# 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.
24185993214740686838286228476807834266456027349950338682387079198013786369	10024215264922216695164475962046648169421438356811212884882524320748660324849
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-787137895126801545886769670290410183231198140347269679440496365832186222	9999212893083363678895400797506441517344271553230645533200374341078252219928
-39593637432098511079178838973981437337061322137415657760477935748410255441	9960484642027793025988077448847743440413417988612524703983072441790892392300
27803074597150555903950107720768887275751751347393386342563841173240454160	10027841760990050396094932190086140636592949420658858910216727901099567791332
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86253198532480608581039924662820462882088138272613551002898028166262571492	10086626251039688833108047101513726190439680134331195125076930594161237950695
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14746718871289400559891410385106862678837978507614890967700484404798409904	10014757597503976895864637368913843025730981600663095629466591462618183338950
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9949770946286256411042227349187707882738802726570358639348466448039383896740	27046623892734694674108219948698827802736597319965842346097549569866696735615
9963336847425482968115391013119078257144878020171543998139597621224112180292	27083339974028185955943138631660624165006434781160604102487584096357695054874
9947489528189200313558583475600167582621135456401951690712435873929087751646	27040454130830463005805940982526782266483013689680781660174710912401400455529
10007208102688963775029251142513310346278909772912770851938196187697492891183	27202419002498244302492121902266263086936145006011597294056481883981586865197
10044381100959909800586132036676229130551501288565009815095699150225316819100	27303726728891183099022405959431659249590404954993677154199345449575115575341
9930883116840259150334910459994575393306084572979395940255028072984569659243	26995586904886064630089764145626469271060546471172807790824600192132098190469
9943374515734092482959231202091521325167832771381200437880148164848534445866	27029329239386776220966173441040707079121801478355135006910175071403519715538
9980486341857806199959673169217143677325061712651015853386413041458786643035	27129826382364321063291198324349395797123070495113079063379966910458013499723
9906069140231186443732391215301831070092883804287623575307190796610994680873	26928683160412040112427193972057456646933142051202835567522954946564696393321
10040750567625914460795599697886992677810141639928841225079044506535154763698	27293815819091310338115090136891495946976739036661359491240315910355511020148
-10098286044950115138378363467872611339494796087352575415456854024916908470738	3642814104174837243513650725453132852911098725012476814932907775365777134054
-10079423196546585036364991335039860899952592439954604616235864978209536451872	3649691973967199318118110289231154956147191144732052381175252718178829194512
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-9915428667048026848404797783734842246215410065877082579306156849303619802685	3710038397474026383566263646752985330763072565024173626921329041725739571428
-9972331265990238620310705060158006301980985193914045754876296717489789952579	3688987264784185075471195497035353034418208158685642373157356191910607477389
-9958389919133688071320637881164009591038543977725295456208355731927371502243	3694133796530598219551291564840793652230078251736361361713955865106408258330
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-10042375919159595300745429407799531667646529699121587235373186190141069525515	3663238166044171020846919239478263883382480425662427897675044497198977607628
-9910267743575084300318261116428186922992437089071417656859354797389761357393	3711953614070935069691416075879097871193712200854938686792068724497470043718
-9980232641869203741834518180324316633856774818649048545176893733463888138242	3686073608531256563427676728008028776132401802674455551918636942732538400820
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618861278337976004364045740504916546547493486746084950584592924862780928829852	7530153418841679850216016003418840539906454533391849692546664335483563666956366293005173977845778058585
950810584160097198129732922946046870804321107976278722440790472102415939624444	1964169683813237211770843089618845913544979114230742391087089509090000811582482915486553681466589244528117816899531289
1157276903266127646253673872940654184812932204050916600838154818857653140391314	1819270646176721382645254604541223434694051767110922564651325447007776372870284933067469633080519273578626453081393011522230687
-958125570507802952969453289170071032103621143524717340277871296386380621801626	24498256407164328441903687722711733
1387726337946576201574327941262920555887158703274060778373432805001204302378984	18543388455139390603315257343418122274362240444532846605320734115092517907906056304944314285666950287433932282107189524186263486705084082
1343187819208072054698433667410490429701009262378620604036780546153029611152330	215727645828615556561467362075670152456484197446744039542896063462526795697909981226051786989412535535989643953760981009588067382364744
328497115690078974876785228678734187359993670775480007578068628424253201755369	1846921625832445693724933390926547428798270089575038056953530736498019268553907984449146419
-1465519293421385002049250119006787138289728960141124334844500587767888429044112	2255826916945
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1566296778496844071694907592935528362833266086110196362124247639172365639524604	1055370115822103727340782036025732166899885156034666873377664707376641115163522552847752365481637163895911274549243633933613856640091858986856371
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1090550682180961999430986173415830975750946691745133078387646990533214168627649	2301517866846057869378420251227461196292995617895055977840076595628552193634998668927130826385431943320050016583549576515378
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1506118718056119843628872430966637869786005918976841478985672250448027033174490	2569832601028216841406496467584137380045588341329930057688143556366663133975251080138409463783825889913740643698099282677878469022703061922960
968529874842559858546688030092175269269193437981750724521194555408966437511861	11553618425526511868943625198571052643658198936774119500777653550531380719282280863228870721640711295985115136345695653
-748898568063723004412181199286478331033499696665265615408903739542418060926559	29905318936394458592242124303869335677495791
952429855193842427722278178754527753768960141708362193622441057364660168538790	2309420683293220560786567159059275035483597914845104687254958670996398529061415763763446025175586678619171294124541303
410832219325428550319802583586662755943683259723911679391483184990860642919130	6953710149818975543698169680808259442668922015855097378138014948816172905583398004844337420505
1366327403362904544825204502396713757441609159439686484914410385694805324619994	2181951914117635001065221293733177552554103401980112832055835550876711947742890650291672937055928739331765760967900344969541013707908118
998512745912401539518656600682755207969805162130064959117812897991386019417661	231663474689783882225202859018288688507806562634973446261379092529552809158824544959196709811887678247759979476303042976
-1344754899098277831763741230587052629112569522089137009884390287717894354461988	396311596943056615
-882938279214364630434817208694277099870579386548894170066886233451950099940077	45131290036311116382285794987674362060
129433466152988189647415582399422549506712335120099523894167321725943495361064	4180459423095956734936384724040664880906577212432879710555080931122290954831306600
1083382712177837789416317039728359409309795395654796215755890490093925617462003	1123862987796922304052527669541057173560101474326686250205013490109395462604579750638461172040677076927038894271378465644012
-558590918441167550297249170322814522271048644546126005741714068672334726011004	5504332342122133181943127889132624884663298355805943
-337894593675762437686667846166987673495960280466287653305447744374503096080630	21155546570950450551471727472312438092579788994517100709974080
-322812257063166956630813606065184345973417820504704329001333255342712795419325	95596459187906512188103511499077639703778017164003933045409530
-733192794384127450904037287302862711182972075987842781996858952248210455951538	143827364593831402878415925082121305728391024
796429254566911587149730926857538312327536146561605667076976645683574676632010	387688615823748276586776333087069120322225585549570293810156165648605145216784778006391506674870152097108092589
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-904668326142704567095701575397817809248664308852521462468040622307312476620305	5137523250677190606357340474679004498
1560868613186934939895356722151560086499300722337776565516159125739905087402733	613285318662143772518781332615667266193712025021142854684157913942857074544821234532403191307239343900427910832149437300086750962829466815830108
1148723592517027841020160846104018468204190931663421062831138555338927850385953	773449113858814035815209071098696531244803535017759961521669460296285420866116228835501104950283711696687012736484374931080445
278198284406264314029643020423991751252766156323940310070318705337466287096030	12078082152494910825048708165915507233270445819517792796164309199071034219108687609899991
32623038159444068406249378077053766250984791045623790075357472529048618262718	261096196644934100557848735264220426658845977186477663393229755714352661452066
848922063455702285433179463325774566542097599709959663169560852310423556228518	73827263741655133009685457811402591698246258864833489688331050400274006981187436056128132521967376537774309812292
164702408956454929374879005457548537206895967520153443198230594818085972841198	142211506337632466918385094179183766132774926319845774632097315357887732072591801028
-348168208917298985470755864921624290920195657462645008698103038850338025102954	7572631249642780349791680215696657782389064441624376674543294
-1030384427000448235802258675143831991645095601967372394294783603163023763775077	17822675974381405979070489621134
-456743265744593506117960142408375123619070718842846241086200758064626182952541	145845154228241113748717723635419189673780517862339715631
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1219463259510674364869917907256939243920516777550322508003694360562644470169575	913306290528408641014619896188254369508959792248363268608865750098568153324637344379571974539788828394770829434775797939695869215
-642434750643212550325900116681311273808298711898944114307203894007820072457417	1257225789925666016684880983424293241818189089006
925006736919303799932051281536955739642574677996061508864994277675402876744435	148775752896497780656915278422381050415752475654064951123033473664060972710000949973324307302416975382019735774135830
-775762495570185322731589144524583587317094553238182546244523302203959231690514	2037337085255039372447372594446111841394906
721827824947175314400142945417447179759750018821372054133376676709370628621801	223143441007146431516695349814102982336782884622448639138403150630395330883165108645201637023585253051103187
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1092766506629776275779044001973262578921593006252557108035531179084347609347073	2872409694376283454228537830508507415341172387804962768650640277043451633166184848341103208739976922522377587922550736222553
204922084663598022352085692528031918619946724400010527878407375018639807288243	7936939300426874561887980913553947306853322236816869568016402326275885051817532426262
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1492453720161618416333923931185379602558577362685462193886763123465379478938046	655302034372544022303378937993839638987948999214727095874273830714663590641513034942953161977776710638361927097219305713478960537817724758235
1494678016581771239813352661481293489914942764022775284580085599277206110631603	818542968887012756580064145818309815078763555796741484593594389569444437975301681995940084510127142245820226363868759019922542450291491255399
1054271386425365576383102443342941842039479293386173684245531388170762948769397	61153955839834762069744665426824863741075793600317291932650206352015463389390412077634558898118788651923827020735671430449
221863834946966465082552513455887442242030644530492542960585389050476637739247	43194049847159987939252719406744442760053872845985410019627857313054975757291986769867
1353021556610043088740859936318751065269911878875125260945920965715314889502320	576739362684828240460366166457476493894354759899000758597792346658048367273377163831995887239470893890583173631058290845047154309113879
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349431351768956688230101917826538644090063743142313620428051126364794354178875	14983414284449164677097987347553502164530728223651530358629305744490234381904316198486643102
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83049203409398344626774043050073020045862395087229835811899409784613159813822	40437200063664460276616269073455231658436992382932546570894828218698968333526626
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153436784535025256876775858023686846950229650761773379548550389250418021512314	46097235859090718075791305331856491622736575150949520634631327313696313793880178704
146589680837468510983788374213539037389740765775441480332803382353029266691713	23243897367826702870299646040438193523008988491637632246074890141281769682441471006
64507382957571772401232965985098545326646556153471520067206603869726083778493	6331695867099179420336957959345430762486194960696168036871256101557442980877506
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52435662431202608314560204136176557899346401895410873080934809360641272231568	1893441470495261406029645401685562435715624208971110299605647710271544031647719
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108208783789101290088813723689301160165667619283362264531452741330979347202087	500550349912875871510353364855823587403413035062365391855321794995392669855052036
193624421904866410686109846560043636924860554183009010159523579858632474138904	2564494662478595572567771313855422583785084441461789134141624764249636551401955285758
144208551486071985928824694688335789993519472560288028738865262035463637747232	18318833499982056530960240965402324835031912562518271967202814357678652767262569923
143338959475044030783847546787163656533073835847768820494643982313213839733736	16793140215775928748071492407689052486698701077623090069891468056740772224568223006
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# ─── hard-input sections (see scripts/gen_hard_inputs.py) ───
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