# 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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-20885787941535441947672175810732244989494618523570693405909781570281371735	-20885757572555747658644710987128106848993612045754919521363965314394339758
-9965497717803264779621711324424970121557888286562567228774198103439070680482	-7836700698462839578591728062469749903216745335300728278127707593465871380223
88423386392497562463685842802615678712693143186318205249306655790485435226	88421081982227623353714696133936392601784075902545809805676259534770965354
-48524957477739002354517899247253826054932401688334913845980277832111840790	-48524576615338739593934615115986169188724022268559820642177066905487221549
36346006757522400710285947791020142642707444336139876495474351211108952663	36345846711305854551238643273034324428619245852310937870861001265729052002
9968595816999081036846520097852403198756691190688835542495320449062963229249	7838254861096752577290968285066891374444230253486096772086398612445136610765
-10083835078943279735183171479174090373935339247311981702269156397634081746773	-7895723956440806922384402436589862300443094147447921771445863390754879451697
9943358549075682352216758571375875061515883735849680923248856426314269834799	7825580550731252226403386293554249053180301225467498830704997263895616077552
-10014617701798143320422253483538889363076045520051827298534759020995680994595	-7861285145546298000729889730552365170518638151938255671528125569564259881662
4340198378087028439713631122498096282015078744046766781722198006578026467	4340198105561345164026421752515345456439687048311508553032629295018793074
9968872860266241223629598611186400161260427449021072937543841604992612437998	7838393816504435820788956311695908608239593034913737436154805082057187252542
10030636534551274013349396223843519835124436006391878433006457306504081583126	7869276460281625897321665511600558185172266026510357430115918789629159616599
10042140287115372709885524445453897075182238084548843095493023253421319545145	7875007444797619172585772081701166920388250876270531365684542129177216289924
-9928568587318335617700581453726415787699339199716824325856367157913594951127	-7818138062741237846024172158311514751465834267844170802606293488438205563198
-10028530953314296961728359557753582691308844074248871397399307024869589225137	-7868226779603019225149463989950854675859957185278552995955568867600870472297
46039670358983610191640361582830929902494929583016329667862658341923299701	46039345069638343242946230581016860990066473599398785877320188274527107532
-9918804493360310116591922770952057344987268470738058033816931081165937178766	-7813218616824014818683960761711863738110878512385527396799073767851875288803
9991853948165304722734645849172193278151775138162817620706379312019152733601	7849906948652659029507243336462249150611589785318563469376920951231866428469
9917065347904661213905196766733979473555248368451894472444325029577413982789	7812341878659138016350443323345160667253636629394484127066716601786219535017
-10038403285490957627754176123960182404960504819930002030940108819308075603366	-7873146453609373922754477633496561913317594893333935026027052192940856235524
10036053163107586872698165282257980758464098599072583372346342868284796775761	7871975758816376110073723290948639140373437231207132696163342273100211982740
10006455675289668371155268004028539906058815184135448853524890110544511512321	7857208429949935335464609321416531177056054281732241528490394766952185166649
83871020841625968404713505820289428086920663597400061417257006420319502116	83869054331426648789281539630821691925980157637026998011770412443895831492
-83510387764557960887195139200335121976260976979308856765901636982388598796	-83508446511852562721314119095912841094501552918231374424972006246590578354
-10081036912791731325917253160023315613781671818623040218823950722839051558815	-7894336359304038372273301462927036982397814404819592793852732335683419892328
-10035060906982262987456081740868712802840307840129540730267710673549277180501	-7871481391701541136127825784210872231080913769892450997833424916151154375120
10064826382941445802077903572447824490947227506532768218191004686417615775514	7886289990969457791775062408427866227218532024985434933510424874280654129326
10052041507380158947632376228867162174881912496228609403308831529260066901926	7879934797155499666153341517174900092079777608732285712499362906683774045564
10034624187438918020924901138150101781909404214626601747948273324347494100935	7871263791425477463139861311030068566616431034834332394002248747163335472480
76672089253039862846235456613697401619340729693774268843568983401807231349	76670586888514838127561403172903698527576328078003650426982631592253151928
-6823853323115635442300797926845105763617040447878099240115846582366986420	-6823852263940752139752264772253018458849871999969937558973302989057395889
1667861740167424966791364271737549642399867275790037946935037676523400307630451845105871610052832976814133681183846387240535837564216544229075010647	15707963267948966192313216916397514420985846996875529104874722961539081971474
4376022616662493015304548097405116405339198344540482132706139030349080893484770285394552239321947837487124873653104941059105503526971230705570453762878	15707963267948966192313216916397514420985846996875529104874722961539082031408
-42707726159406247771340223811312092053299441501649308837620784611048660943837103964978022594910146353542887820727068422971365595661996534543911087711480	-15707963267948966192313216916397514420985846996875529104874722961539082031429
-52024768752552734987825474592414777953925127423581309096762160992595378521922719043260202087764678711407178425944627207596507717481778758803608816077608	-15707963267948966192313216916397514420985846996875529104874722961539082031429
-64235499492435639558239993107636926780101118931662918720643680205093641919837060460513461694946909638693126610167543161571323292954283450787349798833883	-15707963267948966192313216916397514420985846996875529104874722961539082031429
-8171360773546719795834401225033889897647923706733800816359041027053518342502715207036920341059289726034591521448681599613725805451148863594121301348125	-15707963267948966192313216916397514420985846996875529104874722961539082031419
-40554047635874349032922163315764626413045125913823765493128676461985715856138639407638299083426031596199334523654386640493963195472118758177693449	-15707963267948966192313216916397514420985846996875529104874722961539079565586
-4751630960231829164355274093104170511026600583459213902966929704698009089123430651716973113431602170692346729166662642912642954993328461118493981723284	-15707963267948966192313216916397514420985846996875529104874722961539082031410
58745464082747786586116876100665091778824951589790900366980758123833401583910493098329369467430636443275652321503580017617280413875174766389560559	15707963267948966192313216916397514420985846996875529104874722961539080329172
-6652464987389775446859878383936646110762240973335345315454238338566226862762150907250599146066639232531842471692551876999887985544439204172979413424678	-15707963267948966192313216916397514420985846996875529104874722961539082031416
-82395825854035117038684667079843392124976052005887743848963627274936579113093583189293018673011265557047315946923730451726804473450495078796744408608	-15707963267948966192313216916397514420985846996875529104874722961539082030217
-6090473080178266258024236816117038759836648982279010149004568983169113026744956980376576000795063663473115449448424961779000539077126822781163002449331	-15707963267948966192313216916397514420985846996875529104874722961539082031415
-96301067148339374527517359453743675824298972244414331060368090933997279467924327892732744231393772870438557203140646011872905719205198834379630673525	-15707963267948966192313216916397514420985846996875529104874722961539082030393
251682073043229589062925047894196850525391584563389411701864432570263976971199084272027980240486060313649777559675826910709849072215661543470376734953	15707963267948966192313216916397514420985846996875529104874722961539082031034
-6320144200615046569159526840722322329535014249697176578723463472975755041691379060379512300556849776012695419937845526283291457458471603799007951422646	-15707963267948966192313216916397514420985846996875529104874722961539082031415
17574249288861437751384551753437454282720432806464752415772455025811501098810951263646192195772971560388752446489079425951090679613811341473334798	15707963267948966192313216916397514420985846996875529104874722961539076341288
8979675168706418741192084572473357649552349020832226439226018455357189764642344222703031324922836127856405519519454062993610686663660564584597677414820	15707963267948966192313216916397514420985846996875529104874722961539082031420
9475444774805533008321836371474586056062989203343699056791128511767365682888817046456234925551993582094535586462018761012886866102743736012817544757207	15707963267948966192313216916397514420985846996875529104874722961539082031420
12435405781743526754846304731391217936711739853003174557470092657976569209213301225370318779152698345917991913006794476945730035800970716293270821779059	15707963267948966192313216916397514420985846996875529104874722961539082031423
-5007551934591523612709945492727395880255885280090346448620809392572129892344531686166956567664890386070028091231182129245729072171747923344117644	-15707963267948966192313216916397514420985846996875529104874722961539062061593
88834663847488347813797521811729166793937129227149789324609632592029689236007498453961803386022027161875178624199994419451628329660784835168911658059424	15707963267948966192313216916397514420985846996875529104874722961539082031430
70786607324114912582671903357726982296649354549143255706577212128686303450322004042852086738385237963453151436181652103764266898948270696637412427743849	15707963267948966192313216916397514420985846996875529104874722961539082031430
-69747322458985280782005255746218365087523027869674116138457347504248046137059228262215292412118448113363537502925227784766810534169251597606538010366347	-15707963267948966192313216916397514420985846996875529104874722961539082031430
-734328378875125287948854025640157533287040217793725937060303989461563808696653433490576252261910575099488181033485609933033593812979864901695527910457	-15707963267948966192313216916397514420985846996875529104874722961539082031295
-94651389464763833489582127140398473869914573136422828307947884080330864585509038183190317978414689733419258921718585281887284557970813072385850205	-15707963267948966192313216916397514420985846996875529104874722961539080974923
44548400371353160544100948410889875790779825233499288755385686148546281113537882356552837231900433881587458338642047525967368057868680358765736190950	15707963267948966192313216916397514420985846996875529104874722961539082029186
54239797008763263252970100882429136882447425290546651955639056729393443914365668800315748789099482831896147590221524825174547512822633215754208523	15707963267948966192313216916397514420985846996875529104874722961539080187766
-72883859633246839314081311463691397948904827168022421632682561288018312539016876763514845969999241394085557028124493447552634234316386292339791306955	-15707963267948966192313216916397514420985846996875529104874722961539082030059
93963421229512593508800305981974870602046746497427918525549620588243897354255454539631216195925522994441194199117145270216021643242992283276669081	15707963267948966192313216916397514420985846996875529104874722961539080967187
69252878562357292426820012486033560741313019023340889783925701746966153545060978903474867137606493106035868621855480529947066596891992318303207119234856	15707963267948966192313216916397514420985846996875529104874722961539082031430
29762884688481915805512731591559010544843444602166161795463199972607844089794046306497568185121243411126778768905150535552492588010858847190894877255900	15707963267948966192313216916397514420985846996875529104874722961539082031428
74241825229556507546965553473897145462337656544471158971854986289413480484020737135173436056818835530593934404942382374724830658450479363541842870046	15707963267948966192313216916397514420985846996875529104874722961539082030084
2988781255028112140670240461027618814232798339521373721757208432300639270536980137756441936265997602264687754334094155083762761356506323717397032567	15707963267948966192313216916397514420985846996875529104874722961539081997973
31540522169861569716698224429191158761984307489962344288022209087024524803519203427605193374470848065549092244415658162279900320752388410188257570715795	15707963267948966192313216916397514420985846996875529104874722961539082031428
61072623387597536181139047695465160841993377182244927465506897113384972043833527926658296898684598794437256633730849169718198501287649859031852994	15707963267948966192313216916397514420985846996875529104874722961539080394036
9406822459591822766756454407147266731651116215040861372102600856294664053427608933553322681759034898972617314772432227186594272058089813085894148288866	15707963267948966192313216916397514420985846996875529104874722961539082031420
23228225541268348888542524326943569898097641875889059481031968343099982667635303249606153387800915760039253627966363148960813894633190391733524302683138	15707963267948966192313216916397514420985846996875529104874722961539082031427
81354688043486175041617217289342668648419863237171575269588313749148962937714614479064594782744188675620632025812652369827289641305220180123994310	15707963267948966192313216916397514420985846996875529104874722961539080802246
-37960611475247313510822355172238208846987857540420493799584536008465623407359728996380535659275670110378251053469307970802304969750825087387603968	-15707963267948966192313216916397514420985846996875529104874722961539079397122
93005585674640995212791614683543984169576497088254511728393025805085950230883756292255095507722543802539544442518580381816756684056465452828051464	15707963267948966192313216916397514420985846996875529104874722961539080956227
-3347728912455230531461143464191899424400602351445929720076393795790467379698356529149430443837024704594318534933607614569522816654081649657020669615355	-15707963267948966192313216916397514420985846996875529104874722961539082031401
17303631823296618289856366899590094105012294090336624895696084050241948669808392918641469179108541621978956791210577248990378832638418274735616892	15707963267948966192313216916397514420985846996875529104874722961539076252297
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4706690851442601125209477860026923119857724405986063183144044842519728978906851742731423802289622260496962135983402456165325537698484353578594983309100	15707963267948966192313216916397514420985846996875529104874722961539082031410
61896884450898012337498382644800789187913888426002043247720615946229261453680452717799024046104284882856704591228610870356921624775376547343357444194467	15707963267948966192313216916397514420985846996875529104874722961539082031429
88617980987100762233428961337341118025420695523078707180089762481720763382996357236246418225942930622034012290506625354459611766375883303236040556013	15707963267948966192313216916397514420985846996875529104874722961539082030303
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5526242964472813534722687599996651229828339588198394754444934968243086068115094244104422626865497303333408162476548362870699967040871768406346480147643	15707963267948966192313216916397514420985846996875529104874722961539082031413
-37173933110166684776297357368351249582579979693188191041563480023698999967632313860269139642797967711017688531317836021440080376395727597388110891336	-15707963267948966192313216916397514420985846996875529104874722961539082028741
62262749586296262917797707432110661199038330963568926796486835278839312593984126893683552072911756788221464872638259107888150446312574810871679461422	15707963267948966192313216916397514420985846996875529104874722961539082029825
16569901561111229115842903815356147887026798110240865429232147708351240933915381762367008285942067798839605151148766398326912003610084728738530786220	15707963267948966192313216916397514420985846996875529104874722961539082025396
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43833089545620873182969957861751090747261935183615758741562520897005598118848141484348221038658408370851972935014736300206368620000481876907115237	15707963267948966192313216916397514420985846996875529104874722961539079750050
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# ─── hard-input sections (see scripts/gen_hard_inputs.py) ───
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