# 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.
10032857872870069189905109858246586509742183058448519466909685365084621634104	32804008837842309662050996778226942770686597794874452437633804100023820297
10092839509354500597604511934908443849519177901835599603118344411338066944567	92411199527086136532867544401548622860066688234629367292144972334086612521
10075280782133405658711488412882508537161554250930589371539543867642335115952	74998836447449081049700203607433622076370904370485261689158155702034418976
10051811440921256331676791148932437465645414566523158315064131175215214945977	51677681469801506296732305262976130221759635217414404324860686380208117207
9905848919541976294580997950788464591383770796030103638216208816783145349388	-94597103533510639130164311403098658481129272228377875517211889813826598675
10051077652457277672564029806405206809915091020243422708088378802517171862960	50947648626366831979501189267133689571405600667186498200397084589300718854
10030969318716622039457671166729353434850768169984275854602562627656369225891	30921462560912081894225972981519532133172680470868657348293373579587326195
9963732237335477645852960198597609424335821060923551558732043907318433583994	-36333689644831430990551135170294492615688236632754897538797972880099945108
10033692346957494518748632852990483837933326977984147551734781201918230476903	33635715412978301671376057899322580424745332979544766116955581220092101865
9972520675898425486866237035101328743688419116131136501120316623108614696611	-27517149073764295274569873903042989481287656802005607895486544151022838167
9972919692029465033297857700645643727062217932192275867553322240356502475182	-27117041456452027776133823311045277126023936429624913965253649320967037641
10071678952627580446152896494210262185168775607720933294756342399623050201816	71423280044282184173692247368475332531445660258842848677404141289443372006
9979194787414013430550968125346975617897201024066371802998222039272436824090	-20826885495374057996400964274551746630349170559133631574904750270562920904
10075719944720533052346641811646295565547038889711605141360245404583640741664	75434708187170352827749827508278248386778205575318015492054117244671939864
10067319669288668877429217498980492487575153782801243632457044937748071856726	67094084249758328947745330044805677962004070184610995985202209643672731293
9950988882205874070860773957941578358992516037405676994019978273095096691603	-49131616156017362365687534366514007257803957494029779037614310802631410177
27181762481879585522168177652680755579965900797600193081586029434961114078928	9999611584345500647195488504457299628626640756550076690390048647872331352299
27169351690761649346229334353584272113753931638559008748133716998423788027739	9995044689435409391914592049198529869280926909023828364684265488343554436946
27109005590561489207267846062797617651087695596477300135753737390464040598667	9972808893038138162976389856278368279971413824494265248302605361070833380460
27138798742924051389539168730127063246976923761585483981226098398708565946808	9983792989343630152384485866580199695687940172668762672422756125275312717371
27091278967967957722421184796371558923911680287583726222875049422612590582979	9966267737998096933354557855484333208777256620043513808546444064735219760189
27227923367503381479469737336923148023331570412394966545806363114650032572093	10016579481137520442261833549290384118652141905205328392879292431054981182638
27160276957338864371091743554616109251911263965636562371854540991937180277521	9991704068955208358172351369538326993304244706178477509649962406441520112615
27190973402263035907770688885535357363987861885535127542636321110976318177218	10002999650192026031044359345656657850358501624019373840220284206813113765970
27229952609588785119796644670774116999079076466905047913498426188699069019257	10017324733151093813212646607816148818858154380887660895096194063728056279829
27159395237191797655109059173558593466467694200409088919878024755555487556220	9991379427766658279598558569334786273370001122929339723966610596314418912719
27238702884788251233225664952019500564471011529952212180035255427390430969239	10020537691207546812447689878063943817037791666453079655998092339504786804560
27174968138405186600306713168434864699554169973162521786282326054199166771519	9997111675527493832748945252861868633039139310319198269143842544975755784155
27194655433174276492468696763475621623169091805066477571193462172946412817391	10004353695735199763072148015037867040491968344923947689830701694425044367948
27126472523047191503913086294800873238608678355664357070579197305166007215898	9979250039570675123250563706035323446951336321512584670767165794521719073358
27273488846651178174709033138551774754295567407137663288589279402520450107849	10033300328511165345308788767665729855342476557818450920494263973926234541907
27227106078581610494791078023213710464091583920652344344858127407594259377499	10016279310912604290142857072047032790035764292579022591104935298562077869137
116682440237358214428399248091477244421767028242301971596820514508942975735511651839	162723815236811057359669620856958873094808103383834156281542086205012357661267
583390888301526621894886028918877007034320931356906402095242424381138067075573712981	178817829040123023258326273905530992468894979146779909435678206333899249202344
539957975444983981736836326299953763419544259235738691647132152212267720122854479812	178044167782501325814120118330299510870737646041891590809916613592529727301071
348768553543195958446429276049421629669093381312701208975365796843122366926754865500	173673339968145867822445203154364518132913418144267660030132137055954970996422
415451127584135551421427858298455031404577015466886016925115964995450722710067624707	175422904492047122116793025524311365558826327627081056178845469796705973810859
803436633859019927035984987941660831402296123313448556264084377407637489869368305983	182018237843858511897039776371195342010633330116198613179192539656330791529283
395819041764210625426753256138245184842865656959638240650211240129032138386011148569	174938826065423821460366301746034891188876669001811175746235478249527574982134
740866837851867948343805838124098728834134229225259373356579794818229347160323119821	181207463681143795589824017505130673427984413832893481459812871920064479984700
739240120412002071144197807944672908577946511897816371629560931992857964264409045335	181185482592739809283602113704141121370524815002320562069597970575110520984747
596015704791978310085931720318665100445402532984567743615533524854021244230966576334	179031924820105257993358379630787932859477824606964444029761532146219987517172
388755782872104753215838033210323308146769772386874543745750764301404947611062939836	174758768039082857197013863450936252085725403637489891613672766332595188654566
591138406764665632969919259293664037780009462007851655728779585382858084696367811725	178949756457610978883166587535988778541776067864053118053171525341053346448397
740182499853416142945666349589759580070206192262417638393377134342653257129613243264	181198222421859150013957868009930344891400742128109767065326484474079379982404
120753936473939815059797518883428429339139473692728807596002626651206800540417913429	163066803571697949118451161230677122674150193497046679206126202388057913595417
349810485272133775388477617004983862079576262166207858660117660688399119215484999424	173703170021544689451980455450624689789328256750079941265315112731607604249004
488143297725140873307214870567563536021580956582508677312349742633259404326452489262	177035344705981303643066685918162236798228731846998897187344290802674312347181
768614393865723755868718340808577144345798323439860863406087122963859645736345998867	181575148703075107908653265867520675622342540271513268906297004485319154703419
769364954273844531126560842362067292147818196799352294678222100363830088054424540992	181584909048278876707634353288047602306484496359037162455800202918968162737222
662123526047081160165376581805723188185349371593613266110368561521512741414345019579	180083775987377933690539469858971659194786580258120688325920475224146020291164
816972807115291107945755805259820216147261478099072096594884233478076745035450377684	182185312754516994351069540159971238829379482503409583363651306978325533812277
8261736529360802164313510291948350316779692033042978165212979801445794854835420464	136245602639859227241189045007458618933474732297329134382134546561861372687379
217033910278493442969500736763390338886053702302126041433471175319228465110476245936	168929790748665136301622277662634839052111113125332569922593258807950487314642
724920642163657807375514829975609662657448769195261998338621569750054315748274291054	180989876547492104841789726779780196718672592574757074451595105310262152008738
844653154329331481785852186685789362169031699375121291976811479703674092354079185169	182518515398129389959860495655179837947337100004034458657591329147680400090398
331231620905840991704390981997423643775480750324203123574477276725811162871333228807	173157433566735245939755952163509973722417522853964506737962914014441138113014
376654083484430712577963805809576582671075422112272472333557634197209795204486715635	174442526807719869363657090946997748459875857554117520487903157234066721943138
558523231235738298747227826664498147103412817535410472364383954192270754167845896753	178382216783811689846945261285514346224788098679435371812004346632694943902477
680773458242352594824730570433339754154299085688521701801342920216168845217115625783	180361550553389094469731085777602301064715503224288666299892284408808722958773
739902920106018581937904887965968717808943498176289807833146336315031604734152133111	181194444535164874512383656807865831079711074308233019189018521812058724313072
863223099762951788208380898775472155201084047489288068874211366365814635078900163693	182735986391711915185386585955543103371154009557700507501717636506160533125707
612828730899129835111214096251230222741652981247773065222003440612195529012112063592	179310109669240775690683256684470576000638480779429080022030588195684705097126
445295181752753585581989567978783448014153096363522404957763586577493100523791001179	176116628570119792800662031500617565506718868853932160583995971210387243718661
968766873654488194860356013152689468825516717015484306810339264886428058666578494822	183889494634520174618846898342525762053796341917962788404804603084537597990982
786709739634315258444221151585994183173873353204154136843593434026716930258201699371	181807848265952760493928028221542052157339303571696587872253836276104546585395
884956846071627706299762762645932898841660124698081323628142767133388471833045433297	182984643472882916570231766103769481550616194402554766080857341565851821532297
694917668127619076993008928988015366463557530942216569599863519581768284301670011751	180567188403919823260112954628915817709633321038296148193931000181255303347945
569473179690735968928104390458246557346142631682747430781990412078515260394893795398	178576371522633859047828421693577235680897198506121129210833118144372710935369
425378354051133989984298114845347800830966576742857964909286048016380565136259763327	175659044826879443175475934156691293231289137182892219386383950982529830567916
503815215568891631776854662955433195004425531869709008035778879234822503108262290982	177351350300382597797214395725544997366884495503649959387129494766072144410892
184217270767073845277879148338943000829061366684363021406416935369886999034627592087	167290413453466068965826464926139936787188027973992561571354691934418739735566
821005708086055672712284205579465541084113501053546734046960693010915120736057952270	182234555270002604663941608537381821483316983535258746083036066899436972141158
984738290590954966611144365698341923204565917429186696915465058496384871431447285509	184053013760076743763774746131258573935223173887581529969420863474266478034058
193400450542151982584843559935974511606275497429032875604051126959239623382251387873	167776883775738442678251756231729432740177624532350065248194150687406405051978
652042794848690414162060318223732162272698718915252591394340365844005397779254362650	179930356610139131571619137016104228914396377039476050140166461304901226388270
255861618921628414803786859895146500168971531765041566564943385537126185368219510281	170575622122119926371186866598826923189862074235616572092381918113307306805210
36916490852095251676663068250566389826555245199620773638147686600045398570581363783	151215838227445626935377495217576224391542516176574156751803464473484884008245
514507764603128724128029730239604481610768516482315971405709208432415910963496605255	177561361116817270040514234951753990425637891571820202207842486946936631675169
692148174376896924089253086407688344643838264047478970534237198987623051908067474356	180527255224885556222277194849474845875791094348718771640417730487976083335806
720866348825555702713924052623355327052883192472892037469024178348675892920252789856	180933792158982021239356215756165857065091127372273922363075958591397730428818
690260212408201516416007448140558762568614451319511862998865171814576627816286409016	180499941109020493374215960103057765820120218405566626895532599650016800790247
253483748439572570065730010660655487095527351733492393327284104490882325808497645873	170482251772267796438493857522522344737248323037836808224034868940425843030718
53275019992336617945868908965834724785873117502479600077740188815879714816584312544	154883930182215984483745136076072904623929977707704035336066630839752719397071
36341701360754760076425425829645981198461849179989571921436118146377559289542794180	151058913446946920383714542992394400433886538406468050653692713642701788721193
414686065791755264578482785658070050487143233467094500657241930895621917321457976743	175404472309629799570066619437668964163212820657635322671729428662531453071310
305395849908556003510078585907530395721248938949595530047193870668542806795802721655	172345342686269211806261280026248023033956659566446407753585217724923584271468
871831982500790905123516640769533169078423476770344898005860765465701641704471826984	182835221896955538293504843661593602443559081730349854553867765122023453104199
55962959150528426983923271075280659735475409732304109782324801728479218338013360725	155376154931143927353728378741355207323414884088510309325890747819984954070515
855502311793464148696228349316075216276881996298794366583354728549776815299570142192	182646142605705544461723617851928380920113321149289885230265392403087279439400
761687769349612314779010024262980109175806012903506171664410284065360115686325444091	181484621851760907499103910188437630973364005780727528897996021685138541412590
477295296283342254208314961018826345718678427173424576813247350443121524351711137212	176810608340903233910209887690024135930348104946122898578601950757332031601828
82744792628416872870860336993768067817499353001361956549833503895518009133185098377	159286865482855608855871483713002499005220996222650798898178813030807507820843
616816071314561385460605249005363829218281459391802572100072720596515307385614383237	179374963428373576841089788659676307463648233660985533190586662264703970871141
25443162261904158149180414660564021324376620210757873595334143896513993876638110867	147493724984650083661046860047442141238342821506549061269152305810763926878847
255984412030973913457017687530251552427770068991614370386949705254062685889058582996	170580420170918807486194872028957365668779534959245341664210867064746563214150
8431364940127895610958978533869423456242439368672958197192964149271934247324946642	136448841384831562829906364827642471546537206280417184209448745529852498367978
6205325570016004517688261523554088091700777646620310180458657984545107401055257322	133383333512295612516187192370697726522813800871886606223910662039779643475069
323310513602684715313393573091051818906519410422704661449140590608141778930822821	103837833898402306512252909064640728785091346527231610758418532165405514091574
7453612383453521398966023693188247297450515777883758046504645272686867376022747713	135216242635286258637486800593710802401747892806543104298124056895295803780083
3719796759240482434252371857239928226590699692103668460023727411408198973694994971	128265944971499852499848845819202051818854060330099440954481301416695408630921
9713972399303624901864242765989246082279099670290140929460637821851311258722842725	137864907675580200681944153489142617092456096291996492846561078610412640441172
7188131012736358729226935240619152095031431870255255467017461441046646257093458835	134853566603164736166552510321997354703659361422316992493270484364002410738643
8447774960758270513389730215258862472908929749525271183450679091975038653354992293	136468285534115134278121509322205843815355053229906921595968680369072911256759
5510458346022123618124623060283127389524984607497182122006564695545488298367983843	132195732690714512194187766002382278768626528494772365143903707890779936784238
2422240237103998678861911187340584514887838278664616529111538754308883243432825928	123976182947379087290433062039105108066406501412765544978466780281769919416987
9415417148461810000479733560061968378649392266308733781916738321162246939302701066	137552739328914341760428852587856908698221793190389104880176420113713948428543
2064694407897072234928641346350887493287203646861876510385221300869318164454936515	122379076939416214683641108385277207561378359479870737411250693135789485462241
1195965989564862436378028265296796156572708538330855563319651533508554879605981421	116918796832756575275058020177151695210852375409500641111141752286384571142719
7119515967740312971610985077401566173384682547634388837989942476189352328819999715	134757652060242831090087386176339286773047925625099402411300244525519084049907
2097686909448944971429878539475272945339148134265076475918923071545630153962435772	122537607309428660253367302853135630143254116812246646830699631960437164964010
8947919622714037442978773513951857635307970969907109796133733119217355488444908390	137043465258481152123544509730752194393757789862403856040902342266305866937107
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# ─── hard-input sections (see scripts/gen_hard_inputs.py) ───
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