# golden precision oracle table
# generated by scripts/gen_golden_precision.py
# each line: <input_raw>\t<expected_raw>
# input_raw is the storage integer of x at the tier scale.
# expected_raw is the half-to-even rounding of f(x) at the tier scale,
# computed by mpmath at max(700, 2*SCALE + 64)-digit precision.
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-15705335045615312795299455856925074164544792541734955585605079367366025655270	2628222303395756940773639432990521371747021235265927382844242699128589262
-31421043692496763423924642258551073236271138918494963537966207192269911884625	-9999998690735445721559712598141255093805001999887105422819119110581392138399
7848898671474459353856624346295156965280196611214410679345189177008343190469	7074661095504516900310582916249060165631589453123353167034319139941056362131
-15705114500987894938317698552071599867802307149464707147673154968350389876412	2848766922539434283002279473227210224427613420736496643717602835128177497
-15708133994096538298263858978368705577904508998459107225633894540270400337317	-170726147563812240149777246414945585405091066647370156252392202345647622
-7861592584990453611869601817703880321396592823123627055656603328013909528817	7065684009296767767115354360858724931626674887535761603438798390215317575045
31418520431166409521535693670095987425545175328937881860613021823101454898228	-9999999663585368694842844534933884924024506559603514554992886799788041925455
-31411046754417175323557378936038305880680098135816176999709933683241116075248	-9999998809386658629024115865285080722510514998453324060436279244694697587950
7845003241651589871763185462043067344492157989197884273535239747641390309050	7077413643060446743248634238389938192233835218326221062452296690567788692020
31416176165775712407857506883734393649807968999364381867976461762750274966297	-9999999996884246206138331891666859182485841485538833077578398898188461894081
-7859673391271703965860751006233939438708311154220961151995351062474242079673	7067041986525940178294695975839555189040249407516524780451469341207407343490
-7846815024949736227108237380428944484978500758941312268633099271262907680831	7076133553410991534667344415937844751568166890129850892943606043315723407454
31410381398165248420373481710446111472273032238391997691783466400220244537627	-9999998462572415672955109407537426128599163708588482942117491687701318385573
-15703412797664201536851443747016931222073348018917610288644445554536119923713	4550470127722013370922261832742358154732831950027876648912374809303395531
-31421752147927596336824785564842318210481472453819340350859370765208340004159	-9999998303112271982200563129889921979581006800686621093154626343535236709166
7848625919273990810402375491316239742327903879770948403551182112308252912657	7074853859746043052476398066143288381728751969178341950705282293955013136176
-7848389991534886226137800781437379269448093550848998500577848923274611839635	7075020594509995949174536356219248336497519709049880810479654122768981798086
31421768709524990974135787148186280851840985791167025986373720690050303252181	-9999998293450414103581262524957990037037541643368966561226082875014942686533
31418164947956752062564289043619597812694721903154433405869699546344566890465	-9999999749475573792574009553477477366019775491523088775442193103013829026595
-3967799697887468350143780591651601494148946978431541873774495908894107817	9999999212828288199527692195645134134999139752688406238817023025778177779675
31424075854005981672205682406638177935334246693917417374750138164713124360563	-9999996679430902460667465342998569321133119105355951815148340922506776360284
-7844406139709634006310122830699268724333636231644444363674262925547611177865	7077835466024668710476296467793618904277871468008749192171855544809774297056
15702731030899894191622506675705469203146595720850407335131820891285209103530	5232236810339812510619467736476950720792508507586612606788848984196555122
31407276468532167703898003050662436228346216729684512645777986747975364388504	-9999996258816961660842569206391402434090912302112342136199190540069171024173
5012060147351157516866040879321132201305794429418745384134870249795687406	9999998743962680260544683648890252403582380527481767456420944675410901975706
-15706001399610668363253394031568210331163625392132755140344182646501383737566	1961868325712681155739181994557870432922120605085711152740545589549959008
-31415616450088196932479577310988735282199575801046994427672326931316197462290	-9999999995192339530420675182305019133388482882850694474998586564281983889452
-31410749103628922861468447452549281238522747359803963635315364238960963921594	-9999998659709784930577111659078518083400772296080241146429274770838606660774
7845582647226476766279431145091760084540026522327915772678511885065920595362	7077004297581058142998396033652975114993780171227361264153784352746530865600
-31415663644689751898413236634424479347367234712064521508016221932674415422173	-9999999996544410633269231234771586096132811932074491547426959046436013135434
15714960299589350832157752778166476318282109344790476551466115746894311957554	-6997031069444926912827746909499779376663348039883306060289514095412538298
240310843563629214177061845617678295421418480159060373167893345301380881856271	4521188826515574099290282828248974520917116444232118871362498031902551869646
74606760849750719247630784124308123247718862152403037015389363898701712178158	3832436646810090583872613976664825224779695211393626571267067822472695306637
-106878356018070148300344473144517076667472733026203224135868827944884546891676	-3029043328486211436490135684655968820901819693490556576719824535857920934584
212715273312426685405082590681225889588231737422512391754648219521672732673083	-7520554211853935824027426749444267093695814058253371783307808445423953437489
210102319306026614660356632236442093173651539319176992602220193730025018998479	-5562610419888843419869470624299994790165503818315691530884543116251223259230
-240787974798103417033512866317123386625958580485037951390914855189189352277643	4941462879657238521318870500360681254634655688527584952457835318044437926560
71731241169429482030658758991242709062502385733932742384300502029143719994865	6294595745994468557240548984543489633737973100370898932642064241077712327388
54951544024442464405155990797413691866296976107779012945810644074312133456350	7052427034912771107236848054501176255914095208826518988623807954940435659560
33076330446304942583594838108585489951744886055096736556613022083506292889475	-9862469348673665335522065614049461897481921256028402926593674143133456824784
-235916684158751546604211425500271036045564149646414460705449870190535920517187	297191374206166734987383094727369083802476510270686413433081880771209325698
244010274219607751636502271359954001434746942016580605148303758083283149255509	7440304228793297288560815092579970614801278351150355049273758227673038142212
-315687271873737374805927169718206033612440447915464088188968526677486526662807	9883486765729644782330932554614704294724900207203431511024836257520891460633
-227260154524618663574707652988278723127127085221400945876710321788715416702010	-7419200171792382288865589568671813561802170624244944752983778397858404776356
-11991016361934948022684368586924508828018944787138648185410567063041415257233	3631949183233613696751082886395721119938289828439520973615021824256519580604
-22247804779969154606650115447005349370072605674235226435070368444261820265988	-6083533123729283969979677561540960018864367827628145439389468142833930073004
-100514336359367379829922042173022873982117690309212404835444444689356820104532	-8099932773922800014085649853973017596135083099535081569933912370898849976659
123930258459336995785431841540789899732187813258990107862614069231225944951773	9850133790876392869232873719095749457287665173996545071370662984347705642732
-247273924782211122259612943413265089221586312692766625617597582254143450475880	9189649270361701725152198688064498650345862914503083917978021532789040121234
108381824361534623702233173879637947754515241006122677302990971734404917484919	-1567428322112074949372360253728232669106677214381533598615540710899470753886
-248722342720571799520133584596380576750725474266441150374769814592744087736737	9662595252583050900152381863267062856112297259572900555256590207469861846469
-361672979337890582971664286960334811124627847540966537557874999751454404967017	389725451220428811910930338245301407886713994362629064824013469636792911988
-40898087269908270672148575575243593920158616254773259162908538998431599467761	-5831332366770673042614593386442714955753078881114059190052668349228329813907
-300394076360605532472743079543957966379576549036880950771134815952771634982256	1930576058408056106206972130513826102723056209063351383489003521174833893391
-304457515041400187218802702790942295024488973489226545512952463434913231117467	5651551413053169693727876116066579584851377481723609768681068747152316982241
273954138319967522341391678063572731846052790885709332497692858492320544606953	-6379831316971620472509911221160486174542400258228514992306312918945596174851
-325041831388821316118186197081228141964743788293379917916792512333539421555592	4640304059625498005335245285417164354266625128911503550234390294832257585288
-346208607687145967461603123934680860486831746718395861262669657153878956671544	-9979945928055373526351192499610983195489333637117571561865051989349467121392
253989404786823681414093831772389726956153078747790614918833171895613763912425	9647777122780493972070883899039357472067171882941965536670721197081592055255
-117528285127487803708680966509690696738527083111711028514565906094054340553906	6869286141637417369200714583128340906658109369201706434626053262290978774968
45932355830161499282991690442279435014803370947778127583744948989031085522305	-1188716500846510081997272306887365013252104099538469350584792430688636293259
-129002413291463113394937296342655939133800217073903681440297847611361597535752	9447809815195827019386504860371435367861711199535250117242397607321452061133
-311970388611790201125084378214135627853452905120266500097928410915474562145946	9761395878843328414043432606722193131769384727451046311802718922439389043643
-123655516756702678224419951777364825126981172218402674746308555792535299340133	9799035512121509889533147079423718834765100159149272185880105844357017551809
-169160969082443624868716766487560553311935427849011774070161207902674313572320	-3547649813740533371800614574915092067231643952533033724045888752967656674273
262699498520784520869308031196829130107582473736979232398521687859484632535355	4201292120779397840200598232348025609584927551291189627164252723215364790882
-45478384601711740714037992129833718565403977112256474051667068427091147228372	-1638089393015454822202354110252364178478071620199747625523617536632735974934
308771332611979395216932144864284457932890226788858534914119256145349103440809	8583284776304319438244598842309851645332572354749167334675512957609007987305
216301242134601602075747674567719347224052882875909603200441911113534336793566	-9355354764936141714533782196276624194783480122582077645088813011251350793604
-240128910960021081593653921577914967992062966570369440309773923217057772234506	4358173369918313701443880674449611733372843680818669991535431269081794758429
-141309527200335973313311576659806543670550787024264766105116705223816461465863	62141811252587726889169879167778231333031610132192000936014608848856334688
60582322436122396347497831781219847385078805774947587147361486838081577617310	9748045778119304236782331427478303998776358838374264032943493010351847554906
269408721656943253237159766565221944000784720553021168568205411073353737719311	-2351127907885075679826674084871580782781643350903142005083030598270471296029
-336019416279949662999685749412024061350511292986949159105555583065275818065054	-5771371901677458490796324402718887920017783692001026028182543856504004149729
-373213345764133834722153864651987089405797548904755906440294771870175124386325	9294867981368895427699445600508777663980963018218567743961442034039399292375
276192092247618184015627691666392965021211439940791211400790471653490130825518	-7929719856434784216107304241208891292856932897809437830238433985092120871351
-79454536114711115155172028502935471890501031469308968747429804859327709757567	-913444713085953475786355565560788885437712876849902250802638713726314314090
204041113319704157176160974662436653446118720038001081125172378718243001386551	162402024020391744505807005097133366281338061813380903230280896092647527197
-201021497000354594341518384323181135508081957263108074920535856960742474934067	3128598485614011493549474731803291531663685501562969966001364034798268269067
-206456948443489045251631259080563941355383107257522392285202425553851440850941	-2234403096087588756981833253945199333787355922717005062151306959491758793217
45866159669117613313533198426293439854298781654329427271826837268526752491289	-1254416782237382348099354744915575516938187759067581993099348854482467231595
-64164724221337123318082805407734260890272778165421202732900033876884496467245	9911304151832594513667244810467606751650204135999088088115026957283485017735
-275680325715669743163966962400164114987698127342934718638559961659484577021359	-7607676137569729038682174558057480173682920687200099834748489717106652535917
264095974603853717504585241051653251872905460573791093401883159772166903547365	2897255677528927545913597107111276647652897291371138358326154549260769153826
1946696136732445541575983478257042049181724023520968989352775447039125256951	9811116338189570018680823855381686129790173442871889788111337005256492791389
-310521846156089299603580246822346877661246205333133849234627988628908035120942	9345720924625531561815672573396606779675073749333892760825475968330420815488
68856785610130897100412081479459439927085409639110164493235070493872927327954	8239252540852586061291007790476081647455827677146311137039464685879429997891
47529739241473319348529608697817518948493889225578002423700492946278157303862	405738031819669531733544372349588223929339326282437866284595670726186060755
357654520852264623486988960344520767707914322535132189217202227976556308623817	-3549526614541657933650053752282119756107270726700334374869944209226006168038
-46065722294694464494205018184446741366086375669215363824923998912147157920198	-1056193864919145854981796020690450691692507915562589799913420322943413340213
287975274887598186891816616829191048907605218762440494903899176450898856752446	-8662279172679591508841487066469100608509317261294872551374766799598953749259
-103480974578018980297300837407575999542867394616675372478647397976356097034545	-6031758264954717670114665356926804567650540454596629242299112872393166832667
-147390417517786073216180812623015962646350829281960313798296617414306752339751	-5661888281333869596574391675223056423358436259218451232197659470766101736970
298263705600079074356210093216785224846659962054013914483056554087233878521054	-187585487846743024504766425923165383368845315782891620907079983074539514712
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16683247985014415664169771919097454399382675302558414764295818610368994271936	-973739332902017867576241176802150251581970346042264999431505430163581096482
-14442546323495231293119897908660815672189564315242796603638203047175877656577	1262042502467702089894088069235494626008125044517319508735278354301557161324
-6928796645723904713542265616513278224277068120017475925882612827864676074730	7694098061935603946082742891791172531790071010017616260852062590729464710654
15463084799902686861982016183540307797142057718658896136886748698446437389650	244853995028412791227349941952294712023817597381887183010015264094451183402
4645967256103951334992858884771562882845286895892420973409514096132932123181	8940023303521529849493942902899095429309419418610843038283667740189675160973
-29505379863322917075084474827687355423589143416133357092512430803876535125376	-9818045057084671176511583095808415254239398548219181901496432581531106344931
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-35899716680571202770451594120034121471537659889297148942319540711980998413325	-9011509918774220052519862576624092016742423721328610294707946466042980876720
20824497908655103551486326317970083007437727213693765444859765837955971884481	-4896196305872513163206035249978597304592603705799423474730016857850580886775
-3638442768362794469040687468076469991216797781310366589632892644855265125156	9345356717881062035837113447185515326435772532421699656630509024304527453783
36606485951531930012545141568624896544344876356298906896484523955088001396379	-8682878767737806381127506148173841086209153407943266708108076723120375858073
-662270666355969464387470611506493641552877159592886506136204581040186531783	9978077892556457934409458927988612548600335036672997274562800920890944288355
-22858447888321822077213948949677063498924492544702380981260748654671923055537	-6556540092840542529584112591247156420196709243516129724113228569019639222342
16535343968361942836810593613282060121055533501143707307245762619731059833718	-826437038868825147540608961244777830749148317101757434557407424466507260966
-23353264806880982323806682991572044015790902990265698971557121091667570808361	-6921979834430898535165149694561754151780362393402025893202805905887479959704
-4499195712282487138048735114652919667539196808198676751702271909841516550643	9004820831839015131415140797208132756533156004101774138413516443972743143044
25642696609377049010875125457536320835111849978543487502410415982572259557268	-8379267150706208815308413538674164608724629889392023403487372058852430535545
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# ─── hard-input sections (see scripts/gen_hard_inputs.py) ───
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