# 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.
1513209377284344072613418	3889999199594190241218
228010028428875507931127	1510000094135346429751
7903210557128620867912717	8890000313345675505828
1918439580525934769687802	4379999521148301186978
1648359552616368484122810	4059999449034899172252
3564089835767068568720061	5969999862451479628778
4057690914406665803325786	6370000717744595202194
424360902752276704874112	2060002191145137362070
30250161589213149994743	550001468990885059752
2284839404967921281418534	4779999377581467093029
4121639507355996998542610	6419999616320858471631
4488999300670703110249731	6699999478112444681782
2510010225247027921888450	5010000224797428012475
8949160700919416247469035	9460000370464800487871
243359983896765706745844	1559999948387068719091
506250188873566811932761	2250000419718998212287
368640756020842013461762	1920001968803266653207
4083209665089088213638937	6389999737941378205138
36000659213791472926606	600005493423114193129
3445689327887103885464050	5869999427501764148246
9643240142096969700792364	9820000072350798970127
9063040515707604418232183	9520000270854830400209
2134440649172899810747371	4620000702568019968144
295840134307029683121803	1720000390427367557468
5565159757177026617193882	7459999837250016064637
3576039776327673903205424	5979999812983002011429
288999088685442073896201	1699997319660951918103
900000444278110705462491	3000000740463426461423
1204089891907795200156056	3469999844247540020567
10889590939995116357177	329993802062934454096
8667609184619230515054565	9309999562094098463425
5461210917675156596775914	7390000620889795701192
6905609320164638713974111	8309999590953442829161
8968089334312951678279676	9469999648528479052300
3091360530310858594962740	5560000476898233679649
3239861789925069319764	179996160790308783735
210249553624535610844753	1449998460773443755192
9331559798464417680461712	9659999895685515834529
246489125194026218146074	1569997213991242145434
5595039585422593756988469	7479999722876060212046
5169609049797204212998667	7189999339219165890033
2992089902015026416414348	5469999910434209885019
7005690804768088994121616	8370000480745559069589
118810364728623462261799	1090001673065796088743
1149210978567196368673371	3390001443314141671242
3956409471494906707887663	6289999579884649489823
4409541318951363850479	209989078738665927090
3636090351997514086758854	6030000291871895164045
566439099142334659106064	2379998107441127061339
62409377251894807941722	789996058546463938886
384159242712417391470860	1959998068142969857940
5655039945365123179965160	7519999963673619047875
2115999219182452012577728	4599999151285195631408
2714409415173509390663212	5209999438746140009668
1971360371711695563493011	4440000418594232028581
282240098297891198948059	1680000292553222143480
4070440244885276018129752	6380000191916357629264
8197933770125854085874584922789895472	9054244181667431751104238531
5311546091569415499154907082028223032	7288035463394381356373590286
4240736518452600280162456676521918160	6512093763493121173168018947
9600116128526492452910389226485911499	9798018232544014026734051346
4278168037821491734248674689387045839	6540770625714902513262774850
1205986396270353173888970572059264357	3472731484394313452588006459
2303539743374556306265780562665894825	4799520542069339144694611634
1730175207404601110488271536605513533	4159537483188005976895216395
5766603301038941518309093989559818451	7593815444846511094533676875
283734452986645456974929493490922589	1684441904568529359450698307
3434708204796825782397325182688828853	5860638365226799917803989397
8639483051292010541856115322357078448	9294881952608118272645672079
1909403745831668608320293190360196102	4369672465793824927742355844
5316428057633126238927599050507316019	7291383995945575104317481377
4539315954461665820759584592562953449	6737444585643481061164214240
6327435684538482735846964860809371684	7954518014649588268192944700
2056701811041770338970696631526847451	4535087442422439487058572927
5834589043514156972050734694749444394	7638448169303865199888025377
796381227186047031258482579899992273	2822022727027631560527836652
4823598060874254735490770651138717829	6945212783546847339522949825
4944766953100559828599298156291601412	7031903691818140812924540036
7483512055039616769031669394314799513	8650729480823924578996189015
3618649692623624456055565829945360239	6015521334534210141350840883
6312362936293847306270654482352240433	7945038034077525614190189703
5305881577730444119720652311274560535	7284148253385871415078790981
6271541924220384516741898176804899667	7919306739999647542849122021
6085725297073021024680921943312233617	7801105881266463764827486803
5149593949761917051185054289714977526	7176067133020647160718954536
5466198484266798833922636586781209131	7393374388103715415636517674
5037646971563415969283492185019245235	7097638319584491175697318025
4367590799493090078822248123032648564	6608775075226187540750229000
5861976049542614892828868068761806102	7656354256134322114905979754
8158385277459676051543616597388008905	9032378024340918854533979606
4798509647239966765794974641066382016	6927127577315121721111795594
3991247162015879896342259282000003172	6317631804731801475121789119
4535057706484029793738183794803778579	6734283708371685311334353422
9484235713282374446988740367648416179	9738704078717236825017170165
1734568061565471874801346192974993447	4164814595591827632445088709
4069797319004419185612799302965971890	6379496311625565306854572854
4756395576258971251252498151947014914	6896662653964576257532845732
4255520976946403140334474189440496027	6523435426940626305393274544
5953290610511582917671743292776685668	7715757001429984716643653801
7945242411009893091639504273282924175	8913608927370491887256306286
2439537811738477342405479570713638517	4939167755541896293494200635
687656809377662416531367740428903558	2622321127127000852305902234
7839737322374453677238128984331729942	8854229115159858837544646878
4601181100075515836383157936697801368	6783200645768570980273640278
9796235128447836309338185576415900248	9897593206657786412612701432
9945924838105855293115637241679064490	9972925768351961062898813699
8187462599177952423771298210019785629	9048459868495827297925036086
286102490110331086743639612117971669	1691456443749974564338791630
8057845921528784763511568006792029472	8976550518728664049979600904
6631222283962746725653948899404901301	8143231719632413067106259924
4459856898751217983653754360861973063	6678216003358395402698768947
6921013571690170510774306825099961086	8319262931107641407753667353
1985621608464373397522485104557227827	4456031427699285647759845863
169639453702136398726865408737681152	1302457115233113534112143173
2274028301852126833275730291763664989	4768677281859327952813385023
9115135681120884524758570934126867902	9547321970647520026349673172
2930380233802574682302071187343112461	5413298655905264832206196414
8024661939458734231908911529313627051	8958047744603024960988948497
6266499581873213589943742279963079728	7916122524236985046151444642
7750382467525414127218991572450050432	8803625655106772046021220529
5755605075967916779922652987574135051	7586570421453897490950378074
2762730960757421444489139115977454863	5256168719473739880691505033
5153468403301351947459728513585781555	7178766191555030682241732455
5771292384711622323176369591648879252	7596902253360656688749001775
2872981458056525935543191822231558313	5360020016806398023979099302
8005596760241638942152046883361088207	8947400047076043722498523385
9429173898830046006070861028008446901	9710393348793881895590454603
4235812902834244290995841649577618829	6508312302612901112868474694
3948353487209636730435804945110370610	6283592513212196456867302760
3396314538059971357753084953971495398	5827790780441565712602320743
9546954865624918532661792535488243735	9770851992341772512160120586
7828025478657170977830488863000190507	8847612942854796345225010852
4968241854129712633824498594414822148	7048575639183928509106487596
8598389406830133212511210432313931559	9272750081194970506726098985
9191195945128980362962264919163819471	9587072517264579637400099933
3947768273205193820247952860988936705	6283126827627462288299104207
1103427026352408313393632669989246844	3321787209248070293065359899
8028017004573700690941119039768666690	8959920203089813617975316466
7423356855827946854612481442801859990	8615890468099015274651644423
6044514516944978592447469500519963533	7774647591334914385662379495
7846129257333345470668164533929675679	8857837917535715143262010911
2924778518642387464660790286148701413	5408122149732185426556626334
5230169794616155284682466525928031789	7231991284989325320503656505
9777950528091933802272045806707306752	9888352000253598275155260754
5758378862930128913690426052179914967	7588398291424962436629940162
2177037662379587411875527346875037463	4665873618498027226517480263
5189369748012027674772104462734224424	7203728026523508108872556142
8298604296090479930755955193837646690	9109667554905875889153163098
1296655823213839978432083272586025287	3600910750371133508957850822
1260691953906631729507714550962742263	3550622415727461901851924276
3595670228444486324374397529436272585	5996390771492870547320527013
8133583469694969828989115657328601251	9018638184168921314487818362
6130632501767762803022998274102408235	7829835567729224543924462105
4085009014582499685259517971746133320	6391407524624368438895161880
1849770476251176471494525441018806858	4300895809306680323239981281
6376240855295241841169890140702267800	7985136727254732387291407541
6589117953609649771059036861231763891	8117338205107416719713899752
7564349786530641385923306852884868072	8697327052911510114521689591
8288478893049749630158403868340391599	9104108354501142266245313138
9253861472895945046797307466012076903	9619699305537541097428519063
69431303759895813822012326385395163	833254485495852664371949585
1994422081395366992094489760639971984	4465895298140527378405765488
8906608409877879763097560417793400859	9437482932370198338751207893
5832840752932051286706285279869700982	7637303681884105416606466510
8295043194630250723342576650227944990	9107712772496863673446271753
275463802543975753620986291560494316	1659710223334108867840068182
304105608715946949951549743019683700	1743862404881609201415601665
3572062347739090738476465569714970115	5976673278454403465599493758
6871198782137602494300777578181995066	8289269438338702291009608303
3242738897898306375830129960222234269	5694505156638552360799157602
7464395348347651637058287576583412630	8639673227818082030969480876
8670985416313008009040706	9311812614262063214578
5008157240639961803599754	7076833501390266425942
1137171087977490865438025	3372196743930417333677
3523209160642836002722403	5935662693114254115199
8583135531292114003345850	9264521321305334447207
8692972321100673709588024	9323611060689240113766
7257210033993475333992401	8518926008596080847869
7346464969075680829169574	8571152179885549569818
2252226136093341405126279	4745762463601967305196
3973218967574304926525022	6303347497619264942920
4461336056722601919656331	6679323361481013010453
6891136334785414736089319	8301286848908074406542
2287632992813047797198647	4782920648320488075541
8018644740082320456178748	8954688570845063429217
8127737223866078187518764	9015396399419205897305
4268706663905090975183654	6533534008410066411310
318183566694448620888868	1783770071209988153749
2336642399384512645643079	4833882910647001434713
961958369542901037497808	3101545372137736497211
5280711693370767221204097	7266850551215957971680
2287679535244028843092579	4782969302895460610895
3854443784422456413227057	6208416693829801573580
1842796412172657396288058	4292780465121245163403
9930041922713732945085427	9964959569769328946249
8026756057878971276394012	8959216515900802403374
6721749121354219370025639	8198627398140629838648
1101295077721448441820259	3318576619156846349609
4332790675833288684325133	6582393695179048377189
6830192279102940485986948	8264497733742166430837
1535243591090721480259660	3918218461355519518526
4076731242024909184392564	6384928536816139796123
1881594958756837240753234	4337735536840434490567
1920896559381354479724016	4382803394382817258662
1506099599345796141874910	3880849906071859592132
9239375193034625727819820	9612166869668163291993
4813566077693818845051416	6937986795673380960583
4199107913605426096581257	6480052402261440120507
3652874611821618281054558	6043901564239459286674
5121935614700267918194338	7156769952080524935527
2233547104502775454255897	4726041794676360513170
7922247935495592419521417	8900701059745570636834
2552504753839182708204451	5052231936321988284302
2281556962012192031675761	4776564625347585550738
4746400985967762194754300	6889412882073306393508
5632791051422356319271974	7505192236993237949604
8830086756979731803656935	9396854131558993080493
8238535474734445775787648	9076637854808599653161
8881193583882125937385830	9424008480409027060515
8707025655914007711104194	9331144439946264014269
5772055307008823111050585	7597404363997498264955
5089346570641743821533552	7133965636756140011687
5602407382830501381106734	7484923101028160450306
4875714985692270437244783	6982632015001413804093
4034163502570623304862175	6351506516229534110154
4796239201460146827915696	6925488575876901140032
3027135269831938156956900	5501940811960755868775
1173047492966215463707517	3424978091851414257317
0	0
1	3162277660
10000000000000000000	10000000000000000000
40000000000000000000	20000000000000000000
90000000000000000000	30000000000000000000
160000000000000000000	40000000000000000000
1000000000000000000000	100000000000000000000
10000000000000000000000000	10000000000000000000000
5000000000000000000000000000000000000	7071067811865475244008443621

# ─── hard-input sections (see scripts/gen_hard_inputs.py) ───
## category: half-ULP-tie
2117664442202911262369068	4601808820673574290646
2362348291920491467130257	4860399460867894001304
247881022116402214870633	1574423774326347673851
9973944827838614187418137	9986963916946237864493
1541700197258560187800873	3926449028395198953523
3576564924867039972606731	5980438884285199325347
3184976555400330048418656	5643559652737206647288
7482028760584572704052115	8649872114999488652297
5508001285807314776663289	7421590992373073894025
1315662177642280947082492	3627205780821210793030
5167029131977288539097558	7188205013755025434150
9088795712227337729216950	9533517562907899593973
2681205757576969530860561	5178036073239514938152
6208456561092296439400831	7879375965831492444739
1890633023136117425543606	4348141008679591367909
3267764871804817259485548	5716436715126668188772
4160126542716695113055945	6449904295969588348335
9935478407452170474192348	9967686997218647853518
6652343280553054486926470	8156189846094225439959
6737757122590220935514544	8208384203112218440351
5636526673460450758188574	7507680516284940289926
9091820802834353187205724	9535103986236517802146
5332552905946550859624360	7302433091748633652540
7220034513592674565674224	8497078623616869043614
7364608936208204479347783	8581729974899119650899
2986843747215303208805671	5465202418223229185068
8287989777275311103651268	9103839726881900189536
1482417706165357378669413	3850217794054457614235
6722074357100208054812416	8198825743422168900519
6353833910910594933559524	7971093971915395085471
4600698237340379745159745	6782844710989910128034
2704086253501973732329821	5200082935398217023642
8014393539114268005966356	8952314527045097071167
8535350316924805261799339	9238695966923473373512
9906597966982423775929793	9953189421980485836839
9025408490877999196168573	9500214992766215917711
3487246392967064100311626	5905291180769212586273
5142526747781434396195629	7171141295345835253608
2380141094487468922414446	4878668972668128179747
6663730042515084455539412	8163167303513437397213
9342033093756711874835719	9665419335836760204706
8282073922800253125657707	9100590048343158461128
943439347091883118887295	3071545778743795833526
4020566743283316520002776	6340793911872011410045
6123891459685961057591437	7825529668773840293574
3168011065212761604192986	5628508741409896401790
4316763528619965332652869	6570208161557718357290
1443094505408054484123521	3798808372908607881789
2449001173197707362119001	4948738398013889117401
170014319574017107808017	1303895392943840061208
899464833910759263583357	2999107923884632837878
9004702594511163612903970	9489311141759007373318
5886165523754057224353679	7672134985617795570378
3725015928377635558678983	6103290856888302975053
3688074706062007404510634	6072952087792235665425
4539215365839716463715068	6737369936287984820333
8480617433837782822967625	9209026785626037488731
8186757669481858433428380	9048070329900104414544
6124506065200660788172306	7825922351519123517716
4549207448783124482804359	6744781277983092968730
692999609499261652287471	2632488574522711299449
6498175616595918706602484	8061126234339664964358
8634548756597308376340237	9292227266160308660243
974567476599054997558538	3121806330634645563548
568497380959889213315896	2384318311299666241180
7223497781036682177631154	8499116295849046786139
4965797719951797622824007	7046841647115250469685
6947932881438507699312399	8335426132741209589822
3649525924109648031978309	6041130626058046124740
4851254647837009876503486	6965094864994309520437
8111712583576035028006557	9006504640300828173446
6886299156122743058467976	8298372826116420673618
1651653505960273611760224	4064054017800789039803
1175028233966894495192863	3427868483426536735182
3156935726114670389803615	5618661518648965910320
8250170478151193620183455	9083044906941280569562
72398217866864788624228	850871423112004559136
7063104451841722399848345	8404227776447829236838
1475939484823402054693020	3841795784295935288949
3311870147998591894641914	5754885010144504959135
## category: catastrophic cancellation
10000000000000000027	10000000000000000013
9999999999990000000	9999999999995000000
9999999999900000000	9999999999950000000
10000000000000000058	10000000000000000029
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## category: asymptote stress
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## category: inverse-identity
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## category: perfect-power ± ULP
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## category: constant edges
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20000000000000000000	14142135623730950488
