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Type 'q()' to quit R. > library(DPQ) > library(DPQmpfr) Attaching package: 'DPQmpfr' The following objects are masked from 'package:DPQ': ldexp, pnormAsymp, pnormL_LD10, pnormU_S53, qnormAsymp > > ## Imported from 'DPQ', support of the hypergeometric distrib. as function of its parameters: > ## .suppHyper <- DPQ::.suppHyper > .suppHyper <- function(m,n,k) max(0, k-n) : min(k, m) > > ## case where phyper(*, log=TRUE) fails : > phyper(11, 15, 0, 12) # 0 -- correct [1] 0 > phyper(11, 15, 0, 12, log=TRUE) # NaN || correct value: log(0) = -Inf [1] -Inf > (phyp5.0.12 <- cumsum(dhyperQ(0:12, m=15,n=0,k=12))) Big Rational ('bigq') object of length 13: [1] 0 0 0 0 0 0 0 0 0 0 0 0 1 > > require(Rmpfr) Loading required package: Rmpfr Loading required package: gmp Attaching package: 'gmp' The following objects are masked from 'package:base': %*%, apply, crossprod, matrix, tcrossprod C code of R package 'Rmpfr': GMP using 64 bits per limb Attaching package: 'Rmpfr' The following object is masked from 'package:gmp': outer The following object is masked from 'package:DPQ': log1mexp The following objects are masked from 'package:stats': dbinom, dgamma, dnbinom, dnorm, dpois, dt, pnorm The following objects are masked from 'package:base': cbind, pmax, pmin, rbind > .N <- asNumeric # short form for here > > m <- 1000; n <- 1001; k <- 1500 > dhyp.1k <- dhyperQ(.suppHyper(m,n,k), m,n,k) > phyp.1k <- cumsum(dhyp.1k) > ## Rel.Error: number of correct digits > .N(-log10(abs(1 - phyper(.suppHyper(m,n,k), m,n,k) / .bigq2mpfr(phyp.1k, 99)))) [1] 13.94063 12.67192 12.72650 12.84900 12.89942 13.08320 12.70824 13.58930 [9] 13.69480 12.98449 13.24194 12.81612 13.28698 13.80499 13.57763 13.08561 [17] 13.03303 12.68483 12.95202 13.12659 13.34331 12.61424 12.98266 13.65539 [25] 13.36000 12.66594 12.90027 13.21521 13.13923 13.03140 12.78924 13.07508 [33] 13.50277 12.93105 13.36192 13.60143 13.32003 12.95879 13.91596 13.31621 [41] 13.24843 14.34670 13.20243 13.13823 12.88636 13.07275 12.94531 12.91656 [49] 13.62465 13.27334 14.83971 13.34262 13.22993 13.21465 13.03215 13.29972 [57] 13.04690 13.52234 13.96916 12.86350 12.85325 13.42649 12.86408 13.01638 [65] 13.77269 13.06214 13.10120 13.07608 13.04428 13.63074 13.30038 13.29242 [73] 12.98026 13.02517 13.05788 13.32202 12.79155 13.24765 13.35275 13.43870 [81] 13.09916 12.66467 12.94411 13.31648 13.33799 13.65757 12.93577 13.68744 [89] 13.04946 13.46838 13.56208 13.83406 14.47525 13.14021 13.39182 14.01369 [97] 14.06520 14.15307 13.07105 14.37530 13.41126 13.08961 13.11481 13.55995 [105] 13.87761 13.24276 13.11709 13.09825 13.24225 13.75359 13.08165 13.82949 [113] 13.61838 13.83493 13.06885 13.25272 13.93547 13.68070 13.31737 13.77744 [121] 13.29042 13.31419 13.72951 13.20076 13.61768 14.20102 13.11700 14.17233 [129] 13.41775 13.37465 13.97711 13.93264 13.24865 13.59799 13.36104 13.37855 [137] 14.00573 14.01070 13.39338 13.82734 13.40678 14.53167 13.28023 13.44073 [145] 13.94540 13.55593 13.79621 13.86885 13.18253 13.96241 13.13615 13.52912 [153] 13.79702 13.70636 13.34406 13.86959 13.89014 13.40918 13.76484 15.94441 [161] 13.86231 13.90627 13.36350 13.35770 13.21157 13.88048 13.99245 13.20422 [169] 13.60492 13.68793 13.70348 13.67584 13.68064 13.79350 13.66670 14.73418 [177] 13.85003 14.54795 14.53758 13.89694 13.54050 13.66941 13.38625 13.76370 [185] 13.20347 13.77576 15.18572 13.56158 13.76184 13.73873 13.34760 13.70557 [193] 13.55385 13.49182 13.43903 14.48493 14.07743 13.93903 14.05172 13.69389 [201] 14.65711 13.93473 13.95395 14.90740 13.90986 13.86635 14.42159 14.33089 [209] 14.66214 14.36677 14.47430 14.33382 14.37552 14.39072 14.49542 14.58358 [217] 14.69412 14.47677 14.54997 14.52966 14.65492 14.49498 14.56449 14.71047 [225] 14.49724 14.57713 14.49890 14.57510 14.65196 14.54293 14.79248 14.78358 [233] 14.69296 14.76058 14.95958 14.80684 15.61004 14.71132 14.88769 14.81301 [241] 15.04172 15.27197 15.31430 15.28921 15.06104 15.23244 14.95741 15.12565 [249] 15.11650 15.24054 15.46247 15.45626 15.83358 15.58544 15.64896 15.83977 [257] 15.96953 16.45485 15.49280 16.03926 15.91396 15.79843 15.83390 16.31445 [265] 16.74469 16.23990 16.50487 16.01413 16.54917 16.07105 16.54317 16.40252 [273] 16.57424 16.01778 16.86727 16.24312 16.34861 16.61325 16.53554 16.34186 [281] 16.87953 16.15106 17.07513 16.69842 16.09828 16.56529 16.24202 16.87083 [289] 16.21055 16.35158 16.86603 16.27456 16.40955 16.61523 16.21988 16.10853 [297] 17.06287 16.20065 16.14076 18.40364 16.75268 16.12496 16.51330 16.53654 [305] 16.59944 16.28853 17.37042 17.09244 16.91262 16.14307 16.87311 16.61152 [313] 16.63484 16.39208 16.32157 17.03903 16.57398 16.64841 16.29385 16.50953 [321] 16.08315 16.08374 16.78066 16.29498 16.08560 16.23100 17.50270 16.33286 [329] 16.09688 16.80804 16.28030 16.66794 17.06056 17.45818 17.86081 18.26845 [337] 18.68114 19.09887 19.52167 19.94954 20.38250 20.82058 21.26377 21.71209 [345] 22.16557 22.62421 23.08804 23.55706 24.03129 24.51075 24.99546 25.48541 [353] 25.98072 26.48099 26.98772 27.49662 28.00958 28.50094 29.02382 29.50094 [361] Inf Inf Inf Inf Inf Inf Inf Inf [369] Inf Inf Inf Inf Inf Inf Inf Inf [377] Inf Inf Inf Inf Inf Inf Inf Inf [385] Inf Inf Inf Inf Inf Inf Inf Inf [393] Inf Inf Inf Inf Inf Inf Inf Inf [401] Inf Inf Inf Inf Inf Inf Inf Inf [409] Inf Inf Inf Inf Inf Inf Inf Inf [417] Inf Inf Inf Inf Inf Inf Inf Inf [425] Inf Inf Inf Inf Inf Inf Inf Inf [433] Inf Inf Inf Inf Inf Inf Inf Inf [441] Inf Inf Inf Inf Inf Inf Inf Inf [449] Inf Inf Inf Inf Inf Inf Inf Inf [457] Inf Inf Inf Inf Inf Inf Inf Inf [465] Inf Inf Inf Inf Inf Inf Inf Inf [473] Inf Inf Inf Inf Inf Inf Inf Inf [481] Inf Inf Inf Inf Inf Inf Inf Inf [489] Inf Inf Inf Inf Inf Inf Inf Inf [497] Inf Inf Inf Inf Inf Inf > > ## even a bit larger > m <- 9999; n <- 500; k <- 10100 > range(x <- .suppHyper(m,n,k)) # 9600 9999 [1] 9600 9999 > dQ <- dhyperQ(x, m,n,k) # these add exactly to 1 : > stopifnot(sum(dQ) == 1) > > > dM <- .bigq2mpfr(dQ, precB=128) > tail( log(dM) ) # -1395.7599 ... -1443.7188576 6 'mpfr' numbers of precision 128 bits [1] -1395.757990254839459398746551764118117554 [2] -1404.673839260128914187510489913956490702 [3] -1413.82493905206082374395151623677314317 [4] -1423.27591247190571251192036351157402469 [5] -1433.144628660374084805903170971964353083 [6] -1443.718857630955526559087416726687253113 > > 1 - phyper(x, m,n,k, log.p=TRUE) / log(cumsum(dM)) # from 0 --> 1 ??? 400 'mpfr' numbers of precision 128 bits [1] -1.117257907861727714495131721380131208068e-16 [2] -1.595008077465590303095071606307696133825e-16 [3] -5.347305900365189232637596380740120783232e-17 [4] 3.214310466959637793754934207761368871848e-18 [5] -2.241437458771475410899506806364518431404e-16 [6] -4.976914012776012326558001150782140109881e-16 [7] 1.096747576102529822839117314162050691462e-16 [8] 2.397923885510723537324379766475382814242e-17 [9] -1.149243620489414494210355280191764501001e-16 [10] 1.820920232470535447163354314448267042556e-16 [11] -6.968501114923159461309824953086354546516e-16 [12] -7.453124320474243281887085517534326277593e-17 [13] -1.165763987189789512356035890720094548179e-18 [14] -2.672754330800615320991747418481611885658e-16 [15] -1.03061186305887765307512693212117459072e-16 [16] -9.880644351894815699458248137196956476825e-16 [17] -9.597265511154601748364717118001268358139e-16 [18] -2.977464468862734606952451963658298651511e-16 [19] -1.884207937516109485875738794444399817285e-15 [20] -4.386787891278399163647797876549821122194e-16 [21] 1.320555677898452901193545087372930631206e-16 [22] -1.363415783560193411025467474838227299881e-15 [23] 3.909435525758006834176535389912155626367e-16 [24] -8.59249838774539602655099494841938227385e-16 [25] 1.030528427743552784619983025273066042924e-15 [26] -8.855208972748991196515179341403029199563e-16 [27] -1.06355024874152378063813399659565286689e-15 [28] -3.485468107696886823193562616298414813784e-15 [29] -3.213309068704263216654702005448040339205e-15 [30] -1.259157778021697034753453580597930463529e-15 [31] -3.640964750550305782271163521697237179776e-16 [32] 4.250400381079873756643737378714934501676e-16 [33] -8.914565983988658174899838969968893818566e-16 [34] -3.829899035517887705651065460338025411946e-15 [35] -1.011700088814995027538505055806250994852e-14 [36] -3.204197590368960983524317179442416566939e-15 [37] -7.817404892427927614547064367184383976209e-15 [38] -7.984636389711339048271924413046629565717e-15 [39] -3.272086895056314771002130612521213214119e-15 [40] 2.929246754622445516927437007845563535677e-15 [41] -7.344767253991834612919790777613422886556e-15 [42] -1.822029844073211524816306687885771679944e-15 [43] -3.580713620744454524634789232573381687601e-15 [44] -1.0502147566918760683573707090638133275e-14 [45] -4.053591533151374226669942949644389335243e-15 [46] -1.245297003263614849502637896469279378003e-15 [47] 1.884878427496493990773715511459450037362e-15 [48] 5.994815489023650346219991328173984107565e-15 [49] 2.696501053840907023799651497994947406761e-15 [50] -1.038554469765200980265276716174133267665e-14 [51] -5.19389707553510238493598545348168929202e-15 [52] -1.11911409469546226939432197978966876632e-14 [53] -6.543438140214468008841534451123653760349e-15 [54] 5.493212498210793936924580443352296899213e-15 [55] 4.933718200058551598677176961256189246751e-15 [56] 2.265803472787838701777745680104638922099e-15 [57] -2.888049115263706002924330580662555456011e-15 [58] -1.142045646936947033854257929461096859969e-14 [59] 9.585379347333063047783388151054628186161e-15 [60] -1.339246308069166786949003726160000242842e-14 [61] 1.262328661211827986066013098231132422716e-14 [62] 6.063499757542619930133932137803919911355e-15 [63] -1.193876983757114773123638962985950476891e-14 [64] 3.949694958134048590549433855621801785193e-15 [65] -8.247329956439329604530067127628781571281e-15 [66] 8.358645990879618866766891112215115235958e-15 [67] 2.671684906916270803901576701860008724095e-15 [68] 6.244341413641614692488760587273768424177e-15 [69] 1.215661311018061788661034020048201499719e-15 [70] -1.159493154442417950421493500123487346495e-14 [71] 9.740471460444808126641466835037062216701e-15 [72] 1.066862667744536040322651431568505129424e-15 [73] -1.622269756974281268713034827303804848389e-15 [74] -2.967979780812921780403026994401466301998e-15 [75] 2.883319846717172613890851620518210177995e-14 [76] 2.310182564629115843956835925599246701246e-13 [77] 1.439152420040674826870238267911022990762e-12 [78] 8.382290933949356526936605904951099512545e-12 [79] 5.110438248342772001383877691023144721446e-11 [80] 3.652614878551152162224652229124403876935e-10 [81] 2.488420667561234691947130699933611197308e-9 [82] 1.261018602942261985608145156066592183075e-8 [83] 8.92081844646724341241125185244618675053e-8 [84] 5.970576405475736002010782929251607900796e-7 [85] 3.229255853423890039312463965955694521372e-6 [86] 2.286007941471672555098250959808110699957e-5 [87] 0.0001266351162221002498487043508547981618165 [88] 0.0009158647401133755572095626845582954784703 [89] 0.007055139107060584186481701667871499024242 [90] 0.04107601030974771285928586768286843462529 [91] 0.225683959570016735473142365332354198817 [92] 0.6999757451405270169964012438867939636111 [93] 0.9445611845653533270953753723612559648861 [94] 0.9924423253614362873398224706988912657835 [95] 0.9989864182605597246975929574356693289408 [96] 0.9998662586815021517954067686861918673458 [97] 0.9999826360886657815575517584590533222875 [98] 0.9999977815860676940003724937009362457483 [99] 0.9999997210748606673340377990898304727541 [100] 0.9999999654841280263160016979085017128914 [101] 0.9999999957959165451695645721322125844092 [102] 0.999999999495943292289237192861523561096 [103] 0.9999999999405055417203632155823264038741 [104] 0.9999999999930865423479917579798334368313 [105] 0.999999999999209016174956100342620704963 [106] 0.9999999999999108904100984740614152737361 [107] 0.9999999999999901145575107811962982369271 [108] 0.9999999999999989200288736486959922559722 [109] 0.9999999999999998838012794892941828267514 [110] 0.9999999999999999876862078580772458566563 [111] 0.9999999999999999987146808734668164936074 [112] 0.9999999999999999998678444110214498500313 [113] 0.9999999999999999999866142846675734835863 [114] 0.9999999999999999999986643134582349796476 [115] 0.9999999999999999999998686895681432137079 [116] 0.9999999999999999999999872810925460954685 [117] 0.9999999999999999999999987861085153207715 [118] 0.9999999999999999999999998858404112293552 [119] 0.9999999999999999999999999894203861400628 [120] 0.9999999999999999999999999990337845400306 [121] 0.9999999999999999999999999999130346611793 [122] 0.9999999999999999999999999999922855101493 [123] 0.9999999999999999999999999999993255072748 [124] 0.9999999999999999999999999999999418732443 [125] 0.9999999999999999999999999999999950623213 [126] 0.9999999999999999999999999999999995865375 [127] 0.9999999999999999999999999999999999658695 [128] 0.9999999999999999999999999999999999972229 [129] 0.9999999999999999999999999999999999997767 [130] 0.9999999999999999999999999999999999999824 [131] 1 [132] 1 [133] 1 [134] 1 [135] 1 [136] 1 [137] 1 [138] 1 [139] 1 [140] 1 [141] 1 [142] 1 [143] 1 [144] 1 [145] 1 [146] 1 [147] 1 [148] 1 [149] 1 [150] 1 [151] 1 [152] 1 [153] 1 [154] 1 [155] 1 [156] 1 [157] 1 [158] 1 [159] 1 [160] 1 [161] 1 [162] 1 [163] 1 [164] 1 [165] 1 [166] 1 [167] 1 [168] 1 [169] 1 [170] 1 [171] 1 [172] 1 [173] 1 [174] 1 [175] 1 [176] 1 [177] 1 [178] 1 [179] 1 [180] 1 [181] 1 [182] 1 [183] 1 [184] 1 [185] 1 [186] 1 [187] 1 [188] 1 [189] 1 [190] 1 [191] 1 [192] 1 [193] 1 [194] 1 [195] 1 [196] 1 [197] 1 [198] 1 [199] 1 [200] 1 [201] 1 [202] 1 [203] 1 [204] 1 [205] 1 [206] 1 [207] 1 [208] 1 [209] 1 [210] 1 [211] 1 [212] 1 [213] 1 [214] 1 [215] 1 [216] 1 [217] 1 [218] 1 [219] 1 [220] 1 [221] 1 [222] 1 [223] 1 [224] 1 [225] 1 [226] 1 [227] 1 [228] 1 [229] 1 [230] 1 [231] 1 [232] 1 [233] 1 [234] 1 [235] 1 [236] 1 [237] 1 [238] 1 [239] 1 [240] 1 [241] 1 [242] 1 [243] 1 [244] 1 [245] 1 [246] 1 [247] 1 [248] 1 [249] 1 [250] 1 [251] 1 [252] 1 [253] 1 [254] 1 [255] 1 [256] 1 [257] 1 [258] 1 [259] 1 [260] 1 [261] 1 [262] 1 [263] 1 [264] 1 [265] 1 [266] 1 [267] 1 [268] 1 [269] 1 [270] 1 [271] 1 [272] 1 [273] 1 [274] 1 [275] 1 [276] 1 [277] 1 [278] 1 [279] 1 [280] 1 [281] 1 [282] 1 [283] 1 [284] 1 [285] 1 [286] 1 [287] 1 [288] 1 [289] 1 [290] 1 [291] 1 [292] 1 [293] 1 [294] 1 [295] 1 [296] 1 [297] 1 [298] 1 [299] 1 [300] 1 [301] 1 [302] 1 [303] 1 [304] 1 [305] 1 [306] 1 [307] 1 [308] 1 [309] 1 [310] 1 [311] 1 [312] 1 [313] 1 [314] 1 [315] 1 [316] 1 [317] 1 [318] 1 [319] 1 [320] 1 [321] 1 [322] 1 [323] 1 [324] 1 [325] 1 [326] 1 [327] 1 [328] 1 [329] 1 [330] 1 [331] 1 [332] 1 [333] 1 [334] 1 [335] 1 [336] 1 [337] 1 [338] 1 [339] 1 [340] 1 [341] 1 [342] 1 [343] 1 [344] 1 [345] 1 [346] 1 [347] 1 [348] 1 [349] 1 [350] 1 [351] 1 [352] 1 [353] 1 [354] 1 [355] 1 [356] 1 [357] 1 [358] 1 [359] 1 [360] 1 [361] 1 [362] 1 [363] 1 [364] 1 [365] 1 [366] 1 [367] 1 [368] 1 [369] 1 [370] 1 [371] 1 [372] 1 [373] 1 [374] 1 [375] 1 [376] 1 [377] 1 [378] 1 [379] 1 [380] 1 [381] 1 [382] 1 [383] 1 [384] 1 [385] 1 [386] 1 [387] 1 [388] 1 [389] 1 [390] 1 [391] 1 [392] 1 [393] 1 [394] 1 [395] 1 [396] 1 [397] 1 [398] 1 [399] 1 [400] 1 > ## --> > ## this is *bad*: cumsum(dM) suffers from cancellation still! > cbind(x, phyper = phyper(x, m,n,k), cum.dQ = asNumeric(cumsum(dM)), + phyp.log = phyper(x, m,n,k, log.p=TRUE), log.cumQ = asNumeric(log(cumsum(dM)))) x phyper cum.dQ phyp.log log.cumQ [1,] 9600 2.376936e-09 2.376936e-09 -1.985745e+01 -1.985745e+01 [2,] 9601 5.176749e-08 5.176749e-08 -1.677650e+01 -1.677650e+01 [3,] 9602 5.625498e-07 5.625498e-07 -1.439079e+01 -1.439079e+01 [4,] 9603 4.067869e-06 4.067869e-06 -1.241239e+01 -1.241239e+01 [5,] 9604 2.202624e-05 2.202624e-05 -1.072328e+01 -1.072328e+01 [6,] 9605 9.528817e-05 9.528817e-05 -9.258605e+00 -9.258605e+00 [7,] 9606 3.431935e-04 3.431935e-04 -7.977216e+00 -7.977216e+00 [8,] 9607 1.058875e-03 1.058875e-03 -6.850549e+00 -6.850549e+00 [9,] 9608 2.858283e-03 2.858283e-03 -5.857534e+00 -5.857534e+00 [10,] 9609 6.860962e-03 6.860962e-03 -4.981908e+00 -4.981908e+00 [11,] 9610 1.483675e-02 1.483675e-02 -4.210648e+00 -4.210648e+00 [12,] 9611 2.921671e-02 2.921671e-02 -3.533014e+00 -3.533014e+00 [13,] 9612 5.287065e-02 5.287065e-02 -2.939907e+00 -2.939907e+00 [14,] 9613 8.861702e-02 8.861702e-02 -2.423431e+00 -2.423431e+00 [15,] 9614 1.385418e-01 1.385418e-01 -1.976583e+00 -1.976583e+00 [16,] 9615 2.033116e-01 2.033116e-01 -1.593016e+00 -1.593016e+00 [17,] 9616 2.817143e-01 2.817143e-01 -1.266862e+00 -1.266862e+00 [18,] 9617 3.706112e-01 3.706112e-01 -9.926017e-01 -9.926017e-01 [19,] 9618 4.653526e-01 4.653526e-01 -7.649598e-01 -7.649598e-01 [20,] 9619 5.605507e-01 5.605507e-01 -5.788355e-01 -5.788355e-01 [21,] 9620 6.509889e-01 6.509889e-01 -4.292626e-01 -4.292626e-01 [22,] 9621 7.324205e-01 7.324205e-01 -3.114004e-01 -3.114004e-01 [23,] 9622 8.020723e-01 8.020723e-01 -2.205565e-01 -2.205565e-01 [24,] 9623 8.587828e-01 8.587828e-01 -1.522393e-01 -1.522393e-01 [25,] 9624 9.028182e-01 9.028182e-01 -1.022341e-01 -1.022341e-01 [26,] 9625 9.354845e-01 9.354845e-01 -6.669070e-02 -6.669070e-02 [27,] 9626 9.586716e-01 9.586716e-01 -4.220672e-02 -4.220672e-02 [28,] 9627 9.744433e-01 9.744433e-01 -2.588897e-02 -2.588897e-02 [29,] 9628 9.847374e-01 9.847374e-01 -1.538030e-02 -1.538030e-02 [30,] 9629 9.911928e-01 9.911928e-01 -8.846209e-03 -8.846209e-03 [31,] 9630 9.950868e-01 9.950868e-01 -4.925268e-03 -4.925268e-03 [32,] 9631 9.973488e-01 9.973488e-01 -2.654686e-03 -2.654686e-03 [33,] 9632 9.986155e-01 9.986155e-01 -1.385507e-03 -1.385507e-03 [34,] 9633 9.992998e-01 9.992998e-01 -7.004370e-04 -7.004370e-04 [35,] 9634 9.996569e-01 9.996569e-01 -3.431469e-04 -3.431469e-04 [36,] 9635 9.998370e-01 9.998370e-01 -1.629849e-04 -1.629849e-04 [37,] 9636 9.999249e-01 9.999249e-01 -7.509074e-05 -7.509074e-05 [38,] 9637 9.999664e-01 9.999664e-01 -3.357497e-05 -3.357497e-05 [39,] 9638 9.999854e-01 9.999854e-01 -1.457649e-05 -1.457649e-05 [40,] 9639 9.999939e-01 9.999939e-01 -6.147694e-06 -6.147694e-06 [41,] 9640 9.999975e-01 9.999975e-01 -2.520011e-06 -2.520011e-06 [42,] 9641 9.999990e-01 9.999990e-01 -1.004446e-06 -1.004446e-06 [43,] 9642 9.999996e-01 9.999996e-01 -3.894770e-07 -3.894770e-07 [44,] 9643 9.999999e-01 9.999999e-01 -1.469801e-07 -1.469801e-07 [45,] 9644 9.999999e-01 9.999999e-01 -5.400585e-08 -5.400585e-08 [46,] 9645 1.000000e+00 1.000000e+00 -1.932889e-08 -1.932889e-08 [47,] 9646 1.000000e+00 1.000000e+00 -6.741074e-09 -6.741074e-09 [48,] 9647 1.000000e+00 1.000000e+00 -2.291782e-09 -2.291782e-09 [49,] 9648 1.000000e+00 1.000000e+00 -7.598014e-10 -7.598014e-10 [50,] 9649 1.000000e+00 1.000000e+00 -2.457336e-10 -2.457336e-10 [51,] 9650 1.000000e+00 1.000000e+00 -7.755616e-11 -7.755616e-11 [52,] 9651 1.000000e+00 1.000000e+00 -2.389462e-11 -2.389462e-11 [53,] 9652 1.000000e+00 1.000000e+00 -7.188789e-12 -7.188789e-12 [54,] 9653 1.000000e+00 1.000000e+00 -2.112605e-12 -2.112605e-12 [55,] 9654 1.000000e+00 1.000000e+00 -6.066219e-13 -6.066219e-13 [56,] 9655 1.000000e+00 1.000000e+00 -1.702479e-13 -1.702479e-13 [57,] 9656 1.000000e+00 1.000000e+00 -4.671227e-14 -4.671227e-14 [58,] 9657 1.000000e+00 1.000000e+00 -1.253384e-14 -1.253384e-14 [59,] 9658 1.000000e+00 1.000000e+00 -3.289691e-15 -3.289691e-15 [60,] 9659 1.000000e+00 1.000000e+00 -8.448020e-16 -8.448020e-16 [61,] 9660 1.000000e+00 1.000000e+00 -2.123198e-16 -2.123198e-16 [62,] 9661 1.000000e+00 1.000000e+00 -5.223544e-17 -5.223544e-17 [63,] 9662 1.000000e+00 1.000000e+00 -1.258288e-17 -1.258288e-17 [64,] 9663 1.000000e+00 1.000000e+00 -2.968464e-18 -2.968464e-18 [65,] 9664 1.000000e+00 1.000000e+00 -6.859854e-19 -6.859854e-19 [66,] 9665 1.000000e+00 1.000000e+00 -1.553177e-19 -1.553177e-19 [67,] 9666 1.000000e+00 1.000000e+00 -3.446184e-20 -3.446184e-20 [68,] 9667 1.000000e+00 1.000000e+00 -7.494689e-21 -7.494689e-21 [69,] 9668 1.000000e+00 1.000000e+00 -1.597900e-21 -1.597900e-21 [70,] 9669 1.000000e+00 1.000000e+00 -3.340471e-22 -3.340471e-22 [71,] 9670 1.000000e+00 1.000000e+00 -6.848673e-23 -6.848673e-23 [72,] 9671 1.000000e+00 1.000000e+00 -1.377279e-23 -1.377279e-23 [73,] 9672 1.000000e+00 1.000000e+00 -2.717245e-24 -2.717245e-24 [74,] 9673 1.000000e+00 1.000000e+00 -5.260155e-25 -5.260155e-25 [75,] 9674 1.000000e+00 1.000000e+00 -9.993129e-26 -9.993129e-26 [76,] 9675 1.000000e+00 1.000000e+00 -1.863398e-26 -1.863398e-26 [77,] 9676 1.000000e+00 1.000000e+00 -3.410962e-27 -3.410962e-27 [78,] 9677 1.000000e+00 1.000000e+00 -6.130272e-28 -6.130272e-28 [79,] 9678 1.000000e+00 1.000000e+00 -1.081874e-28 -1.081874e-28 [80,] 9679 1.000000e+00 1.000000e+00 -1.875118e-29 -1.875118e-29 [81,] 9680 1.000000e+00 1.000000e+00 -3.192233e-30 -3.192233e-30 [82,] 9681 1.000000e+00 1.000000e+00 -5.338660e-31 -5.338660e-31 [83,] 9682 1.000000e+00 1.000000e+00 -8.771979e-32 -8.771980e-32 [84,] 9683 1.000000e+00 1.000000e+00 -1.416267e-32 -1.416268e-32 [85,] 9684 1.000000e+00 1.000000e+00 -2.247129e-33 -2.247137e-33 [86,] 9685 1.000000e+00 1.000000e+00 -3.504274e-34 -3.504354e-34 [87,] 9686 1.000000e+00 1.000000e+00 -5.371623e-35 -5.372303e-35 [88,] 9687 1.000000e+00 1.000000e+00 -8.094674e-36 -8.102095e-36 [89,] 9688 1.000000e+00 1.000000e+00 -1.199299e-36 -1.207820e-36 [90,] 9689 1.000000e+00 1.000000e+00 -1.747175e-37 -1.822016e-37 [91,] 9690 1.000000e+00 1.000000e+00 -2.503061e-38 -3.232609e-38 [92,] 9691 1.000000e+00 1.000000e+00 -3.526768e-39 -1.175494e-38 [93,] 9692 1.000000e+00 1.000000e+00 -4.887601e-40 -8.816208e-39 [94,] 9693 1.000000e+00 1.000000e+00 -6.663003e-41 -8.816208e-39 [95,] 9694 1.000000e+00 1.000000e+00 -8.935947e-42 -8.816208e-39 [96,] 9695 1.000000e+00 1.000000e+00 -1.179091e-42 -8.816208e-39 [97,] 9696 1.000000e+00 1.000000e+00 -1.530838e-43 -8.816208e-39 [98,] 9697 1.000000e+00 1.000000e+00 -1.955800e-44 -8.816208e-39 [99,] 9698 1.000000e+00 1.000000e+00 -2.459062e-45 -8.816208e-39 [100,] 9699 1.000000e+00 1.000000e+00 -3.042991e-46 -8.816208e-39 [101,] 9700 1.000000e+00 1.000000e+00 -3.706407e-47 -8.816208e-39 [102,] 9701 1.000000e+00 1.000000e+00 -4.443869e-48 -8.816208e-39 [103,] 9702 1.000000e+00 1.000000e+00 -5.245155e-49 -8.816208e-39 [104,] 9703 1.000000e+00 1.000000e+00 -6.095048e-50 -8.816208e-39 [105,] 9704 1.000000e+00 1.000000e+00 -6.973478e-51 -8.816208e-39 [106,] 9705 1.000000e+00 1.000000e+00 -7.856086e-52 -8.816208e-39 [107,] 9706 1.000000e+00 1.000000e+00 -8.715211e-53 -8.816208e-39 [108,] 9707 1.000000e+00 1.000000e+00 -9.521250e-54 -8.816208e-39 [109,] 9708 1.000000e+00 1.000000e+00 -1.024432e-54 -8.816208e-39 [110,] 9709 1.000000e+00 1.000000e+00 -1.085609e-55 -8.816208e-39 [111,] 9710 1.000000e+00 1.000000e+00 -1.133164e-56 -8.816208e-39 [112,] 9711 1.000000e+00 1.000000e+00 -1.165111e-57 -8.816208e-39 [113,] 9712 1.000000e+00 1.000000e+00 -1.180112e-58 -8.816208e-39 [114,] 9713 1.000000e+00 1.000000e+00 -1.177569e-59 -8.816208e-39 [115,] 9714 1.000000e+00 1.000000e+00 -1.157660e-60 -8.816208e-39 [116,] 9715 1.000000e+00 1.000000e+00 -1.121325e-61 -8.816208e-39 [117,] 9716 1.000000e+00 1.000000e+00 -1.070192e-62 -8.816208e-39 [118,] 9717 1.000000e+00 1.000000e+00 -1.006455e-63 -8.816208e-39 [119,] 9718 1.000000e+00 1.000000e+00 -9.327207e-65 -8.816208e-39 [120,] 9719 1.000000e+00 1.000000e+00 -8.518356e-66 -8.816208e-39 [121,] 9720 1.000000e+00 1.000000e+00 -7.667045e-67 -8.816208e-39 [122,] 9721 1.000000e+00 1.000000e+00 -6.801254e-68 -8.816208e-39 [123,] 9722 1.000000e+00 1.000000e+00 -5.946468e-69 -8.816208e-39 [124,] 9723 1.000000e+00 1.000000e+00 -5.124575e-70 -8.816208e-39 [125,] 9724 1.000000e+00 1.000000e+00 -4.353160e-71 -8.816208e-39 [126,] 9725 1.000000e+00 1.000000e+00 -3.645173e-72 -8.816208e-39 [127,] 9726 1.000000e+00 1.000000e+00 -3.008960e-73 -8.816208e-39 [128,] 9727 1.000000e+00 1.000000e+00 -2.448597e-74 -8.816208e-39 [129,] 9728 1.000000e+00 1.000000e+00 -1.964438e-75 -8.816208e-39 [130,] 9729 1.000000e+00 1.000000e+00 -1.553802e-76 -8.816208e-39 [131,] 9730 1.000000e+00 1.000000e+00 -1.211732e-77 -8.816208e-39 [132,] 9731 1.000000e+00 1.000000e+00 -9.317212e-79 -8.816208e-39 [133,] 9732 1.000000e+00 1.000000e+00 -7.063989e-80 -8.816208e-39 [134,] 9733 1.000000e+00 1.000000e+00 -5.280968e-81 -8.816208e-39 [135,] 9734 1.000000e+00 1.000000e+00 -3.893061e-82 -8.816208e-39 [136,] 9735 1.000000e+00 1.000000e+00 -2.830070e-83 -8.816208e-39 [137,] 9736 1.000000e+00 1.000000e+00 -2.028828e-84 -8.816208e-39 [138,] 9737 1.000000e+00 1.000000e+00 -1.434329e-85 -8.816208e-39 [139,] 9738 1.000000e+00 1.000000e+00 -1.000048e-86 -8.816208e-39 [140,] 9739 1.000000e+00 1.000000e+00 -6.876609e-88 -8.816208e-39 [141,] 9740 1.000000e+00 1.000000e+00 -4.663597e-89 -8.816208e-39 [142,] 9741 1.000000e+00 1.000000e+00 -3.119414e-90 -8.816208e-39 [143,] 9742 1.000000e+00 1.000000e+00 -2.057982e-91 -8.816208e-39 [144,] 9743 1.000000e+00 1.000000e+00 -1.339178e-92 -8.816208e-39 [145,] 9744 1.000000e+00 1.000000e+00 -8.595543e-94 -8.816208e-39 [146,] 9745 1.000000e+00 1.000000e+00 -5.441987e-95 -8.816208e-39 [147,] 9746 1.000000e+00 1.000000e+00 -3.398605e-96 -8.816208e-39 [148,] 9747 1.000000e+00 1.000000e+00 -2.093692e-97 -8.816208e-39 [149,] 9748 1.000000e+00 1.000000e+00 -1.272340e-98 -8.816208e-39 [150,] 9749 1.000000e+00 1.000000e+00 -7.627469e-100 -8.816208e-39 [151,] 9750 1.000000e+00 1.000000e+00 -4.510803e-101 -8.816208e-39 [152,] 9751 1.000000e+00 1.000000e+00 -2.631670e-102 -8.816208e-39 [153,] 9752 1.000000e+00 1.000000e+00 -1.514682e-103 -8.816208e-39 [154,] 9753 1.000000e+00 1.000000e+00 -8.600657e-105 -8.816208e-39 [155,] 9754 1.000000e+00 1.000000e+00 -4.818027e-106 -8.816208e-39 [156,] 9755 1.000000e+00 1.000000e+00 -2.662818e-107 -8.816208e-39 [157,] 9756 1.000000e+00 1.000000e+00 -1.451962e-108 -8.816208e-39 [158,] 9757 1.000000e+00 1.000000e+00 -7.811181e-110 -8.816208e-39 [159,] 9758 1.000000e+00 1.000000e+00 -4.146029e-111 -8.816208e-39 [160,] 9759 1.000000e+00 1.000000e+00 -2.171241e-112 -8.816208e-39 [161,] 9760 1.000000e+00 1.000000e+00 -1.121887e-113 -8.816208e-39 [162,] 9761 1.000000e+00 1.000000e+00 -5.719545e-115 -8.816208e-39 [163,] 9762 1.000000e+00 1.000000e+00 -2.877064e-116 -8.816208e-39 [164,] 9763 1.000000e+00 1.000000e+00 -1.427967e-117 -8.816208e-39 [165,] 9764 1.000000e+00 1.000000e+00 -6.993138e-119 -8.816208e-39 [166,] 9765 1.000000e+00 1.000000e+00 -3.379210e-120 -8.816208e-39 [167,] 9766 1.000000e+00 1.000000e+00 -1.611207e-121 -8.816208e-39 [168,] 9767 1.000000e+00 1.000000e+00 -7.580263e-123 -8.816208e-39 [169,] 9768 1.000000e+00 1.000000e+00 -3.518984e-124 -8.816208e-39 [170,] 9769 1.000000e+00 1.000000e+00 -1.611957e-125 -8.816208e-39 [171,] 9770 1.000000e+00 1.000000e+00 -7.286106e-127 -8.816208e-39 [172,] 9771 1.000000e+00 1.000000e+00 -3.249720e-128 -8.816208e-39 [173,] 9772 1.000000e+00 1.000000e+00 -1.430234e-129 -8.816208e-39 [174,] 9773 1.000000e+00 1.000000e+00 -6.211275e-131 -8.816208e-39 [175,] 9774 1.000000e+00 1.000000e+00 -2.661760e-132 -8.816208e-39 [176,] 9775 1.000000e+00 1.000000e+00 -1.125571e-133 -8.816208e-39 [177,] 9776 1.000000e+00 1.000000e+00 -4.696711e-135 -8.816208e-39 [178,] 9777 1.000000e+00 1.000000e+00 -1.933894e-136 -8.816208e-39 [179,] 9778 1.000000e+00 1.000000e+00 -7.857606e-138 -8.816208e-39 [180,] 9779 1.000000e+00 1.000000e+00 -3.150408e-139 -8.816208e-39 [181,] 9780 1.000000e+00 1.000000e+00 -1.246415e-140 -8.816208e-39 [182,] 9781 1.000000e+00 1.000000e+00 -4.866060e-142 -8.816208e-39 [183,] 9782 1.000000e+00 1.000000e+00 -1.874611e-143 -8.816208e-39 [184,] 9783 1.000000e+00 1.000000e+00 -7.126280e-145 -8.816208e-39 [185,] 9784 1.000000e+00 1.000000e+00 -2.673203e-146 -8.816208e-39 [186,] 9785 1.000000e+00 1.000000e+00 -9.895035e-148 -8.816208e-39 [187,] 9786 1.000000e+00 1.000000e+00 -3.614245e-149 -8.816208e-39 [188,] 9787 1.000000e+00 1.000000e+00 -1.302660e-150 -8.816208e-39 [189,] 9788 1.000000e+00 1.000000e+00 -4.632931e-152 -8.816208e-39 [190,] 9789 1.000000e+00 1.000000e+00 -1.625886e-153 -8.816208e-39 [191,] 9790 1.000000e+00 1.000000e+00 -5.630294e-155 -8.816208e-39 [192,] 9791 1.000000e+00 1.000000e+00 -1.923873e-156 -8.816208e-39 [193,] 9792 1.000000e+00 1.000000e+00 -6.486695e-158 -8.816208e-39 [194,] 9793 1.000000e+00 1.000000e+00 -2.158086e-159 -8.816208e-39 [195,] 9794 1.000000e+00 1.000000e+00 -7.084501e-161 -8.816208e-39 [196,] 9795 1.000000e+00 1.000000e+00 -2.294781e-162 -8.816208e-39 [197,] 9796 1.000000e+00 1.000000e+00 -7.334335e-164 -8.816208e-39 [198,] 9797 1.000000e+00 1.000000e+00 -2.312938e-165 -8.816208e-39 [199,] 9798 1.000000e+00 1.000000e+00 -7.196913e-167 -8.816208e-39 [200,] 9799 1.000000e+00 1.000000e+00 -2.209547e-168 -8.816208e-39 [201,] 9800 1.000000e+00 1.000000e+00 -6.693144e-170 -8.816208e-39 [202,] 9801 1.000000e+00 1.000000e+00 -2.000423e-171 -8.816208e-39 [203,] 9802 1.000000e+00 1.000000e+00 -5.898924e-173 -8.816208e-39 [204,] 9803 1.000000e+00 1.000000e+00 -1.716239e-174 -8.816208e-39 [205,] 9804 1.000000e+00 1.000000e+00 -4.926411e-176 -8.816208e-39 [206,] 9805 1.000000e+00 1.000000e+00 -1.395165e-177 -8.816208e-39 [207,] 9806 1.000000e+00 1.000000e+00 -3.898128e-179 -8.816208e-39 [208,] 9807 1.000000e+00 1.000000e+00 -1.074523e-180 -8.816208e-39 [209,] 9808 1.000000e+00 1.000000e+00 -2.922116e-182 -8.816208e-39 [210,] 9809 1.000000e+00 1.000000e+00 -7.839611e-184 -8.816208e-39 [211,] 9810 1.000000e+00 1.000000e+00 -2.074910e-185 -8.816208e-39 [212,] 9811 1.000000e+00 1.000000e+00 -5.417567e-187 -8.816208e-39 [213,] 9812 1.000000e+00 1.000000e+00 -1.395410e-188 -8.816208e-39 [214,] 9813 1.000000e+00 1.000000e+00 -3.545548e-190 -8.816208e-39 [215,] 9814 1.000000e+00 1.000000e+00 -8.886707e-192 -8.816208e-39 [216,] 9815 1.000000e+00 1.000000e+00 -2.197180e-193 -8.816208e-39 [217,] 9816 1.000000e+00 1.000000e+00 -5.358569e-195 -8.816208e-39 [218,] 9817 1.000000e+00 1.000000e+00 -1.289084e-196 -8.816208e-39 [219,] 9818 1.000000e+00 1.000000e+00 -3.058817e-198 -8.816208e-39 [220,] 9819 1.000000e+00 1.000000e+00 -7.159057e-200 -8.816208e-39 [221,] 9820 1.000000e+00 1.000000e+00 -1.652640e-201 -8.816208e-39 [222,] 9821 1.000000e+00 1.000000e+00 -3.762798e-203 -8.816208e-39 [223,] 9822 1.000000e+00 1.000000e+00 -8.449729e-205 -8.816208e-39 [224,] 9823 1.000000e+00 1.000000e+00 -1.871386e-206 -8.816208e-39 [225,] 9824 1.000000e+00 1.000000e+00 -4.087537e-208 -8.816208e-39 [226,] 9825 1.000000e+00 1.000000e+00 -8.804938e-210 -8.816208e-39 [227,] 9826 1.000000e+00 1.000000e+00 -1.870448e-211 -8.816208e-39 [228,] 9827 1.000000e+00 1.000000e+00 -3.918391e-213 -8.816208e-39 [229,] 9828 1.000000e+00 1.000000e+00 -8.094697e-215 -8.816208e-39 [230,] 9829 1.000000e+00 1.000000e+00 -1.648966e-216 -8.816208e-39 [231,] 9830 1.000000e+00 1.000000e+00 -3.312288e-218 -8.816208e-39 [232,] 9831 1.000000e+00 1.000000e+00 -6.560501e-220 -8.816208e-39 [233,] 9832 1.000000e+00 1.000000e+00 -1.281224e-221 -8.816208e-39 [234,] 9833 1.000000e+00 1.000000e+00 -2.467053e-223 -8.816208e-39 [235,] 9834 1.000000e+00 1.000000e+00 -4.683639e-225 -8.816208e-39 [236,] 9835 1.000000e+00 1.000000e+00 -8.766487e-227 -8.816208e-39 [237,] 9836 1.000000e+00 1.000000e+00 -1.617672e-228 -8.816208e-39 [238,] 9837 1.000000e+00 1.000000e+00 -2.942818e-230 -8.816208e-39 [239,] 9838 1.000000e+00 1.000000e+00 -5.277507e-232 -8.816208e-39 [240,] 9839 1.000000e+00 1.000000e+00 -9.329783e-234 -8.816208e-39 [241,] 9840 1.000000e+00 1.000000e+00 -1.625832e-235 -8.816208e-39 [242,] 9841 1.000000e+00 1.000000e+00 -2.792704e-237 -8.816208e-39 [243,] 9842 1.000000e+00 1.000000e+00 -4.728278e-239 -8.816208e-39 [244,] 9843 1.000000e+00 1.000000e+00 -7.890293e-241 -8.816208e-39 [245,] 9844 1.000000e+00 1.000000e+00 -1.297711e-242 -8.816208e-39 [246,] 9845 1.000000e+00 1.000000e+00 -2.103489e-244 -8.816208e-39 [247,] 9846 1.000000e+00 1.000000e+00 -3.360177e-246 -8.816208e-39 [248,] 9847 1.000000e+00 1.000000e+00 -5.289629e-248 -8.816208e-39 [249,] 9848 1.000000e+00 1.000000e+00 -8.205616e-250 -8.816208e-39 [250,] 9849 1.000000e+00 1.000000e+00 -1.254299e-251 -8.816208e-39 [251,] 9850 1.000000e+00 1.000000e+00 -1.889190e-253 -8.816208e-39 [252,] 9851 1.000000e+00 1.000000e+00 -2.803595e-255 -8.816208e-39 [253,] 9852 1.000000e+00 1.000000e+00 -4.099208e-257 -8.816208e-39 [254,] 9853 1.000000e+00 1.000000e+00 -5.904855e-259 -8.816208e-39 [255,] 9854 1.000000e+00 1.000000e+00 -8.379584e-261 -8.816208e-39 [256,] 9855 1.000000e+00 1.000000e+00 -1.171435e-262 -8.816208e-39 [257,] 9856 1.000000e+00 1.000000e+00 -1.613153e-264 -8.816208e-39 [258,] 9857 1.000000e+00 1.000000e+00 -2.188123e-266 -8.816208e-39 [259,] 9858 1.000000e+00 1.000000e+00 -2.923377e-268 -8.816208e-39 [260,] 9859 1.000000e+00 1.000000e+00 -3.846732e-270 -8.816208e-39 [261,] 9860 1.000000e+00 1.000000e+00 -4.985053e-272 -8.816208e-39 [262,] 9861 1.000000e+00 1.000000e+00 -6.362017e-274 -8.816208e-39 [263,] 9862 1.000000e+00 1.000000e+00 -7.995451e-276 -8.816208e-39 [264,] 9863 1.000000e+00 1.000000e+00 -9.894403e-278 -8.816208e-39 [265,] 9864 1.000000e+00 1.000000e+00 -1.205618e-279 -8.816208e-39 [266,] 9865 1.000000e+00 1.000000e+00 -1.446365e-281 -8.816208e-39 [267,] 9866 1.000000e+00 1.000000e+00 -1.708317e-283 -8.816208e-39 [268,] 9867 1.000000e+00 1.000000e+00 -1.986345e-285 -8.816208e-39 [269,] 9868 1.000000e+00 1.000000e+00 -2.273577e-287 -8.816208e-39 [270,] 9869 1.000000e+00 1.000000e+00 -2.561570e-289 -8.816208e-39 [271,] 9870 1.000000e+00 1.000000e+00 -2.840642e-291 -8.816208e-39 [272,] 9871 1.000000e+00 1.000000e+00 -3.100358e-293 -8.816208e-39 [273,] 9872 1.000000e+00 1.000000e+00 -3.330148e-295 -8.816208e-39 [274,] 9873 1.000000e+00 1.000000e+00 -3.519995e-297 -8.816208e-39 [275,] 9874 1.000000e+00 1.000000e+00 -3.661149e-299 -8.816208e-39 [276,] 9875 1.000000e+00 1.000000e+00 -3.746787e-301 -8.816208e-39 [277,] 9876 1.000000e+00 1.000000e+00 -3.772556e-303 -8.816208e-39 [278,] 9877 1.000000e+00 1.000000e+00 -3.736937e-305 -8.816208e-39 [279,] 9878 1.000000e+00 1.000000e+00 -3.641389e-307 -8.816208e-39 [280,] 9879 1.000000e+00 1.000000e+00 -3.490250e-309 -8.816208e-39 [281,] 9880 1.000000e+00 1.000000e+00 -3.290416e-311 -8.816208e-39 [282,] 9881 1.000000e+00 1.000000e+00 -3.050813e-313 -8.816208e-39 [283,] 9882 1.000000e+00 1.000000e+00 -2.781737e-315 -8.816208e-39 [284,] 9883 1.000000e+00 1.000000e+00 -2.494117e-317 -8.816208e-39 [285,] 9884 1.000000e+00 1.000000e+00 -2.198790e-319 -8.816208e-39 [286,] 9885 1.000000e+00 1.000000e+00 -1.907093e-321 -8.816208e-39 [287,] 9886 1.000000e+00 1.000000e+00 -1.482197e-323 -8.816208e-39 [288,] 9887 1.000000e+00 1.000000e+00 0.000000e+00 -8.816208e-39 [289,] 9888 1.000000e+00 1.000000e+00 0.000000e+00 -8.816208e-39 [290,] 9889 1.000000e+00 1.000000e+00 0.000000e+00 -8.816208e-39 [291,] 9890 1.000000e+00 1.000000e+00 0.000000e+00 -8.816208e-39 [292,] 9891 1.000000e+00 1.000000e+00 0.000000e+00 -8.816208e-39 [293,] 9892 1.000000e+00 1.000000e+00 0.000000e+00 -8.816208e-39 [294,] 9893 1.000000e+00 1.000000e+00 0.000000e+00 -8.816208e-39 [295,] 9894 1.000000e+00 1.000000e+00 0.000000e+00 -8.816208e-39 [296,] 9895 1.000000e+00 1.000000e+00 0.000000e+00 -8.816208e-39 [297,] 9896 1.000000e+00 1.000000e+00 0.000000e+00 -8.816208e-39 [298,] 9897 1.000000e+00 1.000000e+00 0.000000e+00 -8.816208e-39 [299,] 9898 1.000000e+00 1.000000e+00 0.000000e+00 -8.816208e-39 [300,] 9899 1.000000e+00 1.000000e+00 0.000000e+00 -8.816208e-39 [301,] 9900 1.000000e+00 1.000000e+00 0.000000e+00 -8.816208e-39 [302,] 9901 1.000000e+00 1.000000e+00 0.000000e+00 -8.816208e-39 [303,] 9902 1.000000e+00 1.000000e+00 0.000000e+00 -8.816208e-39 [304,] 9903 1.000000e+00 1.000000e+00 0.000000e+00 -8.816208e-39 [305,] 9904 1.000000e+00 1.000000e+00 0.000000e+00 -8.816208e-39 [306,] 9905 1.000000e+00 1.000000e+00 0.000000e+00 -8.816208e-39 [307,] 9906 1.000000e+00 1.000000e+00 0.000000e+00 -8.816208e-39 [308,] 9907 1.000000e+00 1.000000e+00 0.000000e+00 -8.816208e-39 [309,] 9908 1.000000e+00 1.000000e+00 0.000000e+00 -8.816208e-39 [310,] 9909 1.000000e+00 1.000000e+00 0.000000e+00 -8.816208e-39 [311,] 9910 1.000000e+00 1.000000e+00 0.000000e+00 -8.816208e-39 [312,] 9911 1.000000e+00 1.000000e+00 0.000000e+00 -8.816208e-39 [313,] 9912 1.000000e+00 1.000000e+00 0.000000e+00 -8.816208e-39 [314,] 9913 1.000000e+00 1.000000e+00 0.000000e+00 -8.816208e-39 [315,] 9914 1.000000e+00 1.000000e+00 0.000000e+00 -8.816208e-39 [316,] 9915 1.000000e+00 1.000000e+00 0.000000e+00 -8.816208e-39 [317,] 9916 1.000000e+00 1.000000e+00 0.000000e+00 -8.816208e-39 [318,] 9917 1.000000e+00 1.000000e+00 0.000000e+00 -8.816208e-39 [319,] 9918 1.000000e+00 1.000000e+00 0.000000e+00 -8.816208e-39 [320,] 9919 1.000000e+00 1.000000e+00 0.000000e+00 -8.816208e-39 [321,] 9920 1.000000e+00 1.000000e+00 0.000000e+00 -8.816208e-39 [322,] 9921 1.000000e+00 1.000000e+00 0.000000e+00 -8.816208e-39 [323,] 9922 1.000000e+00 1.000000e+00 0.000000e+00 -8.816208e-39 [324,] 9923 1.000000e+00 1.000000e+00 0.000000e+00 -8.816208e-39 [325,] 9924 1.000000e+00 1.000000e+00 0.000000e+00 -8.816208e-39 [326,] 9925 1.000000e+00 1.000000e+00 0.000000e+00 -8.816208e-39 [327,] 9926 1.000000e+00 1.000000e+00 0.000000e+00 -8.816208e-39 [328,] 9927 1.000000e+00 1.000000e+00 0.000000e+00 -8.816208e-39 [329,] 9928 1.000000e+00 1.000000e+00 0.000000e+00 -8.816208e-39 [330,] 9929 1.000000e+00 1.000000e+00 0.000000e+00 -8.816208e-39 [331,] 9930 1.000000e+00 1.000000e+00 0.000000e+00 -8.816208e-39 [332,] 9931 1.000000e+00 1.000000e+00 0.000000e+00 -8.816208e-39 [333,] 9932 1.000000e+00 1.000000e+00 0.000000e+00 -8.816208e-39 [334,] 9933 1.000000e+00 1.000000e+00 0.000000e+00 -8.816208e-39 [335,] 9934 1.000000e+00 1.000000e+00 0.000000e+00 -8.816208e-39 [336,] 9935 1.000000e+00 1.000000e+00 0.000000e+00 -8.816208e-39 [337,] 9936 1.000000e+00 1.000000e+00 0.000000e+00 -8.816208e-39 [338,] 9937 1.000000e+00 1.000000e+00 0.000000e+00 -8.816208e-39 [339,] 9938 1.000000e+00 1.000000e+00 0.000000e+00 -8.816208e-39 [340,] 9939 1.000000e+00 1.000000e+00 0.000000e+00 -8.816208e-39 [341,] 9940 1.000000e+00 1.000000e+00 0.000000e+00 -8.816208e-39 [342,] 9941 1.000000e+00 1.000000e+00 0.000000e+00 -8.816208e-39 [343,] 9942 1.000000e+00 1.000000e+00 0.000000e+00 -8.816208e-39 [344,] 9943 1.000000e+00 1.000000e+00 0.000000e+00 -8.816208e-39 [345,] 9944 1.000000e+00 1.000000e+00 0.000000e+00 -8.816208e-39 [346,] 9945 1.000000e+00 1.000000e+00 0.000000e+00 -8.816208e-39 [347,] 9946 1.000000e+00 1.000000e+00 0.000000e+00 -8.816208e-39 [348,] 9947 1.000000e+00 1.000000e+00 0.000000e+00 -8.816208e-39 [349,] 9948 1.000000e+00 1.000000e+00 0.000000e+00 -8.816208e-39 [350,] 9949 1.000000e+00 1.000000e+00 0.000000e+00 -8.816208e-39 [351,] 9950 1.000000e+00 1.000000e+00 0.000000e+00 -8.816208e-39 [352,] 9951 1.000000e+00 1.000000e+00 0.000000e+00 -8.816208e-39 [353,] 9952 1.000000e+00 1.000000e+00 0.000000e+00 -8.816208e-39 [354,] 9953 1.000000e+00 1.000000e+00 0.000000e+00 -8.816208e-39 [355,] 9954 1.000000e+00 1.000000e+00 0.000000e+00 -8.816208e-39 [356,] 9955 1.000000e+00 1.000000e+00 0.000000e+00 -8.816208e-39 [357,] 9956 1.000000e+00 1.000000e+00 0.000000e+00 -8.816208e-39 [358,] 9957 1.000000e+00 1.000000e+00 0.000000e+00 -8.816208e-39 [359,] 9958 1.000000e+00 1.000000e+00 0.000000e+00 -8.816208e-39 [360,] 9959 1.000000e+00 1.000000e+00 0.000000e+00 -8.816208e-39 [361,] 9960 1.000000e+00 1.000000e+00 0.000000e+00 -8.816208e-39 [362,] 9961 1.000000e+00 1.000000e+00 0.000000e+00 -8.816208e-39 [363,] 9962 1.000000e+00 1.000000e+00 0.000000e+00 -8.816208e-39 [364,] 9963 1.000000e+00 1.000000e+00 0.000000e+00 -8.816208e-39 [365,] 9964 1.000000e+00 1.000000e+00 0.000000e+00 -8.816208e-39 [366,] 9965 1.000000e+00 1.000000e+00 0.000000e+00 -8.816208e-39 [367,] 9966 1.000000e+00 1.000000e+00 0.000000e+00 -8.816208e-39 [368,] 9967 1.000000e+00 1.000000e+00 0.000000e+00 -8.816208e-39 [369,] 9968 1.000000e+00 1.000000e+00 0.000000e+00 -8.816208e-39 [370,] 9969 1.000000e+00 1.000000e+00 0.000000e+00 -8.816208e-39 [371,] 9970 1.000000e+00 1.000000e+00 0.000000e+00 -8.816208e-39 [372,] 9971 1.000000e+00 1.000000e+00 0.000000e+00 -8.816208e-39 [373,] 9972 1.000000e+00 1.000000e+00 0.000000e+00 -8.816208e-39 [374,] 9973 1.000000e+00 1.000000e+00 0.000000e+00 -8.816208e-39 [375,] 9974 1.000000e+00 1.000000e+00 0.000000e+00 -8.816208e-39 [376,] 9975 1.000000e+00 1.000000e+00 0.000000e+00 -8.816208e-39 [377,] 9976 1.000000e+00 1.000000e+00 0.000000e+00 -8.816208e-39 [378,] 9977 1.000000e+00 1.000000e+00 0.000000e+00 -8.816208e-39 [379,] 9978 1.000000e+00 1.000000e+00 0.000000e+00 -8.816208e-39 [380,] 9979 1.000000e+00 1.000000e+00 0.000000e+00 -8.816208e-39 [381,] 9980 1.000000e+00 1.000000e+00 0.000000e+00 -8.816208e-39 [382,] 9981 1.000000e+00 1.000000e+00 0.000000e+00 -8.816208e-39 [383,] 9982 1.000000e+00 1.000000e+00 0.000000e+00 -8.816208e-39 [384,] 9983 1.000000e+00 1.000000e+00 0.000000e+00 -8.816208e-39 [385,] 9984 1.000000e+00 1.000000e+00 0.000000e+00 -8.816208e-39 [386,] 9985 1.000000e+00 1.000000e+00 0.000000e+00 -8.816208e-39 [387,] 9986 1.000000e+00 1.000000e+00 0.000000e+00 -8.816208e-39 [388,] 9987 1.000000e+00 1.000000e+00 0.000000e+00 -8.816208e-39 [389,] 9988 1.000000e+00 1.000000e+00 0.000000e+00 -8.816208e-39 [390,] 9989 1.000000e+00 1.000000e+00 0.000000e+00 -8.816208e-39 [391,] 9990 1.000000e+00 1.000000e+00 0.000000e+00 -8.816208e-39 [392,] 9991 1.000000e+00 1.000000e+00 0.000000e+00 -8.816208e-39 [393,] 9992 1.000000e+00 1.000000e+00 0.000000e+00 -8.816208e-39 [394,] 9993 1.000000e+00 1.000000e+00 0.000000e+00 -8.816208e-39 [395,] 9994 1.000000e+00 1.000000e+00 0.000000e+00 -8.816208e-39 [396,] 9995 1.000000e+00 1.000000e+00 0.000000e+00 -8.816208e-39 [397,] 9996 1.000000e+00 1.000000e+00 0.000000e+00 -8.816208e-39 [398,] 9997 1.000000e+00 1.000000e+00 0.000000e+00 -8.816208e-39 [399,] 9998 1.000000e+00 1.000000e+00 0.000000e+00 -8.816208e-39 [400,] 9999 1.000000e+00 1.000000e+00 0.000000e+00 -8.816208e-39 > > ## this shows the cancellation: > cbind(x, + cumD = .N(1 - cumsum(dM)), + revCS= .N(rev(cumsum(rev(dM)))))[ 1:99, ] x cumD revCS [1,] 9600 1.000000e+00 1.000000e+00 [2,] 9601 9.999999e-01 1.000000e+00 [3,] 9602 9.999994e-01 9.999999e-01 [4,] 9603 9.999959e-01 9.999994e-01 [5,] 9604 9.999780e-01 9.999959e-01 [6,] 9605 9.999047e-01 9.999780e-01 [7,] 9606 9.996568e-01 9.999047e-01 [8,] 9607 9.989411e-01 9.996568e-01 [9,] 9608 9.971417e-01 9.989411e-01 [10,] 9609 9.931390e-01 9.971417e-01 [11,] 9610 9.851633e-01 9.931390e-01 [12,] 9611 9.707833e-01 9.851633e-01 [13,] 9612 9.471293e-01 9.707833e-01 [14,] 9613 9.113830e-01 9.471293e-01 [15,] 9614 8.614582e-01 9.113830e-01 [16,] 9615 7.966884e-01 8.614582e-01 [17,] 9616 7.182857e-01 7.966884e-01 [18,] 9617 6.293888e-01 7.182857e-01 [19,] 9618 5.346474e-01 6.293888e-01 [20,] 9619 4.394493e-01 5.346474e-01 [21,] 9620 3.490111e-01 4.394493e-01 [22,] 9621 2.675795e-01 3.490111e-01 [23,] 9622 1.979277e-01 2.675795e-01 [24,] 9623 1.412172e-01 1.979277e-01 [25,] 9624 9.718179e-02 1.412172e-01 [26,] 9625 6.451549e-02 9.718179e-02 [27,] 9626 4.132842e-02 6.451549e-02 [28,] 9627 2.555672e-02 4.132842e-02 [29,] 9628 1.526262e-02 2.555672e-02 [30,] 9629 8.807196e-03 1.526262e-02 [31,] 9630 4.913158e-03 8.807196e-03 [32,] 9631 2.651165e-03 4.913158e-03 [33,] 9632 1.384548e-03 2.651165e-03 [34,] 9633 7.001918e-04 1.384548e-03 [35,] 9634 3.430881e-04 7.001918e-04 [36,] 9635 1.629716e-04 3.430881e-04 [37,] 9636 7.508792e-05 1.629716e-04 [38,] 9637 3.357441e-05 7.508792e-05 [39,] 9638 1.457638e-05 3.357441e-05 [40,] 9639 6.147676e-06 1.457638e-05 [41,] 9640 2.520008e-06 6.147676e-06 [42,] 9641 1.004446e-06 2.520008e-06 [43,] 9642 3.894769e-07 1.004446e-06 [44,] 9643 1.469801e-07 3.894769e-07 [45,] 9644 5.400585e-08 1.469801e-07 [46,] 9645 1.932889e-08 5.400585e-08 [47,] 9646 6.741074e-09 1.932889e-08 [48,] 9647 2.291782e-09 6.741074e-09 [49,] 9648 7.598014e-10 2.291782e-09 [50,] 9649 2.457336e-10 7.598014e-10 [51,] 9650 7.755616e-11 2.457336e-10 [52,] 9651 2.389462e-11 7.755616e-11 [53,] 9652 7.188789e-12 2.389462e-11 [54,] 9653 2.112605e-12 7.188789e-12 [55,] 9654 6.066219e-13 2.112605e-12 [56,] 9655 1.702479e-13 6.066219e-13 [57,] 9656 4.671227e-14 1.702479e-13 [58,] 9657 1.253384e-14 4.671227e-14 [59,] 9658 3.289691e-15 1.253384e-14 [60,] 9659 8.448020e-16 3.289691e-15 [61,] 9660 2.123198e-16 8.448020e-16 [62,] 9661 5.223544e-17 2.123198e-16 [63,] 9662 1.258288e-17 5.223544e-17 [64,] 9663 2.968464e-18 1.258288e-17 [65,] 9664 6.859854e-19 2.968464e-18 [66,] 9665 1.553177e-19 6.859854e-19 [67,] 9666 3.446184e-20 1.553177e-19 [68,] 9667 7.494689e-21 3.446184e-20 [69,] 9668 1.597900e-21 7.494689e-21 [70,] 9669 3.340471e-22 1.597900e-21 [71,] 9670 6.848673e-23 3.340471e-22 [72,] 9671 1.377279e-23 6.848673e-23 [73,] 9672 2.717245e-24 1.377279e-23 [74,] 9673 5.260155e-25 2.717245e-24 [75,] 9674 9.993129e-26 5.260155e-25 [76,] 9675 1.863398e-26 9.993129e-26 [77,] 9676 3.410962e-27 1.863398e-26 [78,] 9677 6.130272e-28 3.410962e-27 [79,] 9678 1.081874e-28 6.130272e-28 [80,] 9679 1.875118e-29 1.081874e-28 [81,] 9680 3.192233e-30 1.875118e-29 [82,] 9681 5.338660e-31 3.192233e-30 [83,] 9682 8.771980e-32 5.338660e-31 [84,] 9683 1.416268e-32 8.771979e-32 [85,] 9684 2.247137e-33 1.416267e-32 [86,] 9685 3.504354e-34 2.247129e-33 [87,] 9686 5.372303e-35 3.504274e-34 [88,] 9687 8.102095e-36 5.371623e-35 [89,] 9688 1.207820e-36 8.094674e-36 [90,] 9689 1.822016e-37 1.199299e-36 [91,] 9690 3.232609e-38 1.747175e-37 [92,] 9691 1.175494e-38 2.503061e-38 [93,] 9692 8.816208e-39 3.526768e-39 [94,] 9693 8.816208e-39 4.887601e-40 [95,] 9694 8.816208e-39 6.663003e-41 [96,] 9695 8.816208e-39 8.935947e-42 [97,] 9696 8.816208e-39 1.179091e-42 [98,] 9697 8.816208e-39 1.530838e-43 [99,] 9698 8.816208e-39 1.955800e-44 > ## Using bigrational ("Q") is still exact: ---- well there's problem somewhere ! > cbind(x, + cumD = .N(1 - cumsum( dQ)), + revCS= .N(rev(cumsum(rev(dQ)))))[ 1:99, ] x cumD revCS [1,] 9600 1.000000e+00 1.000000e+00 [2,] 9601 9.999999e-01 1.000000e+00 [3,] 9602 9.999994e-01 9.999999e-01 [4,] 9603 9.999959e-01 9.999994e-01 [5,] 9604 9.999780e-01 9.999959e-01 [6,] 9605 9.999047e-01 9.999780e-01 [7,] 9606 9.996568e-01 9.999047e-01 [8,] 9607 9.989411e-01 9.996568e-01 [9,] 9608 9.971417e-01 9.989411e-01 [10,] 9609 9.931390e-01 9.971417e-01 [11,] 9610 9.851633e-01 9.931390e-01 [12,] 9611 9.707833e-01 9.851633e-01 [13,] 9612 9.471293e-01 9.707833e-01 [14,] 9613 9.113830e-01 9.471293e-01 [15,] 9614 8.614582e-01 9.113830e-01 [16,] 9615 7.966884e-01 8.614582e-01 [17,] 9616 7.182857e-01 7.966884e-01 [18,] 9617 6.293888e-01 7.182857e-01 [19,] 9618 5.346474e-01 6.293888e-01 [20,] 9619 4.394493e-01 5.346474e-01 [21,] 9620 3.490111e-01 4.394493e-01 [22,] 9621 2.675795e-01 3.490111e-01 [23,] 9622 1.979277e-01 2.675795e-01 [24,] 9623 1.412172e-01 1.979277e-01 [25,] 9624 9.718179e-02 1.412172e-01 [26,] 9625 6.451549e-02 9.718179e-02 [27,] 9626 4.132842e-02 6.451549e-02 [28,] 9627 2.555672e-02 4.132842e-02 [29,] 9628 1.526262e-02 2.555672e-02 [30,] 9629 8.807196e-03 1.526262e-02 [31,] 9630 4.913158e-03 8.807196e-03 [32,] 9631 2.651165e-03 4.913158e-03 [33,] 9632 1.384548e-03 2.651165e-03 [34,] 9633 7.001918e-04 1.384548e-03 [35,] 9634 3.430881e-04 7.001918e-04 [36,] 9635 1.629716e-04 3.430881e-04 [37,] 9636 7.508792e-05 1.629716e-04 [38,] 9637 3.357441e-05 7.508792e-05 [39,] 9638 1.457638e-05 3.357441e-05 [40,] 9639 6.147676e-06 1.457638e-05 [41,] 9640 2.520008e-06 6.147676e-06 [42,] 9641 1.004446e-06 2.520008e-06 [43,] 9642 3.894769e-07 1.004446e-06 [44,] 9643 1.469801e-07 3.894769e-07 [45,] 9644 5.400585e-08 1.469801e-07 [46,] 9645 1.932889e-08 5.400585e-08 [47,] 9646 6.741074e-09 1.932889e-08 [48,] 9647 2.291782e-09 6.741074e-09 [49,] 9648 7.598014e-10 2.291782e-09 [50,] 9649 2.457336e-10 7.598014e-10 [51,] 9650 7.755616e-11 2.457336e-10 [52,] 9651 2.389462e-11 7.755616e-11 [53,] 9652 7.188789e-12 2.389462e-11 [54,] 9653 2.112605e-12 7.188789e-12 [55,] 9654 6.066219e-13 2.112605e-12 [56,] 9655 1.702479e-13 6.066219e-13 [57,] 9656 4.671227e-14 1.702479e-13 [58,] 9657 1.253384e-14 4.671227e-14 [59,] 9658 3.289691e-15 1.253384e-14 [60,] 9659 8.448020e-16 3.289691e-15 [61,] 9660 2.123198e-16 8.448020e-16 [62,] 9661 5.223544e-17 2.123198e-16 [63,] 9662 1.258288e-17 5.223544e-17 [64,] 9663 2.968464e-18 1.258288e-17 [65,] 9664 6.859854e-19 2.968464e-18 [66,] 9665 1.553177e-19 6.859854e-19 [67,] 9666 3.446184e-20 1.553177e-19 [68,] 9667 7.494689e-21 3.446184e-20 [69,] 9668 1.597900e-21 7.494689e-21 [70,] 9669 3.340471e-22 1.597900e-21 [71,] 9670 6.848673e-23 3.340471e-22 [72,] 9671 1.377279e-23 6.848673e-23 [73,] 9672 2.717245e-24 1.377279e-23 [74,] 9673 5.260155e-25 2.717245e-24 [75,] 9674 9.993129e-26 5.260155e-25 [76,] 9675 1.863398e-26 9.993129e-26 [77,] 9676 3.410962e-27 1.863398e-26 [78,] 9677 6.130272e-28 3.410962e-27 [79,] 9678 1.081874e-28 6.130272e-28 [80,] 9679 1.875118e-29 1.081874e-28 [81,] 9680 3.192233e-30 1.875118e-29 [82,] 9681 5.338660e-31 3.192233e-30 [83,] 9682 8.771979e-32 5.338660e-31 [84,] 9683 1.416267e-32 8.771979e-32 [85,] 9684 2.247129e-33 1.416267e-32 [86,] 9685 3.504274e-34 2.247129e-33 [87,] 9686 5.371623e-35 3.504274e-34 [88,] 9687 8.094674e-36 5.371623e-35 [89,] 9688 1.199299e-36 8.094674e-36 [90,] 9689 1.747175e-37 1.199299e-36 [91,] 9690 2.503061e-38 1.747175e-37 [92,] 9691 3.526768e-39 2.503061e-38 [93,] 9692 4.887601e-40 3.526768e-39 [94,] 9693 6.663003e-41 4.887601e-40 [95,] 9694 8.935947e-42 6.663003e-41 [96,] 9695 1.179091e-42 8.935947e-42 [97,] 9696 1.530838e-43 1.179091e-42 [98,] 9697 1.955800e-44 1.530838e-43 [99,] 9698 2.459062e-45 1.955800e-44 > > ## seems good > I_CSd <- .bigq2mpfr(1 - cumsum(dQ), precB=1024) > roundMpfr(I_CSd, precBits = 8) 400 'mpfr' numbers of precision 8 bits [1] 1 1 1 1 1 1 [7] 1 1 0.9961 0.9922 0.9844 0.9727 [13] 0.9453 0.9102 0.8633 0.7969 0.7188 0.6289 [19] 0.5352 0.4395 0.3496 0.2676 0.1982 0.1416 [25] 0.09717 0.06445 0.04126 0.02551 0.01526 0.008789 [31] 0.004913 0.002655 0.001381 0.0007019 0.0003433 0.0001631 [37] 7.486e-5 3.362e-5 1.46e-5 6.139e-6 2.518e-6 1.006e-6 [43] 3.893e-7 1.471e-7 5.402e-8 1.932e-8 6.752e-9 2.285e-9 [49] 7.603e-10 2.456e-10 7.776e-11 2.387e-11 7.191e-12 2.117e-12 [55] 6.075e-13 1.705e-13 4.663e-14 1.255e-14 3.289e-15 8.431e-16 [61] 2.125e-16 5.226e-17 1.258e-17 2.968e-18 6.844e-19 1.55e-19 [67] 3.452e-20 7.517e-21 1.595e-21 3.342e-22 6.866e-23 1.375e-23 [73] 2.714e-24 5.267e-25 9.976e-26 1.868e-26 3.408e-27 6.122e-28 [79] 1.081e-28 1.874e-29 3.18e-30 5.331e-31 8.782e-32 1.416e-32 [85] 2.251e-33 3.506e-34 5.379e-35 8.087e-36 1.199e-36 1.749e-37 [91] 2.498e-38 3.536e-39 4.879e-40 6.672e-41 8.923e-42 1.177e-42 [97] 1.527e-43 1.953e-44 2.463e-45 3.038e-46 3.712e-47 4.447e-48 [103] 5.239e-49 6.081e-50 6.974e-51 7.83e-52 8.744e-53 9.502e-54 [109] 1.025e-54 1.083e-55 1.131e-56 1.165e-57 1.182e-58 1.175e-59 [115] 1.157e-60 1.124e-61 1.071e-62 1.007e-63 9.318e-65 8.531e-66 [121] 7.65e-67 6.81e-68 5.941e-69 5.116e-70 4.358e-71 3.643e-72 [127] 3.007e-73 2.446e-74 1.96e-75 1.555e-76 1.214e-77 9.319e-79 [133] 7.063e-80 5.271e-81 3.892e-82 2.831e-83 2.027e-84 1.438e-85 [139] 9.991e-87 6.873e-88 4.664e-89 3.114e-90 2.061e-91 1.336e-92 [145] 8.577e-94 5.431e-95 3.394e-96 2.094e-97 1.274e-98 7.644e-100 [151] 4.509e-101 2.637e-102 1.517e-103 8.611e-105 4.803e-106 2.661e-107 [157] 1.45e-108 7.817e-110 4.158e-111 2.177e-112 1.122e-113 5.71e-115 [163] 2.875e-116 1.425e-117 7.009e-119 3.389e-120 1.611e-121 7.564e-123 [169] 3.516e-124 1.616e-125 7.3e-127 3.246e-128 1.431e-129 6.199e-131 [175] 2.664e-132 1.128e-133 4.686e-135 1.935e-136 7.852e-138 3.149e-139 [181] 1.246e-140 4.869e-142 1.874e-143 7.107e-145 2.675e-146 9.874e-148 [187] 3.62e-149 1.298e-150 4.624e-152 1.622e-153 5.623e-155 1.921e-156 [193] 6.487e-158 2.161e-159 7.085e-161 2.292e-162 7.326e-164 2.306e-165 [199] 7.207e-167 2.203e-168 6.676e-170 1.997e-171 5.888e-173 1.714e-174 [205] 4.936e-176 1.396e-177 3.904e-179 1.077e-180 2.918e-182 7.833e-184 [211] 2.08e-185 5.423e-187 1.397e-188 3.542e-190 8.877e-192 2.192e-193 [217] 5.351e-195 1.288e-196 3.057e-198 7.144e-200 1.659e-201 3.768e-203 [223] 8.472e-205 1.869e-206 4.076e-208 8.793e-210 1.871e-211 3.922e-213 [229] 8.086e-215 1.654e-216 3.311e-218 6.556e-220 1.279e-221 2.472e-223 [235] 4.686e-225 8.772e-227 1.618e-228 2.947e-230 5.284e-232 9.317e-234 [241] 1.622e-235 2.783e-237 4.739e-239 7.873e-241 1.296e-242 2.105e-244 [247] 3.361e-246 5.28e-248 8.206e-250 1.255e-251 1.886e-253 2.797e-255 [253] 4.11e-257 5.894e-259 8.384e-261 1.171e-262 1.613e-264 2.193e-266 [259] 2.915e-268 3.845e-270 4.991e-272 6.354e-274 8.011e-276 9.916e-278 [265] 1.205e-279 1.442e-281 1.706e-283 1.983e-285 2.278e-287 2.565e-289 [271] 2.843e-291 3.092e-293 3.333e-295 3.512e-297 3.658e-299 3.733e-301 [277] 3.782e-303 3.738e-305 3.644e-307 3.498e-309 3.293e-311 3.05e-313 [283] 2.777e-315 2.493e-317 2.201e-319 1.907e-321 1.621e-323 1.363e-325 [289] 1.121e-327 9.055e-330 7.218e-332 5.639e-334 4.318e-336 3.264e-338 [295] 2.411e-340 1.758e-342 1.255e-344 8.838e-347 6.066e-349 4.116e-351 [301] 2.728e-353 1.779e-355 1.137e-357 7.173e-360 4.401e-362 2.676e-364 [307] 1.585e-366 9.195e-369 5.261e-371 2.938e-373 1.612e-375 8.664e-378 [313] 4.565e-380 2.367e-382 1.195e-384 5.935e-387 2.877e-389 1.367e-391 [319] 6.376e-394 2.906e-396 1.297e-398 5.667e-401 2.422e-403 1.017e-405 [325] 4.153e-408 1.661e-410 6.518e-413 2.487e-415 9.298e-418 3.397e-420 [331] 1.214e-422 4.219e-425 1.433e-427 4.775e-430 1.545e-432 4.879e-435 [337] 1.511e-437 4.531e-440 1.33e-442 3.812e-445 1.058e-447 2.88e-450 [343] 7.573e-453 1.947e-455 4.886e-458 1.187e-460 2.804e-463 6.457e-466 [349] 1.44e-468 3.115e-471 6.556e-474 1.345e-476 2.645e-479 5.096e-482 [355] 9.472e-485 1.703e-487 2.972e-490 5.012e-493 8.14e-496 1.278e-498 [361] 1.943e-501 2.846e-504 4.015e-507 5.465e-510 7.138e-513 9.002e-516 [367] 1.091e-518 1.265e-521 1.406e-524 1.496e-527 1.527e-530 1.485e-533 [373] 1.382e-536 1.22e-539 1.028e-542 8.222e-546 6.231e-549 4.481e-552 [379] 3.033e-555 1.93e-558 1.156e-561 6.512e-565 3.42e-568 1.67e-571 [385] 7.548e-575 3.159e-578 1.205e-581 4.236e-585 1.341e-588 3.811e-592 [391] 9.704e-596 2.16e-599 4.151e-603 6.77e-607 9.075e-611 9.654e-615 [397] 7.555e-619 3.919e-623 9.991e-628 0 > .N(log(I_CSd)) # should be "exact" [1] -2.376936e-09 -5.176749e-08 -5.625500e-07 -4.067877e-06 -2.202648e-05 [6] -9.529271e-05 -3.432524e-04 -1.059436e-03 -2.862375e-03 -6.884606e-03 [11] -1.494791e-02 -2.965202e-02 -5.431961e-02 -9.279208e-02 -1.491287e-01 [16] -2.272916e-01 -3.308879e-01 -4.630061e-01 -6.261478e-01 -8.222330e-01 [21] -1.052652e+00 -1.318339e+00 -1.619853e+00 -1.957456e+00 -2.331172e+00 [26] -2.740850e+00 -3.186205e+00 -3.666855e+00 -4.182348e+00 -4.732186e+00 [31] -5.315838e+00 -5.932756e+00 -6.582382e+00 -7.264156e+00 -7.977523e+00 [36] -8.721934e+00 -9.496851e+00 -1.030175e+01 -1.113611e+01 -1.199944e+01 [41] -1.289125e+01 -1.381107e+01 -1.475846e+01 -1.573297e+01 -1.673417e+01 [46] -1.776166e+01 -1.881505e+01 -1.989394e+01 -2.099796e+01 -2.212677e+01 [51] -2.328002e+01 -2.445737e+01 -2.565850e+01 -2.688310e+01 -2.813087e+01 [56] -2.940152e+01 -3.069477e+01 -3.201034e+01 -3.334798e+01 -3.470743e+01 [61] -3.608844e+01 -3.749077e+01 -3.891419e+01 -4.035849e+01 -4.182343e+01 [66] -4.330881e+01 -4.481443e+01 -4.634009e+01 -4.788560e+01 -4.945076e+01 [71] -5.103540e+01 -5.263935e+01 -5.426242e+01 -5.590447e+01 -5.756531e+01 [76] -5.924481e+01 -6.094280e+01 -6.265914e+01 -6.439369e+01 -6.614630e+01 [81] -6.791683e+01 -6.970516e+01 -7.151116e+01 -7.333470e+01 -7.517565e+01 [86] -7.703391e+01 -7.890935e+01 -8.080186e+01 -8.271133e+01 -8.463765e+01 [91] -8.658072e+01 -8.854044e+01 -9.051670e+01 -9.250942e+01 -9.451849e+01 [96] -9.654383e+01 -9.858534e+01 -1.006429e+02 -1.027165e+02 -1.048061e+02 [101] -1.069114e+02 -1.090326e+02 -1.111694e+02 -1.133218e+02 -1.154897e+02 [106] -1.176731e+02 -1.198719e+02 -1.220861e+02 -1.243155e+02 -1.265600e+02 [111] -1.288198e+02 -1.310945e+02 -1.333843e+02 -1.356891e+02 -1.380087e+02 [116] -1.403432e+02 -1.426924e+02 -1.450564e+02 -1.474351e+02 -1.498284e+02 [121] -1.522363e+02 -1.546587e+02 -1.570956e+02 -1.595469e+02 -1.620126e+02 [126] -1.644927e+02 -1.669871e+02 -1.694958e+02 -1.720187e+02 -1.745558e+02 [131] -1.771070e+02 -1.796724e+02 -1.822518e+02 -1.848453e+02 -1.874528e+02 [136] -1.900743e+02 -1.927097e+02 -1.953590e+02 -1.980223e+02 -2.006994e+02 [141] -2.033903e+02 -2.060950e+02 -2.088135e+02 -2.115458e+02 -2.142918e+02 [146] -2.170514e+02 -2.198248e+02 -2.226118e+02 -2.254125e+02 -2.282268e+02 [151] -2.310546e+02 -2.338961e+02 -2.367511e+02 -2.396196e+02 -2.425017e+02 [156] -2.453972e+02 -2.483063e+02 -2.512288e+02 -2.541648e+02 -2.571142e+02 [161] -2.600771e+02 -2.630534e+02 -2.660431e+02 -2.690462e+02 -2.720627e+02 [166] -2.750926e+02 -2.781358e+02 -2.811924e+02 -2.842624e+02 -2.873457e+02 [171] -2.904423e+02 -2.935523e+02 -2.966756e+02 -2.998123e+02 -3.029622e+02 [176] -3.061255e+02 -3.093021e+02 -3.124920e+02 -3.156953e+02 -3.189118e+02 [181] -3.221416e+02 -3.253848e+02 -3.286413e+02 -3.319110e+02 -3.351941e+02 [186] -3.384906e+02 -3.418003e+02 -3.451234e+02 -3.484597e+02 -3.518095e+02 [191] -3.551725e+02 -3.585489e+02 -3.619387e+02 -3.653418e+02 -3.687583e+02 [196] -3.721881e+02 -3.756314e+02 -3.790880e+02 -3.825581e+02 -3.860415e+02 [201] -3.895384e+02 -3.930487e+02 -3.965725e+02 -4.001097e+02 -4.036604e+02 [206] -4.072245e+02 -4.108022e+02 -4.143934e+02 -4.179982e+02 -4.216165e+02 [211] -4.252483e+02 -4.288938e+02 -4.325528e+02 -4.362255e+02 -4.399118e+02 [216] -4.436117e+02 -4.473254e+02 -4.510527e+02 -4.547938e+02 -4.585486e+02 [221] -4.623172e+02 -4.660996e+02 -4.698958e+02 -4.737058e+02 -4.775298e+02 [226] -4.813676e+02 -4.852193e+02 -4.890849e+02 -4.929646e+02 -4.968582e+02 [231] -5.007659e+02 -5.046877e+02 -5.086235e+02 -5.125735e+02 -5.165376e+02 [236] -5.205159e+02 -5.245084e+02 -5.285152e+02 -5.325363e+02 -5.365717e+02 [241] -5.406215e+02 -5.446857e+02 -5.487643e+02 -5.528574e+02 -5.569650e+02 [246] -5.610872e+02 -5.652239e+02 -5.693754e+02 -5.735415e+02 -5.777223e+02 [251] -5.819179e+02 -5.861283e+02 -5.903536e+02 -5.945938e+02 -5.988489e+02 [256] -6.031191e+02 -6.074043e+02 -6.117046e+02 -6.160201e+02 -6.203508e+02 [261] -6.246967e+02 -6.290580e+02 -6.334346e+02 -6.378267e+02 -6.422342e+02 [266] -6.466574e+02 -6.510961e+02 -6.555505e+02 -6.600206e+02 -6.645065e+02 [271] -6.690082e+02 -6.735259e+02 -6.780596e+02 -6.826093e+02 -6.871752e+02 [276] -6.917572e+02 -6.963555e+02 -7.009702e+02 -7.056013e+02 -7.102488e+02 [281] -7.149130e+02 -7.195937e+02 -7.242912e+02 -7.290055e+02 -7.337367e+02 [286] -7.384849e+02 -7.432502e+02 -7.480326e+02 -7.528322e+02 -7.576491e+02 [291] -7.624835e+02 -7.673354e+02 -7.722050e+02 -7.770922e+02 -7.819973e+02 [296] -7.869202e+02 -7.918612e+02 -7.968204e+02 -8.017977e+02 -8.067935e+02 [301] -8.118076e+02 -8.168404e+02 -8.218919e+02 -8.269622e+02 -8.320514e+02 [306] -8.371597e+02 -8.422872e+02 -8.474340e+02 -8.526003e+02 -8.577862e+02 [311] -8.629919e+02 -8.682174e+02 -8.734630e+02 -8.787287e+02 -8.840148e+02 [316] -8.893214e+02 -8.946486e+02 -8.999967e+02 -9.053657e+02 -9.107559e+02 [321] -9.161674e+02 -9.216005e+02 -9.270553e+02 -9.325319e+02 -9.380307e+02 [326] -9.435517e+02 -9.490953e+02 -9.546615e+02 -9.602507e+02 -9.658631e+02 [331] -9.714988e+02 -9.771581e+02 -9.828413e+02 -9.885486e+02 -9.942802e+02 [336] -1.000037e+03 -1.005818e+03 -1.011624e+03 -1.017456e+03 -1.023313e+03 [341] -1.029197e+03 -1.035107e+03 -1.041044e+03 -1.047008e+03 -1.052999e+03 [346] -1.059018e+03 -1.065065e+03 -1.071141e+03 -1.077246e+03 -1.083380e+03 [351] -1.089543e+03 -1.095738e+03 -1.101962e+03 -1.108218e+03 -1.114506e+03 [356] -1.120826e+03 -1.127179e+03 -1.133565e+03 -1.139985e+03 -1.146440e+03 [361] -1.152930e+03 -1.159456e+03 -1.166019e+03 -1.172620e+03 -1.179259e+03 [366] -1.185937e+03 -1.192655e+03 -1.199414e+03 -1.206215e+03 -1.213060e+03 [371] -1.219949e+03 -1.226883e+03 -1.233864e+03 -1.240894e+03 -1.247974e+03 [376] -1.255105e+03 -1.262290e+03 -1.269529e+03 -1.276827e+03 -1.284184e+03 [381] -1.291603e+03 -1.299088e+03 -1.306640e+03 -1.314265e+03 -1.321965e+03 [386] -1.329746e+03 -1.337613e+03 -1.345571e+03 -1.353627e+03 -1.361790e+03 [391] -1.370071e+03 -1.378481e+03 -1.387036e+03 -1.395758e+03 -1.404674e+03 [396] -1.413825e+03 -1.423276e+03 -1.433145e+03 -1.443719e+03 -Inf > > ## rel.err : > relE.up.ln <- .N(1- phyper(x, m,n,k, lower.tail = FALSE, log.p = TRUE) / log(I_CSd)) > plot(x, relE.up.ln, type = "o", cex = 1/2) > abline(h = c(-1,1)*.Machine$double.eps, col = "thistle", lty=2) > plot(x, log(I_CSd), type="l") > ## rel.err of phyper(*, log=TRUE) : --> is exploding! > 1- phyper(x, m,n,k, log.p=TRUE) / log(cumsum(dM)) 400 'mpfr' numbers of precision 128 bits [1] -1.117257907861727714495131721380131208068e-16 [2] -1.595008077465590303095071606307696133825e-16 [3] -5.347305900365189232637596380740120783232e-17 [4] 3.214310466959637793754934207761368871848e-18 [5] -2.241437458771475410899506806364518431404e-16 [6] -4.976914012776012326558001150782140109881e-16 [7] 1.096747576102529822839117314162050691462e-16 [8] 2.397923885510723537324379766475382814242e-17 [9] -1.149243620489414494210355280191764501001e-16 [10] 1.820920232470535447163354314448267042556e-16 [11] -6.968501114923159461309824953086354546516e-16 [12] -7.453124320474243281887085517534326277593e-17 [13] -1.165763987189789512356035890720094548179e-18 [14] -2.672754330800615320991747418481611885658e-16 [15] -1.03061186305887765307512693212117459072e-16 [16] -9.880644351894815699458248137196956476825e-16 [17] -9.597265511154601748364717118001268358139e-16 [18] -2.977464468862734606952451963658298651511e-16 [19] -1.884207937516109485875738794444399817285e-15 [20] -4.386787891278399163647797876549821122194e-16 [21] 1.320555677898452901193545087372930631206e-16 [22] -1.363415783560193411025467474838227299881e-15 [23] 3.909435525758006834176535389912155626367e-16 [24] -8.59249838774539602655099494841938227385e-16 [25] 1.030528427743552784619983025273066042924e-15 [26] -8.855208972748991196515179341403029199563e-16 [27] -1.06355024874152378063813399659565286689e-15 [28] -3.485468107696886823193562616298414813784e-15 [29] -3.213309068704263216654702005448040339205e-15 [30] -1.259157778021697034753453580597930463529e-15 [31] -3.640964750550305782271163521697237179776e-16 [32] 4.250400381079873756643737378714934501676e-16 [33] -8.914565983988658174899838969968893818566e-16 [34] -3.829899035517887705651065460338025411946e-15 [35] -1.011700088814995027538505055806250994852e-14 [36] -3.204197590368960983524317179442416566939e-15 [37] -7.817404892427927614547064367184383976209e-15 [38] -7.984636389711339048271924413046629565717e-15 [39] -3.272086895056314771002130612521213214119e-15 [40] 2.929246754622445516927437007845563535677e-15 [41] -7.344767253991834612919790777613422886556e-15 [42] -1.822029844073211524816306687885771679944e-15 [43] -3.580713620744454524634789232573381687601e-15 [44] -1.0502147566918760683573707090638133275e-14 [45] -4.053591533151374226669942949644389335243e-15 [46] -1.245297003263614849502637896469279378003e-15 [47] 1.884878427496493990773715511459450037362e-15 [48] 5.994815489023650346219991328173984107565e-15 [49] 2.696501053840907023799651497994947406761e-15 [50] -1.038554469765200980265276716174133267665e-14 [51] -5.19389707553510238493598545348168929202e-15 [52] -1.11911409469546226939432197978966876632e-14 [53] -6.543438140214468008841534451123653760349e-15 [54] 5.493212498210793936924580443352296899213e-15 [55] 4.933718200058551598677176961256189246751e-15 [56] 2.265803472787838701777745680104638922099e-15 [57] -2.888049115263706002924330580662555456011e-15 [58] -1.142045646936947033854257929461096859969e-14 [59] 9.585379347333063047783388151054628186161e-15 [60] -1.339246308069166786949003726160000242842e-14 [61] 1.262328661211827986066013098231132422716e-14 [62] 6.063499757542619930133932137803919911355e-15 [63] -1.193876983757114773123638962985950476891e-14 [64] 3.949694958134048590549433855621801785193e-15 [65] -8.247329956439329604530067127628781571281e-15 [66] 8.358645990879618866766891112215115235958e-15 [67] 2.671684906916270803901576701860008724095e-15 [68] 6.244341413641614692488760587273768424177e-15 [69] 1.215661311018061788661034020048201499719e-15 [70] -1.159493154442417950421493500123487346495e-14 [71] 9.740471460444808126641466835037062216701e-15 [72] 1.066862667744536040322651431568505129424e-15 [73] -1.622269756974281268713034827303804848389e-15 [74] -2.967979780812921780403026994401466301998e-15 [75] 2.883319846717172613890851620518210177995e-14 [76] 2.310182564629115843956835925599246701246e-13 [77] 1.439152420040674826870238267911022990762e-12 [78] 8.382290933949356526936605904951099512545e-12 [79] 5.110438248342772001383877691023144721446e-11 [80] 3.652614878551152162224652229124403876935e-10 [81] 2.488420667561234691947130699933611197308e-9 [82] 1.261018602942261985608145156066592183075e-8 [83] 8.92081844646724341241125185244618675053e-8 [84] 5.970576405475736002010782929251607900796e-7 [85] 3.229255853423890039312463965955694521372e-6 [86] 2.286007941471672555098250959808110699957e-5 [87] 0.0001266351162221002498487043508547981618165 [88] 0.0009158647401133755572095626845582954784703 [89] 0.007055139107060584186481701667871499024242 [90] 0.04107601030974771285928586768286843462529 [91] 0.225683959570016735473142365332354198817 [92] 0.6999757451405270169964012438867939636111 [93] 0.9445611845653533270953753723612559648861 [94] 0.9924423253614362873398224706988912657835 [95] 0.9989864182605597246975929574356693289408 [96] 0.9998662586815021517954067686861918673458 [97] 0.9999826360886657815575517584590533222875 [98] 0.9999977815860676940003724937009362457483 [99] 0.9999997210748606673340377990898304727541 [100] 0.9999999654841280263160016979085017128914 [101] 0.9999999957959165451695645721322125844092 [102] 0.999999999495943292289237192861523561096 [103] 0.9999999999405055417203632155823264038741 [104] 0.9999999999930865423479917579798334368313 [105] 0.999999999999209016174956100342620704963 [106] 0.9999999999999108904100984740614152737361 [107] 0.9999999999999901145575107811962982369271 [108] 0.9999999999999989200288736486959922559722 [109] 0.9999999999999998838012794892941828267514 [110] 0.9999999999999999876862078580772458566563 [111] 0.9999999999999999987146808734668164936074 [112] 0.9999999999999999998678444110214498500313 [113] 0.9999999999999999999866142846675734835863 [114] 0.9999999999999999999986643134582349796476 [115] 0.9999999999999999999998686895681432137079 [116] 0.9999999999999999999999872810925460954685 [117] 0.9999999999999999999999987861085153207715 [118] 0.9999999999999999999999998858404112293552 [119] 0.9999999999999999999999999894203861400628 [120] 0.9999999999999999999999999990337845400306 [121] 0.9999999999999999999999999999130346611793 [122] 0.9999999999999999999999999999922855101493 [123] 0.9999999999999999999999999999993255072748 [124] 0.9999999999999999999999999999999418732443 [125] 0.9999999999999999999999999999999950623213 [126] 0.9999999999999999999999999999999995865375 [127] 0.9999999999999999999999999999999999658695 [128] 0.9999999999999999999999999999999999972229 [129] 0.9999999999999999999999999999999999997767 [130] 0.9999999999999999999999999999999999999824 [131] 1 [132] 1 [133] 1 [134] 1 [135] 1 [136] 1 [137] 1 [138] 1 [139] 1 [140] 1 [141] 1 [142] 1 [143] 1 [144] 1 [145] 1 [146] 1 [147] 1 [148] 1 [149] 1 [150] 1 [151] 1 [152] 1 [153] 1 [154] 1 [155] 1 [156] 1 [157] 1 [158] 1 [159] 1 [160] 1 [161] 1 [162] 1 [163] 1 [164] 1 [165] 1 [166] 1 [167] 1 [168] 1 [169] 1 [170] 1 [171] 1 [172] 1 [173] 1 [174] 1 [175] 1 [176] 1 [177] 1 [178] 1 [179] 1 [180] 1 [181] 1 [182] 1 [183] 1 [184] 1 [185] 1 [186] 1 [187] 1 [188] 1 [189] 1 [190] 1 [191] 1 [192] 1 [193] 1 [194] 1 [195] 1 [196] 1 [197] 1 [198] 1 [199] 1 [200] 1 [201] 1 [202] 1 [203] 1 [204] 1 [205] 1 [206] 1 [207] 1 [208] 1 [209] 1 [210] 1 [211] 1 [212] 1 [213] 1 [214] 1 [215] 1 [216] 1 [217] 1 [218] 1 [219] 1 [220] 1 [221] 1 [222] 1 [223] 1 [224] 1 [225] 1 [226] 1 [227] 1 [228] 1 [229] 1 [230] 1 [231] 1 [232] 1 [233] 1 [234] 1 [235] 1 [236] 1 [237] 1 [238] 1 [239] 1 [240] 1 [241] 1 [242] 1 [243] 1 [244] 1 [245] 1 [246] 1 [247] 1 [248] 1 [249] 1 [250] 1 [251] 1 [252] 1 [253] 1 [254] 1 [255] 1 [256] 1 [257] 1 [258] 1 [259] 1 [260] 1 [261] 1 [262] 1 [263] 1 [264] 1 [265] 1 [266] 1 [267] 1 [268] 1 [269] 1 [270] 1 [271] 1 [272] 1 [273] 1 [274] 1 [275] 1 [276] 1 [277] 1 [278] 1 [279] 1 [280] 1 [281] 1 [282] 1 [283] 1 [284] 1 [285] 1 [286] 1 [287] 1 [288] 1 [289] 1 [290] 1 [291] 1 [292] 1 [293] 1 [294] 1 [295] 1 [296] 1 [297] 1 [298] 1 [299] 1 [300] 1 [301] 1 [302] 1 [303] 1 [304] 1 [305] 1 [306] 1 [307] 1 [308] 1 [309] 1 [310] 1 [311] 1 [312] 1 [313] 1 [314] 1 [315] 1 [316] 1 [317] 1 [318] 1 [319] 1 [320] 1 [321] 1 [322] 1 [323] 1 [324] 1 [325] 1 [326] 1 [327] 1 [328] 1 [329] 1 [330] 1 [331] 1 [332] 1 [333] 1 [334] 1 [335] 1 [336] 1 [337] 1 [338] 1 [339] 1 [340] 1 [341] 1 [342] 1 [343] 1 [344] 1 [345] 1 [346] 1 [347] 1 [348] 1 [349] 1 [350] 1 [351] 1 [352] 1 [353] 1 [354] 1 [355] 1 [356] 1 [357] 1 [358] 1 [359] 1 [360] 1 [361] 1 [362] 1 [363] 1 [364] 1 [365] 1 [366] 1 [367] 1 [368] 1 [369] 1 [370] 1 [371] 1 [372] 1 [373] 1 [374] 1 [375] 1 [376] 1 [377] 1 [378] 1 [379] 1 [380] 1 [381] 1 [382] 1 [383] 1 [384] 1 [385] 1 [386] 1 [387] 1 [388] 1 [389] 1 [390] 1 [391] 1 [392] 1 [393] 1 [394] 1 [395] 1 [396] 1 [397] 1 [398] 1 [399] 1 [400] 1 > > > > proc.time() user system elapsed 1.62 0.17 1.73