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18 package org.apache.commons.rng.sampling.distribution;
19
20 import org.apache.commons.rng.UniformRandomProvider;
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60 public abstract class ZigguratSampler implements SharedStateContinuousSampler {
61
62 private static final int MASK_INT8 = 0xff;
63
64 private static final long MAX_INT64 = Long.MAX_VALUE;
65
66 private static final double TWO_POW_63 = 0x1.0p63;
67
68
69 private final UniformRandomProvider rng;
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258 public static class Exponential extends ZigguratSampler {
259
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264
265
266 private static final int I_MAX = 252;
267
268
269 private static final long E_MAX = 853965788476313647L;
270
271 private static final double X_0 = 7.569274694148063;
272
273
274
275
276 private static final byte[] MAP = {
277 (byte) 0, (byte) 0, (byte) 1, (byte) 235, (byte) 3, (byte) 4, (byte) 5, (byte) 0,
278 (byte) 0, (byte) 0, (byte) 0, (byte) 0, (byte) 0, (byte) 0, (byte) 0, (byte) 0,
279 (byte) 0, (byte) 0, (byte) 1, (byte) 1, (byte) 1, (byte) 1, (byte) 2, (byte) 2,
280 (byte) 252, (byte) 252, (byte) 252, (byte) 252, (byte) 252, (byte) 252, (byte) 252, (byte) 252,
281 (byte) 252, (byte) 252, (byte) 252, (byte) 252, (byte) 252, (byte) 252, (byte) 252, (byte) 252,
282 (byte) 252, (byte) 252, (byte) 252, (byte) 252, (byte) 252, (byte) 252, (byte) 252, (byte) 252,
283 (byte) 252, (byte) 252, (byte) 252, (byte) 252, (byte) 252, (byte) 252, (byte) 252, (byte) 252,
284 (byte) 252, (byte) 252, (byte) 252, (byte) 252, (byte) 252, (byte) 252, (byte) 252, (byte) 252,
285 (byte) 252, (byte) 252, (byte) 252, (byte) 252, (byte) 252, (byte) 252, (byte) 252, (byte) 252,
286 (byte) 252, (byte) 252, (byte) 252, (byte) 252, (byte) 252, (byte) 252, (byte) 252, (byte) 252,
287 (byte) 252, (byte) 252, (byte) 252, (byte) 252, (byte) 252, (byte) 252, (byte) 252, (byte) 252,
288 (byte) 252, (byte) 252, (byte) 252, (byte) 252, (byte) 252, (byte) 252, (byte) 252, (byte) 252,
289 (byte) 252, (byte) 252, (byte) 252, (byte) 252, (byte) 252, (byte) 252, (byte) 252, (byte) 252,
290 (byte) 252, (byte) 252, (byte) 252, (byte) 252, (byte) 252, (byte) 252, (byte) 252, (byte) 252,
291 (byte) 252, (byte) 252, (byte) 252, (byte) 252, (byte) 252, (byte) 252, (byte) 252, (byte) 252,
292 (byte) 252, (byte) 252, (byte) 252, (byte) 252, (byte) 252, (byte) 252, (byte) 252, (byte) 252,
293 (byte) 252, (byte) 252, (byte) 252, (byte) 252, (byte) 252, (byte) 252, (byte) 252, (byte) 252,
294 (byte) 252, (byte) 252, (byte) 252, (byte) 252, (byte) 252, (byte) 252, (byte) 252, (byte) 252,
295 (byte) 252, (byte) 252, (byte) 252, (byte) 252, (byte) 252, (byte) 252, (byte) 252, (byte) 252,
296 (byte) 252, (byte) 252, (byte) 252, (byte) 252, (byte) 252, (byte) 252, (byte) 252, (byte) 252,
297 (byte) 252, (byte) 252, (byte) 252, (byte) 252, (byte) 252, (byte) 252, (byte) 252, (byte) 252,
298 (byte) 252, (byte) 252, (byte) 252, (byte) 252, (byte) 252, (byte) 252, (byte) 252, (byte) 252,
299 (byte) 252, (byte) 251, (byte) 251, (byte) 251, (byte) 251, (byte) 251, (byte) 251, (byte) 251,
300 (byte) 251, (byte) 251, (byte) 251, (byte) 251, (byte) 251, (byte) 251, (byte) 250, (byte) 250,
301 (byte) 250, (byte) 250, (byte) 250, (byte) 250, (byte) 250, (byte) 249, (byte) 249, (byte) 249,
302 (byte) 249, (byte) 249, (byte) 249, (byte) 248, (byte) 248, (byte) 248, (byte) 248, (byte) 247,
303 (byte) 247, (byte) 247, (byte) 247, (byte) 246, (byte) 246, (byte) 246, (byte) 245, (byte) 245,
304 (byte) 244, (byte) 244, (byte) 243, (byte) 243, (byte) 242, (byte) 241, (byte) 241, (byte) 240,
305 (byte) 239, (byte) 237, (byte) 3, (byte) 3, (byte) 4, (byte) 4, (byte) 6, (byte) 0,
306 (byte) 0, (byte) 0, (byte) 0, (byte) 236, (byte) 237, (byte) 238, (byte) 239, (byte) 240,
307 (byte) 241, (byte) 242, (byte) 243, (byte) 244, (byte) 245, (byte) 246, (byte) 247, (byte) 248,
308 (byte) 249, (byte) 250, (byte) 251, (byte) 252, (byte) 2, (byte) 0, (byte) 0, (byte) 0,
309 };
310
311
312
313
314 private static final long[] IPMF = {
315 9223372036854774016L, 1623796909450834944L, 2664290944894291200L, 7387971354164060928L,
316 6515064486552723200L, 8840508362680718848L, 6099647593382936320L, 7673130333659513856L,
317 6220332867583438080L, 5045979640552813824L, 4075305837223955456L, 3258413672162525440L,
318 2560664887087762432L, 1957224924672899584L, 1429800935350577408L, 964606309710808320L,
319 551043923599587072L, 180827629096890368L, -152619738120023552L, -454588624410291456L,
320 -729385126147774976L, -980551509819447040L, -1211029700667463936L, -1423284293868548352L,
321 -1619396356369050368L, -1801135830956211712L, -1970018048575618048L, -2127348289059705344L,
322 -2274257249303686400L, -2411729520096655360L, -2540626634159181056L, -2661705860113406464L,
323 -2775635634532450560L, -2883008316030465280L, -2984350790383654912L, -3080133339198116352L,
324 -3170777096303091200L, -3256660348483819008L, -3338123885075136256L, -3415475560473299200L,
325 -3488994201966428160L, -3558932970354473216L, -3625522261068041216L, -3688972217741989376L,
326 -3749474917563782656L, -3807206277531056128L, -3862327722496843520L, -3914987649156779776L,
327 -3965322714631865344L, -4013458973776895488L, -4059512885612783360L, -4103592206186241024L,
328 -4145796782586128128L, -4186219260694347008L, -4224945717447275264L, -4262056226866285568L,
329 -4297625367836519680L, -4331722680528537344L, -4364413077437472512L, -4395757214229401600L,
330 -4425811824915135744L, -4454630025296932608L, -4482261588141290496L, -4508753193105288192L,
331 -4534148654077808896L, -4558489126279958272L, -4581813295192216576L, -4604157549138257664L,
332 -4625556137145255168L, -4646041313519104512L, -4665643470413305856L, -4684391259530326528L,
333 -4702311703971761664L, -4719430301145103360L, -4735771117539946240L, -4751356876102087168L,
334 -4766209036859133952L, -4780347871386013440L, -4793792531638892032L, -4806561113635132672L,
335 -4818670716409306624L, -4830137496634465536L, -4840976719260837888L, -4851202804490348800L,
336 -4860829371376460032L, -4869869278311657472L, -4878334660640771072L, -4886236965617427200L,
337 -4893586984900802560L, -4900394884772702720L, -4906670234238885376L, -4912422031164496896L,
338 -4917658726580119808L, -4922388247283532288L, -4926618016851066624L, -4930354975163335168L,
339 -4933605596540651264L, -4936375906575303936L, -4938671497741366016L, -4940497543854575616L,
340 -4941858813449629440L, -4942759682136114944L, -4943204143989086720L, -4943195822025528064L,
341 -4942737977813206528L, -4941833520255033344L, -4940485013586738944L, -4938694684624359424L,
342 -4936464429291795968L, -4933795818458825728L, -4930690103114057984L, -4927148218896864000L,
343 -4923170790008275968L, -4918758132519213568L, -4913910257091645696L, -4908626871126539264L,
344 -4902907380349533952L, -4896750889844272896L, -4890156204540531200L, -4883121829162554368L,
345 -4875645967641781248L, -4867726521994927104L, -4859361090668103424L, -4850546966345113600L,
346 -4841281133215539200L, -4831560263698491904L, -4821380714613447424L, -4810738522790066176L,
347 -4799629400105481984L, -4788048727936307200L, -4775991551010514944L, -4763452570642114304L,
348 -4750426137329494528L, -4736906242696389120L, -4722886510751377664L, -4708360188440089088L,
349 -4693320135461421056L, -4677758813316108032L, -4661668273553489152L, -4645040145179241472L,
350 -4627865621182772224L, -4610135444140930048L, -4591839890849345536L, -4572968755929961472L,
351 -4553511334358205696L, -4533456402849101568L, -4512792200036279040L, -4491506405372580864L,
352 -4469586116675402496L, -4447017826233107968L, -4423787395382284800L, -4399880027458416384L,
353 -4375280239014115072L, -4349971829190472192L, -4323937847117721856L, -4297160557210933504L,
354 -4269621402214949888L, -4241300963840749312L, -4212178920821861632L, -4182234004204451584L,
355 -4151443949668877312L, -4119785446662287616L, -4087234084103201536L, -4053764292396156928L,
356 -4019349281473081856L, -3983960974549692672L, -3947569937258423296L, -3910145301787345664L,
357 -3871654685619032064L, -3832064104425388800L, -3791337878631544832L, -3749438533114327552L,
358 -3706326689447984384L, -3661960950051848192L, -3616297773528534784L, -3569291340409189376L,
359 -3520893408440946176L, -3471053156460654336L, -3419717015797782528L, -3366828488034805504L,
360 -3312327947826460416L, -3256152429334010368L, -3198235394669719040L, -3138506482563172864L,
361 -3076891235255162880L, -3013310801389730816L, -2947681612411374848L, -2879915029671670784L,
362 -2809916959107513856L, -2737587429961866240L, -2662820133571325696L, -2585501917733380096L,
363 -2505512231579385344L, -2422722515205211648L, -2336995527534088448L, -2248184604988727552L,
364 -2156132842510765056L, -2060672187261025536L, -1961622433929371904L, -1858790108950105600L,
365 -1751967229002895616L, -1640929916937142784L, -1525436855617582592L, -1405227557075253248L,
366 -1280020420662650112L, -1149510549536596224L, -1013367289578704896L, -871231448632104192L,
367 -722712146453667840L, -567383236774436096L, -404779231966938368L, -234390647591545856L,
368 -55658667960119296L, 132030985907841280L, 329355128892811776L, 537061298001085184L,
369 755977262693564160L, 987022116608033280L, 1231219266829431296L, 1489711711346518528L,
370 1763780090187553792L, 2054864117341795072L, 2364588157623768832L, 2694791916990503168L,
371 3047567482883476224L, 3425304305830816256L, 3830744187097297920L, 4267048975685830400L,
372 4737884547990017280L, 5247525842198998272L, 5800989391535355392L, 6404202162993295360L,
373 7064218894258540544L, 7789505049452331520L, 8590309807749444864L, 7643763810684489984L,
374 8891950541491446016L, 5457384281016206080L, 9083704440929284096L, 7976211653914433280L,
375 8178631350487117568L, 2821287825726744832L, 6322989683301709568L, 4309503753387611392L,
376 4685170734960170496L, 8404845967535199744L, 7330522972447554048L, 1960945799076992000L,
377 4742910674644899072L, -751799822533509888L, 7023456603741959936L, 3843116882594676224L,
378 3927231442413903104L, -9223372036854775808L, -9223372036854775808L, -9223372036854775808L,
379 };
380
381
382
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387
388
389
390 private static final double[] X = {
391 8.2066240675348816e-19, 7.3973732351607284e-19, 6.9133313377915293e-19, 6.5647358820964533e-19,
392 6.2912539959818508e-19, 6.0657224129604964e-19, 5.8735276103737269e-19, 5.7058850528536941e-19,
393 5.557094569162239e-19, 5.4232438903743953e-19, 5.3015297696508776e-19, 5.1898739257708062e-19,
394 5.086692261799833e-19, 4.9907492938796469e-19, 4.9010625894449536e-19, 4.8168379010649187e-19,
395 4.7374238653644714e-19, 4.6622795807196824e-19, 4.5909509017784048e-19, 4.5230527790658154e-19,
396 4.458255881635396e-19, 4.3962763126368381e-19, 4.336867596710647e-19, 4.2798143618469714e-19,
397 4.2249273027064889e-19, 4.172039125346411e-19, 4.1210012522465616e-19, 4.0716811225869233e-19,
398 4.0239599631006903e-19, 3.9777309342877357e-19, 3.9328975785334499e-19, 3.8893725129310323e-19,
399 3.8470763218720385e-19, 3.8059366138180143e-19, 3.765887213854473e-19, 3.7268674692030177e-19,
400 3.6888216492248162e-19, 3.6516984248800068e-19, 3.6154504153287473e-19, 3.5800337915318032e-19,
401 3.5454079284533432e-19, 3.5115350988784242e-19, 3.4783802030030962e-19, 3.4459105288907336e-19,
402 3.4140955396563316e-19, 3.3829066838741162e-19, 3.3523172262289001e-19, 3.3223020958685874e-19,
403 3.2928377502804472e-19, 3.2639020528202049e-19, 3.2354741622810815e-19, 3.2075344331080789e-19,
404 3.1800643250478609e-19, 3.1530463211820845e-19, 3.1264638534265134e-19, 3.1003012346934211e-19,
405 3.0745435970137301e-19, 3.0491768350005559e-19, 3.0241875541094565e-19, 2.999563023214455e-19,
406 2.9752911310742592e-19, 2.9513603463113224e-19, 2.9277596805684267e-19, 2.9044786545442563e-19,
407 2.8815072666416712e-19, 2.8588359639906928e-19, 2.8364556156331615e-19, 2.8143574876779799e-19,
408 2.7925332202553125e-19, 2.7709748061152879e-19, 2.7496745707320232e-19, 2.7286251537873397e-19,
409 2.7078194919206054e-19, 2.687250802641905e-19, 2.6669125693153442e-19, 2.6467985271278891e-19,
410 2.6269026499668434e-19, 2.6072191381359757e-19, 2.5877424068465143e-19, 2.5684670754248168e-19,
411 2.5493879571835479e-19, 2.5305000499077481e-19, 2.511798526911271e-19, 2.4932787286227806e-19,
412 2.474936154663866e-19, 2.4567664563848669e-19, 2.4387654298267842e-19, 2.4209290090801527e-19,
413 2.4032532600140538e-19, 2.3857343743505147e-19, 2.3683686640614648e-19, 2.3511525560671253e-19,
414 2.3340825872163284e-19, 2.3171553995306794e-19, 2.3003677356958333e-19, 2.2837164347843482e-19,
415 2.2671984281957174e-19, 2.2508107358001938e-19, 2.2345504622739592e-19, 2.2184147936140775e-19,
416 2.2024009938224424e-19, 2.1865064017486842e-19, 2.1707284280826716e-19, 2.1550645524878675e-19,
417 2.1395123208673778e-19, 2.124069342755064e-19, 2.1087332888245875e-19, 2.0935018885097035e-19,
418 2.0783729277295508e-19, 2.0633442467130712e-19, 2.0484137379170616e-19, 2.0335793440326865e-19,
419 2.018839056075609e-19, 2.0041909115551697e-19, 1.9896329927183254e-19, 1.975163424864309e-19,
420 1.9607803747261946e-19, 1.9464820489157862e-19, 1.9322666924284314e-19, 1.9181325872045647e-19,
421 1.9040780507449479e-19, 1.8901014347767504e-19, 1.8762011239677479e-19, 1.8623755346860768e-19,
422 1.8486231138030984e-19, 1.8349423375370566e-19, 1.8213317103353295e-19, 1.8077897637931708e-19,
423 1.7943150556069476e-19, 1.7809061685599652e-19, 1.7675617095390567e-19, 1.7542803085801941e-19,
424 1.7410606179414531e-19, 1.727901311201724e-19, 1.7148010823836362e-19, 1.7017586450992059e-19,
425 1.6887727317167824e-19, 1.6758420925479093e-19, 1.6629654950527621e-19, 1.6501417230628659e-19,
426 1.6373695760198277e-19, 1.624647868228856e-19, 1.6119754281258616e-19, 1.5993510975569615e-19,
427 1.5867737310692309e-19, 1.5742421952115544e-19, 1.5617553678444595e-19, 1.5493121374578016e-19,
428 1.5369114024951992e-19, 1.5245520706841019e-19, 1.5122330583703858e-19, 1.4999532898563561e-19,
429 1.4877116967410352e-19, 1.4755072172615974e-19, 1.4633387956347966e-19, 1.4512053813972103e-19,
430 1.4391059287430991e-19, 1.4270393958586506e-19, 1.4150047442513381e-19, 1.4030009380730888e-19,
431 1.3910269434359025e-19, 1.3790817277185197e-19, 1.3671642588626657e-19, 1.3552735046573446e-19,
432 1.3434084320095729e-19, 1.3315680061998685e-19, 1.3197511901207148e-19, 1.3079569434961214e-19,
433 1.2961842220802957e-19, 1.2844319768333099e-19, 1.2726991530715219e-19, 1.2609846895903523e-19,
434 1.2492875177568625e-19, 1.237606560569394e-19, 1.2259407316813331e-19, 1.2142889343858445e-19,
435 1.2026500605581765e-19, 1.1910229895518744e-19, 1.1794065870449425e-19, 1.1677997038316715e-19,
436 1.1562011745554883e-19, 1.1446098163777869e-19, 1.1330244275772562e-19, 1.1214437860737343e-19,
437 1.109866647870073e-19, 1.0982917454048923e-19, 1.0867177858084351e-19, 1.0751434490529747e-19,
438 1.0635673859884002e-19, 1.0519882162526621e-19, 1.0404045260457141e-19, 1.0288148657544097e-19,
439 1.0172177474144965e-19, 1.0056116419943559e-19, 9.9399497648346677e-20, 9.8236613076667446e-20,
440 9.7072343426320094e-20, 9.5906516230690634e-20, 9.4738953224154196e-20, 9.3569469920159036e-20,
441 9.2397875154569468e-20, 9.1223970590556472e-20, 9.0047550180852874e-20, 8.8868399582647627e-20,
442 8.768629551976745e-20, 8.6501005086071005e-20, 8.5312284983141187e-20, 8.4119880684385214e-20,
443 8.292352551651342e-20, 8.1722939648034506e-20, 8.0517828972839211e-20, 7.9307883875099226e-20,
444 7.8092777859524425e-20, 7.6872166028429042e-20, 7.5645683383965122e-20, 7.4412942930179128e-20,
445 7.3173533545093332e-20, 7.1927017587631075e-20, 7.0672928197666785e-20, 6.9410766239500362e-20,
446 6.8139996829256425e-20, 6.6860045374610234e-20, 6.5570293040210081e-20, 6.4270071533368528e-20,
447 6.2958657080923559e-20, 6.1635263438143136e-20, 6.02990337321517e-20, 5.8949030892850181e-20,
448 5.758422635988593e-20, 5.6203486669597397e-20, 5.4805557413499315e-20, 5.3389043909003295e-20,
449 5.1952387717989917e-20, 5.0493837866338355e-20, 4.9011415222629489e-20, 4.7502867933366117e-20,
450 4.5965615001265455e-20, 4.4396673897997565e-20, 4.2792566302148588e-20, 4.1149193273430015e-20,
451 3.9461666762606287e-20, 3.7724077131401685e-20, 3.592916408620436e-20, 3.4067836691100565e-20,
452 3.2128447641564046e-20, 3.0095646916399994e-20, 2.7948469455598328e-20, 2.5656913048718645e-20,
453 2.3175209756803909e-20, 2.0426695228251291e-20, 1.7261770330213488e-20, 1.3281889259442579e-20,
454 0,
455 };
456
457
458
459
460
461
462
463
464
465
466 private static final double[] Y = {
467 5.595205495112736e-23, 1.1802509982703313e-22, 1.8444423386735829e-22, 2.5439030466698309e-22,
468 3.2737694311509334e-22, 4.0307732132706715e-22, 4.8125478319495115e-22, 5.6172914896583308e-22,
469 6.4435820540443526e-22, 7.2902662343463681e-22, 8.1563888456321941e-22, 9.0411453683482223e-22,
470 9.9438488486399206e-22, 1.0863906045969114e-21, 1.1800799775461269e-21, 1.2754075534831208e-21,
471 1.372333117637729e-21, 1.4708208794375214e-21, 1.5708388257440445e-21, 1.6723581984374566e-21,
472 1.7753530675030514e-21, 1.8797999785104595e-21, 1.9856776587832504e-21, 2.0929667704053244e-21,
473 2.201649700995824e-21, 2.3117103852306179e-21, 2.4231341516125464e-21, 2.5359075901420891e-21,
474 2.6500184374170538e-21, 2.7654554763660391e-21, 2.8822084483468604e-21, 3.0002679757547711e-21,
475 3.1196254936130377e-21, 3.2402731888801749e-21, 3.3622039464187092e-21, 3.4854113007409036e-21,
476 3.6098893927859475e-21, 3.7356329310971768e-21, 3.8626371568620053e-21, 3.9908978123552837e-21,
477 4.1204111123918948e-21, 4.2511737184488913e-21, 4.3831827151633737e-21, 4.5164355889510656e-21,
478 4.6509302085234806e-21, 4.7866648071096003e-21, 4.9236379662119969e-21, 5.0618486007478993e-21,
479 5.2012959454434732e-21, 5.3419795423648946e-21, 5.4838992294830959e-21, 5.6270551301806347e-21,
480 5.7714476436191935e-21, 5.9170774358950678e-21, 6.0639454319177027e-21, 6.2120528079531677e-21,
481 6.3614009847804375e-21, 6.5119916214136427e-21, 6.6638266093481696e-21, 6.8169080672926277e-21,
482 6.9712383363524377e-21, 7.1268199756340822e-21, 7.2836557582420336e-21, 7.4417486676430174e-21,
483 7.6011018943746355e-21, 7.7617188330775411e-21, 7.9236030798322572e-21, 8.0867584297834842e-21,
484 8.2511888750363333e-21, 8.4168986028103258e-21, 8.5838919938383098e-21, 8.7521736209986459e-21,
485 8.9217482481700712e-21, 9.0926208292996504e-21, 9.2647965076751277e-21, 9.4382806153938292e-21,
486 9.6130786730210328e-21, 9.7891963894314161e-21, 9.966639661827884e-21, 1.0145414575932636e-20,
487 1.0325527406345955e-20, 1.0506984617068672e-20, 1.0689792862184811e-20, 1.0873958986701341e-20,
488 1.10594900275424e-20, 1.1246393214695825e-20, 1.1434675972510121e-20, 1.1624345921140471e-20,
489 1.1815410878142659e-20, 1.2007878860214202e-20, 1.2201758085082226e-20, 1.239705697353804e-20,
490 1.2593784151618565e-20, 1.2791948452935152e-20, 1.29915589211506e-20, 1.3192624812605428e-20,
491 1.3395155599094805e-20, 1.3599160970797774e-20, 1.3804650839360727e-20, 1.4011635341137284e-20,
492 1.4220124840587164e-20, 1.4430129933836705e-20, 1.4641661452404201e-20, 1.485473046709328e-20,
493 1.5069348292058084e-20, 1.5285526489044053e-20, 1.5503276871808626e-20, 1.5722611510726402e-20,
494 1.5943542737583543e-20, 1.6166083150566702e-20, 1.6390245619451956e-20, 1.6616043290999594e-20,
495 1.6843489594561079e-20, 1.7072598247904713e-20, 1.7303383263267072e-20, 1.7535858953637607e-20,
496 1.7770039939284241e-20, 1.8005941154528286e-20, 1.8243577854777398e-20, 1.8482965623825808e-20,
497 1.8724120381431627e-20, 1.8967058391181452e-20, 1.9211796268653192e-20, 1.9458350989888484e-20,
498 1.9706739900186868e-20, 1.9956980723234356e-20, 2.0209091570579904e-20, 2.0463090951473895e-20,
499 2.0718997783083593e-20, 2.097683140110135e-20, 2.123661157076213e-20, 2.1498358498287976e-20,
500 2.1762092842777868e-20, 2.2027835728562592e-20, 2.2295608758045219e-20, 2.2565434025049041e-20,
501 2.2837334128696004e-20, 2.311133218784001e-20, 2.3387451856080863e-20, 2.3665717337386111e-20,
502 2.394615340234961e-20, 2.422878540511741e-20, 2.4513639301013211e-20, 2.4800741664897764e-20,
503 2.5090119710298442e-20, 2.5381801309347597e-20, 2.56758150135705e-20, 2.5972190075566336e-20,
504 2.6270956471628253e-20, 2.6572144925351523e-20, 2.6875786932281841e-20, 2.7181914785659148e-20,
505 2.7490561603315974e-20, 2.7801761355793055e-20, 2.8115548895739172e-20, 2.8431959988666534e-20,
506 2.8751031345137833e-20, 2.9072800654466307e-20, 2.9397306620015486e-20, 2.9724588996191657e-20,
507 3.0054688627228112e-20, 3.0387647487867642e-20, 3.0723508726057078e-20, 3.1062316707775905e-20,
508 3.1404117064129991e-20, 3.1748956740850969e-20, 3.2096884050352357e-20, 3.2447948726504914e-20,
509 3.2802201982306013e-20, 3.3159696570631373e-20, 3.352048684827223e-20, 3.3884628843476888e-20,
510 3.4252180327233346e-20, 3.4623200888548644e-20, 3.4997752014001677e-20, 3.537589717186906e-20,
511 3.5757701901149035e-20, 3.6143233905835799e-20, 3.65325631548274e-20, 3.6925761987883572e-20,
512 3.7322905228086981e-20, 3.7724070301302117e-20, 3.8129337363171041e-20, 3.8538789434235234e-20,
513 3.8952512543827862e-20, 3.9370595883442399e-20, 3.9793131970351439e-20, 4.0220216822325769e-20,
514 4.0651950144388133e-20, 4.1088435528630944e-20, 4.1529780668232712e-20, 4.1976097586926582e-20,
515 4.2427502885307452e-20, 4.2884118005513604e-20, 4.3346069515987453e-20, 4.3813489418210257e-20,
516 4.4286515477520838e-20, 4.4765291580372353e-20, 4.5249968120658306e-20, 4.5740702418054417e-20,
517 4.6237659171683015e-20, 4.6741010952818368e-20, 4.7250938740823415e-20, 4.7767632507051219e-20,
518 4.8291291852069895e-20, 4.8822126702292804e-20, 4.9360358072933852e-20, 4.9906218905182021e-20,
519 5.0459954986625539e-20, 5.1021825965285324e-20, 5.1592106469178258e-20, 5.2171087345169234e-20,
520 5.2759077033045284e-20, 5.3356403093325858e-20, 5.3963413910399511e-20, 5.4580480596259246e-20,
521 5.5207999124535584e-20, 5.584639272987383e-20, 5.649611461419377e-20, 5.7157651009290713e-20,
522 5.7831524654956632e-20, 5.8518298763794323e-20, 5.9218581558791713e-20, 5.99330314883387e-20,
523 6.0662363246796887e-20, 6.1407354758435e-20, 6.2168855320499763e-20, 6.2947795150103727e-20,
524 6.3745196643214394e-20, 6.4562187737537985e-20, 6.5400017881889097e-20, 6.6260077263309343e-20,
525 6.714392014514662e-20, 6.8053293447301698e-20, 6.8990172088133e-20, 6.9956803158564498e-20,
526 7.095576179487843e-20, 7.199002278894508e-20, 7.3063053739105458e-20, 7.4178938266266881e-20,
527 7.5342542134173124e-20, 7.6559742171142969e-20, 7.783774986341285e-20, 7.9185582674029512e-20,
528 8.06147755373533e-20, 8.2140502769818073e-20, 8.3783445978280519e-20, 8.5573129249678161e-20,
529 8.75544596695901e-20, 8.9802388057706877e-20, 9.2462471421151086e-20, 9.5919641344951721e-20,
530 1.0842021724855044e-19,
531 };
532
533
534
535
536 private static class ExponentialMean extends Exponential {
537
538 private final double mean;
539
540
541
542
543
544 ExponentialMean(UniformRandomProvider rng, double mean) {
545 super(rng);
546 this.mean = mean;
547 }
548
549 @Override
550 public double sample() {
551 return super.sample() * mean;
552 }
553
554 @Override
555 public ExponentialMean withUniformRandomProvider(UniformRandomProvider rng) {
556 return new ExponentialMean(rng, this.mean);
557 }
558 }
559
560
561
562
563 private Exponential(UniformRandomProvider rng) {
564 super(rng);
565 }
566
567
568 @Override
569 public String toString() {
570 return toString("exponential");
571 }
572
573
574 @Override
575 public double sample() {
576
577
578
579 final long x = nextLong();
580
581 final int i = ((int) x) & MASK_INT8;
582
583 if (i < I_MAX) {
584
585
586
587 return X[i] * (x >>> 1);
588 }
589
590
591
592
593
594
595 return edgeSample(x);
596 }
597
598
599
600
601
602
603
604
605
606
607 private double edgeSample(long xx) {
608 int j = selectRegion();
609 if (j != 0) {
610
611 return sampleOverhang(j, xx);
612 }
613
614
615
616
617
618
619
620
621 double x0 = X_0;
622 for (;;) {
623
624 final long x = nextLong();
625 final int i = ((int) x) & 0xff;
626
627 if (i < I_MAX) {
628
629 return x0 + X[i] * (x >>> 1);
630 }
631
632
633 j = selectRegion();
634 if (j != 0) {
635 return x0 + sampleOverhang(j, x);
636 }
637
638
639 x0 += X_0;
640 }
641 }
642
643
644
645
646
647
648 private int selectRegion() {
649 final long x = nextLong();
650
651 final int j = ((int) x) & MASK_INT8;
652
653 return x >= IPMF[j] ? MAP[j] & MASK_INT8 : j;
654 }
655
656
657
658
659
660
661
662
663 private double sampleOverhang(int j, long xx) {
664
665
666 long u1 = xx >>> 1;
667 for (;;) {
668
669
670
671
672
673
674
675
676
677
678
679
680 final long u = randomInt63();
681
682
683 final long u2 = u1 < u ? u : u1;
684 u1 = u1 < u ? u1 : u;
685 final double x = interpolate(X, j, u1);
686 if (u2 - u1 >= E_MAX) {
687
688 return x;
689 }
690
691
692
693
694
695
696 if (interpolate(Y, j, u2) <= Math.exp(-x)) {
697 return x;
698 }
699
700
701 u1 = randomInt63();
702 }
703 }
704
705
706 @Override
707 public Exponential withUniformRandomProvider(UniformRandomProvider rng) {
708 return new Exponential(rng);
709 }
710
711
712
713
714
715
716
717 public static Exponential of(UniformRandomProvider rng) {
718 return new Exponential(rng);
719 }
720
721
722
723
724
725
726
727
728
729 public static Exponential of(UniformRandomProvider rng, double mean) {
730 if (mean > 0) {
731 return new ExponentialMean(rng, mean);
732 }
733 throw new IllegalArgumentException("Mean is not strictly positive: " + mean);
734 }
735 }
736
737
738
739
740
741
742
743
744
745
746
747
748
749 public static final class NormalizedGaussian extends ZigguratSampler
750 implements NormalizedGaussianSampler, SharedStateContinuousSampler {
751
752
753
754
755
756
757
758
759
760 private static final int I_MAX = 253;
761
762
763 private static final int J_INFLECTION = 204;
764
765
766
767
768 private static final long CONVEX_E_MAX = -2269182951627976004L;
769
770
771 private static final long CONCAVE_E_MAX = 760463704284035184L;
772
773 private static final double X_0 = 3.6360066255009455861;
774
775 private static final double ONE_OVER_X_0 = 1.0 / X_0;
776
777
778
779
780 private static final byte[] MAP = {
781 (byte) 0, (byte) 0, (byte) 239, (byte) 2, (byte) 0, (byte) 0, (byte) 0, (byte) 0,
782 (byte) 0, (byte) 0, (byte) 0, (byte) 0, (byte) 1, (byte) 1, (byte) 1, (byte) 253,
783 (byte) 253, (byte) 253, (byte) 253, (byte) 253, (byte) 253, (byte) 253, (byte) 253, (byte) 253,
784 (byte) 253, (byte) 253, (byte) 253, (byte) 253, (byte) 253, (byte) 253, (byte) 253, (byte) 253,
785 (byte) 253, (byte) 253, (byte) 253, (byte) 253, (byte) 253, (byte) 253, (byte) 253, (byte) 253,
786 (byte) 253, (byte) 253, (byte) 253, (byte) 253, (byte) 253, (byte) 253, (byte) 253, (byte) 253,
787 (byte) 253, (byte) 253, (byte) 253, (byte) 253, (byte) 253, (byte) 253, (byte) 253, (byte) 253,
788 (byte) 253, (byte) 253, (byte) 253, (byte) 253, (byte) 253, (byte) 253, (byte) 253, (byte) 253,
789 (byte) 253, (byte) 253, (byte) 253, (byte) 253, (byte) 253, (byte) 253, (byte) 253, (byte) 253,
790 (byte) 253, (byte) 253, (byte) 253, (byte) 253, (byte) 253, (byte) 253, (byte) 253, (byte) 253,
791 (byte) 253, (byte) 253, (byte) 253, (byte) 253, (byte) 253, (byte) 253, (byte) 253, (byte) 253,
792 (byte) 253, (byte) 253, (byte) 253, (byte) 253, (byte) 253, (byte) 253, (byte) 253, (byte) 253,
793 (byte) 253, (byte) 253, (byte) 253, (byte) 253, (byte) 253, (byte) 253, (byte) 253, (byte) 253,
794 (byte) 253, (byte) 253, (byte) 253, (byte) 253, (byte) 253, (byte) 253, (byte) 253, (byte) 253,
795 (byte) 253, (byte) 253, (byte) 253, (byte) 253, (byte) 253, (byte) 253, (byte) 253, (byte) 253,
796 (byte) 253, (byte) 253, (byte) 253, (byte) 253, (byte) 253, (byte) 253, (byte) 253, (byte) 253,
797 (byte) 253, (byte) 253, (byte) 253, (byte) 253, (byte) 253, (byte) 253, (byte) 253, (byte) 253,
798 (byte) 253, (byte) 253, (byte) 253, (byte) 253, (byte) 253, (byte) 253, (byte) 253, (byte) 253,
799 (byte) 253, (byte) 253, (byte) 253, (byte) 253, (byte) 253, (byte) 253, (byte) 253, (byte) 253,
800 (byte) 253, (byte) 253, (byte) 253, (byte) 253, (byte) 253, (byte) 253, (byte) 253, (byte) 253,
801 (byte) 253, (byte) 253, (byte) 253, (byte) 253, (byte) 253, (byte) 253, (byte) 253, (byte) 253,
802 (byte) 253, (byte) 253, (byte) 253, (byte) 253, (byte) 253, (byte) 253, (byte) 253, (byte) 253,
803 (byte) 253, (byte) 253, (byte) 253, (byte) 253, (byte) 253, (byte) 253, (byte) 253, (byte) 253,
804 (byte) 253, (byte) 253, (byte) 253, (byte) 253, (byte) 253, (byte) 253, (byte) 253, (byte) 253,
805 (byte) 253, (byte) 253, (byte) 252, (byte) 252, (byte) 252, (byte) 252, (byte) 252, (byte) 252,
806 (byte) 252, (byte) 252, (byte) 252, (byte) 252, (byte) 251, (byte) 251, (byte) 251, (byte) 251,
807 (byte) 251, (byte) 251, (byte) 251, (byte) 250, (byte) 250, (byte) 250, (byte) 250, (byte) 250,
808 (byte) 249, (byte) 249, (byte) 249, (byte) 248, (byte) 248, (byte) 248, (byte) 247, (byte) 247,
809 (byte) 247, (byte) 246, (byte) 246, (byte) 245, (byte) 244, (byte) 244, (byte) 243, (byte) 242,
810 (byte) 240, (byte) 2, (byte) 2, (byte) 3, (byte) 3, (byte) 0, (byte) 0, (byte) 240,
811 (byte) 241, (byte) 242, (byte) 243, (byte) 244, (byte) 245, (byte) 246, (byte) 247, (byte) 248,
812 (byte) 249, (byte) 250, (byte) 251, (byte) 252, (byte) 253, (byte) 1, (byte) 0, (byte) 0,
813 };
814
815
816
817
818 private static final long[] IPMF = {
819 9223372036854775296L, 1100243796534090752L, 7866600928998383104L, 6788754710675124736L,
820 9022865200181688320L, 6522434035205502208L, 4723064097360024576L, 3360495653216416000L,
821 2289663232373870848L, 1423968905551920384L, 708364817827798016L, 106102487305601280L,
822 -408333464665794560L, -853239722779025152L, -1242095211825521408L, -1585059631105762048L,
823 -1889943050287169024L, -2162852901990669824L, -2408637386594511104L, -2631196530262954496L,
824 -2833704942520925696L, -3018774289025787392L, -3188573753472222208L, -3344920681707410944L,
825 -3489349705062150656L, -3623166100042179584L, -3747487436868335360L, -3863276422712173824L,
826 -3971367044063130880L, -4072485557029824000L, -4167267476830916608L, -4256271432240159744L,
827 -4339990541927306752L, -4418861817133802240L, -4493273980372377088L, -4563574004462246656L,
828 -4630072609770453760L, -4693048910430964992L, -4752754358862894848L, -4809416110052769536L,
829 -4863239903586985984L, -4914412541515875840L, -4963104028439161088L, -5009469424769119232L,
830 -5053650458856559360L, -5095776932695077632L, -5135967952544929024L, -5174333008451230720L,
831 -5210972924952654336L, -5245980700100460288L, -5279442247516297472L, -5311437055462369280L,
832 -5342038772315650560L, -5371315728843297024L, -5399331404632512768L, -5426144845448965120L,
833 -5451811038519422464L, -5476381248265593088L, -5499903320558339072L, -5522421955752311296L,
834 -5543978956085263616L, -5564613449659060480L, -5584362093436146432L, -5603259257517428736L,
835 -5621337193070986240L, -5638626184974132224L, -5655154691220933888L, -5670949470294763008L,
836 -5686035697601807872L, -5700437072199152384L, -5714175914219812352L, -5727273255295220992L,
837 -5739748920271997440L, -5751621603810412032L, -5762908939773946112L, -5773627565915007744L,
838 -5783793183152377600L, -5793420610475628544L, -5802523835894661376L, -5811116062947570176L,
839 -5819209754516120832L, -5826816672854571776L, -5833947916825278208L, -5840613956570608128L,
840 -5846824665591763456L, -5852589350491075328L, -5857916778480726528L, -5862815203334800384L,
841 -5867292388935742464L, -5871355631762284032L, -5875011781262890752L, -5878267259039093760L,
842 -5881128076579883520L, -5883599852028851456L, -5885687825288565248L, -5887396872144963840L,
843 -5888731517955042304L, -5889695949247728384L, -5890294025706689792L, -5890529289910829568L,
844 -5890404977675987456L, -5889924026487208448L, -5889089083913555968L, -5887902514965209344L,
845 -5886366408898372096L, -5884482585690639872L, -5882252601321090304L, -5879677752995027712L,
846 -5876759083794175232L, -5873497386318840832L, -5869893206505510144L, -5865946846617024256L,
847 -5861658367354159104L, -5857027590486131456L, -5852054100063428352L, -5846737243971504640L,
848 -5841076134082373632L, -5835069647234580480L, -5828716424754549248L, -5822014871949021952L,
849 -5814963157357531648L, -5807559211080072192L, -5799800723447229952L, -5791685142338073344L,
850 -5783209670985158912L, -5774371264582489344L, -5765166627072226560L, -5755592207057667840L,
851 -5745644193442049280L, -5735318510777133824L, -5724610813433666560L, -5713516480340333056L,
852 -5702030608556698112L, -5690148005851018752L, -5677863184109371904L, -5665170350903313408L,
853 -5652063400924580608L, -5638535907000141312L, -5624581109999480320L, -5610191908627599872L,
854 -5595360848093632768L, -5580080108034218752L, -5564341489875549952L, -5548136403221394688L,
855 -5531455851545399296L, -5514290416593586944L, -5496630242226406656L, -5478465016761742848L,
856 -5459783954986665216L, -5440575777891777024L, -5420828692432397824L, -5400530368638773504L,
857 -5379667916699401728L, -5358227861294116864L, -5336196115274292224L, -5313557951078385920L,
858 -5290297970633451520L, -5266400072915222272L, -5241847420214015744L, -5216622401043726592L,
859 -5190706591719534080L, -5164080714589203200L, -5136724594099067136L, -5108617109269313024L,
860 -5079736143458214912L, -5050058530461741312L, -5019559997031891968L, -4988215100963582976L,
861 -4955997165645491968L, -4922878208652041728L, -4888828866780320000L, -4853818314258475776L,
862 -4817814175855180032L, -4780782432601701888L, -4742687321746719232L, -4703491227581444608L,
863 -4663154564978699264L, -4621635653358766336L, -4578890580370785792L, -4534873055659683584L,
864 -4489534251700611840L, -4442822631898829568L, -4394683764809104128L, -4345060121983362560L,
865 -4293890858708922880L, -4241111576153830144L, -4186654061692619008L, -4130446006804747776L,
866 -4072410698657718784L, -4012466683838401024L, -3950527400305017856L, -3886500774061896704L,
867 -3820288777467837184L, -3751786943594897664L, -3680883832433527808L, -3607460442623922176L,
868 -3531389562483324160L, -3452535052891361792L, -3370751053395887872L, -3285881101633968128L,
869 -3197757155301365504L, -3106198503156485376L, -3011010550911937280L, -2911983463883580928L,
870 -2808890647470271744L, -2701487041141149952L, -2589507199690603520L, -2472663129329160192L,
871 -2350641842139870464L, -2223102583770035200L, -2089673683684728576L, -1949948966090106880L,
872 -1803483646855993856L, -1649789631480328192L, -1488330106139747584L, -1318513295725618176L,
873 -1139685236927327232L, -951121376596854784L, -752016768184775936L, -541474585642866432L,
874 -318492605725778432L, -81947227249193216L, 169425512612864512L, 437052607232193536L,
875 722551297568809984L, 1027761939299714304L, 1354787941622770432L, 1706044619203941632L,
876 2084319374409574144L, 2492846399593711360L, 2935400169348532480L, 3416413484613111552L,
877 3941127949860576256L, 4515787798793437952L, 5147892401439714304L, 5846529325380406016L,
878 6622819682216655360L, 7490522659874166016L, 8466869998277892096L, 8216968526387345408L,
879 4550693915488934656L, 7628019504138977280L, 6605080500908005888L, 7121156327650272512L,
880 2484871780331574272L, 7179104797032803328L, 7066086283830045440L, 1516500120817362944L,
881 216305945438803456L, 6295963418525324544L, 2889316805630113280L, -2712587580533804032L,
882 6562498853538167040L, 7975754821147501312L, -9223372036854775808L, -9223372036854775808L,
883 };
884
885
886
887
888
889
890
891
892
893
894 private static final double[] X = {
895 3.9421662825398133e-19, 3.7204945004119012e-19, 3.5827024480628678e-19, 3.4807476236540249e-19,
896 3.3990177171882136e-19, 3.3303778360340139e-19, 3.270943881761755e-19, 3.21835771324951e-19,
897 3.1710758541840432e-19, 3.1280307407034065e-19, 3.0884520655804019e-19, 3.0517650624107352e-19,
898 3.01752902925846e-19, 2.985398344070532e-19, 2.9550967462801797e-19, 2.9263997988491663e-19,
899 2.8991225869977476e-19, 2.8731108780226291e-19, 2.8482346327101335e-19, 2.8243831535194389e-19,
900 2.8014613964727031e-19, 2.7793871261807797e-19, 2.7580886921411212e-19, 2.7375032698308758e-19,
901 2.7175754543391047e-19, 2.6982561247538484e-19, 2.6795015188771505e-19, 2.6612724730440033e-19,
902 2.6435337927976633e-19, 2.6262537282028438e-19, 2.6094035335224142e-19, 2.5929570954331002e-19,
903 2.5768906173214726e-19, 2.5611823497719608e-19, 2.5458123593393361e-19, 2.5307623292372459e-19,
904 2.51601538677984e-19, 2.5015559533646191e-19, 2.4873696135403158e-19, 2.4734430003079206e-19,
905 2.4597636942892726e-19, 2.446320134791245e-19, 2.4331015411139206e-19, 2.4200978427132955e-19,
906 2.4072996170445879e-19, 2.3946980340903347e-19, 2.3822848067252674e-19, 2.3700521461931801e-19,
907 2.357992722074133e-19, 2.3460996262069972e-19, 2.3343663401054455e-19, 2.322786705467384e-19,
908 2.3113548974303765e-19, 2.3000654002704238e-19, 2.2889129852797606e-19, 2.2778926905921897e-19,
909 2.2669998027527321e-19, 2.2562298398527416e-19, 2.245578536072726e-19, 2.2350418274933911e-19,
910 2.2246158390513294e-19, 2.2142968725296249e-19, 2.2040813954857555e-19, 2.1939660310297601e-19,
911 2.1839475483749618e-19, 2.1740228540916853e-19, 2.1641889840016519e-19, 2.1544430956570613e-19,
912 2.1447824613540345e-19, 2.1352044616350571e-19, 2.1257065792395107e-19, 2.1162863934653125e-19,
913 2.1069415749082026e-19, 2.0976698805483467e-19, 2.0884691491567363e-19, 2.0793372969963634e-19,
914 2.0702723137954107e-19, 2.0612722589717129e-19, 2.0523352580895635e-19, 2.0434594995315797e-19,
915 2.0346432313698148e-19, 2.0258847584216418e-19, 2.0171824394771313e-19, 2.0085346846857531e-19,
916 1.9999399530912015e-19, 1.9913967503040585e-19, 1.9829036263028144e-19, 1.9744591733545175e-19,
917 1.9660620240469857e-19, 1.9577108494251485e-19, 1.9494043572246307e-19, 1.9411412901962161e-19,
918 1.9329204245152935e-19, 1.9247405682708168e-19, 1.9166005600287074e-19, 1.9084992674649826e-19,
919 1.900435586064234e-19, 1.8924084378793725e-19, 1.8844167703488436e-19, 1.8764595551677749e-19,
920 1.868535787209745e-19, 1.8606444834960934e-19, 1.8527846822098793e-19, 1.8449554417517928e-19,
921 1.8371558398354868e-19, 1.8293849726199566e-19, 1.8216419538767393e-19, 1.8139259141898448e-19,
922 1.8062360001864453e-19, 1.7985713737964743e-19, 1.7909312115393845e-19, 1.78331470383642e-19,
923 1.7757210543468428e-19, 1.7681494793266395e-19, 1.760599207008314e-19, 1.7530694770004409e-19,
924 1.7455595397057217e-19, 1.7380686557563475e-19, 1.7305960954655264e-19, 1.7231411382940904e-19,
925 1.7157030723311378e-19, 1.7082811937877138e-19, 1.7008748065025788e-19, 1.6934832214591352e-19,
926 1.6861057563126349e-19, 1.6787417349268046e-19, 1.6713904869190636e-19, 1.6640513472135291e-19,
927 1.6567236556010242e-19, 1.6494067563053266e-19, 1.6420999975549115e-19, 1.6348027311594532e-19,
928 1.6275143120903661e-19, 1.6202340980646725e-19, 1.6129614491314931e-19, 1.6056957272604589e-19,
929 1.5984362959313479e-19, 1.5911825197242491e-19, 1.5839337639095554e-19, 1.57668939403708e-19,
930 1.5694487755235889e-19, 1.5622112732380261e-19, 1.554976251083707e-19, 1.5477430715767271e-19,
931 1.540511095419833e-19, 1.5332796810709688e-19, 1.5260481843056974e-19, 1.5188159577726683e-19,
932 1.5115823505412761e-19, 1.5043467076406199e-19, 1.4971083695888395e-19, 1.4898666719118714e-19,
933 1.4826209446506113e-19, 1.4753705118554365e-19, 1.468114691066983e-19, 1.4608527927820112e-19,
934 1.4535841199031451e-19, 1.4463079671711862e-19, 1.4390236205786415e-19, 1.4317303567630177e-19,
935 1.4244274423783481e-19, 1.4171141334433217e-19, 1.4097896746642792e-19, 1.4024532987312287e-19,
936 1.3951042255849034e-19, 1.3877416616527576e-19, 1.3803647990516385e-19, 1.3729728147547174e-19,
937 1.3655648697200824e-19, 1.3581401079782068e-19, 1.3506976556752901e-19, 1.3432366200692418e-19,
938 1.3357560884748263e-19, 1.3282551271542047e-19, 1.3207327801488087e-19, 1.3131880680481524e-19,
939 1.3056199866908076e-19, 1.2980275057923788e-19, 1.2904095674948608e-19, 1.2827650848312727e-19,
940 1.2750929400989213e-19, 1.2673919831340482e-19, 1.2596610294799512e-19, 1.2518988584399374e-19,
941 1.2441042110056523e-19, 1.2362757876504165e-19, 1.2284122459762072e-19, 1.2205121982017852e-19,
942 1.2125742084782245e-19, 1.2045967900166973e-19, 1.196578402011802e-19, 1.1885174463419555e-19,
943 1.1804122640264091e-19, 1.1722611314162064e-19, 1.1640622560939109e-19, 1.1558137724540874e-19,
944 1.1475137369333185e-19, 1.1391601228549047e-19, 1.1307508148492592e-19, 1.1222836028063025e-19,
945 1.1137561753107903e-19, 1.1051661125053526e-19, 1.0965108783189755e-19, 1.0877878119905372e-19,
946 1.0789941188076655e-19, 1.070126859970364e-19, 1.0611829414763286e-19, 1.0521591019102928e-19,
947 1.0430518990027552e-19, 1.0338576948035472e-19, 1.0245726392923699e-19, 1.015192652220931e-19,
948 1.0057134029488235e-19, 9.9613028799672809e-20, 9.8643840599459914e-20, 9.7663252964755816e-20,
949 9.6670707427623454e-20, 9.566560624086667e-20, 9.4647308380433213e-20, 9.3615125017323508e-20,
950 9.2568314370887282e-20, 9.1506075837638774e-20, 9.0427543267725716e-20, 8.933177723376368e-20,
951 8.8217756102327883e-20, 8.7084365674892319e-20, 8.5930387109612162e-20, 8.4754482764244349e-20,
952 8.3555179508462343e-20, 8.2330848933585364e-20, 8.1079683729129853e-20, 7.9799669284133864e-20,
953 7.8488549286072745e-20, 7.7143783700934692e-20, 7.5762496979467566e-20, 7.4341413578485329e-20,
954 7.2876776807378431e-20, 7.1364245443525374e-20, 6.9798760240761066e-20, 6.8174368944799054e-20,
955 6.6483992986198539e-20, 6.4719110345162767e-20, 6.2869314813103699e-20, 6.0921687548281263e-20,
956 5.8859873575576818e-20, 5.6662675116090981e-20, 5.4301813630894571e-20, 5.173817174449422e-20,
957 4.8915031722398545e-20, 4.5744741890755301e-20, 4.2078802568583416e-20, 3.7625986722404761e-20,
958 3.1628589805881879e-20, 0,
959 };
960
961
962
963
964
965
966
967
968
969
970 private static final double[] Y = {
971 1.4598410796619063e-22, 3.0066613427942797e-22, 4.6129728815103466e-22, 6.2663350049234362e-22,
972 7.9594524761881544e-22, 9.6874655021705039e-22, 1.1446877002379439e-21, 1.3235036304379167e-21,
973 1.5049857692053131e-21, 1.6889653000719298e-21, 1.8753025382711626e-21, 2.0638798423695191e-21,
974 2.2545966913644708e-21, 2.4473661518801799e-21, 2.6421122727763533e-21, 2.8387681187879908e-21,
975 3.0372742567457284e-21, 3.2375775699986589e-21, 3.439630315794878e-21, 3.6433893657997798e-21,
976 3.8488155868912312e-21, 4.0558733309492775e-21, 4.264530010428359e-21, 4.4747557422305067e-21,
977 4.6865230465355582e-21, 4.8998065902775257e-21, 5.1145829672105489e-21, 5.3308305082046173e-21,
978 5.5485291167031758e-21, 5.7676601252690476e-21, 5.9882061699178461e-21, 6.2101510795442221e-21,
979 6.4334797782257209e-21, 6.6581781985713897e-21, 6.8842332045893181e-21, 7.1116325227957095e-21,
980 7.3403646804903092e-21, 7.5704189502886418e-21, 7.8017853001379744e-21, 8.0344543481570017e-21,
981 8.2684173217333118e-21, 8.5036660203915022e-21, 8.7401927820109521e-21, 8.9779904520281901e-21,
982 9.2170523553061439e-21, 9.457372270392882e-21, 9.698944405926943e-21, 9.9417633789758424e-21,
983 1.0185824195119818e-20, 1.043112223011477e-20, 1.0677653212987396e-20, 1.0925413210432004e-20,
984 1.1174398612392891e-20, 1.1424606118728715e-20, 1.1676032726866302e-20, 1.1928675720361027e-20,
985 1.2182532658289373e-20, 1.2437601365406785e-20, 1.2693879923010674e-20, 1.2951366660454145e-20,
986 1.3210060147261461e-20, 1.3469959185800733e-20, 1.3731062804473644e-20, 1.3993370251385596e-20,
987 1.4256880988463136e-20, 1.4521594685988369e-20, 1.4787511217522902e-20, 1.505463065519617e-20,
988 1.5322953265335218e-20, 1.5592479504415048e-20, 1.5863210015310328e-20, 1.6135145623830982e-20,
989 1.6408287335525592e-20, 1.6682636332737932e-20, 1.6958193971903124e-20, 1.7234961781071113e-20,
990 1.7512941457646084e-20, 1.7792134866331487e-20, 1.807254403727107e-20, 1.8354171164377277e-20,
991 1.8637018603838945e-20, 1.8921088872801004e-20, 1.9206384648209468e-20, 1.9492908765815636e-20,
992 1.9780664219333857e-20, 2.0069654159747839e-20, 2.0359881894760859e-20, 2.0651350888385696e-20,
993 2.0944064760670539e-20, 2.1238027287557466e-20, 2.1533242400870487e-20, 2.1829714188430474e-20,
994 2.2127446894294597e-20, 2.242644491911827e-20, 2.2726712820637798e-20, 2.3028255314272276e-20,
995 2.3331077273843558e-20, 2.3635183732413286e-20, 2.3940579883236352e-20, 2.4247271080830277e-20,
996 2.455526284216033e-20, 2.4864560847940368e-20, 2.5175170944049622e-20, 2.5487099143065929e-20,
997 2.5800351625915997e-20, 2.6114934743643687e-20, 2.6430855019297323e-20, 2.6748119149937411e-20,
998 2.7066734008766247e-20, 2.7386706647381193e-20, 2.7708044298153558e-20, 2.8030754376735269e-20,
999 2.8354844484695747e-20, 2.8680322412291631e-20, 2.9007196141372126e-20, 2.9335473848423219e-20,
1000 2.9665163907753988e-20, 2.9996274894828624e-20, 3.0328815589748056e-20, 3.0662794980885287e-20,
1001 3.099822226867876e-20, 3.1335106869588609e-20, 3.1673458420220558e-20, 3.2013286781622988e-20,
1002 3.2354602043762612e-20, 3.2697414530184806e-20, 3.304173480286495e-20, 3.3387573667257349e-20,
1003 3.3734942177548938e-20, 3.4083851642125208e-20, 3.4434313629256243e-20, 3.4786339973011376e-20,
1004 3.5139942779411164e-20, 3.5495134432826171e-20, 3.585192760263246e-20, 3.6210335250134172e-20,
1005 3.6570370635764384e-20, 3.6932047326575882e-20, 3.7295379204034252e-20, 3.7660380472126401e-20,
1006 3.8027065665798284e-20, 3.8395449659736649e-20, 3.8765547677510167e-20, 3.9137375301086406e-20,
1007 3.9510948480742172e-20, 3.988628354538543e-20, 4.0263397213308566e-20, 4.0642306603393541e-20,
1008 4.1023029246790967e-20, 4.1405583099096438e-20, 4.1789986553048817e-20, 4.2176258451776819e-20,
1009 4.2564418102621759e-20, 4.2954485291566197e-20, 4.3346480298300118e-20, 4.3740423911958146e-20,
1010 4.4136337447563716e-20, 4.4534242763218286e-20, 4.4934162278076256e-20, 4.5336118991149025e-20,
1011 4.5740136500984466e-20, 4.6146239026271279e-20, 4.6554451427421133e-20, 4.6964799229185088e-20,
1012 4.7377308644364938e-20, 4.7792006598684169e-20, 4.8208920756888113e-20, 4.8628079550147814e-20,
1013 4.9049512204847653e-20, 4.9473248772842596e-20, 4.9899320163277674e-20, 5.0327758176068971e-20,
1014 5.0758595537153414e-20, 5.1191865935622696e-20, 5.1627604062866059e-20, 5.2065845653856416e-20,
1015 5.2506627530725194e-20, 5.2949987648783448e-20, 5.3395965145159426e-20, 5.3844600390237576e-20,
1016 5.4295935042099358e-20, 5.4750012104183868e-20, 5.5206875986405073e-20, 5.5666572569983821e-20,
1017 5.6129149276275792e-20, 5.6594655139902476e-20, 5.7063140886520563e-20, 5.7534659015596918e-20,
1018 5.8009263888591218e-20, 5.8487011822987583e-20, 5.8967961192659803e-20, 5.9452172535103471e-20,
1019 5.9939708666122605e-20, 6.0430634802618929e-20, 6.0925018694200531e-20, 6.142293076440286e-20,
1020 6.1924444262401531e-20, 6.2429635426193939e-20, 6.2938583658336214e-20, 6.3451371715447563e-20,
1021 6.3968085912834963e-20, 6.4488816345752736e-20, 6.5013657128995346e-20, 6.5542706656731714e-20,
1022 6.6076067884730717e-20, 6.6613848637404196e-20, 6.715616194241298e-20, 6.770312639595058e-20,
1023 6.8254866562246408e-20, 6.8811513411327825e-20, 6.9373204799659681e-20, 6.9940085998959109e-20,
1024 7.0512310279279503e-20, 7.1090039553397167e-20, 7.1673445090644796e-20, 7.2262708309655784e-20,
1025 7.2858021661057338e-20, 7.34595896130358e-20, 7.4067629754967553e-20, 7.4682374037052817e-20,
1026 7.5304070167226666e-20, 7.5932983190698547e-20, 7.6569397282483754e-20, 7.7213617789487678e-20,
1027 7.7865973566417016e-20, 7.8526819659456755e-20, 7.919654040385056e-20, 7.9875553017037968e-20,
1028 8.056431178890163e-20, 8.1263312996426176e-20, 8.1973100703706304e-20, 8.2694273652634034e-20,
1029 8.3427493508836792e-20, 8.4173494807453416e-20, 8.4933097052832066e-20, 8.5707219578230905e-20,
1030 8.6496899985930695e-20, 8.7303317295655327e-20, 8.8127821378859504e-20, 8.8971970928196666e-20,
1031 8.9837583239314064e-20, 9.0726800697869543e-20, 9.1642181484063544e-20, 9.2586826406702765e-20,
1032 9.3564561480278864e-20, 9.4580210012636175e-20, 9.5640015550850358e-20, 9.675233477050313e-20,
1033 9.7928851697808831e-20, 9.9186905857531331e-20, 1.0055456271343397e-19, 1.0208407377305566e-19,
1034 1.0390360993240711e-19, 1.0842021724855044e-19,
1035 };
1036
1037
1038 private final SharedStateContinuousSampler exponential;
1039
1040
1041
1042
1043 private NormalizedGaussian(UniformRandomProvider rng) {
1044 super(rng);
1045 exponential = ZigguratSampler.Exponential.of(rng);
1046 }
1047
1048
1049 @Override
1050 public String toString() {
1051 return toString("normalized Gaussian");
1052 }
1053
1054
1055 @Override
1056 public double sample() {
1057
1058
1059 final long xx = nextLong();
1060
1061 final int i = ((int) xx) & MASK_INT8;
1062
1063 if (i < I_MAX) {
1064
1065
1066 return X[i] * xx;
1067 }
1068
1069 return edgeSample(xx);
1070 }
1071
1072
1073
1074
1075
1076
1077
1078
1079
1080
1081 private double edgeSample(long xx) {
1082
1083
1084
1085 long u1 = xx & MAX_INT64;
1086
1087
1088 final double signBit = ((xx >>> 62) & 0x2) - 1.0;
1089 final int j = selectRegion();
1090
1091
1092
1093
1094
1095
1096
1097 double x;
1098 if (j > J_INFLECTION) {
1099
1100
1101
1102 for (;;) {
1103 x = interpolate(X, j, u1);
1104
1105 final long uDistance = randomInt63() - u1;
1106 if (uDistance >= 0) {
1107
1108 break;
1109 }
1110 if (uDistance >= CONVEX_E_MAX &&
1111
1112
1113
1114 interpolate(Y, j, u1 + uDistance) < Math.exp(-0.5 * x * x)) {
1115 break;
1116 }
1117
1118 u1 = randomInt63();
1119 }
1120 } else if (j < J_INFLECTION) {
1121 if (j == 0) {
1122
1123
1124
1125
1126
1127 do {
1128 x = ONE_OVER_X_0 * exponential.sample();
1129 } while (exponential.sample() < 0.5 * x * x);
1130 x += X_0;
1131 } else {
1132
1133
1134
1135 for (;;) {
1136
1137 final long u = randomInt63();
1138
1139
1140 final long u2 = u1 < u ? u : u1;
1141 u1 = u1 < u ? u1 : u;
1142 x = interpolate(X, j, u1);
1143 if (u2 - u1 > CONCAVE_E_MAX ||
1144 interpolate(Y, j, u2) < Math.exp(-0.5 * x * x)) {
1145 break;
1146 }
1147 u1 = randomInt63();
1148 }
1149 }
1150 } else {
1151
1152
1153
1154 for (;;) {
1155 x = interpolate(X, j, u1);
1156 if (interpolate(Y, j, randomInt63()) < Math.exp(-0.5 * x * x)) {
1157 break;
1158 }
1159 u1 = randomInt63();
1160 }
1161 }
1162 return signBit * x;
1163 }
1164
1165
1166
1167
1168
1169
1170 private int selectRegion() {
1171 final long x = nextLong();
1172
1173 final int j = ((int) x) & MASK_INT8;
1174
1175 return x >= IPMF[j] ? MAP[j] & MASK_INT8 : j;
1176 }
1177
1178
1179 @Override
1180 public NormalizedGaussian withUniformRandomProvider(UniformRandomProvider rng) {
1181 return new NormalizedGaussian(rng);
1182 }
1183
1184
1185
1186
1187
1188
1189
1190 public static NormalizedGaussian of(UniformRandomProvider rng) {
1191 return new NormalizedGaussian(rng);
1192 }
1193 }
1194
1195
1196
1197
1198 ZigguratSampler(UniformRandomProvider rng) {
1199 this.rng = rng;
1200 }
1201
1202
1203
1204
1205
1206
1207
1208 String toString(String type) {
1209 return "Modified ziggurat " + type + " deviate [" + rng.toString() + "]";
1210 }
1211
1212
1213
1214
1215
1216
1217 long nextLong() {
1218 return rng.nextLong();
1219 }
1220
1221
1222
1223
1224
1225
1226
1227
1228
1229
1230
1231 long randomInt63() {
1232 return rng.nextLong() >>> 1;
1233 }
1234
1235
1236
1237
1238
1239
1240
1241
1242
1243
1244
1245
1246
1247
1248
1249
1250
1251
1252
1253
1254
1255
1256
1257
1258
1259
1260
1261
1262
1263
1264
1265
1266 static double interpolate(double[] v, int j, long u) {
1267
1268
1269
1270
1271
1272
1273
1274
1275 return v[j] * TWO_POW_63 + u * (v[j - 1] - v[j]);
1276 }
1277 }