# 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.
100820594287727370854783991460074518	78948434650784053896004205601466103
99001310531715206410277476441108217	78037969853604759702046478994073956
427799298444141768602645628984455	427796688722539320348893011701122
99932273776090870641582464381596340	78505941758098008764720590445824109
100896770329910518719376875915119140	78986197021828249694841669637660391
-926667830923280079833657803802598	-926641307557749724109471803648306
-100887941392707889638774154153581420	-78981821770239904039943460830054512
558714095578482949619359675490800	558708282054136108146668663580914
-759946882843185046518603871193417	-759932253884591245995994967994985
252398225237936548709320914132056	252397689273497203497711422350640
100766004053388183720056086173948986	78921355206367485019630807044599513
-99930944184498733695295674790329549	-78505276507485838024201800650426818
100216430832547956666428343378176537	78647914734739823361791595899250678
-793245031987160130068492335476783	-793228394626479809458774219049664
100353946904311132254419143680946927	78716476965387215288011194950740152
-99229651904918424204708297541666056	-78153154892199674171273827434473879
-100750790796952150235525317821967789	-78913806047866980065847185976567241
-720234242161849566546263929264507	-720221788802383945343584846646502
99820464661002639325317570654475341	78449968039676729737482299745710266
99470216366213033897308625516737911	78274221606992401195154945849835357
-99010645304571489550510255290450901	-78042683865462366510089297967013579
-99254224609239819068835210673348703	-78165534735538673786729729919084002
-100767350692302707032140183598814832	-78922023383424912215603433877755751
-100322846357679512341173799700357818	-78700979224575393843911855652049063
99841999732989173322885952672626965	78460753763159070232385108027449418
-756271351760235083052141870938856	-756256934033504634100819315182714
-100902482463424156121749618418979097	-78989027510225061143175738323251566
430877663468544879267006605055170	430874997003771448975983074090730
-100663794589014291910158473047874776	-78870614513440035887262882385204597
87674682818229892099476371424783	87674660353502377766749652254715
-486034173150094666693195092465187	-486030346021926397198013215524731
-963358450933480908401134460124193	-963328650793938261020652023751727
-679167439355615784737493822107030	-679156997028439275651746365790470
100118519892818793122704818055106091	78599041182615443782427907834192101
-828609433745210697964273438497669	-828590470595440468798477405266656
-100708247025530881470403739131667074	-78892688778397354192165499559811505
99273110372992073304717666789648157	78175047404420582058428966926599906
-84106246081071312927721603206638	-84106226249217634281746258968219
99738984755230845601662237076600347	78409138246776413807678631469262478
-284480159772638467790699819075969	-284479392353570114321317071068357
-99791948121201667475073083149874612	-78435682111338024093668716042882010
939129810900787711725231816683605	939102203047140201752355574217771
-100703191971100821220503980318037305	-78890179025495509011357856248926866
-99899336580149858844594885040664463	-78489459288509232111738244864725266
-100415657241611007348970495489461124	-78747213631636762624866580236121289
619434051304163577090466693199428	619426128955099177597322545358705
-100789104845949268221781935238354436	-78932816141206235226663548328513700
-888537993219106389173985662173572387120670233087800682696202187407861525	-157079632679489661923132169163975144
5020384023646851084985495789986720999566317469409381303127271993249511319	157079632679489661923132169163975144
783868958738548089582298440714026494423856323275463928393618436841779900	157079632679489661923132169163975144
-937983259486696072861534631634363177340875583632924048413543660661924	-157079632679489661923132169163975134
63103926085601890896726330129971157429523530281984947560038153822102276734	157079632679489661923132169163975144
22261737268101307192211552897961712959112396753887043640714008523221878974	157079632679489661923132169163975144
88594208606265748494844746281531785436347364813846395565503159264661591074	157079632679489661923132169163975144
-30256199389522681413284195666366972757658708363380096514746706916106878432	-157079632679489661923132169163975144
-15656135284762818862730695411150547789325141793591939289894670363393873275	-157079632679489661923132169163975144
-466482439817236605128782942780501430848264836704473760732406586745500873	-157079632679489661923132169163975144
-427043795374719628219002710608400789977429421713008254413999165489983	-157079632679489661923132169163975121
904836768541668526456202200210757211621826959324803860618059667011590405501	157079632679489661923132169163975144
-57363380838667544647408283443349380980335614689294530656798605084492699939	-157079632679489661923132169163975144
857357126918124589041277513306833582359502861367768328963505542819784	157079632679489661923132169163975133
48544466658788194674198556186523538310710981465541957551565034814329166848	157079632679489661923132169163975144
208059084141499284855369539482954613617261983093649314328016194970853	157079632679489661923132169163975096
-780765162425093013914557976615696538093674320690818893782680780243987487626	-157079632679489661923132169163975144
-84946032460213322320007100557686975394451106214795431301844757289092919	-157079632679489661923132169163975144
20447553983211189599647803362872609928117653446409694704531142486677779256	157079632679489661923132169163975144
-7786530171484380259460109830866215262533744866373135014180569990809455418	-157079632679489661923132169163975144
695271846085731865544358382653587863961350618088908715947912455432832707792	157079632679489661923132169163975144
-98082342148165343368988352175030046713478693372824481479527077232251433956	-157079632679489661923132169163975144
422994923011149482036880404596655554766672932489749146963581353613843	157079632679489661923132169163975121
-2656189097112370126333525458692739517638565736788686510521000386447236953	-157079632679489661923132169163975144
-67226942778466833958890046292551358244866059802413904674922635626001182401	-157079632679489661923132169163975144
-644615176638881265897828908010180755378063032481288965533208003463833	-157079632679489661923132169163975129
-76725267479436236252834969878421932994110295299559616231424317876300126904	-157079632679489661923132169163975144
353685294666712586970172655003811298084186811536906753572334995874063579	157079632679489661923132169163975144
-211675985737303003091509607556985693229313168405279784201092434304331148	-157079632679489661923132169163975144
-109009908997511008999076268994218561535504699314865058276785165242122286992	-157079632679489661923132169163975144
69021763922818342368575324588568583294959504810138753259355500685844488481	157079632679489661923132169163975144
-981197099177544533697341927265494042582731703183658159423353323136425	-157079632679489661923132169163975134
-63758801787232818329744327914005041407534044649352640837558661854074197331	-157079632679489661923132169163975144
-404271495547026106957551011950554821823249815341310941339381246985971228237	-157079632679489661923132169163975144
-993542777094927484762670997410967901882983807379282283219966234853461522618	-157079632679489661923132169163975144
-79612466868018627945187375715602618343756586708264866402282179584485738473	-157079632679489661923132169163975144
-10034147070912935673971655413944345745001849077864833919220863463711416715	-157079632679489661923132169163975144
96488689022881944822175544451153847950049019464969471768477341946368180842	157079632679489661923132169163975144
89829687964850987122129315745689398089984408967242760272622206311959106555	157079632679489661923132169163975144
-537237645168986305689477897034377068646222370169613678738362481804892	-157079632679489661923132169163975126
882681463675127147738843035960552840755621118848281751675346626851970010	157079632679489661923132169163975144
-504186791906041167795943981795298564951952409996073895117168311449860	-157079632679489661923132169163975124
587716189615971255578597462222357715437866588517644619110758301865993013	157079632679489661923132169163975144
-207511627441543009315541189568759087266744211179150299675508573591245	-157079632679489661923132169163975096
-409746159467322424546294810611321473580484179517205938749741101904109	-157079632679489661923132169163975120
135865042755732120946569674412815625735581722800261002707692107836289807695	157079632679489661923132169163975144
-139739149252810812217045360286289236125076433367218908347006874507989692	-157079632679489661923132169163975144
908883608302173933684646222249934831423410310044984032742702469726786	157079632679489661923132169163975133
-760780730591973740623060501766408576141299468259335416354638052047133	-157079632679489661923132169163975131
-922664474098858094743533587830331226533371162917558469778300611859608	-157079632679489661923132169163975133
410723564359017068131856474396669830603303540875655958270642839444423	157079632679489661923132169163975120
-12845714095330402848892214406227471067168959305964122688924180013109234905	-157079632679489661923132169163975144
813589502350014435201876727090286086859695256493730159593670457181261769230	157079632679489661923132169163975144
-795154961467586934724091611781012712634702643931873452768877111704869103016	-157079632679489661923132169163975144
-42408547321094783454017256253340157311799374924828099312021820387832114599	-157079632679489661923132169163975144
-70323888396305904298102776226779998851476775032446589785725436760290816925	-157079632679489661923132169163975144
753667619932299498386064444380567069838043098084433771343122902918293252	157079632679489661923132169163975144
79882224843284097514444420922493074851664260815710767372975061060560	157079632679489661923132169163975019
68407971392768481891041131105920436263871675906053169715126917979529	157079632679489661923132169163974998
863370596096779073066166269224658288503030293380434596458486749359411238	157079632679489661923132169163975144
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671652981074747921441814782457940513482977679322677495314823675337086061	157079632679489661923132169163975144
911703157712520608914321339796767918712285992140464744349027011750886991	157079632679489661923132169163975144
96965520909950697133975847318793463367216875093643397726987554554474794277	157079632679489661923132169163975144
-853066591756193302335908087753944220019566233161705973419701939275831597429	-157079632679489661923132169163975144
37223395904542023233955803283176136156243989225728037666487993790812935669	157079632679489661923132169163975144
928148680663774857138969049644975672461402332196634149065630061361365165	157079632679489661923132169163975144
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-299525773369128275836939886848591355671122865597686088015153584035750952	-157079632679489661923132169163975144
955016601963005994605616830091545719429650608123090138842131521266734	157079632679489661923132169163975134
21359115719165651028882345292787920798098087522668765301777378761259026789	157079632679489661923132169163975144
93895404146280473567195802836609051845130183153796515491454464972595046790	157079632679489661923132169163975144
-23941269855075901530745780687760216097300884934499144772114829478328278053	-157079632679489661923132169163975144
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977694883810165994881069890002430978894081812438385684045915520102276	157079632679489661923132169163975134
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27365983640375248089169489865916609295263937351569229037885159711929212441	157079632679489661923132169163975144
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90404482240628177269864102681659178387038818833679191964838890042287915489	157079632679489661923132169163975144
186583550885584038923708693959042787656920624883498048910954322611178198	157079632679489661923132169163975144
913370652764633630750684878334253328622268640723684283561308435067540	157079632679489661923132169163975133
902334027738306464972679080531391944320200187202748247933716446716397	157079632679489661923132169163975133
580227815174444252625051420800365342402672760907884776484909293013338	157079632679489661923132169163975127
66570916770213661156193601593448318138855737329086455020842998094328972214	157079632679489661923132169163975144
16089765031562063626007368940299664815247488791646492344611234950718493795	157079632679489661923132169163975144
217176634329660299953683698134894555570966267140100580045950341265092	157079632679489661923132169163975098
778827199302287943692372145526939109628526189750979734166072859608987	157079632679489661923132169163975131
117754208533504478564593398303197026078629800603891183426335465116064	157079632679489661923132169163975059
197011712979469709127093467377605149129259001440692802174652047870779	157079632679489661923132169163975093
493802607688079785404554394611857921	137098840850333783081132763616685591
826023740617328811331409475219572129	145032071109095251026935384544108860
654748720029575585777441037003224593	141923718744739681120296950684337443
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830456749896387833976203115426364435	145095765868219178815934056803495973
87473207522172793274553426683480548	71867823446472237665404446529153144
-302438656074913216656743260167316925	-125146671219029320208296804322488137
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120785283530073615247248540510318222	87926403303001334156959439244573940
930732951439737162931389759654855428	146376471367601038825765382737073771
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542151229848322554135603452998810122	138839604515869954724672739518393376
716547205969541310384179579455231144	143213377115473461670958945074754419
22430168820703545848027027258096261	22064967981340228403220131742138929
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864014403012854446064476082800017191	145557019318670092547202217839162854
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521874322703751206525914165835764692	138147416940397913048630936564975108
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917787219693155546259305419945814238	146226673864168378047971224709951010
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701054757549714480306718627982958468	142910991265309053532952900642697673
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462569724950871293700366726952393522	135788911297444085045533547936012335
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740619130299486454486176548680718230	143658582852939542728927098331188826
337853579422685460527748711039110119	128302596561477964471565996184956341
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375816532402046881110436605227320524	131073493142489584478197808413195762
129621210118603971813276106108049941	91368997822003849453208802344262500
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879352659257951136366904627409249591	145756275836036933596480473440898138
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910925508425559556669951345033943823	146145569614839859974886429908321708
406008361744614999658631225885476498	132930271056788760194964189822011649
935933444979718695275166938108285049	146435493825336438700232604294748713
0	0
100000000000000000000000000000000000	78539816339744830961566084581987572
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500000000000000000000000000000000000000000000000000000000000000000000000000	157079632679489661923132169163975144
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1000000000000000000000000000000000000	147112767430373459185287557176173085
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# ─── hard-input sections (see scripts/gen_hard_inputs.py) ───
## category: half-ULP-tie
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