Source: rng.go in package math/rand

Source File
	rng.go

Belonging Package
	math/rand

// Copyright 2009 The Go Authors. All rights reserved.
// Use of this source code is governed by a BSD-style
// license that can be found in the LICENSE file.

package rand

/*
 * Uniform distribution
 *
 * algorithm by
 * DP Mitchell and JA Reeds
 */

const (
	rngLen   = 607
	rngTap   = 273
	rngMax   = 1 << 63
	rngMask  = rngMax - 1
	int32max = (1 << 31) - 1
)

var (
	// rngCooked used for seeding. See gen_cooked.go for details.
	rngCooked [rngLen]int64 = [...]int64{
		-4181792142133755926, -4576982950128230565, 1395769623340756751, 5333664234075297259,
		-6347679516498800754, 9033628115061424579, 7143218595135194537, 4812947590706362721,
		7937252194349799378, 5307299880338848416, 8209348851763925077, -7107630437535961764,
		4593015457530856296, 8140875735541888011, -5903942795589686782, -603556388664454774,
		-7496297993371156308, 113108499721038619, 4569519971459345583, -4160538177779461077,
		-6835753265595711384, -6507240692498089696, 6559392774825876886, 7650093201692370310,
		7684323884043752161, -8965504200858744418, -2629915517445760644, 271327514973697897,
		-6433985589514657524, 1065192797246149621, 3344507881999356393, -4763574095074709175,
		7465081662728599889, 1014950805555097187, -4773931307508785033, -5742262670416273165,
		2418672789110888383, 5796562887576294778, 4484266064449540171, 3738982361971787048,
		-4699774852342421385, 10530508058128498, -589538253572429690, -6598062107225984180,
		8660405965245884302, 10162832508971942, -2682657355892958417, 7031802312784620857,
		6240911277345944669, 831864355460801054, -1218937899312622917, 2116287251661052151,
		2202309800992166967, 9161020366945053561, 4069299552407763864, 4936383537992622449,
		457351505131524928, -8881176990926596454, -6375600354038175299, -7155351920868399290,
		4368649989588021065, 887231587095185257, -3659780529968199312, -2407146836602825512,
		5616972787034086048, -751562733459939242, 1686575021641186857, -5177887698780513806,
		-4979215821652996885, -1375154703071198421, 5632136521049761902, -8390088894796940536,
		-193645528485698615, -5979788902190688516, -4907000935050298721, -285522056888777828,
		-2776431630044341707, 1679342092332374735, 6050638460742422078, -2229851317345194226,
		-1582494184340482199, 5881353426285907985, 812786550756860885, 4541845584483343330,
		-6497901820577766722, 4980675660146853729, -4012602956251539747, -329088717864244987,
		-2896929232104691526, 1495812843684243920, -2153620458055647789, 7370257291860230865,
		-2466442761497833547, 4706794511633873654, -1398851569026877145, 8549875090542453214,
		-9189721207376179652, -7894453601103453165, 7297902601803624459, 1011190183918857495,
		-6985347000036920864, 5147159997473910359, -8326859945294252826, 2659470849286379941,
		6097729358393448602, -7491646050550022124, -5117116194870963097, -896216826133240300,
		-745860416168701406, 5803876044675762232, -787954255994554146, -3234519180203704564,
		-4507534739750823898, -1657200065590290694, 505808562678895611, -4153273856159712438,
		-8381261370078904295, 572156825025677802, 1791881013492340891, 3393267094866038768,
		-5444650186382539299, 2352769483186201278, -7930912453007408350, -325464993179687389,
		-3441562999710612272, -6489413242825283295, 5092019688680754699, -227247482082248967,
		4234737173186232084, 5027558287275472836, 4635198586344772304, -536033143587636457,
		5907508150730407386, -8438615781380831356, 972392927514829904, -3801314342046600696,
		-4064951393885491917, -174840358296132583, 2407211146698877100, -1640089820333676239,
		3940796514530962282, -5882197405809569433, 3095313889586102949, -1818050141166537098,
		5832080132947175283, 7890064875145919662, 8184139210799583195, -8073512175445549678,
		-7758774793014564506, -4581724029666783935, 3516491885471466898, -8267083515063118116,
		6657089965014657519, 5220884358887979358, 1796677326474620641, 5340761970648932916,
		1147977171614181568, 5066037465548252321, 2574765911837859848, 1085848279845204775,
		-5873264506986385449, 6116438694366558490, 2107701075971293812, -7420077970933506541,
		2469478054175558874, -1855128755834809824, -5431463669011098282, -9038325065738319171,
		-6966276280341336160, 7217693971077460129, -8314322083775271549, 7196649268545224266,
		-3585711691453906209, -5267827091426810625, 8057528650917418961, -5084103596553648165,
		-2601445448341207749, -7850010900052094367, 6527366231383600011, 3507654575162700890,
		9202058512774729859, 1954818376891585542, -2582991129724600103, 8299563319178235687,
		-5321504681635821435, 7046310742295574065, -2376176645520785576, -7650733936335907755,
		8850422670118399721, 3631909142291992901, 5158881091950831288, -6340413719511654215,
		4763258931815816403, 6280052734341785344, -4979582628649810958, 2043464728020827976,
		-2678071570832690343, 4562580375758598164, 5495451168795427352, -7485059175264624713,
		553004618757816492, 6895160632757959823, -989748114590090637, 7139506338801360852,
		-672480814466784139, 5535668688139305547, 2430933853350256242, -3821430778991574732,
		-1063731997747047009, -3065878205254005442, 7632066283658143750, 6308328381617103346,
		3681878764086140361, 3289686137190109749, 6587997200611086848, 244714774258135476,
		-5143583659437639708, 8090302575944624335, 2945117363431356361, -8359047641006034763,
		3009039260312620700, -793344576772241777, 401084700045993341, -1968749590416080887,
		4707864159563588614, -3583123505891281857, -3240864324164777915, -5908273794572565703,
		-3719524458082857382, -5281400669679581926, 8118566580304798074, 3839261274019871296,
		7062410411742090847, -8481991033874568140, 6027994129690250817, -6725542042704711878,
		-2971981702428546974, -7854441788951256975, 8809096399316380241, 6492004350391900708,
		2462145737463489636, -8818543617934476634, -5070345602623085213, -8961586321599299868,
		-3758656652254704451, -8630661632476012791, 6764129236657751224, -709716318315418359,
		-3403028373052861600, -8838073512170985897, -3999237033416576341, -2920240395515973663,
		-2073249475545404416, 368107899140673753, -6108185202296464250, -6307735683270494757,
		4782583894627718279, 6718292300699989587, 8387085186914375220, 3387513132024756289,
		4654329375432538231, -292704475491394206, -3848998599978456535, 7623042350483453954,
		7725442901813263321, 9186225467561587250, -5132344747257272453, -6865740430362196008,
		2530936820058611833, 1636551876240043639, -3658707362519810009, 1452244145334316253,
		-7161729655835084979, -7943791770359481772, 9108481583171221009, -3200093350120725999,
		5007630032676973346, 2153168792952589781, 6720334534964750538, -3181825545719981703,
		3433922409283786309, 2285479922797300912, 3110614940896576130, -2856812446131932915,
		-3804580617188639299, 7163298419643543757, 4891138053923696990, 580618510277907015,
		1684034065251686769, 4429514767357295841, -8893025458299325803, -8103734041042601133,
		7177515271653460134, 4589042248470800257, -1530083407795771245, 143607045258444228,
		246994305896273627, -8356954712051676521, 6473547110565816071, 3092379936208876896,
		2058427839513754051, -4089587328327907870, 8785882556301281247, -3074039370013608197,
		-637529855400303673, 6137678347805511274, -7152924852417805802, 5708223427705576541,
		-3223714144396531304, 4358391411789012426, 325123008708389849, 6837621693887290924,
		4843721905315627004, -3212720814705499393, -3825019837890901156, 4602025990114250980,
		1044646352569048800, 9106614159853161675, -8394115921626182539, -4304087667751778808,
		2681532557646850893, 3681559472488511871, -3915372517896561773, -2889241648411946534,
		-6564663803938238204, -8060058171802589521, 581945337509520675, 3648778920718647903,
		-4799698790548231394, -7602572252857820065, 220828013409515943, -1072987336855386047,
		4287360518296753003, -4633371852008891965, 5513660857261085186, -2258542936462001533,
		-8744380348503999773, 8746140185685648781, 228500091334420247, 1356187007457302238,
		3019253992034194581, 3152601605678500003, -8793219284148773595, 5559581553696971176,
		4916432985369275664, -8559797105120221417, -5802598197927043732, 2868348622579915573,
		-7224052902810357288, -5894682518218493085, 2587672709781371173, -7706116723325376475,
		3092343956317362483, -5561119517847711700, 972445599196498113, -1558506600978816441,
		1708913533482282562, -2305554874185907314, -6005743014309462908, -6653329009633068701,
		-483583197311151195, 2488075924621352812, -4529369641467339140, -4663743555056261452,
		2997203966153298104, 1282559373026354493, 240113143146674385, 8665713329246516443,
		628141331766346752, -4651421219668005332, -7750560848702540400, 7596648026010355826,
		-3132152619100351065, 7834161864828164065, 7103445518877254909, 4390861237357459201,
		-4780718172614204074, -319889632007444440, 622261699494173647, -3186110786557562560,
		-8718967088789066690, -1948156510637662747, -8212195255998774408, -7028621931231314745,
		2623071828615234808, -4066058308780939700, -5484966924888173764, -6683604512778046238,
		-6756087640505506466, 5256026990536851868, 7841086888628396109, 6640857538655893162,
		-8021284697816458310, -7109857044414059830, -1689021141511844405, -4298087301956291063,
		-4077748265377282003, -998231156719803476, 2719520354384050532, 9132346697815513771,
		4332154495710163773, -2085582442760428892, 6994721091344268833, -2556143461985726874,
		-8567931991128098309, 59934747298466858, -3098398008776739403, -265597256199410390,
		2332206071942466437, -7522315324568406181, 3154897383618636503, -7585605855467168281,
		-6762850759087199275, 197309393502684135, -8579694182469508493, 2543179307861934850,
		4350769010207485119, -4468719947444108136, -7207776534213261296, -1224312577878317200,
		4287946071480840813, 8362686366770308971, 6486469209321732151, -5605644191012979782,
		-1669018511020473564, 4450022655153542367, -7618176296641240059, -3896357471549267421,
		-4596796223304447488, -6531150016257070659, -8982326463137525940, -4125325062227681798,
		-1306489741394045544, -8338554946557245229, 5329160409530630596, 7790979528857726136,
		4955070238059373407, -4304834761432101506, -6215295852904371179, 3007769226071157901,
		-6753025801236972788, 8928702772696731736, 7856187920214445904, -4748497451462800923,
		7900176660600710914, -7082800908938549136, -6797926979589575837, -6737316883512927978,
		4186670094382025798, 1883939007446035042, -414705992779907823, 3734134241178479257,
		4065968871360089196, 6953124200385847784, -7917685222115876751, -7585632937840318161,
		-5567246375906782599, -5256612402221608788, 3106378204088556331, -2894472214076325998,
		4565385105440252958, 1979884289539493806, -6891578849933910383, 3783206694208922581,
		8464961209802336085, 2843963751609577687, 3030678195484896323, -4429654462759003204,
		4459239494808162889, 402587895800087237, 8057891408711167515, 4541888170938985079,
		1042662272908816815, -3666068979732206850, 2647678726283249984, 2144477441549833761,
		-3417019821499388721, -2105601033380872185, 5916597177708541638, -8760774321402454447,
		8833658097025758785, 5970273481425315300, 563813119381731307, -6455022486202078793,
		1598828206250873866, -4016978389451217698, -2988328551145513985, -6071154634840136312,
		8469693267274066490, 125672920241807416, -3912292412830714870, -2559617104544284221,
		-486523741806024092, -4735332261862713930, 5923302823487327109, -9082480245771672572,
		-1808429243461201518, 7990420780896957397, 4317817392807076702, 3625184369705367340,
		-6482649271566653105, -3480272027152017464, -3225473396345736649, -368878695502291645,
		-3981164001421868007, -8522033136963788610, 7609280429197514109, 3020985755112334161,
		-2572049329799262942, 2635195723621160615, 5144520864246028816, -8188285521126945980,
		1567242097116389047, 8172389260191636581, -2885551685425483535, -7060359469858316883,
		-6480181133964513127, -7317004403633452381, 6011544915663598137, 5932255307352610768,
		2241128460406315459, -8327867140638080220, 3094483003111372717, 4583857460292963101,
		9079887171656594975, -384082854924064405, -3460631649611717935, 4225072055348026230,
		-7385151438465742745, 3801620336801580414, -399845416774701952, -7446754431269675473,
		7899055018877642622, 5421679761463003041, 5521102963086275121, -4975092593295409910,
		8735487530905098534, -7462844945281082830, -2080886987197029914, -1000715163927557685,
		-4253840471931071485, -5828896094657903328, 6424174453260338141, 359248545074932887,
		-5949720754023045210, -2426265837057637212, 3030918217665093212, -9077771202237461772,
		-3186796180789149575, 740416251634527158, -2142944401404840226, 6951781370868335478,
		399922722363687927, -8928469722407522623, -1378421100515597285, -8343051178220066766,
		-3030716356046100229, -8811767350470065420, 9026808440365124461, 6440783557497587732,
		4615674634722404292, 539897290441580544, 2096238225866883852, 8751955639408182687,
		-7316147128802486205, 7381039757301768559, 6157238513393239656, -1473377804940618233,
		8629571604380892756, 5280433031239081479, 7101611890139813254, 2479018537985767835,
		7169176924412769570, -1281305539061572506, -7865612307799218120, 2278447439451174845,
		3625338785743880657, 6477479539006708521, 8976185375579272206, -3712000482142939688,
		1326024180520890843, 7537449876596048829, 5464680203499696154, 3189671183162196045,
		6346751753565857109, -8982212049534145501, -6127578587196093755, -245039190118465649,
		-6320577374581628592, 7208698530190629697, 7276901792339343736, -7490986807540332668,
		4133292154170828382, 2918308698224194548, -7703910638917631350, -3929437324238184044,
		-4300543082831323144, -6344160503358350167, 5896236396443472108, -758328221503023383,
		-1894351639983151068, -307900319840287220, -6278469401177312761, -2171292963361310674,
		8382142935188824023, 9103922860780351547, 4152330101494654406,
	}
)

type rngSource struct {
	tap  int           // index into vec
	feed int           // index into vec
	vec  [rngLen]int64 // current feedback register
}

// seed rng x[n+1] = 48271 * x[n] mod (2**31 - 1)
func seedrand(x int32) int32 {
	const (
		A = 48271
		Q = 44488
		R = 3399
	)

	hi := x / Q
	lo := x % Q
	x = A*lo - R*hi
	if x < 0 {
		x += int32max
	}
	return x
}

// Seed uses the provided seed value to initialize the generator to a deterministic state.
func (rng *rngSource) Seed(seed int64) {
	rng.tap = 0
	rng.feed = rngLen - rngTap

	seed = seed % int32max
	if seed < 0 {
		seed += int32max
	}
	if seed == 0 {
		seed = 89482311
	}

	x := int32(seed)
	for i := -20; i < rngLen; i++ {
		x = seedrand(x)
		if i >= 0 {
			var u int64
			u = int64(x) << 40
			x = seedrand(x)
			u ^= int64(x) << 20
			x = seedrand(x)
			u ^= int64(x)
			u ^= rngCooked[i]
			rng.vec[i] = u
		}
	}
}

// Int63 returns a non-negative pseudo-random 63-bit integer as an int64.
func (rng *rngSource) Int63() int64 {
	return int64(rng.Uint64() & rngMask)
}

// Uint64 returns a non-negative pseudo-random 64-bit integer as a uint64.
func (rng *rngSource) Uint64() uint64 {
	rng.tap--
	if rng.tap < 0 {
		rng.tap += rngLen
	}

	rng.feed--
	if rng.feed < 0 {
		rng.feed += rngLen
	}

	x := rng.vec[rng.feed] + rng.vec[rng.tap]
	rng.vec[rng.feed] = x
	return uint64(x)
}


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