# 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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9999377018004061934555008754977241636149818981768323229021742595461425175346923	99997923350222428644938216352943459712982863526924794123881581166639839061542
2874959307867256915895774204045680257578187049641944573939647442400274052999976077	659999947036057650240994276962289722879045040561094178437153523751374009813707
-7049690570230396704088697833078835306701901246775466126360330503567299500143684675	-890000023996565304435052413625844821342359863970352857458441407516436613057409
-8043569674229369303785252824750654091917922259756844141192666792957222769674888878	-929999987444766828758624159084368741705915041191825662463926782437127927010567
-8043570926212982053536561421423615513901376194589414813101208539244699578185331115	-930000035696340482620523032361307127657926158238335078107806451682243306042029
-639999121130613279608374323409287430511548825268381797715859097964807939363008754	-399999816902127287853720211652125815078879644038214254293711815945372863400522
33749332942140264668179046239906680891097589917057264070834251865405149563216986	149999011759622946113695591705974259525862314883872214754453989300214196042990
-2874960235791432836808452567951694526189270833936415376758638277944548190286572328	-660000018043421058357861397220685817689749710433595443248403627861442332884620
393040804366118282945342735603505456691347943731542978101465391494944123303830100	340000231939322250622453002036114219096287305916041959924535387801043932974718
-4218750630829583941033724145061436342932412485540546360294009581657233985996961697	-750000037382491999904727050488390041743327532050924635444582195040127968780779
640252918538647543016096096359039787703734937258339138101061429522043763085696	40005268442279257267428425834021401224416128002979626789487726891780167781000
-1663750737578201003529146949378477465885996485613848151878168568183061559104036022	-550000081275822810853345892431399831916181768327837108588906978682545414580052
196829813622104374905997509766799961219822789489006445286322552195067042661007789	269999914779170346563672385438145076263414914568011451453289414332513063024277
-393040705866841193092756017809514710478639301409561313182127671254860694572590711	-340000203537029594671219899431714848801110110450883867518948994828550772317672
121670014939754843366022334459744724553562329699631111646438988176865240516075407	230000009413833794509246180497226122345124190630747652406102415326017873034279
-1326509951048187844904895624169512524728472181481627605870085826760309755048319378	-509999993726539439030295363260851207781531436213235664578608241068979561037310
-2383280521016507953952208123209862810000414624401275501924126980255126533549217754	-620000045180061566677520894163739724386453373702126824913583432738243783139018
-21970031173468732389061388200391189713390987017352151533031566405380967462998353	-130000061486102540981449168976072502982530926395103398091042407322506507553196
-4930390589313687871541069062234142179166792184443377298805468812450882181634030182	-790000031475386657691159578221133764529951687975436995537164995596959297874742
-68589701512691407641539642834659737418198139414104678507323345362977222636578119	-189999724388050253697040610724507493078304354287050246443747585766876136171297
428749710879870233294808853717892463110086808222466735750811723375476410383887848	349999921327838162055692906691957522396966836210677595637736017011102973033525
9702989831259494775391856298982644194219729124259139988489845985468063042362715305	989999994261112600660730173618761695558129093668518581245716549856728267795154
1951119122679629039483391222079861416357455132383698499505866497983011838765294299	579999913067726669030857308128413749712617604709066337223963405298602563477931
-4052240084060078536935783552823536450590090392959986496416497901998789967084825559	-740000005116878375680881330506699690652297212656979596599112675942662490772939
327680273817589293743047500443623878477095219995131707955829065732477946824316667	320000089133305020889893292495079989338898742919391389267430778983814914444429
-7786880465954125383680707679891194046850684052028590863210666991287656925992930411	-920000018350429902713617821729708930644779339946244544786082087214343277709816
2053789943930127518848192706052252053247058183536047218134619844818187425798044135	589999994630865365182376251031075342002626117102970256723568174391235196834128
-156249453691135264177360891626015679858793240287234891809078291635310168218764435	-249999708634932566616430796105230657895494999966510315993676846412226216758216
-49129802776455275663156159492272742612347902495905416316858078794864376618935790	-169999772521558672353399070579197841831439699380417206152358119660951773989525
1574640148875301128428865841969852392673499305079122506388951652964212116880478259	540000017018209469203665894295016832432792511034176539871385316537671103294352
13309991551449128385498388108850321442065803268947930803804201445645853594569127	109999976725750250155123368171823427511410376413197942459182062290435061110286
53953026425663854485937930626435265527594642592494885342379430048572899033703962940722160605279779268710299266006566031761212641001991072187009155202326	175390178585234963894415428930066098104485171400092875193844701970255076585304092916061240393888572233
-79572050625719957027771496290160288770225522574305715659175036102495351292863429456557851737917995958484702010068767099128385435136216587014836860080522	-199642737719745908771036031063119754248386637605463364027164944424025549997332356900352877708896815739
18760800155634797125983299547810294001140044936458284583387393649670673040609682753743423422544549895031921994647474120731766282168210075398586020605196	123334275149218917484300498699850604951919740959120541069837094609627487796485271905069666934372596506
-64591372710937519456612681874251552498445649749845488615223627634874409613017912958451320638777138694847679610734376199644227161578841316664245693677202	-186233657012300494006519889387201240896292489756147944087713227595652671179077406346911446712741872585
90328090898964375408591208316025362445673770896271714292406313046352355059141054922171538439972311165811192918380946750712128113867995498522219010561025	208260837475102296504518787270487145154511171333198632867581345514536848006853366293434475891218304527
24178927223551752358074414222195563625225697647857625734159462993832977375046853640451603759834075209855288018189894335778055221528239633624238755972910	134218488186233035555754641059309230452495244010651576065939965007764242045196064336524626244609042294
84568321229586878517610051782553216016069000989444218487759925583759461590357671856700798076564032488755495139971982445893308543171232439077349039565449	203736685477367094327061963478478608738117517851196213426052485441179938185821144537281512301400761650
53934824193613943737151515096805797159187735195883193259476240945365943341307375281150973275918536363054143711221632339662829090048302045811162946912682	175370452464028138111245090185329670538348407965418881818660643982088672556301121726797860665724048748
-30196075509601412656796567846399259429510876916519091739061760121411153086183717595981553275122703203133815559263013283414395455275376937798549603216831	-144538485870927427977658955150385196473732514912073264866298394923359758280864746197928929297263854260
-75696190045398715889976404753236619915063284820632598886609164812381503695958881953194238907961244693099773056822550495352919284205734458782085359207027	-196347182490897764135711384217970921932948032512555878697888693181472761347691634513532219767761628733
66505702937247012729282692415590929679672555064173492461246031121396921078364511115395904203822109524654570392761123297139570265411468916577423516875647	188055611035663659019761708915104973147597827124160383560974320050688957958555641171189922826456752510
-25369900643553286395654726048338280546037404665452357563191990874206244512652209055699164769385477233270054671532775419771897692053858917096891206934299	-136386982880201004353181187857233292033003821854519886246142749574310791244363335153759262784687056107
45171262630079644859270769877841908428961171938715669262413369124568082722729506862752817294838541175489346995931455354415739703768861943944048974196741	165305540541757024613943202713497559456710674997788771016940950450926096327314089846959158396245905142
-58941549276228518010684281857986449900820205192306946903327687357343743714879681873450637949684044950578212551140337045692002166581617213560513975436651	-180637195668895969438740695312423940222216622286959077818545388774705862180296381739874592237242209815
41465956132462898136990294444376765454324929389482487220171050015375412891484076618330184815904755069142479384945463765558655342778859767902570270953877	160656102925902002090778100602238478777428852267884348109091852254133321028892363395592642788450211510
48093173461412564900065834133162841631286041106212474182014163129552517708541249057183774705559752201558688683645517494790751725350950364550154371875694	168795609099005985274242415924590073293390751992207850575319982450754750824802483523625590793614228100
55628667783303540243834063134982398767788876144630798716121728531413401577202955583725039502851768608775585399028169375060683502504788774548413530793606	177187420808662908580075636970913748821047534408606463815060564438978487947144613712927979537019169895
78777271936340767419202387663125947717696052724917272563955056746346551608787478822150780073879712136105100498341294700705073382105055478567430875700514	198975824219258664955318597580530627115315718400463892011224827395129312952561901967896655965686196098
97921715243851830212418755219270246450006243559726430781498493425665908198415898356269779228024788396392386924429395412597488871505013634927747625611713	213940498818419870663527447603439670429820765393887346438696205444055405682111311696161054627193081437
-83919729013909395898065204935921370641296167072548223705890038106050546245085343939538775861159528834661164475240168902168973294691674466751546297482751	-203214499029606399389881100048697357952623704427163330403626396592674088213605314954068522160884773907
-42988384011896202374828873894530954054899584844255812293518233091468354681608767001055010446658461068488207791492508798365854693049384950961955599357501	-162598689100791909245769036838731848870082198378853128375225624721847801794872754739736040405730574373
-87088707560475279229108686567062478997103229684089618318829129303292777909178670342344107821535562211301134033948528840666788615918471442211866032281016	-205740890457086983711940000012753669165680695449497643547485071028872263332040342007724568344897701517
-87449516670713106305450403582353732784340506830267123076768410236585370447413333263832815208927343665020474905258709746810935333726657795095305886597993	-206024627613562504633094314317205990223601378677785260805967929807063302206733966801764188756903495299
-88381126482098173129610319522247984830606154026522947570594077739627691044672386647327731855528126635953062713348299883367733606758112178664177926281927	-206753646328497870514889911797145788361063701350944539163333087105930339421036684876147575075917466152
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21385375935987846030616447991906756406384831644227054615011385767631167319059769657190413951686821664178963805457027619515460976762759522402204372488583	128836513315961433624322349028433560348153772670451969803476606161429627298996534754102299784927211136
-9478771458850794868008729260738006271672728412569834691566882458702102745076072547304483088431477074081212360993287070338269517754391160957458503505533	-98231479251164641076453774872481844368883035810987956106680517726027050749997190552821840235652509603
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88449392312790157772067516243061314912313620015807034319763850875202809041310424814784096386757747352294314761133323490919102616016900579194971004280211	206806864994758997564488563734775835972945349560775452285917183835894225847362199298556081516505326675
73489292568293501312166520397377346016177008697205848261613901306248431817998154726276430289730066341709083209215502719129549754387343294690682543651750	194420186582049752643248671399290666772839334020025173287531507293685290292508262497516354988095992221
26300054648817512896424193773927174135710086540790370509313571677501780109091528928635364869353039646450152380191143926160330910033222912950449913653325	138033833769643948718775021831755448602796364080343822002873839964813309901352251474466660753177013374
45888690355781693297220981194852601229315336373779389255111024049863416741832878761279019012671036483258849951812070642049970239343019874685465089737494	166176097003198521414175201736480152453068534098146161117758073724356471854903210780053191462700718678
-22999696298097754929350415934725060575196675847475209838369192893485948940019114929824027535053404560209302139928172379304820513912077650290331527592065	-132000031179396053711898794817718280537243157468629223594935881905355135222476254009847867395880663415
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26672036382342292629338160822663748966406916902997045113723294097764748413475788793465295365027286566346224543139996715854693397319897567111063681291702	138681562127697688299646233786432155119932015749945535356856948863774361568559832802912448558291387740
90252461705428842260560482292492273198009978377886472053572969937017127980219031771878285418258963276616409648760843719891877821267724824609702361819435	208202697580420251244350968546662404761961319059664741306897540183939766942193351907148081324073951194
81239714155970207377366851028979103498354413374075304735973421087687589390363992613209991347745694710660270206375948888943615500822971375900501385987303	201027804174921609469692630170914318665772556712346345911144447694937025173974094535900951025230512225
-98020121615678775746372414830031068875015946507566903437485098430226625621669003632007828506284832105678643981627950642973769640458270048679684489879967	-214012141285471408981874769979258681927408609508204798039096191087210280183329842024996977710867140270
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9166324000144496321539716482972561409569742307310721628217484514481646485798022666264047312393707645890828285284010982496051351774330295053915963699435	97140067600420191798463597205796889410699485488905591040498139212766725887388850208985539226371336831
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75489401236680375055376251248735693601492734598450514987443171120749392192166141425274111794510086795202839874456588298198995363093966763381912132121242	196168223994444828965318147080052300280201244957920576118497683987989236512809065359082007652034134143
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7139270905356822193347392284530147959776049541697104339219223253697844470214036175687503724765119475528001253066672605157040820449838743930246021681554	89375390836821627469807439270909023361664417084548189204953841163199174483332325660105071658577446358
32640609120029650193376816034575630594331196925155531246523422993607655316149652969562273682106283440255112675719442209148263171200053946809179740726402	148338113509536304751687455574458662262255658970096872139076133309837380321905767606363736879263182073
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74810767187383841690517024146395730134287071470254436463923610216469434081524547785483007848932865493156435593326392471610090162062595286242668991359639	195578616425972751937784462130039162048125014311221333332383524510971426498994646492112504950549241524
77840597828549402885335777678516803229190315410024994692988715050101513000706235740389088495669743496875853622642680539165784579853060434142959632412712	198184059900855110350609264034018803367160993969072032407316990607257846830267384962149985882863284999
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# ─── hard-input sections (see scripts/gen_hard_inputs.py) ───
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