src/java.base/share/classes/java/util/random/DoubleZigguratTables.java
author jlaskey
Thu, 14 Nov 2019 12:50:08 -0400
branchJDK-8193209-branch
changeset 59088 da026c172c1e
permissions -rw-r--r--
add missing files

// This Java source file is generated automatically by the program `create_ziggurat_tables.c`.

/*
 * Copyright (c) 2019, Oracle and/or its affiliates. All rights reserved.
 * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
 *
 * This code is free software; you can redistribute it and/or modify it
 * under the terms of the GNU General Public License version 2 only, as
 * published by the Free Software Foundation.  Oracle designates this
 * particular file as subject to the "Classpath" exception as provided
 * by Oracle in the LICENSE file that accompanied this code.
 *
 * This code is distributed in the hope that it will be useful, but WITHOUT
 * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
 * FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
 * version 2 for more details (a copy is included in the LICENSE file that
 * accompanied this code).
 *
 * You should have received a copy of the GNU General Public License version
 * 2 along with this work; if not, write to the Free Software Foundation,
 * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
 *
 * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA
 * or visit www.oracle.com if you need additional information or have any
 * questions.
 */

package java.util.random;

class DoubleZigguratTables {

    // Implementation support for modified-ziggurat implementation of nextExponential()

    // Fraction of the area under the curve that lies outside the layer boxes: 0.0156
    // Fraction of non-box area that lies in the tail of the distribution: 0.0330

    static final int exponentialNumberOfLayers = 252;
    static final int exponentialLayerMask = 0xff;
    static final int exponentialAliasMask = 0xff;
    static final int exponentialSignCorrectionMask = 0xff;
    static final double exponentialX0 = 7.56927469414806264;
    static final long exponentialConvexMargin = 853965788476313645L;   // unscaled convex margin = 0.0926

    // exponential_X[i] = length of ziggurat layer i for exponential distribution, scaled by 2**(-63)
    static final double[] exponentialX = {      // 253 entries, which is exponential_number_of_layers+1
         8.2066240675348816e-19,  7.3973732351607284e-19,  6.9133313377915293e-19,  6.5647358820964533e-19,
         6.2912539959818508e-19,  6.0657224129604964e-19,  5.8735276103737269e-19,  5.7058850528536941e-19,
         5.5570945691622390e-19,  5.4232438903743953e-19,  5.3015297696508776e-19,  5.1898739257708062e-19,
         5.0866922617998330e-19,  4.9907492938796469e-19,  4.9010625894449536e-19,  4.8168379010649187e-19,
         4.7374238653644714e-19,  4.6622795807196824e-19,  4.5909509017784048e-19,  4.5230527790658154e-19,
         4.4582558816353960e-19,  4.3962763126368381e-19,  4.3368675967106470e-19,  4.2798143618469714e-19,
         4.2249273027064889e-19,  4.1720391253464110e-19,  4.1210012522465616e-19,  4.0716811225869233e-19,
         4.0239599631006903e-19,  3.9777309342877357e-19,  3.9328975785334499e-19,  3.8893725129310323e-19,
         3.8470763218720385e-19,  3.8059366138180143e-19,  3.7658872138544730e-19,  3.7268674692030177e-19,
         3.6888216492248162e-19,  3.6516984248800068e-19,  3.6154504153287473e-19,  3.5800337915318032e-19,
         3.5454079284533432e-19,  3.5115350988784242e-19,  3.4783802030030962e-19,  3.4459105288907336e-19,
         3.4140955396563316e-19,  3.3829066838741162e-19,  3.3523172262289001e-19,  3.3223020958685874e-19,
         3.2928377502804472e-19,  3.2639020528202049e-19,  3.2354741622810815e-19,  3.2075344331080789e-19,
         3.1800643250478609e-19,  3.1530463211820845e-19,  3.1264638534265134e-19,  3.1003012346934211e-19,
         3.0745435970137301e-19,  3.0491768350005559e-19,  3.0241875541094565e-19,  2.9995630232144550e-19,
         2.9752911310742592e-19,  2.9513603463113224e-19,  2.9277596805684267e-19,  2.9044786545442563e-19,
         2.8815072666416712e-19,  2.8588359639906928e-19,  2.8364556156331615e-19,  2.8143574876779799e-19,
         2.7925332202553125e-19,  2.7709748061152879e-19,  2.7496745707320232e-19,  2.7286251537873397e-19,
         2.7078194919206054e-19,  2.6872508026419050e-19,  2.6669125693153442e-19,  2.6467985271278891e-19,
         2.6269026499668434e-19,  2.6072191381359757e-19,  2.5877424068465143e-19,  2.5684670754248168e-19,
         2.5493879571835479e-19,  2.5305000499077481e-19,  2.5117985269112710e-19,  2.4932787286227806e-19,
         2.4749361546638660e-19,  2.4567664563848669e-19,  2.4387654298267842e-19,  2.4209290090801527e-19,
         2.4032532600140538e-19,  2.3857343743505147e-19,  2.3683686640614648e-19,  2.3511525560671253e-19,
         2.3340825872163284e-19,  2.3171553995306794e-19,  2.3003677356958333e-19,  2.2837164347843482e-19,
         2.2671984281957174e-19,  2.2508107358001938e-19,  2.2345504622739592e-19,  2.2184147936140775e-19,
         2.2024009938224424e-19,  2.1865064017486842e-19,  2.1707284280826716e-19,  2.1550645524878675e-19,
         2.1395123208673778e-19,  2.1240693427550640e-19,  2.1087332888245875e-19,  2.0935018885097035e-19,
         2.0783729277295508e-19,  2.0633442467130712e-19,  2.0484137379170616e-19,  2.0335793440326865e-19,
         2.0188390560756090e-19,  2.0041909115551697e-19,  1.9896329927183254e-19,  1.9751634248643090e-19,
         1.9607803747261946e-19,  1.9464820489157862e-19,  1.9322666924284314e-19,  1.9181325872045647e-19,
         1.9040780507449479e-19,  1.8901014347767504e-19,  1.8762011239677479e-19,  1.8623755346860768e-19,
         1.8486231138030984e-19,  1.8349423375370566e-19,  1.8213317103353295e-19,  1.8077897637931708e-19,
         1.7943150556069476e-19,  1.7809061685599652e-19,  1.7675617095390567e-19,  1.7542803085801941e-19,
         1.7410606179414531e-19,  1.7279013112017240e-19,  1.7148010823836362e-19,  1.7017586450992059e-19,
         1.6887727317167824e-19,  1.6758420925479093e-19,  1.6629654950527621e-19,  1.6501417230628659e-19,
         1.6373695760198277e-19,  1.6246478682288560e-19,  1.6119754281258616e-19,  1.5993510975569615e-19,
         1.5867737310692309e-19,  1.5742421952115544e-19,  1.5617553678444595e-19,  1.5493121374578016e-19,
         1.5369114024951992e-19,  1.5245520706841019e-19,  1.5122330583703858e-19,  1.4999532898563561e-19,
         1.4877116967410352e-19,  1.4755072172615974e-19,  1.4633387956347966e-19,  1.4512053813972103e-19,
         1.4391059287430991e-19,  1.4270393958586506e-19,  1.4150047442513381e-19,  1.4030009380730888e-19,
         1.3910269434359025e-19,  1.3790817277185197e-19,  1.3671642588626657e-19,  1.3552735046573446e-19,
         1.3434084320095729e-19,  1.3315680061998685e-19,  1.3197511901207148e-19,  1.3079569434961214e-19,
         1.2961842220802957e-19,  1.2844319768333099e-19,  1.2726991530715219e-19,  1.2609846895903523e-19,
         1.2492875177568625e-19,  1.2376065605693940e-19,  1.2259407316813331e-19,  1.2142889343858445e-19,
         1.2026500605581765e-19,  1.1910229895518744e-19,  1.1794065870449425e-19,  1.1677997038316715e-19,
         1.1562011745554883e-19,  1.1446098163777869e-19,  1.1330244275772562e-19,  1.1214437860737343e-19,
         1.1098666478700728e-19,  1.0982917454048923e-19,  1.0867177858084351e-19,  1.0751434490529747e-19,
         1.0635673859884002e-19,  1.0519882162526621e-19,  1.0404045260457141e-19,  1.0288148657544097e-19,
         1.0172177474144965e-19,  1.0056116419943559e-19,  9.9399497648346677e-20,  9.8236613076667446e-20,
         9.7072343426320094e-20,  9.5906516230690634e-20,  9.4738953224154196e-20,  9.3569469920159036e-20,
         9.2397875154569468e-20,  9.1223970590556472e-20,  9.0047550180852874e-20,  8.8868399582647627e-20,
         8.7686295519767450e-20,  8.6501005086071005e-20,  8.5312284983141187e-20,  8.4119880684385214e-20,
         8.2923525516513420e-20,  8.1722939648034506e-20,  8.0517828972839211e-20,  7.9307883875099226e-20,
         7.8092777859524425e-20,  7.6872166028429042e-20,  7.5645683383965122e-20,  7.4412942930179128e-20,
         7.3173533545093332e-20,  7.1927017587631075e-20,  7.0672928197666785e-20,  6.9410766239500362e-20,
         6.8139996829256425e-20,  6.6860045374610234e-20,  6.5570293040210081e-20,  6.4270071533368528e-20,
         6.2958657080923559e-20,  6.1635263438143136e-20,  6.0299033732151700e-20,  5.8949030892850181e-20,
         5.7584226359885930e-20,  5.6203486669597397e-20,  5.4805557413499315e-20,  5.3389043909003295e-20,
         5.1952387717989917e-20,  5.0493837866338355e-20,  4.9011415222629489e-20,  4.7502867933366117e-20,
         4.5965615001265455e-20,  4.4396673897997565e-20,  4.2792566302148588e-20,  4.1149193273430015e-20,
         3.9461666762606287e-20,  3.7724077131401685e-20,  3.5929164086204360e-20,  3.4067836691100565e-20,
         3.2128447641564046e-20,  3.0095646916399994e-20,  2.7948469455598328e-20,  2.5656913048718645e-20,
         2.3175209756803909e-20,  2.0426695228251291e-20,  1.7261770330213485e-20,  1.3281889259442578e-20,
         0.0000000000000000e+00 };

    // exponential_Y[i] = value of the exponential distribution function at exponential_X[i], scaled by 2**(-63)
    static final double[] exponentialY = {      // 253 entries, which is exponential_number_of_layers+1
         5.5952054951127360e-23,  1.1802509982703313e-22,  1.8444423386735829e-22,  2.5439030466698309e-22,
         3.2737694311509334e-22,  4.0307732132706715e-22,  4.8125478319495115e-22,  5.6172914896583308e-22,
         6.4435820540443526e-22,  7.2902662343463681e-22,  8.1563888456321941e-22,  9.0411453683482223e-22,
         9.9438488486399206e-22,  1.0863906045969114e-21,  1.1800799775461269e-21,  1.2754075534831208e-21,
         1.3723331176377290e-21,  1.4708208794375214e-21,  1.5708388257440445e-21,  1.6723581984374566e-21,
         1.7753530675030514e-21,  1.8797999785104595e-21,  1.9856776587832504e-21,  2.0929667704053244e-21,
         2.2016497009958240e-21,  2.3117103852306179e-21,  2.4231341516125464e-21,  2.5359075901420891e-21,
         2.6500184374170538e-21,  2.7654554763660391e-21,  2.8822084483468604e-21,  3.0002679757547711e-21,
         3.1196254936130377e-21,  3.2402731888801749e-21,  3.3622039464187092e-21,  3.4854113007409036e-21,
         3.6098893927859475e-21,  3.7356329310971768e-21,  3.8626371568620053e-21,  3.9908978123552837e-21,
         4.1204111123918948e-21,  4.2511737184488913e-21,  4.3831827151633737e-21,  4.5164355889510656e-21,
         4.6509302085234806e-21,  4.7866648071096003e-21,  4.9236379662119969e-21,  5.0618486007478993e-21,
         5.2012959454434732e-21,  5.3419795423648946e-21,  5.4838992294830959e-21,  5.6270551301806347e-21,
         5.7714476436191935e-21,  5.9170774358950678e-21,  6.0639454319177027e-21,  6.2120528079531677e-21,
         6.3614009847804375e-21,  6.5119916214136427e-21,  6.6638266093481696e-21,  6.8169080672926277e-21,
         6.9712383363524377e-21,  7.1268199756340822e-21,  7.2836557582420336e-21,  7.4417486676430174e-21,
         7.6011018943746355e-21,  7.7617188330775411e-21,  7.9236030798322572e-21,  8.0867584297834842e-21,
         8.2511888750363333e-21,  8.4168986028103258e-21,  8.5838919938383098e-21,  8.7521736209986459e-21,
         8.9217482481700712e-21,  9.0926208292996504e-21,  9.2647965076751277e-21,  9.4382806153938292e-21,
         9.6130786730210328e-21,  9.7891963894314161e-21,  9.9666396618278840e-21,  1.0145414575932636e-20,
         1.0325527406345955e-20,  1.0506984617068672e-20,  1.0689792862184811e-20,  1.0873958986701341e-20,
         1.1059490027542400e-20,  1.1246393214695825e-20,  1.1434675972510121e-20,  1.1624345921140471e-20,
         1.1815410878142659e-20,  1.2007878860214202e-20,  1.2201758085082226e-20,  1.2397056973538040e-20,
         1.2593784151618565e-20,  1.2791948452935152e-20,  1.2991558921150600e-20,  1.3192624812605428e-20,
         1.3395155599094805e-20,  1.3599160970797774e-20,  1.3804650839360727e-20,  1.4011635341137284e-20,
         1.4220124840587164e-20,  1.4430129933836705e-20,  1.4641661452404201e-20,  1.4854730467093280e-20,
         1.5069348292058084e-20,  1.5285526489044050e-20,  1.5503276871808626e-20,  1.5722611510726402e-20,
         1.5943542737583543e-20,  1.6166083150566702e-20,  1.6390245619451956e-20,  1.6616043290999594e-20,
         1.6843489594561079e-20,  1.7072598247904713e-20,  1.7303383263267072e-20,  1.7535858953637607e-20,
         1.7770039939284241e-20,  1.8005941154528286e-20,  1.8243577854777398e-20,  1.8482965623825808e-20,
         1.8724120381431627e-20,  1.8967058391181452e-20,  1.9211796268653192e-20,  1.9458350989888484e-20,
         1.9706739900186868e-20,  1.9956980723234356e-20,  2.0209091570579904e-20,  2.0463090951473895e-20,
         2.0718997783083593e-20,  2.0976831401101350e-20,  2.1236611570762130e-20,  2.1498358498287976e-20,
         2.1762092842777868e-20,  2.2027835728562592e-20,  2.2295608758045219e-20,  2.2565434025049041e-20,
         2.2837334128696004e-20,  2.3111332187840010e-20,  2.3387451856080863e-20,  2.3665717337386111e-20,
         2.3946153402349610e-20,  2.4228785405117410e-20,  2.4513639301013211e-20,  2.4800741664897764e-20,
         2.5090119710298442e-20,  2.5381801309347597e-20,  2.5675815013570500e-20,  2.5972190075566336e-20,
         2.6270956471628253e-20,  2.6572144925351523e-20,  2.6875786932281841e-20,  2.7181914785659148e-20,
         2.7490561603315974e-20,  2.7801761355793055e-20,  2.8115548895739172e-20,  2.8431959988666534e-20,
         2.8751031345137833e-20,  2.9072800654466307e-20,  2.9397306620015486e-20,  2.9724588996191657e-20,
         3.0054688627228112e-20,  3.0387647487867642e-20,  3.0723508726057078e-20,  3.1062316707775905e-20,
         3.1404117064129991e-20,  3.1748956740850969e-20,  3.2096884050352357e-20,  3.2447948726504914e-20,
         3.2802201982306013e-20,  3.3159696570631373e-20,  3.3520486848272230e-20,  3.3884628843476888e-20,
         3.4252180327233346e-20,  3.4623200888548644e-20,  3.4997752014001677e-20,  3.5375897171869060e-20,
         3.5757701901149035e-20,  3.6143233905835799e-20,  3.6532563154827400e-20,  3.6925761987883572e-20,
         3.7322905228086981e-20,  3.7724070301302117e-20,  3.8129337363171041e-20,  3.8538789434235234e-20,
         3.8952512543827862e-20,  3.9370595883442399e-20,  3.9793131970351439e-20,  4.0220216822325769e-20,
         4.0651950144388133e-20,  4.1088435528630944e-20,  4.1529780668232712e-20,  4.1976097586926582e-20,
         4.2427502885307452e-20,  4.2884118005513604e-20,  4.3346069515987453e-20,  4.3813489418210257e-20,
         4.4286515477520838e-20,  4.4765291580372353e-20,  4.5249968120658306e-20,  4.5740702418054417e-20,
         4.6237659171683015e-20,  4.6741010952818368e-20,  4.7250938740823415e-20,  4.7767632507051219e-20,
         4.8291291852069895e-20,  4.8822126702292804e-20,  4.9360358072933852e-20,  4.9906218905182021e-20,
         5.0459954986625539e-20,  5.1021825965285324e-20,  5.1592106469178258e-20,  5.2171087345169234e-20,
         5.2759077033045284e-20,  5.3356403093325858e-20,  5.3963413910399511e-20,  5.4580480596259246e-20,
         5.5207999124535584e-20,  5.5846392729873830e-20,  5.6496114614193770e-20,  5.7157651009290713e-20,
         5.7831524654956632e-20,  5.8518298763794323e-20,  5.9218581558791713e-20,  5.9933031488338700e-20,
         6.0662363246796887e-20,  6.1407354758435000e-20,  6.2168855320499763e-20,  6.2947795150103727e-20,
         6.3745196643214394e-20,  6.4562187737537985e-20,  6.5400017881889097e-20,  6.6260077263309343e-20,
         6.7143920145146620e-20,  6.8053293447301698e-20,  6.8990172088133000e-20,  6.9956803158564498e-20,
         7.0955761794878430e-20,  7.1990022788945080e-20,  7.3063053739105458e-20,  7.4178938266266893e-20,
         7.5342542134173124e-20,  7.6559742171142969e-20,  7.7837749863412850e-20,  7.9185582674029512e-20,
         8.0614775537353300e-20,  8.2140502769818073e-20,  8.3783445978280519e-20,  8.5573129249678161e-20,
         8.7554459669590100e-20,  8.9802388057706877e-20,  9.2462471421151086e-20,  9.5919641344951721e-20,
         1.0842021724855044e-19 };

    // alias_threshold[j] is a threshold for the probability mass function that has been
    // scaled by (2**64 - 1), translated by -(2**63), and represented as a long value;
    // in this way it can be directly compared to a randomly chosen long value.
    static final long[] exponentialAliasThreshold = {    // 256 entries
         9223372036854775807L,  1623796909450829958L,  2664290944894281002L,  7387971354164055035L,
         6515064486552722205L,  8840508362680707094L,  6099647593382923818L,  7673130333659514446L,
         6220332867583438718L,  5045979640552814279L,  4075305837223956071L,  3258413672162525964L,
         2560664887087763045L,  1957224924672900129L,  1429800935350578000L,   964606309710808688L,
          551043923599587587L,   180827629096889062L,  -152619738120023316L,  -454588624410291246L,
         -729385126147774679L,  -980551509819444511L, -1211029700667463575L, -1423284293868546830L,
        -1619396356369066372L, -1801135830956194794L, -1970018048575634032L, -2127348289059688469L,
        -2274257249303687482L, -2411729520096654942L, -2540626634159182211L, -2661705860113406183L,
        -2775635634532464842L, -2883008316030448462L, -2984350790383654449L, -3080133339198118132L,
        -3170777096303105047L, -3256660348483802362L, -3338123885075135933L, -3415475560473298752L,
        -3488994201966444258L, -3558932970354456420L, -3625522261068040742L, -3688972217741991689L,
        -3749474917563779627L, -3807206277531072172L, -3862327722496826830L, -3914987649156779312L,
        -3965322714631864882L, -4013458973776911635L, -4059512885612766613L, -4103592206186240662L,
        -4145796782586127736L, -4186219260694346585L, -4224945717447274810L, -4262056226866285147L,
        -4297625367836519229L, -4331722680528536958L, -4364413077437472159L, -4395757214229421760L,
        -4425811824915119137L, -4454630025296932322L, -4482261588141294467L, -4508753193105275908L,
        -4534148654077813412L, -4558489126279965349L, -4581813295192216486L, -4604157549138252679L,
        -4625556137145250151L, -4646041313519109096L, -4665643470413305673L, -4684391259530342697L,
        -4702311703971745066L, -4719430301145102986L, -4735771117539946027L, -4751356876102086987L,
        -4766209036859150188L, -4780347871385996716L, -4793792531638885869L, -4806561113635132333L,
        -4818670716409312334L, -4830137496634465358L, -4840976719260854030L, -4851202804490332239L,
        -4860829371376476047L, -4869869278311650511L, -4878334660640770576L, -4886236965617426832L,
        -4893586984900802224L, -4900394884772702384L, -4906670234238884945L, -4912422031164489009L,
        -4917658726580135697L, -4922388247283531793L, -4926618016851042065L, -4930354975163351025L,
        -4933605596540650674L, -4936375906575303186L, -4938671497741357106L, -4940497543854583186L,
        -4941858813449628882L, -4942759682136114354L, -4943204143989086194L, -4943195822025527282L,
        -4942737977813222130L, -4941833520255011698L, -4940485013586759090L, -4938694684624342322L,
        -4936464429291795314L, -4933795818458824946L, -4930690103114057265L, -4927148218896863345L,
        -4923170790008291569L, -4918758132519196401L, -4913910257091661489L, -4908626871126522161L,
        -4902907380349538608L, -4896750889844272240L, -4890156204540530416L, -4883121829162570096L,
        -4875645967641780528L, -4867726521994909999L, -4859361090668119087L, -4850546966345102383L,
        -4841281133215538414L, -4831560263698491374L, -4821380714613452974L, -4810738522790065581L,
        -4799629400105481389L, -4788048727936296621L, -4775991551010524588L, -4763452570642113772L,
        -4750426137329493931L, -4736906242696388587L, -4722886510751367403L, -4708360188440104938L,
        -4693320135461420394L, -4677758813316098089L, -4661668273553495721L, -4645040145179234152L,
        -4627865621182771687L, -4610135444140936871L, -4591839890849352486L, -4572968755929944934L,
        -4553511334358213029L, -4533456402849109028L, -4512792200036270244L, -4491506405372580067L,
        -4469586116675401954L, -4447017826233099938L, -4423787395382284961L, -4399880027458416864L,
        -4375280239014124063L, -4349971829190464606L, -4323937847117722654L, -4297160557210942813L,
        -4269621402214950684L, -4241300963840750107L, -4212178920821854874L, -4182234004204445017L,
        -4151443949668869272L, -4119785446662323159L, -4087234084103169942L, -4053764292396165205L,
        -4019349281473092435L, -3983960974549686930L, -3947569937258414993L, -3910145301787337104L,
        -3871654685619049615L, -3832064104425389837L, -3791337878631529676L, -3749438533114328651L,
        -3706326689447979465L, -3661960950051859912L, -3616297773528542022L, -3569291340409179909L,
        -3520893408440947267L, -3471053156460649921L, -3419717015797783872L, -3366828488034801534L,
        -3312327947826461820L, -3256152429334023226L, -3198235394669709240L, -3138506482563174262L,
        -3076891235255164340L, -3013310801389715890L, -2947681612411392816L, -2879915029671670702L,
        -2809916959107519276L, -2737587429961855017L, -2662820133571332903L, -2585501917733374884L,
        -2505512231579392929L, -2422722515205190175L, -2336995527534106140L, -2248184604988712345L,
        -2156132842510782614L, -2060672187261016979L, -1961622433929380112L, -1858790108950090508L,
        -1751967229002904073L, -1640929916937134981L, -1525436855617591297L, -1405227557075245821L,
        -1280020420662651897L, -1149510549536605301L, -1013367289578706928L,  -871231448632089708L,
         -722712146453677415L,  -567383236774421729L,  -404779231966956764L,  -234390647591531478L,
          -55658667960121553L,   132030985907831093L,   329355128892817467L,   537061298001091010L,
          755977262693561929L,   987022116608030929L,  1231219266829437401L,  1489711711346524770L,
         1763780090187559275L,  2054864117341782772L,  2364588157623782527L,  2694791916990482441L,
         3047567482883491349L,  3425304305830820514L,  3830744187097285423L,  4267048975685836605L,
         4737884547990014029L,  5247525842199011422L,  5800989391535342064L,  6404202162993303300L,
         7064218894258526746L,  7789505049452354354L,  8590309807749425484L,  7643763810684501605L,
         8891950541491453167L,  5457384281016234818L,  9083704440929285914L,  7976211653914461751L,
         8178631350487124609L,  2821287825726757492L,  6322989683301736617L,  4309503753387630347L,
         4685170734960191673L,  8404845967535252693L,  7330522972447610419L,  1960945799077061994L,
         4742910674644933674L,  -751799822533438695L,  7023456603742021660L,  3843116882594755262L,
         3927231442413889375L, -9223372036854775807L, -9223372036854775807L, -9223372036854775807L };

    static final byte[] exponentialAliasMap = {    // 256 entries
        (byte)  0, (byte)  0, (byte)  1, (byte)235, (byte)  3, (byte)  4, (byte)  5, (byte)  0,
        (byte)  0, (byte)  0, (byte)  0, (byte)  0, (byte)  0, (byte)  0, (byte)  0, (byte)  0,
        (byte)  0, (byte)  0, (byte)  1, (byte)  1, (byte)  1, (byte)  1, (byte)  2, (byte)  2,
        (byte)252, (byte)252, (byte)252, (byte)252, (byte)252, (byte)252, (byte)252, (byte)252,
        (byte)252, (byte)252, (byte)252, (byte)252, (byte)252, (byte)252, (byte)252, (byte)252,
        (byte)252, (byte)252, (byte)252, (byte)252, (byte)252, (byte)252, (byte)252, (byte)252,
        (byte)252, (byte)252, (byte)252, (byte)252, (byte)252, (byte)252, (byte)252, (byte)252,
        (byte)252, (byte)252, (byte)252, (byte)252, (byte)252, (byte)252, (byte)252, (byte)252,
        (byte)252, (byte)252, (byte)252, (byte)252, (byte)252, (byte)252, (byte)252, (byte)252,
        (byte)252, (byte)252, (byte)252, (byte)252, (byte)252, (byte)252, (byte)252, (byte)252,
        (byte)252, (byte)252, (byte)252, (byte)252, (byte)252, (byte)252, (byte)252, (byte)252,
        (byte)252, (byte)252, (byte)252, (byte)252, (byte)252, (byte)252, (byte)252, (byte)252,
        (byte)252, (byte)252, (byte)252, (byte)252, (byte)252, (byte)252, (byte)252, (byte)252,
        (byte)252, (byte)252, (byte)252, (byte)252, (byte)252, (byte)252, (byte)252, (byte)252,
        (byte)252, (byte)252, (byte)252, (byte)252, (byte)252, (byte)252, (byte)252, (byte)252,
        (byte)252, (byte)252, (byte)252, (byte)252, (byte)252, (byte)252, (byte)252, (byte)252,
        (byte)252, (byte)252, (byte)252, (byte)252, (byte)252, (byte)252, (byte)252, (byte)252,
        (byte)252, (byte)252, (byte)252, (byte)252, (byte)252, (byte)252, (byte)252, (byte)252,
        (byte)252, (byte)252, (byte)252, (byte)252, (byte)252, (byte)252, (byte)252, (byte)252,
        (byte)252, (byte)252, (byte)252, (byte)252, (byte)252, (byte)252, (byte)252, (byte)252,
        (byte)252, (byte)252, (byte)252, (byte)252, (byte)252, (byte)252, (byte)252, (byte)252,
        (byte)252, (byte)252, (byte)252, (byte)252, (byte)252, (byte)252, (byte)252, (byte)252,
        (byte)252, (byte)251, (byte)251, (byte)251, (byte)251, (byte)251, (byte)251, (byte)251,
        (byte)251, (byte)251, (byte)251, (byte)251, (byte)251, (byte)251, (byte)250, (byte)250,
        (byte)250, (byte)250, (byte)250, (byte)250, (byte)250, (byte)249, (byte)249, (byte)249,
        (byte)249, (byte)249, (byte)249, (byte)248, (byte)248, (byte)248, (byte)248, (byte)247,
        (byte)247, (byte)247, (byte)247, (byte)246, (byte)246, (byte)246, (byte)245, (byte)245,
        (byte)244, (byte)244, (byte)243, (byte)243, (byte)242, (byte)241, (byte)241, (byte)240,
        (byte)239, (byte)237, (byte)  3, (byte)  3, (byte)  4, (byte)  4, (byte)  6, (byte)  0,
        (byte)  0, (byte)  0, (byte)  0, (byte)236, (byte)237, (byte)238, (byte)239, (byte)240,
        (byte)241, (byte)242, (byte)243, (byte)244, (byte)245, (byte)246, (byte)247, (byte)248,
        (byte)249, (byte)250, (byte)251, (byte)252, (byte)  2, (byte)  0, (byte)  0, (byte)  0 };

    // Implementation support for modified-ziggurat implementation of nextGaussian()

    // Fraction of the area under the curve that lies outside the layer boxes: 0.0117
    // Fraction of non-box area that lies in the tail of the distribution: 0.0236

    static final int normalNumberOfLayers = 253;
    static final int normalLayerMask = 0xff;
    static final int normalAliasMask = 0xff;
    static final int normalSignCorrectionMask = 0xff;
    static final double normalX0 = 3.63600662550094578;
    static final int normalInflectionIndex = 204;
    static final long normalConvexMargin = 760463704284035183L;   // unscaled convex margin = 0.0824
    static final long normalConcaveMargin = 2269182951627976012L;   // unscaled concave margin = 0.2460

    // normal_X[i] = length of ziggurat layer i for normal distribution, scaled by 2**(-63)
    static final double[] normalX = {      // 254 entries, which is normal_number_of_layers+1
         3.9421662825398133e-19,  3.7204945004119012e-19,  3.5827024480628678e-19,  3.4807476236540249e-19,
         3.3990177171882136e-19,  3.3303778360340139e-19,  3.2709438817617550e-19,  3.2183577132495100e-19,
         3.1710758541840432e-19,  3.1280307407034065e-19,  3.0884520655804019e-19,  3.0517650624107352e-19,
         3.0175290292584600e-19,  2.9853983440705320e-19,  2.9550967462801797e-19,  2.9263997988491663e-19,
         2.8991225869977476e-19,  2.8731108780226291e-19,  2.8482346327101335e-19,  2.8243831535194389e-19,
         2.8014613964727031e-19,  2.7793871261807797e-19,  2.7580886921411212e-19,  2.7375032698308758e-19,
         2.7175754543391047e-19,  2.6982561247538484e-19,  2.6795015188771505e-19,  2.6612724730440033e-19,
         2.6435337927976633e-19,  2.6262537282028438e-19,  2.6094035335224142e-19,  2.5929570954331002e-19,
         2.5768906173214726e-19,  2.5611823497719608e-19,  2.5458123593393361e-19,  2.5307623292372459e-19,
         2.5160153867798400e-19,  2.5015559533646191e-19,  2.4873696135403158e-19,  2.4734430003079206e-19,
         2.4597636942892726e-19,  2.4463201347912450e-19,  2.4331015411139206e-19,  2.4200978427132955e-19,
         2.4072996170445879e-19,  2.3946980340903347e-19,  2.3822848067252674e-19,  2.3700521461931801e-19,
         2.3579927220741330e-19,  2.3460996262069972e-19,  2.3343663401054455e-19,  2.3227867054673840e-19,
         2.3113548974303765e-19,  2.3000654002704238e-19,  2.2889129852797606e-19,  2.2778926905921897e-19,
         2.2669998027527321e-19,  2.2562298398527416e-19,  2.2455785360727260e-19,  2.2350418274933911e-19,
         2.2246158390513294e-19,  2.2142968725296249e-19,  2.2040813954857555e-19,  2.1939660310297601e-19,
         2.1839475483749618e-19,  2.1740228540916853e-19,  2.1641889840016519e-19,  2.1544430956570613e-19,
         2.1447824613540345e-19,  2.1352044616350571e-19,  2.1257065792395107e-19,  2.1162863934653125e-19,
         2.1069415749082026e-19,  2.0976698805483467e-19,  2.0884691491567363e-19,  2.0793372969963634e-19,
         2.0702723137954107e-19,  2.0612722589717129e-19,  2.0523352580895635e-19,  2.0434594995315797e-19,
         2.0346432313698148e-19,  2.0258847584216418e-19,  2.0171824394771313e-19,  2.0085346846857531e-19,
         1.9999399530912015e-19,  1.9913967503040585e-19,  1.9829036263028144e-19,  1.9744591733545175e-19,
         1.9660620240469857e-19,  1.9577108494251485e-19,  1.9494043572246307e-19,  1.9411412901962161e-19,
         1.9329204245152935e-19,  1.9247405682708168e-19,  1.9166005600287074e-19,  1.9084992674649826e-19,
         1.9004355860642340e-19,  1.8924084378793725e-19,  1.8844167703488436e-19,  1.8764595551677749e-19,
         1.8685357872097450e-19,  1.8606444834960934e-19,  1.8527846822098793e-19,  1.8449554417517928e-19,
         1.8371558398354868e-19,  1.8293849726199566e-19,  1.8216419538767393e-19,  1.8139259141898448e-19,
         1.8062360001864453e-19,  1.7985713737964743e-19,  1.7909312115393845e-19,  1.7833147038364200e-19,
         1.7757210543468428e-19,  1.7681494793266395e-19,  1.7605992070083140e-19,  1.7530694770004409e-19,
         1.7455595397057217e-19,  1.7380686557563475e-19,  1.7305960954655264e-19,  1.7231411382940904e-19,
         1.7157030723311378e-19,  1.7082811937877138e-19,  1.7008748065025788e-19,  1.6934832214591352e-19,
         1.6861057563126349e-19,  1.6787417349268046e-19,  1.6713904869190636e-19,  1.6640513472135291e-19,
         1.6567236556010242e-19,  1.6494067563053266e-19,  1.6420999975549115e-19,  1.6348027311594532e-19,
         1.6275143120903661e-19,  1.6202340980646725e-19,  1.6129614491314931e-19,  1.6056957272604589e-19,
         1.5984362959313479e-19,  1.5911825197242491e-19,  1.5839337639095554e-19,  1.5766893940370800e-19,
         1.5694487755235889e-19,  1.5622112732380261e-19,  1.5549762510837070e-19,  1.5477430715767271e-19,
         1.5405110954198330e-19,  1.5332796810709688e-19,  1.5260481843056974e-19,  1.5188159577726683e-19,
         1.5115823505412761e-19,  1.5043467076406199e-19,  1.4971083695888395e-19,  1.4898666719118714e-19,
         1.4826209446506113e-19,  1.4753705118554365e-19,  1.4681146910669830e-19,  1.4608527927820112e-19,
         1.4535841199031451e-19,  1.4463079671711862e-19,  1.4390236205786415e-19,  1.4317303567630177e-19,
         1.4244274423783481e-19,  1.4171141334433217e-19,  1.4097896746642792e-19,  1.4024532987312287e-19,
         1.3951042255849034e-19,  1.3877416616527576e-19,  1.3803647990516385e-19,  1.3729728147547174e-19,
         1.3655648697200824e-19,  1.3581401079782068e-19,  1.3506976556752901e-19,  1.3432366200692418e-19,
         1.3357560884748263e-19,  1.3282551271542047e-19,  1.3207327801488087e-19,  1.3131880680481524e-19,
         1.3056199866908076e-19,  1.2980275057923788e-19,  1.2904095674948608e-19,  1.2827650848312727e-19,
         1.2750929400989213e-19,  1.2673919831340482e-19,  1.2596610294799512e-19,  1.2518988584399374e-19,
         1.2441042110056523e-19,  1.2362757876504165e-19,  1.2284122459762072e-19,  1.2205121982017852e-19,
         1.2125742084782245e-19,  1.2045967900166973e-19,  1.1965784020118020e-19,  1.1885174463419555e-19,
         1.1804122640264091e-19,  1.1722611314162064e-19,  1.1640622560939109e-19,  1.1558137724540874e-19,
         1.1475137369333185e-19,  1.1391601228549047e-19,  1.1307508148492592e-19,  1.1222836028063025e-19,
         1.1137561753107903e-19,  1.1051661125053526e-19,  1.0965108783189755e-19,  1.0877878119905372e-19,
         1.0789941188076655e-19,  1.0701268599703640e-19,  1.0611829414763286e-19,  1.0521591019102928e-19,
         1.0430518990027552e-19,  1.0338576948035472e-19,  1.0245726392923699e-19,  1.0151926522209310e-19,
         1.0057134029488235e-19,  9.9613028799672809e-20,  9.8643840599459914e-20,  9.7663252964755816e-20,
         9.6670707427623454e-20,  9.5665606240866670e-20,  9.4647308380433213e-20,  9.3615125017323508e-20,
         9.2568314370887282e-20,  9.1506075837638774e-20,  9.0427543267725716e-20,  8.9331777233763680e-20,
         8.8217756102327883e-20,  8.7084365674892319e-20,  8.5930387109612162e-20,  8.4754482764244349e-20,
         8.3555179508462343e-20,  8.2330848933585364e-20,  8.1079683729129853e-20,  7.9799669284133864e-20,
         7.8488549286072745e-20,  7.7143783700934692e-20,  7.5762496979467566e-20,  7.4341413578485329e-20,
         7.2876776807378431e-20,  7.1364245443525374e-20,  6.9798760240761066e-20,  6.8174368944799054e-20,
         6.6483992986198539e-20,  6.4719110345162767e-20,  6.2869314813103699e-20,  6.0921687548281263e-20,
         5.8859873575576818e-20,  5.6662675116090981e-20,  5.4301813630894571e-20,  5.1738171744494220e-20,
         4.8915031722398545e-20,  4.5744741890755301e-20,  4.2078802568583416e-20,  3.7625986722404761e-20,
         3.1628589805881879e-20,  0.0000000000000000e+00 };

    // normal_Y[i] = value of the normal distribution function at normal_X[i], scaled by 2**(-63)
    static final double[] normalY = {      // 254 entries, which is normal_number_of_layers+1
         1.4598410796619063e-22,  3.0066613427942797e-22,  4.6129728815103466e-22,  6.2663350049234362e-22,
         7.9594524761881544e-22,  9.6874655021705039e-22,  1.1446877002379439e-21,  1.3235036304379167e-21,
         1.5049857692053131e-21,  1.6889653000719298e-21,  1.8753025382711626e-21,  2.0638798423695191e-21,
         2.2545966913644708e-21,  2.4473661518801799e-21,  2.6421122727763533e-21,  2.8387681187879908e-21,
         3.0372742567457284e-21,  3.2375775699986589e-21,  3.4396303157948780e-21,  3.6433893657997798e-21,
         3.8488155868912312e-21,  4.0558733309492775e-21,  4.2645300104283590e-21,  4.4747557422305067e-21,
         4.6865230465355582e-21,  4.8998065902775257e-21,  5.1145829672105489e-21,  5.3308305082046173e-21,
         5.5485291167031758e-21,  5.7676601252690476e-21,  5.9882061699178461e-21,  6.2101510795442221e-21,
         6.4334797782257209e-21,  6.6581781985713897e-21,  6.8842332045893181e-21,  7.1116325227957095e-21,
         7.3403646804903092e-21,  7.5704189502886418e-21,  7.8017853001379744e-21,  8.0344543481570017e-21,
         8.2684173217333118e-21,  8.5036660203915022e-21,  8.7401927820109521e-21,  8.9779904520281901e-21,
         9.2170523553061439e-21,  9.4573722703928820e-21,  9.6989444059269430e-21,  9.9417633789758424e-21,
         1.0185824195119818e-20,  1.0431122230114770e-20,  1.0677653212987396e-20,  1.0925413210432004e-20,
         1.1174398612392891e-20,  1.1424606118728715e-20,  1.1676032726866302e-20,  1.1928675720361027e-20,
         1.2182532658289373e-20,  1.2437601365406785e-20,  1.2693879923010674e-20,  1.2951366660454145e-20,
         1.3210060147261461e-20,  1.3469959185800733e-20,  1.3731062804473644e-20,  1.3993370251385596e-20,
         1.4256880988463136e-20,  1.4521594685988369e-20,  1.4787511217522902e-20,  1.5054630655196170e-20,
         1.5322953265335218e-20,  1.5592479504415048e-20,  1.5863210015310328e-20,  1.6135145623830982e-20,
         1.6408287335525592e-20,  1.6682636332737932e-20,  1.6958193971903124e-20,  1.7234961781071113e-20,
         1.7512941457646084e-20,  1.7792134866331487e-20,  1.8072544037271070e-20,  1.8354171164377277e-20,
         1.8637018603838945e-20,  1.8921088872801004e-20,  1.9206384648209468e-20,  1.9492908765815636e-20,
         1.9780664219333857e-20,  2.0069654159747839e-20,  2.0359881894760859e-20,  2.0651350888385696e-20,
         2.0944064760670539e-20,  2.1238027287557466e-20,  2.1533242400870487e-20,  2.1829714188430474e-20,
         2.2127446894294597e-20,  2.2426444919118270e-20,  2.2726712820637798e-20,  2.3028255314272276e-20,
         2.3331077273843558e-20,  2.3635183732413286e-20,  2.3940579883236352e-20,  2.4247271080830277e-20,
         2.4555262842160330e-20,  2.4864560847940368e-20,  2.5175170944049622e-20,  2.5487099143065929e-20,
         2.5800351625915997e-20,  2.6114934743643687e-20,  2.6430855019297323e-20,  2.6748119149937411e-20,
         2.7066734008766247e-20,  2.7386706647381193e-20,  2.7708044298153558e-20,  2.8030754376735269e-20,
         2.8354844484695747e-20,  2.8680322412291631e-20,  2.9007196141372126e-20,  2.9335473848423219e-20,
         2.9665163907753988e-20,  2.9996274894828624e-20,  3.0328815589748056e-20,  3.0662794980885287e-20,
         3.0998222268678760e-20,  3.1335106869588609e-20,  3.1673458420220558e-20,  3.2013286781622988e-20,
         3.2354602043762612e-20,  3.2697414530184806e-20,  3.3041734802864950e-20,  3.3387573667257349e-20,
         3.3734942177548938e-20,  3.4083851642125208e-20,  3.4434313629256243e-20,  3.4786339973011376e-20,
         3.5139942779411164e-20,  3.5495134432826171e-20,  3.5851927602632460e-20,  3.6210335250134172e-20,
         3.6570370635764384e-20,  3.6932047326575882e-20,  3.7295379204034252e-20,  3.7660380472126401e-20,
         3.8027065665798284e-20,  3.8395449659736649e-20,  3.8765547677510167e-20,  3.9137375301086406e-20,
         3.9510948480742172e-20,  3.9886283545385430e-20,  4.0263397213308566e-20,  4.0642306603393541e-20,
         4.1023029246790967e-20,  4.1405583099096438e-20,  4.1789986553048817e-20,  4.2176258451776819e-20,
         4.2564418102621759e-20,  4.2954485291566197e-20,  4.3346480298300118e-20,  4.3740423911958146e-20,
         4.4136337447563716e-20,  4.4534242763218286e-20,  4.4934162278076256e-20,  4.5336118991149025e-20,
         4.5740136500984466e-20,  4.6146239026271279e-20,  4.6554451427421133e-20,  4.6964799229185088e-20,
         4.7377308644364938e-20,  4.7792006598684169e-20,  4.8208920756888113e-20,  4.8628079550147814e-20,
         4.9049512204847653e-20,  4.9473248772842596e-20,  4.9899320163277674e-20,  5.0327758176068971e-20,
         5.0758595537153414e-20,  5.1191865935622696e-20,  5.1627604062866059e-20,  5.2065845653856416e-20,
         5.2506627530725194e-20,  5.2949987648783448e-20,  5.3395965145159426e-20,  5.3844600390237576e-20,
         5.4295935042099358e-20,  5.4750012104183868e-20,  5.5206875986405073e-20,  5.5666572569983821e-20,
         5.6129149276275792e-20,  5.6594655139902476e-20,  5.7063140886520563e-20,  5.7534659015596918e-20,
         5.8009263888591218e-20,  5.8487011822987583e-20,  5.8967961192659803e-20,  5.9452172535103471e-20,
         5.9939708666122605e-20,  6.0430634802618929e-20,  6.0925018694200531e-20,  6.1422930764402860e-20,
         6.1924444262401531e-20,  6.2429635426193939e-20,  6.2938583658336214e-20,  6.3451371715447563e-20,
         6.3968085912834963e-20,  6.4488816345752736e-20,  6.5013657128995346e-20,  6.5542706656731714e-20,
         6.6076067884730717e-20,  6.6613848637404196e-20,  6.7156161942412980e-20,  6.7703126395950580e-20,
         6.8254866562246408e-20,  6.8811513411327825e-20,  6.9373204799659681e-20,  6.9940085998959109e-20,
         7.0512310279279503e-20,  7.1090039553397167e-20,  7.1673445090644796e-20,  7.2262708309655784e-20,
         7.2858021661057338e-20,  7.3459589613035800e-20,  7.4067629754967553e-20,  7.4682374037052817e-20,
         7.5304070167226666e-20,  7.5932983190698547e-20,  7.6569397282483754e-20,  7.7213617789487678e-20,
         7.7865973566417016e-20,  7.8526819659456755e-20,  7.9196540403850560e-20,  7.9875553017037968e-20,
         8.0564311788901630e-20,  8.1263312996426176e-20,  8.1973100703706304e-20,  8.2694273652634034e-20,
         8.3427493508836792e-20,  8.4173494807453416e-20,  8.4933097052832066e-20,  8.5707219578230905e-20,
         8.6496899985930695e-20,  8.7303317295655327e-20,  8.8127821378859504e-20,  8.8971970928196666e-20,
         8.9837583239314064e-20,  9.0726800697869543e-20,  9.1642181484063544e-20,  9.2586826406702765e-20,
         9.3564561480278864e-20,  9.4580210012636175e-20,  9.5640015550850358e-20,  9.6752334770503130e-20,
         9.7928851697808831e-20,  9.9186905857531331e-20,  1.0055456271343397e-19,  1.0208407377305566e-19,
         1.0390360993240711e-19,  1.0842021724855044e-19 };

    // alias_threshold[j] is a threshold for the probability mass function that has been
    // scaled by (2**64 - 1), translated by -(2**63), and represented as a long value;
    // in this way it can be directly compared to a randomly chosen long value.
    static final long[] normalAliasThreshold = {    // 256 entries
         9223372036854775732L,  1100243796470199922L,  7866600928967318259L,  6788754710669718688L,
         9022865200207136940L,  6522434035182564354L,  4723064097388367094L,  3360495653202227820L,
         2289663232347306830L,  1423968905585875379L,   708364817795238883L,   106102487338962592L,
         -408333464668584328L,  -853239722790494085L, -1242095211827090004L, -1585059631108655444L,
        -1889943050267333598L, -2162852901996526266L, -2408637386596951353L, -2631196530256993348L,
        -2833704942542501760L, -3018774289008775598L, -3188573753501888049L, -3344920681670389334L,
        -3489349705095933019L, -3623166100045386711L, -3747487436861293578L, -3863276422709141026L,
        -3971367044055496571L, -4072485557008423504L, -4167267476835653997L, -4256271432259158584L,
        -4339990541931699221L, -4418861817116128356L, -4493273980399812066L, -4563574004455583972L,
        -4630072609765608272L, -4693048910437239656L, -4752754358851355990L, -4809416110064308151L,
        -4863239903553549801L, -4914412541525462120L, -4963104028438393907L, -5009469424783376781L,
        -5053650458852410933L, -5095776932714599237L, -5135967952538787362L, -5174333008440005397L,
        -5210972924976812191L, -5245980700089102084L, -5279442247516610920L, -5311437055455710870L,
        -5342038772315685218L, -5371315728848281940L, -5399331404596850615L, -5426144845492958401L,
        -5451811038482575296L, -5476381248268660540L, -5499903320574200237L, -5522421955754019296L,
        -5543978956088644891L, -5564613449670076120L, -5584362093426489951L, -5603259257517942559L,
        -5621337193067953247L, -5638626184957155131L, -5655154691206501482L, -5670949470299055313L,
        -5686035697633988263L, -5700437072176015065L, -5714175914241450413L, -5727273255262198220L,
        -5739748920276454057L, -5751621603817308582L, -5762908939796390234L, -5773627565922293024L,
        -5783793183134813122L, -5793420610488485693L, -5802523835876777512L, -5811116062947540603L,
        -5819209754528321254L, -5826816672847738703L, -5833947916812588598L, -5840613956576464230L,
        -5846824665611918318L, -5852589350480860931L, -5857916778478181241L, -5862815203308620040L,
        -5867292388942958035L, -5871355631785040459L, -5875011781271709877L, -5878267259014830525L,
        -5881128076587168793L, -5883599852042383670L, -5885687825255517495L, -5887396872158140520L,
        -5888731517940791413L, -5889695949285098191L, -5890294025685452079L, -5890529289913339019L,
        -5890404977673728891L, -5889924026498433105L, -5889089083917111413L, -5887902514943630556L,
        -5886366408911444323L, -5884482585689698188L, -5882252601307215732L, -5879677753010810505L,
        -5876759083779777633L, -5873497386319005871L, -5869893206546653493L, -5865946846595933526L,
        -5861658367342436656L, -5857027590471882377L, -5852054100098427498L, -5846737243942430862L,
        -5841076134076202917L, -5835069647242632620L, -5828716424752710909L, -5822014871963881822L,
        -5814963157341321336L, -5807559211102860368L, -5799800723445392235L, -5791685142351319976L,
        -5783209670970726741L, -5774371264573181466L, -5765166627063894671L, -5755592207054728713L,
        -5745644193480823967L, -5735318510752045177L, -5724610813425415465L, -5713516480385581414L,
        -5702030608515423737L, -5690148005840583288L, -5677863184127162093L, -5665170350911168791L,
        -5652063400935782694L, -5638535906971010691L, -5624581109986711207L, -5610191908648783765L,
        -5595360848105231304L, -5580080108024969737L, -5564341489852042876L, -5548136403231016978L,
        -5531455851558564459L, -5514290416611714856L, -5496630242199355791L, -5478465016777918644L,
        -5459783954970839371L, -5440575777921757436L, -5420828692410297267L, -5400530368650229789L,
        -5379667916685479525L, -5358227861290596404L, -5336196115276119372L, -5313557951090901350L,
        -5290297970603367798L, -5266400072934326313L, -5241847420204395031L, -5216622401044877639L,
        -5190706591710560934L, -5164080714616987256L, -5136724594109421094L, -5108617109256031912L,
        -5079736143434386281L, -5050058530465123570L, -5019559997019987907L, -4988215101007960589L,
        -4955997165616088151L, -4922878208649305943L, -4888828866781574127L, -4853818314291958392L,
        -4817814175818125756L, -4780782432613346925L, -4742687321741700014L, -4703491227589533028L,
        -4663154565006030194L, -4621635653315226847L, -4578890580363657638L, -4534873055674290590L,
        -4489534251682380820L, -4442822631912146606L, -4394683764829968681L, -4345060121963632469L,
        -4293890858720706245L, -4241111576152819891L, -4186654061709945180L, -4130446006793453666L,
        -4072410698652140640L, -4012466683862855933L, -3950527400292573339L, -3886500774045756804L,
        -3820288777448438119L, -3751786943603804843L, -3680883832458819395L, -3607460442634330728L,
        -3531389562479403081L, -3452535052892669800L, -3370751053387208615L, -3285881101636362572L,
        -3197757155290696249L, -3106198503163967069L, -3011010550898974052L, -2911983463889090176L,
        -2808890647471134035L, -2701487041141521265L, -2589507199668960785L, -2472663129352313038L,
        -2350641842148622058L, -2223102583752258356L, -2089673683718520949L, -1949948966041670625L,
        -1803483646850545328L, -1649789631543398131L, -1488330106106063370L, -1318513295716695859L,
        -1139685236949889721L,  -951121376566993538L,  -752016768187462359L,  -541474585679321485L,
         -318492605702529265L,   -81947227237782935L,   169425512586600501L,   437052607251310002L,
          722551297576808029L,  1027761939321803391L,  1354787941562529921L,  1706044619231670700L,
         2084319374410687061L,  2492846399585974279L,  2935400169364870493L,  3416413484632185639L,
         3941127949845221101L,  4515787798750242711L,  5147892401460631081L,  5846529325404347588L,
         6622819682189677227L,  7490522659877439279L,  8466869998300400224L,  8216968526327386835L,
         4550693915429835301L,  7628019504075715697L,  6605080500885794707L,  7121156327618549405L,
         2484871780310660533L,  7179104797025802172L,  7066086283790288107L,  1516500120772178463L,
          216305945406470492L,  6295963418490399062L,  2889316805640753770L, -2712587580563247199L,
         6562498853480442900L,  7975754821117214681L, -9223372036854775807L, -9223372036854775807L };

    static final byte[] normalAliasMap = {    // 256 entries
        (byte)  0, (byte)  0, (byte)239, (byte)  2, (byte)  0, (byte)  0, (byte)  0, (byte)  0,
        (byte)  0, (byte)  0, (byte)  0, (byte)  0, (byte)  1, (byte)  1, (byte)  1, (byte)253,
        (byte)253, (byte)253, (byte)253, (byte)253, (byte)253, (byte)253, (byte)253, (byte)253,
        (byte)253, (byte)253, (byte)253, (byte)253, (byte)253, (byte)253, (byte)253, (byte)253,
        (byte)253, (byte)253, (byte)253, (byte)253, (byte)253, (byte)253, (byte)253, (byte)253,
        (byte)253, (byte)253, (byte)253, (byte)253, (byte)253, (byte)253, (byte)253, (byte)253,
        (byte)253, (byte)253, (byte)253, (byte)253, (byte)253, (byte)253, (byte)253, (byte)253,
        (byte)253, (byte)253, (byte)253, (byte)253, (byte)253, (byte)253, (byte)253, (byte)253,
        (byte)253, (byte)253, (byte)253, (byte)253, (byte)253, (byte)253, (byte)253, (byte)253,
        (byte)253, (byte)253, (byte)253, (byte)253, (byte)253, (byte)253, (byte)253, (byte)253,
        (byte)253, (byte)253, (byte)253, (byte)253, (byte)253, (byte)253, (byte)253, (byte)253,
        (byte)253, (byte)253, (byte)253, (byte)253, (byte)253, (byte)253, (byte)253, (byte)253,
        (byte)253, (byte)253, (byte)253, (byte)253, (byte)253, (byte)253, (byte)253, (byte)253,
        (byte)253, (byte)253, (byte)253, (byte)253, (byte)253, (byte)253, (byte)253, (byte)253,
        (byte)253, (byte)253, (byte)253, (byte)253, (byte)253, (byte)253, (byte)253, (byte)253,
        (byte)253, (byte)253, (byte)253, (byte)253, (byte)253, (byte)253, (byte)253, (byte)253,
        (byte)253, (byte)253, (byte)253, (byte)253, (byte)253, (byte)253, (byte)253, (byte)253,
        (byte)253, (byte)253, (byte)253, (byte)253, (byte)253, (byte)253, (byte)253, (byte)253,
        (byte)253, (byte)253, (byte)253, (byte)253, (byte)253, (byte)253, (byte)253, (byte)253,
        (byte)253, (byte)253, (byte)253, (byte)253, (byte)253, (byte)253, (byte)253, (byte)253,
        (byte)253, (byte)253, (byte)253, (byte)253, (byte)253, (byte)253, (byte)253, (byte)253,
        (byte)253, (byte)253, (byte)253, (byte)253, (byte)253, (byte)253, (byte)253, (byte)253,
        (byte)253, (byte)253, (byte)253, (byte)253, (byte)253, (byte)253, (byte)253, (byte)253,
        (byte)253, (byte)253, (byte)253, (byte)253, (byte)253, (byte)253, (byte)253, (byte)253,
        (byte)253, (byte)253, (byte)252, (byte)252, (byte)252, (byte)252, (byte)252, (byte)252,
        (byte)252, (byte)252, (byte)252, (byte)252, (byte)251, (byte)251, (byte)251, (byte)251,
        (byte)251, (byte)251, (byte)251, (byte)250, (byte)250, (byte)250, (byte)250, (byte)250,
        (byte)249, (byte)249, (byte)249, (byte)248, (byte)248, (byte)248, (byte)247, (byte)247,
        (byte)247, (byte)246, (byte)246, (byte)245, (byte)244, (byte)244, (byte)243, (byte)242,
        (byte)240, (byte)  2, (byte)  2, (byte)  3, (byte)  3, (byte)  0, (byte)  0, (byte)240,
        (byte)241, (byte)242, (byte)243, (byte)244, (byte)245, (byte)246, (byte)247, (byte)248,
        (byte)249, (byte)250, (byte)251, (byte)252, (byte)253, (byte)  1, (byte)  0, (byte)  0 };

}