ms_lut.py

import numpy as np

# [ 32, 32 ]
# GGX_E[32-roughness][32-cos_theta]
GGX_E = np.array([
[0.9635857939720154, 0.995747983455658, 0.9983890056610107, 0.9992253184318542, 0.9995855093002319, 0.9996441006660461, 0.9998587369918823, 0.99983811378479, 0.9998855590820312, 0.9998201727867126, 0.9998736381530762, 0.9998807311058044, 0.9998859763145447, 0.9998285174369812, 0.9999691247940063, 0.9998969435691833, 0.9999278783798218, 0.9999445676803589, 0.999960720539093, 0.9999779462814331, 0.9999331831932068, 0.9999798536300659, 0.999980628490448, 0.9999813437461853, 0.9999666213989258, 0.9999518990516663, 0.999967634677887, 0.9999833106994629, 0.9999531507492065, 0.9999687671661377, 0.9999690651893616, 0.9999998807907104],
[0.9624530076980591, 0.9955804944038391, 0.9987631440162659, 0.9992542862892151, 0.9995307326316833, 0.9997747540473938, 0.9998279809951782, 0.999792218208313, 0.999916136264801, 0.9996671080589294, 0.9998441338539124, 0.9997889399528503, 0.9998522996902466, 0.9998584389686584, 0.9999077916145325, 0.9999716281890869, 0.9999582767486572, 0.9999406933784485, 0.9999462366104126, 0.999954104423523, 0.9999637007713318, 0.9999645948410034, 0.9999653697013855, 0.999966025352478, 0.9999495148658752, 0.9999824166297913, 0.999937117099762, 0.9999810457229614, 0.9999531507492065, 0.9999687671661377, 0.9999995827674866, 0.999984622001648],
[0.9328259229660034, 0.990190863609314, 0.9964872598648071, 0.9983128905296326, 0.998899519443512, 0.9993115663528442, 0.9995121955871582, 0.9996293187141418, 0.9997661113739014, 0.9997414350509644, 0.9998139142990112, 0.9997804760932922, 0.9998407363891602, 0.9997414350509644, 0.9997649788856506, 0.9997093081474304, 0.9998055696487427, 0.9998250007629395, 0.9998658895492554, 0.9999068379402161, 0.9998948574066162, 0.9999427199363708, 0.9998825788497925, 0.9999004602432251, 0.9999170303344727, 0.9999791979789734, 0.9999498724937439, 0.9999508857727051, 0.9999822974205017, 0.9999220371246338, 0.9999837875366211, 0.9999691247940063],
[0.8930054306983948, 0.963340699672699, 0.9859972596168518, 0.9929569363594055, 0.996091365814209, 0.9974014759063721, 0.998002827167511, 0.9985195398330688, 0.9987627267837524, 0.9990635514259338, 0.999199390411377, 0.9992281198501587, 0.9993909001350403, 0.9995043873786926, 0.9994504451751709, 0.9996720552444458, 0.9996840357780457, 0.9995111227035522, 0.9997578859329224, 0.9997982382774353, 0.9997780919075012, 0.9995821714401245, 0.9997304677963257, 0.9997903108596802, 0.9998418092727661, 0.9998234510421753, 0.9997690916061401, 0.9998010993003845, 0.9998071193695068, 0.9998663067817688, 0.9998665452003479, 0.9998453259468079],
[0.8982181549072266, 0.9266762137413025, 0.9636628031730652, 0.98019939661026, 0.9873616695404053, 0.9918653964996338, 0.9942402243614197, 0.9956909418106079, 0.996512234210968, 0.9973861575126648, 0.9977238774299622, 0.9982470870018005, 0.998320996761322, 0.9985633492469788, 0.9987225532531738, 0.998935341835022, 0.9990522861480713, 0.9990097880363464, 0.9990995526313782, 0.9992167353630066, 0.9993321895599365, 0.9992751479148865, 0.9993900060653687, 0.9994798898696899, 0.9994648098945618, 0.9994661808013916, 0.9993231296539307, 0.9995315074920654, 0.9995622038841248, 0.9995185732841492, 0.9995428919792175, 0.99954754114151],
[0.9151620268821716, 0.8979942798614502, 0.9348788261413574, 0.9588434100151062, 0.9736459255218506, 0.9823293089866638, 0.9873502850532532, 0.9898392558097839, 0.9922816753387451, 0.993818998336792, 0.9948622584342957, 0.9954609870910645, 0.9965735077857971, 0.9967789649963379, 0.9972547292709351, 0.9973844885826111, 0.9976301193237305, 0.9977455139160156, 0.9979255795478821, 0.9983596801757812, 0.9982226490974426, 0.9983841776847839, 0.9987102150917053, 0.998901903629303, 0.9987770915031433, 0.9991421103477478, 0.9986880421638489, 0.9989207983016968, 0.9987643957138062, 0.9987972974777222, 0.9989362955093384, 0.9991236925125122],
[0.9330495595932007, 0.8908846378326416, 0.9079879522323608, 0.9335653781890869, 0.9522469639778137, 0.965967059135437, 0.9742348790168762, 0.9801027774810791, 0.9846681356430054, 0.9871715903282166, 0.9900511503219604, 0.9913052320480347, 0.992600679397583, 0.9934586882591248, 0.9945163130760193, 0.9951238632202148, 0.9950239658355713, 0.9956044554710388, 0.996037483215332, 0.9963870644569397, 0.9962829947471619, 0.9968684315681458, 0.9971612095832825, 0.9972022175788879, 0.9974944591522217, 0.9974798560142517, 0.997612714767456, 0.9979535937309265, 0.9980898499488831, 0.9980645179748535, 0.9982076287269592, 0.9981849193572998],
[0.9453397989273071, 0.8931507468223572, 0.8936023116111755, 0.9110523462295532, 0.930195152759552, 0.9464243054389954, 0.9567159414291382, 0.9660252332687378, 0.972061812877655, 0.9772922396659851, 0.9808592796325684, 0.9842429757118225, 0.985924482345581, 0.9886795282363892, 0.9899022579193115, 0.9898055791854858, 0.9914050698280334, 0.9922351241111755, 0.9925453662872314, 0.9938244819641113, 0.9941720366477966, 0.9945185780525208, 0.9945670366287231, 0.9954984188079834, 0.9955605864524841, 0.9953851699829102, 0.9958810806274414, 0.996248722076416, 0.9964290261268616, 0.9964909553527832, 0.9967811703681946, 0.9969521164894104],
[0.9544344544410706, 0.9022103548049927, 0.8864280581474304, 0.8952941298484802, 0.9088196158409119, 0.9242581129074097, 0.9367639422416687, 0.947743833065033, 0.9565682411193848, 0.9628447890281677, 0.969174861907959, 0.9732633829116821, 0.9772542119026184, 0.9795423150062561, 0.9819976687431335, 0.9845349788665771, 0.9857139587402344, 0.9868486523628235, 0.9881422519683838, 0.9892463088035583, 0.9899702668190002, 0.9913380146026611, 0.9913980960845947, 0.9914693236351013, 0.9926061034202576, 0.9922316074371338, 0.9932136535644531, 0.9937698245048523, 0.993614673614502, 0.9941533207893372, 0.9941940903663635, 0.9942945837974548],
[0.9617866277694702, 0.9104193449020386, 0.8869238495826721, 0.8837536573410034, 0.8927567601203918, 0.906217634677887, 0.9172398447990417, 0.9285588264465332, 0.9377991557121277, 0.9461573362350464, 0.953217089176178, 0.9600023031234741, 0.964180052280426, 0.9693463444709778, 0.9721860289573669, 0.9742137789726257, 0.9777005314826965, 0.9793358445167542, 0.9813347458839417, 0.9839100241661072, 0.9844508171081543, 0.984897255897522, 0.9853436350822449, 0.9872106909751892, 0.9869411587715149, 0.9885827898979187, 0.9889422655105591, 0.9895589351654053, 0.990011990070343, 0.9906002283096313, 0.9904730916023254, 0.9904001951217651],
[0.9664388298988342, 0.9197866916656494, 0.8905799388885498, 0.883156418800354, 0.8827630877494812, 0.8896644711494446, 0.8999561071395874, 0.9085540771484375, 0.918840229511261, 0.9277880787849426, 0.9360264539718628, 0.9443001747131348, 0.9497106671333313, 0.9545363783836365, 0.9582120180130005, 0.9616508483886719, 0.9655871391296387, 0.9689820408821106, 0.9717747569084167, 0.9725849628448486, 0.9756177067756653, 0.97783362865448, 0.9788875579833984, 0.9798064827919006, 0.9813156723976135, 0.9821791052818298, 0.9827338457107544, 0.983195960521698, 0.9844823479652405, 0.9845951199531555, 0.9858988523483276, 0.9854810833930969],
[0.9694132804870605, 0.9257479310035706, 0.8974544405937195, 0.8827428221702576, 0.8775234818458557, 0.8790539503097534, 0.885047435760498, 0.8924179077148438, 0.8990315794944763, 0.9091772437095642, 0.9173170328140259, 0.9247027635574341, 0.9310639500617981, 0.9368415474891663, 0.9423990249633789, 0.9467107653617859, 0.9521124958992004, 0.9548688530921936, 0.9582838416099548, 0.9622583985328674, 0.9648769497871399, 0.9657583832740784, 0.9693913459777832, 0.9698737263679504, 0.9720104932785034, 0.9729395508766174, 0.9751629829406738, 0.9754497408866882, 0.9765639901161194, 0.9774071574211121, 0.9781448841094971, 0.9796364307403564],
[0.9719973802566528, 0.9306831359863281, 0.9013428092002869, 0.8835747838020325, 0.8736779689788818, 0.8725164532661438, 0.8706512451171875, 0.8772178888320923, 0.8831602334976196, 0.8910667300224304, 0.8990358114242554, 0.9044378995895386, 0.9113524556159973, 0.9180989861488342, 0.923933207988739, 0.9308220744132996, 0.936453640460968, 0.9393223524093628, 0.9423696398735046, 0.9479364156723022, 0.9496214389801025, 0.9525513052940369, 0.9555701613426208, 0.9576094746589661, 0.9587423801422119, 0.9622700810432434, 0.9637910723686218, 0.9662023782730103, 0.9664798378944397, 0.9684286117553711, 0.969126284122467, 0.9697811007499695],
[0.9727442264556885, 0.9345206022262573, 0.903929591178894, 0.8853692412376404, 0.8722270131111145, 0.8659079670906067, 0.864499568939209, 0.8654941916465759, 0.8688635230064392, 0.8752998113632202, 0.8800772428512573, 0.8857589960098267, 0.8938597440719604, 0.8992937803268433, 0.9035927653312683, 0.9089774489402771, 0.9148463606834412, 0.9191759824752808, 0.9240384101867676, 0.9290494322776794, 0.9338057637214661, 0.9356728792190552, 0.9390535950660706, 0.9426724314689636, 0.9452378153800964, 0.946725606918335, 0.9497633576393127, 0.9519825577735901, 0.9538668990135193, 0.9557593464851379, 0.9576612114906311, 0.9602978825569153],
[0.9740354418754578, 0.9360936284065247, 0.9068396091461182, 0.8849396109580994, 0.8705020546913147, 0.8618043065071106, 0.856893002986908, 0.8550428748130798, 0.8556362390518188, 0.856810450553894, 0.8621847033500671, 0.8672357201576233, 0.8719860315322876, 0.877931535243988, 0.8839832544326782, 0.8895988464355469, 0.8940945863723755, 0.8994845151901245, 0.9039913415908813, 0.9069719314575195, 0.911770224571228, 0.9165511727333069, 0.91954106092453, 0.9230077266693115, 0.9257956147193909, 0.9294732213020325, 0.931367039680481, 0.9356260299682617, 0.9380109310150146, 0.9394761919975281, 0.9417126178741455, 0.9439557194709778],
[0.9739981889724731, 0.9375192523002625, 0.9077275991439819, 0.8862419724464417, 0.8690840601921082, 0.8569494485855103, 0.849721372127533, 0.8470186591148376, 0.8441779613494873, 0.8441599607467651, 0.8484534025192261, 0.8481707572937012, 0.8540400266647339, 0.8571040630340576, 0.8619566559791565, 0.8666855096817017, 0.8700076937675476, 0.8751792907714844, 0.8810882568359375, 0.8854482769966125, 0.8874629139900208, 0.8928744792938232, 0.8970271348953247, 0.9019522070884705, 0.9066221714019775, 0.9097342491149902, 0.9117311835289001, 0.9172227382659912, 0.9188991785049438, 0.9202398061752319, 0.9223057627677917, 0.9261207580566406],
[0.9727393984794617, 0.9361352920532227, 0.9085666537284851, 0.8859085440635681, 0.8672027587890625, 0.8535550236701965, 0.8440457582473755, 0.8386754989624023, 0.8331448435783386, 0.8296475410461426, 0.8320701718330383, 0.8320614099502563, 0.8323298096656799, 0.8349127769470215, 0.838715672492981, 0.8465678691864014, 0.8484311103820801, 0.8528343439102173, 0.8562976717948914, 0.8612843155860901, 0.8653582334518433, 0.8667944669723511, 0.8734550476074219, 0.8771005272865295, 0.8789620995521545, 0.884890615940094, 0.8878726363182068, 0.8908778429031372, 0.8952533602714539, 0.8985325694084167, 0.9012224674224854, 0.9012179374694824],
[0.971888542175293, 0.9342792630195618, 0.9053354263305664, 0.8812361359596252, 0.8638301491737366, 0.8498647809028625, 0.838006317615509, 0.8286341428756714, 0.8225927352905273, 0.81831294298172, 0.8161141872406006, 0.8173704743385315, 0.8161450028419495, 0.8175442814826965, 0.8166856169700623, 0.8204942345619202, 0.8225816488265991, 0.8278079628944397, 0.831208348274231, 0.8327621817588806, 0.8355974555015564, 0.844249427318573, 0.8467186689376831, 0.8493362665176392, 0.8558359742164612, 0.857487678527832, 0.8598876595497131, 0.8659135699272156, 0.8665709495544434, 0.8707684278488159, 0.8741219639778137, 0.8765773773193359],
[0.9710095524787903, 0.9338454604148865, 0.9036157131195068, 0.877607524394989, 0.8578240871429443, 0.8432600498199463, 0.8305211663246155, 0.8208866119384766, 0.8131844401359558, 0.8055910468101501, 0.8015779852867126, 0.7981212735176086, 0.7982315421104431, 0.7956949472427368, 0.7954166531562805, 0.7972602248191833, 0.8004674911499023, 0.8004806637763977, 0.8046951293945312, 0.8071873784065247, 0.8093246817588806, 0.8131558299064636, 0.8173164129257202, 0.8185374140739441, 0.8223480582237244, 0.8259267210960388, 0.8300665020942688, 0.833354651927948, 0.8377440571784973, 0.8400111198425293, 0.8443475365638733, 0.8454246520996094],
[0.9692757725715637, 0.9289442300796509, 0.8985018134117126, 0.8732277154922485, 0.8531774282455444, 0.8375513553619385, 0.8204666972160339, 0.8106128573417664, 0.7999300956726074, 0.7946382761001587, 0.7874180674552917, 0.7818766236305237, 0.7762027382850647, 0.778640866279602, 0.7773511409759521, 0.7748728394508362, 0.7739964723587036, 0.7777711749076843, 0.7774655818939209, 0.7789250612258911, 0.7829545140266418, 0.7826940417289734, 0.7831856608390808, 0.7891747355461121, 0.7912577390670776, 0.7930949330329895, 0.7984800338745117, 0.7998455762863159, 0.8031460642814636, 0.8041367530822754, 0.8093941807746887, 0.8118780255317688],
[0.9678109884262085, 0.9257891178131104, 0.8953890800476074, 0.8692840933799744, 0.8453633189201355, 0.8281145691871643, 0.8132898211479187, 0.7980917096138, 0.7865176796913147, 0.778489351272583, 0.7721652388572693, 0.7661490440368652, 0.761102557182312, 0.757210373878479, 0.7516317963600159, 0.7535516619682312, 0.7507131695747375, 0.7495840787887573, 0.7510761022567749, 0.7481979727745056, 0.7509517073631287, 0.753508985042572, 0.7549266815185547, 0.7539642453193665, 0.7587844729423523, 0.759218692779541, 0.7613121271133423, 0.763555109500885, 0.7690894603729248, 0.7680454850196838, 0.7723889946937561, 0.777347207069397],
[0.9660150408744812, 0.9225035905838013, 0.8882213234901428, 0.8598896265029907, 0.8357637524604797, 0.8175596594810486, 0.8007370829582214, 0.7871596217155457, 0.7766233086585999, 0.7633563876152039, 0.755810022354126, 0.7483093738555908, 0.7413790822029114, 0.7362120151519775, 0.7327252626419067, 0.7272384166717529, 0.7241917848587036, 0.7221750020980835, 0.7233375310897827, 0.720094621181488, 0.7215690016746521, 0.7186169028282166, 0.7187048196792603, 0.7217579483985901, 0.7245560884475708, 0.7235075235366821, 0.7248634696006775, 0.7254680395126343, 0.728445827960968, 0.7316557765007019, 0.7313493490219116, 0.7326483726501465],
[0.9635928273200989, 0.9175184369087219, 0.8811678886413574, 0.8519929647445679, 0.8290166258811951, 0.8079210519790649, 0.7884736061096191, 0.7743305563926697, 0.7603301405906677, 0.7466346621513367, 0.7341760993003845, 0.7301218509674072, 0.7192374467849731, 0.7129997611045837, 0.7071272730827332, 0.703703761100769, 0.6980226039886475, 0.6942259073257446, 0.6924406290054321, 0.6905739903450012, 0.6901945471763611, 0.6889991760253906, 0.6875786781311035, 0.688380777835846, 0.6873308420181274, 0.6864210963249207, 0.6877439618110657, 0.6873460412025452, 0.6892338395118713, 0.6908681392669678, 0.6908101439476013, 0.6928497552871704],
[0.9606138467788696, 0.9123191833496094, 0.8734177947044373, 0.8437621593475342, 0.8188437223434448, 0.7935510277748108, 0.776088297367096, 0.763528048992157, 0.7447196245193481, 0.7319169640541077, 0.7186697125434875, 0.7098387479782104, 0.7018877267837524, 0.6930599808692932, 0.6833780407905579, 0.6803670525550842, 0.6719420552253723, 0.6678754687309265, 0.6664694547653198, 0.6577346324920654, 0.6592447757720947, 0.6535136103630066, 0.6533161997795105, 0.65375155210495, 0.6503185033798218, 0.649732232093811, 0.6496500372886658, 0.6476905941963196, 0.6492652893066406, 0.6487405896186829, 0.6486935019493103, 0.6494285464286804],
[0.9589792490005493, 0.907049298286438, 0.8663603067398071, 0.8338260054588318, 0.8069382905960083, 0.7830407619476318, 0.7615501880645752, 0.7456327676773071, 0.7279130816459656, 0.7121050357818604, 0.7002737522125244, 0.6900581121444702, 0.677975058555603, 0.6671620011329651, 0.6626728177070618, 0.6520846486091614, 0.6455555558204651, 0.6443655490875244, 0.6352166533470154, 0.6321080923080444, 0.6260237097740173, 0.6220016479492188, 0.619264543056488, 0.6140581965446472, 0.6142064332962036, 0.613476574420929, 0.607298731803894, 0.6056899428367615, 0.6075679659843445, 0.6077565550804138, 0.6065330505371094, 0.6052879095077515],
[0.9557879567146301, 0.9005533456802368, 0.8588030338287354, 0.825423002243042, 0.7951205372810364, 0.770338237285614, 0.7503594756126404, 0.7273393273353577, 0.7100672125816345, 0.6953598856925964, 0.6791097521781921, 0.6675797700881958, 0.6593767404556274, 0.6467294096946716, 0.6401093602180481, 0.6280235648155212, 0.6182970404624939, 0.6143262982368469, 0.6079819798469543, 0.6016060709953308, 0.5938466787338257, 0.5901145339012146, 0.5842138528823853, 0.579093337059021, 0.5782942175865173, 0.5723434090614319, 0.5709050297737122, 0.5662955641746521, 0.5656022429466248, 0.5652378797531128, 0.5615172386169434, 0.5623427033424377],
[0.952154815196991, 0.8950967192649841, 0.8491784930229187, 0.8132340908050537, 0.7853431701660156, 0.7554711103439331, 0.7335531115531921, 0.7133386135101318, 0.6914552450180054, 0.6771699786186218, 0.6601822376251221, 0.648333728313446, 0.6317825317382812, 0.623458743095398, 0.6104113459587097, 0.6014859080314636, 0.5958805084228516, 0.587882399559021, 0.5781434774398804, 0.5675230622291565, 0.562690258026123, 0.5575666427612305, 0.5529671311378479, 0.5477975010871887, 0.5410810708999634, 0.5358807444572449, 0.5298721790313721, 0.5271962881088257, 0.5252378582954407, 0.523171603679657, 0.5204212665557861, 0.5160762071609497],
[0.9495982527732849, 0.8873708248138428, 0.8410618305206299, 0.8019973635673523, 0.7691025733947754, 0.7420552372932434, 0.716372013092041, 0.6941580772399902, 0.6743897795677185, 0.6584060788154602, 0.6379660367965698, 0.6232298612594604, 0.6088681817054749, 0.5971347689628601, 0.5859493017196655, 0.5768652558326721, 0.5613412857055664, 0.5551052689552307, 0.5488882064819336, 0.5394439697265625, 0.5308660268783569, 0.5253705382347107, 0.5201205015182495, 0.511916995048523, 0.5061615109443665, 0.5004174113273621, 0.4944411516189575, 0.49030831456184387, 0.48184946179389954, 0.4848729968070984, 0.4802219569683075, 0.4770890772342682],
[0.9472714066505432, 0.8809747695922852, 0.8306245803833008, 0.7899670004844666, 0.7571653723716736, 0.7262875437736511, 0.700050413608551, 0.6779297590255737, 0.654941201210022, 0.6340962648391724, 0.6164668202400208, 0.6038222312927246, 0.5884117484092712, 0.5741749405860901, 0.5597718954086304, 0.5484079718589783, 0.5381782650947571, 0.5275606513023376, 0.5174355506896973, 0.5067463517189026, 0.49964338541030884, 0.4894179701805115, 0.485622376203537, 0.4781540632247925, 0.47223958373069763, 0.463691383600235, 0.45937180519104004, 0.45384371280670166, 0.4475385546684265, 0.44385814666748047, 0.4391520023345947, 0.43212005496025085],
[0.9439537525177002, 0.8743938207626343, 0.8199770450592041, 0.7754250168800354, 0.7422483563423157, 0.7083220481872559, 0.6840007901191711, 0.6559059619903564, 0.6352874636650085, 0.6168107390403748, 0.5955669283866882, 0.5801939368247986, 0.5613912343978882, 0.5469002723693848, 0.5342342853546143, 0.5242854356765747, 0.506807804107666, 0.4992485046386719, 0.4875054955482483, 0.4779147207736969, 0.4678249955177307, 0.4620799422264099, 0.4548194706439972, 0.44655734300613403, 0.4404577314853668, 0.4287540316581726, 0.4257289171218872, 0.4141024947166443, 0.4096221327781677, 0.404634565114975, 0.40095895528793335, 0.39724573493003845],
[0.9396477341651917, 0.865368664264679, 0.810107409954071, 0.7658436894416809, 0.7266921997070312, 0.6943004131317139, 0.6668904423713684, 0.6397178173065186, 0.6153740286827087, 0.5925664901733398, 0.5777354836463928, 0.5549141764640808, 0.540705144405365, 0.5247938632965088, 0.5114121437072754, 0.4967556595802307, 0.48490816354751587, 0.4715813398361206, 0.4616187512874603, 0.4509361982345581, 0.43918880820274353, 0.432326078414917, 0.42018333077430725, 0.4142012596130371, 0.40603402256965637, 0.39709874987602234, 0.3892274498939514, 0.382876455783844, 0.3741002082824707, 0.37226662039756775, 0.36697328090667725, 0.36021992564201355],
[0.9371616840362549, 0.8578751087188721, 0.7993580102920532, 0.7542229294776917, 0.7148508429527283, 0.6786023378372192, 0.6488820910453796, 0.6179985404014587, 0.5960205793380737, 0.572606086730957, 0.5521941781044006, 0.5315218567848206, 0.5164572596549988, 0.4980998933315277, 0.4836742877960205, 0.46899306774139404, 0.45790210366249084, 0.4433338940143585, 0.43130964040756226, 0.42270514369010925, 0.41120871901512146, 0.39908701181411743, 0.3913979232311249, 0.38395124673843384, 0.3760665953159332, 0.36838075518608093, 0.3593154847621918, 0.35242190957069397, 0.344034880399704, 0.3394070565700531, 0.33127161860466003, 0.3257504403591156],
], dtype=np.float32)
# print("GGX_E", GGX_E.shape)

# [1, 32]
# GGX_E_avg[32-roughness]
GGX_E_avg = np.array([[0.9998808541567996, 0.9998751356033608, 0.999749131326098, 0.9992710567894392, 0.9982443900662474, 0.996493035228923, 0.9937197098624893, 0.9898084800806828, 0.9844009779044427, 0.9773833737708628, 0.9684953742544167, 0.9576433806214482, 0.9448006303282455, 0.9298767051077448, 0.9122511356836185, 0.8930473587242886, 0.8712663453188725, 0.8477540977182798, 0.8217689249431714, 0.794493677385617, 0.7658798263873905, 0.7352253056596965, 0.7041580225923099, 0.6725652447785251, 0.6399820749647915, 0.6076094987802207, 0.5751849029911682, 0.5431709525873885, 0.5113315780181438, 0.480556503898697, 0.45143645713687874, 0.42275982978753746]], dtype=np.float32)
# GGX_E_avg = np.array([[0., 0.5, 1.],[0., 0.5, 1.]], dtype=np.float32)
# GGX_E_avg = np.array([[0., 0.5, 1.],[0., 0.5, 1.]], dtype=np.float32)

# [ 16, 16, 16 ]
# Base_E[16-f0][16-roughness][16-cos_theta] = 
Base_E = np.array([
[
[0.8421937227249146, 0.6212553381919861, 0.44462865591049194, 0.312858521938324, 0.2171303629875183, 0.14923842251300812, 0.10282757133245468, 0.07229289412498474, 0.053220611065626144, 0.04200417920947075, 0.0359174907207489, 0.032964158803224564, 0.03173751011490822, 0.0313417948782444, 0.031257178634405136, 0.031249679625034332],
[0.793359637260437, 0.6129189133644104, 0.44188055396080017, 0.3117724657058716, 0.21654336154460907, 0.14908695220947266, 0.10279705375432968, 0.07236727327108383, 0.05334487184882164, 0.04207776486873627, 0.03595847636461258, 0.03298415616154671, 0.031748540699481964, 0.031342651695013046, 0.03125610575079918, 0.03124796785414219],
[0.6449769139289856, 0.5590384006500244, 0.42157450318336487, 0.3043023645877838, 0.21321971714496613, 0.14791950583457947, 0.10265253484249115, 0.07276185601949692, 0.05368881672620773, 0.042353641241788864, 0.03618064522743225, 0.03308890759944916, 0.031801994889974594, 0.031351931393146515, 0.031246917322278023, 0.031239653006196022],
[0.5336897373199463, 0.4647226333618164, 0.3737685978412628, 0.28111812472343445, 0.20329920947551727, 0.14433704316616058, 0.10186189413070679, 0.07281597703695297, 0.054305873811244965, 0.04291112348437309, 0.0365799218416214, 0.033355552703142166, 0.03189091756939888, 0.03135669231414795, 0.031221548095345497, 0.031184658408164978],
[0.4312838912010193, 0.3700290024280548, 0.30872467160224915, 0.24383409321308136, 0.18347395956516266, 0.13505049049854279, 0.09840506315231323, 0.07221014052629471, 0.05443095415830612, 0.04336255416274071, 0.03703949972987175, 0.03361274674534798, 0.03200630471110344, 0.03131799027323723, 0.03111935593187809, 0.03108946979045868],
[0.34661322832107544, 0.2940141260623932, 0.24542342126369476, 0.19976769387722015, 0.15699909627437592, 0.12020549923181534, 0.09080448001623154, 0.06911411881446838, 0.05366712808609009, 0.043631862848997116, 0.03720821440219879, 0.03375135362148285, 0.031957853585481644, 0.03118312545120716, 0.03088085725903511, 0.03083467110991478],
[0.27619850635528564, 0.23240439593791962, 0.1956561803817749, 0.16051585972309113, 0.13002848625183105, 0.10284608602523804, 0.08076723664999008, 0.06383407115936279, 0.05113038420677185, 0.042559076100587845, 0.03694886341691017, 0.03348968178033829, 0.03165213763713837, 0.030790602788329124, 0.03045612946152687, 0.030394675210118294],
[0.22130973637104034, 0.18689176440238953, 0.15512192249298096, 0.12895707786083221, 0.10627337545156479, 0.08596943318843842, 0.07019619643688202, 0.057025108486413956, 0.04751306772232056, 0.04048885405063629, 0.0356159433722496, 0.0326162613928318, 0.030886242166161537, 0.030016055330634117, 0.029735824093222618, 0.029603198170661926],
[0.17853382229804993, 0.14975102245807648, 0.12503322958946228, 0.10428202897310257, 0.08671637624502182, 0.07212989032268524, 0.05996997654438019, 0.050443004816770554, 0.04302484542131424, 0.03763715550303459, 0.03374592587351799, 0.03125600889325142, 0.02971324883401394, 0.028915440663695335, 0.02851981855928898, 0.02848171442747116],
[0.14850729703903198, 0.1215180903673172, 0.10236962884664536, 0.08548573404550552, 0.07187233120203018, 0.06027305871248245, 0.051521290093660355, 0.044198546558618546, 0.03869401663541794, 0.03439762443304062, 0.03128400444984436, 0.02929198183119297, 0.028035417199134827, 0.027255723252892494, 0.026889987289905548, 0.02680002711713314],
[0.12256166338920593, 0.10258181393146515, 0.08453494310379028, 0.07112066447734833, 0.060465533286333084, 0.05152657628059387, 0.04422221705317497, 0.03875558078289032, 0.03450155630707741, 0.031050294637680054, 0.028686411678791046, 0.027071360498666763, 0.02595505677163601, 0.02532133460044861, 0.024938782677054405, 0.02480435185134411],
[0.1037021055817604, 0.08520776778459549, 0.07038716226816177, 0.05949549376964569, 0.05088257044553757, 0.0448182038962841, 0.03923493251204491, 0.03419758379459381, 0.030789418146014214, 0.027742430567741394, 0.025977304205298424, 0.024645723402500153, 0.023682106286287308, 0.022991662845015526, 0.02265523001551628, 0.022449353709816933],
[0.09135788679122925, 0.07518035918474197, 0.0611053928732872, 0.05263172462582588, 0.044067900627851486, 0.038070499897003174, 0.0336780846118927, 0.029648277908563614, 0.0271754153072834, 0.02492981031537056, 0.02332671731710434, 0.022048188373446465, 0.021226543933153152, 0.02062056213617325, 0.02020273730158806, 0.019915413111448288],
[0.08112220466136932, 0.06460349261760712, 0.05320892855525017, 0.04506880044937134, 0.03805055841803551, 0.03353291004896164, 0.029465455561876297, 0.026374880224466324, 0.024150099605321884, 0.022269297391176224, 0.020776594057679176, 0.01965133100748062, 0.01886509172618389, 0.018175380304455757, 0.017719151452183723, 0.017368601635098457],
[0.07282509654760361, 0.0564996711909771, 0.04698844254016876, 0.03982824087142944, 0.03381529450416565, 0.02940106764435768, 0.0260758176445961, 0.023232651874423027, 0.021294506266713142, 0.01957853138446808, 0.018368467688560486, 0.017276225611567497, 0.01653001457452774, 0.01584213227033615, 0.015326153486967087, 0.014898356981575489],
[0.06656854599714279, 0.05143279954791069, 0.04190923646092415, 0.03462069854140282, 0.029766051098704338, 0.025854574516415596, 0.022802313789725304, 0.02058759517967701, 0.018798431381583214, 0.017273176461458206, 0.016039639711380005, 0.015089662745594978, 0.014320971444249153, 0.013662794604897499, 0.013108750805258751, 0.012649758718907833],
],
[
[0.8520684242248535, 0.6456496119499207, 0.48045414686203003, 0.3571869730949402, 0.2676254212856293, 0.20411793887615204, 0.16070353984832764, 0.13213993608951569, 0.1142958551645279, 0.10381060838699341, 0.09811528027057648, 0.09535325318574905, 0.09420306980609894, 0.09383498132228851, 0.09375673532485962, 0.09374880790710449],
[0.8046021461486816, 0.6376386284828186, 0.4778207540512085, 0.35612136125564575, 0.2670665979385376, 0.20396412909030914, 0.16067014634609222, 0.1322079300880432, 0.11440404504537582, 0.10386849194765091, 0.09814110398292542, 0.09536106884479523, 0.09420647472143173, 0.0938291922211647, 0.09375060349702835, 0.0937434732913971],
[0.6620649695396423, 0.585474967956543, 0.4581124484539032, 0.348814994096756, 0.26373541355133057, 0.20275038480758667, 0.1604156643152237, 0.13249024748802185, 0.1146683543920517, 0.10406281799077988, 0.09830605983734131, 0.09541929513216019, 0.0942305326461792, 0.09380975365638733, 0.0937059074640274, 0.09371640533208847],
[0.5587419867515564, 0.4946118891239166, 0.4115193784236908, 0.3260189890861511, 0.2537211775779724, 0.19889481365680695, 0.15933191776275635, 0.13221363723278046, 0.11502466350793839, 0.1043887585401535, 0.09852166473865509, 0.09553584456443787, 0.09417800605297089, 0.0936865285038948, 0.09359242767095566, 0.09354353696107864],
[0.4641639292240143, 0.404712438583374, 0.3484703004360199, 0.2892877459526062, 0.23370835185050964, 0.18904076516628265, 0.15519116818904877, 0.13103336095809937, 0.11454643309116364, 0.10429056733846664, 0.09851828962564468, 0.0954120010137558, 0.09396839141845703, 0.09333620965480804, 0.09321488440036774, 0.09324372559785843],
[0.38571128249168396, 0.3336699306964874, 0.2879128158092499, 0.24591916799545288, 0.20704030990600586, 0.1733238846063614, 0.1465253233909607, 0.12671968340873718, 0.11265116930007935, 0.10368633270263672, 0.09778100252151489, 0.09478731453418732, 0.09323973208665848, 0.09260652214288712, 0.0923818051815033, 0.09246222674846649],
[0.32031333446502686, 0.27632665634155273, 0.24067750573158264, 0.20789818465709686, 0.1798798143863678, 0.15511122345924377, 0.1350426822900772, 0.1199159175157547, 0.10856310278177261, 0.10108650475740433, 0.09612207114696503, 0.093231700360775, 0.09167318791151047, 0.09111509472131729, 0.0909874364733696, 0.09111778438091278],
[0.26906535029411316, 0.2338080257177353, 0.20260173082351685, 0.17740193009376526, 0.15613995492458344, 0.13735967874526978, 0.12310852855443954, 0.11124011874198914, 0.10291033983230591, 0.09683457762002945, 0.09270873665809631, 0.09022921323776245, 0.08906298875808716, 0.08853461593389511, 0.08871042728424072, 0.08872738480567932],
[0.22902163863182068, 0.19911786913871765, 0.17407740652561188, 0.15342803299427032, 0.13623389601707458, 0.12274996936321259, 0.11132576316595078, 0.102773018181324, 0.0960690975189209, 0.09160487353801727, 0.08828826248645782, 0.08653290569782257, 0.08544078469276428, 0.08507982641458511, 0.08498383313417435, 0.08535799384117126],
[0.2006669044494629, 0.1721811443567276, 0.15213079750537872, 0.13481935858726501, 0.12125997245311737, 0.10993117839097977, 0.10140432417392731, 0.09453017264604568, 0.08948193490505219, 0.0856301337480545, 0.08294276893138885, 0.08135621249675751, 0.08066961914300919, 0.08013021945953369, 0.08009235560894012, 0.08033013343811035],
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[0.8402775526046753, 0.8311749696731567, 0.8168171048164368, 0.8108091354370117, 0.8059143424034119, 0.8044090867042542, 0.8016589283943176, 0.797970712184906, 0.7954890727996826, 0.7883919477462769, 0.7900556325912476, 0.7897970676422119, 0.7906918525695801, 0.7891635894775391, 0.7895987033843994, 0.7893071174621582],
[0.8404834866523743, 0.825545072555542, 0.8100142478942871, 0.8044083714485168, 0.7979962825775146, 0.7903255224227905, 0.7861966490745544, 0.7784280776977539, 0.7778433561325073, 0.7748134732246399, 0.7729676365852356, 0.7721705436706543, 0.7709949612617493, 0.772462010383606, 0.7694695591926575, 0.7680424451828003],
[0.8322499990463257, 0.8151132464408875, 0.8013020753860474, 0.7917159199714661, 0.7816143035888672, 0.775998592376709, 0.7700164318084717, 0.7642545700073242, 0.7613789439201355, 0.7583811283111572, 0.7542951107025146, 0.7509276866912842, 0.7508945465087891, 0.7491291761398315, 0.7472679615020752, 0.7443957924842834],
[0.8262794613838196, 0.8069819211959839, 0.7908615469932556, 0.7782831192016602, 0.7674234509468079, 0.7596306204795837, 0.7527555227279663, 0.7454455494880676, 0.7418495416641235, 0.7370808720588684, 0.7336384654045105, 0.728544294834137, 0.7265560626983643, 0.724111795425415, 0.721450924873352, 0.7185142636299133],
[0.8256108164787292, 0.7951461672782898, 0.7777432799339294, 0.7612255215644836, 0.749982476234436, 0.7397047877311707, 0.7305406332015991, 0.7239423990249634, 0.7179387211799622, 0.7122533917427063, 0.7076981663703918, 0.7032841444015503, 0.6987308263778687, 0.6957769393920898, 0.6924270987510681, 0.6888837814331055],
],
[
[0.9951662421226501, 0.9636780619621277, 0.9468821883201599, 0.933956503868103, 0.9240744113922119, 0.9175776243209839, 0.9131010174751282, 0.9101908802986145, 0.9082866907119751, 0.9073296785354614, 0.9066987037658691, 0.9064562916755676, 0.9062619209289551, 0.906305193901062, 0.9062546491622925, 0.906242847442627],
[0.9858178496360779, 0.9631907343864441, 0.9470005631446838, 0.9331951141357422, 0.9244330525398254, 0.9175951480865479, 0.913141667842865, 0.9102410674095154, 0.9082683324813843, 0.9072014689445496, 0.9065595865249634, 0.9063003659248352, 0.9062004089355469, 0.9062035083770752, 0.9062334299087524, 0.9062276482582092],
[0.9451786875724792, 0.9535436630249023, 0.9438127279281616, 0.9322779178619385, 0.9233673810958862, 0.9176898002624512, 0.9125382900238037, 0.9101296663284302, 0.9085240364074707, 0.9074203372001648, 0.9067510962486267, 0.9063531160354614, 0.9063187837600708, 0.9064341187477112, 0.9061459898948669, 0.9063478112220764],
[0.9391327500343323, 0.9394899010658264, 0.9342883825302124, 0.9295914173126221, 0.920350968837738, 0.9173731803894043, 0.9126537442207336, 0.9093694686889648, 0.9086598753929138, 0.9068710803985596, 0.9068391919136047, 0.906575620174408, 0.9059982895851135, 0.9059260487556458, 0.9060167670249939, 0.9057098627090454],
[0.9359671473503113, 0.9274840354919434, 0.9227895140647888, 0.9245464205741882, 0.9173184037208557, 0.9147120714187622, 0.9104215502738953, 0.9097324013710022, 0.9074429273605347, 0.9054521918296814, 0.9058107733726501, 0.9059036374092102, 0.9058680534362793, 0.9050611853599548, 0.9055145978927612, 0.9065533876419067],
[0.9289685487747192, 0.9204607605934143, 0.9162500500679016, 0.9119691252708435, 0.9142403602600098, 0.9078423976898193, 0.9072846174240112, 0.9048901200294495, 0.9047819972038269, 0.9071463942527771, 0.9036819934844971, 0.9047943949699402, 0.9046448469161987, 0.9045669436454773, 0.9043905735015869, 0.9051101803779602],
[0.9246817827224731, 0.9168351292610168, 0.9084755182266235, 0.9084740281105042, 0.9067508578300476, 0.9048263430595398, 0.9022567272186279, 0.9028738141059875, 0.9020599722862244, 0.9036134481430054, 0.9023168087005615, 0.9035251140594482, 0.902187168598175, 0.9027212858200073, 0.9035050272941589, 0.904000461101532],
[0.9189903736114502, 0.9107345938682556, 0.9077585935592651, 0.9028509855270386, 0.90287846326828, 0.8996177911758423, 0.8986115455627441, 0.8967380523681641, 0.8978040218353271, 0.8969419002532959, 0.8983417749404907, 0.8976101279258728, 0.8985612392425537, 0.8987457752227783, 0.9016934633255005, 0.900661051273346],
[0.9156842231750488, 0.9098760485649109, 0.9042972326278687, 0.898676335811615, 0.8924862146377563, 0.8968113660812378, 0.892998456954956, 0.8926874399185181, 0.8916665315628052, 0.8950063586235046, 0.8936778903007507, 0.8957294821739197, 0.8950376510620117, 0.8970087170600891, 0.8960099220275879, 0.8978895545005798],
[0.9109605550765991, 0.9048160910606384, 0.899487316608429, 0.8947945237159729, 0.8931396007537842, 0.8935787081718445, 0.8903406858444214, 0.8908360004425049, 0.8901921510696411, 0.8877037167549133, 0.888519287109375, 0.8890424966812134, 0.891988217830658, 0.8882347941398621, 0.8893097043037415, 0.889213502407074],
[0.9076955914497375, 0.900671124458313, 0.8971759676933289, 0.8900815844535828, 0.8854500651359558, 0.8864372372627258, 0.8818429112434387, 0.8782835006713867, 0.8787533640861511, 0.8771634101867676, 0.8795799016952515, 0.882163941860199, 0.8816329836845398, 0.8843132853507996, 0.881987988948822, 0.8821660280227661],
[0.901028037071228, 0.8976945877075195, 0.8867121338844299, 0.8835362792015076, 0.8808894157409668, 0.8812474012374878, 0.8797779083251953, 0.8770796060562134, 0.8753851056098938, 0.8683993220329285, 0.8705817461013794, 0.8705494403839111, 0.8717458248138428, 0.8701736927032471, 0.8705672025680542, 0.8702065348625183],
[0.9030541181564331, 0.8942419290542603, 0.8826823830604553, 0.8803369402885437, 0.8765788674354553, 0.8707194328308105, 0.8681344985961914, 0.8612969517707825, 0.8619281649589539, 0.8596751689910889, 0.8585687279701233, 0.85846346616745, 0.8575811982154846, 0.8597542643547058, 0.8565943837165833, 0.8552359938621521],
[0.89609694480896, 0.8861877918243408, 0.8770402073860168, 0.8710745573043823, 0.8637493848800659, 0.8605403900146484, 0.8565383553504944, 0.8522178530693054, 0.8507354259490967, 0.8489119410514832, 0.8457344770431519, 0.8430001735687256, 0.843982994556427, 0.8429672718048096, 0.8415164351463318, 0.8387920260429382],
[0.8915641903877258, 0.8809455037117004, 0.8701712489128113, 0.8616387248039246, 0.8540829420089722, 0.848986804485321, 0.8444530367851257, 0.8389975428581238, 0.8372547626495361, 0.833958625793457, 0.8317915797233582, 0.8275384902954102, 0.8266427516937256, 0.8252255320549011, 0.8233092427253723, 0.820977509021759],
[0.8929219245910645, 0.8717999458312988, 0.8607881665229797, 0.8489599227905273, 0.8416170477867126, 0.83442622423172, 0.8278988599777222, 0.823615312576294, 0.8194736838340759, 0.8155434727668762, 0.8126267790794373, 0.8095886707305908, 0.8060542941093445, 0.8043830394744873, 0.8020358681678772, 0.7992810010910034],
],
[
[1.0, 0.9882112741470337, 0.9828148484230042, 0.9783618450164795, 0.9745715260505676, 0.9724611043930054, 0.9709784984588623, 0.970043957233429, 0.9693638682365417, 0.9691415429115295, 0.968898355960846, 0.9688522815704346, 0.9687284827232361, 0.9688073992729187, 0.968754768371582, 0.968742847442627],
[1.0, 0.9885560870170593, 0.9832419157028198, 0.9776268601417542, 0.9750431776046753, 0.9725073575973511, 0.9710333943367004, 0.9700978398323059, 0.9693421721458435, 0.9690004587173462, 0.9687489867210388, 0.9686833620071411, 0.9686646461486816, 0.9686976671218872, 0.9687362909317017, 0.9687296748161316],
[0.9716575741767883, 0.9837374091148376, 0.9819998741149902, 0.9775296449661255, 0.9743340611457825, 0.9728500247001648, 0.9704865217208862, 0.9700383543968201, 0.9696763157844543, 0.9693048596382141, 0.9690020084381104, 0.9687818884849548, 0.968826949596405, 0.9689955711364746, 0.9686778783798218, 0.9688913822174072],
[0.9726333618164062, 0.9780755639076233, 0.9769818782806396, 0.9775591492652893, 0.9724937677383423, 0.9733558297157288, 0.9710829854011536, 0.969537079334259, 0.9700412750244141, 0.9688541293144226, 0.9692557454109192, 0.9691722393035889, 0.9686077833175659, 0.9685572385787964, 0.9686351418495178, 0.9683005213737488],
[0.9757315516471863, 0.9733231067657471, 0.9714778065681458, 0.9768842458724976, 0.9722957015037537, 0.9723953604698181, 0.9698475003242493, 0.970727801322937, 0.9693267345428467, 0.9677919745445251, 0.9685416221618652, 0.9688048958778381, 0.968822181224823, 0.9679310917854309, 0.9683950543403625, 0.9695308208465576],
[0.9735405445098877, 0.9712679982185364, 0.9706277847290039, 0.968460738658905, 0.9731482267379761, 0.9678425788879395, 0.9686993956565857, 0.9670801162719727, 0.9677308797836304, 0.9707610011100769, 0.9671425223350525, 0.9684183597564697, 0.9682333469390869, 0.9680958986282349, 0.9678469300270081, 0.9685356020927429],
[0.9736881852149963, 0.9717711806297302, 0.9665704965591431, 0.9692603349685669, 0.9690868854522705, 0.9682239294052124, 0.9662966132164001, 0.967494010925293, 0.9669185280799866, 0.9687426090240479, 0.9673427939414978, 0.9685977697372437, 0.9669991135597229, 0.9673847556114197, 0.9680938124656677, 0.9684438109397888],
[0.9714381098747253, 0.9684557318687439, 0.9694135785102844, 0.9667200446128845, 0.9686217904090881, 0.9661934971809387, 0.9656544923782349, 0.9639647603034973, 0.9652498960494995, 0.964188814163208, 0.9656608700752258, 0.9646409749984741, 0.9653155207633972, 0.9652402997016907, 0.9681351184844971, 0.9667695760726929],
[0.9711755514144897, 0.9706273674964905, 0.9686295986175537, 0.9653720855712891, 0.9605723023414612, 0.9665735363960266, 0.9631741642951965, 0.9631074666976929, 0.9622063040733337, 0.9657763838768005, 0.9641179442405701, 0.9659565091133118, 0.9648146033287048, 0.9666702747344971, 0.9651792645454407, 0.9668352603912354],
[0.9685986042022705, 0.9680646061897278, 0.9663307666778564, 0.9643011689186096, 0.9646050930023193, 0.9667177200317383, 0.9641067385673523, 0.9653121829032898, 0.9648648500442505, 0.962070107460022, 0.9629653096199036, 0.9633564352989197, 0.9662298560142517, 0.9616390466690063, 0.9625062942504883, 0.9619565606117249],
[0.967568576335907, 0.9661186933517456, 0.9669537544250488, 0.9624844193458557, 0.9598240852355957, 0.9628141522407532, 0.9590999484062195, 0.9560701847076416, 0.9571890830993652, 0.9558404088020325, 0.9586358666419983, 0.9615285992622375, 0.9607477784156799, 0.9635546207427979, 0.960628092288971, 0.9605359435081482],
[0.96259605884552, 0.9660401940345764, 0.959100604057312, 0.9592476487159729, 0.9592408537864685, 0.9617643356323242, 0.9617878794670105, 0.9602565765380859, 0.9594922661781311, 0.9527023434638977, 0.9554544687271118, 0.9556770920753479, 0.9572068452835083, 0.9555948376655579, 0.9559266567230225, 0.9554844498634338],
[0.9667049646377563, 0.9653363227844238, 0.9586399793624878, 0.9602189064025879, 0.9596584439277649, 0.9560340642929077, 0.9553259015083313, 0.9496855139732361, 0.9517666101455688, 0.9504733085632324, 0.9502718448638916, 0.9510014653205872, 0.9504825472831726, 0.9534809589385986, 0.9501603245735168, 0.948904812335968],
[0.961406946182251, 0.9604794383049011, 0.9571645855903625, 0.9557191729545593, 0.9518972039222717, 0.951695442199707, 0.950186550617218, 0.9477043747901917, 0.9479632377624512, 0.9476178288459778, 0.9456160664558411, 0.9437092542648315, 0.9459390044212341, 0.9458735585212708, 0.9449581503868103, 0.9424638152122498],
[0.9588176012039185, 0.9592710137367249, 0.9554159641265869, 0.9521284103393555, 0.9488643407821655, 0.9472593069076538, 0.9457693696022034, 0.9427589178085327, 0.943401575088501, 0.9420366287231445, 0.9415338635444641, 0.9384305477142334, 0.938946545124054, 0.938868522644043, 0.937941312789917, 0.9364288449287415],
[0.9629194736480713, 0.9543077349662781, 0.9517936706542969, 0.9462804794311523, 0.9441599249839783, 0.9411327242851257, 0.9381774067878723, 0.937006950378418, 0.935385525226593, 0.9338352084159851, 0.933127224445343, 0.9319595098495483, 0.9298385381698608, 0.9298891425132751, 0.9289112687110901, 0.9272536039352417],
],
], dtype=np.float32)
# print("Base_E", Base_E.shape)

# [ 16, 16 ]
# Base_E_avg[16-f0][16-roughness]
Base_E_avg = np.array([
[0.07760233452427201, 0.077225886976521, 0.07533786466228776, 0.07182926698442316, 0.0668093262866023, 0.06092921699018916, 0.05490817294048611, 0.049094110559963156, 0.043752715493610594, 0.038888096481969114, 0.034547973416920286, 0.03058731030614581, 0.027000264417438302, 0.023761922369885724, 0.02084247647508164, 0.018207700002676575],
[0.1371075171919074, 0.13673636756720953, 0.1348606270912569, 0.13129399239551276, 0.12604187885881402, 0.11960413894848898, 0.11262397153768688, 0.10532105117454194, 0.09803798800567165, 0.09067467451677658, 0.08333751463214867, 0.07603728017420508, 0.0687758353742538, 0.06178059994999785, 0.05509666028956417, 0.04880636105372105],
[0.19661397632444277, 0.196250349865295, 0.19440202822443098, 0.19081589247798547, 0.18540758633753285, 0.1785330708953552, 0.17076762730721384, 0.16219384205760434, 0.15322951413691044, 0.14365312096197158, 0.1335986569756642, 0.12321964689181186, 0.11250047673820518, 0.10190498764859512, 0.09154808637686074, 0.08162344165612012],
[0.2561217119800858, 0.2557678389712237, 0.2539620832540095, 0.2503950363607146, 0.24490690638776869, 0.23771769844461232, 0.22934400965459645, 0.2197240015375428, 0.20935087837278843, 0.19786638056393713, 0.18540141178527847, 0.1722391710500233, 0.15831907780375332, 0.14432192302774638, 0.13042382322601043, 0.11691946972860023],
[0.3156307217432186, 0.3152888334589079, 0.31354078731965274, 0.31003152241464704, 0.3045402974821627, 0.2971597326686606, 0.2883580500492826, 0.2779233150649816, 0.26642649224959314, 0.2533594790729694, 0.2388203211594373, 0.22320924588711932, 0.20639125112211332, 0.18924102664459497, 0.171983344189357, 0.15499743237160146],
[0.3751410163240507, 0.3748133262852207, 0.37313816614914685, 0.36972542910370976, 0.36430821660906076, 0.3568608971545473, 0.3478147638961673, 0.3368038614280522, 0.32448161707725376, 0.31017968466039747, 0.29393480508588254, 0.27625277114566416, 0.25689325970597565, 0.2368982675834559, 0.2165245162905194, 0.19621178007218987],
[0.4346525790169835, 0.4343413262395188, 0.43275422882288694, 0.42947684589307755, 0.42421113164164126, 0.4168229216011241, 0.40771925274748355, 0.39637799782212824, 0.3835424371063709, 0.3683765768073499, 0.3508295699721202, 0.33150320895947516, 0.3100202330388129, 0.28756025386974216, 0.2643909926409833, 0.2409798577427864],
[0.4941654179710895, 0.49387283984106034, 0.4923889630008489, 0.48928585182875395, 0.48424950684420764, 0.47704756318125874, 0.4680766850942746, 0.45665839686989784, 0.44363604788668454, 0.42800228216219693, 0.40959506027866155, 0.38910573080647737, 0.36598877352662385, 0.34152938157785684, 0.31598133547231555, 0.28979649546090513],
[0.5536795402877033, 0.5534078478813171, 0.5520423983689398, 0.5491525367833674, 0.5444238013587892, 0.5375365945510566, 0.5288922928739339, 0.5176580399274826, 0.5047905774554238, 0.4891115720383823, 0.4703279653331265, 0.4492185132112354, 0.4250399873126298, 0.39915000612381846, 0.37176045041996986, 0.3432528495322913],
[0.6131949371192604, 0.6129463652614504, 0.611714533995837, 0.6090769760776311, 0.6047344957478344, 0.5982917861547321, 0.5901714283972979, 0.5793901989236474, 0.5670350939035416, 0.5517620448954403, 0.5331317405216396, 0.5120142509695143, 0.48744305316358805, 0.46081602363847196, 0.43227399210445583, 0.4020610743900761],
[0.6727116163820028, 0.6724883953575045, 0.671405375469476, 0.6690592719241977, 0.6651820687111467, 0.6593149409163743, 0.6519195102155209, 0.6418685452081263, 0.6303998499643058, 0.6160143443848938, 0.5981172269675881, 0.5776818364392966, 0.5534994280897081, 0.5269801001995802, 0.4981667072279379, 0.4670869179535657],
[0.7322295531630516, 0.732033922104165, 0.7311149439774454, 0.729099499527365, 0.7257669582031667, 0.720607883296907, 0.7141420196276158, 0.7051070036832243, 0.6949161535594612, 0.6819323084782809, 0.6654033227823675, 0.6464283384848386, 0.6235478259623051, 0.5981650485191494, 0.5702059550676495, 0.5393935048487037],
[0.791748789139092, 0.791582964360714, 0.7908432537224144, 0.7891977296676487, 0.7864896776154637, 0.782172451261431, 0.7768445557449013, 0.7691199264954776, 0.760616495506838, 0.7495832294225693, 0.7351177234668285, 0.7184812058694661, 0.6979701996315271, 0.6749779898673296, 0.649312362074852, 0.6203009814489633],
[0.8512692812364548, 0.8511355102527887, 0.8505902830511332, 0.8493540917988867, 0.8473506830632687, 0.8440104795154184, 0.8400327831041068, 0.8339219673071057, 0.8275346315931529, 0.8190380702726543, 0.8073977567255497, 0.7940908831078559, 0.7771987917367369, 0.7581279939040542, 0.7366000472102314, 0.7114691569004208],
[0.9107910678721964, 0.9106915674638003, 0.9103560629300773, 0.9095686404034495, 0.9083504662849009, 0.9061238502617925, 0.9037124796304852, 0.8995281695388258, 0.8957055921200663, 0.8903717293869704, 0.882391300285235, 0.8735337264370173, 0.8617247452493757, 0.8484485007356852, 0.8334303291048855, 0.8150143353268504],
[0.9703141208738089, 0.9702511334326118, 0.9701406031381339, 0.9698414613958448, 0.9694895278662443, 0.9685144207905978, 0.9678894716780633, 0.9659540066495538, 0.9651657626964152, 0.9636633051559329, 0.960257813334465, 0.9571155172307044, 0.9521085240412503, 0.9469258114695549, 0.9414842531550676, 0.9336777592543513],
], dtype=np.float32)
# print("Base_E_avg", Base_E_avg.shape)

# [ 16, 16 ]
# Sheen_E[16-alpha][16-cos_theta]
Sheen_E = np.array([
[0.6127333045005798, 0.36205002665519714, 0.2254251092672348, 0.1443474292755127, 0.09062162786722183, 0.05381035432219505, 0.03168118745088577, 0.01876574009656906, 0.009852374903857708, 0.005163963884115219, 0.0024197606835514307, 0.0010819404851645231, 0.00043056474532932043, 0.00012632596190087497, 2.6183362933807075e-05, 2.393934209976578e-06],
[0.7363263964653015, 0.5273519158363342, 0.3989941477775574, 0.3010554909706116, 0.23174616694450378, 0.1767258197069168, 0.13566163182258606, 0.10031110048294067, 0.07451994717121124, 0.0546228289604187, 0.03813162446022034, 0.026747722178697586, 0.017195245251059532, 0.010546267963945866, 0.005597887095063925, 0.002269081538543105],
[0.7725144028663635, 0.5870190858840942, 0.4632125198841095, 0.376593679189682, 0.3078637719154358, 0.2509633004665375, 0.20521008968353271, 0.16350790858268738, 0.13076643645763397, 0.10498521476984024, 0.08085092902183533, 0.062417171895504, 0.045740291476249695, 0.03244922310113907, 0.021475816145539284, 0.012272297404706478],
[0.7979311943054199, 0.6227427124977112, 0.5103753805160522, 0.4263576865196228, 0.3554655909538269, 0.2997346818447113, 0.2508918344974518, 0.20834703743457794, 0.17557695508003235, 0.14403130114078522, 0.11843548715114594, 0.09435398876667023, 0.07434457540512085, 0.05655037984251976, 0.0414116233587265, 0.02793339639902115],
[0.8144521117210388, 0.64854496717453, 0.5376975536346436, 0.45629361271858215, 0.3891298770904541, 0.33425381779670715, 0.28499847650527954, 0.24093127250671387, 0.2066112756729126, 0.17415018379688263, 0.14728084206581116, 0.12228307873010635, 0.09946046024560928, 0.08017965406179428, 0.061737824231386185, 0.045148544013500214],
[0.8207204937934875, 0.6656689047813416, 0.557377278804779, 0.47782382369041443, 0.41390472650527954, 0.356874018907547, 0.3095383644104004, 0.26553380489349365, 0.23023122549057007, 0.19771765172481537, 0.16893891990184784, 0.14445756375789642, 0.12121213227510452, 0.10011427849531174, 0.08056001365184784, 0.06217300146818161],
[0.8295156359672546, 0.6796684861183167, 0.5681592226028442, 0.49393802881240845, 0.4275750517845154, 0.3783359229564667, 0.3284263610839844, 0.2884153127670288, 0.25009238719940186, 0.2184663861989975, 0.18937285244464874, 0.1641167551279068, 0.13968001306056976, 0.11813642084598541, 0.09728415310382843, 0.07793601602315903],
[0.8335033059120178, 0.6849249601364136, 0.5833916664123535, 0.5095957517623901, 0.4424544870853424, 0.3916865885257721, 0.3429959714412689, 0.30444473028182983, 0.26676270365715027, 0.23430119454860687, 0.2047705054283142, 0.18033793568611145, 0.15701515972614288, 0.13353331387043, 0.11300265789031982, 0.09263114631175995],
[0.8410661220550537, 0.697619616985321, 0.5914795398712158, 0.5182439684867859, 0.45755529403686523, 0.402972012758255, 0.3587772846221924, 0.31694215536117554, 0.2815619707107544, 0.24844197928905487, 0.22051548957824707, 0.19394654035568237, 0.1698925495147705, 0.14700978994369507, 0.1260586977005005, 0.10592689365148544],
[0.8484604358673096, 0.7023067474365234, 0.6015301942825317, 0.5295441150665283, 0.46613001823425293, 0.41483065485954285, 0.36997392773628235, 0.3281089663505554, 0.2913501262664795, 0.26190710067749023, 0.23318815231323242, 0.2057400345802307, 0.1824234426021576, 0.15830835700035095, 0.1380082368850708, 0.1179661750793457],
[0.8551042675971985, 0.7079752683639526, 0.6084671020507812, 0.5358502864837646, 0.4741434156894684, 0.42210912704467773, 0.3791273534297943, 0.3398391604423523, 0.3023475706577301, 0.27144643664360046, 0.2429533153772354, 0.2175404131412506, 0.19221292436122894, 0.17030392587184906, 0.14993935823440552, 0.1290118396282196],
[0.8501632809638977, 0.7116678357124329, 0.6153939366340637, 0.5396509170532227, 0.48145586252212524, 0.4302736222743988, 0.38758015632629395, 0.3471345901489258, 0.311533123254776, 0.2810713052749634, 0.25147807598114014, 0.22633324563503265, 0.20167292654514313, 0.17984476685523987, 0.15825243294239044, 0.1386963576078415],
[0.8622049689292908, 0.7152209281921387, 0.6199618577957153, 0.5467249751091003, 0.4874902069568634, 0.43770989775657654, 0.3937734067440033, 0.35552412271499634, 0.3192523717880249, 0.28733202815055847, 0.26128682494163513, 0.23516692221164703, 0.21098822355270386, 0.18748076260089874, 0.16716741025447845, 0.148191899061203],
[0.8601170182228088, 0.7174697518348694, 0.6260602474212646, 0.5531914234161377, 0.4940868020057678, 0.44637519121170044, 0.40059515833854675, 0.3622063994407654, 0.3252628445625305, 0.29459384083747864, 0.26769447326660156, 0.24287304282188416, 0.21857008337974548, 0.19655127823352814, 0.17506280541419983, 0.15629635751247406],
[0.8618876338005066, 0.7259172201156616, 0.6283632516860962, 0.5577455759048462, 0.4994502067565918, 0.4518873691558838, 0.40735799074172974, 0.3683125674724579, 0.331371009349823, 0.301642507314682, 0.27395009994506836, 0.24869343638420105, 0.22504563629627228, 0.20242752134799957, 0.1830613911151886, 0.16299892961978912],
[0.8728474974632263, 0.7256279587745667, 0.6346219182014465, 0.5620977282524109, 0.5043411254882812, 0.45523110032081604, 0.4108377695083618, 0.3711701035499573, 0.33912673592567444, 0.3076936602592468, 0.2809484302997589, 0.2553638815879822, 0.23264753818511963, 0.21060876548290253, 0.18985334038734436, 0.17014266550540924],
], dtype=np.float32)
# print("Sheen_E", Sheen_E.shape)

# [ 16, 16 ]
# Sheen_ash_E[16-alpha][16-cos_theta]
Sheen_ash_E = np.array([
[1.0, 0.9838606715202332, 0.6200262904167175, 0.40005072951316833, 0.252230703830719, 0.15019986033439636, 0.08855579793453217, 0.052468910813331604, 0.02755708619952202, 0.014369060285389423, 0.006679311860352755, 0.002955903299152851, 0.0011634858092293143, 0.00033794110640883446, 6.934259727131575e-05, 6.289055363595253e-06],
[1.0, 0.8166638016700745, 0.6264232993125916, 0.47681576013565063, 0.3692566752433777, 0.28283801674842834, 0.2179974615573883, 0.16180576384067535, 0.12056494504213333, 0.08809089660644531, 0.061084382236003876, 0.04240790754556656, 0.026981793344020844, 0.01635201834142208, 0.008582253009080887, 0.0034416348207741976],
[0.931864321231842, 0.7221881747245789, 0.5792673826217651, 0.47601351141929626, 0.3922376036643982, 0.3218442499637604, 0.2647128105163574, 0.21216773986816406, 0.17058365046977997, 0.1368219405412674, 0.10488437861204147, 0.08035232871770859, 0.05834868550300598, 0.0409933365881443, 0.02684617042541504, 0.015181244350969791],
[0.837207019329071, 0.6687302589416504, 0.5585128664970398, 0.4726698100566864, 0.397951602935791, 0.3384082317352295, 0.28542274236679077, 0.23896349966526031, 0.2028227597475052, 0.16668713092803955, 0.13673023879528046, 0.10833190381526947, 0.08478739857673645, 0.06397195905447006, 0.04643622040748596, 0.03101356513798237],
[0.7763281464576721, 0.6347008347511292, 0.537436842918396, 0.4629773795604706, 0.3994271755218506, 0.34656408429145813, 0.29840201139450073, 0.2548285722732544, 0.22056227922439575, 0.18654784560203552, 0.15771614015102386, 0.1305922567844391, 0.10568913072347641, 0.08464501798152924, 0.06472857296466827, 0.04691318795084953],
[0.7283147573471069, 0.6081956624984741, 0.521221399307251, 0.45444256067276, 0.39885413646698, 0.3480645418167114, 0.30532070994377136, 0.26511937379837036, 0.2322876751422882, 0.20070691406726837, 0.17167925834655762, 0.14656713604927063, 0.12262976914644241, 0.10083720833063126, 0.08069051802158356, 0.06180427223443985],
[0.6960227489471436, 0.5885429978370667, 0.5045895576477051, 0.44677734375, 0.3926233649253845, 0.35195058584213257, 0.30952388048171997, 0.27532073855400085, 0.24177518486976624, 0.21267667412757874, 0.18491889536380768, 0.1603708267211914, 0.13631075620651245, 0.11498570442199707, 0.09432476758956909, 0.07506509870290756],
[0.6682984828948975, 0.5680185556411743, 0.49695903062820435, 0.4426625370979309, 0.3906835615634918, 0.35100340843200684, 0.31173110008239746, 0.28059884905815125, 0.24934548139572144, 0.22079209983348846, 0.19387516379356384, 0.17109566926956177, 0.1489424854516983, 0.1265336275100708, 0.10673804581165314, 0.0871172845363617],
[0.6493096351623535, 0.558093786239624, 0.48677411675453186, 0.4354790449142456, 0.3912656903266907, 0.3501231372356415, 0.3164410889148712, 0.284045547246933, 0.2560179829597473, 0.22814272344112396, 0.20357775688171387, 0.17953667044639587, 0.15762211382389069, 0.13639234006404877, 0.11682628840208054, 0.09777993708848953],
[0.6342411041259766, 0.5450001358985901, 0.4807107150554657, 0.43266594409942627, 0.38799455761909485, 0.3510940670967102, 0.31822720170021057, 0.28702983260154724, 0.2589797079563141, 0.23518984019756317, 0.21087250113487244, 0.18698479235172272, 0.16615411639213562, 0.1445145457983017, 0.12588857114315033, 0.10729772597551346],
[0.621673583984375, 0.5350744724273682, 0.47425949573516846, 0.4274314343929291, 0.38566774129867554, 0.349478155374527, 0.31924793124198914, 0.2911602854728699, 0.2635200023651123, 0.2393985390663147, 0.21593035757541656, 0.19434528052806854, 0.17241008579730988, 0.15310871601104736, 0.13486111164093018, 0.11582540720701218],
[0.6032047867774963, 0.5256738662719727, 0.4692630171775818, 0.4216444790363312, 0.3837791681289673, 0.34948641061782837, 0.3203381299972534, 0.292219877243042, 0.2669890522956848, 0.24400702118873596, 0.2202529013156891, 0.19944588840007782, 0.17861667275428772, 0.15979883074760437, 0.14082832634449005, 0.12329835444688797],
[0.5986766815185547, 0.5176916122436523, 0.4636857509613037, 0.41925254464149475, 0.38177490234375, 0.3495742678642273, 0.32044005393981934, 0.29480624198913574, 0.26966556906700134, 0.2460826188325882, 0.22578193247318268, 0.2047601044178009, 0.18471172451972961, 0.16497822105884552, 0.14737051725387573, 0.13056235015392303],
[0.5858066082000732, 0.5100440979003906, 0.4602128267288208, 0.4172801673412323, 0.3810053765773773, 0.3510725498199463, 0.3214000463485718, 0.2963111698627472, 0.2712300419807434, 0.24912507832050323, 0.228778675198555, 0.20910681784152985, 0.18946106731891632, 0.1713251769542694, 0.15309086441993713, 0.13663290441036224],
[0.5769227147102356, 0.5077014565467834, 0.4548371732234955, 0.414576917886734, 0.37973421812057495, 0.3505387306213379, 0.32256799936294556, 0.297669380903244, 0.2731708586215973, 0.2523551881313324, 0.2317737638950348, 0.21235117316246033, 0.19338101148605347, 0.1751231551170349, 0.15890640020370483, 0.14178310334682465],
[0.5750976800918579, 0.5000414252281189, 0.452933669090271, 0.41233959794044495, 0.3785347640514374, 0.3490264117717743, 0.3217995762825012, 0.2968665659427643, 0.27645760774612427, 0.25480249524116516, 0.23534445464611053, 0.2160816341638565, 0.19821089506149292, 0.18069957196712494, 0.16365939378738403, 0.14698821306228638],
], dtype=np.float32)
# print("Sheen_ash_E", Sheen_ash_E.shape)