# 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.
825194495943402650914841434927907	100828608610290567773657846806625005
720918116748588641428094287740639	100723522987302725546850793644058958
-575101486607513759350989566335108	99426549056377079867058619544450107
-709584086731888293232732288042911	99292927516990886880954768010087396
759965100760484869835435252328029	100762860164710682084520916004475198
-847789656570436342724883088524333	99155793945651491508111532075552079
-41051008361860963539257009333329	99958957416411719059542523857291804
895423206383061373431446121801277	100899444112390273101509330726058736
-199828564364636428001480992828557	99800370959986699685637668431675005
-89155305171234006490427084417172	99910884426362499617427545077902717
781646439565295965749790863836293	100784709270316126800122599162284590
351924847751583705163975160698205	100352544830321470490554308776243223
486783246679605110654171415865464	100487969961120170620917346784131175
863566721740214193378990201758210	100867306215745734888453060346179406
591738855550819230975776883254904	100593493088368797552169846700763224
99725370051050163414864185090321247	271082685394313994630435792341385426
99420623987441535875165867288061067	270257829078397927578874795257045805
100051921979742694426515292989646110	271969358067250013258834894274016397
99142984739485424148519502435812519	269508527932558487501576741110638075
100848228720722569331806299147939685	274143714181365875196009664543828136
99666111580707430488536939219995975	270922093528426339193559577904788957
99760419029827638697951440970633973	271177713759450224244596603390762480
99816911769174804386620018333208438	271330952758830773689967379882886346
99636199082100061922214623803982577	270841066080243915500062940232311618
100329390294757887015731382795999810	272725034759307948300579509694305949
99504640021330677667751528690149892	270484984397747704068174561815485689
99588820153869942160684445021087661	270712774879825812310083161004805126
100068862025696679293706642345555052	272015433703994197902691046138919963
100930942170032158713266332397726620	274370561707204179815671789034937223
99766672567258156794812072420968806	271194672489538134911056514632302370
-99392324406001403333427896095435034	37012176086537224811858659181231364
-99794511728378450885754080818405959	36863616750240996811865112775935485
-100183251979111825494972601509619101	36720591213088158430140365189698755
-99528311373161203222910218994202394	36961878557590423449580667472208738
-99255529743929337299398179091355979	37062841413571031018549516887860505
-100252929161834032421936942795117521	36695014251339908400038812214610581
-99361594026572067251277337318321503	37023551816496638543615694730464886
-99086239896125270265849409490509983	37125638180670187465826367953270677
-100409501835078758504992051609379373	36637604842030741371905118641039202
-100893586747001410473695350459733323	36460676312567779953125388142714802
-99255131015535787693687525195508182	37062989193937824133756611290339919
-99205981231649278665513665693889614	37081210050417514573970894569350640
-100756455687646519516885768411473901	36510709521937590626436877764522242
-100513515277534484591473623637483150	36599516619870644747801685111843633
-99995023260307610260964196548085292	36789775002919955900012813881977568
-100864625629749993670815891626801971	36471237260995834511065104494402337
-99866042858665843456329875741885327	36837257217274620597708634194235071
-3801630131463507133481372868092087331	3088375628948611772
2313836977117982109794538236552257128	1119093341819671222131098447160439881530844308
4587994931576200770907963586773499513	8421875516478359112791027034532824728770385774070489292
-4298387469394814008661867140113555241	21495146510086750
-4469580572426605367297536184200564802	3880236617295773
-4230883921080008966040842903500392622	42218674594017189
-3914097928011199472376745386257106285	1002971707581445254
-5571382166711047320447046742365448507	63649454250
-4949176990948935455645493133694575166	32062503412820
-3221681597770991405323944147307755525	1019564243955339108325
2439729201442690670182473171507097028	3941025956589670002597630891125615623959049790
-5584135976894762381090258888363901156	56028060685
-814190864488091260487116382448136303	29108109725853892945921417489211
1911200244696755296864516306617346358	19963523752519546942151494182628961063858616
1208290807313930135355494789240273213	17682362982995701437453273497388448030699
-2721063903418787217623526466951832311	152254318044608403235313
624107801153748851844250371065731694	51341167644054897852550281129477333872
-7128709449259274521259609695398650831	10975
-4377139000894411492310078811362008952	9779729751918827
1726756143267201691718536289549008354	3156506195862538570555654212005845313793503
-7304376107651310985184324882602360190	1895
3303435229686648630052318745437361145	22214519085022547148204018291483409650706520701096
2177969060593683199688024847901573669	287606997143370946246261382129856534542568587
7282101047029627290125402790887542350	4224380350632143458418484359397006659340593126038453956585987975336
3102728029387130615356857447832264196	2985221907488867171113546217576146287304248656376
-4669964890198851277790792062678576458	523118615628320
3814993167140071359858594649217372573	3700878350469673158025938081535714394317356055231477
-6570621667102174033169838518826674396	2911741
8175054185208710023418012943714769126	31901361536965395771265759128313251698621033968677488046016431268989587
3737268626718314014393557245492925272	1701184510442189749847196307437253666219290641676763
2421807995041171347648251780054425093	3294416350740335198864630507860889335259208267
-1546616987922069043263006335666499257	19192332776701683877300031438
-6401121877371557099581424840546142666	15859187
-7430140743621927293139009197303450526	539
1626345443848080309836910185408835939	1156454417257842381970139757679083329703657
6263602251033441459108171642468923853	159396560045987696021143406457793043778546005425353555917166888
-1783572902546015676408754073276051599	1794904322860763253134121292
3203017990491539254641783364412159735	8138238010791903043708604539548954554056264193949
-4195009191698154570396741736083730468	60437510255389725
-7785192119256774120566502438428186686	15
-3853017245324069692947338452822293766	1847390545920896356
4618791181879942323146370138968159934	11459224649803671674618916887932977994371484837448341550
7771876059349357906177205773590506951	566016206212849521290545733036772297312469764930205941289074609239291
-5210821340632075394674888983687953744	2342558557169
-6712877567140287581079162975405623985	702010
-1563806931655927161887344554448916918	16161169611014714425900256898
3779399860162152607296664762670675614	2592537468623943847643862415216920372468441219368322
3522181243298397012475213581570146740	197987960652674314980955547505932022545694013108105
1455651439662277279908269448946100561	209804055197176393413785997055565480039546
1833702088456310442477590780383864837	9197440451972277682686493145988731364637886
903881715145302566368798937617681297	842380707272199420152012694599625648237
-6903542301692618993156786313800827157	104303
-1229775229357104822451631421942477309	456198695512120771800166677581
-4227284956573789838928278402174842849	43765782654681810
-3292405630773191406113151985774204758	502648075012738682669
-2384610636926182660463312715787198058	4403191653107559876645090
-5941448793539812646401749806045529857	1572590850
-6554196671112279930885845713559419339	3431512
5762411638474764448155297772090982110	1061294150248180112639226173903495796211986328024570524365359
-3546887419872490124971116184887836626	39451512340082093594
-4399367502864186286617021484195010110	7830503651478104
6221882023511493910230840990394070676	105024421650799515092629516440320935084628845144219141447227187
3574407990837311378131432663263351896	333777198307586628678432633713712769976920145547177
-6653786574216657800649302700675803333	1267570
1387517532330104071577200445252436343	106148064178740853761615315436087679659641
6184740995458943895174092880967829312	72441738343477410897540206061406902083456515343812870357477307
334188413687556763946853852546499704	2827234552265483874582285680575724105
6697827763347677495094186007750490645	12254522219503965911429918838693136901268230145835666668138859724
-6037629818614942015977709011779931456	601044822
-7010938117570523843704327641774559052	35635
7521338678797183261197312253710230465	46212434419595077721813999342273934814610414510237070096788888889747
3611685853791333785599190305483434881	484565362324745922713523750593397733432409762187629
-6677301681688895837496733914537955771	1001953
3185769346977784471853091901480088698	6848894557987477713753476858820785368812931726850
7892412341683305547072573801964886093	1889345088566072540881469828737728374380049594157359127414859677693321
4588341112416102589349067938452695476	8451080958532307860623345811001796777375531092053265569
-3006520382808441454269848339052371841	8766936888573545322587
5079014884067064490426276805430381598	1142566210953591552884751304541678090137768749480890572575
1669355963330702080438272397292585634	1777955275429444883001685869289308169191916
7435648160636174356320402961118422991	19615963980987268321548514028688252736497066114034686855882703653191
3008397280372290632591011940767893183	1162260243200500355587216717950553492897556458271
-2777475421860368444805038552629574603	86611888202594097443276
8113966880215684737201180018480642474	17318505993176600575532482623359510549914990810235952851046655644709157
5513008476676135602166637275591398955	87637827095245499185878631603775394265223687555363968414468
6333273068640642357368828249696072128	319930364621479100367808290742185308038151413070618574073794580
-2283274815029422076748003616148250686	12130074595900208301301399
6208826677918276011694878146756239072	92170438391614147312190182592313719024211425409326297521689914
-4607351734606692477234872156565836145	978420750541265
1091095768718082767338487484598575570	5477327585896824085679322891400173774620
-5083712536771861384040825706637071690	8350586460146
1831827393744071039675904842220887704	9026622680787841872234537857033027399155549
-1437551405888643141961749985278721290	57120706409384729312671643739
5961893174615390897135459279254593807	7801409490671236018070199218955123635152250539136178911003514
-4010226681402045062600854879130805694	383536597254003543
102566421568929007832711828965338215	278894730804329855492172223940603350
935953736224936232330151582556615002	1160901653019835857325656478215966813407
1981190527180035720531314900887902320	40197693599891129540935356925990733741684311
1859119856262763001172416967589674005	11859187832472512856127491500967788681734147
487359762458722796423080341969341274	13079060700906836593191745925503627717
-1508082526381699509846315334224907517	28215048775715202264961627785
1311768353767027625445951029341780498	49766554682688270694821011314755468549720
916836240723845211879795470927093305	958890909752374307719932217475020145240
248898155591359908507766807337242118	1204899863813124397643237519672968920
-1392565604275285782421352610213210469	89570381453682250466664241343
635175297598161785965049859746616511	57349715510994855586011747924836388611
-1902212215351114857692721715324078147	548021143604369124581617249
1858115406507976499725320381407784375	11740664499535416104021707223901440799452653
1954953010438053305809447005964588443	30920965637494722016915415481706576416736930
1573639173760454492510685091247140000	682697160795961730235459705983911059502518
-967655374549577562042860561366810967	6273734048932144959529382952519
-273960146577159221624887089776807975	6459608551506581903218871102806267
515445928368801067037988433471836481	17320212821841114253548338697247582144
-1701428638330967964878142210274734391	4081213459100166260238156577
652425127192441702904045156214920738	68146934735627700786891503987432631171
-726328523446527042834395562455575315	70080195094359244420372593950468
1686525572472343079897968775841225217	2110996421644668691479544110685780253310660
1202983444962112853246820968097421852	16768365035055177525453515180230541710723
1774619601742338691138655308491934191	5094188430075326738710660131293289327413527
-1519490854188161048547858501407992947	25173005299287426377591714790
381259740759386850604738082289684750	4526786539535729152183067487066755732
-1404794941397915631851748116942643661	79259821047839553405300581633
373409961336630181177322084264134527	4185032711890816124304413637108477352
1161498365873058328048383817375510124	11074479164114290864015561706282122511499
1239616508063952796950255242400024722	24187227598845435111787786064526678416751
1832290735364940132882988899266164551	9068543824681737698090469210414906068880621
743851021380801037114739330323275866	170021537604033062563801346001756945918
1234793863193754217067026330142642481	23048443958980431047817872933342256549522
-291905012273847249923638298478209897	5398494202254674952705196333889638
1653489552235166164040815868849712742	1517098867669496860691378203245387030783701
-1901618821977955607732356565407572004	551282732208882894499712039
462861975833628898948319562975591260	10237266753126420075293822717028219501
-1321012354042512898524426984550141579	183196107277174069184463434246
-1475795924040643070387140809937821954	38967248199252955406889300982
1711088636439591325729014292920421050	2698755426087142639434730333745342483719415
-1238881590853066526388566572771711559	416490992791261510729106280156
692540042482619148525251323801020562	101780174112290040659846961599612508378
-273585229999208664145405088126123937	6483872150543240771969823944979585
-78405733212077496750705172273410005	45654987390045678773163597534004006
-1306164428695724842808536532896222281	212520075532251264440624675231
1296034768959545075299789026247958373	42521393154290176339012038385873584020695
-1590939528899828745373069375892370187	12320757664472786915133561812
0	100000000000000000000000000000000000
1	100000000000000000000000000000000001
-1	99999999999999999999999999999999999
100000000000000000000000000000000000	271828182845904523536028747135266250
-100000000000000000000000000000000000	36787944117144232159552377016146087
4600000000000000000000000000000000000	9496119420602448874513364911711832310181715892107998785
-4600000000000000000000000000000000000	1053061735755381
50000000000000000000000000000000000	164872127070012814684865078781416357
-50000000000000000000000000000000000	60653065971263342360379953499118045

# ─── hard-input sections (see scripts/gen_hard_inputs.py) ───
## category: half-ULP-tie
-3535794062197966646330632348949516458	44079990922802739877
-3671486413355441164317631027752345745	11348464487659548757
3331740135447131399701966699957534780	29482449247887361671674724254830884059727170694109
-858698414526902319756547992764850766	18651775072320931318023342416551
1066304234628722809841072708741029655	4274648916885013798852266801976903326092
4220746416229752702755430617477019110	214027106822012418066568293490419596896649265213984437
623022346336660084311553735754258171	50786896092409757317588615836830302691
1427278620322471266070822122287483693	157976427877551997098994728437854927744647
-3127179105466001791331929803110201864	2623213904854918355192
2409149315835852427838406502515057463	2902702583655690575666580363857495268224454346
943392726883190563515071164397127676	1250554304792091241713158837443385625174
-2793616585412133539422923488652610406	73701669220723662330689
-2860471211879656198360549200276452520	37768642056777669034052
-330715923852278310796719310279780555	3662005497446093202495911553743325
-3288546653095949647320038676729354326	522424277524923464366
-1366862721458687762146144917774576527	115821884125032729145228939865
-2853648974530491410222430584974279167	40435234930617894520390
82340680115063127008772650884241120	227824817001130425301414562409476713
-3575116244002777582673874732345909855	29748661544270557914
-2247475447636357205059052920943288252	17351544915868151767432089
-2221077664426765755693538962855514385	22593435029681217741619711
-2056635162726831057041364498878117523	116989524390602475521481872
-3768285151279329383013391574433816687	4310677430028560343
1431309993707065536467050854807625024	164475161534662880009502374189731208536601
-1024873795112104141183323856779964982	3540215191470727696409581849081
-1551277197997390533067672832067952609	18318450280249361731315469432
3826000833210562534793867188845534823	4131526057625338503158807258436148672802942808409657
4165189290462992303744098680852243602	122796856484527599438259862744916245411028421356241886
940227673587204676413000020579207091	1211593413427014898833181148736249315228
3790718726467967589527569235303635821	2903235418844440444784048772271111246806282599679197
-1143214284963879655915712859268146099	1084135196578515341544587579752
2165763202376706204334376152321001291	254559951180300911535920576209334359843862354
-3778313974180278881091001499207984112	3899338171407900083
-3040751842192200907585628319608144288	6225619030109961181050
1427314225956186764084977612335770672	158032686400826418491592533573954451798594
3549274418073666412144853113701006737	259598958223171858674851922795508551418626222783656
1269864418690710608251530628787967296	32730383807906055054801092713706629199887
3415255797972031962967308519377499522	67962206968466210117468235996271556282845943464307
4450766098662565718405467344037987128	2135165624903191872006974337321194334450128896578272609
-277132718699502433411993469196449386	6257889570719159421365376082204950
2904359609671583511679285637754062134	410651600137463061395813787923828539169227944420
4323361777268876381695558817538256143	597202519663180713909228898189998116816476407124913879
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