// @generated by scripts/generate_decomposition_refs.py: do not edit by hand.
// Reproduce: python3 scripts/generate_decomposition_refs.py --random --seed 20260916 --cases 64
// mpmath 120 digits, cross-checked against exact characteristic-polynomial roots.
use super::data::Case;
/// Seed of this draw.
pub const SEED: u64 = 20260916;
/// Singular values, descending.
pub const SVD: &[(Case, &[&str])] = &[
(Case { name: "bidiagonal_interior_zero_0", rows: 4, cols: 4, entries: &[-3, 5, 0, 0, 0, 1, 5, 0, 0, 0, 0, 5, 0, 0, 0, -1], shift: 0 }, &["6.033500164699827758386919203804048583309199764164285271607211324599509338146894999477699871", "5.099019513592784830028224109022781989563770946099596407584970804425933632062224195588348851", "4.857661552904561023305062040322183168828752780238487388085591068777101866415859757277319664", "0.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"]),
(Case { name: "bidiagonal_interior_zero_1", rows: 4, cols: 4, entries: &[-2, -3, 0, 0, 0, 0, 1, 0, 0, 0, -9, -3, 0, 0, 0, 8], shift: 0 }, &["10.240724163180160014698860973144297743618587598692929914333925227706755440229137174025291718", "7.080082528732134164677169174199713647015875649054306412472140435048840184166205917397775334", "3.605551275463989293119221267470495946251296573845246212710453056227166948293010445204619082", "0.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"]),
(Case { name: "dyadic_2", rows: 2, cols: 2, entries: &[1, -10, -8, -8], shift: 6 }, &["0.214099388177958012021717699297722804005806522805314132475127007812334406791915228734838352", "0.100347671157949914035822347867612916603030434015056672500467917323520098375901085245313674"]),
(Case { name: "full_3", rows: 3, cols: 3, entries: &[5, -3, 9, 0, -6, -6, 0, -10, 0], shift: 0 }, &["12.153035325154457843730180910315812262796777528280499296642284099351548983800508742989899638", "11.609594604084587717111880971724725810458918275243909498788143820279476868395131759066576414", "2.126275032623462398850738609240874673580272084003746099963139541222390369585019142328208345"]),
(Case { name: "full_4", rows: 7, cols: 7, entries: &[-2, 1, 10, -3, -9, 8, -10, -6, -8, 4, 7, 8, 1, -6, -10, -10, 0, -5, 6, -9, -8, -6, 3, 10, -7, -3, 2, 1, 0, 1, 8, 2, 0, -6, -5, 7, -4, -9, 5, -5, -6, 0, 0, -6, -5, 10, -6, 6, 4], shift: 0 }, &["26.424154106302333767104012853702516679591006589819661722292398915736864972680818277019364804", "23.163564666980615591691099804155708128223491065910970381049935976879154534902223453203298894", "17.215608204245300960907629720949156109358264267817607992752999086478613409009960421241271253", "12.792728928567553833549819360438780135406735707373017514549641140982967406957763122600580398", "10.363083961422787418760894029838963879428383212208050414215177718470513767069919623668383561", "6.854786375898766467893299291377524419693231132555502616432592599480963776486606381893730006", "0.894799951050450347938385624808493308186576074881767719599496966105373617086238593976571068"]),
(Case { name: "rank_deficient_5", rows: 6, cols: 6, entries: &[-2, -1, -3, -3, 0, 0, -6, -3, -9, -9, 0, 0, -6, -3, -9, -9, 0, 0, 6, 3, 9, 9, 0, 0, 6, 3, 9, 9, 0, 0, 6, 3, 9, 9, 0, 0], shift: 0 }, &["32.526911934581186122438840656823055807102453133669805683063633973786847004628461893558913290", "0.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", "0.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", "0.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", "0.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", "0.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"]),
(Case { name: "dyadic_6", rows: 3, cols: 3, entries: &[-5, 3, -3, 3, -7, -6, -3, 1, 4], shift: 6 }, &["0.169216979325159688330637377968407305251086639602931592813289983219472357997078320205217535", "0.096760412370771561338590635876685030740424919614668032859816398216804265405689738527347911", "0.042402339332950916648120403786129944128397903136804191920958193558624516017462951689133349"]),
(Case { name: "bidiagonal_interior_zero_7", rows: 3, cols: 3, entries: &[-6, 1, 0, 0, 0, 2, 0, 0, 6], shift: 0 }, &["6.324555320336758663997787088865437067439110278650433653715009705585188877278476442688496217", "6.082762530298219688999684245202067062084970094786411186419153046486332725318910239803066428", "0.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"]),
(Case { name: "rectangular_8", rows: 7, cols: 2, entries: &[-6, 4, -3, 4, -2, -5, -10, 0, -2, 2, -10, 6, 3, -3], shift: 0 }, &["17.607830906321199334143446735709188292514244837384285142616151817311512720744757603511967765", "7.613428319384111206689754914593491422688857079604225325212790379458527386205885583970724432"]),
(Case { name: "rectangular_9", rows: 8, cols: 4, entries: &[-8, 7, 10, -9, 7, -5, 9, 9, 4, 6, 10, -3, 5, 8, -8, 3, 4, 9, -4, 5, -7, -4, 3, -9, 7, 5, 3, -7, -1, -9, -1, -9], shift: 0 }, &["24.835529307479251490269460377767880616070006969574957137479518995014435920798095112331216263", "19.831562190285035512146571822767793561171952165821513145604673886588671824957466632579082845", "17.417106037915995449609451652671381754045542845709511650494034399180021728019705225066012199", "11.337991108401274041604526579701609205395870736495919972960199770914243949837423809585234293"]),
(Case { name: "full_10", rows: 4, cols: 4, entries: &[8, 10, -8, -9, -10, 0, -3, -5, -1, 2, 6, 0, 10, 3, -1, -7], shift: 0 }, &["20.956782517192252988262901689094271198641026036951377181281724407037539355597033050526115452", "12.201928831009215628377245075816805776898832484140075239584964974604874560235686143187320561", "6.141269341246347504408833037544078813538485997745037140578418703569255801998364538682052911", "4.148615456795057801861540746767710878853502351967972107688974279629117382585500443055492780"]),
(Case { name: "full_11", rows: 9, cols: 9, entries: &[0, 10, -3, 8, 3, -4, 0, 0, -6, -7, 2, 2, -2, -4, 8, 3, 2, -6, -1, 1, 0, -8, 2, -6, 1, -1, 0, -2, 2, 9, 6, -6, 7, 5, 8, 0, -1, -10, 3, 2, -1, 8, -7, -4, -9, 4, 9, 2, -1, -2, -7, 8, 2, 7, 1, -9, -6, -5, 2, 0, 6, 6, 2, -9, 4, -6, 4, 0, 10, -6, 0, -7, -7, -6, -2, -8, 7, 0, 1, -8, -7], shift: 0 }, &["29.266889731038456634437664103655766857704726880557674681161728819077938225856207011310865904", "24.499064759635155901649546650848537271739601917131659752085879041496535842613444990733262934", "19.346816916093908113454025423941915880775185367150832446633596387237451959606986980443197147", "15.036255128926377044094983280395221704035785739078115760446106599848274301509395863902330884", "11.982011363362192413259142233331579589752241725665369673401173676516628320330305216144917787", "8.333610819565251135088404451996970316827297291603988265916963916045908132237704719924293139", "4.382410961970091572225290994396220496028610172637248118840512178681206373380001154758745320", "3.405132619718111098897515741315531422593793858694994535769580986599213825690947862707403907", "0.196414577454699605929055620184685706214748138181487937168034115306247332766568773234221853"]),
(Case { name: "dyadic_12", rows: 9, cols: 9, entries: &[1, 5, -6, 2, 0, -8, -6, -5, 5, 6, 0, 3, -2, -3, -1, -1, -1, -10, -10, -10, 3, 5, 2, 10, 0, 2, 10, 2, -2, 1, -2, -1, 6, 6, 6, -7, 6, -10, 7, -2, -8, -6, -3, 7, -1, 3, -1, -7, 8, -2, 7, -8, -2, 9, 8, -10, -3, 0, -5, -1, -1, -5, 4, -3, 8, -7, 3, 0, 8, 4, 8, 4, -2, -3, -10, 6, 6, -4, 7, 7, -5], shift: 6 }, &["0.433105837317493024653364586675561837343620112269041676824131312770557616301902488471485623", "0.381405098045894753720023377840170417059044336848789992227021492154529361579799848416370450", "0.348541987708837562973091459084432172547828851910811808164759966807876090881140346244268183", "0.265315059551511753089269726680144454771341559485401154030317422320330667613092088745973211", "0.221467188297276442066458113216045191468977691155996077456957769047580128926465916845462679", "0.168505398965902780902088572362379100224462142527023035789133723713762425975734906017923378", "0.109703263419053485171727707526058478779789773329582620647502453654019907972200114011637936", "0.021823400244199011041081291467084835270861664659173456034342547413560036591512020850930579", "0.010642811860446479097678176399863667488047007372870888901631335102192800803242407978167993"]),
(Case { name: "scaled_13", rows: 7, cols: 7, entries: &[180, -240, 360, -240, -540, 120, -240, -180, -540, 120, -420, 420, -240, 300, 60, -60, -540, 120, 480, 120, 300, -540, 120, 240, -360, -540, 420, 180, -180, -540, -120, 60, -240, -120, 480, 120, 300, -540, -540, -240, 300, 540, 480, -480, -120, -420, 540, 120, 60], shift: 0 }, &["1431.355575038248013805127202860932223179496284650648255296589917583830313314884606435136443106", "1223.925075344017030707476011753634575844106435727841602712658661316964268133384713879748885902", "1072.794829459330508722061490827057497790376603364328811842216269448850712727158934770684331364", "834.517632860305633255324451700637616838946949804242755241441590984880053520668979448288518244", "585.331259256874266397061603238219985825483542095731584529345016831368477060868771760229940418", "339.538206663939689819910513146341899634860845582656199815245214388813229632516150091989241252", "40.265683079072729436611138546765037496721744526970496474832667806326513655062936761327253255"]),
(Case { name: "rectangular_14", rows: 4, cols: 9, entries: &[-8, -4, 9, -8, 8, 2, -9, 0, 0, -8, -4, 10, -1, -9, 8, -8, -8, 4, 0, 10, -6, 0, 5, 6, 8, 3, -9, -5, 5, -6, -7, -3, 7, -1, 10, -7], shift: 0 }, &["28.368260035293589224915766871969458607072394934394360202287788965976119625420858583895869781", "20.746094946816065156102322848814056115759617658153770116053199299306553415768480250375245862", "14.379213943254907995501540888877367324514832432679079843036224830095511881865189918858672917", "9.802018843164969861451449793737735157201231533419797098292794319225507676397060530359155490"]),
(Case { name: "scaled_15", rows: 7, cols: 7, entries: &[-360, -120, -600, -540, -420, -480, -480, 120, -60, -180, -300, -120, -180, -300, 300, 600, 240, 120, -180, -60, -60, -60, 180, 300, -180, -60, 0, -180, 180, 420, -420, 420, 540, -480, 120, 420, 240, -480, -60, 60, 540, 540, -180, -240, 120, 240, 240, 120, -480], shift: 0 }, &["1421.315940510884060911216810612197211158898715475967822189713347436210546582516842115959599547", "1080.635014499197656547873405933884155060575395076765200588492588397508438077957504128245746417", "977.974891100566185333942826502966834710119660511652381064703424284137764565926101712586939797", "805.976692276906713181308446520236569839302128809256950934241947755571511500173924079459678813", "434.602642083487042479372470260009630330846786626994857559325914584107507008369160154447144878", "243.259379583845068584610705575795576100649671303955532399570533729873001689741995778952870134", "202.980453023751337853005639324841353779790859742938998396334793799430568605326160246022197500"]),
(Case { name: "near_rank_deficient_16", rows: 10, cols: 10, entries: &[-6, 3, -6, 6, 9, -9, -6, -6, -3, -3, 6, -3, 6, -6, -9, 9, 6, 6, 3, 3, 2, -1, 2, -2, -3, 3, 2, 2, 1, 1, -4, 2, -4, 4, 6, -6, -4, -4, -2, -2, -4, 2, -4, 4, 6, -6, -4, -4, -2, -2, -6, 3, -6, 6, 9, -9, -6, -6, -3, -3, 2, -1, 2, -2, -3, 3, 2, 2, 1, 1, 4, -2, 4, -4, -6, 6, 4, 4, 2, 2, -2, 1, -2, 2, 3, -3, -2, -2, -1, -1, 2, -1, 2, -2, -2, 3, 2, 2, 1, 1], shift: 0 }, &["41.919388856818294620230182178856923751112748309006769326088282266370128037309120447563660200", "0.874550096254177136847564837015842943034076049672389841367472310947577037426389888585578522", "0.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", "0.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", "0.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", "0.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", "0.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", "0.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", "0.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", "0.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"]),
(Case { name: "near_rank_deficient_17", rows: 3, cols: 3, entries: &[4, -2, 4, -7, 4, -4, 1, 0, 2], shift: 0 }, &["10.880525930311083439261177111783674905749305310318447487838996319391387991165979949659418893", "1.891128064135148097712916346397666768501365426753759644795617930475935447146496329085521124", "0.194396823195697898660639551394096119378052485213722311889874529321452131138873845012893280"]),
(Case { name: "rank_deficient_18", rows: 5, cols: 5, entries: &[3, 1, 3, -2, 0, -9, -3, -9, 6, 0, 3, 1, 3, -2, 0, -6, -2, -6, 4, 0, -6, -2, -6, 4, 0], shift: 0 }, &["20.904544960366872333964101859373162182270117391494743949795772397691749541863833452002496013", "0.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", "0.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", "0.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", "0.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"]),
(Case { name: "scaled_19", rows: 6, cols: 6, entries: &[60, -540, -60, 420, 420, 420, -480, 300, 420, 300, -300, 120, -240, 540, 360, -420, 300, 360, -60, -240, -240, -240, 360, 240, -600, -180, -240, 420, 240, -540, 60, 480, -540, 480, -420, -480], shift: 0 }, &["1379.027054906903893360182892349195369963284357658662277550598475236138843954921135626751061400", "1188.160615323122154308409461671728757899600407357725327065369875777141609060816419873917121385", "920.014969182144082826047433863815162936867065408270399731364728052398285867842725250839719430", "680.747387834555269586561441022585633470687090878248560629792555679254047602764869864187418637", "478.888663934588030012746889247542291965703035669250306304848453256116131398402435164097048673", "208.278256238917282177325638249734452371229771114456823529115340878794483535349557113073225014"]),
(Case { name: "full_20", rows: 10, cols: 10, entries: &[-3, -9, -8, -2, 7, 2, -6, -8, 1, 4, -5, 6, 6, 0, 5, 4, 10, -7, 7, 5, -10, 0, -1, 9, -1, -1, -2, 0, -7, 2, -9, 1, 5, -8, -2, 3, 10, 10, 9, 3, -2, -9, -2, 8, -1, -5, -7, 4, 8, 1, -7, 8, -5, -5, -7, -5, -6, 1, -7, 9, -5, 8, 6, -7, 1, 10, 9, 1, -6, -5, 5, 4, 10, 0, 8, 4, 6, 9, -4, 1, 3, 2, 8, -2, 9, -6, -7, 0, -1, 0, -10, -1, -2, -4, 5, -10, 1, 3, 10, 7], shift: 0 }, &["33.659469296398272756394652477075377210220697516309767799744993774522393200023395681225517013", "27.242407067527812635675983168376331237578464740301139567453075271374513085770905446390898562", "22.959577100460998870430704443168058205588379901272984805526169394899456622399750592089960404", "18.988844625657322003611583301194516281520738784795574684343731705856340614910321400958346749", "18.046389058575031238509827826856834029940757580749110764196228850113647853362012849907917184", "14.861172625122570360509323900001976815378179028199907503301841016102663628826266896222541096", "11.786100003910537452819844378189056514823551854843219803332354521299124111233295780960867056", "7.938402301875887200941175519584553428878540286103820801560624536035235172745986357708246769", "5.410927828300184917547545655969194201503023772351884368638928086243881675982684716747523701", "1.561361195794815850552282968041549555427390196360637952084339461617681901628299138204029435"]),
(Case { name: "dyadic_21", rows: 8, cols: 8, entries: &[-10, -2, 2, -5, 4, 7, -4, -6, -2, 1, 5, 0, 0, 1, -2, 9, 6, 4, 6, 3, -6, -10, 2, -6, 3, 7, -8, -6, -4, -6, 1, -6, -5, 4, -6, -10, 10, 8, 7, -9, 6, -10, -4, -4, 5, 4, -9, 10, 10, -10, -1, -1, -3, -9, 8, 9, 0, 7, -7, 8, 9, -3, 9, -5], shift: 6 }, &["0.483571010796301645479477436998133348564378235554402871417131232978918806441981777549504665", "0.423198866278433163403382238775027487542540753677149478581973184453988630792343011659346072", "0.305882970523862360594611159178539846321028728141173160957868267251394847280342229376344574", "0.238200483564552943127369477693981048255188367564495033240324624707884650484473758518360483", "0.173904064988234890280724749791458476844776241798660136401348657396779642860701284509002573", "0.128480732986359237571907130374921539287400229965396703376872178297763826935809987404441652", "0.087165110082794590357478282979325235348491624769215856269079192740874670760106054127291388", "0.054915615605335744769647700670287980377854780004475713675876167863807383811107502424285070"]),
(Case { name: "near_rank_deficient_22", rows: 4, cols: 4, entries: &[0, -14, -12, -14, -1, 4, 6, 5, 9, -1, 3, 2, 0, -8, -12, -10], shift: 0 }, &["30.260959159002535633358096630368021167862160390743645664360947920901547120219113322756085337", "9.493083424235603304905341775424353188519429175773529777657151318163702048936024104770966566", "3.338118279519777460731552001472541851985552247572775436443413420650147030758417337630342948", "0.112624285212847253203246055394101977413586083848859756949314265690801537805478200179678581"]),
(Case { name: "full_23", rows: 5, cols: 5, entries: &[-7, -1, -9, -10, 7, 8, 1, 5, -6, -10, -8, 9, -7, 0, 8, -2, 1, -3, -8, 6, -2, 8, 7, 4, 0], shift: 0 }, &["24.974852223788516607391915137774223545940491043495767350646066268961556286679732802840815751", "15.762908652030847799506155990635233510791691677156552560399511984362031603386060462802885038", "10.542527390225536269963946381916835277291085635390294053186783709258454263202632533676162402", "4.661686077796165560944844271730259149762593963158440802868911040955897924028130186432163085", "2.431309598978002045943502966280048035690150680275807271007842018957064073008311420567509330"]),
(Case { name: "bidiagonal_interior_zero_24", rows: 8, cols: 8, entries: &[-2, -3, 0, 0, 0, 0, 0, 0, 0, 3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 5, -2, 0, 0, 0, 0, 0, 0, 0, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -4, -3, 0, 0, 0, 0, 0, 0, 0, -4], shift: 0 }, &["6.119760590179697836194963894289610611805275772213124048125683307059016386307029386968475641", "5.895561947103198987282330377929151735106319784997376467545806163288671319780792736750478140", "4.984051649625503446989274486564020051937557703481401938331136905949811683423827258068896217", "3.200367061427288397376973058292648155903382705016833631323109558459298043909504947633837427", "2.841163070014610261194560264924688515519941040099156580065448895658159325966100105041819643", "2.481779432960410731787022377886881262189114095281518704468945192170975556369280761799429162", "0.690161378569238151744963727782518336525556433551134306765546447189653804214316581569883562", "0.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"]),
(Case { name: "full_25", rows: 8, cols: 8, entries: &[7, -8, -7, -9, 0, 8, 9, 4, 10, 8, 3, 5, 7, 5, 8, -5, -7, 8, -4, -9, 6, 1, -1, -3, -1, 5, -4, -3, 1, -10, -9, 2, 2, -6, 2, 2, 6, 7, -2, 10, -10, 4, 7, 6, 0, -6, 5, 2, 3, 10, 8, 8, -3, -10, 2, 4, 3, 1, -3, -2, -6, -6, 10, -9], shift: 0 }, &["29.093293933428412532286769158640769052320355216196560698425149789107508910425413250408259670", "23.047960192618090791244062749948843868074111193016093226142689081161459996102924258651344260", "21.004037270105964617544114454096806035093076757415801588421106952391489087580029174456533776", "16.452784488934868599471260974582164509779302512769391273128909245123167564355142052931491302", "13.810185068655588974226351157219023117578043853144403618737973357234540898896754617740112920", "10.410448159917560802887496738160147261464903454085613898145812866140311074732250409652936921", "3.889807779106723024191630761977572685759039884852486779956513068338618868769656655064094339", "0.528046304830627704498599854031780978413309704601809443952550753398169520797636978455382651"]),
(Case { name: "full_26", rows: 4, cols: 4, entries: &[-6, -10, 6, -3, -4, 0, 8, 6, -10, 7, -10, 7, 9, 2, -7, 6], shift: 0 }, &["20.178315551677102810804536217823426592361891346863779884386422114156609307587176727342500865", "15.458129787194003830062848922109428899672296342032127791280840208391718012937644651543422929", "9.133907487502692709906811224267154001949249069277389060586673424566869044588791329360755503", "5.954287445946297890616888116249128475616303976553130831813125600539689392919778944867233552"]),
(Case { name: "rectangular_27", rows: 6, cols: 10, entries: &[9, 7, -5, 0, -2, -2, 7, 3, -4, 10, -1, 3, 3, -1, 10, -2, 6, 7, 3, 2, -8, 4, 1, 2, 2, 2, 10, -1, 4, 2, -6, 7, 3, 2, 3, 2, 5, 0, 1, 8, 10, -7, -1, 7, 7, -6, -7, -10, -2, -2, -7, -7, -3, -2, -8, 3, 6, 2, 0, -4], shift: 0 }, &["26.828829078177584066944516742966149775984748240588186020911834107236156719046246895123795480", "21.295268382568989875386740153875009656870166021219000718985142984292945936977742261007888331", "16.171353146530574025564006542190029487052766590847380021580432454989623759115673873562548775", "10.882618576585457567323991921841069389402947642373215262909656373370048905044948181702286427", "9.526646002771329935452960700383965088877325472963792661890784950010496968558268677702073444", "3.320307376271705415814438083913612167251944774775213395653903660352109811085157360950249798"]),
(Case { name: "near_rank_deficient_28", rows: 3, cols: 3, entries: &[2, 6, 0, -1, -3, 0, 1, 2, 0], shift: 0 }, &["7.410056689886487684619528037970801773002646753857729077790118983487104480829925051020211828", "0.301761251105090171005725525373574603130141463522786825281381694236199301381827729801324108", "0.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"]),
(Case { name: "full_29", rows: 2, cols: 2, entries: &[-8, 7, -10, 1], shift: 0 }, &["13.935804645677686815209317024012115311282199898937987715934675576128652767962553084543891136", "4.448971665172548819212636390713959710123534480962337235362161017750869452044838420511146811"]),
(Case { name: "full_30", rows: 10, cols: 10, entries: &[4, -1, -10, 7, -5, 7, -6, 9, -9, -2, 9, -7, -10, 2, -5, 9, 1, -10, 5, -4, -4, 1, 9, -1, -1, -3, 7, 10, 2, -2, 1, 7, -7, -3, -1, 10, -4, 4, 9, -9, 7, 3, 1, 1, -3, -7, 8, 5, -2, 9, -6, -3, -9, 6, -2, -6, 2, 10, 3, 9, -7, -3, 3, 3, 3, -6, -8, 6, 2, 8, -6, -5, 4, 3, 1, 5, -8, -7, 8, 1, -10, -1, 8, -9, 7, 2, -9, 2, -9, 0, 1, -10, 1, -1, -2, -3, -2, 4, 0, 6], shift: 0 }, &["33.256429580446433296988462523214470191900102038853766779973146478364284392501019604592214589", "28.232317737761331648901622822538361017717073153802271476003006293069294563584551569730373666", "23.258277020297845468423774776426835218576005617330902019794038811047977122110524465690053106", "21.293012854694516801416553011141326177789675259174590088538792855374838284059697121826468854", "18.048636586986197790759993980898348508689399402642647466006109218756791085279641029404237400", "11.107521617188061989083882758734810576795577350094644616158353022391711495337665796955867956", "8.528504592865357974813262346195675913619353489945123135009765291262551572849933526705678893", "7.870973934851108225708972294812976960602969802704235681468778404570348925240075801946624663", "3.917912713512114800742976642024434970371403174030640082765255282414755620596546244329204076", "0.662042220757710074415113394796662482182103955582457977795020688006689530030639419645325148"]),
(Case { name: "bidiagonal_interior_zero_31", rows: 9, cols: 9, entries: &[-7, 1, 0, 0, 0, 0, 0, 0, 0, 0, 5, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 5, 2, 0, 0, 0, 0, 0, 0, 0, 0, -6, 3, 0, 0, 0, 0, 0, 0, 0, 0, -8, -5, 0, 0, 0, 0, 0, 0, 0, 0, 8, 1, 0, 0, 0, 0, 0, 0, 0, 0, -3, 3, 0, 0, 0, 0, 0, 0, 0, 0, -8], shift: 0 }, &["11.123977128058336321193464017901118033900243416130841166600886187644070639121437187776331453", "8.617889634124553521558250113808849896951733614530776211456237861121980209161105314409198422", "7.465995683316412197494723936255803737023191177367724080772673576256329944731552265236739852", "7.150503712999036490904701803128257553066676845139200749991847150455383239910104778583671267", "6.038137152882378273556257411942815278459999054549947743155501333135715097018466899894008730", "5.279232581577268677490157162748631219837408232473340841293166773576983169887126193713320094", "4.610684059331568003277335609833422492349825731210447112339165251842810908246496655019724854", "2.744177799121539589636100687112991999263752137113438600910389884394911764880908178222001592", "0.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"]),
(Case { name: "full_32", rows: 3, cols: 3, entries: &[-5, 10, -6, -2, 0, 7, 1, 0, -3], shift: 0 }, &["13.112836812606119342971323237725755954295973772818551886186121562897747091724132991685398558", "7.214037403897504930624259218716841222828089921614173962866750158262268548861019257008002675", "0.105712161691717864838354439941318226200873648154640821481050688165231211482873954206131352"]),
(Case { name: "near_rank_deficient_33", rows: 12, cols: 12, entries: &[-2, 8, -1, -6, -7, 0, 7, 1, 5, 4, -5, -3, 4, -9, 5, -15, -4, 12, 10, 10, -1, 13, 13, 3, -3, 12, -4, 0, -6, -5, 3, -3, 6, -2, -10, -3, 7, -9, -11, 3, -4, -3, -3, -1, 5, -11, 3, 14, -1, 0, 8, -12, -2, 9, 9, 7, -2, 14, 6, -5, -1, 6, 2, -12, -8, 5, 11, 5, 4, 10, 0, -3, 5, -15, -1, 6, 7, 1, -8, 0, -5, -6, 9, 8, -8, 12, 8, 3, 5, -2, -1, -3, -4, 5, -8, -14, -1, 9, -5, -3, -8, -3, 5, -1, 7, -1, -7, 0, -2, -6, 10, 3, 11, 4, -5, 1, -10, 5, 6, -6, -9, 9, 15, 0, 9, 3, 0, 0, -9, 12, -3, -18, 0, -6, 2, 9, 9, -2, -9, -3, -6, -5, 2, 0], shift: 0 }, &["54.880583480027909383129178173797031401910879678267655162642984057353974808433830834224384407", "45.203757795646055320336207970209486306359235265651751196532082211192130742735352682126502137", "44.701728824753079243765675551820282016683619230704092081827508346707408488457456304834505274", "0.705179496650245366258454771119360812686978298644056397628648765360557126033419726574974432", "0.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", "0.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", "0.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", "0.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", "0.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", "0.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", "0.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", "0.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"]),
(Case { name: "bidiagonal_interior_zero_34", rows: 4, cols: 4, entries: &[-8, -3, 0, 0, 0, -9, 2, 0, 0, 0, 0, -3, 0, 0, 0, -7], shift: 0 }, &["10.327566672352140372310676088534733881641875071991566345103762543698012312314688052169984544", "7.615773105863908285661411027158323005360705592546598468950484240520352157373001244642269714", "7.165289012183761040311782544102015347922319932666349518246257690905417873675449830825736435", "0.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"]),
(Case { name: "near_rank_deficient_35", rows: 7, cols: 7, entries: &[-1, 2, 0, 6, -6, -6, 4, 0, -2, 0, -6, 6, 6, -4, 0, 2, 0, 6, -6, -6, 4, 0, -1, 0, -3, 3, 3, -2, 0, 2, 0, 6, -6, -6, 4, 0, 2, 0, 6, -6, -6, 4, 0, -1, 0, -3, 3, 3, -2], shift: 0 }, &["26.536428351988540005915354632939322105696866838321760017379677304887207049306691600190670257", "0.904417116035946502300409654220202801913500849721913291653723543572260591324796456947754166", "0.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", "0.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", "0.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", "0.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", "0.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"]),
(Case { name: "dyadic_36", rows: 7, cols: 7, entries: &[-2, -5, 6, 10, 2, -1, 8, -6, 5, 8, 3, 8, -7, 2, 5, -6, 3, 3, -5, -10, -7, 10, -5, -7, -6, -8, 6, -9, -2, -3, 8, -8, -5, 8, 7, -7, -7, -8, 0, -6, 3, -9, 8, -6, 5, 4, -2, -7, -10], shift: 6 }, &["0.459077107912013746581770488234651249935007364954074620607877034390196904133238375932823641", "0.371278455021848487664027196893920317380550958941061943140079608894783739088668289942944830", "0.249387356212650589804699321238818578344372026483426522251018131223756242605492443971694174", "0.213058309338828294444515633390093755264475776404521759114307845937831593644622380970164941", "0.156549129286771900097094848682022210488826948878271356216047448733896723302023191099305775", "0.071623964462401587159363969400758917143701727493518204698830474530311075817758390908660981", "0.003852634801977128432034080177164691105742226429377403232955335166344694829804505178658086"]),
(Case { name: "dyadic_37", rows: 8, cols: 8, entries: &[3, 9, -8, 5, -9, -8, -10, 0, -5, -2, 7, 0, -7, 10, 8, 8, 9, -1, -4, 10, 2, 1, -3, -7, 0, -2, 1, 5, -6, 6, 2, -9, 5, -1, -7, 0, 0, -6, 7, 2, 2, 10, 5, 5, -2, -9, 10, -1, -6, 7, 7, 1, 5, -10, 9, 6, 0, -3, -8, -8, -3, 7, -8, 0], shift: 6 }, &["0.464675839882250010081238130639083081029323174453457539612439403146338850206448625341820256", "0.408300505080888434603213447846267269767862392168497580259779338668531161739213782606929064", "0.289551648359418275147648614877058339014385947954263834748200365193620789500117930614431202", "0.243835097698241474821292096480035308645517718662995227362425672204607349313967324451872782", "0.182469051901918696622479541002515402671336230787072893001833772476873959255060972916738442", "0.116361759128516724541908778486358942394305396084467862524789961087954227707930509781497485", "0.062383160630857037663330921513722045472966806352766461475441114525859080534085520022836943", "0.035007659140342643448533460969885602721908394311661769163020378419021023501427296073701820"]),
(Case { name: "rectangular_38", rows: 2, cols: 10, entries: &[9, -3, -10, 0, -9, -4, -4, 3, -2, 10, -6, 10, -8, -4, -2, -8, -1, 0, -1, -10], shift: 0 }, &["21.243567587453869806405109277288124808917360557689270466718853871361462037852956239037404271", "18.727275193078126217922791476771910280221467547151340282803439758939707905318667588494504913"]),
(Case { name: "rank_deficient_39", rows: 8, cols: 8, entries: &[11, -4, -5, 10, 9, 7, -2, -4, -6, 9, 6, -6, -9, -9, 3, -6, -14, 6, 1, -11, -6, 0, -6, 1, -10, 7, 5, -9, -9, -7, 1, -1, 5, 5, 1, 4, 0, -2, 1, -10, -14, 5, 4, -12, -9, -5, -1, 4, 3, -1, 1, 2, 0, -2, 3, 0, -15, 11, 6, -13, -12, -8, -1, -3], shift: 0 }, &["51.325171515980568070026800576950969206885436124082622909789718152436528532341837294013440105", "18.714709018253789471395783638179176079513303019103642282727989309292238572457851008430796035", "10.511252790094396710795915303384461018075349798826253986213852384125065281829919430848243968", "0.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", "0.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", "0.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", "0.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", "0.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"]),
(Case { name: "rank_deficient_40", rows: 5, cols: 5, entries: &[16, -3, -5, 4, 0, 10, -8, -4, 2, 0, -13, 9, 5, -10, 0, 9, -10, -4, 12, 0, 3, -1, -1, 4, 0], shift: 0 }, &["33.494166963726336892686963027012566521978304064828264981075782772414726044256916695217950292", "9.359887766659372032078812832460085463095714875211286131242979275176042629454957668316767074", "4.851111254296637045057973793905684997359984273843495051093864641141253445012829897838964002", "0.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", "0.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"]),
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(Case { name: "dyadic_42", rows: 7, cols: 7, entries: &[7, -1, 7, 9, 7, 5, -9, -8, 7, 4, 10, -9, -5, -6, 1, 2, 8, -4, -2, -10, 5, 5, -2, -1, -7, -3, 6, -4, 7, -6, 1, 7, 1, 4, 4, 4, 9, -5, -2, 9, -10, 1, -1, -4, 8, 1, 2, -7, 1], shift: 6 }, &["0.354968438608771887669337355476828691996002455856583287617748071123142910791710774359402494", "0.323821626100183542604064591023392990571684783991954129050280230686271467055205118786826605", "0.281882727647927164529666635794012237895454467849268609974645318208355142786229209123352308", "0.239393075051380586643934811935463445021314390072187736957199062908204693871920062390177963", "0.166747214094723055241776147177341237724565812487821528585501493761962158507476768257915385", "0.105662092320362730270238597322084253617949155709615955016064465248715666311449943746766753", "0.040050709991506874772437154386127944145840869112656219679302241363490723401196460974916472"]),
(Case { name: "rank_deficient_43", rows: 11, cols: 11, entries: &[-3, 1, 20, -3, -6, 0, -4, 1, 0, 15, 6, 3, -2, -10, 14, 1, 5, -1, -13, -6, -14, -3, 10, 10, -5, 10, 16, 0, 2, -2, -3, -15, 9, 1, 12, 19, -5, 5, -3, -8, 10, 1, 15, 11, 1, -11, -19, 5, -16, 16, -5, -15, 6, -6, -24, 10, 4, 9, 4, -4, 12, -5, -14, 0, -1, -2, -12, -4, -10, -2, 4, -17, 15, 15, -16, -4, 7, 27, 13, 0, 8, 14, 19, -15, -29, 15, -20, -5, 9, -14, -14, 21, 1, 11, -15, -31, 12, -25, -9, -9, 2, 6, -3, 17, -22, 5, 14, -3, 0, 19, 6, 9, 10, -1, 9, -1, 2, 3, 2, 1, 10], shift: 0 }, &["94.579049473121271027096926200448387185898889653582073276664268386324048619064617645786781900", "56.451069447704799825488311377414016530183791807502565716703618552328973631978502823837834275", "49.634880792824913933338613048711006346431219607928592575657649490525876129478893139798038597", "22.589224932428075482522926736108796501567055774556592984742072885253810019309545526089220909", "17.591395488658477197594414451686762705364707794358714111510275600977761310858162339046568218", "8.970703751253076393773717035059957607914148468979223002273483267468017804557313582303883809", "5.719729122005846207289284320701398179093734092324628049650439028569537202896523145151526525", "2.557276352930471774680392074458470472170044898508185410581675712158566102917435169637045621", "0.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", "0.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", "0.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"]),
(Case { name: "full_44", rows: 5, cols: 5, entries: &[-8, -6, -7, 2, -9, -6, -2, -4, 7, 6, -9, 9, -3, 10, 0, -1, -6, -4, 3, -7, 3, 9, -1, 2, -6], shift: 0 }, &["20.068207156079123969947154340857533480922989004394148656101776888541530782763437653209726655", "16.872600176110339133214958342224462443889886991274772626662920350496953168966261373649904405", "13.325835032763251181260897842198081393468675808593320956736918037864606606567385667313243299", "4.445051889581678808618808439067733897395739400495001721133191101447877915866890431290965932", "1.801682329469315495800169404869046957806022339598969349818989662304339800325400702493028944"]),
(Case { name: "rank_deficient_45", rows: 5, cols: 5, entries: &[-6, 6, -6, -6, 6, 0, -9, 6, 9, -3, 4, -4, -11, -1, -14, 6, 12, 9, -7, 10, 4, 11, 6, -7, 9], shift: 0 }, &["31.523715242086991359798876903086935262641144402777625830443958076409892600041496822266401228", "17.829828862849557494144254935563268450023340261659335042262939902227100683522604948928377846", "11.762337355190470612401629100419745651160190036208120867169430797471954590830419031435970562", "0.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", "0.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"]),
(Case { name: "dyadic_46", rows: 5, cols: 5, entries: &[-6, 10, -9, 4, 6, 9, -5, 10, -9, -4, -4, 1, -2, -3, 1, -4, 9, 3, -8, -9, 0, 6, 0, 2, -5], shift: 6 }, &["0.367955287378913402996345526022078468473036528871988591452999701254799843839338374903937565", "0.266885834836114340320161200399213415144231410255502240048645957840898024177823896853441656", "0.109261882952329547164606777907022547670010640545127135762083542201619207437448532437992156", "0.075902051644110352709990286450568977030682907768883277568703959636302545963387875499724192", "0.006841894376398321154729774165048642405871618154005774537062430884021858098051899129388806"]),
(Case { name: "scaled_47", rows: 2, cols: 2, entries: &[540, 420, -240, 180], shift: 0 }, &["689.610735857972264297416107485329855809907841766557795598514640304452526973736396317101289865", "287.118499908010118943764847113700133430596537036483165229753136130558760358931514422506696357"]),
(Case { name: "scaled_48", rows: 8, cols: 8, entries: &[-420, 60, -600, -420, -420, 300, -540, -600, -360, -600, 120, -360, -360, 300, -240, -60, -480, -420, 300, -300, -420, -600, -420, -540, -240, -480, -480, 420, 0, -300, -120, -120, -60, 60, 120, 540, 420, -300, -300, -240, 600, -480, -60, 540, 300, 540, 180, -120, -360, 60, -300, -120, -120, 540, -420, -360, 60, 540, -180, -120, -240, 360, -540, -360], shift: 0 }, &["1938.944554504809331736195633747048328453231390793240382426568309100483750382824841191429458584", "1368.483666294837863418238129987101136209157707907258153867574176254555555739085392652393447282", "1172.647644525980038520217951721217012835453772361572782115955247424386604944696427734864275230", "1033.045907831477901251772124985760071089011040717787574370567863540526249851471219221607666192", "690.871446070800794493767859780998069044243617645367758385983354792553555716631810517863082962", "431.214945298618589077034802438496399980687351758087326312791104469247547102629696315811852637", "227.550237375335613758045960395992753958577035507139151457840278328022030571695514220218871272", "72.327927982710271089611951622694628358388811060891864238122813977734777086201166356134154827"]),
(Case { name: "bidiagonal_interior_zero_49", rows: 7, cols: 7, entries: &[-3, -2, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, -6, 1, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 6, 5, 0, 0, 0, 0, 0, 0, -5, -5, 0, 0, 0, 0, 0, 0, -8], shift: 0 }, &["10.260638152624040491442824752574610234522807386997633816796608269818939686688374464886837970", "8.335347964345540265263488107096740107746496295660156464062953256053067040222909539692353282", "7.259226804203011741678621870976465059945080107741570236494967748211174182925070876334338139", "4.030047023819520589865501427056161600852078921001570914715594159550095799561387311491306732", "3.605551275463989293119221267470495946251296573845246212710453056227166948293010445204619082", "0.551022871703642652451100864782636353623225028906993063682276011979611406011656178091094914", "0.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"]),
(Case { name: "dyadic_50", rows: 3, cols: 3, entries: &[3, -6, -4, -8, 4, 3, 7, -1, 9], shift: 6 }, &["0.195601311344311737313773447084102928689755390571893655057957154031817646240578289006842140", "0.169148504432739567113231565329992135069702521384648499777894970401177567507342289417392008", "0.041622422725654827913019097658210169451360117436702349352417166088382303186588392909116500"]),
(Case { name: "scaled_51", rows: 2, cols: 2, entries: &[180, -60, -240, 480], shift: 0 }, &["554.184661885705651061068016301481055508252374581465323565742785873478238856226664523617960287", "129.920593173777136420561399038571631937350811968380901612738864476258495317594552868501699989"]),
(Case { name: "dyadic_52", rows: 2, cols: 2, entries: &[-10, 1, 9, 9], shift: 6 }, &["0.230727877358456547824814937588615572630404178169860486189988508256462468440845181218647546", "0.104755100041291709506586605865119148706429235894726527003479252174214422331068803047395135"]),
(Case { name: "rectangular_53", rows: 7, cols: 2, entries: &[10, -10, 1, 0, -6, 10, 3, 8, -7, 10, 7, -7, -9, -1], shift: 0 }, &["24.889606262203036804258767189008696597061153074197709536122248051305760633839341428135307666", "10.931948596316366467044981342992397976803872259700236303823492995423275551377829294819834982"]),
(Case { name: "dyadic_54", rows: 2, cols: 2, entries: &[-2, 5, 5, 8], shift: 6 }, &["0.157360434560398050687631931578882662388255615263824068216928104530525974879852112410186526", "0.063610434560398050687631931578882662388255615263824068216928104530525974879852112410186526"]),
(Case { name: "rectangular_55", rows: 7, cols: 8, entries: &[-1, 5, -8, 4, 4, -2, -9, 3, -7, -8, -6, 10, 9, 10, 9, 4, -1, -6, 0, 7, 2, 0, -1, 6, 8, 5, -8, 7, -2, -2, 9, 7, -5, -4, -9, -5, 1, -1, -7, -1, 5, 3, 1, -7, 0, -2, 4, 3, -8, -1, -2, 10, 0, 0, -8, 5], shift: 0 }, &["26.933668521432511427591125735994275486354549624862085491029436013746679737151619554984540847", "21.702195814100272101787921718828204941431977539311927357537288509038535619946945597756332598", "17.920744704228302453743933338582196851280434781811454807320946853942123626855933890984292544", "12.756321604898060123816885808637140069883357501786687323941650023151903169255934830498818208", "7.198151181648688546056770151014257184219273165146800003451568385851544282930114809356515717", "5.845373872485711535325894000845019467711737352407732770540890288345526043103277768651089068", "3.705885729393079786675491241271369648831369397806800769807320044950689992100294590695381727"]),
(Case { name: "near_rank_deficient_56", rows: 12, cols: 12, entries: &[-1, -2, 24, -8, -1, 0, -6, -18, -7, -6, 15, 18, -6, 22, -9, -7, 8, 7, -3, -2, 6, -9, -6, -3, -1, 9, 15, 5, -1, -4, -1, -14, -4, 12, 13, 18, 10, -7, -10, 14, 4, -3, 3, 13, 2, 18, -3, -9, -2, 4, -7, -9, -2, 0, -1, 8, 4, -3, -18, -5, 7, 2, 4, -4, 7, 0, -6, 2, 1, 6, -5, 2, -1, 4, 6, 10, 1, 0, 2, -10, -3, 6, 17, 8, -2, 5, -6, 14, 3, 3, 5, -4, 0, 3, 15, -2, -2, -9, 7, 13, -6, -2, 6, -9, -6, 3, 21, 6, 5, 0, -19, 11, 9, 5, 3, 12, 5, 3, -1, -17, -6, 16, 10, -22, 9, 10, -11, -14, 1, -24, 1, 7, -7, 19, 12, -8, 3, 3, -5, -17, -1, -6, 8, 15], shift: 0 }, &["78.968887546902259330571764136834787207661777514327385945722968162037625828983737848743087956", "61.150121265603312319130077605370330516351237039537784100789561112978248500102369720820380935", "36.024415341548923264833350387219688869862432812311737013400914322514081575598817717290237822", "25.515173287904759948454220138824895393750131700568601446942571039768319119426876652534646197", "17.725923355361068110854825562416619690133942013447606858126106248716774173528887755072964504", "0.765859905169223743289913614249421826269721377824181345522246396047299613113938775243059757", "0.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", "0.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", "0.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", "0.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", "0.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", "0.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"]),
(Case { name: "scaled_57", rows: 6, cols: 6, entries: &[-300, -480, 540, 600, -240, 420, -600, -540, 180, 60, -180, -240, 180, -540, -540, 0, -240, 180, 600, -240, -600, -180, 300, -60, 540, 120, 480, -540, 240, 300, 420, -180, -60, -480, 240, -120], shift: 0 }, &["1586.490619914740448623235299287303040053017215613829103512632646470611829256976424145919533172", "1126.235847161105949722640025256546837282772753660317588707527405788559461715954693141692293207", "876.124169824210536347079689309936893866972904067175391559953113697123527579595292814577382803", "657.762944902990911440100243321245737360705940802836964431221212008011310719263647015924679723", "309.447204007242049245399351858098000143548283902374420188483322362615566796521608475360393251", "42.861460384962563139516687820584489543618810438221377480653165950663914858229431945847662801"]),
(Case { name: "near_rank_deficient_58", rows: 3, cols: 3, entries: &[8, -3, -5, 5, 0, -2, -2, -3, 0], shift: 0 }, &["11.193629404850226407273354985972418087273945798916495332207950803676659792779797031811622837", "3.818310181510025262973166787383986202588029732332895705402625132412773559348640194542298386", "0.350953137397636165706894572715711646779529662030705421415254600862280134751887386984324049"]),
(Case { name: "dyadic_59", rows: 8, cols: 8, entries: &[-8, 2, 6, 8, -5, -5, 8, 1, 7, -9, 5, 5, -6, 0, 1, 3, -5, 6, -10, 0, 5, 2, -3, 10, -5, -8, -10, 10, 3, 9, 4, 5, -4, -9, 6, -6, 5, -3, 5, -8, 9, 0, -5, 1, -9, -4, 1, -6, -6, 6, 5, -10, 8, -1, -5, -3, 1, -10, 8, -1, -6, -2, 7, -1], shift: 6 }, &["0.447674341340973519466082504475186325303996258378213475021896507040726602453491418198688127", "0.405652258012487427806849986963833897359039011535681187032479851921088726961199935957018146", "0.313782633724963536517769756129265454423401366394848322964110925594607330959522278539010235", "0.246658301277163475747458604055989971628802965224227755936590967879925616015792631977169386", "0.168721707885794869238446796752980215030650834357406145643298153390109137993409458003284799", "0.096764133906566949913789967805615691464954504369363856736194247622503260421955817789811010", "0.047723117263835577975683992102258519551023690042262410555261916871991572739732040120306913", "0.017986890754657186435626223196966990287440330050480381397088554585868656549174741279486731"]),
(Case { name: "rectangular_60", rows: 2, cols: 8, entries: &[6, -6, 4, 10, -10, -4, -6, 5, -5, -8, 2, -3, -5, -8, 8, -5], shift: 0 }, &["19.112642593884269681537398271861961101856612229539264503287979437280303254896668906844794974", "16.724439992969593467485039955044763888845753766627681057243623084653948161867070099976782746"]),
(Case { name: "rank_deficient_61", rows: 9, cols: 9, entries: &[-2, -8, 3, -6, 0, -4, 1, -4, -8, 4, 7, -9, 3, 0, 5, -8, -1, -5, -2, -3, 3, -3, -2, -3, 2, -1, 1, 6, 10, -7, 12, 8, 10, -3, 6, 2, 0, -3, 4, 3, 6, 1, 5, 3, 1, 4, 4, -10, 0, 0, 4, -10, -4, -12, 2, 3, -3, 3, 2, 3, -2, 1, -1, -3, -1, 9, 3, 1, -2, 10, 6, 15, 3, 2, -7, 0, 1, 3, -7, -3, -10], shift: 0 }, &["38.109854128546522268283450129194183007065338844807468641463954137012901995124323076348698904", "27.679691486954542754148650636880457749572330008996141650477190679622614334617786966996840704", "10.652403366748829873412188068707752431764332855290234869542208248990047550472666201168913426", "0.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", "0.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", "0.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", "0.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", "0.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", "0.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"]),
(Case { name: "bidiagonal_interior_zero_62", rows: 10, cols: 10, entries: &[1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -7, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4], shift: 0 }, &["8.734427137688555437858357177960102884921217823796709420994324393302626538458059204231943131", "7.537358086656003775295328799801077432711341033933276573587160805877270962301263120894640444", "4.472135954999579392818347337462552470881236719223051448541794490821041851275609798828828817", "4.113629200990835601619679027157695171091169632031525553557453317269830735701575737335946680", "4.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", "3.837351400959050479027491577490491889170370717855051286396297328690751834043361328422974558", "3.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", "0.992228200550317572636883871749591500406520606729681533636388365713919522552019066230964150", "0.516030881127133084104743743409449705655040036048457947503707063721831048236806298204706958", "0.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"]),
(Case { name: "rectangular_63", rows: 9, cols: 3, entries: &[8, 4, 7, -2, 10, -9, 0, 9, 5, 5, -2, 2, -6, 5, -10, -9, -8, 5, 6, -9, 7, 4, 8, -7, -3, -3, -10], shift: 0 }, &["26.133722137660539521991992020096632245147122662057063211794053673741598970424843640318436632", "19.327285769960858773323030433333066119282075151252633717276558996313100653926893027920778386", "11.852619625965389724758311156217006587712159779656384814568211444993673603051289379807694864"]),
];
/// Eigenvalues of symmetric matrices, ascending.
pub const EIGEN: &[(Case, &[&str])] = &[
(Case { name: "dyadic_0", rows: 10, cols: 10, entries: &[-2, 6, 2, -4, 6, 10, 10, -8, -7, -2, 6, -7, 10, -1, 1, -6, 1, 0, 1, -4, 2, 10, 3, 1, -1, -5, -5, 6, -4, -7, -4, -1, 1, 4, -10, 8, 4, 8, 10, -3, 6, 1, -1, -10, 9, 1, 0, -2, 2, 10, 10, -6, -5, 8, 1, 6, -5, 4, -9, 5, 10, 1, -5, 4, 0, -5, 6, 8, -1, -2, -8, 0, 6, 8, -2, 4, 8, 1, -8, -4, -7, 1, -4, 10, 2, -9, -1, -8, -8, 6, -2, -4, -7, -3, 10, 5, -2, -4, 6, -8], shift: 6 }, &["-0.397570427706565429089956612391891647100806406179990035645768492978759843467417053068161916", "-0.393790426968902942233847132651845199578845170443609978452183981538320874479088918239652164", "-0.241991044123175255183888075541923555418635566448922454916387609737528359935834431438482454", "-0.234358989073677159538872160393033924742397820460718022071444539980080938437216928036152492", "0.044663188867408180439382313799903242849332858303840398283133484172071562115245585374294248", "0.077787398986696466538165941157262318025121564596309071702761923446321424662545561938653825", "0.187264946786611157055887706612683051879972413806056838525482556126187499591886326021631836", "0.290884767503174663872242161840741640793985484317845853991630952766048480287996608328190432", "0.311601266227943936144987399824236780107563829457486506670537449902538362910984355812111063", "0.418009319500486381995898457743867293184708813051701821912238257821522686750898893307567622"]),
(Case { name: "dyadic_1", rows: 5, cols: 5, entries: &[-2, 10, 10, 1, -8, 10, 0, 0, 3, -6, 10, 0, -9, 0, 8, 1, 3, 0, -4, -10, -8, -6, 8, -10, -7], shift: 6 }, &["-0.393695423698634586461623084833131789404740096630972397887247710693986226049975397455118560", "-0.181858000201640378753210710465606481416402100029217910432300852783545146563044123706310677", "-0.094863758031661411912277898314628129882108307943351833047857318072436325404546973014335872", "0.069410401848885006878618877628353666963162296429173906848221087759200086207983224455225103", "0.257256780083051370248492815985012733740088208174368234519184793790767611809583269720540006"]),
(Case { name: "scaled_2", rows: 7, cols: 7, entries: &[-400, -40, 240, -320, 120, -160, 200, -40, -280, 360, 40, 320, -360, 240, 240, 360, 320, -80, -280, 0, 0, -320, 40, -80, -360, 80, -320, 240, 120, 320, -280, 80, -160, -280, -240, -160, -360, 0, -320, -280, 280, 120, 200, 240, 0, 240, -240, 120, 120], shift: 0 }, &["-1101.446563557219036331832816125122628874823013179484246264800474604700968540983425113292793757", "-646.478252596603566437764211777853010898670600311714543802854669100921178841081956607806758599", "-258.217963419260230740027793120160881227650266118955565236692448307167506618915616840706762807", "-107.749145600573466085626295281699158813111542050335384335770238455124708876114656602831054733", "274.775788523359182486045530598791048638488751458795500132882518234080961893980968785610474805", "615.157481653353697101826467902940258952601392825532000229729805707104920565180108525962639758", "743.958654996943420007379117803104372223165277376162239277505506526728480417934577853064255333"]),
(Case { name: "gram_low_rank_3", rows: 6, cols: 6, entries: &[22, 6, -5, 8, 11, 3, 6, 19, -9, 3, 4, 3, -5, -9, 13, 2, -1, 0, 8, 3, 2, 5, 5, 2, 11, 4, -1, 5, 6, 2, 3, 3, 0, 2, 2, 1], shift: 0 }, &["0.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", "0.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", "0.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", "8.606607741099652616003996986253697628715954596122860373118414875583552200757145639012729276", "19.452087817064992515662202164809385193952764986186191997948414534500545216190573841495118378", "37.941304441835354868333800848936917177331280417690947628933170589915902583052280519492152346"]),
(Case { name: "zero_diagonal_4", rows: 6, cols: 6, entries: &[0, 1, -4, 8, -4, 4, 1, 0, -8, -5, -2, -3, -4, -8, 0, 10, 3, 8, 8, -5, 10, 0, -3, 9, -4, -2, 3, -3, 0, 1, 4, -3, 8, 9, 1, 0], shift: 0 }, &["-15.207103150401645142447674367860172415079479053705303348844823051400573004712802610675996740", "-9.519443244253832110388866033822872728645184976947386052894276846925380938271693644048803349", "-4.986219198060713393326056345281422378769707697360346937011727716959783084256838367113727395", "-2.497461984270074164102743805182279411661783248651156309047627151982080439338122398418206902", "9.537194195582917613634463577274911694821586673165345338248608921133135140126500127661618818", "22.673033381403347196630876974871835239334568303498847309549845846134682326452956892595115568"]),
(Case { name: "large_pattern_5", rows: 4, cols: 4, entries: &[0, 6590, 6590, 6590, 6590, 0, 6590, 6590, 6590, 6590, 0, 6590, 6590, 6590, 6590, 0], shift: 0 }, &["-6590.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", "-6590.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", "-6590.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", "19770.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"]),
(Case { name: "large_pattern_6", rows: 7, cols: 7, entries: &[0, 3647, 3647, 3647, 3647, 3647, 3647, 3647, 0, 3647, 3647, 3647, 3647, 3647, 3647, 3647, 0, 3647, 3647, 3647, 3647, 3647, 3647, 3647, 0, 3647, 3647, 3647, 3647, 3647, 3647, 3647, 0, 3647, 3647, 3647, 3647, 3647, 3647, 3647, 0, 3647, 3647, 3647, 3647, 3647, 3647, 3647, 0], shift: 0 }, &["-3647.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", "-3647.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", "-3647.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", "-3647.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", "-3647.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", "-3647.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", "21882.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"]),
(Case { name: "dyadic_7", rows: 7, cols: 7, entries: &[4, -5, -3, -8, 1, 1, 6, -5, 2, 5, 1, 10, 6, -4, -3, 5, -4, 0, -8, 6, 7, -8, 1, 0, 4, 9, 5, 3, 1, 10, -8, 9, -8, 10, 6, 1, 6, 6, 5, 10, 4, 2, 6, -4, 7, 3, 6, 2, -7], shift: 6 }, &["-0.419242502863169796814872562455854966131612919900896946298822164263853956048975316370523899", "-0.207495857101427294205232510296700945648458529500383349529440978691509130569011488439670005", "-0.101226824648961404619332597091647815879408424214713458006511368323590925234886430975735019", "0.044330489752559138735942248616167997852555758610109465120717883554930599028914595814227778", "0.082498636729946995632587414365760675689589649828925290144189500308391954796141844576838482", "0.161085877533630984591885214019880833316587284706595759147855677195556157264021009380089627", "0.361925180597421376679022792842394220800747180470363239422011450220075300763795786014773036"]),
(Case { name: "repeated_8", rows: 6, cols: 6, entries: &[-5, 2, 0, 0, 0, 0, 2, -5, 0, 0, 0, 0, 0, 0, -5, 0, 2, 0, 0, 0, 0, -5, 0, 2, 0, 0, 2, 0, -5, 0, 0, 0, 0, 2, 0, -5], shift: 0 }, &["-7.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", "-7.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", "-7.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", "-3.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", "-3.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", "-3.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"]),
(Case { name: "zero_diagonal_9", rows: 12, cols: 12, entries: &[0, 7, -4, 3, -3, -5, -6, 1, -6, -2, 6, 10, 7, 0, 6, -6, -1, -9, 0, -3, -10, 6, 10, -6, -4, 6, 0, -10, 9, -3, -5, -10, 2, 3, 2, -2, 3, -6, -10, 0, 7, -9, 9, 7, -10, -1, -8, -5, -3, -1, 9, 7, 0, -8, -2, 6, -8, -2, -1, 8, -5, -9, -3, -9, -8, 0, -10, -1, -2, -3, -1, 1, -6, 0, -5, 9, -2, -10, 0, 4, -10, 10, -5, -7, 1, -3, -10, 7, 6, -1, 4, 0, -7, 10, -1, 5, -6, -10, 2, -10, -8, -2, -10, -7, 0, 8, -7, -5, -2, 6, 3, -1, -2, -3, 10, 10, 8, 0, -10, 10, 6, 10, 2, -8, -1, -1, -5, -1, -7, -10, 0, 9, 10, -6, -2, -5, 8, 1, -7, 5, -5, 10, 9, 0], shift: 0 }, &["-34.709519386947853171468778782818630145652079759475697356167303259119543635513142202611594633", "-25.418120357830489194491379316710520674593003171362141265391970995483050062086634965179832405", "-19.655718190254784544570240524934783070068692777788776348420254278568999705006300069450364913", "-18.020562178836089522248675842087968211927497819506806964476303827103536911351897169138701291", "-8.360127081976502000081149397173708264721628479076523705446092035962093207511366380805744383", "-7.186128066463826109800950638374990364287446501932344401019091154115672566666361154651618752", "2.152925046234968296042295631233998194074483616342017094735521356236142607080295955054078376", "10.997177370125534152191654345870691147588955421728460198072589521766076870663436480339062073", "16.314701765240355560195453674221591212609685502785068873622989654103939877775643419543546829", "19.004779784593753590830746002997648106186530151156899118557791939578645430824258805370809318", "29.535245477199121550600186108412055520905309882763923478148942867336158310019575376853256770", "35.345345818915811392800838739364616549885383934365921277783180211331932991772491904677103013"]),
(Case { name: "symmetric_10", rows: 10, cols: 10, entries: &[10, 4, -3, 5, -1, -5, 10, -9, -7, 10, 4, 6, -10, -8, 9, -8, -4, 9, 6, 6, -3, -10, -1, 3, -8, 9, -5, -6, -7, 1, 5, -8, 3, -5, -2, 6, 3, -2, 8, -2, -1, 9, -8, -2, -2, 0, -2, -10, -3, -3, -5, -8, 9, 6, 0, 7, 4, 2, 10, 6, 10, -4, -5, 3, -2, 4, -1, 4, -10, 3, -9, 9, -6, -2, -10, 2, 4, 7, -7, -2, -7, 6, -7, 8, -3, 10, -10, -7, 7, 3, 10, 6, 1, -2, -3, 6, 3, -2, 3, -9], shift: 0 }, &["-28.269252933742135768086255653934634962421802674077296755531322465124420419659347078413859312", "-20.087622261565571669568123619620096567697150099248065369767479428046041453244331515728168576", "-17.332794503865865061425682516536381362226644483190270380652633033368813884250184918476726387", "-9.678918875021636338428865548890692172500145628433765156622599618456312070848734575136147213", "0.882002096322585712114629270349207778204698917963483951737143546533594625827959766006039116", "1.680420753366139766898449748481976554061976828459044797975737608229982687751753751262249825", "14.090899157012322005262534148219094506047425592121345083883657822386146254924480503870020590", "20.742701821164399308863167121651126968004218995057867249508461876364295556664066285089196760", "25.948753244877172750246738623774840101023694141989714354471369066228944409876082680803222573", "31.023811501452589294123408426505559157503728409357942224997664625252624292958255100724172625"]),
(Case { name: "zero_diagonal_11", rows: 3, cols: 3, entries: &[0, 3, 4, 3, 0, 9, 4, 9, 0], shift: 0 }, &["-9.064862298802249237646694809865845318198143363580003995530349270000187048003024656823386834", "-2.128740191122642533991612017110394289747228817832898601321064973776613434065951356641802823", "11.193602489924891771638306826976239607945372181412902596851414243776800482068976013465189657"]),
(Case { name: "symmetric_12", rows: 3, cols: 3, entries: &[-10, -2, 0, -2, 7, -2, 0, -2, 9], shift: 0 }, &["-10.234921471766743233911896768871615202670864655732502595674640974939514331822144636068453508", "5.942599261035874062936591826519080567495067892165796920196211230832332160966566807851473385", "10.292322210730869170975304942352534635175796763566705675478429744107182170855577828216980123"]),
(Case { name: "scaled_13", rows: 3, cols: 3, entries: &[80, -360, 280, -360, -360, -120, 280, -120, 280], shift: 0 }, &["-563.320420594903280462731286567052916619369417009311694662896429541840794125696850052613474084", "-20.998967335717037186929882351961162484883645369637940232681875421621348912775174558437644201", "584.319387930620317649661168919014079104253062378949634895578304963462143038472024611051118285"]),
(Case { name: "zero_diagonal_14", rows: 11, cols: 11, entries: &[0, 0, 4, 5, 7, -7, -1, 3, 4, 6, -8, 0, 0, 0, 4, -5, 6, 5, -10, 9, 4, -2, 4, 0, 0, 2, 5, 3, 0, -9, -3, 5, 4, 5, 4, 2, 0, 1, -1, -9, 2, 0, 8, 5, 7, -5, 5, 1, 0, -7, -5, 3, -3, -3, 5, -7, 6, 3, -1, -7, 0, 4, 5, -6, -1, 10, -1, 5, 0, -9, -5, 4, 0, -6, 0, -8, 6, 3, -10, -9, 2, 3, 5, -6, 0, -1, 3, -2, 4, 9, -3, 0, -3, -6, 0, -1, 0, -5, -3, 6, 4, 5, 8, -3, -1, -8, 3, -5, 0, -6, -8, -2, 4, 5, 5, 10, 6, -2, -3, -6, 0], shift: 0 }, &["-24.844288116537315792900618944282168855990780749949451655404396274459387335859078081668350308", "-18.961127621730445947280864520054197777470831025525350653425405876329699399574766513838474053", "-14.299987602530480973922322578124381995398625951146976125508307878102972205668678131153088890", "-10.022735660270345242032428984462103018471876132824728095363197853346039189258082712648301263", "-7.839054118739763366272185754941905461492895703055786986471886227566682894509169862322935658", "-1.542779088615735746650102478083103893135781133051973519772919807041992314533764933850344815", "3.491351883399146656610411521682978449254586207259002653974550435884498060230992453371420217", "11.674059870098718677150444050025298812348295116204999857470140890779789742993625855323428880", "15.760087959089256905261054399724881526418754474433609068565036777284222084256870980291205747", "18.467764681328898183749768756268535013496600667621448894510451464470386078907144364486805093", "28.116707814508066646286844532246167200442554230035206561425934348427877373014906582008635051"]),
(Case { name: "zero_diagonal_15", rows: 4, cols: 4, entries: &[0, 5, 2, 0, 5, 0, -1, -7, 2, -1, 0, 7, 0, -7, 7, 0], shift: 0 }, &["-9.726247027465153634410397281405089673473702613770149726656354220294687034356652260750609632", "-5.311610846417943050320232557775369584454268226106689589202851355575425291030392537631732363", "4.347310717531573308376294866063943839391804603594947952711314654615391846674808129055225216", "10.690547156351523376354334973116515418536166236281891363147890921254720478712236669327116778"]),
(Case { name: "zero_diagonal_16", rows: 6, cols: 6, entries: &[0, 4, 5, -3, -9, 0, 4, 0, 5, 2, -8, 7, 5, 5, 0, -1, 1, 2, -3, 2, -1, 0, 9, 10, -9, -8, 1, 9, 0, 5, 0, 7, 2, 10, 5, 0], shift: 0 }, &["-15.615638115568089704084447538530983843116493008746617291386975576955417421234732332980401591", "-11.240602834832521238761360560141429132566724534737625479149667360192460206077745600695763117", "-5.746729811976727248145988258723076285297976677592121358656664599285205893364163803880280211", "-0.629754420937651838913396554113711184966955136489186023366335740776269774142431864184071950", "13.954390725187977777438629847980132620609157780706502110484256115502155045640000401506727691", "19.278334458127012252466563063529067825338991576859048042075387161707198249179073200233789177"]),
(Case { name: "scaled_17", rows: 9, cols: 9, entries: &[-120, 240, -200, -40, 360, 280, -160, -360, -400, 240, -320, 160, -320, -400, 0, -320, -240, 280, -200, 160, -320, -280, -160, -160, 200, 400, -200, -40, -320, -280, -280, -240, 40, -360, 40, 400, 360, -400, -160, -240, -40, -80, 320, -320, 280, 280, 0, -160, 40, -80, 360, 280, -320, 280, -160, -320, 200, -360, 320, 280, 80, 240, -240, -360, -240, 400, 40, -320, -320, 240, -280, -120, -400, 280, -200, 400, 280, 280, -240, -120, 80], shift: 0 }, &["-1368.285417791084099353576583082146885175204306647982042018386684898039349811322061031321355105", "-876.261653744064866164837282558446523742145149772923988411350733158523096729044957272156588226", "-760.307131315981602920069965071774869290997578457144109286454020687828623452468321959123927631", "-548.905780728053989529227820983845161050244189643832564297215254740277585759555005969913146525", "39.524179990883412054440139709800621676497086157353423417884304081330392798816979364773116500", "329.365191991737828330178548583247069931222437293799974313230088856417133159573093892308239559", "489.309684279372825172717392360818137145476514144298666849395512214984844234139733743432054976", "818.292326244120756789225500943012320430216293241269908401490622893695805225517488562970452674", "1037.268601073069735621150070099335290075178893685160731031406165438240480334343050669031153778"]),
(Case { name: "repeated_18", rows: 4, cols: 4, entries: &[4, 0, 1, 0, 0, 4, 0, 1, 1, 0, 4, 0, 0, 1, 0, 4], shift: 0 }, &["3.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", "3.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", "5.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", "5.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"]),
(Case { name: "gram_low_rank_19", rows: 2, cols: 2, entries: &[4, -6, -6, 9], shift: 0 }, &["0.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", "13.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"]),
(Case { name: "scaled_20", rows: 8, cols: 8, entries: &[240, 0, -40, -120, -280, 240, -360, 240, 0, -120, -280, -360, 400, 280, -240, -360, -40, -280, 120, 240, 160, 80, 0, -200, -120, -360, 240, 320, 360, 280, -200, -40, -280, 400, 160, 360, 240, -80, 200, -360, 240, 280, 80, 280, -80, 280, 0, -320, -360, -240, 0, -200, 200, 0, -200, 0, 240, -360, -200, -40, -360, -320, 0, -80], shift: 0 }, &["-985.869242749670909249002829311771581562511945541567300629701564835197066239785008913804036804", "-595.621727744671832366516712759677511296689297126605498696261491843882112447717207547205622933", "-243.415762860498674253773334256848198108188411411310240634752479499619834619083589101845475247", "-1.006579945150928098600759772917623586760124891575362858491564662296754999922202635038306628", "94.884474071240189119542002990274292335472845428727367179388322250120386376164768985511246952", "696.615126619849347954812677402366310621868758754441665682421100255280308681413429933182290492", "731.153350200233831635111382328126127005855265504983757575949901809176547928546021688375017857", "1103.260362408668975258427573380448184590952909282905612381447776526418525320383787590824886312"]),
(Case { name: "symmetric_21", rows: 3, cols: 3, entries: &[4, 5, 10, 5, -9, 0, 10, 0, -3], shift: 0 }, &["-12.795504446466795186833409221313183328912678308709996892425599314862673175669304822999439728", "-7.109524845212832123174934542699667595086998727112540769530266763081933387484301338623539709", "11.905029291679627310008343764012850923999677035822537661955866077944606563153606161622979437"]),
(Case { name: "zero_diagonal_22", rows: 11, cols: 11, entries: &[0, -8, 10, -1, -10, 5, 2, -8, -8, -6, 8, -8, 0, -9, -7, -10, 9, 5, 9, -8, -4, -10, 10, -9, 0, -8, -1, -9, 6, 0, 4, -2, -3, -1, -7, -8, 0, 0, -2, 5, 9, -1, 4, 6, -10, -10, -1, 0, 0, -5, 5, -5, -10, 0, -9, 5, 9, -9, -2, -5, 0, 2, 1, 8, -3, 4, 2, 5, 6, 5, 5, 2, 0, -6, -4, 1, 6, -8, 9, 0, 9, -5, 1, -6, 0, 6, -9, 2, -8, -8, 4, -1, -10, 8, -4, 6, 0, 9, -10, -6, -4, -2, 4, 0, -3, 1, -9, 9, 0, -3, 8, -10, -3, 6, -9, 4, 6, 2, -10, -3, 0], shift: 0 }, &["-36.056101615260955174231220714103647737313979276849445695588732942562017709199252831164959612", "-26.681696038557506516329880424970518672717309648722861019404961155917939922848572185888581049", "-18.744526770158132942440330192596445681393373876148037170992708947590634617686770755835606777", "-10.774052865001341949619686182781818191125516136066615517721688266043227008769421290162607913", "-3.594300093327091415619992401720001226192811813204518515230993600186655215926196866640400397", "2.364564000843781133545701629933536983690888826931680680435930208175192650631460360656299007", "8.869443954959833276930591129464337507666586711043631706346085835732646286173202514786229543", "14.871309767323532711474217267643107054134332364907168739038875985851747459464385576891449517", "17.092219818091172985097305565356863504238335927503847182943647163737579631552658516265507656", "24.095702193886938708960340925282249726992571845613250336171767480313040194518759001414298358", "28.557437647199769182232953398492336732020275074991899274002778238490268252089747959678371667"]),
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(Case { name: "repeated_24", rows: 10, cols: 10, entries: &[6, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 6, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 6, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 6], shift: 0 }, &["4.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", "4.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", "4.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", "4.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", "4.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", "8.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", "8.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", "8.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", "8.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", "8.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"]),
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(Case { name: "zero_diagonal_27", rows: 2, cols: 2, entries: &[0, 4, 4, 0], shift: 0 }, &["-4.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", "4.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"]),
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(Case { name: "zero_diagonal_59", rows: 11, cols: 11, entries: &[0, -6, -8, -6, 9, 8, -8, -6, -10, -3, 2, -6, 0, 10, -5, 9, -3, 1, 1, -1, 4, -3, -8, 10, 0, -2, -6, -10, -7, -10, -8, 3, -3, -6, -5, -2, 0, -4, 6, 10, 4, 7, 9, -6, 9, 9, -6, -4, 0, 9, 3, -2, 4, -7, 1, 8, -3, -10, 6, 9, 0, -2, 9, -10, -2, 2, -8, 1, -7, 10, 3, -2, 0, -7, 1, 7, -1, -6, 1, -10, 4, -2, 9, -7, 0, -1, 8, -5, -10, -1, -8, 7, 4, -10, 1, -1, 0, 10, -2, -3, 4, 3, 9, -7, -2, 7, 8, 10, 0, 4, 2, -3, -3, -6, 1, 2, -1, -5, -2, 4, 0], shift: 0 }, &["-32.438200195266822307564804273582360640352176355256942429188705895639642805655938248387477662", "-21.745270042254881507148451914305069316385773103149204244284307377243964665831745262223756582", "-20.861277693275713832538817785846030656981281338898513541802467725283116595177300500467889096", "-9.829907536286482214332310028992436424732020212645259388640116972296845732010230002208617875", "-5.082591515338915248227541793694239796445712175707130159681741826709721654157377620130112470", "3.018207033482333155390356469833242743039758886383277774133816358704770021634270834423624536", "4.341142556972690241781518301370142439905255464788887456231110907483022195769145236157983291", "10.218894717353428011047275615706411124602789569034994753689737139423437927852904012405993720", "11.922054061074520457116369567129129791875106056339276661604518954576694105369840139287354881", "26.677694061883833583837272849214885361776546505900897784490766493525524277717565739640683363", "33.779254551656009660639132993166325373697506703209715333447389943459842924488865671502213894"]),
(Case { name: "large_pattern_60", rows: 4, cols: 4, entries: &[0, 9476, 9476, 9476, 9476, 0, 9476, 9476, 9476, 9476, 0, 9476, 9476, 9476, 9476, 0], shift: 0 }, &["-9476.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", "-9476.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", "-9476.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", "28428.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"]),
(Case { name: "large_pattern_61", rows: 9, cols: 9, entries: &[0, 748, 748, 748, 748, 748, 748, 748, 748, 748, 0, 748, 748, 748, 748, 748, 748, 748, 748, 748, 0, 748, 748, 748, 748, 748, 748, 748, 748, 748, 0, 748, 748, 748, 748, 748, 748, 748, 748, 748, 0, 748, 748, 748, 748, 748, 748, 748, 748, 748, 0, 748, 748, 748, 748, 748, 748, 748, 748, 748, 0, 748, 748, 748, 748, 748, 748, 748, 748, 748, 0, 748, 748, 748, 748, 748, 748, 748, 748, 748, 0], shift: 0 }, &["-748.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", "-748.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", "-748.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", "-748.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", "-748.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", "-748.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", "-748.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", "-748.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", "5984.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"]),
(Case { name: "scaled_62", rows: 8, cols: 8, entries: &[0, 160, 40, 40, 40, -320, 280, -280, 160, 40, 160, 80, 360, 160, -200, -80, 40, 160, 320, 0, 160, -240, -160, -240, 40, 80, 0, 40, -280, -240, -240, 400, 40, 360, 160, -280, 80, -120, 160, -240, -320, 160, -240, -240, -120, 80, 160, 240, 280, -200, -160, -240, 160, 160, -280, 200, -280, -80, -240, 400, -240, 240, 200, 0], shift: 0 }, &["-875.694288592916294510311345314703960477949893059306960813492640940034184563227470415780422242", "-673.888042967140165451024151886624455578159164370920834558173296014520217722722348953603508177", "-161.913274585744783156251491792239352213656303010563640167412027297208136317045101367625464350", "-87.755727500040770812162517129575251381092658404619116167721941593558745162381526557102095848", "172.360065839456457409071170707288089651675866832298961400835038863185228053775917417451095549", "333.386908285082251707201846814884183758140355929702921467029764516968774640294777030401302230", "573.322291217384581761830934601337345984251173598518570756263952335205650959771216248398227046", "1000.182068303918723051645553999633400256790622484890098082671150129961630111534536597860865792"]),
(Case { name: "symmetric_63", rows: 12, cols: 12, entries: &[-5, -6, -2, 4, -5, -5, -2, 7, 8, 2, -2, -3, -6, 0, -8, 0, 5, -4, 1, -2, 4, -6, -9, -2, -2, -8, -2, -1, -5, -4, 10, 7, -1, 0, 4, 9, 4, 0, -1, 2, 1, -7, -4, 2, -7, 10, -7, -3, -5, 5, -5, 1, -3, -5, -5, 1, -9, 5, 7, -9, -5, -4, -4, -7, -5, 4, 1, 8, 10, -7, -8, 1, -2, 1, 10, -4, -5, 1, 3, 2, -9, -4, 5, -1, 7, -2, 7, 2, 1, 8, 2, 3, 5, -1, 9, -3, 8, 4, -1, -7, -9, 10, -9, 5, 8, 4, -10, 4, 2, -6, 0, 10, 5, -7, -4, -1, 4, 4, 9, 8, -2, -9, 4, -7, 7, -8, 5, 9, -10, 9, -1, 3, -3, -2, 9, -3, -9, 1, -1, -3, 4, 8, 3, 6], shift: 0 }, &["-27.128563158168256611222433009139540743721461780440294740449923020401761390177010395826060624", "-24.364234557432434620526600333200912112877572016017670919027120478213776788697658391856021315", "-17.910092967112646432275733263791914234836076292908587402382196596572400861232229638669276951", "-11.062782324180290597854722571203188787140320759753685456312934785253061661236332721660196277", "-6.673855786439347951414867921398054373462099892218657230940192642065509872060217068661209422", "-0.578535189672592386392876832507323033042912240683430382242374610982509778691190747558378019", "0.701556346923060567591718788021130216394230844835537448222024663325288096785983581985710308", "7.811362682634636506943921666879771548241210152774214839841395446382803361746261756296805565", "14.390822446915508443809135474645781529226854964366025995785947323448905800227291491509364912", "22.665671356516188295163355333544171127583922252710312015617987264703576234438727304115308429", "27.453689999039630077042998695858122422350541473965366446828489952582954191509154485344167625", "33.694961150976544709136103972291956441283683293370869385058897483045492667387220344979785769"]),
];
/// Eigenvalues as (re, im), sorted by (re, im).
pub const SCHUR: &[(Case, &[(&str, &str)])] = &[
(Case { name: "rank_deficient_0", rows: 6, cols: 6, entries: &[6, -5, 1, -2, 17, -5, -11, 17, -2, -1, 1, -4, -4, 10, -3, -9, 4, -5, 3, 6, -9, -9, -2, -1, 2, 8, -8, -8, 6, -4, 5, -7, 0, -1, -2, 2], shift: 0 }, &[]),
(Case { name: "complex_blocks_1", rows: 8, cols: 8, entries: &[2, 0, 0, -1, 0, 0, 0, 0, 0, 3, 0, 5, 4, 1, -4, 0, -1, 3, -2, 3, 3, 4, 1, 3, 1, 0, 0, 2, 0, 0, 0, 0, 5, -4, 0, -5, 3, -3, -5, 0, 0, 0, 0, -3, 0, -3, -1, 0, -2, 0, 0, -3, 0, 1, -3, 0, 3, -1, 0, -3, 2, 1, -5, -3], shift: 0 }, &[("-3.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", "-1.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"), ("-3.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", "0.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"), ("-3.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", "1.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"), ("-2.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", "0.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"), ("2.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", "-1.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"), ("2.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", "1.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"), ("3.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", "-4.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"), ("3.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", "4.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000")]),
(Case { name: "full_2", rows: 9, cols: 9, entries: &[1, 10, 1, -3, -10, -8, -3, 1, -6, 5, 2, -7, -4, 6, -10, 8, -8, 0, 10, -5, -8, 4, 4, 8, -10, 3, 4, 9, -4, -1, 4, -3, -8, 2, 2, 8, 7, 9, -9, 4, 10, 4, -10, 5, 7, -3, -5, 3, -10, -8, 8, 1, -10, 1, 9, 3, -9, 10, 1, 9, 8, -9, -6, 2, 5, -8, 7, 2, 2, -8, 1, 5, 5, 1, -4, -1, -2, -7, 2, -5, -4], shift: 0 }, &[("-10.272972095671776080919612843684661400520631644592993920035013349962856823781080394400540186", "-2.085383191496062020283869173785588162071306029608838885740030214237636770240640959425234732"), ("-10.272972095671776080919612843684661400520631644592993920035013349962856823781080394400540186", "2.085383191496062020283869173785588162071306029608838885740030214237636770240640959425234732"), ("-3.965859565683342081130350477016834432949420143861309334787819982037670686988945418721993660", "-15.890584456540165088540249299876561590532565245431626522307833103533650544083407417657633685"), ("-3.965859565683342081130350477016834432949420143861309334787819982037670686988945418721993660", "15.890584456540165088540249299876561590532565245431626522307833103533650544083407417657633685"), ("-1.100735431326016514069141602796667950445721778341264317762285541945771498303332069421039074", "-3.929088809012567477515391641957179412606076777126489232563977877020573435994930696430265440"), ("-1.100735431326016514069141602796667950445721778341264317762285541945771498303332069421039074", "3.929088809012567477515391641957179412606076777126489232563977877020573435994930696430265440"), ("13.570500218278799374851694214260680029452401047083984442637913956982411587480816847098985903", "0.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"), ("16.333592026022499462357083862014668228394692679745996527068003100606595236392969079579508389", "0.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"), ("22.775041941060970515029431770720979309984453406761154175464320690303591194272929838408651548", "0.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000")]),
(Case { name: "companion_3", rows: 5, cols: 5, entries: &[4, 13, -52, -36, 144, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0], shift: 0 }, &[("-3.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", "0.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"), ("-2.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", "0.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"), ("2.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", "0.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"), ("3.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", "0.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"), ("4.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", "0.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000")]),
(Case { name: "rank_deficient_4", rows: 10, cols: 10, entries: &[-20, 7, -10, -7, -24, 5, -25, -5, -11, 1, -11, -22, -14, 8, 13, -6, -8, 23, 5, -10, 15, -7, -21, 1, -1, -11, 2, 5, -3, -16, -4, -22, -9, 23, 21, -10, 10, 9, 14, -5, -13, 10, 7, 1, -5, -7, -15, 1, -19, 7, -16, 1, -11, 7, -8, -9, -20, 8, -10, 2, 2, -2, 4, 3, 9, -19, -1, -2, -23, -9, 5, 17, 18, -30, -17, 20, 7, -6, 14, 4, 1, -14, -34, -10, -16, 20, -3, 15, 10, -24, -10, -4, -11, 0, -6, -16, -3, 11, -13, -21], shift: 0 }, &[]),
(Case { name: "dyadic_5", rows: 6, cols: 6, entries: &[-10, -8, 8, -5, -5, 3, 10, 8, -10, -6, -10, 9, -10, -6, 2, -3, 9, 5, -8, -1, -7, 1, -5, -4, 3, -8, 7, -10, 6, -6, 7, 7, 3, 3, -3, -5], shift: 6 }, &[("-0.220278911386951077381861541231117540375067055434834058316795091524376857132699789532973087", "0.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"), ("-0.159771270952158049390957069318017536069816667901696340033191356241313794542693009150337435", "0.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"), ("-0.035312107203308621909602620479918258703365399921696728002591960799973074744268183724082584", "-0.147003764705577256540857545626217037646135395403151794713333361317387130269965012347479305"), ("-0.035312107203308621909602620479918258703365399921696728002591960799973074744268183724082584", "0.147003764705577256540857545626217037646135395403151794713333361317387130269965012347479305"), ("0.121016877117519433626723486032115804559492919361804948104323671126732080971160889460999244", "0.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"), ("0.360907519628206936965300365476855789292121603818118906250846698238904720192768276670476446", "0.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000")]),
(Case { name: "symmetric_6", rows: 3, cols: 3, entries: &[3, -5, 1, -5, 7, 3, 1, 3, 4], shift: 0 }, &[("-1.580335599611604922365506283845711095921010599647312096492362971315960597701453342806625313", "0.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"), ("4.617699463136555671424367038577289272615616986421562573427072311416308057994326751966547653", "0.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"), ("10.962636136475049250941139245268421823305393613225749523065290659899652539707126590840077660", "0.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000")]),
(Case { name: "symmetric_7", rows: 7, cols: 7, entries: &[-8, -6, 2, -3, 5, 10, -5, -6, -4, -7, -7, -1, -1, 2, 2, -7, -5, 2, -5, -6, 10, -3, -7, 2, -4, 7, 4, -6, 5, -1, -5, 7, 9, 9, -1, 10, -1, -6, 4, 9, -7, 10, -5, 2, 10, -6, -1, 10, -1], shift: 0 }, &[("-29.526121756426318231497942766650686411628906434515524760893516317933550331669981582101816951", "0.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"), ("-16.139080120565141824848222461519054281758471521149819709992774837579941692913867207604985180", "0.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"), ("-8.633124006809789261335879046552947773243435317138263470393914198814161204636860025918665850", "0.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"), ("-2.055379452829033451192069939982021275465404131802980555158731725098502962060773142334803199", "0.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"), ("6.776437322508875518403332514739273541475366042501875447683908555238116043603183737852134306", "0.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"), ("9.327163614431797146624540640600605907897528780314832315572532376243173470129391589833281027", "0.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"), ("20.250104399689610103846241059364830292723322581789880733182496147944866677548906630274855846", "0.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000")]),
(Case { name: "signed_permutation_8", rows: 6, cols: 6, entries: &[0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 1, 0, 0], shift: 0 }, &[("-1.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", "0.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"), ("-0.809016994374947424102293417182819058860154589902881431067724311352630231409451224853603602", "-0.587785252292473129168705954639072768597652437643145991072272480757278474162351957508504050"), ("-0.809016994374947424102293417182819058860154589902881431067724311352630231409451224853603602", "0.587785252292473129168705954639072768597652437643145991072272480757278474162351957508504050"), ("0.309016994374947424102293417182819058860154589902881431067724311352630231409451224853603602", "-0.951056516295153572116439333379382143405698634125750222447305644430153170085193501718792811"), ("0.309016994374947424102293417182819058860154589902881431067724311352630231409451224853603602", "0.951056516295153572116439333379382143405698634125750222447305644430153170085193501718792811"), ("1.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", "0.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000")]),
(Case { name: "scaled_9", rows: 2, cols: 2, entries: &[-20, -20, 40, 60], shift: 0 }, &[("-8.284271247461900976033774484193961571393437507538961463533594759814649569242140777007750687", "0.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"), ("48.284271247461900976033774484193961571393437507538961463533594759814649569242140777007750687", "0.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000")]),
(Case { name: "symmetric_10", rows: 3, cols: 3, entries: &[-3, -2, 3, -2, -6, 9, 3, 9, -10], shift: 0 }, &[("-18.075496943987035246985251491808605984523493870357454472515210044261496506275409123878063400", "0.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"), ("-2.172376856400090791753165436871236789707843108901473581764984359505265323101330163661592606", "0.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"), ("1.247873800387126038738416928679842774231336979258928054280194403766761829376739287539656006", "0.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000")]),
(Case { name: "dyadic_11", rows: 6, cols: 6, entries: &[8, -5, 6, -3, -3, 7, -10, 5, 4, -2, -2, -4, -2, -4, 8, -6, 1, 8, -3, -10, 6, 1, -1, 5, 4, -4, 0, -2, 0, -10, -2, 8, 5, 8, 7, -8], shift: 6 }, &[("-0.137263430933036738696739608130282411846175841113529480889652365805663053079582728648485636", "-0.136133269170058262144041318929276922559537656076974734334557190965731030768026415224371902"), ("-0.137263430933036738696739608130282411846175841113529480889652365805663053079582728648485636", "0.136133269170058262144041318929276922559537656076974734334557190965731030768026415224371902"), ("0.078764581815437007804527019451075879828792821756397002348038518864654915523282576663846210", "-0.112512322778582935356392089156854913331386520789451229610251349023891322765832297086007206"), ("0.078764581815437007804527019451075879828792821756397002348038518864654915523282576663846210", "0.112512322778582935356392089156854913331386520789451229610251349023891322765832297086007206"), ("0.167873849117599730892212588679206532017383019357132478541613846941008137556300151984639425", "-0.032239021940317751266163505028713424477931993873250603321099246963776558802376180717673150"), ("0.167873849117599730892212588679206532017383019357132478541613846941008137556300151984639425", "0.032239021940317751266163505028713424477931993873250603321099246963776558802376180717673150")]),
(Case { name: "complex_blocks_12", rows: 8, cols: 8, entries: &[4, -5, 0, 0, 0, 1, 2, 1, 0, 5, 0, 0, 0, 0, 0, 4, 0, -5, -1, 0, 3, -5, -2, -1, 0, 2, 0, 2, 0, -4, 0, 0, -2, 1, -3, -4, -1, 3, 3, -4, 0, 4, 0, 4, 0, 2, 0, -4, -2, 5, 0, -5, 0, -5, 4, 5, 0, -4, 0, 0, 0, 0, 0, 5], shift: 0 }, &[("-1.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", "-3.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"), ("-1.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", "3.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"), ("2.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", "-4.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"), ("2.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", "4.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"), ("4.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", "-2.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"), ("4.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", "2.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"), ("5.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", "-4.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"), ("5.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", "4.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000")]),
(Case { name: "dyadic_13", rows: 2, cols: 2, entries: &[-3, -3, -1, -8], shift: 6 }, &[("-0.133459082267954841320310033165641148922538828865518837393899633175674474416553986248461456", "0.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"), ("-0.038415917732045158679689966834358851077461171134481162606100366824325525583446013751538544", "0.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000")]),
(Case { name: "companion_14", rows: 4, cols: 4, entries: &[2, 11, -12, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0], shift: 0 }, &[("-3.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", "0.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"), ("0.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", "0.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"), ("1.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", "0.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"), ("4.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", "0.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000")]),
(Case { name: "rank_deficient_15", rows: 5, cols: 5, entries: &[-1, 3, -4, 1, 5, -1, -3, 2, 1, -4, 2, -6, 8, -2, -10, 1, 3, -2, -1, 4, 2, 2, 0, -2, 2], shift: 0 }, &[]),
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];