# 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.
-138240042209040174383485	-240000024426525392631
-2159999773508482159056634	-599999979028562429874
-8043570407473651587322096	-930000015704075411673
640490155778750046282	40010208972924086202
49129882366508885099570	169999864321124568008
-292893780333413978	-3082502114253278979
-8305839070231488653642242	-939999964924983173397
973359000189574182287991	459999842499878994258
795070417829443586589118	430000075325287613717
-4930390467068409653153895	-790000024946236976141
-1250000381356087627365735	-500000050847473179384
-7290000660761134564952452	-900000027191815415691
639229704181333320913	39983945727815105890
6141250224022458580764729	850000010335522761558
-270000409508235085949751	-300000151669640019555
8847359274773356722202815	959999973769290252689
-8305840732584316706827327	-940000027636347335468
80273400526752868606	20022757472280382097
8847359115692227953170782	959999968015487503274
-7535710290671808996129349	-910000011700350410933
-5717869032798976655598571	-829999953200702671905
-740880685063240403026778	-420000129452575444556
740880705747380682645828	420000133361140700903
911249986627152863359863	449999997798708279497
639999206414586475634779	399999834669637180444
-2159039916466055243883	-59991109020221712672
-68590421470393240570918	-190000389168541055132
-106479177897032562895207	-219999433811926177507
8573750213521593939725775	950000007886300726397
121669566840456010865293	229999727057304333229
-156250966730928858088217	-250000515588765396483
-175760875308451526373271	-260000431610945995612
7289999245984502870322417	899999968970554603869
6141250567296761969114613	850000026172860184597
-80000347303358053115676	-200000289419046227139
6141250655660336097771943	850000030249610738836
-3732480222683938610290384	-720000014318668607367
9702990758278136609685514	990000025789141137191
-1326509218710362170408205	-509999899873152477511
640902524814472943164	40018793768774969828
-3890170998803032954380013	-730000062475945923146
-7535709118016223002519842	-909999964497693056121
3579109151414567047034617	709999943887753751385
-2874960668697137356375560	-660000051170575873240
973359116147185460639916	459999860766685244963
-9999999174400694218280886	-999999972480022383260
-5927040550994840332979675	-840000026029611831961
-1488769674232475817496953	-529999961342405607735
-2500470875502231435738148	-630000073528355526532
40960947298458774726936	160001233452026064112
-156250557852342023466231	-250000297520895004310
2159875968890953378993	59998851541822661051
-1574640497724713422654054	-540000056895823157415
79169187021836090826	19930524522510345797
-17279280960992643091753	-119998335534766409618
-3579109207752302870492831	-709999947613055902595
-1756159175883690175922219	-559999912402589420109
4240363430877647800957568527465885685	7512786148571966342082809
2735554503715179764452588468790449044	6491550760367052685650296
7316085755312451935458351604378847593	9010722099942641882898686
-3989151207361505164171462280358901322	-7361395750377587769406477
6319903545783550688453982965009676220	8581637196694104821684799
-292681441796600312007262409731682559	-3081757029324468005804591
-5483410086526675729839183773758010411	-8184966549356514945598260
-1140711547507385860122179379909131099	-4849816193845288189730673
-5861816109924751241073314147606585863	-8369073783605340854922137
-3201075438885498097059701711731463471	-6840669940312562465857868
4575944515853496713874630117037527657	7705962950535387843105014
-2987307236807856035004842203466539425	-6684875094745269702458826
188639419467448564984897154677852810	2662016953807471817478454
4489342396153996145249862283239685803	7657039895547487987952972
-9794700135364716303210206240625054155	-9931092984721743548199885
-4303232470804858364907302888800887018	-7549733172333919314220616
4129902245943796931151178866474386554	7446975482610876794750379
5620705136738193411492894201221745679	8252716650108951552243107
1805173930007474283008009595021468676	5651620836577693621658165
1713233427133687605241453558260069916	5553995366895144393976912
-2766212586046741403047398922772509468	-6515711566755724940260388
-8733828477994180172152267456750230847	-9558759897467890066855289
-6641060973959228214151493987634206231	-8724605981154146938910108
3172231849775836649982499917748343559	6820061753421736457625971
-5779326180772213247254856139344343256	-8329630477232719566911330
-9577253689372574884328603869659196656	-9857050854258547629466979
4257980411202517409433211590900262982	7523175960627924613065779
-2954705966742819063639562641691529690	-6660468158061389691230023
-1336966990684224136950044447131105326	-5113366183023263553324220
-4851918231098421086019294151185195661	-7857863693436304686118570
-3024986133988230032674833761628837014	-6712863187735391740870878
-5315547396716752782144975593482396009	-8100577816178448585937488
-128640459077297147508062343064716032	-2343109188336571998279121
5601802999756373011315228359581239102	8243455109029424694100557
-9277396313083026515587793631676890975	-9753085611360065541718938
8140227947096166252859183723502477574	9337103841817071642697235
9458112142295530310305458755560753030	9816006101580604111277545
-2362611189473372765453774483064247375	-6182024930951632669334070
4917771386329838500812129587961605803	7893254609747562749090976
-2872127162864763789338010346515420481	-6597831521205445555727176
5410593891670939614128131375013526969	8148574601946968638823407
7397637961480962911037770121467485825	9044079218561413259227979
7285393059427346114675655653426989549	8998103740176615658171750
6966316507770514373790433391708989207	8864775347217911721567558
-1047818483815364668698334306360854153	-4714424500477853646102434
2756457494956939370806349266088230137	6508043293343308273013130
-5025350941879428002947366242296345305	-7950396690187731606769446
6288478206099430442709363577296893132	8567389664195283423913224
2292203446821715068384515786766145570	6119994808635538148730234
4138590797323851202210816288003457653	7452194178157643827838380
2724092275152267629097569813664797094	6482471332896723401757705
8373026135044595639844699380830067912	9425277572068399346603327
-9653399167053111774871144313981853460	-9883105275671906277343597
4404870164298288016252287355043870234	7608710099423252005333864
8827850815061061077194933964361933518	9592938533587072110082647
-4497605667741581556410360111647259363	-7661734972153022628388771
294985024550629244650901270791638147	3089821017029744186791987
-5996132697914634510753511329481108136	-8432514147486125279919729
2370616598231976466500271290451314281	6188999395656546139090778
-9556832664719282895387578400397397059	-9850039995618399797625473
-4345851652326596902879578611120649519	-7574575505743714692850790
3502233732705966066768986813592646315	7048797630541336941835717
-6080074725090392035879036092837951872	-8471681874760170961267155
-5370898721030244638968596454474998381	-8128598155008268809476525
5715212734770695798571818901937395861	8298714048012534586847313
-4100366530275344737442187285284681102	-7429180211950004272302152
3846314679155438109208082457414534434	7272464402409685819215174
-9511772785886070406501846706746258321	-9834534823586456417744550
-468431095187443405622754106236607443	-3604806068573685508227286
7072728525206200301092490554833009508	8909684582707548287606442
7775942849947741169520157321696360726	9195690660568625790962810
-2839198635775517629733665487854596221	-6572520144691544589029573
4046055967487115301864458742656376397	7396233758854562541085723
9747778308934446545191737449697166125	9915209186784324183200154
-782104224615056210670065232029016649	-4276497382944069748961778
3609992729583494985650762014738775614	7120362578840024955534888
-9885067711374883328251564046761925603	-9961541521273664471228394
-2760891980968586897688346899434306304	-6511531389279613169198789
6539522366803613976173459968799988978	8679912419746948325315541
-581149715915487991924940665681515631	-3873432658489538300695831
-6566076367092538090817175225123648262	-8691644934719572773736197
-4630507705939731784621290818546525315	-7736470438741025104715235
-8347191689270176399680967476639905085	-9415573884697792514569944
-2843363075912931854191949676993831379	-6575732024624221272299825
-3316962906198769805853981401679693353	-6922243490972236733044491
9668019136250327673423240840562862801	9888092044591824750954745
249651284990225802957802393595878703	2922657573771477801698528
5200286197041922036611703970026056647	8041599042653509385796210
-8055150020988679076405419605312835935	-9304460811779468152997734
524529412792194433351444932134608880	3743317075818382332681436
-9233027585756146300660579504182473247	-9737512862981132296608287
-848882906751969958848882687041018143	-4394902683140526015371358
-224042870393241398879773576851039721	-2819099314966515175636185
1370928576415415491675233009628986780	5156301177636376684681451
3989681269766451249618761762208822044	7361721786846484758170892
1190833702116242038854224641849210348	4919833126784817270836749
-6519467931042910714733043928535070374	-8671030579038908944057992
5751762346799517181849356696465464573	8316366962533474996681617
6070196768388209080157595677533473881	8467091565715362403791792
4162593965114112223651947151318175315	7466573594407480729191618
-5632259234683578137579552811143403022	-8258367627582461719924731
-9611609729319245006148696717643759182	-9868823369592336529880081
-3037558608292962010769978505722254185	-6722150353711143340902670
-2470286577078651320397848264541015401	-6274548002831556006329399
4864657875569543147692496174818064332	7864735126986490223824536
4120737401642230300626990912821836973	7441462767873066358149385
4147568913204645935313105052928577673	7457579130244786307990277
8756377620544844974211659197939974341	9566979149357000883963495
6416961149771605852987384660310985517	8625344896838767084755744
623859057856374311565009754390103384	3966086315311360345491808
5287396597748925929328560808383759546	8086252450295312632525634
1883986421672410394369942861007731297	5732700541044888304018044
5838404518935407757231914614071552171	8357917129762742416516790
6170923372756442712467544369632124650	8513668146975872465337964
5130496189585648321977633	800546303396749418349
-6901562961859882530796361	-883722307975580638074
5179989230312724918522330	803112315244260660300
4290124163793304122106343	754205949306381789707
7943588606973495536227101	926130630396844314729
8354694354864986982756349	941839402471317529752
-1652941523859399718241066	-548806394867947678989
379937320950788243709495	336179054977347313782
-1091565667634909465477940	-477914223334779986355
5681340316471774134618395	828228685679713345721
-2596120473286056708250858	-637932821915425783942
-4640768945695858625844523	-774218091480797496348
-8375305812685022772956605	-942613288389441691913
1695792765008538826458031	553508455140001900829
-9915954560697952906448435	-997190600019625565638
-3367830239137595639359835	-695744952070883108676
-97057764252003252759449	-213309449225094896437
6291289591690489971733480	856866621296438554961
-3906409159279481610151416	-731014362622248737811
-4364650262432402716413622	-758548143652795779700
-2172986340751340840758951	-601200037209468461347
-5940091440858249770911896	-840616112657331524646
5830022532416611609003062	835391549422210674720
1313326948709559626070009	508304887130612699679
-5694432998430605195690669	-828864416862770311636
1717594890685585591491664	555870440056646138550
6067199949988905190358763	846569795286534595577
9646602711999914138952538	988078533808830729982
8697558093823230254589433	954550946793897785474
395530646966607496510127	340716667945122202433
2523205561308493774595680	631903670066474485311
-8918544988411808628621142	-962567813998812354437
893738474872219603003322	447098780004012345284
-8266110607794322063401504	-938498834048031240927
5390807262609317207644725	813862931250010683584
-6801568594229353418703188	-879433545327793390622
-6121326380428618802764628	-849079806040086107961
-76815004597371291035478	-197309813901153688500
-7243539556029484771409565	-898083971394998275898
759484435839110222736089	423486554353654322092
-9973883344286416482472395	-999128685841681920227
-8372291301894316573058036	-942500183707040311847
-3461256904220994351311424	-702119893607280869271
5682131633878333996687302	828267136779453998064
6882500174381106544936633	882907915410933707158
512647833870390254265496	371483654142448503588
-9543427490502054994018708	-984543235721334523989
-5655074680430917875257003	-826950374445917715614
6318540427823676776171353	858102017119563831934
-2409968817724476085172921	-622305741354288872793
-7896182847321679498081975	-924284632087085396410
7833633914805584463716052	921837612340312441547
789189173833989568843832	428937193898711551823
-7694101415482832867930973	-916331540625781032482
-1459109095240119193877920	-526456616425085554050
908832181726110028072696	449601652702967501068
6649787754089278453017405	872842587242323047189
0	0
1	4641588833613
-1	-4641588833613
10000000000000000000	10000000000000000000
-10000000000000000000	-10000000000000000000
80000000000000000000	20000000000000000000
-80000000000000000000	-20000000000000000000
270000000000000000000	30000000000000000000
-270000000000000000000	-30000000000000000000
5000000000000000000000000000000000000	7937005259840997373758528
-5000000000000000000000000000000000000	-7937005259840997373758528

# ─── hard-input sections (see scripts/gen_hard_inputs.py) ───
## category: half-ULP-tie
-2783546042149077128383649	-652929267764273474490
4119367773579255194649261	744063822567406072669
-4826728665089120270962096	-784424160982353562945
103793589730772358266233	218134074113076886244
-1465684890971898105749989	-527246295461271013602
-9260202084382451968199955	-974705660330102066374
-2172230102080354014381368	-601130286277146787318
1441131706170088161843767	524285553497740567920
-7623234096684636626431874	-913509536469761165538
-2347609967753518177011352	-616891304019301159533
9821508003779021105333426	994014512207341110170
369148426648727644598646	332966346326728303793
4820814309668244028568888	784103636128273247793
-303731036346717496051465	-312006080155836349159
-4986166641889521562338742	-792967880330908738107
9463314490464263487168760	981780550652920129524
-3203018262835482502856390	-684205359296478356280
-8311056199814533653609075	-940196737145132224263
3535919927643656232220891	707132515030728381856
5757989227046309852088455	831936699056658490404
-8703202146563382800178436	-954757379100601873952
659371107379525273051548	403995602380717734504
8223967962018816772786850	936901217382805182923
4749850439715739369008502	780237186235001590859
7007280406235409878441629	888211718982683484737
2272561790241934286327887	610246410369223018569
7427007103583690321664756	905603195791452068013
-6452198143674671564692127	-864110399687156135505
5629359311784394322714834	825695003535326352922
-121038192604895627431203	-229601194595778617335
-2399644462374964028642465	-621415812506818814094
-1034178452675493647528059	-469387833261074073393
-2550439650797697563540917	-634169012482207894676
293637611998519690869818	308510934434481208895
-1525861894809307301167042	-534365497509480815533
-6109367053714864113332368	-848526492247662336661
-8838518980004904723169830	-959680122738501519481
-9520732257237546780503676	-983762168531479220124
2024248016863583318469477	587157447930146671453
3619516255808229716523876	712661849321817628497
-9210777427558434745204716	-972968460827504989521
-5015618318782957566297792	-794526084845954320844
8934996062719537288351243	963159298674153113537
6699838765194922981707244	875026993026105492157
7052027989270645489625477	890098376924546971647
-8408487506803565230637916	-943856478453175352624
1766468112453591339262941	561093538424232444734
3444085018095486590363544	700956855938485843147
3871414502898278529211041	728824937776523652500
-2546922813123904294512434	-633877390163052903994
4045407706277832762260014	739583872827241015231
-6982412074785132521446231	-887159740480218977940
1320282086389388421442440	509200604162772938896
3357171042585329027167688	695010164444986017812
7401295337834439323826611	904556943079657985800
-3756722175700129704392758	-721555419274718535638
-4150596747318557864511557	-745939343162288876551
4862720689834904290823487	786369103331694924530
-5304212954551149682515443	-809481604720630822732
-9398813237048852770571448	-979544882281921106926
-9948076507602170301294285	-998266212638723916332
1645964913049192228242098	548033185809877991132
5998460807123605677668962	843360536603057038201
-7867972700966725307099944	-923182609409534217918
8228609688918277257386954	937077451113151640463
-4244662062323012105834020	-751532396501353401519
4146782472529111362103588	745710774452266711791
-1849094835044153431033571	-569708975787889901378
4852323406903933461002839	785808241982306260536
8358073325823715157421340	941966357805797326962
7733319445706239328252759	917885797585733169994
19099605837787429342526	124072291001844052293
2138899173846390352216126	598039822950833642989
-1218345611869848772718956	-495743278398973346934
-2044760999854919122061960	-589134131586617207919
-5947518132480961892412823	-840966297875209083199
-6772176242655013277701016	-878164919158013423361
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## category: catastrophic cancellation
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## category: inverse-identity
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