2021-01-18 15:20:06 +03:00
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// Copyright (c) 2019-2021 Alexander Medvednikov. All rights reserved.
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2019-12-27 06:08:17 +03:00
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// Use of this source code is governed by an MIT license
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// that can be found in the LICENSE file.
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module factorial
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const (
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2021-05-08 13:32:29 +03:00
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log_sqrt_2pi = 9.18938533204672741780329736e-1
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2019-12-27 06:08:17 +03:00
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2021-05-08 13:32:29 +03:00
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b_numbers = [
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/*
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Bernoulli numbers B(2),B(4),B(6),...,B(20). Only B(2),...,B(10) currently
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2019-12-27 06:08:17 +03:00
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* used.
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2021-05-08 13:32:29 +03:00
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*/
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f64(1.0 / (6.0 * 2.0 * 1.0)),
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-1.0 / (30.0 * 4.0 * 3.0),
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1.0 / (42.0 * 6.0 * 5.0),
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-1.0 / (30.0 * 8.0 * 7.0),
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5.0 / (66.0 * 10.0 * 9.0),
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-691.0 / (2730.0 * 12.0 * 11.0),
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7.0 / (6.0 * 14.0 * 13.0),
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-3617.0 / (510.0 * 16.0 * 15.0),
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43867.0 / (796.0 * 18.0 * 17.0),
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-174611.0 / (330.0 * 20.0 * 19.0),
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]
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2019-12-27 06:08:17 +03:00
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2021-05-08 13:32:29 +03:00
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factorials_table = [
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f64(1.000000000000000000000e+0), /* 0! */
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1.000000000000000000000e+0, /* 1! */
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2.000000000000000000000e+0, /* 2! */
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6.000000000000000000000e+0, /* 3! */
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2.400000000000000000000e+1, /* 4! */
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1.200000000000000000000e+2, /* 5! */
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7.200000000000000000000e+2, /* 6! */
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5.040000000000000000000e+3, /* 7! */
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4.032000000000000000000e+4, /* 8! */
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3.628800000000000000000e+5, /* 9! */
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3.628800000000000000000e+6, /* 10! */
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3.991680000000000000000e+7, /* 11! */
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4.790016000000000000000e+8, /* 12! */
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6.227020800000000000000e+9, /* 13! */
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8.717829120000000000000e+10, /* 14! */
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1.307674368000000000000e+12, /* 15! */
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2.092278988800000000000e+13, /* 16! */
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3.556874280960000000000e+14, /* 17! */
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6.402373705728000000000e+15, /* 18! */
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1.216451004088320000000e+17, /* 19! */
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2.432902008176640000000e+18, /* 20! */
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5.109094217170944000000e+19, /* 21! */
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1.124000727777607680000e+21, /* 22! */
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2.585201673888497664000e+22, /* 23! */
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6.204484017332394393600e+23, /* 24! */
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1.551121004333098598400e+25, /* 25! */
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4.032914611266056355840e+26, /* 26! */
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1.088886945041835216077e+28, /* 27! */
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3.048883446117138605015e+29, /* 28! */
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8.841761993739701954544e+30, /* 29! */
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2.652528598121910586363e+32, /* 30! */
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8.222838654177922817726e+33, /* 31! */
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2.631308369336935301672e+35, /* 32! */
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8.683317618811886495518e+36, /* 33! */
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2.952327990396041408476e+38, /* 34! */
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1.033314796638614492967e+40, /* 35! */
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3.719933267899012174680e+41, /* 36! */
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1.376375309122634504632e+43, /* 37! */
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5.230226174666011117600e+44, /* 38! */
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2.039788208119744335864e+46, /* 39! */
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8.159152832478977343456e+47, /* 40! */
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3.345252661316380710817e+49, /* 41! */
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1.405006117752879898543e+51, /* 42! */
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6.041526306337383563736e+52, /* 43! */
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2.658271574788448768044e+54, /* 44! */
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1.196222208654801945620e+56, /* 45! */
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5.502622159812088949850e+57, /* 46! */
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2.586232415111681806430e+59, /* 47! */
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1.241391559253607267086e+61, /* 48! */
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6.082818640342675608723e+62, /* 49! */
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3.041409320171337804361e+64, /* 50! */
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1.551118753287382280224e+66, /* 51! */
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8.065817517094387857166e+67, /* 52! */
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4.274883284060025564298e+69, /* 53! */
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2.308436973392413804721e+71, /* 54! */
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1.269640335365827592597e+73, /* 55! */
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7.109985878048634518540e+74, /* 56! */
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4.052691950487721675568e+76, /* 57! */
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2.350561331282878571829e+78, /* 58! */
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1.386831185456898357379e+80, /* 59! */
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8.320987112741390144276e+81, /* 60! */
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5.075802138772247988009e+83, /* 61! */
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3.146997326038793752565e+85, /* 62! */
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1.982608315404440064116e+87, /* 63! */
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1.268869321858841641034e+89, /* 64! */
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8.247650592082470666723e+90, /* 65! */
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5.443449390774430640037e+92, /* 66! */
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3.647111091818868528825e+94, /* 67! */
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2.480035542436830599601e+96, /* 68! */
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1.711224524281413113725e+98, /* 69! */
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1.197857166996989179607e+100, /* 70! */
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8.504785885678623175212e+101, /* 71! */
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6.123445837688608686152e+103, /* 72! */
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4.470115461512684340891e+105, /* 73! */
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3.307885441519386412260e+107, /* 74! */
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2.480914081139539809195e+109, /* 75! */
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1.885494701666050254988e+111, /* 76! */
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1.451830920282858696341e+113, /* 77! */
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1.132428117820629783146e+115, /* 78! */
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8.946182130782975286851e+116, /* 79! */
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7.156945704626380229481e+118, /* 80! */
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5.797126020747367985880e+120, /* 81! */
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4.753643337012841748421e+122, /* 82! */
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3.945523969720658651190e+124, /* 83! */
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3.314240134565353266999e+126, /* 84! */
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2.817104114380550276949e+128, /* 85! */
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2.422709538367273238177e+130, /* 86! */
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2.107757298379527717214e+132, /* 87! */
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1.854826422573984391148e+134, /* 88! */
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1.650795516090846108122e+136, /* 89! */
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1.485715964481761497310e+138, /* 90! */
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1.352001527678402962552e+140, /* 91! */
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1.243841405464130725548e+142, /* 92! */
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1.156772507081641574759e+144, /* 93! */
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1.087366156656743080274e+146, /* 94! */
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1.032997848823905926260e+148, /* 95! */
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9.916779348709496892096e+149, /* 96! */
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9.619275968248211985333e+151, /* 97! */
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9.426890448883247745626e+153, /* 98! */
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9.332621544394415268170e+155, /* 99! */
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9.332621544394415268170e+157, /* 100! */
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9.425947759838359420852e+159, /* 101! */
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9.614466715035126609269e+161, /* 102! */
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9.902900716486180407547e+163, /* 103! */
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1.029901674514562762385e+166, /* 104! */
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1.081396758240290900504e+168, /* 105! */
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1.146280563734708354534e+170, /* 106! */
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1.226520203196137939352e+172, /* 107! */
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1.324641819451828974500e+174, /* 108! */
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1.443859583202493582205e+176, /* 109! */
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1.588245541522742940425e+178, /* 110! */
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1.762952551090244663872e+180, /* 111! */
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1.974506857221074023537e+182, /* 112! */
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2.231192748659813646597e+184, /* 113! */
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2.543559733472187557120e+186, /* 114! */
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2.925093693493015690688e+188, /* 115! */
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3.393108684451898201198e+190, /* 116! */
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3.969937160808720895402e+192, /* 117! */
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4.684525849754290656574e+194, /* 118! */
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5.574585761207605881323e+196, /* 119! */
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6.689502913449127057588e+198, /* 120! */
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8.094298525273443739682e+200, /* 121! */
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9.875044200833601362412e+202, /* 122! */
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1.214630436702532967577e+205, /* 123! */
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1.506141741511140879795e+207, /* 124! */
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1.882677176888926099744e+209, /* 125! */
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2.372173242880046885677e+211, /* 126! */
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3.012660018457659544810e+213, /* 127! */
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3.856204823625804217357e+215, /* 128! */
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4.974504222477287440390e+217, /* 129! */
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6.466855489220473672507e+219, /* 130! */
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8.471580690878820510985e+221, /* 131! */
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1.118248651196004307450e+224, /* 132! */
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1.487270706090685728908e+226, /* 133! */
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1.992942746161518876737e+228, /* 134! */
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2.690472707318050483595e+230, /* 135! */
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3.659042881952548657690e+232, /* 136! */
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5.012888748274991661035e+234, /* 137! */
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6.917786472619488492228e+236, /* 138! */
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9.615723196941089004197e+238, /* 139! */
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1.346201247571752460588e+241, /* 140! */
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1.898143759076170969429e+243, /* 141! */
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2.695364137888162776589e+245, /* 142! */
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3.854370717180072770522e+247, /* 143! */
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5.550293832739304789551e+249, /* 144! */
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8.047926057471991944849e+251, /* 145! */
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1.174997204390910823948e+254, /* 146! */
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1.727245890454638911203e+256, /* 147! */
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2.556323917872865588581e+258, /* 148! */
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3.808922637630569726986e+260, /* 149! */
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5.713383956445854590479e+262, /* 150! */
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8.627209774233240431623e+264, /* 151! */
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1.311335885683452545607e+267, /* 152! */
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2.006343905095682394778e+269, /* 153! */
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3.089769613847350887959e+271, /* 154! */
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4.789142901463393876336e+273, /* 155! */
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7.471062926282894447084e+275, /* 156! */
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1.172956879426414428192e+278, /* 157! */
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1.853271869493734796544e+280, /* 158! */
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2.946702272495038326504e+282, /* 159! */
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4.714723635992061322407e+284, /* 160! */
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7.590705053947218729075e+286, /* 161! */
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1.229694218739449434110e+289, /* 162! */
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2.004401576545302577600e+291, /* 163! */
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3.287218585534296227263e+293, /* 164! */
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5.423910666131588774984e+295, /* 165! */
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9.003691705778437366474e+297, /* 166! */
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1.503616514864999040201e+300, /* 167! */
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2.526075744973198387538e+302, /* 168! */
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4.269068009004705274939e+304, /* 169! */
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7.257415615307998967397e+306, /* 170! */
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2019-12-27 06:08:17 +03:00
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]
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2020-04-09 05:21:11 +03:00
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log_factorials_table = [
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2021-05-08 13:32:29 +03:00
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f64(0.000000000000000000000e+0), /* 0! */
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0.000000000000000000000e+0, /* 1! */
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6.931471805599453094172e-1, /* 2! */
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1.791759469228055000812e+0, /* 3! */
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3.178053830347945619647e+0, /* 4! */
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4.787491742782045994248e+0, /* 5! */
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6.579251212010100995060e+0, /* 6! */
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8.525161361065414300166e+0, /* 7! */
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1.060460290274525022842e+1, /* 8! */
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1.280182748008146961121e+1, /* 9! */
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1.510441257307551529523e+1, /* 10! */
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1.750230784587388583929e+1, /* 11! */
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1.998721449566188614952e+1, /* 12! */
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2.255216385312342288557e+1, /* 13! */
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2.519122118273868150009e+1, /* 14! */
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2.789927138384089156609e+1, /* 15! */
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3.067186010608067280376e+1, /* 16! */
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3.350507345013688888401e+1, /* 17! */
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3.639544520803305357622e+1, /* 18! */
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3.933988418719949403622e+1, /* 19! */
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4.233561646075348502966e+1, /* 20! */
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4.538013889847690802616e+1, /* 21! */
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4.847118135183522387964e+1, /* 22! */
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5.160667556776437357045e+1, /* 23! */
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5.478472939811231919009e+1, /* 24! */
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5.800360522298051993929e+1, /* 25! */
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6.126170176100200198477e+1, /* 26! */
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6.455753862700633105895e+1, /* 27! */
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6.788974313718153498289e+1, /* 28! */
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7.125703896716800901007e+1, /* 29! */
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7.465823634883016438549e+1, /* 30! */
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7.809222355331531063142e+1, /* 31! */
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8.155795945611503717850e+1, /* 32! */
|
|
|
|
|
8.505446701758151741396e+1, /* 33! */
|
|
|
|
|
8.858082754219767880363e+1, /* 34! */
|
|
|
|
|
9.213617560368709248333e+1, /* 35! */
|
|
|
|
|
9.571969454214320248496e+1, /* 36! */
|
|
|
|
|
9.933061245478742692933e+1, /* 37! */
|
|
|
|
|
1.029681986145138126988e+2, /* 38! */
|
|
|
|
|
1.066317602606434591262e+2, /* 39! */
|
|
|
|
|
1.103206397147573954291e+2, /* 40! */
|
|
|
|
|
1.140342117814617032329e+2, /* 41! */
|
|
|
|
|
1.177718813997450715388e+2, /* 42! */
|
|
|
|
|
1.215330815154386339623e+2, /* 43! */
|
|
|
|
|
1.253172711493568951252e+2, /* 44! */
|
|
|
|
|
1.291239336391272148826e+2, /* 45! */
|
|
|
|
|
1.329525750356163098828e+2, /* 46! */
|
|
|
|
|
1.368027226373263684696e+2, /* 47! */
|
|
|
|
|
1.406739236482342593987e+2, /* 48! */
|
|
|
|
|
1.445657439463448860089e+2, /* 49! */
|
|
|
|
|
1.484777669517730320675e+2, /* 50! */
|
|
|
|
|
1.524095925844973578392e+2, /* 51! */
|
|
|
|
|
1.563608363030787851941e+2, /* 52! */
|
|
|
|
|
1.603311282166309070282e+2, /* 53! */
|
|
|
|
|
1.643201122631951814118e+2, /* 54! */
|
|
|
|
|
1.683274454484276523305e+2, /* 55! */
|
|
|
|
|
1.723527971391628015638e+2, /* 56! */
|
|
|
|
|
1.763958484069973517152e+2, /* 57! */
|
|
|
|
|
1.804562914175437710518e+2, /* 58! */
|
|
|
|
|
1.845338288614494905025e+2, /* 59! */
|
|
|
|
|
1.886281734236715911873e+2, /* 60! */
|
|
|
|
|
1.927390472878449024360e+2, /* 61! */
|
|
|
|
|
1.968661816728899939914e+2, /* 62! */
|
|
|
|
|
2.010093163992815266793e+2, /* 63! */
|
|
|
|
|
2.051681994826411985358e+2, /* 64! */
|
|
|
|
|
2.093425867525368356464e+2, /* 65! */
|
|
|
|
|
2.135322414945632611913e+2, /* 66! */
|
|
|
|
|
2.177369341139542272510e+2, /* 67! */
|
|
|
|
|
2.219564418191303339501e+2, /* 68! */
|
|
|
|
|
2.261905483237275933323e+2, /* 69! */
|
|
|
|
|
2.304390435657769523214e+2, /* 70! */
|
|
|
|
|
2.347017234428182677427e+2, /* 71! */
|
|
|
|
|
2.389783895618343230538e+2, /* 72! */
|
|
|
|
|
2.432688490029827141829e+2, /* 73! */
|
|
|
|
|
2.475729140961868839366e+2, /* 74! */
|
|
|
|
|
2.518904022097231943772e+2, /* 75! */
|
|
|
|
|
2.562211355500095254561e+2, /* 76! */
|
|
|
|
|
2.605649409718632093053e+2, /* 77! */
|
|
|
|
|
2.649216497985528010421e+2, /* 78! */
|
|
|
|
|
2.692910976510198225363e+2, /* 79! */
|
|
|
|
|
2.736731242856937041486e+2, /* 80! */
|
|
|
|
|
2.780675734403661429141e+2, /* 81! */
|
|
|
|
|
2.824742926876303960274e+2, /* 82! */
|
|
|
|
|
2.868931332954269939509e+2, /* 83! */
|
|
|
|
|
2.913239500942703075662e+2, /* 84! */
|
|
|
|
|
2.957666013507606240211e+2, /* 85! */
|
|
|
|
|
3.002209486470141317540e+2, /* 86! */
|
|
|
|
|
3.046868567656687154726e+2, /* 87! */
|
|
|
|
|
3.091641935801469219449e+2, /* 88! */
|
|
|
|
|
3.136528299498790617832e+2, /* 89! */
|
|
|
|
|
3.181526396202093268500e+2, /* 90! */
|
|
|
|
|
3.226634991267261768912e+2, /* 91! */
|
|
|
|
|
3.271852877037752172008e+2, /* 92! */
|
|
|
|
|
3.317178871969284731381e+2, /* 93! */
|
|
|
|
|
3.362611819791984770344e+2, /* 94! */
|
|
|
|
|
3.408150588707990178690e+2, /* 95! */
|
|
|
|
|
3.453794070622668541074e+2, /* 96! */
|
|
|
|
|
3.499541180407702369296e+2, /* 97! */
|
|
|
|
|
3.545390855194408088492e+2, /* 98! */
|
|
|
|
|
3.591342053695753987760e+2, /* 99! */
|
|
|
|
|
3.637393755555634901441e+2, /* 100! */
|
|
|
|
|
3.683544960724047495950e+2, /* 101! */
|
|
|
|
|
3.729794688856890206760e+2, /* 102! */
|
|
|
|
|
3.776141978739186564468e+2, /* 103! */
|
|
|
|
|
3.822585887730600291111e+2, /* 104! */
|
|
|
|
|
3.869125491232175524822e+2, /* 105! */
|
|
|
|
|
3.915759882173296196258e+2, /* 106! */
|
|
|
|
|
3.962488170517915257991e+2, /* 107! */
|
|
|
|
|
4.009309482789157454921e+2, /* 108! */
|
|
|
|
|
4.056222961611448891925e+2, /* 109! */
|
|
|
|
|
4.103227765269373054205e+2, /* 110! */
|
|
|
|
|
4.150323067282496395563e+2, /* 111! */
|
|
|
|
|
4.197508055995447340991e+2, /* 112! */
|
|
|
|
|
4.244781934182570746677e+2, /* 113! */
|
|
|
|
|
4.292143918666515701285e+2, /* 114! */
|
|
|
|
|
4.339593239950148201939e+2, /* 115! */
|
|
|
|
|
4.387129141861211848399e+2, /* 116! */
|
|
|
|
|
4.434750881209189409588e+2, /* 117! */
|
|
|
|
|
4.482457727453846057188e+2, /* 118! */
|
|
|
|
|
4.530248962384961351041e+2, /* 119! */
|
|
|
|
|
4.578123879812781810984e+2, /* 120! */
|
|
|
|
|
4.626081785268749221865e+2, /* 121! */
|
|
|
|
|
4.674121995716081787447e+2, /* 122! */
|
|
|
|
|
4.722243839269805962399e+2, /* 123! */
|
|
|
|
|
4.770446654925856331047e+2, /* 124! */
|
|
|
|
|
4.818729792298879342285e+2, /* 125! */
|
|
|
|
|
4.867092611368394122258e+2, /* 126! */
|
|
|
|
|
4.915534482232980034989e+2, /* 127! */
|
|
|
|
|
4.964054784872176206648e+2, /* 128! */
|
|
|
|
|
5.012652908915792927797e+2, /* 129! */
|
|
|
|
|
5.061328253420348751997e+2, /* 130! */
|
|
|
|
|
5.110080226652360267439e+2, /* 131! */
|
|
|
|
|
5.158908245878223975982e+2, /* 132! */
|
|
|
|
|
5.207811737160441513633e+2, /* 133! */
|
|
|
|
|
5.256790135159950627324e+2, /* 134! */
|
|
|
|
|
5.305842882944334921812e+2, /* 135! */
|
|
|
|
|
5.354969431801695441897e+2, /* 136! */
|
|
|
|
|
5.404169241059976691050e+2, /* 137! */
|
|
|
|
|
5.453441777911548737966e+2, /* 138! */
|
|
|
|
|
5.502786517242855655538e+2, /* 139! */
|
|
|
|
|
5.552202941468948698523e+2, /* 140! */
|
|
|
|
|
5.601690540372730381305e+2, /* 141! */
|
|
|
|
|
5.651248810948742988613e+2, /* 142! */
|
|
|
|
|
5.700877257251342061414e+2, /* 143! */
|
|
|
|
|
5.750575390247102067619e+2, /* 144! */
|
|
|
|
|
5.800342727671307811636e+2, /* 145! */
|
|
|
|
|
5.850178793888391176022e+2, /* 146! */
|
|
|
|
|
5.900083119756178539038e+2, /* 147! */
|
|
|
|
|
5.950055242493819689670e+2, /* 148! */
|
|
|
|
|
6.000094705553274281080e+2, /* 149! */
|
|
|
|
|
6.050201058494236838580e+2, /* 150! */
|
|
|
|
|
6.100373856862386081868e+2, /* 151! */
|
|
|
|
|
6.150612662070848845750e+2, /* 152! */
|
|
|
|
|
6.200917041284773200381e+2, /* 153! */
|
|
|
|
|
6.251286567308909491967e+2, /* 154! */
|
|
|
|
|
6.301720818478101958172e+2, /* 155! */
|
|
|
|
|
6.352219378550597328635e+2, /* 156! */
|
|
|
|
|
6.402781836604080409209e+2, /* 157! */
|
|
|
|
|
6.453407786934350077245e+2, /* 158! */
|
|
|
|
|
6.504096828956552392500e+2, /* 159! */
|
|
|
|
|
6.554848567108890661717e+2, /* 160! */
|
|
|
|
|
6.605662610758735291676e+2, /* 161! */
|
|
|
|
|
6.656538574111059132426e+2, /* 162! */
|
|
|
|
|
6.707476076119126755767e+2, /* 163! */
|
|
|
|
|
6.758474740397368739994e+2, /* 164! */
|
|
|
|
|
6.809534195136374546094e+2, /* 165! */
|
|
|
|
|
6.860654073019939978423e+2, /* 166! */
|
|
|
|
|
6.911834011144107529496e+2, /* 167! */
|
|
|
|
|
6.963073650938140118743e+2, /* 168! */
|
|
|
|
|
7.014372638087370853465e+2, /* 169! */
|
|
|
|
|
7.065730622457873471107e+2, /* 170! */
|
|
|
|
|
7.117147258022900069535e+2, /* 171! */
|
2019-12-27 06:08:17 +03:00
|
|
|
]
|
|
|
|
|
)
|
