parquet_ziggurat Module

Layer tables for the Ziggurat normal draw. Data only -- no procedures.

A leaf module: iso_fortran_env and nothing else, which is what lets tools/check_random_kernels.sh keep compiling parquet_random standalone.

Every constant here is the unique solution of one equation rather than a choice, and tools/generate_parquet_ziggurat.py --self-test re-derives it: 256 regions of equal area under exp(-x*x/2), closing exactly at the peak. Do not hand-edit -- a single wrong digit leaves a table that still terminates and draws from a slightly wrong distribution, which no casual test would see.

These values are frozen contract, named by pf_normal_algorithm: they decide every value pf_random_normal_at and %normal return, so changing the layer count or the solver would change published draws.


Uses


Variables

Type Visibility Attributes Name Initial
integer(kind=int32), public, parameter :: zig_layers = 256

Layers, including the base strip at index 0. The index costs 8 bits of a 64-bit draw, which is why it is a power of two and why it is this one.
real(kind=real64), public, parameter :: zig_r = 3.654152885361009_real64

Where the tail begins: the outer edge of layer 255, and the point beyond which a draw is generated by the tail algorithm rather than by a rectangle.
real(kind=real64), public, parameter :: zig_v = 0.004928673233974655_real64

The shared area of every region, base strip and tail included. Not used by the draw itself -- published so a reader can check the construction.
real(kind=real64), public, parameter :: zig_accept_rate = 0.9850809499905381_real64

Fraction of draws accepted with no wedge test and no tail walk: 0.98508. Published for the same reason as zig_v; nothing reads it.
real(kind=real64), public, parameter :: zig_w(0:zig_layers-1) = [3.910757959524916_real64, 0.2152418959848817_real64, 0.2861745917920725_real64, 0.33573751921442524_real64, 0.37512133287838056_real64, 0.40838913461199117_real64, 0.4375184022078717_real64, 0.46363433679088223_real64, 0.487443966139236_real64, 0.5094233296020918_real64, 0.5299097206615582_real64, 0.5491517023271651_real64, 0.5673382570538188_real64, 0.5846167661063794_real64, 0.6011046177559927_real64, 0.6168969900077514_real64, 0.6320722363860611_real64, 0.6466957148949938_real64, 0.6608225742444197_real64, 0.6744998228372938_real64, 0.6877678927957885_real64, 0.7006618411068151_real64, 0.7132122851909759_real64, 0.7254461409099996_real64, 0.7373872114342956_real64, 0.7490566620178153_real64, 0.7604734064301081_real64, 0.7716544242245681_real64, 0.7826150233072331_real64, 0.7933690588406233_real64, 0.8039291169899713_real64, 0.8143066701352152_real64, 0.8245122087522921_real64, 0.8345553540863822_real64, 0.8444449549091539_real64, 0.8541891710081638_real64, 0.8637955455533088_real64, 0.8732710680888608_real64, 0.8826222295851656_real64, 0.8918550707329416_real64, 0.9009752244612218_real64, 0.9099879534967185_real64, 0.9188981836495906_real64, 0.9277105334020002_real64, 0.9364293402865751_real64, 0.9450586844681654_real64, 0.953602409881086_real64, 0.9620641432230406_real64, 0.9704473110642244_real64, 0.9787551552942246_real64, 0.9869907470990624_real64, 0.995156999635091_real64, 1.003256679544673_real64, 1.0112924174399958_real64, 1.0192667174654841_real64, 1.0271819660356458_real64, 1.035040439833441_real64, 1.042844313144149_real64, 1.05059566459093_real64, 1.0582964833306752_real64, 1.0659486747621225_real64, 1.0735540657924363_real64, 1.0811144097034038_real64, 1.0886313906539797_real64, 1.0961066278520215_real64, 1.1035416794246398_real64, 1.1109380460135758_real64, 1.118297174119345_real64, 1.1256204592155334_real64, 1.1329092486525338_real64, 1.1401648443681514_real64, 1.147388505420849_real64, 1.1545814503599277_real64, 1.1617448594456115_real64, 1.168879876730833_real64, 1.175987612015452_real64, 1.1830691426826867_real64, 1.190125515426692_real64, 1.1971577478794415_real64, 1.2041668301443815_real64, 1.211153726243699_real64, 1.2181193754854815_real64, 1.2250646937565308_real64, 1.2319905747461362_real64, 1.2388978911056874_real64, 1.2457874955486272_real64, 1.2526602218948972_real64, 1.2595168860637143_real64, 1.2663582870182295_real64, 1.2731852076653563_real64, 1.279998415713818_real64, 1.2867986644932436_real64, 1.2935866937369478_real64, 1.3003632303308372_real64, 1.3071289890307312_real64, 1.3138846731502205_real64, 1.3206309752210563_real64, 1.3273685776279258_real64, 1.33409815321936_real64, 1.340820365896404_real64, 1.3475358711805872_real64, 1.354245316762635_real64, 1.360949343033283_real64, 1.367648583597476_real64, 1.3743436657731662_real64, 1.3810352110758555_real64, 1.3877238356899761_real64, 1.394410150928141_real64, 1.401094763679251_real64, 1.407778276846399_real64, 1.4144612897754711_real64, 1.421144398675309_real64, 1.427828197030256_real64, 1.4345132760058923_real64, 1.441200224848724_real64, 1.447889631280576_real64, 1.4545820818884103_real64, 1.4612781625102755_real64, 1.4679784586180795_real64, 1.4746835556978555_real64, 1.4813940396281873_real64, 1.4881104970574475_real64, 1.4948335157804935_real64, 1.5015636851154637_real64, 1.5083015962813116_real64, 1.5150478427767147_real64, 1.521803020760998_real64, 1.5285677294377125_real64, 1.535342571441514_real64, 1.5421281532290019_real64, 1.5489250854741734_real64, 1.5557339834691764_real64, 1.562555467531045_real64, 1.5693901634151237_real64, 1.5762387027359064_real64, 1.5831017233960292_real64, 1.5899798700241907_real64, 1.5968737944227882_real64, 1.6037841560260946_real64, 1.6107116223698301_real64, 1.6176568695730156_real64, 1.6246205828330347_real64, 1.6316034569348736_real64, 1.6386061967755476_real64, 1.6456295179047824_real64, 1.652674147083056_real64, 1.6597408228581825_real64, 1.6668302961616654_real64, 1.673943330926125_real64, 1.681080704725174_real64, 1.6882432094371953_real64, 1.6954316519345616_real64, 1.7026468547999232_real64, 1.7098896570713018_real64, 1.717160915017823_real64, 1.724461502948045_real64, 1.7317923140529632_real64, 1.7391542612859117_real64, 1.7465482782817223_real64, 1.7539753203176716_real64, 1.7614363653189102_real64, 1.7689324149112686_real64, 1.7764644955245228_real64, 1.7840336595494415_real64, 1.7916409865521625_real64, 1.7992875845497203_real64, 1.8069745913508208_real64, 1.8147031759662826_real64, 1.8224745400938858_real64, 1.830289919682757_real64, 1.8381505865828067_real64, 1.8460578502851854_real64, 1.8540130597602018_real64, 1.8620176053996742_real64, 1.8700729210712668_real64, 1.8781804862929958_real64, 1.8863418285367828_real64, 1.8945585256707047_real64, 1.9028322085504292_real64, 1.9111645637712533_real64, 1.9195573365931882_real64, 1.9280123340526658_real64, 1.9365314282756947_real64, 1.9451165600086784_real64, 1.9537697423846467_real64, 1.962493064944363_real64, 1.9712886979336592_real64, 1.9801588969004766_real64, 1.989106007617438_real64, 1.9981324713584196_real64, 2.0072408305605287_real64, 2.016433734906204_real64, 2.025713947863854_real64, 2.035084353729619_real64, 2.0445479652175313_real64, 2.0541079316506523_real64, 2.0637675478117323_real64, 2.073530263518743_real64, 2.0833996939983046_real64, 2.093379631138792_real64, 2.1034740557148774_real64, 2.113687150686653_real64, 2.1240233156895236_real64, 2.134487182846017_real64, 2.145083634047889_real64, 2.1558178198767375_real64, 2.1666951803543086_real64, 2.177721467740293_real64, 2.1889027716263607_real64, 2.2002455466112765_real64, 2.211756642884161_real64, 2.2234433400925107_real64, 2.235313384929921_real64, 2.247375032947389_real64, 2.2596370951737876_real64, 2.2721089902283818_real64, 2.284800802724492_real64, 2.2977233489028634_real64, 2.310888250601372_real64, 2.3243080188711325_real64, 2.337996148796529_real64, 2.3519672273791445_real64, 2.366237056717291_real64, 2.3808227951720857_real64, 2.3957431197819274_real64, 2.4110184139011195_real64, 2.4266709849371466_real64, 2.442725318200364_real64, 2.459208374334705_real64, 2.476149939670523_real64, 2.4935830412710467_real64, 2.5115444416266945_real64, 2.530075232159854_real64, 2.5492215503247833_real64, 2.569035452681844_real64, 2.5895759867082866_real64, 2.6109105184888235_real64, 2.6331163936315827_real64, 2.6562830375767432_real64, 2.680514643285745_real64, 2.705933656123062_real64, 2.7326853590440114_real64, 2.760944005279986_real64, 2.7909211740019275_real64, 2.822877396826443_real64, 2.8571387308732246_real64, 2.894121053613412_real64, 2.9343668672088876_real64, 2.978603279881843_real64, 3.0278377917695933_real64, 3.0835261320021434_real64, 3.147889289518001_real64, 3.2245750520478014_real64, 3.3202447338398255_real64, 3.449278298561431_real64, 3.654152885361009_real64]

Layer half-widths. A draw is u * zig_w(i). Index 0 is the base strip and is WIDER than zig_r, because its area has to cover the tail as well.
real(kind=real64), public, parameter :: zig_k(0:zig_layers-1) = [0.934384823397488_real64, 0.0_real64, 0.7521348930280688_real64, 0.8523759645978131_real64, 0.8950104667155143_real64, 0.9185389646440566_real64, 0.9334216173562437_real64, 0.9436712673962501_real64, 0.95115412026343_real64, 0.9568544230590622_real64, 0.9613398466555957_real64, 0.9649605353419385_real64, 0.9679440712828072_real64, 0.9704447254093693_real64, 0.9725707453202327_real64, 0.9744003091155293_real64, 0.9759912783623027_real64, 0.9773873891969315_real64, 0.9786223111921101_real64, 0.9797223837134004_real64, 0.9807085063180839_real64, 0.9815974731966873_real64, 0.9824029333975924_real64, 0.9831360937371897_real64, 0.9838062413625681_real64, 0.984421137711953_real64, 0.9849873193253577_real64, 0.9855103302158918_real64, 0.9859949032969659_real64, 0.9864451034313017_real64, 0.9868644412471508_real64, 0.9872559644592855_real64, 0.9876223317147473_real64, 0.9879658727429954_real64, 0.9882886376841038_real64, 0.9885924377998035_real64, 0.9888788792734609_real64, 0.9891493914297551_real64, 0.9894052504198768_real64, 0.9896475991999594_real64, 0.9898774644622064_real64, 0.990095771047447_real64, 0.9903033542655582_real64, 0.9905009704696423_real64, 0.9906893061660084_real64, 0.9908689858911285_real64, 0.9910405790459507_real64, 0.9912046058450878_real64, 0.9913615425117819_real64, 0.9915118258278776_real64, 0.991655857130329_real64, 0.9917940058312177_real64, 0.9919266125262599_real64, 0.9920539917468534_real64, 0.9921764344024522_real64, 0.9922942099531692_real64, 0.9924075683467405_real64, 0.9925167417491307_real64, 0.9926219460939818_real64, 0.9927233824726421_real64, 0.9928212383835882_real64, 0.9929156888575519_real64, 0.9930068974725426_real64, 0.9930950172711258_real64, 0.9931801915907666_real64, 0.9932625548166928_real64, 0.9933422330655821_real64, 0.9934193448073724_real64, 0.9934940014316263_real64, 0.9935663077641307_real64, 0.9936363625387534_real64, 0.9937042588290108_real64, 0.9937700844432964_real64, 0.9938339222872894_real64, 0.9938958506966711_real64, 0.9939559437429468_real64, 0.9940142715148695_real64, 0.9940709003777006_real64, 0.994125893212314_real64, 0.9941793096359418_real64, 0.9942312062061791_real64, 0.9942816366097073_real64, 0.9943306518370454_real64, 0.9943783003445197_real64, 0.9944246282045192_real64, 0.9944696792450097_real64, 0.9945134951791846_real64, 0.9945561157260497_real64, 0.9945975787226662_real64, 0.9946379202287109_real64, 0.9946771746239529_real64, 0.9947153746991929_real64, 0.9947525517411634_real64, 0.9947887356118449_real64, 0.994823954822614_real64, 0.9948582366036041_real64, 0.9948916069686261_real64, 0.9949240907759697_real64, 0.9949557117853775_real64, 0.9949864927114603_real64, 0.9950164552738031_real64, 0.9950456202439844_real64, 0.9950740074897233_real64, 0.9951016360163432_real64, 0.9951285240057307_real64, 0.9951546888529538_real64, 0.9951801472006893_real64, 0.9952049149715997_real64, 0.9952290073987884_real64, 0.9952524390544513_real64, 0.995275223876835_real64, 0.9952973751956048_real64, 0.9953189057557145_real64, 0.9953398277398663_real64, 0.995360152789642_real64, 0.9953798920253778_real64, 0.9953990560648556_real64, 0.9954176550408703_real64, 0.9954356986177362_real64, 0.9954531960067847_real64, 0.9954701559809056_real64, 0.9954865868881773_real64, 0.9955024966646298_real64, 0.9955178928461814_real64, 0.9955327825797838_real64, 0.9955471726338101_real64, 0.9955610694077178_real64, 0.9955744789410131_real64, 0.9955874069215439_real64, 0.9955998586931444_real64, 0.9956118392626518_real64, 0.9956233533063155_real64, 0.9956344051756147_real64, 0.9956449989024998_real64, 0.9956551382040705_real64, 0.995664826486702_real64, 0.9956740668496281_real64, 0.9956828620879903_real64, 0.9956912146953558_real64, 0.9956991268657122_real64, 0.9957066004949376_real64, 0.99571363718175_real64, 0.9957202382281313_real64, 0.9957264046392268_real64, 0.9957321371227124_real64, 0.9957374360876237_real64, 0.99574230164264_real64, 0.9957467335938107_real64, 0.9957507314417124_real64, 0.9957542943780229_real64, 0.9957574212814934_real64, 0.995760110713302_real64, 0.9957623609117644_real64, 0.9957641697863802_real64, 0.9957655349111846_real64, 0.9957664535173786_real64, 0.9957669224852016_real64, 0.9957669383350128_real64, 0.9957664972175375_real64, 0.9957655949032373_real64, 0.9957642267707537_real64, 0.9957623877943724_real64, 0.9957600725304503_real64, 0.9957572751027409_real64, 0.9957539891865498_real64, 0.9957502079916417_real64, 0.9957459242438189_real64, 0.995741130165077_real64, 0.9957358174522412_real64, 0.995729977253972_real64, 0.9957236001460235_real64, 0.9957166761046208_real64, 0.9957091944778181_real64, 0.9957011439546759_real64, 0.9956925125320898_real64, 0.9956832874790797_real64, 0.9956734552983338_real64, 0.9956630016847787_real64, 0.9956519114809248_real64, 0.9956401686287119_real64, 0.9956277561175484_real64, 0.9956146559282091_real64, 0.9956008489722191_real64, 0.9955863150263112_real64, 0.9955710326615014_real64, 0.9955549791662761_real64, 0.9955381304633278_real64, 0.9955204610192133_real64, 0.9955019437462368_real64, 0.995482549895781_real64, 0.9954622489422131_real64, 0.9954410084563959_real64, 0.9954187939677089_real64, 0.9953955688133556_real64, 0.9953712939735774_real64, 0.9953459278912192_real64, 0.9953194262738929_real64, 0.9952917418767528_real64, 0.9952628242636338_real64, 0.9952326195439963_real64, 0.9952010700827709_real64, 0.9951681141797839_real64, 0.995133685714973_real64, 0.9950977137550475_real64, 0.995060122116602_real64, 0.9950208288799365_real64, 0.9949797458469481_real64, 0.9949367779354144_real64, 0.99489182250075_real64, 0.9948447685748596_real64, 0.9947954960099616_real64, 0.9947438745131849_real64, 0.9946897625552479_real64, 0.9946330061335381_real64, 0.9945734373662974_real64, 0.994510872890239_real64, 0.9944451120285952_real64, 0.9943759346900741_real64, 0.994303098951201_real64, 0.9942263382646339_real64, 0.9941453582237755_real64, 0.9940598327986975_real64, 0.9939693999391832_real64, 0.9938736564164405_real64, 0.9937721517442154_real64, 0.993664380980618_real64, 0.9935497761611747_real64, 0.9934276960476893_real64, 0.9932974137912165_real64, 0.9931581019935843_real64, 0.9930088145002632_real64, 0.9928484640534514_real64, 0.9926757946571649_real64, 0.992489347125404_real64, 0.9922874157550544_real64, 0.9920679933194188_real64, 0.9918287005129209_real64, 0.9915666944323214_real64, 0.9912785484011166_real64, 0.9909600920219936_real64, 0.990606195100239_real64, 0.9902104708716601_real64, 0.9897648607932891_real64, 0.9892590414228875_real64, 0.988679556944116_real64, 0.9880085157655923_real64, 0.9872215701917465_real64, 0.9862846687490864_real64, 0.9851486053977923_real64, 0.9837393825978453_real64, 0.9819400459575832_real64, 0.9795535510952761_real64, 0.976218335348994_real64, 0.9711859548132216_real64, 0.9625911412322338_real64, 0.9439337670790047_real64]

Fraction of zig_w(i) that lies wholly under the curve, so a uniform below it is accepted immediately. zig_k(1) is 0: layer 1 contains the peak.
real(kind=real64), public, parameter :: zig_f(0:zig_layers-1) = [1.0_real64, 0.9771017012676713_real64, 0.9598790918001063_real64, 0.9451989534422993_real64, 0.9320600759592301_real64, 0.9199915050393467_real64, 0.9087264400521305_real64, 0.8980959218983431_real64, 0.887984660755833_real64, 0.8783096558089171_real64, 0.8690086880368567_real64, 0.8600336211963312_real64, 0.8513462584586777_real64, 0.842915653112204_real64, 0.8347162929868832_real64, 0.826726833946221_real64, 0.818929191603702_real64, 0.8113078743126559_real64, 0.8038494831709639_real64, 0.7965423304229586_real64, 0.7893761435660241_real64, 0.7823418326548021_real64, 0.7754313049811867_real64, 0.7686373157984858_real64, 0.7619533468367949_real64, 0.7553735065070958_real64, 0.7488924472191565_real64, 0.7425052963401507_real64, 0.7362075981268623_real64, 0.7299952645614758_real64, 0.7238645334686298_real64, 0.7178119326307216_real64, 0.7118342488782481_real64, 0.7059285013327539_real64, 0.7000919181365113_real64, 0.6943219161261164_real64, 0.6886160830046714_real64, 0.6829721616449944_real64, 0.6773880362187731_real64, 0.6718617198970818_real64, 0.6663913439087499_real64, 0.6609751477766629_real64, 0.655611470579697_real64, 0.6502987431108165_real64, 0.6450354808208221_real64, 0.6398202774530563_real64, 0.6346517992876233_real64, 0.6295287799248364_real64, 0.6244500155470262_real64, 0.6194143606058341_real64, 0.6144207238889136_real64, 0.6094680649257731_real64, 0.6045553906974674_real64, 0.5996817526191249_real64, 0.594846243767987_real64, 0.5900479963328256_real64, 0.5852861792633709_real64, 0.5805599961007905_real64, 0.5758686829723533_real64, 0.5712115067352528_real64, 0.566587763256164_real64, 0.561996775814524_real64, 0.5574378936187656_real64, 0.552910490425832_real64, 0.5484139632552655_real64, 0.5439477311900258_real64, 0.5395112342569517_real64, 0.5351039323804572_real64, 0.5307253044036616_real64, 0.526374847171684_real64, 0.5220520746723215_real64, 0.5177565172297559_real64, 0.5134877207473266_real64, 0.5092452459957476_real64, 0.5050286679434679_real64, 0.5008375751261485_real64, 0.4966715690524894_real64, 0.4925302636438682_real64, 0.48841328470545764_real64, 0.48432026942668294_real64, 0.4802508659090465_real64, 0.47620473271950553_real64, 0.4721815384677298_real64, 0.46818096140569326_real64, 0.464202689048174_real64, 0.46024641781284253_real64, 0.45631185267871616_real64, 0.4523987068618483_real64, 0.4485067015072028_real64, 0.4446355653957392_real64, 0.4407850346658038_real64, 0.4369548525479854_real64, 0.43314476911265215_real64, 0.4293545410294413_real64, 0.42558393133802186_real64, 0.4218327092294958_real64, 0.418100649837848_real64, 0.41438753404089096_real64, 0.41069314827018805_real64, 0.4070172843294732_real64, 0.40335973922111434_real64, 0.39972031498019706_real64, 0.39609881851583223_real64, 0.3924950614593154_real64, 0.3889088600187886_real64, 0.3853400348400771_real64, 0.38178841087339344_real64, 0.37825381724561896_real64, 0.3747360871378909_real64, 0.3712350576682393_real64, 0.3677505697790323_real64, 0.3642824681290038_real64, 0.3608306009896478_real64, 0.3573948201457803_real64, 0.3539749808000766_real64, 0.35057094148140594_real64, 0.34718256395679353_real64, 0.3438097131468506_real64, 0.3404522570445217_real64, 0.33711006663700593_real64, 0.3337830158307183_real64, 0.3304709813791634_real64, 0.32717384281360135_real64, 0.3238914823763911_real64, 0.32062378495690536_real64, 0.3173706380299135_real64, 0.3141319315963371_real64, 0.31090755812628634_real64, 0.30769741250429195_real64, 0.3045013919766498_real64, 0.30131939610080294_real64, 0.29815132669668537_real64, 0.2949970877999617_real64, 0.29185658561709504_real64, 0.28872972848218276_real64, 0.2856164268155016_real64, 0.28251659308370747_real64, 0.2794301417616378_real64, 0.2763569892956681_real64, 0.2732970540685769_real64, 0.27025025636587524_real64, 0.26721651834356114_real64, 0.2641957639972608_real64, 0.2611879191327209_real64, 0.25819291133761896_real64, 0.2552106699546617_real64, 0.25224112605594196_real64, 0.24928421241852827_real64, 0.24633986350126366_real64, 0.24340801542275015_real64, 0.24048860594050042_real64, 0.23758157443123798_real64, 0.23468686187232993_real64, 0.2318044108243386_real64, 0.22893416541468026_real64, 0.22607607132238022_real64, 0.22323007576391746_real64, 0.22039612748015197_real64, 0.21757417672433116_real64, 0.2147641752511736_real64, 0.21196607630703018_real64, 0.20917983462112502_real64, 0.20640540639788074_real64, 0.20364274931033488_real64, 0.2008918224946566_real64, 0.19815258654577514_real64, 0.19542500351413428_real64, 0.19270903690358915_real64, 0.19000465167046499_real64, 0.18731181422380028_real64, 0.18463049242679927_real64, 0.18196065559952257_real64, 0.17930227452284767_real64, 0.176655321443735_real64, 0.17401977008183878_real64, 0.17139559563750595_real64, 0.1687827748012115_real64, 0.16618128576448207_real64, 0.16359110823236572_real64, 0.1610122234375111_real64, 0.1584446141559243_real64, 0.15588826472447923_real64, 0.15334316106026286_real64, 0.1508092906818457_real64, 0.14828664273257455_real64, 0.14577520800599406_real64, 0.14327497897351343_real64, 0.1407859498144447_real64, 0.13830811644855073_real64, 0.13584147657125373_real64, 0.13338602969166913_real64, 0.13094177717364433_real64, 0.12850872227999954_real64, 0.12608687022018586_real64, 0.12367622820159656_real64, 0.12127680548479022_real64, 0.11888861344290999_real64, 0.11651166562561081_real64, 0.11414597782783836_real64, 0.111791568163838_real64, 0.10944845714681165_real64, 0.10711666777468365_real64, 0.1047962256224869_real64, 0.1024871589419351_real64, 0.10018949876880982_real64, 0.0979032790388623_real64, 0.09562853671300883_real64, 0.09336531191269087_real64, 0.09111364806637363_real64, 0.0888735920682758_real64, 0.08664519445055796_real64, 0.08442850957035337_real64, 0.08222359581320286_real64, 0.08003051581466306_real64, 0.07784933670209605_real64, 0.07568013035892708_real64, 0.07352297371398127_real64, 0.07137794905889037_real64, 0.06924514439700677_real64, 0.0671246538277885_real64, 0.06501657797124286_real64, 0.06292102443775813_real64, 0.060838108349539864_real64, 0.058767952920933765_real64, 0.0567106901062029_real64, 0.05466646132488892_real64, 0.05263541827679218_real64, 0.05061772386094777_real64, 0.04861355321586853_real64, 0.04662309490193037_real64, 0.04464655225129445_real64, 0.04268414491647444_real64, 0.04073611065594093_real64, 0.03880270740452612_real64, 0.03688421568856729_real64, 0.034980941461716084_real64, 0.03309321945857852_real64, 0.03122141719192025_real64, 0.029365939758133317_real64, 0.027527235669603085_real64, 0.025705804008548896_real64, 0.023902203305795882_real64, 0.022117062707308868_real64, 0.02035109623004452_real64, 0.018605121275724647_real64, 0.01688008315254317_real64, 0.015177088307935327_real64, 0.01349745060173988_real64, 0.01184275785790789_real64, 0.010214971439701471_real64, 0.008616582769398732_real64, 0.007050875471373227_real64, 0.005522403299250998_real64, 0.0040379725933630305_real64, 0.002609072746102163_real64, 0.0012602859304985975_real64]

exp(-zig_w(i)**2/2), the curve's height at the layer's outer edge, for the wedge test. zig_f(0) is 1 rather than f(zig_w(0)): layer 0 never runs that test, and 1 is what makes layer 1's wedge span the full height.