ksref.py

"""
A collection of reference values for the Kolmogorov-Smirnov two-sided,
one-sample, distribution-free statistic.
"""
from __future__ import division

from fractions import Fraction as F
from math import sqrt

from funcsim.ksdist import ks_unif_durbin_recurrence_rational as reference


def print_reference(samples_min, samples_max, samples_step):
    """
    Prepares a testing reference using an exact rational arithmetic.

    The printed values are as accurate as the language float type allows.
    The tuples are (sample count, statistic value, Pr(D <= st), P(D > st)).
    """
    for samples in range(samples_min, samples_max, samples_step):
        for factor in (1 / 5, 1 / 4, 1 / 3, 1 / 2, 1, 2, 3, 4, 5):
            statistic = F.from_float(.868731160636 / sqrt(samples) * factor)
            probability = reference(samples, statistic)
            print('    ({}, {}, {}, {}),'.format(samples, float(statistic),
                                float(probability), float(1 - probability)))


if __name__ == '__main__':
    import argparse
    parser = argparse.ArgumentParser(description="Generate a reference table.")
    parser.add_argument('samples_min', type=int, help="from count")
    parser.add_argument('samples_max', type=int, help="up to count")
    parser.add_argument('samples_step', type=int, help="in steps")
    print_reference(**vars(parser.parse_args()))


# A few exact values after doi:10.18637/jss.v026.i02 or in the easy regions.
exact_values = (
    (1, F(3, 4), F(1, 2)),
    (2, F(3, 8), F(1, 8)),
    (3, F(3, 7), F(166, 343)),
    (3, F(5, 8), F(341, 384)),
    (3, F(85, 123), F(1751123, 1860867)),
    (4, F(3, 10), F(2292, 10000)),
    (4, F(31, 100), F(26074392, 100000000)),
    (5, F(2, 11), F(1417176, 100656875)),
    (5, F(7, 17), F(127996134, 177482125)),
    (5, F(6, 11), F(18855437, 20131375)),
    (6, F(3, 10), F(1802189, 4050000)),
    (7, F(6, 7), F(823541, 823543)))

# Computed with the above function (using exact rational arithmetic), printed
# on an IEEE-binary64-based machine (with accuracy of 15 decimal digits).
almost_exact_values = (
    # First series: samples 1-100, step 1.
    (1, 0.1737462321272, 0.0, 1.0),
    (1, 0.217182790159, 0.0, 1.0),
    (1, 0.2895770535453333, 0.0, 1.0),
    (1, 0.434365580318, 0.0, 1.0),
    (1, 0.868731160636, 0.737462321272, 0.26253767872800005),
    (1, 1.737462321272, 1.0, 0.0),
    (1, 2.606193481908, 1.0, 0.0),
    (1, 3.474924642544, 1.0, 0.0),
    (1, 4.34365580318, 1.0, 0.0),
    (2, 0.1228571389427551, 0.0, 1.0),
    (2, 0.15357142367844387, 0.0, 1.0),
    (2, 0.20476189823792515, 0.0, 1.0),
    (2, 0.30714284735688774, 0.026122440032420577, 0.9738775599675794),
    (2, 0.6142856947137755, 0.7024489493951304, 0.29755105060486964),
    (2, 1.228571389427551, 1.0, 0.0),
    (2, 1.8428570841413263, 1.0, 0.0),
    (2, 2.457142778855102, 1.0, 0.0),
    (2, 3.0714284735688775, 1.0, 0.0),
    (3, 0.10031243388932212, 0.0, 1.0),
    (3, 0.12539054236165265, 0.0, 1.0),
    (3, 0.16718738981553685, 6.777380857668046e-09, 0.9999999932226191),
    (3, 0.2507810847233053, 0.028566206494883235, 0.9714337935051167),
    (3, 0.5015621694466106, 0.6703019519661314, 0.3296980480338686),
    (3, 1.0031243388932212, 1.0, 0.0),
    (3, 1.5046865083398318, 1.0, 0.0),
    (3, 2.0062486777864423, 1.0, 0.0),
    (3, 2.5078108472330527, 1.0, 0.0),
    (4, 0.0868731160636, 0.0, 1.0),
    (4, 0.1085913950795, 0.0, 1.0),
    (4, 0.14478852677266665, 5.888234202820654e-05, 0.9999411176579718),
    (4, 0.217182790159, 0.027728770970605478, 0.9722712290293946),
    (4, 0.434365580318, 0.6654322040584092, 0.33456779594159086),
    (4, 0.868731160636, 0.9994061502511358, 0.0005938497488642675),
    (4, 1.303096740954, 1.0, 0.0),
    (4, 1.737462321272, 1.0, 0.0),
    (4, 2.17182790159, 1.0, 0.0),
    (5, 0.07770167717417542, 0.0, 1.0),
    (5, 0.09712709646771926, 0.0, 1.0),
    (5, 0.12950279529029235, 8.58315694334606e-05, 0.9999141684305666),
    (5, 0.19425419293543852, 0.02856502573887674, 0.9714349742611232),
    (5, 0.38850838587087705, 0.6592324313022009, 0.34076756869779906),
    (5, 0.7770167717417541, 0.9988953004675888, 0.0011046995324112227),
    (5, 1.165525157612631, 1.0, 0.0),
    (5, 1.5540335434835082, 1.0, 0.0),
    (5, 1.9425419293543853, 1.0, 0.0),
    (6, 0.07093160224046692, 0.0, 1.0),
    (6, 0.08866450280058365, 1.0579067764294849e-09, 0.9999999989420932),
    (6, 0.11821933706744486, 8.306533254338826e-05, 0.9999169346674566),
    (6, 0.1773290056011673, 0.02735357643036074, 0.9726464235696393),
    (6, 0.3546580112023346, 0.6483094667209588, 0.35169053327904126),
    (6, 0.7093160224046692, 0.9985437107164574, 0.001456289283542579),
    (6, 1.0639740336070038, 1.0, 0.0),
    (6, 1.4186320448093384, 1.0, 0.0),
    (6, 1.7732900560116729, 1.0, 0.0),
    (7, 0.06566990306329601, 0.0, 1.0),
    (7, 0.08208737882912001, 1.0083256375140556e-08, 0.9999999899167437),
    (7, 0.10944983843882668, 7.410143215622697e-05, 0.9999258985678438),
    (7, 0.16417475765824002, 0.02512621007340651, 0.9748737899265935),
    (7, 0.32834951531648005, 0.6420271669189849, 0.35797283308101513),
    (7, 0.6566990306329601, 0.9982632869409671, 0.0017367130590328558),
    (7, 0.9850485459494401, 0.9999999999996659, 3.340519482933153e-13),
    (7, 1.3133980612659202, 1.0, 0.0),
    (7, 1.6417475765824001, 1.0, 0.0),
    (8, 0.06142856947137755, 0.0, 1.0),
    (8, 0.07678571183922193, 1.7905051464238595e-08, 0.9999999820949486),
    (8, 0.10238094911896257, 6.605175667757484e-05, 0.9999339482433224),
    (8, 0.15357142367844387, 0.023495506534202158, 0.9765044934657978),
    (8, 0.30714284735688774, 0.6379667887631915, 0.3620332112368085),
    (8, 0.6142856947137755, 0.9980296619852402, 0.001970338014759718),
    (8, 0.9214285420706632, 0.9999999970949842, 2.905015738993609e-09),
    (8, 1.228571389427551, 1.0, 0.0),
    (8, 1.5357142367844387, 1.0, 0.0),
    (9, 0.05791541070906667, 4.216975883592928e-16, 0.9999999999999996),
    (9, 0.07239426338633333, 2.0221429224678802e-08, 0.9999999797785708),
    (9, 0.0965256845151111, 6.042810462951509e-05, 0.9999395718953705),
    (9, 0.14478852677266665, 0.022338747830212627, 0.9776612521697874),
    (9, 0.2895770535453333, 0.6346685113522246, 0.36533148864777537),
    (9, 0.5791541070906666, 0.99784480353911, 0.0021551964608900135),
    (9, 0.868731160636, 0.9999999768531018, 2.3146898224791866e-08),
    (9, 1.1583082141813332, 1.0, 0.0),
    (9, 1.4478852677266665, 1.0, 0.0),
    (10, 0.0549433828394274, 3.238213252053576e-14, 0.9999999999999676),
    (10, 0.06867922854928425, 1.9215529170715146e-08, 0.9999999807844708),
    (10, 0.091572304732379, 5.729332278483503e-05, 0.9999427066772152),
    (10, 0.1373584570985685, 0.02152332262234909, 0.9784766773776509),
    (10, 0.274716914197137, 0.6315665889427162, 0.36843341105728383),
    (10, 0.549433828394274, 0.9976855916236906, 0.0023144083763093864),
    (10, 0.824150742591411, 0.9999999420800234, 5.791997656252677e-08),
    (10, 1.098867656788548, 1.0, 0.0),
    (10, 1.373584570985685, 1.0, 0.0),
    (11, 0.05238646006399231, 1.4516800781160223e-13, 0.9999999999998548),
    (11, 0.06548307507999038, 1.7006909832828687e-08, 0.9999999829930901),
    (11, 0.0873107667733205, 5.6473652337811264e-05, 0.9999435263476621),
    (11, 0.13096615015998075, 0.02093322165080396, 0.9790667783491961),
    (11, 0.2619323003199615, 0.6285490290884524, 0.37145097091154755),
    (11, 0.523864600639923, 0.9975497877144126, 0.0024502122855874294),
    (11, 0.7857969009598845, 0.9999998988445798, 1.011554201118241e-07),
    (11, 1.047729201279846, 1.0, 0.0),
    (11, 1.3096615015998077, 1.0, 0.0),
    (12, 0.05015621694466106, 2.7498761136539654e-13, 0.999999999999725),
    (12, 0.06269527118082632, 1.4669737799692126e-08, 0.9999999853302622),
    (12, 0.08359369490776843, 5.752181863774531e-05, 0.9999424781813623),
    (12, 0.12539054236165265, 0.020467183276583503, 0.9795328167234165),
    (12, 0.2507810847233053, 0.6257839393164454, 0.37421606068355456),
    (12, 0.5015621694466106, 0.9974330234184614, 0.0025669765815386305),
    (12, 0.7523432541699159, 0.9999998498292979, 1.501707020680627e-07),
    (12, 1.0031243388932212, 1.0, 0.0),
    (12, 1.2539054236165263, 1.0, 0.0),
    (13, 0.04818853452717603, 3.5595400421407143e-13, 0.9999999999996441),
    (13, 0.06023566815897003, 1.2615391450571807e-08, 0.9999999873846086),
    (13, 0.08031422421196004, 5.4556088983941774e-05, 0.999945443911016),
    (13, 0.12047133631794006, 0.020052984385345973, 0.979947015614654),
    (13, 0.24094267263588012, 0.6234817418539983, 0.37651825814600176),
    (13, 0.48188534527176025, 0.9973302774514855, 0.002669722548514499),
    (13, 0.7228280179076404, 0.9999997979600089, 2.020399911163095e-07),
    (13, 0.9637706905435205, 1.0, 3.705192085001096e-19),
    (13, 1.2047133631794007, 1.0, 0.0),
    (14, 0.04643563377591984, 3.787213825342755e-13, 0.9999999999996213),
    (14, 0.0580445422198998, 1.0948137838027757e-08, 0.9999999890518622),
    (14, 0.07739272295986639, 5.125528655202595e-05, 0.999948744713448),
    (14, 0.1160890844397996, 0.019681430488785415, 0.9803185695112145),
    (14, 0.2321781688795992, 0.621517555598019, 0.37848244440198103),
    (14, 0.4643563377591984, 0.9972393038471503, 0.0027606961528497316),
    (14, 0.6965345066387976, 0.9999997448716915, 2.551283084660524e-07),
    (14, 0.9287126755183968, 0.9999999999999998, 1.7506624230097593e-16),
    (14, 1.160890844397996, 1.0, 0.0),
    (15, 0.04486108423299558, 3.615083194631342e-13, 0.9999999999996385),
    (15, 0.05607635529124447, 9.653217821579847e-09, 0.9999999903467822),
    (15, 0.07476847372165929, 4.805186735277818e-05, 0.9999519481326472),
    (15, 0.11215271058248893, 0.019348609332779265, 0.9806513906672207),
    (15, 0.22430542116497787, 0.619765011972901, 0.38023498802709893),
    (15, 0.44861084232995574, 0.9971583073340143, 0.002841692665985682),
    (15, 0.6729162634949336, 0.9999996917683799, 3.082316200693141e-07),
    (15, 0.8972216846599115, 0.999999999999997, 3.017013589160165e-15),
    (15, 1.1215271058248892, 1.0, 0.0),
    (16, 0.0434365580318, 3.2448639994100316e-13, 0.9999999999996755),
    (16, 0.05429569753975, 8.680350232347951e-09, 0.9999999913196498),
    (16, 0.07239426338633333, 4.51266675445849e-05, 0.9999548733324554),
    (16, 0.1085913950795, 0.01904691568721539, 0.9809530843127846),
    (16, 0.217182790159, 0.6181556687795959, 0.38184433122040407),
    (16, 0.434365580318, 0.9970855159203056, 0.0029144840796944235),
    (16, 0.651548370477, 0.9999996394356542, 3.6056434577262166e-07),
    (16, 0.868731160636, 0.9999999999999843, 1.564705334432605e-14),
    (16, 1.085913950795, 1.0, 0.0),
    (17, 0.04213965100667825, 2.814720794678921e-13, 0.9999999999997186),
    (17, 0.05267456375834781, 7.976859044107832e-09, 0.9999999920231409),
    (17, 0.07023275167779708, 4.253799070698208e-05, 0.999957462009293),
    (17, 0.10534912751669562, 0.018767673362799143, 0.9812323266372008),
    (17, 0.21069825503339124, 0.616656403810566, 0.383343596189434),
    (17, 0.42139651006678247, 0.9970196190796893, 0.002980380920310696),
    (17, 0.6320947651001737, 0.9999995883498467, 4.116501533492358e-07),
    (17, 0.8427930201335649, 0.999999999999954, 4.596531413167499e-14),
    (17, 1.053491275166956, 1.0, 0.0),
    (18, 0.04095237964758504, 2.3996944142303e-13, 0.9999999999997601),
    (18, 0.051190474559481294, 7.499060772237495e-09, 0.9999999925009392),
    (18, 0.06825396607930839, 4.028606578824489e-05, 0.9999597139342118),
    (18, 0.10238094911896259, 0.01850246730728633, 0.9814975326927137),
    (18, 0.20476189823792518, 0.615254678277135, 0.3847453217228651),
    (18, 0.40952379647585035, 0.99695967458817, 0.0030403254118300063),
    (18, 0.6142856947137756, 0.9999995388238465, 4.6117615352257875e-07),
    (18, 0.8190475929517007, 0.9999999999998995, 1.0042831238738921e-13),
    (18, 1.0238094911896258, 1.0, 0.0),
    (19, 0.03986011935070656, 2.0326259638445571e-13, 0.9999999999997967),
    (19, 0.0498251491883832, 7.215056898123358e-09, 0.9999999927849431),
    (19, 0.0664335322511776, 3.834514198374714e-05, 0.9999616548580162),
    (19, 0.0996502983767664, 0.01824386306778303, 0.981756136932217),
    (19, 0.1993005967535328, 0.6139483419354267, 0.3860516580645733),
    (19, 0.3986011935070656, 0.9969048771300638, 0.003095122869936223),
    (19, 0.5979017902605983, 0.9999994910237199, 5.089762801532561e-07),
    (19, 0.7972023870141312, 0.9999999999998161, 1.838099167579699e-13),
    (19, 0.996502983767664, 1.0, 4.2784386770098444e-47),
    (20, 0.03885083858708771, 1.7228437581696803e-13, 0.9999999999998277),
    (20, 0.04856354823385963, 7.104577973076549e-09, 0.9999999928954221),
    (20, 0.06475139764514617, 3.667930830876974e-05, 0.9999633206916912),
    (20, 0.09712709646771926, 0.017985829271761265, 0.9820141707282387),
    (20, 0.19425419293543852, 0.6127380411231367, 0.38726195887686327),
    (20, 0.38850838587087705, 0.9968545344093718, 0.0031454655906281927),
    (20, 0.5827625788063155, 0.9999994450323424, 5.549676575664135e-07),
    (20, 0.7770167717417541, 0.9999999999997011, 2.9891216377121335e-13),
    (20, 0.9712709646771926, 1.0, 2.933937522930443e-31),
    (21, 0.037914536211250585, 1.4683065621132705e-13, 0.9999999999998531),
    (21, 0.04739317026406323, 7.15820100685273e-09, 0.999999992841799),
    (21, 0.06319089368541764, 3.5250087183489563e-05, 0.9999647499128165),
    (21, 0.09478634052812646, 0.017724011874625797, 0.9822759881253742),
    (21, 0.1895726810562529, 0.6116212719154331, 0.38837872808456686),
    (21, 0.3791453621125058, 0.996808084224567, 0.003191915775432937),
    (21, 0.5687180431687587, 0.9999994008735085, 5.991264915261013e-07),
    (21, 0.7582907242250116, 0.999999999999553, 4.469346610778588e-13),
    (21, 0.9478634052812646, 1.0, 2.2962855734483508e-27),
    (22, 0.037042821153607214, 1.2624154077266613e-13, 0.9999999999998738),
    (22, 0.04630352644200902, 7.017161825481009e-09, 0.9999999929828381),
    (22, 0.06173803525601202, 3.40198682949729e-05, 0.999965980131705),
    (22, 0.09260705288401803, 0.017466895782078353, 0.9825331042179216),
    (22, 0.18521410576803607, 0.6105878326181611, 0.3894121673818389),
    (22, 0.37042821153607214, 0.9967650691848655, 0.0032349308151344305),
    (22, 0.5556423173041082, 0.9999993585298771, 6.414701229596339e-07),
    (22, 0.7408564230721443, 0.9999999999993723, 6.277635175621316e-13),
    (22, 0.9260705288401804, 1.0, 2.6002638851222296e-25),
    (23, 0.036228593786627614, 1.0974563252160142e-13, 0.9999999999998902),
    (23, 0.045285742233284514, 6.73241298759555e-09, 0.999999993267587),
    (23, 0.06038098964437935, 3.295325859792454e-05, 0.999967046741402),
    (23, 0.09057148446656903, 0.017234389706796836, 0.9827656102932032),
    (23, 0.18114296893313805, 0.6096229307963994, 0.39037706920360066),
    (23, 0.3622859378662761, 0.9967251008014079, 0.003274899198592111),
    (23, 0.5434289067994141, 0.9999993179593587, 6.820406413020582e-07),
    (23, 0.7245718757325522, 0.9999999999991597, 8.403393660093739e-13),
    (23, 0.9057148446656903, 1.0, 5.168268912565062e-24),
    (24, 0.03546580112023346, 9.661563371292926e-14, 0.9999999999999034),
    (24, 0.044332251400291824, 6.406819111282814e-09, 0.9999999935931809),
    (24, 0.05910966853372243, 3.201741800751906e-05, 0.9999679825819925),
    (24, 0.08866450280058365, 0.017023517697485564, 0.9829764823025144),
    (24, 0.1773290056011673, 0.6087154881244689, 0.3912845118755311),
    (24, 0.3546580112023346, 0.9966878440150406, 0.0033121559849593587),
    (24, 0.5319870168035019, 0.9999992791035774, 7.208964225955446e-07),
    (24, 0.7093160224046692, 0.9999999999989171, 1.0829427818738234e-12),
    (24, 0.8866450280058364, 1.0, 4.071538658024216e-23),
    (25, 0.03474924642544, 8.622662022729818e-14, 0.9999999999999137),
    (25, 0.0434365580318, 6.0673166043226364e-09, 0.9999999939326834),
    (25, 0.05791541070906667, 3.118193582116463e-05, 0.9999688180641788),
    (25, 0.0868731160636, 0.01683105245046661, 0.9831689475495334),
    (25, 0.1737462321272, 0.6078581079392689, 0.39214189206073113),
    (25, 0.3474924642544, 0.9966530121656446, 0.00334698783435534),
    (25, 0.5212386963816, 0.9999992418943346, 7.581056653344532e-07),
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    (75, 0.5015621694466106, 1.0, 5.583141681847728e-18),
    (76, 0.01993005967535328, 1.1021449883663581e-14, 0.999999999999989),
    (76, 0.0249125745941916, 1.3831937762567084e-09, 0.9999999986168062),
    (76, 0.0332167661255888, 1.5432459907630436e-05, 0.9999845675400924),
    (76, 0.0498251491883832, 0.013097222434004192, 0.9869027775659958),
    (76, 0.0996502983767664, 0.5894574662299644, 0.41054253377003563),
    (76, 0.1993005967535328, 0.9959745862539909, 0.004025413746009064),
    (76, 0.29895089513029915, 0.9999983873322321, 1.6126677678606186e-06),
    (76, 0.3986011935070656, 0.9999999999791198, 2.0880151803638377e-11),
    (76, 0.498251491883832, 1.0, 5.802464167695136e-18),
    (77, 0.019800220770905777, 1.0750278083453488e-14, 0.9999999999999892),
    (77, 0.02475027596363222, 1.362283776129616e-09, 0.9999999986377163),
    (77, 0.033000367951509624, 1.5318827060847266e-05, 0.9999846811729391),
    (77, 0.04950055192726444, 0.013064655383629583, 0.9869353446163704),
    (77, 0.09900110385452889, 0.5892910051177497, 0.4107089948822503),
    (77, 0.19800220770905777, 0.9959690408475399, 0.004030959152460125),
    (77, 0.29700331156358667, 0.9999983797359203, 1.6202640796791095e-06),
    (77, 0.39600441541811554, 0.9999999999788215, 2.1178481456379565e-11),
    (77, 0.4950055192726444, 1.0, 6.023443122859171e-18),
    (78, 0.019672886840678448, 1.0487137656197683e-14, 0.9999999999999896),
    (78, 0.02459110855084806, 1.341895316974186e-09, 0.9999999986581047),
    (78, 0.03278814473446408, 1.5207817055590119e-05, 0.9999847921829444),
    (78, 0.04918221710169612, 0.013032735888339347, 0.9869672641116607),
    (78, 0.09836443420339223, 0.5891276609407298, 0.4108723390592703),
    (78, 0.19672886840678447, 0.9959636098879499, 0.004036390112050175),
    (78, 0.2950933026101767, 0.99999837229465, 1.6277053499619562e-06),
    (78, 0.39345773681356894, 0.9999999999785272, 2.1472797893940612e-11),
    (78, 0.4918221710169612, 1.0, 6.2459463995567295e-18),
    (79, 0.019547978359779714, 1.0232074343994918e-14, 0.9999999999999898),
    (79, 0.024434972949724642, 1.3219986694660736e-09, 0.9999999986780014),
    (79, 0.03257996393296619, 1.5099325292992408e-05, 0.999984900674707),
    (79, 0.048869945899449284, 0.013001446652429704, 0.9869985533475703),
    (79, 0.09773989179889857, 0.5889673368874796, 0.41103266311252046),
    (79, 0.19547978359779714, 0.9959582895722998, 0.004041710427700143),
    (79, 0.2932196753966957, 0.9999983650035413, 1.6349964586201457e-06),
    (79, 0.39095956719559427, 0.9999999999782369, 2.176316058860531e-11),
    (79, 0.48869945899449285, 1.0, 6.469846862671229e-18),
    (80, 0.019425419293543855, 9.985070676647448e-15, 0.99999999999999),
    (80, 0.024281774116929816, 1.302567103777691e-09, 0.999999998697433),
    (80, 0.03237569882257309, 1.499325238814942e-05, 0.9999850067476118),
    (80, 0.04856354823385963, 0.012970770619725512, 0.9870292293802745),
    (80, 0.09712709646771926, 0.5888099403889897, 0.4111900596110103),
    (80, 0.19425419293543852, 0.995953076270346, 0.004046923729654035),
    (80, 0.2913812894031578, 0.9999983578579191, 1.6421420809058457e-06),
    (80, 0.38850838587087705, 0.9999999999779504, 2.2049629252606066e-11),
    (80, 0.4856354823385963, 1.0, 6.695022301325512e-18),
    (81, 0.019305136903022223, 9.746057461580266e-15, 0.9999999999999902),
    (81, 0.024131421128777777, 1.2835768060008362e-09, 0.9999999987164232),
    (81, 0.0321752281717037, 1.4889504103632389e-05, 0.9999851104958963),
    (81, 0.048262842257555554, 0.012940690842596882, 0.9870593091574031),
    (81, 0.09652568451511111, 0.5886553828758538, 0.4113446171241461),
    (81, 0.19305136903022221, 0.9959479665146377, 0.00405203348536233),
    (81, 0.2895770535453333, 0.999998350853302, 1.6491466980175558e-06),
    (81, 0.38610273806044443, 0.9999999999776678, 2.2332263689428797e-11),
    (81, 0.48262842257555555, 1.0, 6.9213553300665745e-18),
    (82, 0.019187061563561227, 9.514923594218317e-15, 0.9999999999999905),
    (82, 0.02398382695445153, 1.265006794054876e-09, 0.9999999987349932),
    (82, 0.031978435939268704, 1.4787991250457504e-05, 0.9999852120087496),
    (82, 0.04796765390890306, 0.012911190358242737, 0.9870888096417573),
    (82, 0.09593530781780613, 0.5885035795451777, 0.4114964204548223),
    (82, 0.19187061563561225, 0.9959429569913141, 0.00405704300868596),
    (82, 0.2878059234534184, 0.9999983439853929, 1.6560146070578418e-06),
    (82, 0.3837412312712245, 0.9999999999773889, 2.2611123662178636e-11),
    (82, 0.47967653908903063, 1.0, 7.148733281626678e-18),
    (83, 0.01907112659543907, 9.291524410202806e-15, 0.9999999999999907),
    (83, 0.023838908244298837, 1.2468388336475215e-09, 0.9999999987531611),
    (83, 0.03178521099239845, 1.4688629562841004e-05, 0.9999853113704371),
    (83, 0.047677816488597674, 0.012882252071219123, 0.9871177479287809),
    (83, 0.09535563297719535, 0.588354449139634, 0.41164555086036597),
    (83, 0.1907112659543907, 0.995938044531525, 0.004061955468475021),
    (83, 0.28606689893158604, 0.9999983372500696, 1.662749930388494e-06),
    (83, 0.3814225319087814, 0.9999999999771138, 2.2886268777281102e-11),
    (83, 0.47677816488597674, 1.0, 7.377048092981217e-18),
    (84, 0.018957268105625293, 9.07568877522366e-15, 0.9999999999999909),
    (84, 0.023696585132031614, 1.2290573547365393e-09, 0.9999999987709427),
    (84, 0.03159544684270882, 1.4591339552103143e-05, 0.9999854086604479),
    (84, 0.04739317026406323, 0.012853858641292133, 0.9871461413587078),
    (84, 0.09478634052812646, 0.588207913740958, 0.41179208625904196),
    (84, 0.1895726810562529, 0.9959332261034282, 0.004066773896571803),
    (84, 0.28435902158437937, 0.9999983306433756, 1.6693566244248027e-06),
    (84, 0.3791453621125058, 0.9999999999768422, 2.3157758381974506e-11),
    (84, 0.4739317026406323, 1.0, 7.60619618621247e-18),
    (85, 0.018845424839810002, 8.867225084747307e-15, 0.9999999999999911),
    (85, 0.023556781049762502, 1.211652310766779e-09, 0.9999999987883477),
    (85, 0.031409041399683334, 1.4496046344275515e-05, 0.9999855039536557),
    (85, 0.047113562099525004, 0.012825992375929457, 0.9871740076240706),
    (85, 0.09422712419905001, 0.5880638985796418, 0.41193610142035825),
    (85, 0.18845424839810002, 0.995928498804717, 0.004071501195282954),
    (85, 0.28268137259715004, 0.9999983241615121, 1.6758384879072325e-06),
    (85, 0.37690849679620003, 0.9999999999765743, 2.342565147419714e-11),
    (85, 0.47113562099525, 1.0, 7.836078345491686e-18),
    (86, 0.018735538043924322, 8.665926324609899e-15, 0.9999999999999913),
    (86, 0.0234194225549054, 1.1947104887065129e-09, 0.9999999988052896),
    (86, 0.031225896739873867, 1.4402679505282562e-05, 0.9999855973204947),
    (86, 0.0468388451098108, 0.012798635268724708, 0.9872013647312753),
    (86, 0.0936776902196216, 0.58792233186161, 0.4120776681383899),
    (86, 0.1873553804392432, 0.9959238598556381, 0.004076140144361852),
    (86, 0.28103307065886485, 0.9999983178008303, 1.6821991696860152e-06),
    (86, 0.3747107608784864, 0.99999999997631, 2.3690006623617436e-11),
    (86, 0.468388451098108, 1.0, 8.066599591323909e-18),
    (87, 0.01862755133444083, 8.471574324300877e-15, 0.9999999999999916),
    (87, 0.023284439168051035, 1.1782635532954358e-09, 0.9999999988217364),
    (87, 0.031045918890734714, 1.4311172856999853e-05, 0.999985688827143),
    (87, 0.04656887833610207, 0.012771769807943827, 0.9872282301920562),
    (87, 0.09313775667220414, 0.5877831446112737, 0.41221685538872627),
    (87, 0.18627551334440828, 0.9959193065924615, 0.0040806934075385244),
    (87, 0.2794132700166124, 0.9999983115578239, 1.688442176051403e-06),
    (87, 0.37255102668881657, 0.9999999999760492, 2.3950881902677452e-11),
    (87, 0.4656887833610207, 1.0, 8.297669053045905e-18),
    (88, 0.018521410576803607, 8.283943317694853e-15, 0.9999999999999917),
    (88, 0.02315176322100451, 1.1622939178544292e-09, 0.9999999988377061),
    (88, 0.03086901762800601, 1.422146428701172e-05, 0.999985778535713),
    (88, 0.04630352644200902, 0.012745379480982614, 0.9872546205190174),
    (88, 0.09260705288401803, 0.5876462705289613, 0.4123537294710387),
    (88, 0.18521410576803607, 0.9959148364613687, 0.0040851635386312795),
    (88, 0.2778211586520541, 0.9999983054291224, 1.6945708776399382e-06),
    (88, 0.37042821153607214, 0.9999999999757917, 2.420833482663425e-11),
    (88, 0.4630352644200902, 1.0, 8.52919984043348e-18),
    (89, 0.018417063771392492, 8.102802910864529e-15, 0.9999999999999919),
    (89, 0.023021329714240615, 1.1467842932801265e-09, 0.9999999988532157),
    (89, 0.030695106285654153, 1.4133495554489688e-05, 0.9999858665044455),
    (89, 0.04604265942848123, 0.012719448727698202, 0.9872805512723017),
    (89, 0.09208531885696246, 0.5875116458602513, 0.4124883541397487),
    (89, 0.18417063771392492, 0.9959104470127288, 0.004089552987271189),
    (89, 0.27625595657088736, 0.9999982994114841, 1.700588515944805e-06),
    (89, 0.36834127542784983, 0.9999999999755376, 2.4462422301681818e-11),
    (89, 0.4604265942848123, 1.0, 8.761108915152027e-18),
    (90, 0.0183144609464758, 7.927920543272774e-15, 0.9999999999999921),
    (90, 0.022893076183094753, 1.1317177474311368e-09, 0.9999999988682823),
    (90, 0.03052410157745967, 1.4047212094273703e-05, 0.9999859527879057),
    (90, 0.045786152366189506, 0.012693962870558332, 0.9873060371294416),
    (90, 0.09157230473237901, 0.5873792092750435, 0.4126207907249565),
    (90, 0.18314460946475802, 0.995906135895732, 0.004093864104268039),
    (90, 0.27471691419713706, 0.9999982935017906, 1.7064982094562501e-06),
    (90, 0.36628921892951605, 0.9999999999752868, 2.471320058033055e-11),
    (90, 0.45786152366189503, 1.0, 8.993316962681517e-18),
    (91, 0.01821355405765104, 7.759063516938617e-15, 0.9999999999999922),
    (91, 0.022766942572063797, 1.1170777520196935e-09, 0.9999999988829222),
    (91, 0.030355923429418397, 1.3962562820957933e-05, 0.9999860374371791),
    (91, 0.045533885144127595, 0.012668908049943998, 0.987331091950056),
    (91, 0.09106777028825519, 0.5872489017546583, 0.41275109824534173),
    (91, 0.18213554057651038, 0.9959019008533562, 0.00409809914664379),
    (91, 0.27320331086476557, 0.9999982876970406, 1.71230295945614e-06),
    (91, 0.36427108115302076, 0.9999999999750393, 2.496072522329792e-11),
    (91, 0.45533885144127595, 1.0, 9.225748265248749e-18),
    (92, 0.018114296893313807, 7.596000657928115e-15, 0.9999999999999925),
    (92, 0.022642871116642257, 1.1028482189259648e-09, 0.9999999988971517),
    (92, 0.030190494822189676, 1.387949993454078e-05, 0.9999861205000654),
    (92, 0.045285742233284514, 0.012644271164251118, 0.9873557288357488),
    (92, 0.09057148446656903, 0.5871206664856273, 0.4128793335143726),
    (92, 0.18114296893313805, 0.9958977397176423, 0.0041022602823577335),
    (92, 0.27171445339970707, 0.9999982819943445, 1.7180056554890431e-06),
    (92, 0.3622859378662761, 0.9999999999747949, 2.5205051067245172e-11),
    (92, 0.45285742233284515, 1.0, 9.458330576223577e-18),
    (93, 0.01801664498573259, 7.438503665600497e-15, 0.9999999999999926),
    (93, 0.02252080623216574, 1.0890135275744314e-09, 0.9999999989109865),
    (93, 0.03002774164288765, 1.3797978729004927e-05, 0.999986202021271),
    (93, 0.04504161246433148, 0.012620039814452455, 0.9873799601855475),
    (93, 0.09008322492866296, 0.5869944487591743, 0.4130055512408258),
    (93, 0.1801664498573259, 0.9958936504052549, 0.004106349594745102),
    (93, 0.2702496747859889, 0.9999982763909194, 1.723609080530511e-06),
    (93, 0.3603328997146518, 0.9999999999745538, 2.544623219774945e-11),
    (93, 0.45041612464331476, 1.0, 9.690994996352918e-18),
    (94, 0.017920555527340624, 7.286348197264627e-15, 0.9999999999999927),
    (94, 0.02240069440917578, 1.0755585447727658e-09, 0.9999999989244415),
    (94, 0.029867592545567704, 1.3717957405021062e-05, 0.999986282042595),
    (94, 0.04480138881835156, 0.01259620225279532, 0.9874037977472047),
    (94, 0.08960277763670312, 0.5868701958756394, 0.4131298041243606),
    (94, 0.17920555527340623, 0.9958896309133105, 0.004110369086689544),
    (94, 0.26880833291010936, 0.9999982708840841, 1.7291159158718403e-06),
    (94, 0.35841111054681246, 0.9999999999743157, 2.568432192697119e-11),
    (94, 0.44801388818351556, 1.0, 9.923675852151866e-18),
    (95, 0.017825987291886933, 7.139314729167165e-15, 0.9999999999999929),
    (95, 0.022282484114858666, 1.062468638209419e-09, 0.9999999989375313),
    (95, 0.029709978819811553, 1.3639396887832047e-05, 0.9999863606031122),
    (95, 0.04456496822971733, 0.012572747335327586, 0.9874272526646725),
    (95, 0.08912993645943466, 0.5867478570533302, 0.4132521429466698),
    (95, 0.17825987291886933, 0.995885679315452, 0.004114320684548024),
    (95, 0.267389809378304, 0.9999982654712543, 1.7345287457391161e-06),
    (95, 0.35651974583773866, 0.9999999999740806, 2.591937277552384e-11),
    (95, 0.44564968229717333, 1.0, 1.0156310576709872e-17),
    (96, 0.01773290056011673, 6.9971892288947465e-15, 0.999999999999993),
    (96, 0.022166125700145912, 1.0497296846307927e-09, 0.9999999989502704),
    (96, 0.029554834266861216, 1.3562260651257508e-05, 0.9999864377393487),
    (96, 0.044332251400291824, 0.012549664477961454, 0.9874503355220385),
    (96, 0.08866450280058365, 0.5866273833414452, 0.4133726166585549),
    (96, 0.1773290056011673, 0.9958817937581548, 0.004118206241845255),
    (96, 0.26599350840175096, 0.9999982601499383, 1.7398500616632288e-06),
    (96, 0.3546580112023346, 0.9999999999738486, 2.6151436458103163e-11),
    (96, 0.4433225140029182, 1.0, 1.0388839593121148e-17),
    (97, 0.017641257049676812, 6.8597636692246335e-15, 0.9999999999999931),
    (97, 0.022051571312096015, 1.0373280735687962e-09, 0.9999999989626719),
    (97, 0.029402095082794684, 1.3486514548661403e-05, 0.9999865134854513),
    (97, 0.04410314262419203, 0.012526943615802453, 0.9874730563841976),
    (97, 0.08820628524838406, 0.586508727536856, 0.413491272463144),
    (97, 0.17641257049676812, 0.9958779724572466, 0.004122027542753387),
    (97, 0.2646188557451522, 0.9999982549177334, 1.7450822666162424e-06),
    (97, 0.35282514099353623, 0.9999999999736194, 2.638056387247388e-11),
    (97, 0.44103142624192027, 1.0, 1.0621206200703813e-17),
    (98, 0.017551019848965014, 6.72683640910105e-15, 0.9999999999999932),
    (98, 0.021938774811206267, 1.0252507073607111e-09, 0.9999999989747493),
    (98, 0.02925169974827502, 1.341212665164477e-05, 0.9999865878733484),
    (98, 0.04387754962241253, 0.01250457516548878, 0.9874954248345112),
    (98, 0.08775509924482507, 0.5863918441046233, 0.41360815589537664),
    (98, 0.17551019848965013, 0.9958742136946284, 0.0041257863053715945),
    (98, 0.2632652977344752, 0.9999982497723211, 1.7502276789284798e-06),
    (98, 0.35102039697930026, 0.9999999999733932, 2.6606805091456452e-11),
    (98, 0.4387754962241253, 1.0, 1.0853356464139913e-17),
    (99, 0.0174621533546641, 6.598212463657343e-15, 0.9999999999999934),
    (99, 0.021827691693330126, 1.013484998093267e-09, 0.999999998986515),
    (99, 0.029103588924440166, 1.3339067097159941e-05, 0.9999866609329029),
    (99, 0.04365538338666025, 0.012482549990305214, 0.9875174500096948),
    (99, 0.0873107667733205, 0.5862766891021863, 0.4137233108978137),
    (99, 0.174621533546641, 0.9958705158151812, 0.004129484184818898),
    (99, 0.2619323003199615, 0.999998244711464, 1.7552885359997216e-06),
    (99, 0.349243067093282, 0.9999999999731698, 2.6830209357585597e-11),
    (99, 0.4365538338666025, 1.0, 1.1085239105629122e-17),
    # Second series: samples 100+, step 10.
    (100, 0.01737462321272, 6.473703681969444e-15, 0.9999999999999936),
    (100, 0.0217182790159, 1.0020188620082437e-09, 0.9999999989979811),
    (100, 0.028957705354533333, 1.326730794368905e-05, 0.9999867326920563),
    (100, 0.0434365580318, 0.012460859367854071, 0.9875391406321459),
    (100, 0.0868731160636, 0.5861632201072006, 0.41383677989279943),
    (100, 0.1737462321272, 0.9958668772238473, 0.004133122776152691),
    (100, 0.2606193481908, 0.9999982397330022, 1.7602669978170197e-06),
    (100, 0.3474924642544, 0.9999999999729492, 2.7050825080149146e-11),
    (100, 0.434365580318, 1.0, 1.1316805400125278e-17),
    (110, 0.016566053235566584, 5.418491679241947e-15, 0.9999999999999946),
    (110, 0.02070756654445823, 9.015166010325563e-10, 0.9999999990984834),
    (110, 0.027610088725944303, 1.2616166581384716e-05, 0.9999873838334186),
    (110, 0.04141513308891646, 0.012260676886138374, 0.9877393231138616),
    (110, 0.08283026617783291, 0.5851128879792205, 0.4148871120207796),
    (110, 0.16566053235566583, 0.9958334390971256, 0.004166560902874364),
    (110, 0.24849079853349876, 0.9999981940540781, 1.8059459218939107e-06),
    (110, 0.33132106471133166, 0.9999999999708863, 2.911366993335675e-11),
    (110, 0.41415133088916456, 1.0, 1.360598090677705e-17),
    (120, 0.01586078843626604, 4.6172675254482685e-15, 0.9999999999999953),
    (120, 0.01982598554533255, 8.209916165276452e-10, 0.9999999991790084),
    (120, 0.026434647393776732, 1.206852433035564e-05, 0.9999879314756697),
    (120, 0.0396519710906651, 0.012086513441053544, 0.9879134865589465),
    (120, 0.0793039421813302, 0.5841935646900176, 0.4158064353099824),
    (120, 0.1586078843626604, 0.9958045317953282, 0.004195468204671804),
    (120, 0.23791182654399062, 0.9999981547040431, 1.8452959569129297e-06),
    (120, 0.3172157687253208, 0.9999999999690551, 3.094487216616905e-11),
    (120, 0.396519710906651, 1.0, 1.5825362299251e-17),
    (130, 0.015238552621154138, 3.981506971376443e-15, 0.999999999999996),
    (130, 0.01904819077644267, 7.54742270424985e-10, 0.9999999992452577),
    (130, 0.02539758770192356, 1.1599452167384703e-05, 0.9999884005478327),
    (130, 0.03809638155288534, 0.011933357410775438, 0.9880666425892246),
    (130, 0.07619276310577068, 0.5833799866886901, 0.41662001331130993),
    (130, 0.15238552621154136, 0.9957792304905194, 0.00422076950948053),
    (130, 0.22857828931731206, 0.9999981204045577, 1.8795954422729057e-06),
    (130, 0.3047710524230827, 0.99999999996742, 3.25800610004164e-11),
    (130, 0.3809638155288534, 1.0, 1.7955255730886202e-17),
    (140, 0.014684236732535156, 3.467961744829668e-15, 0.9999999999999966),
    (140, 0.018355295915668944, 6.99239619609546e-10, 0.9999999993007603),
    (140, 0.02447372788755859, 1.1191396098096952e-05, 0.9999888086039019),
    (140, 0.03671059183133789, 0.011797290695073515, 0.9882027093049265),
    (140, 0.07342118366267578, 0.5826532396068723, 0.4173467603931277),
    (140, 0.14684236732535155, 0.995756852946992, 0.004243147053008),
    (140, 0.22026355098802733, 0.999998090204374, 1.909795625975354e-06),
    (140, 0.2936847346507031, 0.9999999999659516, 3.404848092024851e-11),
    (140, 0.3671059183133789, 1.0, 1.9986084638001886e-17),
    (150, 0.014186320448093382, 3.0580781142008757e-15, 0.9999999999999969),
    (150, 0.017732900560116727, 6.520586846457575e-10, 0.9999999993479414),
    (150, 0.023643867413488968, 1.0832191336423938e-05, 0.9999891678086635),
    (150, 0.03546580112023345, 0.011675320822642561, 0.9883246791773574),
    (150, 0.0709316022404669, 0.5819988398054936, 0.4180011601945064),
    (150, 0.1418632044809338, 0.9957368837260597, 0.004263116273940285),
    (150, 0.21279480672140072, 0.9999980633804098, 1.9366195902653106e-06),
    (150, 0.2837264089618676, 0.9999999999646259, 3.5374145080912415e-11),
    (150, 0.35465801120233453, 1.0, 2.191463384552106e-17),
    (160, 0.01373584570985685, 2.7263588495283635e-15, 0.9999999999999972),
    (160, 0.017169807137321063, 6.114209920922329e-10, 0.999999999388579),
    (160, 0.02289307618309475, 1.0513079035720533e-05, 0.9999894869209642),
    (160, 0.034339614274642126, 0.011565192341321192, 0.9884348076586789),
    (160, 0.06867922854928425, 0.5814054821769084, 0.41859451782309165),
    (160, 0.1373584570985685, 0.9957189253833221, 0.004281074616677893),
    (160, 0.20603768564785274, 0.9999980393727677, 1.9606272322951503e-06),
    (160, 0.274716914197137, 0.9999999999634231, 3.657684300080896e-11),
    (160, 0.3433961427464213, 1.0, 2.3741603934688108e-17),
    (170, 0.013325727698571058, 2.4533724810548926e-15, 0.9999999999999976),
    (170, 0.016657159623213822, 5.760416604228301e-10, 0.9999999994239583),
    (170, 0.022209546164285096, 1.0227551704735477e-05, 0.9999897724482952),
    (170, 0.033314319246427644, 0.011465135234063905, 0.9885348647659361),
    (170, 0.06662863849285529, 0.5808641947136667, 0.41913580528633326),
    (170, 0.13325727698571058, 0.9957026660083748, 0.004297333991625284),
    (170, 0.19988591547856588, 0.9999980177408346, 1.9822591653617204e-06),
    (170, 0.26651455397142115, 0.999999999962327, 3.76729689338356e-11),
    (170, 0.3331431924642764, 1.0, 2.5470032163040355e-17),
    (180, 0.012950279529029236, 2.225110507195331e-15, 0.9999999999999978),
    (180, 0.016187849411286544, 5.449936355876676e-10, 0.9999999994550064),
    (180, 0.021583799215048723, 9.970581871390147e-06, 0.9999900294181286),
    (180, 0.03237569882257309, 0.011373717001139049, 0.9886262829988609),
    (180, 0.06475139764514617, 0.5803677530995353, 0.4196322469004648),
    (180, 0.12950279529029235, 0.9956878570219521, 0.004312142978047954),
    (180, 0.19425419293543852, 0.9999979981328798, 2.001867120222344e-06),
    (180, 0.2590055905805847, 0.9999999999613238, 3.8676185401027866e-11),
    (180, 0.32375698822573085, 1.0, 2.710427853720645e-17),
    (190, 0.012604876495438469, 2.0315954982057123e-15, 0.999999999999998),
    (190, 0.015756095619298086, 5.175952232560829e-10, 0.9999999994824048),
    (190, 0.021008127492397447, 9.73808777931441e-06, 0.9999902619122207),
    (190, 0.03151219123859617, 0.011289763983004028, 0.9887102360169959),
    (190, 0.06302438247719234, 0.5799102654619068, 0.4200897345380932),
    (190, 0.1260487649543847, 0.9956742976148064, 0.004325702385193604),
    (190, 0.18907314743157705, 0.9999979802645377, 2.0197354622726807e-06),
    (190, 0.2520975299087694, 0.999999999960402, 3.959794913718855e-11),
    (190, 0.3151219123859617, 1.0, 2.864937871112668e-17),
    (200, 0.012285713894275511, 1.8657051000674983e-15, 0.9999999999999981),
    (200, 0.015357142367844388, 4.933130219749461e-10, 0.9999999995066869),
    (200, 0.020476189823792516, 9.526580286986155e-06, 0.999990473419713),
    (200, 0.030714284735688775, 0.011212313840533674, 0.9887876861594663),
    (200, 0.06142856947137755, 0.5794868717804904, 0.4205131282195096),
    (200, 0.1228571389427551, 0.995661823605658, 0.004338176394341921),
    (200, 0.18428570841413267, 0.9999979639032807, 2.0360967193278076e-06),
    (200, 0.2457142778855102, 0.999999999959552, 4.0447926822309473e-11),
    (200, 0.30714284735688774, 1.0, 3.011063480783186e-17),
    (210, 0.01198962908564828, 1.7222468212993649e-15, 0.9999999999999982),
    (210, 0.014987036357060349, 4.716495119236842e-10, 0.9999999995283505),
    (210, 0.01998271514274713, 9.333100255542873e-06, 0.9999906668997445),
    (210, 0.029974072714120698, 0.01114057369556164, 0.9888594263044383),
    (210, 0.059948145428241395, 0.5790935223151144, 0.42090647768488565),
    (210, 0.11989629085648279, 0.9956502993106433, 0.004349700689356743),
    (210, 0.17984443628472419, 0.9999979488570164, 2.051142983575276e-06),
    (210, 0.23979258171296558, 0.9999999999587657, 4.123432413049335e-11),
    (210, 0.299740727141207, 1.0, 3.1493360655890154e-17),
    (220, 0.011713968580366477, 1.597253820133587e-15, 0.9999999999999984),
    (220, 0.014642460725458096, 4.5218876343752577e-10, 0.9999999995478113),
    (220, 0.01952328096727746, 9.155257709706761e-06, 0.9999908447422903),
    (220, 0.029284921450916192, 0.011073880810536216, 0.9889261191894638),
    (220, 0.058569842901832384, 0.578726811579811, 0.421273188420189),
    (220, 0.11713968580366477, 0.9956396115091443, 0.004360388490855694),
    (220, 0.17570952870549716, 0.9999979349655841, 2.065034415900981e-06),
    (220, 0.23427937160732953, 0.9999999999580359, 4.1964147106247866e-11),
    (220, 0.2928492145091619, 1.0, 3.2802727275448543e-17),
    (230, 0.011456487279076742, 1.4875629925071446e-15, 0.9999999999999986),
    (230, 0.014320609098845928, 4.3460119911200134e-10, 0.9999999995653988),
    (230, 0.0190941454651279, 8.991108881784716e-06, 0.9999910088911182),
    (230, 0.028641218197691855, 0.0110116741169428, 0.9889883258830572),
    (230, 0.05728243639538371, 0.5783838521279262, 0.4216161478720738),
    (230, 0.11456487279076742, 0.995629664896983, 0.00437033510301704),
    (230, 0.17184730918615113, 0.9999979220943207, 2.07790567932335e-06),
    (230, 0.22912974558153484, 0.9999999999573566, 4.26434107907295e-11),
    (230, 0.28641218197691853, 1.0, 3.404367337034118e-17),
    (240, 0.011215271058248894, 1.3906448045848905e-15, 0.9999999999999986),
    (240, 0.014019088822811117, 4.1862247361792736e-10, 0.9999999995813775),
    (240, 0.018692118430414822, 8.83904794417799e-06, 0.9999911609520559),
    (240, 0.028038177645622234, 0.010953474765533827, 0.9890465252344661),
    (240, 0.05607635529124447, 0.5780621773247729, 0.42193782267522706),
    (240, 0.11215271058248893, 0.9956203786130886, 0.0043796213869113365),
    (240, 0.1682290658737334, 0.9999979101291312, 2.089870868772373e-06),
    (240, 0.22430542116497787, 0.9999999999567227, 4.327730665901717e-11),
    (240, 0.2803817764562223, 1.0, 3.522085780829751e-17),
    (250, 0.010988676567885483, 1.3044830459729999e-15, 0.9999999999999987),
    (250, 0.013735845709856852, 4.040376222081045e-10, 0.9999999995959624),
    (250, 0.0183144609464758, 8.697728404554118e-06, 0.9999913022715955),
    (250, 0.027471691419713704, 0.010898871937950695, 0.9891011280620493),
    (250, 0.05494338283942741, 0.5777596655495548, 0.4222403344504452),
    (250, 0.10988676567885482, 0.9956116835530071, 0.004388316446992907),
    (250, 0.16483014851828223, 0.9999978989726668, 2.101027333222321e-06),
    (250, 0.21977353135770963, 0.9999999999561296, 4.3870337779742716e-11),
    (250, 0.27471691419713706, 1.0, 3.633863900395765e-17))

# Values produced by the Marsaglia & Tsang code (without its approximation).
# With about 14 digits of accuracy. See doi:10.18637/jss.v008.i18.
# The statistics are 1/5, 1/4, ..., 4, 5 times the mean for each sample count.
marsaglia_values = (
    (10, .054943382839427402, .32382132520535754e-13),
    (10, .068679228549284252, .19215529170715173e-7),
    (10, .091572304732378998, .57293322784834989e-4),
    (10, .1373584570985685, .021523322622349104),
    (10, .27471691419713701, .63156658894271622),
    (10, .54943382839427402, .99768559162369053),
    (10, .82415074259141097, .9999999420800233),
    (10, 1.098867656788548, 1),
    (10, 1.3735845709856851, 1),
    (20, .038850838587087703, .17228437581696657e-12),
    (20, .048563548233859631, .71045779730765533e-8),
    (20, .064751397645146175, .3667930830876966e-4),
    (20, .097127096467719262, .017985829271761268),
    (20, .19425419293543852, .6127380411231369),
    (20, .38850838587087705, .996854534409372),
    (20, .58276257880631555, .99999944503234328),
    (20, .7770167717417541, .99999999999970091),
    (20, .97127096467719265, 1.0000000000000004),
    (30, .031721576872532083, .60940362155938466e-13),
    (30, .039651971090665102, .45636258941820899e-8),
    (30, .052869294787553471, .27728653822523069e-4),
    (30, .079303942181330203, .016061192511760566),
    (30, .15860788436266041, .6041862525220193),
    (30, .31721576872532081, .99650770235258646),
    (30, .47582365308798125, .9999990779543303),
    (30, .63443153745064162, .99999999999695954),
    (30, .793039421813302, .99999999999999878),
    (40, .027471691419713701, .44890656943321606e-13),
    (40, .034339614274642126, .29755417909055264e-8),
    (40, .045786152366189499, .2305894059904745e-4),
    (40, .068679228549284252, .015007081301604349),
    (40, .1373584570985685, .59896461546470081),
    (40, .27471691419713701, .9963091952001456),
    (40, .41207537129570548, .99999883398748979),
    (40, .54943382839427402, .99999999999274536),
    (40, .68679228549284255, 1),
    (50, .024571427788551019, .26278753848717178e-13),
    (50, .030714284735688775, .22809622413858878e-8),
    (50, .040952379647585031, .19914256263711656e-4),
    (50, .06142856947137755, .014261793427981397),
    (50, .1228571389427551, .59534554170231924),
    (50, .2457142778855102, .99617770116110449),
    (50, .36857141682826533, .99999866231263879),
    (50, .4914285557710204, .99999999998842937),
    (50, .61428569471377548, .99999999999999911),
    (60, .022430542116497788, .17306629728992625e-13),
    (60, .028038177645622234, .18255819850919381e-8),
    (60, .037384236860829645, .17723225033102087e-4),
    (60, .056076355291244467, .01372402561964047),
    (60, .11215271058248893, .59264451465977663),
    (60, .22430542116497787, .99608285271783381),
    (60, .3364581317474668, .99999853494355739),
    (60, .44861084232995574, .99999999998448241),
    (60, .56076355291244462, .99999999999999933),
    (70, .020766646740248397, .12832664352687508e-13),
    (70, .025958308425310498, .15216690215385908e-8),
    (70, .034611077900413997, .16175881497136119e-4),
    (70, .051916616850620996, .013307259395076043),
    (70, .10383323370124199, .59052770891543271),
    (70, .20766646740248398, .99601049965278143),
    (70, .31149970110372599, .99999843646804842),
    (70, .41533293480496797, .99999999998099642),
    (70, .51916616850621, 1),
    (80, .019425419293543852, .99850706766473548e-14),
    (80, .024281774116929816, .13025671037776924e-8),
    (80, .032375698822573087, .14993252388149402e-4),
    (80, .048563548233859631, .012970770619725519),
    (80, .097127096467719262, .58880994038898993),
    (80, .19425419293543852, .99595307627034479),
    (80, .29138128940315777, .99999835785791991),
    (80, .38850838587087705, .99999999997795064),
    (80, .48563548233859632, 1.0000000000000004),
    (90, .018314460946475802, .7927920543272791e-14),
    (90, .022893076183094753, .11317177474311404e-8),
    (90, .030524101577459672, .14047212094273758e-4),
    (90, .045786152366189506, .012693962870558333),
    (90, .091572304732379012, .58737920927504295),
    (90, .18314460946475802, .99590613589573118),
    (90, .27471691419713706, .9999982935017897),
    (90, .36628921892951605, .99999999997528766),
    (90, .45786152366189503, .99999999999999933),
    (100, .01737462321272, .64737036819694295e-14),
    (100, .0217182790159, .10020188620082422e-8),
    (100, .028957705354533333, .13267307943689059e-4),
    (100, .0434365580318, .012460859367854047),
    (100, .0868731160636, .58616322010719946),
    (100, .1737462321272, .99586687722384593),
    (100, .26061934819080002, .99999823973299984),
    (100, .3474924642544, .99999999997294875),
    (100, .43436558031799999, .99999999999999956),
    (110, .016566053235566584, .54184916792419637e-14),
    (110, .020707566544458229, .90151660103256042e-9),
    (110, .027610088725944306, .12616166581384756e-4),
    (110, .041415133088916457, .012260676886138374),
    (110, .082830266177832915, .58511288797921979),
    (110, .16566053235566583, .99583343909712463),
    (110, .24849079853349876, .99999819405407697),
    (110, .33132106471133166, .99999999997088418),
    (110, .41415133088916456, .99999999999999856),
    (120, .015860788436266041, .4617267525448274e-14),
    (120, .019825985545332551, .82099161652764474e-9),
    (120, .026434647393776736, .12068524330355696e-4),
    (120, .039651971090665102, .012086513441053538),
    (120, .079303942181330203, .58419356469001682),
    (120, .15860788436266041, .99580453179532702),
    (120, .23791182654399062, .99999815470404096),
    (120, .31721576872532081, .99999999996905387),
    (120, .396519710906651, .999999999999999),
    (130, .015238552621154136, .39815069713764172e-14),
    (130, .01904819077644267, .75474227042498141e-9),
    (130, .02539758770192356, .11599452167384669e-4),
    (130, .03809638155288534, .011933357410775435),
    (130, .076192763105770681, .58337998668868973),
    (130, .15238552621154136, .9957792304905192),
    (130, .22857828931731206, .99999812040455627),
    (130, .30477105242308272, .99999999996741806),
    (130, .38096381552885339, 1.0000000000000004),
    (140, .014684236732535156, .34679617448296338e-14),
    (140, .018355295915668944, .69923961960954503e-9),
    (140, .024473727887558593, .11191396098097002e-4),
    (140, .036710591831337888, .011797290695073522),
    (140, .073421183662675776, .58265323960687143),
    (140, .14684236732535155, .99575685294699101),
    (140, .22026355098802733, .99999809020437347),
    (140, .29368473465070311, .99999999996595057),
    (140, .36710591831337891, .99999999999999856),
    (150, .014186320448093381, .30580781142008584e-14),
    (150, .017732900560116727, .65205868464575603e-9),
    (150, .023643867413488968, .10832191336423951e-4),
    (150, .035465801120233453, .011675320822642552),
    (150, .070931602240466907, .5819988398054935),
    (150, .14186320448093381, .9957368837260604),
    (150, .21279480672140072, .99999806338040875),
    (150, .28372640896186763, .99999999996462352),
    (150, .35465801120233453, .99999999999999922),
    (160, .01373584570985685, .27263588495283679e-14),
    (160, .017169807137321063, .6114209920922327e-9),
    (160, .022893076183094749, .10513079035720496e-4),
    (160, .034339614274642126, .011565192341321183),
    (160, .068679228549284252, .58140548217690802),
    (160, .1373584570985685, .99571892538332352),
    (160, .20603768564785274, .99999803937276766),
    (160, .27471691419713701, .99999999996342326),
    (160, .34339614274642127, 1.0000000000000002),
    (170, .013325727698571058, .24533724810549112e-14),
    (170, .016657159623213822, .57604166042282698e-9),
    (170, .022209546164285096, .10227551704735462e-4),
    (170, .033314319246427644, .011465135234063907),
    (170, .066628638492855288, .58086419471366657),
    (170, .13325727698571058, .99570266600837387),
    (170, .19988591547856588, .99999801774083474),
    (170, .26651455397142115, .99999999996232791),
    (170, .33314319246427643, .99999999999999867),
    (180, .012950279529029236, .2225110507195345e-14),
    (180, .016187849411286544, .54499363558766639e-9),
    (180, .021583799215048726, .99705818713901797e-5),
    (180, .032375698822573087, .011373717001139049),
    (180, .064751397645146175, .58036775309953559),
    (180, .12950279529029235, .99568785702195206),
    (180, .19425419293543852, .99999799813287893),
    (180, .2590055905805847, .99999999996132227),
    (180, .32375698822573085, .99999999999999822),
    (190, .012604876495438469, .2031595498205708e-14),
    (190, .015756095619298086, .51759522325608342e-9),
    (190, .021008127492397447, .97380877793144015e-5),
    (190, .031512191238596172, .011289763983004037),
    (190, .063024382477192345, .57991026546190738),
    (190, .12604876495438469, .99567429761480519),
    (190, .18907314743157705, .99999798026453857),
    (190, .25209752990876938, .99999999996040223),
    (190, .31512191238596171, .99999999999999878),
    (200, .01228571389427551, .18657051000674754e-14),
    (200, .015357142367844388, .49331302197494576e-9),
    (200, .020476189823792516, .95265802869861482e-5),
    (200, .030714284735688775, .011212313840533648),
    (200, .06142856947137755, .57948687178048996),
    (200, .1228571389427551, .99566182360565525),
    (200, .18428570841413267, .99999796390327944),
    (200, .2457142778855102, .99999999995954969),
    (200, .30714284735688774, .999999999999997),
    (200, .01228571389427551, .18657051000674754e-14),
    (200, .015357142367844388, .49331302197494576e-9),
    (200, .020476189823792516, .95265802869861482e-5),
    (200, .030714284735688775, .011212313840533648),
    (200, .06142856947137755, .57948687178048996),
    (200, .1228571389427551, .99566182360565525),
    (200, .18428570841413267, .99999796390327944),
    (200, .2457142778855102, .99999999995954969),
    (200, .30714284735688774, .999999999999997),
    (210, .011989629085648278, .17222468212993471e-14),
    (210, .014987036357060349, .47164951192368483e-9),
    (210, .019982715142747132, .93331002555428238e-5),
    (210, .029974072714120698, .011140573695561642),
    (210, .059948145428241395, .57909352231511191),
    (210, .11989629085648279, .99565029931064097),
    (210, .17984443628472419, .99999794885701365),
    (210, .23979258171296558, .9999999999587631),
    (210, .29974072714120698, .99999999999999811),
    (220, .011713968580366477, .15972538201335833e-14),
    (220, .014642460725458096, .45218876343752385e-9),
    (220, .01952328096727746, .91552577097067593e-5),
    (220, .029284921450916192, .011073880810536183),
    (220, .058569842901832384, .57872681157980899),
    (220, .11713968580366477, .9956396115091426),
    (220, .17570952870549716, .99999793496558276),
    (220, .23427937160732953, .99999999995803535),
    (220, .2928492145091619, .99999999999999789),
    (230, .011456487279076742, .14875629925071405e-14),
    (230, .014320609098845928, .4346011991119999e-9),
    (230, .019094145465127905, .89911088817847063e-5),
    (230, .028641218197691855, .011011674116942765),
    (230, .057282436395383711, .57838385212792487),
    (230, .11456487279076742, .99562966489697979),
    (230, .17184730918615113, .99999792209431815),
    (230, .22912974558153484, .99999999995735223),
    (230, .28641218197691853, .99999999999999789),
    (240, .011215271058248894, .13906448045848864e-14),
    (240, .014019088822811117, .41862247361792715e-9),
    (240, .018692118430414822, .88390479441779598e-5),
    (240, .028038177645622234, .010953474765533813),
    (240, .056076355291244467, .57806217732477083),
    (240, .11215271058248893, .99562037861308472),
    (240, .1682290658737334, .99999791012912809),
    (240, .22430542116497787, .99999999995671951),
    (240, .28038177645622231, .99999999999999722),
    (250, .010988676567885481, .13044830459729825e-14),
    (250, .013735845709856852, .40403762220810372e-9),
    (250, .018314460946475802, .86977284045540992e-5),
    (250, .027471691419713704, .010898871937950664),
    (250, .054943382839427408, .5777596655495536),
    (250, .10988676567885482, .99561168355300456),
    (250, .16483014851828223, .99999789897266367),
    (250, .21977353135770963, .99999999995612765),
    (250, .27471691419713706, .99999999999999689))

# Produced using code from doi:10.18637/jss.v039.i11; above n = 140 various
# approximations are used, that should be correct to at least 5 places,
simard_values = (
    (100, .01737462321272, .64737036819694295e-14),
    (100, .01737462321272, .64737036819694295e-14),
    (100, .0217182790159, .10020188620082422e-8),
    (100, .028957705354533333, .13267307943689059e-4),
    (100, .0434365580318, .012460859367854047),
    (100, .0868731160636, .58616322010718647),
    (100, .1737462321272, .99586687722382983),
    (100, .26061934819080002, .99999823973300217),
    (100, .3474924642544, .99999999997294919),
    (100, .43436558031799999, 1),
    (200, .01228571389427551, .18657051000674754e-14),
    (200, .015357142367844388, .49331302197494576e-9),
    (200, .020476189823792516, .95265802869861482e-5),
    (200, .030714284735688775, .011212313840533648),
    (200, .06142856947137755, .57948780154936952),
    (200, .1228571389427551, .99566173241321476),
    (200, .18428570841413267, .99999796801371688),
    (200, .2457142778855102, .99999999996108679),
    (200, .30714284735688774, 1),
    (500, .0077701677174175409, .49222980407757474e-15),
    (500, .0097127096467719259, .2370492928425123e-9),
    (500, .012950279529029234, .68500245771156684e-5),
    (500, .019425419293543852, .010130922099801815),
    (500, .038850838587087703, .57342737549406875),
    (500, .077701677174175407, .99549119201752911),
    (500, .1165525157612631, .99999775069457475),
    (500, .15540335434835081, .99999999994828859),
    (500, .19425419293543852, 1),
    (1000, .0054943382839427405, .22828291272095521e-15),
    (1000, .0068679228549284261, .15699087359273087e-9),
    (1000, .0091572304732379008, .57173827554681008e-5),
    (1000, .013735845709856852, .0095972657972610842),
    (1000, .027471691419713704, .57032272985354993),
    (1000, .054943382839427408, .995409540843322),
    (1000, .082415074259141116, .99999765686491948),
    (1000, .10988676567885482, .99999999994310595),
    (1000, .13735845709856853, 1),
    (10000, .0017374623212720001, .54268172862651013e-16),
    (10000, .00217182790159, .73977977502723284e-10),
    (10000, .0028957705354533333, .41427919674787538e-5),
    (10000, .00434365580318, .0087354464742361304),
    (10000, .00868731160636, .56512082152219023),
    (10000, .01737462321272, .99528147213504992),
    (10000, .02606193481908, .99999752796750419),
    (10000, .03474924642544, .99999999993678501),
    (10000, .0434365580318, 1),
    (1000000, .00017374623212720002, .27804435836746087e-16),
    (1000000, .00021718279015900001, .52508618772364787e-10),
    (1000000, .00028957705354533332, .35886458051877108e-5),
    (1000000, .00043436558031800001, .0083844278160627207),
    (1000000, .00086873116063600003, .56292657767087761),
    (1000000, .0017374623212720001, .99523074173621529),
    (1000000, .0026061934819080002, .99999748464522642),
    (1000000, .0034749246425440001, .9999999999350736),
    (1000000, .00434365580318, 1))

# By Simard's Pelz-Good code (that should be roughly equivalent to ours).
simard_pelz_values = (
    (10000, .0017374623212720001, .54062919936190177e-16),
    (10000, .00217182790159, .73964566000969386e-10),
    (10000, .0028957705354533333, .41427919674787538e-05),
    (10000, .00434365580318, .0087354464742361304),
    (10000, .00868731160636, .56512082152219023),
    (10000, .01737462321272, .99528147213504992),
    (10000, .02606193481908, .99999752796750419),
    (10000, .03474924642544, .99999999993678501),
    (10000, .0434365580318, .99999999999982658),
    (20000, .0012285713894275509, 4.3820570050344886e-17),
    (20000, .0015357142367844387, 6.630049233533343e-11),
    (20000, .0020476189823792515, 3.9561924437450867e-06),
    (20000, .0030714284735688774, .008620692172980839),
    (20000, .0061428569471377549, .56440863983336531),
    (20000, .01228571389427551, .99526479248545108),
    (20000, .018428570841413264, .99999751317397578),
    (20000, .024571427788551019, .99999999993616517),
    (20000, .030714284735688775, .99999999999982647),
    (30000, .0010031243388932214, 3.9843819583486292e-17),
    (30000, .0012539054236165267, 6.312299969995627e-11),
    (30000, .0016718738981553688, 3.8754743114746502e-06),
    (30000, .0025078108472330533, .008570013062233631),
    (30000, .0050156216944661066, .56409254557761279),
    (30000, .010031243388932213, .9952574553528124),
    (30000, .015046865083398319, .99999750683279676),
    (30000, .020062486777864427, .99999999993590949),
    (30000, .025078108472330534, .99999999999982636),
    (40000, .00086873116063600003, 3.7625558612803881e-17),
    (40000, .001085913950795, 6.1290130087862491e-11),
    (40000, .0014478852677266667, 3.8279204462945956e-06),
    (40000, .00217182790159, .0085398491575781003),
    (40000, .00434365580318, .56390394415322609),
    (40000, .00868731160636, .99525309687989194),
    (40000, .01303096740954, .99999750311532642),
    (40000, .01737462321272, .99999999993576316),
    (40000, .0217182790159, .99999999999982658),
    (50000, .00077701677174175422, 3.6174521055758216e-17),
    (50000, .00097127096467719272, 6.0065081506268013e-11),
    (50000, .0012950279529029237, 3.7957086096396189e-06),
    (50000, .0019425419293543854, .0085192844905780975),
    (50000, .0038850838587087709, .56377516246844517),
    (50000, .0077701677174175417, .99525012910160737),
    (50000, .011655251576126312, .99999750060537107),
    (50000, .015540335434835083, .99999999993566557),
    (50000, .019425419293543855, .99999999999982658),
    (60000, .00070931602240466914, 3.5135217056646299e-17),
    (60000, .0008866450280058364, 5.9174020031217313e-11),
    (60000, .0011821933706744486, 3.7720555765316763e-06),
    (60000, .0017732900560116728, .0085041148231109961),
    (60000, .0035465801120233456, .5636800613370041),
    (60000, .0070931602240466912, .99524794181336085),
    (60000, .010639740336070036, .9999974987666751),
    (60000, .014186320448093382, .99999999993559474),
    (60000, .017732900560116727, .99999999999982647),
    (70000, .0006566990306329601, 3.4345762285363617e-17),
    (70000, .00082087378829120007, 5.8489174499714385e-11),
    (70000, .0010944983843882668, 3.7537454559482322e-06),
    (70000, .0016417475765824001, .0084923311602366561),
    (70000, .0032834951531648003, .56360612621348027),
    (70000, .0065669903063296006, .99524624387097327),
    (70000, .0098504854594944, .9999974973459147),
    (70000, .013133980612659201, .99999999993554045),
    (70000, .016417475765824002, .99999999999982647),
    (80000, .00061428569471377544, 3.3720867987913558e-17),
    (80000, .00076785711839221936, 5.7941994021470206e-11),
    (80000, .0010238094911896257, 3.7390324874861117e-06),
    (80000, .0015357142367844387, .0084828365744289494),
    (80000, .0030714284735688774, .56354651444977188),
    (80000, .0061428569471377549, .99524487648432958),
    (80000, .0092142854207066319, .99999749620594847),
    (80000, .01228571389427551, .99999999993549726),
    (80000, .015357142367844388, .99999999999982669),
    (90000, .00057915410709066665, 3.3210912729122299e-17),
    (90000, .00072394263386333334, 5.7492020003290333e-11),
    (90000, .00096525684515111115, 3.7268768324895699e-06),
    (90000, .0014478852677266667, .0084749747442567445),
    (90000, .0028957705354533333, .56349712743040958),
    (90000, .0057915410709066667, .99524374472729571),
    (90000, .00868731160636, .99999749526526771),
    (90000, .011583082141813333, .99999999993546185),
    (90000, .014478852677266667, .99999999999982658),
    (100000, .00054943382839427407, 3.278486443553414e-17),
    (100000, .00068679228549284256, 5.7113652853325419e-11),
    (100000, .00091572304732379008, 3.7166156362114221e-06),
    (100000, .0013735845709856851, .0084683257638839739),
    (100000, .0027471691419713703, .56345534059919011),
    (100000, .0054943382839427405, .99524278790991583),
    (100000, .0082415074259141116, .99999749447200825),
    (100000, .010988676567885481, .99999999993543198),
    (100000, .01373584570985685, .99999999999982647))

# Some values from (half-width) tables 13 and 14 in doi:10.18637/jss.v026.i02
# (with about 5 digits of accuracy of the probabilities).
brown_values = (
    (2, .683772, .80), (2, .776393, .90), (2, .841886, .95),
    (2, .900000, .98), (2, .929289, .99), (2, .977639, .999),
    (5, .446973, .80), (5, .509449, .90), (5, .563275, .95),
    (5, .627180, .98), (5, .668531, .99), (5, .781369, .999),
    (10, .322568, .80), (10, .368662, .90), (10, .409246, .95),
    (10, .456624, .98), (10, .488932, .99), (10, .580417, .999),
    (20, .231519, .80), (20, .264731, .90), (20, .294075, .95),
    (20, .328661, .98), (20, .352411, .99), (20, .420851, .999),
    (50, .148369, .80), (50, .169592, .90), (50, .188406, .95),
    (50, .210677, .98), (50, .226037, .99), (50, .270675, .999),
    (100, .105605, .80), (100, .120663, .90), (100, .134028, .95),
    (100, .149868, .98), (100, .160809, .99), (100, .192684, .999),
    (200, .0750204, .80), (200, .0856863, .90), (200, .0951578, .95),
    (200, .106391, .98), (200, .114155, .99), (200, .136804, .999),
    (500, .0476412, .80), (500, .0543938, .90), (500, .0603923, .95),
    (500, .0675093, .98), (500, .0724304, .99), (500, .0867964, .999))

# A few values from doi:10.1002/9781119961260.app3 (correct to about 4 places).
oconnor_values = (
    (1, .95000, .90), (1, .97500, .95), (1, .99000, .98), (1, .99500, .99),
    (5, .50945, .90), (5, .56328, .95), (5, .62718, .98), (5, .66853, .99),
    (10, .36866, .90), (10, .40925, .95), (10, .45662, .98), (10, .48893, .99),
    (20, .26473, .90), (20, .29408, .95), (20, .32866, .98), (20, .35241, .99),
    (30, .21756, .90), (30, .24170, .95), (30, .27023, .98), (30, .28987, .99),
    (40, .18913, .90), (40, .21012, .95), (40, .23494, .98), (40, .25205, .99))

# Highly approximate, but hardly computable exactly.
oconnor_asymptotic_values = (
    (10000, .0122, .90), (10000, .0136, .95),
    (10000, .0151, .98), (10000, .0163, .99),
    (1000000, .00122, .90), (1000000, .00136, .95),
    (1000000, .00151, .98), (1000000, .00163, .99),
    (100000000, .000122, .90), (100000000, .000136, .95),
    (100000000, .000151, .98), (100000000, .000163, .99))