940866e-01) }},
{{ SC_(-1.5605529785156250000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+02), SC_(1.3547700643539428710937500000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(9.8507961426602883228803019073961981958060099984011753039084360078720386446123667023988475150255949526e-01), SC_(-1.7209925495914224056702706138188187847064943449563917074969927279924070607243598857996086522477531487e-01), SC_(9.9105478803571702730047795909209167869766318761675764394396722003662904738763622827899377822295432355e-01) }},
{{ SC_(-1.5605529785156250000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+02), SC_(2.2103404998779296875000000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(1.8248612785073414182685509102670101867866606445715181205154091509183064961414026941361152523421096695e-01), SC_(-9.8320842812805745037945796017375413735001762909773273395230181538881053153180460745843274908711290409e-01), SC_(9.9918618660790569357913493985971747365339871345709645144590218630847755475249250020453080799416154091e-01) }},
{{ SC_(-1.5605529785156250000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+02), SC_(3.0816698074340820312500000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(-9.9158838874949604426827150019504117982370531426684233581077142421174586823163566938385360504094435130e-01), SC_(1.2943132270504812677590848413999258821957368076167066407580166536160746634327211207828164566323979708e-01), SC_(9.5216807427332399209612601388142889559348170701718081235058316586516533919961845371369694752105796844e-01) }},
{{ SC_(-1.5605529785156250000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+02), SC_(6.3235926628112792968750000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(3.4850849856189024097670989535486539667872022677162829380888596814546374460520548474036175153271561409e-01), SC_(9.3730562061162150476751438595734314944960838837159437927593351031354238223322792887550880643854386618e-01), SC_(9.7541351185979966500632289702714211007616769474888190781321539444569874004850576581698447098984473774e-01) }},
{{ SC_(-1.5605529785156250000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+02), SC_(8.1472349166870117187500000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(-9.9768647828943160251387270175978040354991051978569998213156792178899072069031856957855604912863677927e-01), SC_(-6.7983020221460620602477920740337096785069318374339062937396833159665852445264612438240658448058446372e-02), SC_(5.8248896313210669614394305122189656389869009767463887294045928688078276659240087367291744920068430718e-01) }},
{{ SC_(-1.5605529785156250000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+02), SC_(8.3500838279724121093750000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(9.1666788045635083193371938920056375449022051643456650047952514782286715843857567412246372159950161759e-01), SC_(3.9964984291209386199380881912105158376718408574530690430179110562688471984148465105325478026822099931e-01), SC_(6.4352467823650631744048456295799149574644278344437481712696368654316089787975896784931564053208489969e-01) }},
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{{ SC_(1.8823712158203125000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+02), SC_(8.3500838279724121093750000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(-9.9022828187136105906196471291564661403216999556757961785350022987381939378971005699176778462832894500e-01), SC_(-1.3945590622878728025275854877999384343506864919871791332943482097212062454797896291672769010179047126e-01), SC_(5.6242410128269651318638171879962105108484764950203276397137500430679996064342827157574945687032422251e-01) }},
{{ SC_(1.8823712158203125000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+02), SC_(9.0579175949096679687500000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(7.2225293676454039847118730433582317542163291424397756014069541407687639646436394282675749314004670213e-01), SC_(-6.9162901568326122999320827132211815197583814088740484133524667749619742473863985710935207989711357306e-01), SC_(7.5631229238157511512726921373977239294597026454840710311514394398122215634666408751297112080708332221e-01) }},
{{ SC_(1.8823712158203125000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+02), SC_(9.1337585449218750000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(6.6919704659039880874104416778008264328976415154519431700721206335721748887374586283547213989879869821e-01), SC_(7.4308499704588815369829896587146266571422905434113689822016960417977298702809469111464391421393157846e-01), SC_(7.9145423960264861511754592359292301577723424563365416540082864616725536077630976832346945222872767651e-01) }},
{{ SC_(1.8823712158203125000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+02), SC_(9.6886777877807617187500000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(-9.9985839569062744995928782846034896099475389962834323200371629156589152732329808666213597004256925246e-01), SC_(-1.6828207479249452270256743531578358888618739675818335576364041725962045072745517542819807243357365933e-02), SC_(2.4811500902814415099421134839814839535952252216355001408696023657939687982338280967593714006707275461e-01) }},
{{ SC_(1.9244384765625000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+02), SC_(1.2698680162429809570312500000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(-2.7036961459445298652770365297301720178848257840545640891758154226512202840739891134316480516791739677e-02), SC_(-9.9963443453846690181960398703795842128843708482823352311391890992732287276687485991931020863560061815e-01), SC_(9.9999410608025568418304767245109278077965678455924012818036381723154626938361519854564227409987215862e-01) }},
{{ SC_(1.9244384765625000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+02), SC_(1.3547700643539428710937500000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(8.1734915482199356102130036278032201601634483451974860767412689226690706880940935534712712022144078460e-02), SC_(-9.9665410428649604191931323210153286395288532319830878052000669565077331605137318973713012303054678671e-01), SC_(9.9993869022293475410189485316834760785303971582466027682533179798447934328845846384682182793416357727e-01) }},
{{ SC_(1.9244384765625000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+02), SC_(2.2103404998779296875000000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(9.9995218373496773263651925578727064401670607131470342952612607571530019811079404407381908664393766975e-01), SC_(9.7790717181812860926422150641412403956874639089016646724060828887361930395181076922422679433611939212e-03), SC_(9.7526848655233394716795552507461466168951466979791086946976388120506542592942753981208637632441756244e-01) }},
{{ SC_(1.9244384765625000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+02), SC_(3.0816698074340820312500000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(-7.0063055207436460764834115746422976632488080032668076636963831213632189271948763173884625585587269580e-01), SC_(7.1352423189403390000873839748233370773517976931635994639101499750601024513038405989182990240690226540e-01), SC_(9.7641300325014709214627720331871351426028634446146550972861679142906428089751954497725756354213272840e-01) }},
{{ SC_(1.9244384765625000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+02), SC_(6.3235926628112792968750000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(4.5629311263560406562094673001634381052191835088565210424531588861173882757186208678216556508550679430e-01), SC_(8.8982953163025104299147108375948216001789684883235282506986645023899414807723796165371648531014475864e-01), SC_(9.5746748699222340507907981437994911748902154858264449133550586012444476527797310093949750934672288837e-01) }},
{{ SC_(1.9244384765625000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+02), SC_(8.1472349166870117187500000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(-9.9953404483308624966483176051214847508294522252026131907613636431223482652177643759261486975328029866e-01), SC_(3.0523650168515675894001852148723589874270849466598069951938747857113554940361394490823395543773394233e-02), SC_(5.8038268943952965692251653605728871453525294638209731912241246940641332498081284925022636386294524695e-01) }},
{{ SC_(1.9244384765625000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+02), SC_(8.3500838279724121093750000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(9.9459247800658676097860133561593808854776558809024148626279523955355290381658953398402930347507821901e-01), SC_(1.0385471916440403216307539217164608185195547329915757301062076486879434279879750738514700230252212763e-01), SC_(5.5702897854142442809611654478963959324261775797147550071864942887044712808658131231637010349995702522e-01) }},
{{ SC_(1.9244384765625000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+02), SC_(9.0579175949096679687500000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(-8.8270115775193423620255579638055734154142840720846053962016385963039891369058232571134438249971299782e-01), SC_(4.6993474664403664402801695571076121740057255160045194624946246537172391662751582864322860663846755794e-01), SC_(6.0060827158178863368404500172080102632076625684813771196020909629280641279574615153270312721676292993e-01) }},
{{ SC_(1.9244384765625000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+02), SC_(9.1337585449218750000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(-3.0499633309357216160837947685508809398255521078686485810289070559124369255099465411452008206591216497e-01), SC_(-9.5235352511526662520363937890584200804697113358196926071621691184261145069006498967839187367230278540e-01), SC_(9.6041410479017780647642546421853134094118233510049076119516206412560578636505769948373386720382050372e-01) }},
{{ SC_(1.9244384765625000000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+02), SC_(9.6886777877807617187500000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(8.7703562086186605707652810260085804979481250950420318258041728072494841225884138094911078872313703606e-01), SC_(4.8042535293158825529589641475682597199231357338121232115205565947900759506420661006157314061468657855e-01), SC_(5.2721559756651726382324256487897356272038238081316030704213375897027127034023294653929546320025247369e-01) }},
{{ SC_(1.9715252685546875000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+02), SC_(1.2698680162429809570312500000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(9.9999149217579438025155419990378050503774435663431440953044152660042130222829826356772642068616800226e-01), SC_(-4.1249940640159451218905143653088260520196509809885200974912119735128876297229127837040396959124726935e-03), SC_(9.9190454510523192870151020257793218111789942952070638913195077330681594450955229828271818098523095175e-01) }},
{{ SC_(1.9715252685546875000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+02), SC_(1.3547700643539428710937500000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(9.9434482768426277476649034779467733059368058898480629473319245010863119376582776653994755154495576583e-01), SC_(1.0619964057167881835341514888736790094923878910656293614977154420369967365183882337460116321223340636e-01), SC_(9.9088494994688427220084094311943729183292306647285928784964966773416757025282807085924859312912955955e-01) }},
{{ SC_(1.9715252685546875000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+02), SC_(2.2103404998779296875000000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(-7.2863923780197472375944729124012739432330206691625337430224005433942015077316427862679405956591677094e-02), SC_(9.9734189153537192292701855468804208804195911507161872562581122221034533964836167194345541261731262046e-01), SC_(9.9987029950271100759091086168773309508042475821354228254985342328629376377136953466595469759241932790e-01) }},
{{ SC_(1.9715252685546875000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+02), SC_(3.0816698074340820312500000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(-6.4438953143877535562212080854310540201100159071875241724085078651193139555040088765595284332588609031e-01), SC_(-7.6469741190363365029329825419758457032026733632510013400465585566734752595369338949010268046961883438e-01), SC_(9.8008476769416633442530577739220493732979907125425643755174397779481355690658870638758907227004465396e-01) }},
{{ SC_(1.9715252685546875000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+02), SC_(6.3235926628112792968750000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(-9.9387502689389878225183349526237932217471297287328121519769701617770894461916996339991668619614720106e-01), SC_(-1.1050986796052184360390211918956482356707307302792124668112446870634519675064841811303841609817046435e-01), SC_(7.7782083010783148384110038999967915981917233380252884615756446459464833713263012454253928377642176473e-01) }},
{{ SC_(1.9715252685546875000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+02), SC_(8.1472349166870117187500000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(9.0692896438948333078582609551292864727528807834406627454741719659705582459890889300047150852328383914e-01), SC_(-4.2128357854468915494007141925104755456992245674324379641374290838680438635975287956170633686988273788e-01), SC_(6.7381912240981059330307389773430099004172998609294423672920782115012163917779546323448667567467913871e-01) }},
{{ SC_(1.9715252685546875000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+02), SC_(8.3500838279724121093750000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(-9.7776321201636010382337424408562096668543234507605495641318225337144791625772419859562530121151790673e-01), SC_(2.0971194822291466346030421849595858014680805590559492690127261632363629066019576649612096090094549878e-01), SC_(5.7742960193439094700348356947016724682361321289632632659151235741183259429995820997477679950807256189e-01) }},
{{ SC_(1.9715252685546875000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+02), SC_(9.0579175949096679687500000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(8.5335552637509468619177212910424271793500604536736315130170091868994872898355573407901286288639274304e-01), SC_(-5.2132940220659440319333211591248886524580006933686352224178661371782672213885596221974167956318085725e-01), SC_(6.3445182831800375269300932933670770833130898600306348885566817247186267453097547880914732346671069865e-01) }},
{{ SC_(1.9715252685546875000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+02), SC_(9.1337585449218750000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(3.2552432416186685026934526193128921379766826802420069334155189741447969109871574924231483351424206599e-01), SC_(9.4553366644396106872879025738016398857917167142462917144519103981246913164050418116860896385695109638e-01), SC_(9.5477600273005629053462961893870689852992588659840987337775533495567475431257098929765560217201525781e-01) }},
{{ SC_(1.9715252685546875000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+02), SC_(9.6886777877807617187500000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(-3.9412307228568629478091636297546153976117178431143042104414325984436672903094560979335786919432390159e-01), SC_(-9.1905767168991723490423535241594951632963991958559280799910799985557761425472976757206816773545655546e-01), SC_(9.2422301160881704148508838860716761915357124551323944774087944758929470657071593948190980722116431319e-01) }},
{{ SC_(1.9858453369140625000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+02), SC_(1.2698680162429809570312500000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(1.4054705213152072851451664130651061216499217259757217431721599006205998223273563720851776196554659711e-01), SC_(-9.9007400033388392914671454535086242072251869165129442669867317682364702240378428827847175171458794744e-01), SC_(9.9984071853366842614471458726841084906264079357521344888761890568442619129819452826610841761945249390e-01) }},
{{ SC_(1.9858453369140625000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+02), SC_(1.3547700643539428710937500000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(2.5070640492058129942565255217740163494695763216559037381456171424195061110398681756028914124819463101e-01), SC_(-9.6806316866813889172199931228900862951312842168003652810485498962347027876607999917857526043808893858e-01), SC_(9.9942302452559713852269084116030636732630369591763149069010267256421389522467628458268739532812633610e-01) }},
{{ SC_(1.9858453369140625000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+02), SC_(2.2103404998779296875000000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(9.7460959847396629023213294151850600468186754526453359707119955774767291431614264354511495305616871082e-01), SC_(2.2391098803411637082502445867797619686052486034294717623183478584718412642662476193997851593899862294e-01), SC_(9.7652107100176220018304071389988193041833109679443427832086050938061220329457600374867819614433504174e-01) }},
{{ SC_(1.9858453369140625000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+02), SC_(3.0816698074340820312500000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(-8.7591137819560965793227178075846254493991687812511266984816459225474516690755277726181572540400781692e-01), SC_(4.8247202773577212421607049007306835524095045191215664111886203507494519542708812099117851390243407605e-01), SC_(9.6288079930202121551356736451843753542939778244370285463921850847493493915725115345472885123365413983e-01) }},
{{ SC_(1.9858453369140625000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+02), SC_(6.3235926628112792968750000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(-4.6250242396649649980482066020190351615612321919279456557494609907194412689120822625415608757186732226e-01), SC_(8.8661801686245645800217768700725799498166537819118235942894900353237994345457404176820430584219016246e-01), SC_(9.5627540398922768507958728734673192109735702301637317713655951281056100713965361590625156345008848052e-01) }},
{{ SC_(1.9858453369140625000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+02), SC_(8.1472349166870117187500000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(-1.1735531008826291520919245508896005477690524195845718339880048475212741686661323687535843820697763115e-01), SC_(-9.9308999148822744363057759901009520225182513004952136286524553869898571573704761432739426689545184600e-01), SC_(9.9541866617977664359846799474228301142404409511589411389238630589212796142638172458066619231854538725e-01) }},
{{ SC_(1.9858453369140625000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+02), SC_(8.3500838279724121093750000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(-2.5661560264047896550977697577574285271994983541443544067356972715404806414952219948705677776708497000e-01), SC_(9.6651354490325887257750254185816231220218423716636053686841904330333698328423906111679391851744157820e-01), SC_(9.7677311539491902219065627087092296908401907255979252384756489646051968319678552175412452558572875080e-01) }},
{{ SC_(1.9858453369140625000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+02), SC_(9.0579175949096679687500000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(-2.3043688031022365976100265167863985776533246242764453911544714145699594137367180026912374835735577553e-01), SC_(-9.7308727470504497158374043000785726585723147362213332885195842776034698222933783780401814107209214425e-01), SC_(9.7797376965032175821022437157898388837314600109117623736975241337618528076029566654878957935590182792e-01) }},
{{ SC_(1.9858453369140625000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+02), SC_(9.1337585449218750000000000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(9.7024515945744297738657357466434755079331657796883714801833862664891641843430559561966177382852691399e-01), SC_(2.4212461780950951071551165255952297503000013061390990430320407464582844014750946659296356182356525586e-01), SC_(4.6330574762904332411829744686422163790342838342235753322328220006082956185458756739898418452935999869e-01) }},
{{ SC_(1.9858453369140625000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+02), SC_(9.6886777877807617187500000000000000000000000000000000000000000000000000000000000000000000000000000000e-01), SC_(-9.6271921666412527706611162998623278828344436746037642935689292731054871089839252562699168099269047894e-01), SC_(-2.7050269844423550857864806232371501929916695397580524032916105445727409203649388936347088607548210605e-01), SC_(3.6052997174588038100329734639411992177585754440288098151836194079410246809516008674605501002506176314e-01) }}
}};
//#undef SC_

685
test/jacobi_near_1.ipp
View File

@@ -1,346 +1,353 @@
// Copyright John Maddock 2012.
// Use, modification and distribution are subject to the
// Boost Software License, Version 1.0.
// (See accompanying file LICENSE_1_0.txt
// or copy at http://www.boost.org/LICENSE_1_0.txt)
#ifndef SC_
# define SC_(x) static_cast<T>(BOOST_JOIN(x, L))
#endif
static const boost::array<boost::array<T, 5>, 340> jacobi_near_1 = {{
{{ SC_(-4.0245971679687500000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(1.0000004768371582031250000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(-9.9936124862178929657881621645181864085183918423681860187396785862520605717123413406685399380582107113e-01), SC_(3.5736462515171262671173658796361885282655550407797367368767246967565775142270960241294075546367351927e-02), SC_(3.5723133911895480121899640922445600550831965573961005650871698226561870552026541364948342613336582806e-02) }},
{{ SC_(-4.0245971679687500000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(1.0000014305114746093750000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(-9.9936077436182305740265762942505880070947367818181132794898773596144577761932318153752214737153329561e-01), SC_(3.5749722613432715628553169307272741195011102329188833383668050964850356815583084732679478209132508739e-02), SC_(3.5709736745792682671599404581373263526701044801333523535341814550620045496488948203712498732057017070e-02) }},
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{{ SC_(4.9646129608154296875000000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(1.0000290870666503906250000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(9.9988747544293069353066537829179260575882047757007492549019748069539230620040354484126779384912576694e-01), SC_(1.5001215029545749933847659975864641865931391330840461915721059755185086271628874400178167869847889009e-02), SC_(1.2917993826264694721926108892215877113225794890847741738148129932526099630756216503817814024316857591e-02) }},
{{ SC_(4.9646129608154296875000000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(1.0000371932983398437500000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(9.9988308226099731657983151576240197041049174012751792764812244409087930727657331644783678448792904087e-01), SC_(1.5291233051905047096038520294638906781972874594444499867815398497101742249334516320782151364484948558e-02), SC_(1.2627399643574478880468698035197591815527455130858562493759790443716432493078723746069108350777491985e-02) }},
{{ SC_(4.9646129608154296875000000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(1.0000996589660644531250000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(9.9984640219639140402613273019667554862930150639016202863777830939274528021875552024478939209428846017e-01), SC_(1.7526323485885982097641938428519069579260358421271219311888913372990209058618455439095372023020540344e-02), SC_(1.0387751384930428488122047379910627057886096355738392117524671170521488626705245794637004721422908426e-02) }},
{{ SC_(4.9646129608154296875000000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(1.0001597404479980468750000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(9.9980639884593669404425893776595290662877785980161533745963098103525238097471831481848178344690376077e-01), SC_(1.9676504433454567937248530268282368308302071162458460119591299806242144124305023388268650598619695861e-02), SC_(8.2329894545034209975015153877461219543875964135604078659255758514717666391596123103417229683686485863e-03) }},
{{ SC_(4.9646129608154296875000000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(1.0002679824829101562500000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(9.9972263242283481540743599408497747360870457548541412998469672217116875570127792798886879974903796487e-01), SC_(2.3551183018216021253938001600501009008155573150038780116288028548084796733896793416599159415959118251e-02), SC_(4.3495699021134300166444124225546063387545267250507797699122981168308214469028322968675084635890943764e-03) }},
{{ SC_(4.9646129608154296875000000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(1.0007553100585937500000000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(9.9915879545421819350530688005623615186240544270827593274622412564050735515128475466608299752025526140e-01), SC_(4.1008553576976706311793253202245137451698422113077721150856829330199964424353347050839790650622532029e-02), SC_(-1.3154931678629558158982660699935247723551027344608329867102808264119755379967383078768146573341990972e-02) }},
{{ SC_(4.9646129608154296875000000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(1.0012483596801757812500000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(9.9827648539531403745215917352563214138968446312144447102479978693505240691548978979441840473622948646e-01), SC_(5.8686103182775385959094432164210470495146664187835729337215293512993909532328740626483958923893141231e-02), SC_(-3.0893124798500284820335880409303644182778189826173654652430374404846006649343381743921738919251947699e-02) }},
{{ SC_(4.9646129608154296875000000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(1.0023207664489746093750000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(9.9526992589997827420306117917427182178979741082729092965897483434868497193943333068777040666157481100e-01), SC_(9.7148209448510965618814190119451117927847310257093339481999337817751394945307795550093447421264799168e-02), SC_(-6.9532095588469802480589239010157975152091841708321990467488846359840797625840328044562828776517609113e-02) }},
{{ SC_(4.9646129608154296875000000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(1.0060424804687500000000000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(9.7327357090730138720367359153239323902247504897821653720406237386695349159240208217001492967466592893e-01), SC_(2.2964876697546228888931649787788742930944361620108470728002449961617243383843764035729632038084809597e-01), SC_(-2.0311659859397708228829612914540972881961033272228812487026550233039579579564016302202736438925829861e-01) }},
{{ SC_(4.9646129608154296875000000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(1.0155692100524902343750000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(8.4069051112564740388498305703743050846741943876819566564676351892344788777074732833738047977587592836e-01), SC_(5.4151589496828042658602571182616923878595213758699386834940240440502083614232854508648303249637786229e-01), SC_(-5.2063493838617445779646407770009371209785483807741597530330738738065076402146210854614754006055477215e-01) }},
{{ SC_(4.9646129608154296875000000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(1.0305857658386230468750000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(4.8671357579638665629126370168770921319757407213502466576345439294626879685237098285286502834996393092e-01), SC_(8.7356161496227327149253838986791328231133879539230423927448398220130445285498224963240552394450600870e-01), SC_(-8.6509962228485538958789361261824061503929655387763193064181839580439422746694246738587153880942281811e-01) }},
{{ SC_(4.9646129608154296875000000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(1.0623893737792968750000000000000000000000000000000000000000000000000000000000000000000000000000000000e+00), SC_(-2.2293187234404279005404405123453640992362355261738577610576210777344443465871289033909805344032394449e-01), SC_(9.7483402704931233304677248889105249284034868811789307005518001217555908178599047906139783223849231970e-01), SC_(-9.7154855780636670580019454689623684007923466283994781397066875280116362115119765459157832338091463773e-01) }}
}};
//#undef SC_

14
test/owens_t_T7.hpp
View File

@@ -1,4 +1,4 @@
// (C) Benjamin Sobotta 2012
// Copyright (C) Benjamin Sobotta 2012
// Use, modification and distribution are subject to the
// Boost Software License, Version 1.0. (See accompanying file
@@ -145,10 +145,10 @@ namespace boost
val *= exp(-half<RealType>()*hs*as);
val *= exp(-half<RealType>()*hs);
val *= one_div_two_pi<RealType>() * a;
return val;
} // RealType compute_owens_t_T7(const RealType h, const RealType a)
// compute Owen's T function, T(h,a), for arbitrary values of h and a
template<typename RealType, class Policy>
inline RealType owens_t_T7(RealType h, RealType a, const Policy&)
@@ -170,7 +170,7 @@ namespace boost
{
val = compute_owens_t_T7(h, fabs_a);
} // if(fabs_a <= 1.0)
else
else
{
if( h <= 0.67 )
{
@@ -196,9 +196,9 @@ namespace boost
return val;
} // RealType owens_t(RealType h, RealType a)
} // namespace detail
template <class T1, class T2, class Policy>
inline typename tools::promote_args<T1, T2>::type owens_t_T7(T1 h, T2 a, const Policy& pol)
{
@@ -212,7 +212,7 @@ namespace boost
{
return owens_t_T7(h, a, policies::policy<>());
}
} // namespace math
} // namespace boost

1313
test/owens_t_large_data.ipp
View File

File diff suppressed because it is too large Load Diff

6
test/table_type.hpp
View File

@@ -1,3 +1,9 @@
// Copyright John Maddock 2012.
// Use, modification and distribution are subject to the
// Boost Software License, Version 1.0.
// (See accompanying file LICENSE_1_0.txt
// or copy at http://www.boost.org/LICENSE_1_0.txt)
#ifndef BOOST_MATH_TEST_TABLE_TYPE_HPP
#define BOOST_MATH_TEST_TABLE_TYPE_HPP

540
test/test_constants.cpp
View File

@@ -24,7 +24,7 @@
#include <boost/test/floating_point_comparison.hpp>
#include <boost/math/constants/constants.hpp>
#include <boost/math/tools/test.hpp>
#include <boost/math/tools/test.hpp>
#include <boost/static_assert.hpp>
#include <boost/utility/enable_if.hpp>
@@ -91,7 +91,7 @@ void test_spots(RealType)
// it can never really have precision greater than a long double.
typedef typename boost::math::constants::construction_traits<RealType, boost::math::policies::policy<> >::type construction_type;
RealType tolerance = std::max(static_cast<RealType>(boost::math::tools::epsilon<long double>()), boost::math::tools::epsilon<RealType>()) * 2; // double
RealType tolerance = (std::max)(static_cast<RealType>(boost::math::tools::epsilon<long double>()), boost::math::tools::epsilon<RealType>()) * 2; // double
if((construction_type::value == 0) && (boost::math::tools::digits<RealType>() > boost::math::constants::max_string_digits))
tolerance *= 30; // Allow a little extra tolerance
// for calculated (perhaps using a series representation) constants.
@@ -104,61 +104,63 @@ void test_spots(RealType)
using namespace boost::math::constants;
BOOST_MATH_STD_USING
BOOST_CHECK_CLOSE_FRACTION(3.14159265358979323846264338327950288419716939937510L, pi<RealType>(), tolerance);
BOOST_CHECK_CLOSE_FRACTION(sqrt(3.14159265358979323846264338327950288419716939937510L), root_pi<RealType>(), tolerance);
BOOST_CHECK_CLOSE_FRACTION(sqrt(3.14159265358979323846264338327950288419716939937510L/2), root_half_pi<RealType>(), tolerance);
BOOST_CHECK_CLOSE_FRACTION(sqrt(3.14159265358979323846264338327950288419716939937510L * 2), root_two_pi<RealType>(), tolerance);
BOOST_CHECK_CLOSE_FRACTION(sqrt(log(4.0L)), root_ln_four<RealType>(), tolerance);
BOOST_CHECK_CLOSE_FRACTION(2.71828182845904523536028747135266249775724709369995L, e<RealType>(), tolerance);
BOOST_CHECK_CLOSE_FRACTION(0.5L, half<RealType>(), tolerance);
BOOST_CHECK_CLOSE_FRACTION(0.57721566490153286060651209008240243104259335L, euler<RealType>(), tolerance);
BOOST_CHECK_CLOSE_FRACTION(sqrt(2.0L), root_two<RealType>(), tolerance);
BOOST_CHECK_CLOSE_FRACTION(log(2.0L), ln_two<RealType>(), tolerance);
BOOST_CHECK_CLOSE_FRACTION(log(log(2.0L)), ln_ln_two<RealType>(), tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<long double>(1)/3, third<RealType>(), tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<long double>(2)/3, twothirds<RealType>(), tolerance);
BOOST_CHECK_CLOSE_FRACTION(0.14159265358979323846264338327950288419716939937510L, pi_minus_three<RealType>(), tolerance);
BOOST_CHECK_CLOSE_FRACTION(4.L - 3.14159265358979323846264338327950288419716939937510L, four_minus_pi<RealType>(), tolerance);
BOOST_CHECK_CLOSE_FRACTION(3.14159265358979323846264338327950288419716939937510L, pi<RealType>(), tolerance);
BOOST_CHECK_CLOSE_FRACTION(sqrt(3.14159265358979323846264338327950288419716939937510L), root_pi<RealType>(), tolerance);
BOOST_CHECK_CLOSE_FRACTION(sqrt(3.14159265358979323846264338327950288419716939937510L/2), root_half_pi<RealType>(), tolerance);
BOOST_CHECK_CLOSE_FRACTION(sqrt(3.14159265358979323846264338327950288419716939937510L * 2), root_two_pi<RealType>(), tolerance);
BOOST_CHECK_CLOSE_FRACTION(sqrt(log(4.0L)), root_ln_four<RealType>(), tolerance);
BOOST_CHECK_CLOSE_FRACTION(2.71828182845904523536028747135266249775724709369995L, e<RealType>(), tolerance);
BOOST_CHECK_CLOSE_FRACTION(0.5L, half<RealType>(), tolerance);
BOOST_CHECK_CLOSE_FRACTION(0.57721566490153286060651209008240243104259335L, euler<RealType>(), tolerance);
BOOST_CHECK_CLOSE_FRACTION(sqrt(2.0L), root_two<RealType>(), tolerance);
BOOST_CHECK_CLOSE_FRACTION(log(2.0L), ln_two<RealType>(), tolerance);
BOOST_CHECK_CLOSE_FRACTION(log(10.0L), ln_ten<RealType>(), tolerance);
BOOST_CHECK_CLOSE_FRACTION(log(log(2.0L)), ln_ln_two<RealType>(), tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<long double>(1)/3, third<RealType>(), tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<long double>(2)/3, twothirds<RealType>(), tolerance);
BOOST_CHECK_CLOSE_FRACTION(0.14159265358979323846264338327950288419716939937510L, pi_minus_three<RealType>(), tolerance);
BOOST_CHECK_CLOSE_FRACTION(4.L - 3.14159265358979323846264338327950288419716939937510L, four_minus_pi<RealType>(), tolerance);
#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
BOOST_CHECK_CLOSE_FRACTION(pow((4 - 3.14159265358979323846264338327950288419716939937510L), 1.5L), pow23_four_minus_pi<RealType>(), tolerance);
BOOST_CHECK_CLOSE_FRACTION(pow((3.14159265358979323846264338327950288419716939937510L), 2.71828182845904523536028747135266249775724709369995L), pi_pow_e<RealType>(), tolerance);
BOOST_CHECK_CLOSE_FRACTION(pow((3.14159265358979323846264338327950288419716939937510L), 0.33333333333333333333333333333333333333333333333333L), cbrt_pi<RealType>(), tolerance);
BOOST_CHECK_CLOSE_FRACTION(exp(-0.5L), exp_minus_half<RealType>(), tolerance);
BOOST_CHECK_CLOSE_FRACTION(pow(2.71828182845904523536028747135266249775724709369995L, 3.14159265358979323846264338327950288419716939937510L), e_pow_pi<RealType>(), tolerance);
BOOST_CHECK_CLOSE_FRACTION(pow((4 - 3.14159265358979323846264338327950288419716939937510L), 1.5L), pow23_four_minus_pi<RealType>(), tolerance);
BOOST_CHECK_CLOSE_FRACTION(pow((3.14159265358979323846264338327950288419716939937510L), 2.71828182845904523536028747135266249775724709369995L), pi_pow_e<RealType>(), tolerance);
BOOST_CHECK_CLOSE_FRACTION(pow((3.14159265358979323846264338327950288419716939937510L), 0.33333333333333333333333333333333333333333333333333L), cbrt_pi<RealType>(), tolerance);
BOOST_CHECK_CLOSE_FRACTION(exp(-0.5L), exp_minus_half<RealType>(), tolerance);
BOOST_CHECK_CLOSE_FRACTION(pow(2.71828182845904523536028747135266249775724709369995L, 3.14159265358979323846264338327950288419716939937510L), e_pow_pi<RealType>(), tolerance);
#else // Only double, so no suffix L.
BOOST_CHECK_CLOSE_FRACTION(pow((4 - 3.14159265358979323846264338327950288419716939937510), 1.5), pow23_four_minus_pi<RealType>(), tolerance);
BOOST_CHECK_CLOSE_FRACTION(pow((3.14159265358979323846264338327950288419716939937510), 2.71828182845904523536028747135266249775724709369995), pi_pow_e<RealType>(), tolerance);
BOOST_CHECK_CLOSE_FRACTION(pow((3.14159265358979323846264338327950288419716939937510), 0.33333333333333333333333333333333333333333333333333), cbrt_pi<RealType>(), tolerance);
BOOST_CHECK_CLOSE_FRACTION(exp(-0.5), exp_minus_half<RealType>(), tolerance);
BOOST_CHECK_CLOSE_FRACTION(pow((4 - 3.14159265358979323846264338327950288419716939937510), 1.5), pow23_four_minus_pi<RealType>(), tolerance);
BOOST_CHECK_CLOSE_FRACTION(pow((3.14159265358979323846264338327950288419716939937510), 2.71828182845904523536028747135266249775724709369995), pi_pow_e<RealType>(), tolerance);
BOOST_CHECK_CLOSE_FRACTION(pow((3.14159265358979323846264338327950288419716939937510), 0.33333333333333333333333333333333333333333333333333), cbrt_pi<RealType>(), tolerance);
BOOST_CHECK_CLOSE_FRACTION(exp(-0.5), exp_minus_half<RealType>(), tolerance);
#endif
// Rational fractions.
BOOST_CHECK_CLOSE_FRACTION(0.333333333333333333333333333333333333333L, third<RealType>(), tolerance);
BOOST_CHECK_CLOSE_FRACTION(0.666666666666666666666666666666666666667L, two_thirds<RealType>(), tolerance);
BOOST_CHECK_CLOSE_FRACTION(0.75L, three_quarters<RealType>(), tolerance);
BOOST_CHECK_CLOSE_FRACTION(0.333333333333333333333333333333333333333L, third<RealType>(), tolerance);
BOOST_CHECK_CLOSE_FRACTION(0.666666666666666666666666666666666666667L, two_thirds<RealType>(), tolerance);
BOOST_CHECK_CLOSE_FRACTION(0.75L, three_quarters<RealType>(), tolerance);
// Two and related.
BOOST_CHECK_CLOSE_FRACTION(sqrt(2.L), root_two<RealType>(), tolerance);
BOOST_CHECK_CLOSE_FRACTION(sqrt(3.L), root_three<RealType>(), tolerance);
BOOST_CHECK_CLOSE_FRACTION(sqrt(2.L)/2, half_root_two<RealType>(), tolerance);
BOOST_CHECK_CLOSE_FRACTION(log(2.L), ln_two<RealType>(), tolerance);
BOOST_CHECK_CLOSE_FRACTION(log(log(2.0L)), ln_ln_two<RealType>(), tolerance);
BOOST_CHECK_CLOSE_FRACTION(sqrt(log(4.0L)), root_ln_four<RealType>(), tolerance);
BOOST_CHECK_CLOSE_FRACTION(1/sqrt(2.0L), one_div_root_two<RealType>(), tolerance);
BOOST_CHECK_CLOSE_FRACTION(sqrt(2.L), root_two<RealType>(), tolerance);
BOOST_CHECK_CLOSE_FRACTION(sqrt(3.L), root_three<RealType>(), tolerance);
BOOST_CHECK_CLOSE_FRACTION(sqrt(2.L)/2, half_root_two<RealType>(), tolerance);
BOOST_CHECK_CLOSE_FRACTION(log(2.L), ln_two<RealType>(), tolerance);
BOOST_CHECK_CLOSE_FRACTION(log(log(2.0L)), ln_ln_two<RealType>(), tolerance);
BOOST_CHECK_CLOSE_FRACTION(sqrt(log(4.0L)), root_ln_four<RealType>(), tolerance);
BOOST_CHECK_CLOSE_FRACTION(1/sqrt(2.0L), one_div_root_two<RealType>(), tolerance);
// pi.
BOOST_CHECK_CLOSE_FRACTION(3.14159265358979323846264338327950288419716939937510L, pi<RealType>(), tolerance);
BOOST_CHECK_CLOSE_FRACTION(3.14159265358979323846264338327950288419716939937510L/2, half_pi<RealType>(), tolerance);
BOOST_CHECK_CLOSE_FRACTION(3.14159265358979323846264338327950288419716939937510L/3, third_pi<RealType>(), tolerance);
BOOST_CHECK_CLOSE_FRACTION(3.14159265358979323846264338327950288419716939937510L/6, sixth_pi<RealType>(), tolerance);
BOOST_CHECK_CLOSE_FRACTION(2 * 3.14159265358979323846264338327950288419716939937510L, two_pi<RealType>(), tolerance);
BOOST_CHECK_CLOSE_FRACTION(3 * 3.14159265358979323846264338327950288419716939937510L / 4, three_quarters_pi<RealType>(), tolerance);
BOOST_CHECK_CLOSE_FRACTION(4 * 3.14159265358979323846264338327950288419716939937510L / 3, four_thirds_pi<RealType>(), tolerance);
BOOST_CHECK_CLOSE_FRACTION(1 / (2 * 3.14159265358979323846264338327950288419716939937510L), one_div_two_pi<RealType>(), tolerance);
BOOST_CHECK_CLOSE_FRACTION(sqrt(3.14159265358979323846264338327950288419716939937510L), root_pi<RealType>(), tolerance);
BOOST_CHECK_CLOSE_FRACTION(sqrt(3.14159265358979323846264338327950288419716939937510L / 2), root_half_pi<RealType>(), tolerance);
BOOST_CHECK_CLOSE_FRACTION(sqrt(2 * 3.14159265358979323846264338327950288419716939937510L), root_two_pi<RealType>(), tolerance);
BOOST_CHECK_CLOSE_FRACTION(1 / sqrt(3.14159265358979323846264338327950288419716939937510L), one_div_root_pi<RealType>(), tolerance);
BOOST_CHECK_CLOSE_FRACTION(3.14159265358979323846264338327950288419716939937510L, pi<RealType>(), tolerance);
BOOST_CHECK_CLOSE_FRACTION(3.14159265358979323846264338327950288419716939937510L/2, half_pi<RealType>(), tolerance);
BOOST_CHECK_CLOSE_FRACTION(3.14159265358979323846264338327950288419716939937510L/3, third_pi<RealType>(), tolerance);
BOOST_CHECK_CLOSE_FRACTION(3.14159265358979323846264338327950288419716939937510L/6, sixth_pi<RealType>(), tolerance);
BOOST_CHECK_CLOSE_FRACTION(2 * 3.14159265358979323846264338327950288419716939937510L, two_pi<RealType>(), tolerance);
BOOST_CHECK_CLOSE_FRACTION(3 * 3.14159265358979323846264338327950288419716939937510L / 4, three_quarters_pi<RealType>(), tolerance);
BOOST_CHECK_CLOSE_FRACTION(4 * 3.14159265358979323846264338327950288419716939937510L / 3, four_thirds_pi<RealType>(), tolerance);
BOOST_CHECK_CLOSE_FRACTION(1 / (2 * 3.14159265358979323846264338327950288419716939937510L), one_div_two_pi<RealType>(), tolerance);
BOOST_CHECK_CLOSE_FRACTION(sqrt(3.14159265358979323846264338327950288419716939937510L), root_pi<RealType>(), tolerance);
BOOST_CHECK_CLOSE_FRACTION(sqrt(3.14159265358979323846264338327950288419716939937510L / 2), root_half_pi<RealType>(), tolerance);
BOOST_CHECK_CLOSE_FRACTION(sqrt(2 * 3.14159265358979323846264338327950288419716939937510L), root_two_pi<RealType>(), tolerance);
BOOST_CHECK_CLOSE_FRACTION(1 / sqrt(3.14159265358979323846264338327950288419716939937510L), one_div_root_pi<RealType>(), tolerance);
BOOST_CHECK_CLOSE_FRACTION(1 / sqrt(2 * 3.14159265358979323846264338327950288419716939937510L), one_div_root_two_pi<RealType>(), tolerance);
BOOST_CHECK_CLOSE_FRACTION(sqrt(1. / 3.14159265358979323846264338327950288419716939937510L), root_one_div_pi<RealType>(), tolerance);
BOOST_CHECK_CLOSE_FRACTION(3.14159265358979323846264338327950288419716939937510L - 3.L, pi_minus_three<RealType>(), tolerance * 2 ); // tolerance * 2 because of cancellation loss.
@@ -171,11 +173,11 @@ void test_spots(RealType)
BOOST_CHECK_CLOSE_FRACTION(3.14159265358979323846264338327950288419716939937510L * 3.14159265358979323846264338327950288419716939937510L * 3.14159265358979323846264338327950288419716939937510L, pi_cubed<RealType>(), tolerance); // See above.
// BOOST_CHECK_CLOSE_FRACTION(3.14159265358979323846264338327950288419716939937510L * 3.14159265358979323846264338327950288419716939937510L, cbrt_pi<RealType>(), tolerance); // See above.
BOOST_CHECK_CLOSE_FRACTION(cbrt_pi<RealType>() * cbrt_pi<RealType>() * cbrt_pi<RealType>(), pi<RealType>(), tolerance);
BOOST_CHECK_CLOSE_FRACTION((1)/cbrt_pi<RealType>(), one_div_cbrt_pi<RealType>(), tolerance);
BOOST_CHECK_CLOSE_FRACTION(cbrt_pi<RealType>() * cbrt_pi<RealType>() * cbrt_pi<RealType>(), pi<RealType>(), tolerance);
BOOST_CHECK_CLOSE_FRACTION((1)/cbrt_pi<RealType>(), one_div_cbrt_pi<RealType>(), tolerance);
// Euler
BOOST_CHECK_CLOSE_FRACTION(2.71828182845904523536028747135266249775724709369995L, e<RealType>(), tolerance);
BOOST_CHECK_CLOSE_FRACTION(2.71828182845904523536028747135266249775724709369995L, e<RealType>(), tolerance);
//BOOST_CHECK_CLOSE_FRACTION(exp(-0.5L), exp_minus_half<RealType>(), tolerance); // See above.
BOOST_CHECK_CLOSE_FRACTION(pow(e<RealType>(), pi<RealType>()), e_pow_pi<RealType>(), tolerance); // See also above.
@@ -207,7 +209,7 @@ void test_spots(RealType)
BOOST_CHECK_CLOSE_FRACTION(.91596559417721901505460351493238411077414937428167213L, catalan<RealType>(), tolerance); // A006752 as a constant in OEIS.
BOOST_CHECK_CLOSE_FRACTION(1.1395470994046486574927930193898461120875997958365518247216557100852480077060706857071875468869385150L, extreme_value_skewness<RealType>(), tolerance); // Mathematica: N[12 Sqrt[6] Zeta[3]/Pi^3, 1101]
BOOST_CHECK_CLOSE_FRACTION(0.6311106578189371381918993515442277798440422031347194976580945856929268196174737254599050270325373067L, rayleigh_skewness<RealType>(), tolerance); // Mathematica: N[2 Sqrt[Pi] (Pi - 3)/((4 - Pi)^(3/2)), 1100]
BOOST_CHECK_CLOSE_FRACTION(2.450893006876380628486604106197544154e-01L, rayleigh_kurtosis_excess<RealType>(), tolerance * 2);
BOOST_CHECK_CLOSE_FRACTION(2.450893006876380628486604106197544154e-01L, rayleigh_kurtosis_excess<RealType>(), tolerance * 2);
BOOST_CHECK_CLOSE_FRACTION(2.68545200106530644530971483548179569382038229399446295305115234555721885953715200280114117493184769799515L, khinchin<RealType>(), tolerance ); // A002210 as a constant https://oeis.org/A002210/constant
BOOST_CHECK_CLOSE_FRACTION(1.2824271291006226368753425688697917277676889273250011L, glaisher<RealType>(), tolerance ); // https://oeis.org/A074962/constant
@@ -217,20 +219,20 @@ void test_spots(RealType)
if(boost::math::tools::digits<RealType>() > boost::math::constants::max_string_digits)
{
// This suffers from cancellation error, so increased tolerance:
BOOST_CHECK_CLOSE_FRACTION(static_cast<RealType>(4. - 3.14159265358979323846264338327950288419716939937510L), four_minus_pi<RealType>(), tolerance * 3);
BOOST_CHECK_CLOSE_FRACTION(static_cast<RealType>(0.14159265358979323846264338327950288419716939937510L), pi_minus_three<RealType>(), tolerance * 3);
BOOST_CHECK_CLOSE_FRACTION(static_cast<RealType>(4. - 3.14159265358979323846264338327950288419716939937510L), four_minus_pi<RealType>(), tolerance * 3);
BOOST_CHECK_CLOSE_FRACTION(static_cast<RealType>(0.14159265358979323846264338327950288419716939937510L), pi_minus_three<RealType>(), tolerance * 3);
}
else
{
BOOST_CHECK_CLOSE_FRACTION(static_cast<RealType>(4. - 3.14159265358979323846264338327950288419716939937510L), four_minus_pi<RealType>(), tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<RealType>(0.14159265358979323846264338327950288419716939937510L), pi_minus_three<RealType>(), tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<RealType>(4. - 3.14159265358979323846264338327950288419716939937510L), four_minus_pi<RealType>(), tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<RealType>(0.14159265358979323846264338327950288419716939937510L), pi_minus_three<RealType>(), tolerance);
}
} // template <class RealType>void test_spots(RealType)
void test_float_spots()
{
// Basic sanity checks for constants in boost::math::float_constants::
// for example: boost::math::float_constants::pi
// Basic sanity checks for constants in boost::math::float_constants::
// for example: boost::math::float_constants::pi
// (rather than boost::math::constants::pi<float>() ).
float tolerance = boost::math::tools::epsilon<float>() * 2;
@@ -238,61 +240,61 @@ void test_float_spots()
using namespace boost::math::float_constants;
BOOST_MATH_STD_USING
BOOST_CHECK_CLOSE_FRACTION(static_cast<float>(3.14159265358979323846264338327950288419716939937510F), pi, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<float>(sqrt(3.14159265358979323846264338327950288419716939937510F)), root_pi, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<float>(sqrt(3.14159265358979323846264338327950288419716939937510F/2)), root_half_pi, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<float>(sqrt(3.14159265358979323846264338327950288419716939937510F * 2)), root_two_pi, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<float>(sqrt(log(4.0F))), root_ln_four, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<float>(2.71828182845904523536028747135266249775724709369995F), e, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<float>(0.5), half, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<float>(0.57721566490153286060651209008240243104259335F), euler, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<float>(sqrt(2.0F)), root_two, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<float>(log(2.0F)), ln_two, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<float>(log(log(2.0F))), ln_ln_two, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<float>(1)/3, third, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<float>(2)/3, twothirds, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<float>(0.14159265358979323846264338327950288419716939937510F), pi_minus_three, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<float>(4.F - 3.14159265358979323846264338327950288419716939937510F), four_minus_pi, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<float>(3.14159265358979323846264338327950288419716939937510F), pi, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<float>(sqrt(3.14159265358979323846264338327950288419716939937510F)), root_pi, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<float>(sqrt(3.14159265358979323846264338327950288419716939937510F/2)), root_half_pi, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<float>(sqrt(3.14159265358979323846264338327950288419716939937510F * 2)), root_two_pi, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<float>(sqrt(log(4.0F))), root_ln_four, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<float>(2.71828182845904523536028747135266249775724709369995F), e, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<float>(0.5), half, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<float>(0.57721566490153286060651209008240243104259335F), euler, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<float>(sqrt(2.0F)), root_two, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<float>(log(2.0F)), ln_two, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<float>(log(log(2.0F))), ln_ln_two, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<float>(1)/3, third, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<float>(2)/3, twothirds, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<float>(0.14159265358979323846264338327950288419716939937510F), pi_minus_three, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<float>(4.F - 3.14159265358979323846264338327950288419716939937510F), four_minus_pi, tolerance);
#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
BOOST_CHECK_CLOSE_FRACTION(static_cast<float>(pow((4 - 3.14159265358979323846264338327950288419716939937510F), 1.5F)), pow23_four_minus_pi, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<float>(pow((3.14159265358979323846264338327950288419716939937510F), 2.71828182845904523536028747135266249775724709369995F)), pi_pow_e, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<float>(pow((3.14159265358979323846264338327950288419716939937510F), 0.33333333333333333333333333333333333333333333333333F)), cbrt_pi, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<float>(exp(-0.5F)), exp_minus_half, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<float>(pow(2.71828182845904523536028747135266249775724709369995F, 3.14159265358979323846264338327950288419716939937510F)), e_pow_pi, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<float>(pow((4 - 3.14159265358979323846264338327950288419716939937510F), 1.5F)), pow23_four_minus_pi, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<float>(pow((3.14159265358979323846264338327950288419716939937510F), 2.71828182845904523536028747135266249775724709369995F)), pi_pow_e, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<float>(pow((3.14159265358979323846264338327950288419716939937510F), 0.33333333333333333333333333333333333333333333333333F)), cbrt_pi, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<float>(exp(-0.5F)), exp_minus_half, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<float>(pow(2.71828182845904523536028747135266249775724709369995F, 3.14159265358979323846264338327950288419716939937510F)), e_pow_pi, tolerance);
#else // Only double, so no suffix F.
BOOST_CHECK_CLOSE_FRACTION(static_cast<float>(pow((4 - 3.14159265358979323846264338327950288419716939937510), 1.5)), pow23_four_minus_pi, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<float>(pow((3.14159265358979323846264338327950288419716939937510), 2.71828182845904523536028747135266249775724709369995)), pi_pow_e, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<float>(pow((3.14159265358979323846264338327950288419716939937510), 0.33333333333333333333333333333333333333333333333333)), cbrt_pi, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<float>(exp(-0.5)), exp_minus_half, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<float>(pow((4 - 3.14159265358979323846264338327950288419716939937510), 1.5)), pow23_four_minus_pi, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<float>(pow((3.14159265358979323846264338327950288419716939937510), 2.71828182845904523536028747135266249775724709369995)), pi_pow_e, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<float>(pow((3.14159265358979323846264338327950288419716939937510), 0.33333333333333333333333333333333333333333333333333)), cbrt_pi, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<float>(exp(-0.5)), exp_minus_half, tolerance);
#endif
// Rational fractions.
BOOST_CHECK_CLOSE_FRACTION(static_cast<float>(0.333333333333333333333333333333333333333F), third, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<float>(0.666666666666666666666666666666666666667F), two_thirds, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<float>(0.75F), three_quarters, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<float>(0.333333333333333333333333333333333333333F), third, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<float>(0.666666666666666666666666666666666666667F), two_thirds, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<float>(0.75F), three_quarters, tolerance);
// Two and related.
BOOST_CHECK_CLOSE_FRACTION(static_cast<float>(sqrt(2.F)), root_two, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<float>(sqrt(3.F)), root_three, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<float>(sqrt(2.F)/2), half_root_two, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<float>(log(2.F)), ln_two, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<float>(log(log(2.0F))), ln_ln_two, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<float>(sqrt(log(4.0F))), root_ln_four, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<float>(1/sqrt(2.0F)), one_div_root_two, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<float>(sqrt(2.F)), root_two, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<float>(sqrt(3.F)), root_three, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<float>(sqrt(2.F)/2), half_root_two, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<float>(log(2.F)), ln_two, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<float>(log(log(2.0F))), ln_ln_two, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<float>(sqrt(log(4.0F))), root_ln_four, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<float>(1/sqrt(2.0F)), one_div_root_two, tolerance);
// pi.
BOOST_CHECK_CLOSE_FRACTION(static_cast<float>(3.14159265358979323846264338327950288419716939937510F), pi, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<float>(3.14159265358979323846264338327950288419716939937510F/2), half_pi, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<float>(3.14159265358979323846264338327950288419716939937510F/3), third_pi, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<float>(3.14159265358979323846264338327950288419716939937510F/6), sixth_pi, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<float>(2 * 3.14159265358979323846264338327950288419716939937510F), two_pi, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<float>(3 * 3.14159265358979323846264338327950288419716939937510F / 4), three_quarters_pi, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<float>(4 * 3.14159265358979323846264338327950288419716939937510F / 3), four_thirds_pi, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<float>(1 / (2 * 3.14159265358979323846264338327950288419716939937510F)), one_div_two_pi, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<float>(sqrt(3.14159265358979323846264338327950288419716939937510F)), root_pi, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<float>(sqrt(3.14159265358979323846264338327950288419716939937510F / 2)), root_half_pi, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<float>(sqrt(2 * 3.14159265358979323846264338327950288419716939937510F)), root_two_pi, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<float>(1 / sqrt(3.14159265358979323846264338327950288419716939937510F)), one_div_root_pi, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<float>(3.14159265358979323846264338327950288419716939937510F), pi, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<float>(3.14159265358979323846264338327950288419716939937510F/2), half_pi, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<float>(3.14159265358979323846264338327950288419716939937510F/3), third_pi, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<float>(3.14159265358979323846264338327950288419716939937510F/6), sixth_pi, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<float>(2 * 3.14159265358979323846264338327950288419716939937510F), two_pi, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<float>(3 * 3.14159265358979323846264338327950288419716939937510F / 4), three_quarters_pi, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<float>(4 * 3.14159265358979323846264338327950288419716939937510F / 3), four_thirds_pi, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<float>(1 / (2 * 3.14159265358979323846264338327950288419716939937510F)), one_div_two_pi, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<float>(sqrt(3.14159265358979323846264338327950288419716939937510F)), root_pi, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<float>(sqrt(3.14159265358979323846264338327950288419716939937510F / 2)), root_half_pi, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<float>(sqrt(2 * 3.14159265358979323846264338327950288419716939937510F)), root_two_pi, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<float>(1 / sqrt(3.14159265358979323846264338327950288419716939937510F)), one_div_root_pi, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<float>(1 / sqrt(2 * 3.14159265358979323846264338327950288419716939937510F)), one_div_root_two_pi, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<float>(sqrt(1. / 3.14159265358979323846264338327950288419716939937510F)), root_one_div_pi, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<float>(3.14159265358979323846264338327950288419716939937510L - 3.L), pi_minus_three, tolerance * 2 ); // tolerance * 2 because of cancellation loss.
@@ -305,11 +307,11 @@ void test_float_spots()
BOOST_CHECK_CLOSE_FRACTION(static_cast<float>(3.14159265358979323846264338327950288419716939937510F * 3.14159265358979323846264338327950288419716939937510F * 3.14159265358979323846264338327950288419716939937510F), pi_cubed, tolerance); // See above.
// BOOST_CHECK_CLOSE_FRACTION(static_cast<float>(3.14159265358979323846264338327950288419716939937510F * 3.14159265358979323846264338327950288419716939937510F), cbrt_pi, tolerance); // See above.
BOOST_CHECK_CLOSE_FRACTION(cbrt_pi * cbrt_pi * cbrt_pi, pi, tolerance);
BOOST_CHECK_CLOSE_FRACTION((static_cast<float>(1)/cbrt_pi), one_div_cbrt_pi, tolerance);
BOOST_CHECK_CLOSE_FRACTION(cbrt_pi * cbrt_pi * cbrt_pi, pi, tolerance);
BOOST_CHECK_CLOSE_FRACTION((static_cast<float>(1)/cbrt_pi), one_div_cbrt_pi, tolerance);
// Euler
BOOST_CHECK_CLOSE_FRACTION(static_cast<float>(2.71828182845904523536028747135266249775724709369995F), e, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<float>(2.71828182845904523536028747135266249775724709369995F), e, tolerance);
//BOOST_CHECK_CLOSE_FRACTION(static_cast<float>(exp(-0.5F)), exp_minus_half, tolerance); // See above.
BOOST_CHECK_CLOSE_FRACTION(pow(e, pi), e_pow_pi, tolerance); // See also above.
@@ -341,7 +343,7 @@ void test_float_spots()
BOOST_CHECK_CLOSE_FRACTION(.91596559417721901505460351493238411077414937428167213F, catalan, tolerance); // A006752 as a constant in OEIS.
BOOST_CHECK_CLOSE_FRACTION(1.1395470994046486574927930193898461120875997958365518247216557100852480077060706857071875468869385150F, extreme_value_skewness, tolerance); // Mathematica: N[12 Sqrt[6] Zeta[3]/Pi^3, 1101]
BOOST_CHECK_CLOSE_FRACTION(0.6311106578189371381918993515442277798440422031347194976580945856929268196174737254599050270325373067F, rayleigh_skewness, tolerance); // Mathematica: N[2 Sqrt[Pi] (Pi - 3)/((4 - Pi)^(3/2)), 1100]
BOOST_CHECK_CLOSE_FRACTION(2.450893006876380628486604106197544154e-01F, rayleigh_kurtosis_excess, tolerance);
BOOST_CHECK_CLOSE_FRACTION(2.450893006876380628486604106197544154e-01F, rayleigh_kurtosis_excess, tolerance);
BOOST_CHECK_CLOSE_FRACTION(2.68545200106530644530971483548179569382038229399446295305115234555721885953715200280114117493184769799515F, khinchin, tolerance ); // A002210 as a constant https://oeis.org/A002210/constant
BOOST_CHECK_CLOSE_FRACTION(1.2824271291006226368753425688697917277676889273250011F, glaisher, tolerance ); // https://oeis.org/A074962/constant
@@ -350,7 +352,7 @@ void test_float_spots()
void test_double_spots()
{
// Basic sanity checks for constants in boost::math::double_constants::
// for example: boost::math::double_constants::pi
// for example: boost::math::double_constants::pi
// (rather than boost::math::constants::pi<double>() ).
double tolerance = boost::math::tools::epsilon<double>() * 2;
@@ -358,61 +360,61 @@ void test_double_spots()
using namespace boost::math::double_constants;
BOOST_MATH_STD_USING
BOOST_CHECK_CLOSE_FRACTION(static_cast<double>(3.14159265358979323846264338327950288419716939937510), pi, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<double>(sqrt(3.14159265358979323846264338327950288419716939937510)), root_pi, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<double>(sqrt(3.14159265358979323846264338327950288419716939937510/2)), root_half_pi, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<double>(sqrt(3.14159265358979323846264338327950288419716939937510 * 2)), root_two_pi, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<double>(sqrt(log(4.0))), root_ln_four, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<double>(2.71828182845904523536028747135266249775724709369995), e, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<double>(0.5), half, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<double>(0.57721566490153286060651209008240243104259335), euler, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<double>(sqrt(2.0)), root_two, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<double>(log(2.0)), ln_two, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<double>(log(log(2.0))), ln_ln_two, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<double>(1)/3, third, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<double>(2)/3, twothirds, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<double>(0.14159265358979323846264338327950288419716939937510), pi_minus_three, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<double>(4. - 3.14159265358979323846264338327950288419716939937510), four_minus_pi, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<double>(3.14159265358979323846264338327950288419716939937510), pi, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<double>(sqrt(3.14159265358979323846264338327950288419716939937510)), root_pi, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<double>(sqrt(3.14159265358979323846264338327950288419716939937510/2)), root_half_pi, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<double>(sqrt(3.14159265358979323846264338327950288419716939937510 * 2)), root_two_pi, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<double>(sqrt(log(4.0))), root_ln_four, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<double>(2.71828182845904523536028747135266249775724709369995), e, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<double>(0.5), half, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<double>(0.57721566490153286060651209008240243104259335), euler, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<double>(sqrt(2.0)), root_two, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<double>(log(2.0)), ln_two, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<double>(log(log(2.0))), ln_ln_two, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<double>(1)/3, third, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<double>(2)/3, twothirds, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<double>(0.14159265358979323846264338327950288419716939937510), pi_minus_three, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<double>(4. - 3.14159265358979323846264338327950288419716939937510), four_minus_pi, tolerance);
#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
BOOST_CHECK_CLOSE_FRACTION(static_cast<double>(pow((4 - 3.14159265358979323846264338327950288419716939937510), 1.5)), pow23_four_minus_pi, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<double>(pow((3.14159265358979323846264338327950288419716939937510), 2.71828182845904523536028747135266249775724709369995)), pi_pow_e, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<double>(pow((3.14159265358979323846264338327950288419716939937510), 0.33333333333333333333333333333333333333333333333333)), cbrt_pi, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<double>(exp(-0.5)), exp_minus_half, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<double>(pow(2.71828182845904523536028747135266249775724709369995, 3.14159265358979323846264338327950288419716939937510)), e_pow_pi, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<double>(pow((4 - 3.14159265358979323846264338327950288419716939937510), 1.5)), pow23_four_minus_pi, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<double>(pow((3.14159265358979323846264338327950288419716939937510), 2.71828182845904523536028747135266249775724709369995)), pi_pow_e, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<double>(pow((3.14159265358979323846264338327950288419716939937510), 0.33333333333333333333333333333333333333333333333333)), cbrt_pi, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<double>(exp(-0.5)), exp_minus_half, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<double>(pow(2.71828182845904523536028747135266249775724709369995, 3.14159265358979323846264338327950288419716939937510)), e_pow_pi, tolerance);
#else // Only double, so no suffix .
BOOST_CHECK_CLOSE_FRACTION(static_cast<double>(pow((4 - 3.14159265358979323846264338327950288419716939937510), 1.5)), pow23_four_minus_pi, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<double>(pow((3.14159265358979323846264338327950288419716939937510), 2.71828182845904523536028747135266249775724709369995)), pi_pow_e, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<double>(pow((3.14159265358979323846264338327950288419716939937510), 0.33333333333333333333333333333333333333333333333333)), cbrt_pi, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<double>(exp(-0.5)), exp_minus_half, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<double>(pow((4 - 3.14159265358979323846264338327950288419716939937510), 1.5)), pow23_four_minus_pi, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<double>(pow((3.14159265358979323846264338327950288419716939937510), 2.71828182845904523536028747135266249775724709369995)), pi_pow_e, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<double>(pow((3.14159265358979323846264338327950288419716939937510), 0.33333333333333333333333333333333333333333333333333)), cbrt_pi, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<double>(exp(-0.5)), exp_minus_half, tolerance);
#endif
// Rational fractions.
BOOST_CHECK_CLOSE_FRACTION(static_cast<double>(0.333333333333333333333333333333333333333), third, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<double>(0.666666666666666666666666666666666666667), two_thirds, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<double>(0.75), three_quarters, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<double>(0.333333333333333333333333333333333333333), third, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<double>(0.666666666666666666666666666666666666667), two_thirds, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<double>(0.75), three_quarters, tolerance);
// Two and related.
BOOST_CHECK_CLOSE_FRACTION(static_cast<double>(sqrt(2.)), root_two, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<double>(sqrt(3.)), root_three, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<double>(sqrt(2.)/2), half_root_two, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<double>(log(2.)), ln_two, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<double>(log(log(2.0))), ln_ln_two, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<double>(sqrt(log(4.0))), root_ln_four, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<double>(1/sqrt(2.0)), one_div_root_two, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<double>(sqrt(2.)), root_two, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<double>(sqrt(3.)), root_three, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<double>(sqrt(2.)/2), half_root_two, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<double>(log(2.)), ln_two, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<double>(log(log(2.0))), ln_ln_two, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<double>(sqrt(log(4.0))), root_ln_four, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<double>(1/sqrt(2.0)), one_div_root_two, tolerance);
// pi.
BOOST_CHECK_CLOSE_FRACTION(static_cast<double>(3.14159265358979323846264338327950288419716939937510), pi, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<double>(3.14159265358979323846264338327950288419716939937510/2), half_pi, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<double>(3.14159265358979323846264338327950288419716939937510/3), third_pi, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<double>(3.14159265358979323846264338327950288419716939937510/6), sixth_pi, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<double>(2 * 3.14159265358979323846264338327950288419716939937510), two_pi, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<double>(3 * 3.14159265358979323846264338327950288419716939937510 / 4), three_quarters_pi, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<double>(4 * 3.14159265358979323846264338327950288419716939937510 / 3), four_thirds_pi, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<double>(1 / (2 * 3.14159265358979323846264338327950288419716939937510)), one_div_two_pi, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<double>(sqrt(3.14159265358979323846264338327950288419716939937510)), root_pi, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<double>(sqrt(3.14159265358979323846264338327950288419716939937510 / 2)), root_half_pi, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<double>(sqrt(2 * 3.14159265358979323846264338327950288419716939937510)), root_two_pi, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<double>(1 / sqrt(3.14159265358979323846264338327950288419716939937510)), one_div_root_pi, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<double>(3.14159265358979323846264338327950288419716939937510), pi, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<double>(3.14159265358979323846264338327950288419716939937510/2), half_pi, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<double>(3.14159265358979323846264338327950288419716939937510/3), third_pi, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<double>(3.14159265358979323846264338327950288419716939937510/6), sixth_pi, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<double>(2 * 3.14159265358979323846264338327950288419716939937510), two_pi, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<double>(3 * 3.14159265358979323846264338327950288419716939937510 / 4), three_quarters_pi, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<double>(4 * 3.14159265358979323846264338327950288419716939937510 / 3), four_thirds_pi, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<double>(1 / (2 * 3.14159265358979323846264338327950288419716939937510)), one_div_two_pi, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<double>(sqrt(3.14159265358979323846264338327950288419716939937510)), root_pi, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<double>(sqrt(3.14159265358979323846264338327950288419716939937510 / 2)), root_half_pi, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<double>(sqrt(2 * 3.14159265358979323846264338327950288419716939937510)), root_two_pi, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<double>(1 / sqrt(3.14159265358979323846264338327950288419716939937510)), one_div_root_pi, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<double>(1 / sqrt(2 * 3.14159265358979323846264338327950288419716939937510)), one_div_root_two_pi, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<double>(sqrt(1. / 3.14159265358979323846264338327950288419716939937510)), root_one_div_pi, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<double>(3.14159265358979323846264338327950288419716939937510 - 3.), pi_minus_three, tolerance * 2 ); // tolerance * 2 because of cancellation loss.
@@ -425,11 +427,11 @@ void test_double_spots()
BOOST_CHECK_CLOSE_FRACTION(static_cast<double>(3.14159265358979323846264338327950288419716939937510 * 3.14159265358979323846264338327950288419716939937510 * 3.14159265358979323846264338327950288419716939937510), pi_cubed, tolerance); // See above.
// BOOST_CHECK_CLOSE_FRACTION(static_cast<double>(3.14159265358979323846264338327950288419716939937510 * 3.14159265358979323846264338327950288419716939937510), cbrt_pi, tolerance); // See above.
BOOST_CHECK_CLOSE_FRACTION(cbrt_pi * cbrt_pi * cbrt_pi, pi, tolerance);
BOOST_CHECK_CLOSE_FRACTION((static_cast<double>(1)/cbrt_pi), one_div_cbrt_pi, tolerance);
BOOST_CHECK_CLOSE_FRACTION(cbrt_pi * cbrt_pi * cbrt_pi, pi, tolerance);
BOOST_CHECK_CLOSE_FRACTION((static_cast<double>(1)/cbrt_pi), one_div_cbrt_pi, tolerance);
// Euler
BOOST_CHECK_CLOSE_FRACTION(static_cast<double>(2.71828182845904523536028747135266249775724709369995), e, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<double>(2.71828182845904523536028747135266249775724709369995), e, tolerance);
//BOOST_CHECK_CLOSE_FRACTION(static_cast<double>(exp(-0.5)), exp_minus_half, tolerance); // See above.
BOOST_CHECK_CLOSE_FRACTION(pow(e, pi), e_pow_pi, tolerance); // See also above.
@@ -461,7 +463,7 @@ void test_double_spots()
BOOST_CHECK_CLOSE_FRACTION(.91596559417721901505460351493238411077414937428167213, catalan, tolerance); // A006752 as a constant in OEIS.
BOOST_CHECK_CLOSE_FRACTION(1.1395470994046486574927930193898461120875997958365518247216557100852480077060706857071875468869385150, extreme_value_skewness, tolerance); // Mathematica: N[12 Sqrt[6] Zeta[3]/Pi^3, 1101]
BOOST_CHECK_CLOSE_FRACTION(0.6311106578189371381918993515442277798440422031347194976580945856929268196174737254599050270325373067, rayleigh_skewness, tolerance); // Mathematica: N[2 Sqrt[Pi] (Pi - 3)/((4 - Pi)^(3/2)), 1100]
BOOST_CHECK_CLOSE_FRACTION(2.450893006876380628486604106197544154e-01, rayleigh_kurtosis_excess, tolerance);
BOOST_CHECK_CLOSE_FRACTION(2.450893006876380628486604106197544154e-01, rayleigh_kurtosis_excess, tolerance);
BOOST_CHECK_CLOSE_FRACTION(2.68545200106530644530971483548179569382038229399446295305115234555721885953715200280114117493184769799515, khinchin, tolerance ); // A002210 as a constant https://oeis.org/A002210/constant
BOOST_CHECK_CLOSE_FRACTION(1.2824271291006226368753425688697917277676889273250011, glaisher, tolerance ); // https://oeis.org/A074962/constant
@@ -470,7 +472,7 @@ void test_double_spots()
void test_long_double_spots()
{
// Basic sanity checks for constants in boost::math::long double_constants::
// for example: boost::math::long_double_constants::pi
// for example: boost::math::long_double_constants::pi
// (rather than boost::math::constants::pi<long double>() ).
// All constants are tested here using at least long double precision
@@ -482,61 +484,61 @@ void test_long_double_spots()
using namespace boost::math::long_double_constants;
BOOST_MATH_STD_USING
BOOST_CHECK_CLOSE_FRACTION(static_cast<long double>(3.14159265358979323846264338327950288419716939937510L), pi, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<long double>(sqrt(3.14159265358979323846264338327950288419716939937510L)), root_pi, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<long double>(sqrt(3.14159265358979323846264338327950288419716939937510L/2)), root_half_pi, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<long double>(sqrt(3.14159265358979323846264338327950288419716939937510L * 2)), root_two_pi, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<long double>(sqrt(log(4.0L))), root_ln_four, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<long double>(2.71828182845904523536028747135266249775724709369995L), e, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<long double>(0.5), half, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<long double>(0.57721566490153286060651209008240243104259335L), euler, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<long double>(sqrt(2.0L)), root_two, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<long double>(log(2.0L)), ln_two, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<long double>(log(log(2.0L))), ln_ln_two, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<long double>(1)/3, third, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<long double>(2)/3, twothirds, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<long double>(0.14159265358979323846264338327950288419716939937510L), pi_minus_three, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<long double>(4.L - 3.14159265358979323846264338327950288419716939937510L), four_minus_pi, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<long double>(3.14159265358979323846264338327950288419716939937510L), pi, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<long double>(sqrt(3.14159265358979323846264338327950288419716939937510L)), root_pi, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<long double>(sqrt(3.14159265358979323846264338327950288419716939937510L/2)), root_half_pi, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<long double>(sqrt(3.14159265358979323846264338327950288419716939937510L * 2)), root_two_pi, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<long double>(sqrt(log(4.0L))), root_ln_four, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<long double>(2.71828182845904523536028747135266249775724709369995L), e, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<long double>(0.5), half, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<long double>(0.57721566490153286060651209008240243104259335L), euler, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<long double>(sqrt(2.0L)), root_two, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<long double>(log(2.0L)), ln_two, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<long double>(log(log(2.0L))), ln_ln_two, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<long double>(1)/3, third, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<long double>(2)/3, twothirds, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<long double>(0.14159265358979323846264338327950288419716939937510L), pi_minus_three, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<long double>(4.L - 3.14159265358979323846264338327950288419716939937510L), four_minus_pi, tolerance);
#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
BOOST_CHECK_CLOSE_FRACTION(static_cast<long double>(pow((4 - 3.14159265358979323846264338327950288419716939937510L), 1.5L)), pow23_four_minus_pi, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<long double>(pow((3.14159265358979323846264338327950288419716939937510L), 2.71828182845904523536028747135266249775724709369995L)), pi_pow_e, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<long double>(pow((3.14159265358979323846264338327950288419716939937510L), 0.33333333333333333333333333333333333333333333333333L)), cbrt_pi, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<long double>(exp(-0.5L)), exp_minus_half, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<long double>(pow(2.71828182845904523536028747135266249775724709369995L, 3.14159265358979323846264338327950288419716939937510L)), e_pow_pi, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<long double>(pow((4 - 3.14159265358979323846264338327950288419716939937510L), 1.5L)), pow23_four_minus_pi, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<long double>(pow((3.14159265358979323846264338327950288419716939937510L), 2.71828182845904523536028747135266249775724709369995L)), pi_pow_e, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<long double>(pow((3.14159265358979323846264338327950288419716939937510L), 0.33333333333333333333333333333333333333333333333333L)), cbrt_pi, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<long double>(exp(-0.5L)), exp_minus_half, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<long double>(pow(2.71828182845904523536028747135266249775724709369995L, 3.14159265358979323846264338327950288419716939937510L)), e_pow_pi, tolerance);
#else // Only double, so no suffix L.
BOOST_CHECK_CLOSE_FRACTION(static_cast<long double>(pow((4 - 3.14159265358979323846264338327950288419716939937510), 1.5)), pow23_four_minus_pi, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<long double>(pow((3.14159265358979323846264338327950288419716939937510), 2.71828182845904523536028747135266249775724709369995)), pi_pow_e, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<long double>(pow((3.14159265358979323846264338327950288419716939937510), 0.33333333333333333333333333333333333333333333333333)), cbrt_pi, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<long double>(exp(-0.5)), exp_minus_half, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<long double>(pow((4 - 3.14159265358979323846264338327950288419716939937510), 1.5)), pow23_four_minus_pi, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<long double>(pow((3.14159265358979323846264338327950288419716939937510), 2.71828182845904523536028747135266249775724709369995)), pi_pow_e, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<long double>(pow((3.14159265358979323846264338327950288419716939937510), 0.33333333333333333333333333333333333333333333333333)), cbrt_pi, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<long double>(exp(-0.5)), exp_minus_half, tolerance);
#endif
// Rational fractions.
BOOST_CHECK_CLOSE_FRACTION(static_cast<long double>(0.333333333333333333333333333333333333333L), third, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<long double>(0.666666666666666666666666666666666666667L), two_thirds, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<long double>(0.75L), three_quarters, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<long double>(0.333333333333333333333333333333333333333L), third, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<long double>(0.666666666666666666666666666666666666667L), two_thirds, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<long double>(0.75L), three_quarters, tolerance);
// Two and related.
BOOST_CHECK_CLOSE_FRACTION(static_cast<long double>(sqrt(2.L)), root_two, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<long double>(sqrt(3.L)), root_three, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<long double>(sqrt(2.L)/2), half_root_two, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<long double>(log(2.L)), ln_two, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<long double>(log(log(2.0L))), ln_ln_two, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<long double>(sqrt(log(4.0L))), root_ln_four, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<long double>(1/sqrt(2.0L)), one_div_root_two, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<long double>(sqrt(2.L)), root_two, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<long double>(sqrt(3.L)), root_three, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<long double>(sqrt(2.L)/2), half_root_two, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<long double>(log(2.L)), ln_two, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<long double>(log(log(2.0L))), ln_ln_two, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<long double>(sqrt(log(4.0L))), root_ln_four, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<long double>(1/sqrt(2.0L)), one_div_root_two, tolerance);
// pi.
BOOST_CHECK_CLOSE_FRACTION(static_cast<long double>(3.14159265358979323846264338327950288419716939937510L), pi, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<long double>(3.14159265358979323846264338327950288419716939937510L/2), half_pi, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<long double>(3.14159265358979323846264338327950288419716939937510L/3), third_pi, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<long double>(3.14159265358979323846264338327950288419716939937510L/6), sixth_pi, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<long double>(2 * 3.14159265358979323846264338327950288419716939937510L), two_pi, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<long double>(3 * 3.14159265358979323846264338327950288419716939937510L / 4), three_quarters_pi, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<long double>(4 * 3.14159265358979323846264338327950288419716939937510L / 3), four_thirds_pi, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<long double>(1 / (2 * 3.14159265358979323846264338327950288419716939937510L)), one_div_two_pi, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<long double>(sqrt(3.14159265358979323846264338327950288419716939937510L)), root_pi, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<long double>(sqrt(3.14159265358979323846264338327950288419716939937510L / 2)), root_half_pi, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<long double>(sqrt(2 * 3.14159265358979323846264338327950288419716939937510L)), root_two_pi, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<long double>(1 / sqrt(3.14159265358979323846264338327950288419716939937510L)), one_div_root_pi, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<long double>(3.14159265358979323846264338327950288419716939937510L), pi, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<long double>(3.14159265358979323846264338327950288419716939937510L/2), half_pi, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<long double>(3.14159265358979323846264338327950288419716939937510L/3), third_pi, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<long double>(3.14159265358979323846264338327950288419716939937510L/6), sixth_pi, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<long double>(2 * 3.14159265358979323846264338327950288419716939937510L), two_pi, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<long double>(3 * 3.14159265358979323846264338327950288419716939937510L / 4), three_quarters_pi, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<long double>(4 * 3.14159265358979323846264338327950288419716939937510L / 3), four_thirds_pi, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<long double>(1 / (2 * 3.14159265358979323846264338327950288419716939937510L)), one_div_two_pi, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<long double>(sqrt(3.14159265358979323846264338327950288419716939937510L)), root_pi, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<long double>(sqrt(3.14159265358979323846264338327950288419716939937510L / 2)), root_half_pi, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<long double>(sqrt(2 * 3.14159265358979323846264338327950288419716939937510L)), root_two_pi, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<long double>(1 / sqrt(3.14159265358979323846264338327950288419716939937510L)), one_div_root_pi, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<long double>(1 / sqrt(2 * 3.14159265358979323846264338327950288419716939937510L)), one_div_root_two_pi, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<long double>(sqrt(1. / 3.14159265358979323846264338327950288419716939937510L)), root_one_div_pi, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<long double>(3.14159265358979323846264338327950288419716939937510L - 3.L), pi_minus_three, tolerance * 2 ); // tolerance * 2 because of cancellation loss.
@@ -549,14 +551,14 @@ void test_long_double_spots()
BOOST_CHECK_CLOSE_FRACTION(static_cast<long double>(3.14159265358979323846264338327950288419716939937510L * 3.14159265358979323846264338327950288419716939937510L * 3.14159265358979323846264338327950288419716939937510L), pi_cubed, tolerance); // See above.
// BOOST_CHECK_CLOSE_FRACTION(static_cast<long double>(3.14159265358979323846264338327950288419716939937510L * 3.14159265358979323846264338327950288419716939937510L), cbrt_pi, tolerance); // See above.
BOOST_CHECK_CLOSE_FRACTION(cbrt_pi * cbrt_pi * cbrt_pi, pi, tolerance);
BOOST_CHECK_CLOSE_FRACTION((static_cast<long double>(1)/cbrt_pi), one_div_cbrt_pi, tolerance);
BOOST_CHECK_CLOSE_FRACTION(cbrt_pi * cbrt_pi * cbrt_pi, pi, tolerance);
BOOST_CHECK_CLOSE_FRACTION((static_cast<long double>(1)/cbrt_pi), one_div_cbrt_pi, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<long double>(6.366197723675813430755350534900574481378385829618257E-1L), two_div_pi, tolerance * 3); // 2/pi
BOOST_CHECK_CLOSE_FRACTION(static_cast<long double>(6.366197723675813430755350534900574481378385829618257E-1L), two_div_pi, tolerance * 3); // 2/pi
BOOST_CHECK_CLOSE_FRACTION(static_cast<long double>(7.97884560802865355879892119868763736951717262329869E-1L), root_two_div_pi, tolerance * 3); // sqrt(2/pi)
// Euler
BOOST_CHECK_CLOSE_FRACTION(static_cast<long double>(2.71828182845904523536028747135266249775724709369995L), e, tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<long double>(2.71828182845904523536028747135266249775724709369995L), e, tolerance);
//BOOST_CHECK_CLOSE_FRACTION(static_cast<long double>(exp(-0.5L)), exp_minus_half, tolerance); // See above.
BOOST_CHECK_CLOSE_FRACTION(pow(e, pi), e_pow_pi, tolerance); // See also above.
@@ -588,7 +590,7 @@ void test_long_double_spots()
BOOST_CHECK_CLOSE_FRACTION(.91596559417721901505460351493238411077414937428167213L, catalan, tolerance); // A006752 as a constant in OEIS.
BOOST_CHECK_CLOSE_FRACTION(1.1395470994046486574927930193898461120875997958365518247216557100852480077060706857071875468869385150L, extreme_value_skewness, tolerance); // Mathematica: N[12 Sqrt[6] Zeta[3]/Pi^3, 1101]
BOOST_CHECK_CLOSE_FRACTION(0.6311106578189371381918993515442277798440422031347194976580945856929268196174737254599050270325373067L, rayleigh_skewness, tolerance); // Mathematica: N[2 Sqrt[Pi] (Pi - 3)/((4 - Pi)^(3/2)), 1100]
BOOST_CHECK_CLOSE_FRACTION(2.450893006876380628486604106197544154e-01L, rayleigh_kurtosis_excess, tolerance);
BOOST_CHECK_CLOSE_FRACTION(2.450893006876380628486604106197544154e-01L, rayleigh_kurtosis_excess, tolerance);
BOOST_CHECK_CLOSE_FRACTION(2.68545200106530644530971483548179569382038229399446295305115234555721885953715200280114117493184769799515L, khinchin, tolerance ); // A002210 as a constant https://oeis.org/A002210/constant
BOOST_CHECK_CLOSE_FRACTION(1.2824271291006226368753425688697917277676889273250011L, glaisher, tolerance ); // https://oeis.org/A074962/constant
@@ -598,7 +600,7 @@ template <class Policy>
void test_real_concept_policy(const Policy&)
{
// Basic sanity checks for constants using real_concept.
// Parameter Policy is used to control precision.
// Parameter Policy is used to control precision.
using boost::math::concepts::real_concept;
@@ -612,61 +614,61 @@ void test_real_concept_policy(const Policy&)
using namespace boost::math::constants;
BOOST_MATH_STD_USING
BOOST_CHECK_CLOSE_FRACTION(3.14159265358979323846264338327950288419716939937510L, (pi<real_concept, Policy>)(), tolerance);
BOOST_CHECK_CLOSE_FRACTION(sqrt(3.14159265358979323846264338327950288419716939937510L), (root_pi<real_concept, Policy>)(), tolerance);
BOOST_CHECK_CLOSE_FRACTION(sqrt(3.14159265358979323846264338327950288419716939937510L/2), (root_half_pi<real_concept, Policy>)(), tolerance);
BOOST_CHECK_CLOSE_FRACTION(sqrt(3.14159265358979323846264338327950288419716939937510L * 2), (root_two_pi<real_concept, Policy>)(), tolerance);
BOOST_CHECK_CLOSE_FRACTION(sqrt(log(4.0L)), (root_ln_four<real_concept, Policy>)(), tolerance);
BOOST_CHECK_CLOSE_FRACTION(2.71828182845904523536028747135266249775724709369995L, (e<real_concept, Policy>)(), tolerance);
BOOST_CHECK_CLOSE_FRACTION(0.5, (half<real_concept, Policy>)(), tolerance);
BOOST_CHECK_CLOSE_FRACTION(0.57721566490153286060651209008240243104259335L, (euler<real_concept, Policy>)(), tolerance);
BOOST_CHECK_CLOSE_FRACTION(sqrt(2.0L), (root_two<real_concept, Policy>)(), tolerance);
BOOST_CHECK_CLOSE_FRACTION(log(2.0L), (ln_two<real_concept, Policy>)(), tolerance);
BOOST_CHECK_CLOSE_FRACTION(log(log(2.0L)), (ln_ln_two<real_concept, Policy>)(), tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<long double>(1)/3, (third<real_concept, Policy>)(), tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<long double>(2)/3, (twothirds<real_concept, Policy>)(), tolerance);
BOOST_CHECK_CLOSE_FRACTION(0.14159265358979323846264338327950288419716939937510L, (pi_minus_three<real_concept, Policy>)(), tolerance);
BOOST_CHECK_CLOSE_FRACTION(4.L - 3.14159265358979323846264338327950288419716939937510L, (four_minus_pi<real_concept, Policy>)(), tolerance);
BOOST_CHECK_CLOSE_FRACTION(3.14159265358979323846264338327950288419716939937510L, (pi<real_concept, Policy>)(), tolerance);
BOOST_CHECK_CLOSE_FRACTION(sqrt(3.14159265358979323846264338327950288419716939937510L), (root_pi<real_concept, Policy>)(), tolerance);
BOOST_CHECK_CLOSE_FRACTION(sqrt(3.14159265358979323846264338327950288419716939937510L/2), (root_half_pi<real_concept, Policy>)(), tolerance);
BOOST_CHECK_CLOSE_FRACTION(sqrt(3.14159265358979323846264338327950288419716939937510L * 2), (root_two_pi<real_concept, Policy>)(), tolerance);
BOOST_CHECK_CLOSE_FRACTION(sqrt(log(4.0L)), (root_ln_four<real_concept, Policy>)(), tolerance);
BOOST_CHECK_CLOSE_FRACTION(2.71828182845904523536028747135266249775724709369995L, (e<real_concept, Policy>)(), tolerance);
BOOST_CHECK_CLOSE_FRACTION(0.5, (half<real_concept, Policy>)(), tolerance);
BOOST_CHECK_CLOSE_FRACTION(0.57721566490153286060651209008240243104259335L, (euler<real_concept, Policy>)(), tolerance);
BOOST_CHECK_CLOSE_FRACTION(sqrt(2.0L), (root_two<real_concept, Policy>)(), tolerance);
BOOST_CHECK_CLOSE_FRACTION(log(2.0L), (ln_two<real_concept, Policy>)(), tolerance);
BOOST_CHECK_CLOSE_FRACTION(log(log(2.0L)), (ln_ln_two<real_concept, Policy>)(), tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<long double>(1)/3, (third<real_concept, Policy>)(), tolerance);
BOOST_CHECK_CLOSE_FRACTION(static_cast<long double>(2)/3, (twothirds<real_concept, Policy>)(), tolerance);
BOOST_CHECK_CLOSE_FRACTION(0.14159265358979323846264338327950288419716939937510L, (pi_minus_three<real_concept, Policy>)(), tolerance);
BOOST_CHECK_CLOSE_FRACTION(4.L - 3.14159265358979323846264338327950288419716939937510L, (four_minus_pi<real_concept, Policy>)(), tolerance);
#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
BOOST_CHECK_CLOSE_FRACTION(pow((4 - 3.14159265358979323846264338327950288419716939937510L), 1.5L), (pow23_four_minus_pi<real_concept, Policy>)(), tolerance);
BOOST_CHECK_CLOSE_FRACTION(pow((3.14159265358979323846264338327950288419716939937510L), 2.71828182845904523536028747135266249775724709369995L), (pi_pow_e<real_concept, Policy>)(), tolerance);
BOOST_CHECK_CLOSE_FRACTION(pow((3.14159265358979323846264338327950288419716939937510L), 0.33333333333333333333333333333333333333333333333333L), (cbrt_pi<real_concept, Policy>)(), tolerance);
BOOST_CHECK_CLOSE_FRACTION(exp(-0.5L), (exp_minus_half<real_concept, Policy>)(), tolerance);
BOOST_CHECK_CLOSE_FRACTION(pow(2.71828182845904523536028747135266249775724709369995L, 3.14159265358979323846264338327950288419716939937510L), (e_pow_pi<real_concept, Policy>)(), tolerance);
BOOST_CHECK_CLOSE_FRACTION(pow((4 - 3.14159265358979323846264338327950288419716939937510L), 1.5L), (pow23_four_minus_pi<real_concept, Policy>)(), tolerance);
BOOST_CHECK_CLOSE_FRACTION(pow((3.14159265358979323846264338327950288419716939937510L), 2.71828182845904523536028747135266249775724709369995L), (pi_pow_e<real_concept, Policy>)(), tolerance);
BOOST_CHECK_CLOSE_FRACTION(pow((3.14159265358979323846264338327950288419716939937510L), 0.33333333333333333333333333333333333333333333333333L), (cbrt_pi<real_concept, Policy>)(), tolerance);
BOOST_CHECK_CLOSE_FRACTION(exp(-0.5L), (exp_minus_half<real_concept, Policy>)(), tolerance);
BOOST_CHECK_CLOSE_FRACTION(pow(2.71828182845904523536028747135266249775724709369995L, 3.14159265358979323846264338327950288419716939937510L), (e_pow_pi<real_concept, Policy>)(), tolerance);
#else // Only double, so no suffix L.
BOOST_CHECK_CLOSE_FRACTION(pow((4 - 3.14159265358979323846264338327950288419716939937510), 1.5), (pow23_four_minus_pi<real_concept, Policy>)(), tolerance);
BOOST_CHECK_CLOSE_FRACTION(pow((3.14159265358979323846264338327950288419716939937510), 2.71828182845904523536028747135266249775724709369995), (pi_pow_e<real_concept, Policy>)(), tolerance);
BOOST_CHECK_CLOSE_FRACTION(pow((3.14159265358979323846264338327950288419716939937510), 0.33333333333333333333333333333333333333333333333333), (cbrt_pi<real_concept, Policy>)(), tolerance);
BOOST_CHECK_CLOSE_FRACTION(exp(-0.5), (exp_minus_half<real_concept, Policy>)(), tolerance);
BOOST_CHECK_CLOSE_FRACTION(pow((4 - 3.14159265358979323846264338327950288419716939937510), 1.5), (pow23_four_minus_pi<real_concept, Policy>)(), tolerance);
BOOST_CHECK_CLOSE_FRACTION(pow((3.14159265358979323846264338327950288419716939937510), 2.71828182845904523536028747135266249775724709369995), (pi_pow_e<real_concept, Policy>)(), tolerance);
BOOST_CHECK_CLOSE_FRACTION(pow((3.14159265358979323846264338327950288419716939937510), 0.33333333333333333333333333333333333333333333333333), (cbrt_pi<real_concept, Policy>)(), tolerance);
BOOST_CHECK_CLOSE_FRACTION(exp(-0.5), (exp_minus_half<real_concept, Policy>)(), tolerance);
#endif
// Rational fractions.
BOOST_CHECK_CLOSE_FRACTION(0.333333333333333333333333333333333333333L, (third<real_concept, Policy>)(), tolerance);
BOOST_CHECK_CLOSE_FRACTION(0.666666666666666666666666666666666666667L, (two_thirds<real_concept, Policy>)(), tolerance);
BOOST_CHECK_CLOSE_FRACTION(0.75L, (three_quarters<real_concept, Policy>)(), tolerance);
BOOST_CHECK_CLOSE_FRACTION(0.333333333333333333333333333333333333333L, (third<real_concept, Policy>)(), tolerance);
BOOST_CHECK_CLOSE_FRACTION(0.666666666666666666666666666666666666667L, (two_thirds<real_concept, Policy>)(), tolerance);
BOOST_CHECK_CLOSE_FRACTION(0.75L, (three_quarters<real_concept, Policy>)(), tolerance);
// Two and related.
BOOST_CHECK_CLOSE_FRACTION(sqrt(2.L), (root_two<real_concept, Policy>)(), tolerance);
BOOST_CHECK_CLOSE_FRACTION(sqrt(3.L), (root_three<real_concept, Policy>)(), tolerance);
BOOST_CHECK_CLOSE_FRACTION(sqrt(2.L)/2, (half_root_two<real_concept, Policy>)(), tolerance);
BOOST_CHECK_CLOSE_FRACTION(log(2.L), (ln_two<real_concept, Policy>)(), tolerance);
BOOST_CHECK_CLOSE_FRACTION(log(log(2.0L)), (ln_ln_two<real_concept, Policy>)(), tolerance);
BOOST_CHECK_CLOSE_FRACTION(sqrt(log(4.0L)), (root_ln_four<real_concept, Policy>)(), tolerance);
BOOST_CHECK_CLOSE_FRACTION(1/sqrt(2.0L), (one_div_root_two<real_concept, Policy>)(), tolerance);
BOOST_CHECK_CLOSE_FRACTION(sqrt(2.L), (root_two<real_concept, Policy>)(), tolerance);
BOOST_CHECK_CLOSE_FRACTION(sqrt(3.L), (root_three<real_concept, Policy>)(), tolerance);
BOOST_CHECK_CLOSE_FRACTION(sqrt(2.L)/2, (half_root_two<real_concept, Policy>)(), tolerance);
BOOST_CHECK_CLOSE_FRACTION(log(2.L), (ln_two<real_concept, Policy>)(), tolerance);
BOOST_CHECK_CLOSE_FRACTION(log(log(2.0L)), (ln_ln_two<real_concept, Policy>)(), tolerance);
BOOST_CHECK_CLOSE_FRACTION(sqrt(log(4.0L)), (root_ln_four<real_concept, Policy>)(), tolerance);
BOOST_CHECK_CLOSE_FRACTION(1/sqrt(2.0L), (one_div_root_two<real_concept, Policy>)(), tolerance);
// pi.
BOOST_CHECK_CLOSE_FRACTION(3.14159265358979323846264338327950288419716939937510L, (pi<real_concept, Policy>)(), tolerance);
BOOST_CHECK_CLOSE_FRACTION(3.14159265358979323846264338327950288419716939937510L/2, (half_pi<real_concept, Policy>)(), tolerance);
BOOST_CHECK_CLOSE_FRACTION(3.14159265358979323846264338327950288419716939937510L/3, (third_pi<real_concept, Policy>)(), tolerance);
BOOST_CHECK_CLOSE_FRACTION(3.14159265358979323846264338327950288419716939937510L/6, (sixth_pi<real_concept, Policy>)(), tolerance);
BOOST_CHECK_CLOSE_FRACTION(2 * 3.14159265358979323846264338327950288419716939937510L, (two_pi<real_concept, Policy>)(), tolerance);
BOOST_CHECK_CLOSE_FRACTION(3 * 3.14159265358979323846264338327950288419716939937510L / 4, (three_quarters_pi<real_concept, Policy>)(), tolerance);
BOOST_CHECK_CLOSE_FRACTION(4 * 3.14159265358979323846264338327950288419716939937510L / 3, (four_thirds_pi<real_concept, Policy>)(), tolerance);
BOOST_CHECK_CLOSE_FRACTION(1 / (2 * 3.14159265358979323846264338327950288419716939937510L), (one_div_two_pi<real_concept, Policy>)(), tolerance);
BOOST_CHECK_CLOSE_FRACTION(sqrt(3.14159265358979323846264338327950288419716939937510L), (root_pi<real_concept, Policy>)(), tolerance);
BOOST_CHECK_CLOSE_FRACTION(sqrt(3.14159265358979323846264338327950288419716939937510L / 2), (root_half_pi<real_concept, Policy>)(), tolerance);
BOOST_CHECK_CLOSE_FRACTION(sqrt(2 * 3.14159265358979323846264338327950288419716939937510L), (root_two_pi<real_concept, Policy>)(), tolerance);
BOOST_CHECK_CLOSE_FRACTION(1 / sqrt(3.14159265358979323846264338327950288419716939937510L), (one_div_root_pi<real_concept, Policy>)(), tolerance);
BOOST_CHECK_CLOSE_FRACTION(3.14159265358979323846264338327950288419716939937510L, (pi<real_concept, Policy>)(), tolerance);
BOOST_CHECK_CLOSE_FRACTION(3.14159265358979323846264338327950288419716939937510L/2, (half_pi<real_concept, Policy>)(), tolerance);
BOOST_CHECK_CLOSE_FRACTION(3.14159265358979323846264338327950288419716939937510L/3, (third_pi<real_concept, Policy>)(), tolerance);
BOOST_CHECK_CLOSE_FRACTION(3.14159265358979323846264338327950288419716939937510L/6, (sixth_pi<real_concept, Policy>)(), tolerance);
BOOST_CHECK_CLOSE_FRACTION(2 * 3.14159265358979323846264338327950288419716939937510L, (two_pi<real_concept, Policy>)(), tolerance);
BOOST_CHECK_CLOSE_FRACTION(3 * 3.14159265358979323846264338327950288419716939937510L / 4, (three_quarters_pi<real_concept, Policy>)(), tolerance);
BOOST_CHECK_CLOSE_FRACTION(4 * 3.14159265358979323846264338327950288419716939937510L / 3, (four_thirds_pi<real_concept, Policy>)(), tolerance);
BOOST_CHECK_CLOSE_FRACTION(1 / (2 * 3.14159265358979323846264338327950288419716939937510L), (one_div_two_pi<real_concept, Policy>)(), tolerance);
BOOST_CHECK_CLOSE_FRACTION(sqrt(3.14159265358979323846264338327950288419716939937510L), (root_pi<real_concept, Policy>)(), tolerance);
BOOST_CHECK_CLOSE_FRACTION(sqrt(3.14159265358979323846264338327950288419716939937510L / 2), (root_half_pi<real_concept, Policy>)(), tolerance);
BOOST_CHECK_CLOSE_FRACTION(sqrt(2 * 3.14159265358979323846264338327950288419716939937510L), (root_two_pi<real_concept, Policy>)(), tolerance);
BOOST_CHECK_CLOSE_FRACTION(1 / sqrt(3.14159265358979323846264338327950288419716939937510L), (one_div_root_pi<real_concept, Policy>)(), tolerance);
BOOST_CHECK_CLOSE_FRACTION(1 / sqrt(2 * 3.14159265358979323846264338327950288419716939937510L), (one_div_root_two_pi<real_concept, Policy>)(), tolerance);
BOOST_CHECK_CLOSE_FRACTION(sqrt(1. / 3.14159265358979323846264338327950288419716939937510L), (root_one_div_pi<real_concept, Policy>)(), tolerance);
BOOST_CHECK_CLOSE_FRACTION(3.14159265358979323846264338327950288419716939937510L - 3.L, (pi_minus_three<real_concept, Policy>)(), tolerance * 2 ); // tolerance * 2 because of cancellation loss.
@@ -679,11 +681,11 @@ void test_real_concept_policy(const Policy&)
BOOST_CHECK_CLOSE_FRACTION(3.14159265358979323846264338327950288419716939937510L * 3.14159265358979323846264338327950288419716939937510L * 3.14159265358979323846264338327950288419716939937510L, (pi_cubed<real_concept, Policy>)(), tolerance); // See above.
// BOOST_CHECK_CLOSE_FRACTION(3.14159265358979323846264338327950288419716939937510L * 3.14159265358979323846264338327950288419716939937510L, (cbrt_pi<real_concept, Policy>)(), tolerance); // See above.
BOOST_CHECK_CLOSE_FRACTION((cbrt_pi<real_concept, Policy>)() * (cbrt_pi<real_concept, Policy>)() * (cbrt_pi<real_concept, Policy>)(), (pi<real_concept, Policy>)(), tolerance);
BOOST_CHECK_CLOSE_FRACTION((1)/(cbrt_pi<real_concept, Policy>)(), (one_div_cbrt_pi<real_concept, Policy>)(), tolerance);
BOOST_CHECK_CLOSE_FRACTION((cbrt_pi<real_concept, Policy>)() * (cbrt_pi<real_concept, Policy>)() * (cbrt_pi<real_concept, Policy>)(), (pi<real_concept, Policy>)(), tolerance);
BOOST_CHECK_CLOSE_FRACTION((1)/(cbrt_pi<real_concept, Policy>)(), (one_div_cbrt_pi<real_concept, Policy>)(), tolerance);
// Euler
BOOST_CHECK_CLOSE_FRACTION(2.71828182845904523536028747135266249775724709369995L, (e<real_concept, Policy>)(), tolerance);
BOOST_CHECK_CLOSE_FRACTION(2.71828182845904523536028747135266249775724709369995L, (e<real_concept, Policy>)(), tolerance);
//BOOST_CHECK_CLOSE_FRACTION(exp(-0.5L), (exp_minus_half<real_concept, Policy>)(), tolerance); // See above.
BOOST_CHECK_CLOSE_FRACTION(pow(e<real_concept, Policy>(), (pi<real_concept, Policy>)()), (e_pow_pi<real_concept, Policy>)(), tolerance); // See also above.
@@ -715,7 +717,7 @@ void test_real_concept_policy(const Policy&)
BOOST_CHECK_CLOSE_FRACTION(.91596559417721901505460351493238411077414937428167213L, (catalan<real_concept, Policy>)(), tolerance); // A006752 as a constant in OEIS.
BOOST_CHECK_CLOSE_FRACTION(1.1395470994046486574927930193898461120875997958365518247216557100852480077060706857071875468869385150L, (extreme_value_skewness<real_concept, Policy>)(), tolerance); // Mathematica: N[12 Sqrt[6] Zeta[3]/Pi^3, 1101]
BOOST_CHECK_CLOSE_FRACTION(0.6311106578189371381918993515442277798440422031347194976580945856929268196174737254599050270325373067L, (rayleigh_skewness<real_concept, Policy>)(), tolerance); // Mathematica: N[2 Sqrt[Pi] (Pi - 3)/((4 - Pi)^(3/2)), 1100]
BOOST_CHECK_CLOSE_FRACTION(2.450893006876380628486604106197544154e-01L, (rayleigh_kurtosis_excess<real_concept, Policy>)(), tolerance);
BOOST_CHECK_CLOSE_FRACTION(2.450893006876380628486604106197544154e-01L, (rayleigh_kurtosis_excess<real_concept, Policy>)(), tolerance);
BOOST_CHECK_CLOSE_FRACTION(2.68545200106530644530971483548179569382038229399446295305115234555721885953715200280114117493184769799515L, (khinchin<real_concept, Policy>)(), tolerance ); // A002210 as a constant https://oeis.org/A002210/constant
BOOST_CHECK_CLOSE_FRACTION(1.2824271291006226368753425688697917277676889273250011L, (glaisher<real_concept, Policy>)(), tolerance ); // https://oeis.org/A074962/constant
@@ -725,13 +727,13 @@ void test_real_concept_policy(const Policy&)
if(boost::math::tools::digits<real_concept>() > boost::math::constants::max_string_digits)
{
// This suffers from cancellation error, so increased tolerance:
BOOST_CHECK_CLOSE_FRACTION((static_cast<real_concept>(4. - 3.14159265358979323846264338327950288419716939937510L)), (four_minus_pi<real_concept, Policy>)(), tolerance * 3);
BOOST_CHECK_CLOSE_FRACTION((static_cast<real_concept>(0.14159265358979323846264338327950288419716939937510L)), (pi_minus_three<real_concept, Policy>)(), tolerance * 3);
BOOST_CHECK_CLOSE_FRACTION((static_cast<real_concept>(4. - 3.14159265358979323846264338327950288419716939937510L)), (four_minus_pi<real_concept, Policy>)(), tolerance * 3);
BOOST_CHECK_CLOSE_FRACTION((static_cast<real_concept>(0.14159265358979323846264338327950288419716939937510L)), (pi_minus_three<real_concept, Policy>)(), tolerance * 3);
}
else
{
BOOST_CHECK_CLOSE_FRACTION((static_cast<real_concept>(4. - 3.14159265358979323846264338327950288419716939937510L)), (four_minus_pi<real_concept, Policy>)(), tolerance);
BOOST_CHECK_CLOSE_FRACTION((static_cast<real_concept>(0.14159265358979323846264338327950288419716939937510L)), (pi_minus_three<real_concept, Policy>)(), tolerance);
BOOST_CHECK_CLOSE_FRACTION((static_cast<real_concept>(4. - 3.14159265358979323846264338327950288419716939937510L)), (four_minus_pi<real_concept, Policy>)(), tolerance);
BOOST_CHECK_CLOSE_FRACTION((static_cast<real_concept>(0.14159265358979323846264338327950288419716939937510L)), (pi_minus_three<real_concept, Policy>)(), tolerance);
}
} // template <class boost::math::concepts::real_concept>void test_spots(boost::math::concepts::real_concept)
@@ -750,7 +752,7 @@ int test_main(int, char* [])
// (Parameter value, arbitrarily zero, only communicates the floating-point type).
test_spots(0.0F); // Test float.
test_spots(0.0); // Test double.
test_spots(0.0); // Test double.
#ifndef BOOST_MATH_NO_LONG_DOUBLE_MATH_FUNCTIONS
test_spots(0.0L); // Test long double.
#if !BOOST_WORKAROUND(__BORLANDC__, BOOST_TESTED_AT(0x0582))
@@ -771,7 +773,7 @@ int test_main(int, char* [])
Output:
1 Feb 2012
1 Feb 2012
test_constants.cpp
test_constants.vcxproj -> J:\Cpp\MathToolkit\test\Math_test\Debug\test_constants.exe
@@ -784,7 +786,7 @@ test_constants.cpp
Tolerance for type long double is 4.44089e-016.
Tolerance for type class boost::math::concepts::real_concept is 4.44089e-016.
Tolerance for type class boost::math::concepts::big_real_concept is 1.33227e-014.
*** No errors detected
*/