# 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.
-88473590364731040065650671431918854913054	-9599999651502122767919417332122223577
-31443202524929665979554935128311664488589	-6800000182016262860043082700103821207
-274398076532072924900723982801083556161	-1399996728788398948569510080224643600
-83058394260303373363555575492487132008499	-9399999783473036108000792606239695227
133092772884014233366573770403368348390	1099980090229210362347639277015511621
-1562502545899711500365584726347810962861	-2500001357812442004877068571407001686
-491291430577195285084917140401624723207	-1699990115948525028986275186052103843
1216690678941103231946444673254361345798	2299994126601953659121843838226772043
-799999239070677683502320038671040549118	-1999999365892030356481264846329648960
34299087207830559104727942278466126596	699993790474376593668849895440131952
-32850909878160296753149467143876152678340	-6900000691602555950636344891893622466
-219709829219274760266579100313364574922	-1300019386731152558501965641830231514
409593288729416641442872015202790341061	1599991261318700161149148076860807572
799998254332136720608468959651918527239	1999998545275722489401811481482136731
800000193243017030672856080947363773013	2000000161035834559290359291536597739
14887690949734521393801795858074868402412	5299998926039241426498783188227339873
21592781191738795769806171622237104336	599933151735225718431116208409815419
-12504397399752371023439578136371181141	-500058625122619624011047336170217946
-1216696021885310134176321260786611132143	-2299997493308742608708306517271421309
-10382297042356341018872839463229007167085	-4699999553697911599102223123916650299
5065309984371289785892187213063579206609	3700002431060318876116693883371312935
4665606174021877414285445227592449336138	3600001587967889413710335086375140651
1757590201847525116876018326382475605539	2599995168554890382600168690756134260
-685905339820943364367609094727830755405	-1900004930569793496622963733656758007
1382404064767973197356407597073373757212	2400002352293975248526448305278589216
-65850301578963760431418892152125017499787	-8700000069536431400504071283114263059
65850293920213176655260777005715627287285	8699999732250539020784468922875984521
-72900006438677625626584223371457249939516	-9000000264966149632408195282219706112
97029895152569237303305289648580139932588	9899999835138222514045195405996802256
-7950698049228413180293992733570064922372	-4299999648319497680577190241830125048
5487202674191682993696249247113828446725	3800000617310999208356698401011828419
-63605600783879628094995185830852078909117	-8600000035328989763601964382199475917
-3593696413806453484345762669213325816220	-3299998902297294332035598417436208543
34299990898225543300294368092568511711900	6999999380831614845196655590805077076
409604778443960949380916090162863938929	1600006221908045700813259894588460131
17561603623091178161720175647472107071581	5600000385107454188423929432806079435
3593692049659419643590033107812833120443	3299997566468796079477177227938923184
-2700008617084968374110565841084494907274	-3000003191509556004051229882785031652
-3276791262754474113783877379732951881467	-3199997155842027490525682892033569937
-12499990973110375218953098410895492279628	-4999998796414426972237340154617248061
94119200905929599306855076781828627968549	9800000031442787602395784068363227073
-22698104850802921608625518565981651913878	-6100000434542916425173137974456355898
-1216695397462237691276282804595669442897	-2299997099846524372709424598093719207
-18519295693835003129016285890816609221823	-5699999558206080780551168311963992562
-4665603340238788557160099445161810835031	-3600000859114709730649551555230824612
-1757609107035014085199817226069048646555	-2600004490640672934070215656812424006
5931898054865260877660263477090383185394	3899999573715767755274910603549640411
659430260756385789456695334055526502984108803563704689701477483478363264993	1875237550471625805121672066608903768332594055337
421451909188177667271233985122028551578287862262349165229039725384835282070	1615285675948763345382455980474089082444618919448
514299891889992351340364935645630577604542057970085208499263285275370816710	1726124609386332985905545298887539195234004722759
715770218563236235924064075982248573309203091673692649085176290192960486592	1927190035576633810340550894214460499518355739165
-789711151725678608924654017008845262230429874814309173796749965191840794135	-1991388937784630602275914801055490486119958120159
-656248121897472836907992834610624528718652295391900719613647488505923642079	-1872216310787665105830864513040091473714973695998
651905534929563051603506312663653994995708287460931061709982522302291618344	1868077499288971250979206550090099743693746865011
316698472962501746144713408809093897983683614529990595071254305294800822104	1468527182607124955844381694472063739218934361784
-21284099165520827067886277194372059076161056415305447967635592042465971388	-597060615822789456917260176540513264885340484957
194728170896210261765203520724288418768530728091090229102812942915597117965	1248752186027965975215181978917503066602566331134
-218526389619417819805602990205789630961311847413242652745945056164672538553	-1297681052533864045154814145550614910844542670438
-333080634047235190012401894476222085685889638262638381425454661815033449952	-1493424004162553982180800164268246231192053800193
-502148234233112169080500338841701051753368202645879620320647529338982440359	-1712421400319544876906933732438142834115309120594
-520731412049186865828096588586615723522403828178591729097433382475361786627	-1733290109265986630826697585216631446133711627687
-481478300425779858979798339884529601565785286204641223465503496182768941625	-1688595287608966784980091026551555139797317829813
167459812391523289103220255898257364608039170146125883485424930010448891683	1187508882410291027542780721699971390575406905190
253645518317405423777563790786235646630749879158365732671742972745464130485	1363773972483988742458472562846624250990000092165
-746660919487045010997557544375887484242513396696983537825118948452628715050	-1954524597078018173781914369025396402483133236550
-104141537512337292318683150494337847962361910190110315756709195438621186400	-1013618811057074893826731175462192509701975623243
715711153682343380151498144761033632057189390295287121092192127528718139116	1927137023973124518962382801518865048071782954814
-77657316525819799414416744744759594495050515351974907702907485757747045465	-919166370434760330822978281099255288438540752580
212434195893921802640665268387953096536660244005302815637967674046162411156	1285508075050820177329692868623200932874304778316
-885193794924347228114365350992381441086806146712602270465748858574922662679	-2068613971701699807463262217484876450009302984651
169842199143671900853290656939416054809016776879002284915260841267430468127	1193113797863751810359550365041630307355688331683
364824046364817237104642116768967301511562138813519771301487880823671223722	1539434275766904820372974523665357048178705365793
-335839316972935507318209475640054166671240230056741209926714724351150939563	-1497535682492044763045178557644078726160814149562
-78198645964541839610872936787464695075518560278731820185559058826076523368	-921297185427758190435841223520342390992186485792
-211182823268049172456136056072275568149377521241647761286437072396395928072	-1282978948885270661163775034967014661330413986908
-815980051082843252942644089312494704545704623271547977162128571513701044948	-2013229012913783849057429567598929515028665034308
291007102850979525802879583914082108337065822727927048672374857900569060957	1427692012454409811521206631986616945283514248780
-782129780897647136677150465281209500988586830999999129154639129843264909603	-1984995870276013101947559694433340346387602522165
-919489897362555642085163463917012949108441253726762446121440277683859492197	-2094991767207186617659792175750688236533006792704
544172750246389575030382160056672495175892263347954831042891507940274521070	1758918014212103401949393917160986773378358898842
773138928698386902347059645684536642048390367932493565450105313927090978622	1977360466668774424246757629691419431449398355358
-753925076320689514122091953685750274022220494513302212047353931678953464186	-1960842581922137589824817830840683530827859120010
370002262294412845057336438904796378683264657235455923618015413827818381328	1546683526059636038085437020144478558416195628191
-373977291247374705940949034284992453044177237981195506070078065786271475209	-1552202614258513216041333151141498819023578844768
409086613086359048199866943461080538685697584736756976421267105844508558155	1599331247976847304707128553736206486823670266481
-64881822132631073821237690005319984052692567860825867495470883484082251997	-865713811015939208137329036186779199673205047517
-165491849540862364661707660530571290002055545907040860784718141791969774461	-1182838730686978485706489133899376343208404689457
-376935939469337427951627566354112474931633273595156185923377172792345870906	-1556285182799223138444929053187844384911730777588
-871311352912283255876211421434701638253935943659443028149708256296785662356	-2057742958670700866226435193919669422697592746416
-865257021788255190778228855328404092556323161290895897744956673412778076482	-2052965782053328057789958634073716501289193861464
-990648885605908637729147849027427784039330427535921952499644071633070485110	-2147698193194577949720457970131195414955551787347
-324943457893952224526308966337384812098157749726742714616335595138614015220	-1481162128828411770128261272171725655636552476091
-322598877916915235142402452484974104750534549379465817287076615133130830233	-1477591159909833407546421892852704997765475429295
-887846829137188992294848503731860282748404165655388669557354603466871919196	-2070678540290350636862292344372499922409563873461
115257176253871740325833329140149709648754012397649211509324978118105152564	1048469959757422135416966396373297891749289508539
-94645691150959348281316190715698383703008958371174767739748013020026454612	-981823936143704368586074659378719029698741138276
-567017630305396649867421890543685320112017099058748130703958158744928967478	-1783195067676055908383167567779508280249858382014
521364229692019389431154456151231149020928736578494506676989751413824523403	1733991950636405161029962196883397740169725025728
-351289352318859867193322022073799509799449824723905030133653815494757914472	-1520156597899400518846777433415689575858786937886
-957744847242853219327233721051699434460271277703628034153659700895669842844	-2123651626993699732348882815264060515780729493111
-578965108610528166784227142165730401520290643562380804477646615223882413602	-1795632527304340717638344512261085366930804877056
-522431875288339089985496283123286931177610705287219022467325349466307105456	-1735174762009284260358213836829371876459512631048
-666613433542958482245973139571468226272120222780258133865425324173623436764	-1882021962141320850997777420791827504868750452720
-538209852395839238138294850713617750353043850215659010362716974292513482974	-1752469821366002050414054887363225245943227760057
982788977555400673077652820106607061928503246917618379876618366222997719547	2142003086746156687916196024994514205048633591963
147944237750069551020253954763488254122507393578685621870236150615084637010	1139460701491456996813563438093902816722646010192
79442660954831943649698636392370033784944325013203566054626377928157490204	926156958758612641313096835225388759166211451640
693554949201615729533852729948949729094173643748383739426181369621003198485	1907042148587221041474443288643026022045186452674
-546723868101568939025340023271353141527598568921591932004147034425164702770	-1761662371433130369243718045034328930631175591022
-877521304069578525644681130217613961563486748630628295249764906706735672889	-2062619992534715841553086256102416418714339365687
4255216308052177712070717568421938819671157650462181812742871720401419962	349119318048557109282891809823765152786344943924
-423897737409964367938574746427200406554085329411590680262271317604367992988	-1618404334181316283642998940149683396742747113136
-583500143278428070003210773125140426173401378876306142775679498037939450085	-1800308736423527238618977641817340735337416426337
820972333727689855558145835136932068446720489240180144307418731143145317729	2017326409091640548146631929298734003010653207097
675256254888203880486000857033183200183095582861319077013558858652490348620	1890120700827320032446917238938021629641507305365
407681771100145097459652490740265005542389354936406515326510163296096559520	1597498396897099363359067598121686410421419171342
-243138534098897966978676059118013666234290856456499646743867455892319733319	-1344676859945746249182140574018492376965997627089
-226526564914525551231032812929636728596281744233816437496193571936910513880	-1313327525139738225232886333785992607360379207230
-942897628409782668925666335634981546104219586381711513527174838870455234313	-2112620620520929971468774066280928991502429393859
835494745308099292530939036502093092195601337368505104675716195953916738710	2029151971175371968674900202852508227415158712295
-108645875232584993747322632133291223104936559873090405292698220109259736676	-1028026747225385011889902153493706972379532175315
686878726716587338333462127459882144743374076799979123652248570566490912170	1900903288608133721142327345491696325791345973833
-804117454198756008334978574319807500593978138696445292778730036988863029324	-2003425341999271734299826209237457442179599048899
-843340448706231666037803715757126437576145483616642711832262290750124489701	-2035483768545434860580737061148696659758172919065
563063011307151854298338099416418566569429303222629927719171457510367105655	1779039808804896572543501087742706819142349543451
-520302146636809070689782635454146846177487732225036901488930897808023034497	-1732813698573631940661132241245372796537423484042
689145251063176913740410189815441900885052113076373838339021207926793101793	1902991824844070276762101851056831685383314957648
183111943604633033299411791510017093085715598610023946269621431358938691425	1223410558003997932209224635898464994990760671179
636051799668143030941361095061269988787422163116428098625749934617613523085	1852809754934278606472497487050353758655940502063
643526474280434569998618698601561956916894195252500757570043872565179036626	1860039381638550462868864474650498964612191353529
-440563508387106397558725698499376909996899861115447837189430615958177007109	-1639341779762436204459357958741166626601897880996
417158722591488024933459008489649743313675250394976967998790491544028326189	1609782158187994549497328599861689087706373370444
-826563367304629435081380959654307417266240532554952708259741876744306405749	-2021895556957655375974512837823953521593886374737
-311633505687938637454428570720832987842624085542196712490179736246047147032	-1460656341052820332752681406378332620120371282560
456146057718416990579863084917653281917987153334576594188481027648665873776	1658445898423061199953297853774378264793305298323
-848139119452832885471313570711491000008082654642355318421373401014315615876	-2039337154452657257056827247912749421236178174713
-491690638925004052617886348558603038409636729017090216519304060581587342626	-1700450444563678195608147474385813844892470497831
425531073278161144514026854446483461725308708705361792502230685362182982132	1620480314415915083860691002168767184134446556363
333635969020319752488298594825723931140245784293224308512886681481388977901	1494253523107898783523052840939075316223805742782
-541095215510236178279147804364811792471989156574787964707516532038320589909	-1755595926995898599686214752760921585342836669460
-998365363786127346706796449724682377219604286805240320043510935875451256808	-2153260144159228040010259199690117153260662207703
82192497253999938496283130286404430003297	9367220108124761023958624892395807122
-80376711516449516368322112415124655914740	-9297726021913955684517561162601919274
-52426207857838197164542138527612850619830	-8063361827550711686306174561423357929
-12893232711402509659999972236740691384138	-5051890637564087861381882949318143453
85726829377138502534015751878079158663691	9499605870154399615195577996577012968
6893721189681949300814119437969283074287	4100321448063480680281455762061112844
-91013559659126340131983440408862406348744	-9691002378805892805586205539179623873
14008590595030164890842632348198230866255	5193555946931768687298710473872333421
1457457064908478546829810741571176903602	2442672576015941637375886351829526540
18500075064524082602690805688149951535612	5698026921945103197775647308354493624
11188218673255259593844423796662741621259	4818593776237575545165888249903970730
-51241379555679360881571781988518558178531	-8002154604849280636216520240040924351
-34338056090042621815277064289032704653222	-7002587892803552342017913811564863539
-58578655751200848238393397216700310889552	-8367193265872238331587179836711024254
-5655265512557862939480583843417228954252	-3838406799057132053832608977843997774
-93684278459442532441667852608973181733776	-9784881535999520794476080502647069670
93439623913442501322824996938866416770240	9776356439064185085345102447756856610
-19576347949842543628113740592146222306835	-5806448233682353089126252979893954244
50283218114967740768485816948746500349434	7951963077578668921442167815693896271
89960239805736762020645915420344438118670	9653471857171052168441297406504062433
-58878026322242345007850283150298233976307	-8381422773893426296286538347230240174
32694616219502907819478001122562222746360	6889040658776948348104138597507456423
-30787375697057676530800740164325725032378	-6752390607978291221208082632109773199
-12086311669195979254544441319351069441333	-4944221624309862127283837711551975393
-44698998588118970388478859494505954043472	-7645970143930977905901635727886654082
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# ─── hard-input sections (see scripts/gen_hard_inputs.py) ───
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