Big_pi epsilon=0E-301 n_test_int=7 n_test_double=0.333333333333333314829616256247390992939472198486328125 test_double, converted back, =0.3333333333333333 test simple operations a=0.12345678901234567890 b=0.2345678901234567890 a+b=c=0.35802467913580246790 a.compareTo(b)=-1 b.compareTo(a)=1 a.movePointLeft(25)=1.2345678901234567890E-26 a.movePointRight(25)=1234567890123456789000000 a.scale()=20 a.doubleValue()=0.12345678901234568 b.setScale(8,BigDecimal.ROUND_DOWN)=0.23456789 test factorials 0! = 1 1! = 1 2! = 2 3! = 6 4! = 24 5! = 120 6! = 720 7! = 5040 8! = 40320 9! = 362880 10! = 3628800 11! = 39916800 12! = 479001600 13! = 6227020800 14! = 87178291200 15! = 1307674368000 16! = 20922789888000 17! = 355687428096000 18! = 6402373705728000 19! = 121645100408832000 20! = 2432902008176640000 21! = 51090942171709440000 22! = 1124000727777607680000 23! = 25852016738884976640000 24! = 620448401733239439360000 25! = 15511210043330985984000000 26! = 403291461126605635584000000 27! = 10888869450418352160768000000 28! = 304888344611713860501504000000 29! = 8841761993739701954543616000000 30! = 265252859812191058636308480000000 31! = 8222838654177922817725562880000000 32! = 263130836933693530167218012160000000 33! = 8683317618811886495518194401280000000 34! = 295232799039604140847618609643520000000 35! = 10333147966386144929666651337523200000000 36! = 371993326789901217467999448150835200000000 37! = 13763753091226345046315979581580902400000000 38! = 523022617466601111760007224100074291200000000 39! = 20397882081197443358640281739902897356800000000 40! = 815915283247897734345611269596115894272000000000 41! = 33452526613163807108170062053440751665152000000000 42! = 1405006117752879898543142606244511569936384000000000 43! = 60415263063373835637355132068513997507264512000000000 44! = 2658271574788448768043625811014615890319638528000000000 45! = 119622220865480194561963161495657715064383733760000000000 46! = 5502622159812088949850305428800254892961651752960000000000 47! = 258623241511168180642964355153611979969197632389120000000000 48! = 12413915592536072670862289047373375038521486354677760000000000 49! = 608281864034267560872252163321295376887552831379210240000000000 50! = 30414093201713378043612608166064768844377641568960512000000000000 51! = 1551118753287382280224243016469303211063259720016986112000000000000 52! = 80658175170943878571660636856403766975289505440883277824000000000000 53! = 4274883284060025564298013753389399649690343788366813724672000000000000 54! = 230843697339241380472092742683027581083278564571807941132288000000000000 55! = 12696403353658275925965100847566516959580321051449436762275840000000000000 56! = 710998587804863451854045647463724949736497978881168458687447040000000000000 57! = 40526919504877216755680601905432322134980384796226602145184481280000000000000 58! = 2350561331282878571829474910515074683828862318181142924420699914240000000000000 59! = 138683118545689835737939019720389406345902876772687432540821294940160000000000000 60! = 8320987112741390144276341183223364380754172606361245952449277696409600000000000000 61! = 507580213877224798800856812176625227226004528988036003099405939480985600000000000000 62! = 31469973260387937525653122354950764088012280797258232192163168247821107200000000000000 63! = 1982608315404440064116146708361898137544773690227268628106279599612729753600000000000000 64! = 126886932185884164103433389335161480802865516174545192198801894375214704230400000000000000 65! = 8247650592082470666723170306785496252186258551345437492922123134388955774976000000000000000 66! = 544344939077443064003729240247842752644293064388798874532860126869671081148416000000000000000 67! = 36471110918188685288249859096605464427167635314049524593701628500267962436943872000000000000000 68! = 2480035542436830599600990418569171581047399201355367672371710738018221445712183296000000000000000 69! = 171122452428141311372468338881272839092270544893520369393648040923257279754140647424000000000000000 70! = 11978571669969891796072783721689098736458938142546425857555362864628009582789845319680000000000000000 71! = 850478588567862317521167644239926010288584608120796235886430763388588680378079017697280000000000000000 72! = 61234458376886086861524070385274672740778091784697328983823014963978384987221689274204160000000000000000 73! = 4470115461512684340891257138125051110076800700282905015819080092370422104067183317016903680000000000000000 74! = 330788544151938641225953028221253782145683251820934971170611926835411235700971565459250872320000000000000000 75! = 24809140811395398091946477116594033660926243886570122837795894512655842677572867409443815424000000000000000000 76! = 1885494701666050254987932260861146558230394535379329335672487982961844043495537923117729972224000000000000000000 77! = 145183092028285869634070784086308284983740379224208358846781574688061991349156420080065207861248000000000000000000 78! = 11324281178206297831457521158732046228731749579488251990048962825668835325234200766245086213177344000000000000000000 79! = 894618213078297528685144171539831652069808216779571907213868063227837990693501860533361810841010176000000000000000000 80! = 71569457046263802294811533723186532165584657342365752577109445058227039255480148842668944867280814080000000000000000000 81! = 5797126020747367985879734231578109105412357244731625958745865049716390179693892056256184534249745940480000000000000000000 82! = 475364333701284174842138206989404946643813294067993328617160934076743994734899148613007131808479167119360000000000000000000 83! = 39455239697206586511897471180120610571436503407643446275224357528369751562996629334879591940103770870906880000000000000000000 84! = 3314240134565353266999387579130131288000666286242049487118846032383059131291716864129885722968716753156177920000000000000000000 85! = 281710411438055027694947944226061159480056634330574206405101912752560026159795933451040286452340924018275123200000000000000000000 86! = 24227095383672732381765523203441259715284870552429381750838764496720162249742450276789464634901319465571660595200000000000000000000 87! = 2107757298379527717213600518699389595229783738061356212322972511214654115727593174080683423236414793504734471782400000000000000000000 88! = 185482642257398439114796845645546284380220968949399346684421580986889562184028199319100141244804501828416633516851200000000000000000000 89! = 16507955160908461081216919262453619309839666236496541854913520707833171034378509739399912570787600662729080382999756800000000000000000000 90! = 1485715964481761497309522733620825737885569961284688766942216863704985393094065876545992131370884059645617234469978112000000000000000000000 91! = 135200152767840296255166568759495142147586866476906677791741734597153670771559994765685283954750449427751168336768008192000000000000000000000 92! = 12438414054641307255475324325873553077577991715875414356840239582938137710983519518443046123837041347353107486982656753664000000000000000000000 93! = 1156772507081641574759205162306240436214753229576413535186142281213246807121467315215203289516844845303838996289387078090752000000000000000000000 94! = 108736615665674308027365285256786601004186803580182872307497374434045199869417927630229109214583415458560865651202385340530688000000000000000000000 95! = 10329978488239059262599702099394727095397746340117372869212250571234293987594703124871765375385424468563282236864226607350415360000000000000000000000 96! = 991677934870949689209571401541893801158183648651267795444376054838492222809091499987689476037000748982075094738965754305639874560000000000000000000000 97! = 96192759682482119853328425949563698712343813919172976158104477319333745612481875498805879175589072651261284189679678167647067832320000000000000000000000 98! = 9426890448883247745626185743057242473809693764078951663494238777294707070023223798882976159207729119823605850588608460429412647567360000000000000000000000 99! = 933262154439441526816992388562667004907159682643816214685929638952175999932299156089414639761565182862536979208272237582511852109168640000000000000000000000 100! = 93326215443944152681699238856266700490715968264381621468592963895217599993229915608941463976156518286253697920827223758251185210916864000000000000000000000000 test sqrt sqrt(1) = 1.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 err=0E-301 sqrt(2) = 1.4142135623730950488016887242096980785696718753769480731766797379907324784621070388503875343276415727350138462309122970249248360558507372126441214970999358314132226659275055927557999505011527820605714701095599716059702745345968620147285174186408891986095523292304843087143214508397626036279952514079896 err=2E-301 sqrt(3) = 1.7320508075688772935274463415058723669428052538103806280558069794519330169088000370811461867572485756756261414154067030299699450949989524788116555120943736485280932319023055820679748201010846749232650153123432669033228866506722546689218379712270471316603678615880190499865373798593894676503475065760507 err=1E-301 sqrt(4) = 2.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 err=0E-301 sqrt(5) = 2.2360679774997896964091736687312762354406183596115257242708972454105209256378048994144144083787822749695081761507737835042532677244470738635863601215334527088667781731918791658112766453226398565805357613504175337850034233924140644420864325390972525926272288762995174024406816117759089094984923713907297 err=1E-301 sqrt(6) = 2.4494897427831780981972840747058913919659474806566701284326925672509603774573150265398594331046402348185946012266141891248588654598377573416257839512372785528289127475276765712476301052709117702234813106789866908536324433525456040338088089393745855678465747243613041442702702161742018383000815898078380 err=0E-301 sqrt(7) = 2.6457513110645905905016157536392604257102591830824501803683344592010688232302836277603928864745436106150645783384974630957435298886272147844273905558801077227171507297283238922996895948650872607009780542037238280237159411003419391160015785255963059457410351523968027164073737990740415815199044034743194 err=2E-301 sqrt(8) = 2.8284271247461900976033774484193961571393437507538961463533594759814649569242140777007750686552831454700276924618245940498496721117014744252882429941998716628264453318550111855115999010023055641211429402191199432119405490691937240294570348372817783972191046584609686174286429016795252072559905028159793 err=4E-301 sqrt(9) = 3.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 err=0E-301 sqrt(10) = 3.1622776601683793319988935444327185337195551393252168268575048527925944386392382213442481083793002951873472841528400551485488560304538800146905195967001539033449216571792599406591501534741133394841240853169295770904715764610443692578790620378086099418283717115484063285529991185968245642033269616046913 err=0E-301 sqrt(11) = 3.3166247903553998491149327366706866839270885455893535970586821461164846426090438467088433991282906509070125578495274565922754397848575474797793249330447288473028739748286556825773944446120980444771931123571441329715210988326604957100372485207381068208074875839658949945251593152984006827197105182895572 err=3E-301 sqrt(12) = 3.4641016151377545870548926830117447338856105076207612561116139589038660338176000741622923735144971513512522828308134060599398901899979049576233110241887472970561864638046111641359496402021693498465300306246865338066457733013445093378436759424540942633207357231760380999730747597187789353006950131521015 err=0E-301 sqrt(13) = 3.6055512754639892931192212674704959462512965738452462127104530562271669482930104452046190820184907176735141820240635403760306782646978077051630171668927097577426905642741526332338303949623469447962732299962880032688564272130721127331690722052975017855588384448146538689210753953924825633102446828366387 err=2E-301 sqrt(14) = 3.7416573867739413855837487323165493017560198077787269463037454673200351563069390279768098951943795715009910887277519775455065653681642425926600420525518351174074011244748586319111000152304026279990638550213390300377330889721284945398105001694377593170299544731950604999264384946787198435019847883431263 err=0E-301 sqrt(15) = 3.8729833462074168851792653997823996108329217052915908265875737661134830919369790335192873768586735179163022068609496470131895404391636496156798917461212035110687547910134935812839195312288892925658464170280625091931734126598648184554646285513159402626176726405086463004505778106319728809397819251883003 err=4E-301 sqrt(16) = 4.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 err=0E-301 sqrt(17) = 4.1231056256176605498214098559740770251471992253736204343986335730949543463376215935878636508106842966845440409392141416153014208404158683630795481457469069776770232664362408630877905675723857082255213807325630838603091427498046719135293221479787181678157964759060805654969739007667213836892121067089210 err=2E-301 sqrt(18) = 4.2426406871192851464050661726290942357090156261308442195300392139721974353863211165511626029829247182050415386927368910747745081675522116379323644912998074942396679977825167782673998515034583461817144103286799148179108236037905860441855522559226675958286569876914529261429643525192878108839857542239690 err=5E-301 sqrt(19) = 4.3588989435406735522369819838596156591370039252324449368903441381595573282031580856561591558519445269056586212982742136295839927838261170121565608364174699009777529188794058900619967156631207402231024023243567359810484091999315007271878765601001355045664223659721579875507265474021334814033952938332531 err=5E-301 sqrt(20) = 4.4721359549995793928183473374625524708812367192230514485417944908210418512756097988288288167575645499390163523015475670085065354488941477271727202430669054177335563463837583316225532906452797131610715227008350675700068467848281288841728650781945051852544577525990348048813632235518178189969847427814594 err=5E-301 sqrt(21) = 4.5825756949558400065880471937280084889844565767679719026072421239068684255477708866043615594934450326776009053975857408733118991707556019635738633623447553702817228244277981919405969049143449200907589407063891768364965598654748231477641506627774586518102302361748154008139424109257393659219939175422411 err=7E-301 sqrt(22) = 4.6904157598234295545656301135444662805882283534117371536057018910170246327532397214821155960615431353545958966615086074816519524407829256216669587091816644475006412621612507549281883318625299999547606735605004577761471186401246176232605036362090494527493856828175679527030353269322757131712060606256169 err=1E-301 sqrt(23) = 4.7958315233127195415974380641626939199967070419041293464853091144482572359074640824921914464369188606174745632457368651339289039212302654888457837943340796647275696716534943439784345614167987213151199128895631880449641132459392571845949603945392600435614646020215248650353293436308627473193766801187702 err=4E-301 sqrt(24) = 4.8989794855663561963945681494117827839318949613133402568653851345019207549146300530797188662092804696371892024532283782497177309196755146832515679024745571056578254950553531424952602105418235404469626213579733817072648867050912080676176178787491711356931494487226082885405404323484036766001631796156760 err=2E-301 sqrt(25) = 5.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 err=0E-301 sqrt(26) = 5.0990195135927848300282241090227819895637709460995964075849708044259336320622241955883488510939320083611902582410399106614317793411215362998027726261199368133520082339240815865151806094369250287447030884686971127028666876703708002538306916010980296796499813372578201208508189137304387279123791952953254 err=3E-301 sqrt(27) = 5.1961524227066318805823390245176171008284157614311418841674209383557990507264001112434385602717457270268784242462201090899098352849968574364349665362831209455842796957069167462039244603032540247697950459370298007099686599520167640067655139136811413949811035847640571499596121395781684029510425197281522 err=7E-301 sqrt(28) = 5.2915026221291811810032315072785208514205183661649003607366689184021376464605672555207857729490872212301291566769949261914870597772544295688547811117602154454343014594566477845993791897301745214019561084074476560474318822006838782320031570511926118914820703047936054328147475981480831630398088069486389 err=0E-301 sqrt(29) = 5.3851648071345040312507104915403295562951201616447888376803886700166459628276586928766337816798354844187048217939457606076886214019815556269532167282089245286717225261852146812359900130524480162903887045278269438713694073940103168871959102567772596508381141949558419398082634896941753261340364163612310 err=9E-301 sqrt(30) = 5.4772255750516611345696978280080213395274469499798325422689444973249327712272273380085843616387062576472682594285139224407200789882646558891471252604198935050656868264028988871051985377336304477847146986536309464713769216003880339617152830231153776148436193230087510835045256841092499066463397468011771 err=8E-301 sqrt(31) = 5.5677643628300219221194712989185495204763933775704143039684325856035898392542362929272183961849266784232165273979702662246059605013064646282681808419453379149333606084327393411893979331802930420688912492742193367884881463424397017656913988273174390854202354979424967929598733672298945006278161249671468 err=2E-301 sqrt(32) = 5.6568542494923801952067548968387923142786875015077922927067189519629299138484281554015501373105662909400553849236491880996993442234029488505764859883997433256528906637100223710231998020046111282422858804382398864238810981383874480589140696745635567944382093169219372348572858033590504145119810056319587 err=5E-301 sqrt(33) = 5.7445626465380286598506114682189293182202644579827923676998774705659007214574046270271253655967881224195574769456508378699348226152034034016185320195623077727279780166059158065937139742960566892208393019974705911320869929741626490020777642568108103163299037486665041130657306085804634905305471379278910 err=5E-301 sqrt(34) = 5.8309518948453004708741528775455830765213983348859719544500067448678100619967126276652403264530353985567896220753549113518138736161708062859032260788244471816650543597702392681686483765432696564217299781470979253183633897711547062311368561884349867175053513175363683719401993764472348334096370632893300 err=6E-301 sqrt(35) = 5.9160797830996160425673282915616170484155012307943403228797196691428224591056530367657525271831091780886256351142545557014556938552338585094349499376739498383895803700961289381157992259578429781758256786338345944208920622807759173749934450276179066816306751474489164369464652245251841184483321078375839 err=1E-301 sqrt(36) = 6.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 err=0E-301 sqrt(37) = 6.0827625302982196889996842452020670620849700947864111864191530464863327253189102398030664279578486634309351009051311637335380630767099485320383186097849995856628707940771530658337937645881664262317752030679940671361105524546839617002400992935361771111189687925464048646465693770730702547382567543809569 err=6E-301 sqrt(38) = 6.1644140029689764502501923814542442252356240234445745448745720724583996502636642129667297991988999451485573039376372358875471600792658521760774197322762213297753418109603138362566974097121924856614308930259173041767063212816103354712838652277636442388344752930314717357860105872294205476594282925904299 err=1.1E-300 sqrt(39) = 6.2449979983983982058468931209397944610729599779916563084529719306096112005835145006333361122213405871078349258574629044252950568604567243495990597880972889480590074765230840349978985860648346791063789840700535029994646582062276217569255843853761430916745014587780717892930058854388407449699629025960327 err=2E-301 sqrt(40) = 6.3245553203367586639977870888654370674391102786504336537150097055851888772784764426884962167586005903746945683056801102970977120609077600293810391934003078066898433143585198813183003069482266789682481706338591541809431529220887385157581240756172198836567434230968126571059982371936491284066539232093826 err=3E-301 sqrt(41) = 6.4031242374328486864882176746218132645204201326210188855292726266681827581968760742893543022498699631708118325037971832624697443725142112330988364172050650439039921343140743747700211730776936057203655988194747785122207029374726018241849747773677060422813374414956505414146148680257916131396673863986273 err=0E-301 sqrt(42) = 6.4807406984078602309659674360879966577052043070583465497113543978096173778440443714003609066056102356754505420974116943354919134049066086889458189616646739513055852278226360956688226806687615217766336725991428129904321601398449572804993635523055589894921151533847686331572027483679374437866401142848728 err=4E-301 sqrt(43) = 6.5574385243020006523441099976360016279269663198837897698654601055856598534885756393558052909696785480205411487092432948778350774256228665603878572113758557372053351090456851332197091046894344386347945222354433398294139601533084388113306954531941115786626694420531355765851278622241208830468002376962204 err=2E-301 sqrt(44) = 6.6332495807107996982298654733413733678541770911787071941173642922329692852180876934176867982565813018140251156990549131845508795697150949595586498660894576946057479496573113651547888892241960889543862247142882659430421976653209914200744970414762136416149751679317899890503186305968013654394210365791144 err=1.2E-300 sqrt(45) = 6.7082039324993690892275210061938287063218550788345771728126917362315627769134146982432432251363468249085245284523213505127598031733412215907590803646003581266003345195756374974338299359679195697416072840512526013550102701772421933262592976172917577778816866288985522073220448353277267284954771141721891 err=1.1E-300 sqrt(46) = 6.7823299831252681390645563266259691051957483239232882327502195820807282639871125898626409409363300442287000181967426685942998961358601841490652156523645059927977397852813630015367571073924151444703591291039082949714923560567903188666557204010091781894473939407653615829525220753831316175951773103924632 err=9E-301 sqrt(47) = 6.8556546004010441249358714490848489604606434610013262754851081856785171151368169992273251485000668369387569463435050661463046586231209369361955981526052741257505749402788460391895965942489416118534617901954041917301559371999654154560287161604562613853347934508886104501025197961260065393536125689910133 err=7E-301 sqrt(48) = 6.9282032302755091741097853660234894677712210152415225122232279178077320676352001483245847470289943027025045656616268121198797803799958099152466220483774945941123729276092223282718992804043386996930600612493730676132915466026890186756873518849081885266414714463520761999461495194375578706013900263042030 err=3E-301 sqrt(49) = 7.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 err=0E-301 test exp exp_series x=0 y=1.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 exp_series x=1 y=2.7182818284590452353602874713526624977572470936999595749669676277240766303535475945713821785251664274274663919320030599218174135966290435729003342952605956307381323286279434907632338298807531952510190115738341879307021540891499348841675092447614606680822648001684774118537423454424371075390777449920614 e=2.7182818284590452353602874713526624977572470936999595749669676277240766303535475945713821785251664274274663919320030599218174135966290435729003342952605956307381323286279434907632338298807531952510190115738341879307021540891499348841675092447614606680822648001684774118537423454424371075390777449920614 exp(1)=2.7182818284590452353602874713526624977572470936999595749669676277240766303535475945713821785251664274274663919320030599218174135966290435729003342952605956307381323286279434907632338298807531952510190115738341879307021540891499348841675092447614606680822648001684774118537423454424371075390777449920614 err e-exp(1)=0E-301 exp(2)=7.3890560989306502272304274605750078131803155705518473240871278225225737960790577633843124850791217947737531612654788661238846036927812733744783922133980777749001228956074107537023913309475506820865818202696478682084042209822552348757424625414146799281293318880707633010193378997407299869600953033074710 exp(1)-sqrt(exp(2))=1E-301 exp_series x=0.001 y=1.0010005001667083416680557539930583115630762005807014602285146744603597482514482984127182260041532609430682188720950993420636786961196238409723309055317683119235561984980236529093776777302838684862874098703172243368272906685243422270076506460803353776835394018643729355574114241076044969921559104238647 exp(.001)=1.0010005001667083416680557539930583115630762005807014602285146744603597482514482984127182260041532609430682188720950993420636786961196238409723309055317683119235561984980236529093776777302838684862874098703172243368272906685243422270076506460803353776835394018643729355574114241076044969921559104238647 exp_series x=1.0 y=2.7182818284590452353602874713526624977572470936999595749669676277240766303535475945713821785251664274274663919320030599218174135966290435729003342952605956307381323286279434907632338298807531952510190115738341879307021540891499348841675092447614606680822648001684774118537423454424371075390777449920614 exp(100)=26881171418161354484126255515800135873611118.7737419224151916086152802870349095649141588710972198457108116708791905760686975977097618682335484596389298719660896291336261200293809572765340329622698656680169177435144518460651628044422377567622969602847319114021298622810400579115938787903849741733400768511892515141934093466028955537668129016557974 test atan, compute Pi atan(1) atan(0.5773502691896257645091487805019574556476017512701268760186023264839776723029333456937153955857495252252087138051355676766566483649996508262705518373647912161760310773007685273559916067003615583077550051041144223011076288835574182229739459904090157105534559538626730166621791266197964892167825021920169) atan(0.2679491924311227064725536584941276330571947461896193719441930205480669830911999629188538132427514243243738585845932969700300549050010475211883444879056263514719067680976944179320251798989153250767349846876567330966771133493277453310781620287729528683396321384119809500134626201406105323496524934239493) atan(0.1316524975873958534715264574097171035928141022232375735535653257897598390106220283091007806750332318779823060421197831198137564206895420754582499362428407357140421815528765819354552356709798773607877654762033955562798312364702113796154883867884276347957591920037694029980542871545749742777293346397771) atan(1)=0.7837315152482714943084302664123395169379154490801558951573745868165873715253489729891296187134550755389002864463509055698048029932968971908281772786339489679288278061079347830086547737744980112467918498558762862937465896162973945781292871754830611792459487728691521229243901022717817256855997958496922 atan(1/sqrt(3))=0.5235987755982988730771072305465838140328615665625176368291574320513027343771402196779383577228460189778181758017547563537824322642191977782310950149741675801224950825914469450465608963799604588873140389812913111432607638171156115417961475474962030325459211833969651707182126195321142809077557589737928 atan(2-sqrt(3))=0.2617993877991494365385536152732919070164307832812588184145787160256513671905174165523362354451764223318456738761068588872578203841292151859771132840107067597875236752251615432090413031372846558261277250103849969844337914165393431740208829993739274661946792505400639972765160880952641504707762560528593 atan(b2)=0.1308996938995747182692768076366459535082153916406294092072893580128256835952587082761681177225882111659228369380534294436289101920646075929885566420053533798937618376125807717127316518592895397887659151845337906527472269220198186764077826318863000795477353569551441809022482285617388825334999309721278 Pi 4*a1=3.1349260609930859772337210656493580677516617963206235806294983472663494861013958919565184748538203021556011457854036222792192119731875887633127091145357958717153112244317391320346190950979920449871673994235051451749863584651895783125171487019322447169837950914766084916975604090871269027423991833987688 Pi 6*a2=3.1415926535897932384626433832795028841971693993751058209749445923078164062628413180676301463370761138669090548105285381226945935853151866693865700898450054807349704955486816702793653782797627533238842338877478668595645829026936692507768852849772181952755271003817910243092757171926856854465345538427568 Pi 12*a3=3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679821480865132823066470938446095505822317253594081284811174502841027019385185084956376474158699135327001246199638132054969984721180882505959924871295943361510064807679673181930571431698056493150726343116 Pi 24*a4=3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679821480865132823066470938446095505822317253594081284811174502841027019385211055596446229489549303819644288109756659334461284756482337867831652712019091456485669234603416539574854817331808039983433310672 Pi Npi =3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679821480865132823066470938446095505822317253594081284811174502841027019385211055596446229489549303819644288109756659334461284756482337867831652712019091456485669234603486104543266482133936072986810973861 err npi-Pi24=6.9564968411664802128033003377663189E-267 test sin sin(50pi+pi/2)= 1 =1.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 sin(-50pi-pi/2)= -1 =-1.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000012118195638971824217968408884592772545754600892233986911698049877092003383449949468281573125492003852021147437719182878277085842018251 fraction of Pi as bits 00100100001111110110101010001000100001011010001100 00100011010011000100110001100110001010001011100000 00110111000001110011010001001010010000001001001110 00001000100010100110011111001100011101000000001000 00101110111110101001100011101100010011100110110010 00100101000101001010000010000111100110001110001101 00000001001101110111101111100101010001100110110011 11001101001110100100001100011011001100000010101100 00101001101101111100100101111100010100001101110100 11111110000100110101011011010110110101010001110000 10010001011110010010000101101101010111011001100010 01011110011111101100011011110100010011000100001011 10100110100110001101111110110101101011000010111111 11110101110010110110111101000000011010110111111011 01111011100011100001101011111110110101101010001001 10011111101001011010111010011111001001000001000101 11110001001011000111111110011001001001001010000110 01100101000111101100111001000101011110100110111111 00111011100100010001110001001100100000001110010110 00001010001011001001100010000011101110001100111110 fraction of e as bits 10110111111000010101000101100010100010101110110100 10101001101010101111110111000101011000100000001001 11001111010011110011110001110110001011100111000101 10000011110011100010110100110110100101011010100111 10000100110110010000010001010001100100001100111111 10111100110010010011100111011100111000100100100110 11001111101111100101111101001011111110001101100011 01100011000011000111010111011000111101101000000110 11001000000010101011101100010001100001011110101101 00111101111100011110110101011101010111111101011001 01011000010010010000110011111101010001111101011111 00000110011011101101000010000101011000110110010101 01010100111101111011010001101011110011101101010101 01110001001101011110011111110101011111001001001101 01100110000100111100001100011100001110000011100110 10001011011101111110001010100110100010011101101011 11001111101111111010000111001000011101111100010101 10001010000100110110101011011110011100110101001100 00101011001100101001001111010010000011101001111001 01111010101111000000101010110001100000101001110101 exp_series x=0.1091699911325197553500836229041400539005348122458734406107015404701087892483085085878768851896494383341424421451139299967810376950239284751279678912058102241793938013964540220956521226943388594643772609244889394877355956713716084679896374759349144185100848486717815403372848589011586421636768333156535 y=1.1153519341656537004316642221302437188277530385891012548432101634798135825021677245424413163596764782953399061482062714797307883662472658396936443340589204093599310731606038124727489762794501568021572860265251735035794539650609390256913357521154518555664117715040980336035584979591584286569961945515296 e^Pi*sqrt(163) =262537412640768743.9999999999992500725971981856888793538563373369908627075374103782106479101186073129511813461860645041930838879497538640449057287144771968148523224320391164782914886422827201311783170650104522268780144484177034696946335570768172388768100092370653951938650636275765788855823682994217725831255313991488940 end Big_pi