# Licensed to the Apache Software Foundation (ASF) under one or more
# contributor license agreements.  See the NOTICE file distributed with
# this work for additional information regarding copyright ownership.
# The ASF licenses this file to You under the Apache License, Version 2.0
# (the "License"); you may not use this file except in compliance with
# the License.  You may obtain a copy of the License at
#
#     http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.

# P-values for the one-sample Kolmogorov-Smirnov distribution:
# D_n = sup_x |F(x) - CDF_n(x)|
# Data was computed by SciPy:
# import numpy as np
# from scipy.stats import kstwo, ksone
# with open("ks.onesample.large.txt", "w") as f:
#   n = 1000
#   for x in np.linspace(0, 1, n * 2):
#     print(x, n, kstwo.sf(x, n), ksone.sf(x, n), file=f)
0.0 1000 1.0 1.0
0.0005002501250625312 1000 1.0 0.9991755362787644
0.0010005002501250625 1000 1.0 0.9972835771571262
0.0015007503751875936 1000 1.0 0.9945252478155243
0.002001000500250125 1000 1.0 0.9906953101873051
0.0025012506253126563 1000 1.0 0.9859245019554314
0.003001500750375187 1000 1.0 0.9801845025607244
0.0035017508754377185 1000 1.0 0.9735036487974895
0.00400200100050025 1000 1.0 0.9659024588529891
0.004502251125562781 1000 1.0 0.9574010380863334
0.0050025012506253125 1000 1.0 0.9480256162328577
0.005502751375687844 1000 0.9999999999999998 0.937802837709402
0.006003001500750374 1000 0.9999999999999035 0.9267623272331224
0.006503251625812906 1000 0.9999999999900958 0.9149356484888871
0.007003501750875437 1000 0.9999999996061779 0.9023563224744056
0.007503751875937968 1000 0.9999999922841325 0.8890596940963487
0.0080040020010005 1000 0.9999999117958798 0.8750827261419324
0.00850425212606303 1000 0.9999993356834161 0.8604638507636033
0.009004502251125562 1000 0.9999963962714763 0.8452427859295267
0.009504752376188093 1000 0.9999849499703772 0.8294603583592086
0.010005002501250625 1000 0.9999491038877543 0.8131583220670711
0.010505252626313155 1000 0.9998550887109582 0.7963791754289435
0.011005502751375688 1000 0.9996419180388395 0.779165978443528
0.011505752876438218 1000 0.9992134264688278 0.7615621706826199
0.012006003001500749 1000 0.9984343968375335 0.7436113912807407
0.01250625312656328 1000 0.9971325004377144 0.7253573018931501
0.013006503251625811 1000 0.9951061843100883 0.7068434136238879
0.013506753376688344 1000 0.9921373806229999 0.68811291885681
0.014007003501750874 1000 0.9880064322331928 0.6692085288620881
0.014507253626813406 1000 0.982507486544052 0.6501723179939705
0.015007503751875937 1000 0.9754619113057026 0.6310455752264638
0.015507753876938469 1000 0.9667285940467106 0.6118686637037044
0.016008004002001 1000 0.9562104870494593 0.5926808889074731
0.01650825412706353 1000 0.9438574030744631 0.5735203759675203
0.01700850425212606 1000 0.9296654993237286 0.5544239565617428
0.017508754377188594 1000 0.9136741302565166 0.5354270657734345
0.018009004502251125 1000 0.8959608336013216 0.5165636491926594
0.018509254627313655 1000 0.8766351834805801 0.497866080468936
0.019009504752376186 1000 0.8558321451808679 0.479365089443591
0.01950975487743872 1000 0.83370543493967 0.46108970091299767
0.02001000500250125 1000 0.8104212517544026 0.4430671839990778
0.02051025512756378 1000 0.7861526231990407 0.4253230120314983
0.02101050525262631 1000 0.7610745020892227 0.40788083277746684
0.02151075537768884 1000 0.7353596684189935 0.3907624487903866
0.022011005502751375 1000 0.7091754305677396 0.3739878075883089
0.022511255627813906 1000 0.6826810786555546 0.35757500131746917
0.023011505752876436 1000 0.6560260176060037 0.3415402755055098
0.023511755877938967 1000 0.6293484943633378 0.3258980464635362
0.024012006003001497 1000 0.6027748295304273 0.310660926856077
0.02451225612806403 1000 0.5764190656747514 0.2958397589234635
0.02501250625312656 1000 0.5503829504810087 0.28144365481216027
0.025512756378189092 1000 0.5247561811266039 0.2674800434451636
0.026013006503251623 1000 0.49961684549575924 0.25395472334670194
0.026513256628314157 1000 0.47503200528017475 0.2408719208230014
0.027013506753376687 1000 0.4510583750834012 0.2282343528936816
0.027513756878439218 1000 0.42774306001656714 0.21604329436622075
0.028014007003501748 1000 0.4051243217674215 0.20429864844864454
0.02851425712856428 1000 0.38323234967498543 0.19299902030287214
0.029014507253626812 1000 0.36209001895276083 0.18214179295270502
0.029514757378689343 1000 0.34171362292351737 0.17172320497593532
0.030015007503751873 1000 0.32211357003262786 0.16173842942913558
0.030515257628814404 1000 0.30329503958119597 0.1521816534760105
0.031015507753876938 1000 0.28525859265474307 0.14304615821536298
0.03151575787893947 1000 0.268000736705841 0.1343243982323757
0.032016008004002 1000 0.2515144437625396 0.1260080804266479
0.03251625812906453 1000 0.23578962335462372 0.11808824170187761
0.03301650825412706 1000 0.2208135520450064 0.11055532513486022
0.03351675837918959 1000 0.20657126198455167 0.10339925427522621
0.03401700850425212 1000 0.19304589122845983 0.09660950526170431
0.03451725862931466 1000 0.18021899870697944 0.09017517647533888
0.03501750875437719 1000 0.16807084677194073 0.0840850554846899
0.03551775887943972 1000 0.15658065417647316 0.07832768307230169
0.03601800900450225 1000 0.14572682221580335 0.07289141416537274
0.03651825912956478 1000 0.13548713658460965 0.06776447552633227
0.03701850925462731 1000 0.1258389473089273 0.06293502009071139
0.03751875937968984 1000 0.11675932890203755 0.05839117787008333
0.03801900950475237 1000 0.10822522268466872 0.05412110336676314
0.0385192596298149 1000 0.10021356300784956 0.05011301947425604
0.03901950975487744 1000 0.0927013889271362 0.04635525786300117
0.03951975987993997 1000 0.08566594270299244 0.04283629587467847
0.0400200100050025 1000 0.07908475634557033 0.039544789970156084
0.04052026013006503 1000 0.07293572728356212 0.03646960579600979
0.04102051025512756 1000 0.06719718411583164 0.033599844952412146
0.04152076038019009 1000 0.0618479433002177 0.030924868561068315
0.04202101050525262 1000 0.05686735754483874 0.028434317745777683
0.04252126063031515 1000 0.052235356591818216 0.026118131150160144
0.04302151075537768 1000 0.04793248101984271 0.02396655962715047
0.04352176088044022 1000 0.04393990963868477 0.021970178243096404
0.04402201100550275 1000 0.04023948100406327 0.020119895745772075
0.04452226113056528 1000 0.03681370954351715 0.018406961650422195
0.04502251125562781 1000 0.033645796751914925 0.016822971101182683
0.04552276138069034 1000 0.03071963788764831 0.015359867666977882
0.04602301150575287 1000 0.02801982457640928 0.014009944231385536
0.0465232616308154 1000 0.02553164370789396 0.012765842135097221
0.047023511755877934 1000 0.023241097455199842 0.011620548727599921
0.047523761880940464 1000 0.021134786963357473 0.010567393481678736
0.048024012006002995 1000 0.019200085640813675 0.009600042820406838
0.04852426213106553 1000 0.017424987603120983 0.008712493801560492
0.04902451225612806 1000 0.015798133597971272 0.007899066798985636
0.04952476238119059 1000 0.014308794628911195 0.007154397314455598
0.05002501250625312 1000 0.012946854094203649 0.0064734270471018245
0.050525262631315654 1000 0.011702788681335587 0.005851394340667794
0.051025512756378184 1000 0.010567648243451208 0.005283824121725604
0.051525762881440715 1000 0.009533034869381691 0.0047665174346908454
0.052026013006503245 1000 0.008591081344111294 0.004295540672055647
0.052526263131565776 1000 0.007734429181612379 0.0038672145908061895
0.05302651325662831 1000 0.006956206397133921 0.0034781031985669604
0.053526763381690844 1000 0.006250005171360419 0.0031250025856802096
0.054027013506753374 1000 0.0056098595444782256 0.0028049297722391128
0.054527263631815905 1000 0.005030223264189319 0.0025151116320946596
0.055027513756878435 1000 0.0045059478981785035 0.0022529739490892518
0.055527763881940966 1000 0.004032261308538947 0.0020161306542694733
0.056028014007003496 1000 0.0036047465732488232 0.0018023732866244116
0.056528264132066026 1000 0.003219321428014283 0.0016096607140071416
0.05702851425712856 1000 0.0028722182906857 0.00143610914534285
0.057528764382191094 1000 0.002559964920039872 0.001279982460019936
0.058029014507253625 1000 0.0022793657510161904 0.0011396828755080952
0.058529264632316155 1000 0.0020274839395068886 0.0010137419697534443
0.059029514757378686 1000 0.0018016241415303128 0.0009008120707651564
0.059529764882441216 1000 0.0015993160440541836 0.0007996580220270918
0.06003001500750375 1000 0.00141829865787058 0.00070914932893529
0.06053026513256628 1000 0.0012565053767373852 0.0006282526883686926
0.06103051525762881 1000 0.001112049801469797 0.0005560249007348985
0.06153076538269134 1000 0.0009832123227639586 0.0004916061613819793
0.062031015507753876 1000 0.0008684274522336316 0.0004342137261168158
0.0625312656328164 1000 0.0007662718874084897 0.00038313594370424485
0.06303151575787894 1000 0.0006754532932457126 0.0003377266466228563
0.06353176588294146 1000 0.0005947997800106891 0.00029739989000534455
0.064032016008004 1000 0.0005232500551521851 0.00026162502757609254
0.06453226613306653 1000 0.00045984422499724045 0.00022992211249862023
0.06503251625812906 1000 0.00040371522068535 0.000201857610342675
0.0655327663831916 1000 0.0003540808217157046 0.0001770404108578523
0.06603301650825412 1000 0.00031023624976094557 0.00015511812488047279
0.06653326663331666 1000 0.00027154730497296693 0.00013577365248648347
0.06703351675837918 1000 0.00023744401683907857 0.00011872200841953928
0.06753376688344172 1000 0.0002074147817096128 0.0001037073908548064
0.06803401700850424 1000 0.00018100095938227003 9.050047969113502e-05
0.06853426713356678 1000 0.00015779190156669498 7.889595078334749e-05
0.06903451725862932 1000 0.00013742038563977608 6.871019281988804e-05
0.06953476738369184 1000 0.00011955842781411573 5.977921390705786e-05
0.07003501750875438 1000 0.00010391345065737377 5.1956725328686885e-05
0.0705352676338169 1000 9.022478079861883e-05 4.5112390399309415e-05
0.07103551775887944 1000 7.826045362121588e-05 3.913022681060794e-05
0.07153576788394196 1000 6.781430275368943e-05 3.390715137684471e-05
0.0720360180090045 1000 5.8703313215527045e-05 2.9351656607763523e-05
0.07253626813406702 1000 5.076521814093584e-05 2.538260907046792e-05
0.07303651825912956 1000 4.3856320078391175e-05 2.1928160039195587e-05
0.0735367683841921 1000 3.784951893731204e-05 1.892475946865602e-05
0.07403701850925462 1000 3.263252971646842e-05 1.631626485823421e-05
0.07453726863431716 1000 2.8106274194280814e-05 1.4053137097140407e-05
0.07503751875937968 1000 2.4183431782615188e-05 1.2091715891307594e-05
0.07553776888444222 1000 2.0787135737739197e-05 1.0393567868869599e-05
0.07603801900950474 1000 1.7849801880521803e-05 8.924900940260902e-06
0.07653826913456728 1000 1.531207789932036e-05 7.65603894966018e-06
0.0770385192596298 1000 1.312190219076888e-05 6.56095109538444e-06
0.07753876938469234 1000 1.123366203398817e-05 5.616831016994085e-06
0.07803901950975488 1000 9.607441691406928e-06 4.803720845703464e-06
0.0785392696348174 1000 8.208351783757748e-06 4.104175891878874e-06
0.07903951975987994 1000 7.0059319977658246e-06 3.5029659988829123e-06
0.07953976988494246 1000 5.973619852851314e-06 2.986809926425657e-06
0.080040020010005 1000 5.088278878461295e-06 2.5441394392306474e-06
0.08054027013506752 1000 4.329780137378744e-06 2.164890068689372e-06
0.08104052026013006 1000 3.6806315737069515e-06 1.8403157868534758e-06
0.08154077038519258 1000 3.1256501685953118e-06 1.5628250842976559e-06
0.08204102051025512 1000 2.651672353695948e-06 1.325836176847974e-06
0.08254127063531766 1000 2.247298563490057e-06 1.1236492817450284e-06
0.08304152076038018 1000 1.9026682047406698e-06 9.513341023703349e-07
0.08354177088544272 1000 1.609261686219219e-06 8.046308431096095e-07
0.08404202101050524 1000 1.3597264863421044e-06 6.798632431710522e-07
0.08454227113556778 1000 1.147724542272917e-06 5.738622711364584e-07
0.0850425212606303 1000 9.677985232139467e-07 4.838992616069733e-07
0.08554277138569284 1000 8.152548048112974e-07 4.076274024056487e-07
0.08604302151075537 1000 6.860611925746584e-07 3.430305962873292e-07
0.0865432716358179 1000 5.767576516501054e-07 2.883788258250527e-07
0.08704352176088044 1000 4.843784898060897e-07 2.4218924490304484e-07
0.08754377188594296 1000 4.063846116500788e-07 2.031923058250394e-07
0.0880440220110055 1000 3.406046163642691e-07 1.7030230818213455e-07
0.08854427213606803 1000 2.851836500320004e-07 1.425918250160002e-07
0.08904452226113056 1000 2.3853904824139513e-07 1.1926952412069757e-07
0.08954477238619309 1000 1.993219163382805e-07 9.966095816914025e-08
0.09004502251125562 1000 1.6638389461491013e-07 8.319194730745507e-08
0.09054527263631815 1000 1.387484449445105e-07 6.937422247225525e-08
0.09104552276138068 1000 1.1558607490652206e-07 5.779303745326103e-08
0.09154577288644322 1000 9.619298622190352e-08 4.809649311095176e-08
0.09204602301150575 1000 7.997269718796461e-08 3.998634859398231e-08
0.09254627313656828 1000 6.642024455564368e-08 3.321012227782184e-08
0.0930465232616308 1000 5.510861965115164e-08 2.755430982557582e-08
0.09354677338669334 1000 4.5677137169134507e-08 2.2838568584567253e-08
0.09404702351175587 1000 3.7821473558586816e-08 1.8910736779293408e-08
0.0945472736368184 1000 3.128514583381579e-08 1.5642572916907894e-08
0.09504752376188093 1000 2.585223146837559e-08 1.2926115734187795e-08
0.09554777388694347 1000 2.1341156220333346e-08 1.0670578110166673e-08
0.09604802401200599 1000 1.7599399699258156e-08 8.799699849629078e-09
0.09654827413706853 1000 1.4498988585325632e-08 7.249494292662816e-09
0.09704852426213106 1000 1.1932664978362473e-08 5.9663324891812365e-09
0.09754877438719359 1000 9.810632684960465e-09 4.9053163424802324e-09
0.09804902451225612 1000 8.057797609462629e-09 4.028898804731314e-09
0.09854927463731865 1000 6.611430035861211e-09 3.3057150179306056e-09
0.09904952476238119 1000 5.419186682992903e-09 2.7095933414964516e-09
0.09954977488744371 1000 4.437439172152732e-09 2.218719586076366e-09
0.10005002501250625 1000 3.629863130617875e-09 1.8149315653089376e-09
0.10055027513756877 1000 2.9662487138885285e-09 1.4831243569442643e-09
0.10105052526263131 1000 2.4214989939643344e-09 1.2107494969821672e-09
0.10155077538769385 1000 1.974787545660605e-09 9.873937728303026e-10
0.10205102551275637 1000 1.6088507691101067e-09 8.044253845550533e-10
0.1025512756378189 1000 1.3093941032683548e-09 6.546970516341774e-10
0.10305152576288143 1000 1.0645943906241173e-09 5.322971953120587e-10
0.10355177588794397 1000 8.646833159192227e-10 4.3234165795961135e-10
0.10405202601300649 1000 7.01599121424067e-10 3.507995607120335e-10
0.10455227613806903 1000 5.686957505153845e-10 2.8434787525769225e-10
0.10505252626313155 1000 4.605002355673138e-10 2.302501177836569e-10
0.10555277638819409 1000 3.7251056517765965e-10 1.8625528258882983e-10
0.10605302651325663 1000 3.0102747398350883e-10 1.5051373699175442e-10
0.10655327663831915 1000 2.4301462567067633e-10 1.2150731283533817e-10
0.10705352676338169 1000 1.9598253213728165e-10 9.799126606864083e-11
0.10755377688844421 1000 1.5789229150966498e-10 7.894614575483249e-11
0.10805402701350675 1000 1.2707585414117255e-10 6.353792707058627e-11
0.10855427713856927 1000 1.0217005549153994e-10 5.108502774576997e-11
0.10905452726363181 1000 8.206210220189191e-11 4.1031051100945954e-11
0.10955477738869433 1000 6.584457504410116e-11 3.292228752205058e-11
0.11005502751375687 1000 5.2778330278199435e-11 2.6389165139099718e-11
0.11055527763881941 1000 4.226194832732452e-11 2.113097416366226e-11
0.11105552776388193 1000 3.380660329589921e-11 1.6903301647949606e-11
0.11155577788894447 1000 2.7015415303489966e-11 1.3507707651744983e-11
0.11205602801400699 1000 2.156650550108061e-11 1.0783252750540305e-11
0.11255627813906953 1000 1.7199105758945782e-11 8.599552879472891e-12
0.11305652826413205 1000 1.3702185428561661e-11 6.8510927142808306e-12
0.11355677838919459 1000 1.090514973237516e-11 5.45257486618758e-12
0.11405702851425711 1000 8.6702411457859e-12 4.33512057289295e-12
0.11455727863931965 1000 6.88633907668451e-12 3.443169538342255e-12
0.11505752876438219 1000 5.4639063072486404e-12 2.7319531536243202e-12
0.11555777888944471 1000 4.330874801771312e-12 2.165437400885656e-12
0.11605802901450725 1000 3.4293000868861367e-12 1.7146500434430683e-12
0.11655827913956977 1000 2.712643724806415e-12 1.3563218624032074e-12
0.11705852926463231 1000 2.1435684745682338e-12 1.0717842372841169e-12
0.11755877938969483 1000 1.6921514502215893e-12 8.460757251107947e-13
0.11805902951475737 1000 1.3344376751063593e-12 6.672188375531797e-13
0.1185592796398199 1000 1.0512705139762732e-12 5.256352569881366e-13
0.11905952976488243 1000 8.273470544878951e-13 4.1367352724394754e-13
0.11955977988994497 1000 6.504560357849617e-13 3.2522801789248087e-13
0.1200600300150075 1000 5.108637422008014e-13 2.554318711004007e-13
0.12056028014007003 1000 4.008196919588585e-13 2.0040984597942925e-13
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