1// Copyright 2009 The Go Authors. All rights reserved. 2// Use of this source code is governed by a BSD-style 3// license that can be found in the LICENSE file. 4 5package rand 6 7/* 8 * Uniform distribution 9 * 10 * algorithm by 11 * DP Mitchell and JA Reeds 12 */ 13 14const ( 15 rngLen = 607 16 rngTap = 273 17 rngMax = 1 << 63 18 rngMask = rngMax - 1 19 int32max = (1 << 31) - 1 20) 21 22var ( 23 // rngCooked used for seeding. See gen_cooked.go for details. 24 rngCooked [rngLen]int64 = [...]int64{ 25 -4181792142133755926, -4576982950128230565, 1395769623340756751, 5333664234075297259, 26 -6347679516498800754, 9033628115061424579, 7143218595135194537, 4812947590706362721, 27 7937252194349799378, 5307299880338848416, 8209348851763925077, -7107630437535961764, 28 4593015457530856296, 8140875735541888011, -5903942795589686782, -603556388664454774, 29 -7496297993371156308, 113108499721038619, 4569519971459345583, -4160538177779461077, 30 -6835753265595711384, -6507240692498089696, 6559392774825876886, 7650093201692370310, 31 7684323884043752161, -8965504200858744418, -2629915517445760644, 271327514973697897, 32 -6433985589514657524, 1065192797246149621, 3344507881999356393, -4763574095074709175, 33 7465081662728599889, 1014950805555097187, -4773931307508785033, -5742262670416273165, 34 2418672789110888383, 5796562887576294778, 4484266064449540171, 3738982361971787048, 35 -4699774852342421385, 10530508058128498, -589538253572429690, -6598062107225984180, 36 8660405965245884302, 10162832508971942, -2682657355892958417, 7031802312784620857, 37 6240911277345944669, 831864355460801054, -1218937899312622917, 2116287251661052151, 38 2202309800992166967, 9161020366945053561, 4069299552407763864, 4936383537992622449, 39 457351505131524928, -8881176990926596454, -6375600354038175299, -7155351920868399290, 40 4368649989588021065, 887231587095185257, -3659780529968199312, -2407146836602825512, 41 5616972787034086048, -751562733459939242, 1686575021641186857, -5177887698780513806, 42 -4979215821652996885, -1375154703071198421, 5632136521049761902, -8390088894796940536, 43 -193645528485698615, -5979788902190688516, -4907000935050298721, -285522056888777828, 44 -2776431630044341707, 1679342092332374735, 6050638460742422078, -2229851317345194226, 45 -1582494184340482199, 5881353426285907985, 812786550756860885, 4541845584483343330, 46 -6497901820577766722, 4980675660146853729, -4012602956251539747, -329088717864244987, 47 -2896929232104691526, 1495812843684243920, -2153620458055647789, 7370257291860230865, 48 -2466442761497833547, 4706794511633873654, -1398851569026877145, 8549875090542453214, 49 -9189721207376179652, -7894453601103453165, 7297902601803624459, 1011190183918857495, 50 -6985347000036920864, 5147159997473910359, -8326859945294252826, 2659470849286379941, 51 6097729358393448602, -7491646050550022124, -5117116194870963097, -896216826133240300, 52 -745860416168701406, 5803876044675762232, -787954255994554146, -3234519180203704564, 53 -4507534739750823898, -1657200065590290694, 505808562678895611, -4153273856159712438, 54 -8381261370078904295, 572156825025677802, 1791881013492340891, 3393267094866038768, 55 -5444650186382539299, 2352769483186201278, -7930912453007408350, -325464993179687389, 56 -3441562999710612272, -6489413242825283295, 5092019688680754699, -227247482082248967, 57 4234737173186232084, 5027558287275472836, 4635198586344772304, -536033143587636457, 58 5907508150730407386, -8438615781380831356, 972392927514829904, -3801314342046600696, 59 -4064951393885491917, -174840358296132583, 2407211146698877100, -1640089820333676239, 60 3940796514530962282, -5882197405809569433, 3095313889586102949, -1818050141166537098, 61 5832080132947175283, 7890064875145919662, 8184139210799583195, -8073512175445549678, 62 -7758774793014564506, -4581724029666783935, 3516491885471466898, -8267083515063118116, 63 6657089965014657519, 5220884358887979358, 1796677326474620641, 5340761970648932916, 64 1147977171614181568, 5066037465548252321, 2574765911837859848, 1085848279845204775, 65 -5873264506986385449, 6116438694366558490, 2107701075971293812, -7420077970933506541, 66 2469478054175558874, -1855128755834809824, -5431463669011098282, -9038325065738319171, 67 -6966276280341336160, 7217693971077460129, -8314322083775271549, 7196649268545224266, 68 -3585711691453906209, -5267827091426810625, 8057528650917418961, -5084103596553648165, 69 -2601445448341207749, -7850010900052094367, 6527366231383600011, 3507654575162700890, 70 9202058512774729859, 1954818376891585542, -2582991129724600103, 8299563319178235687, 71 -5321504681635821435, 7046310742295574065, -2376176645520785576, -7650733936335907755, 72 8850422670118399721, 3631909142291992901, 5158881091950831288, -6340413719511654215, 73 4763258931815816403, 6280052734341785344, -4979582628649810958, 2043464728020827976, 74 -2678071570832690343, 4562580375758598164, 5495451168795427352, -7485059175264624713, 75 553004618757816492, 6895160632757959823, -989748114590090637, 7139506338801360852, 76 -672480814466784139, 5535668688139305547, 2430933853350256242, -3821430778991574732, 77 -1063731997747047009, -3065878205254005442, 7632066283658143750, 6308328381617103346, 78 3681878764086140361, 3289686137190109749, 6587997200611086848, 244714774258135476, 79 -5143583659437639708, 8090302575944624335, 2945117363431356361, -8359047641006034763, 80 3009039260312620700, -793344576772241777, 401084700045993341, -1968749590416080887, 81 4707864159563588614, -3583123505891281857, -3240864324164777915, -5908273794572565703, 82 -3719524458082857382, -5281400669679581926, 8118566580304798074, 3839261274019871296, 83 7062410411742090847, -8481991033874568140, 6027994129690250817, -6725542042704711878, 84 -2971981702428546974, -7854441788951256975, 8809096399316380241, 6492004350391900708, 85 2462145737463489636, -8818543617934476634, -5070345602623085213, -8961586321599299868, 86 -3758656652254704451, -8630661632476012791, 6764129236657751224, -709716318315418359, 87 -3403028373052861600, -8838073512170985897, -3999237033416576341, -2920240395515973663, 88 -2073249475545404416, 368107899140673753, -6108185202296464250, -6307735683270494757, 89 4782583894627718279, 6718292300699989587, 8387085186914375220, 3387513132024756289, 90 4654329375432538231, -292704475491394206, -3848998599978456535, 7623042350483453954, 91 7725442901813263321, 9186225467561587250, -5132344747257272453, -6865740430362196008, 92 2530936820058611833, 1636551876240043639, -3658707362519810009, 1452244145334316253, 93 -7161729655835084979, -7943791770359481772, 9108481583171221009, -3200093350120725999, 94 5007630032676973346, 2153168792952589781, 6720334534964750538, -3181825545719981703, 95 3433922409283786309, 2285479922797300912, 3110614940896576130, -2856812446131932915, 96 -3804580617188639299, 7163298419643543757, 4891138053923696990, 580618510277907015, 97 1684034065251686769, 4429514767357295841, -8893025458299325803, -8103734041042601133, 98 7177515271653460134, 4589042248470800257, -1530083407795771245, 143607045258444228, 99 246994305896273627, -8356954712051676521, 6473547110565816071, 3092379936208876896, 100 2058427839513754051, -4089587328327907870, 8785882556301281247, -3074039370013608197, 101 -637529855400303673, 6137678347805511274, -7152924852417805802, 5708223427705576541, 102 -3223714144396531304, 4358391411789012426, 325123008708389849, 6837621693887290924, 103 4843721905315627004, -3212720814705499393, -3825019837890901156, 4602025990114250980, 104 1044646352569048800, 9106614159853161675, -8394115921626182539, -4304087667751778808, 105 2681532557646850893, 3681559472488511871, -3915372517896561773, -2889241648411946534, 106 -6564663803938238204, -8060058171802589521, 581945337509520675, 3648778920718647903, 107 -4799698790548231394, -7602572252857820065, 220828013409515943, -1072987336855386047, 108 4287360518296753003, -4633371852008891965, 5513660857261085186, -2258542936462001533, 109 -8744380348503999773, 8746140185685648781, 228500091334420247, 1356187007457302238, 110 3019253992034194581, 3152601605678500003, -8793219284148773595, 5559581553696971176, 111 4916432985369275664, -8559797105120221417, -5802598197927043732, 2868348622579915573, 112 -7224052902810357288, -5894682518218493085, 2587672709781371173, -7706116723325376475, 113 3092343956317362483, -5561119517847711700, 972445599196498113, -1558506600978816441, 114 1708913533482282562, -2305554874185907314, -6005743014309462908, -6653329009633068701, 115 -483583197311151195, 2488075924621352812, -4529369641467339140, -4663743555056261452, 116 2997203966153298104, 1282559373026354493, 240113143146674385, 8665713329246516443, 117 628141331766346752, -4651421219668005332, -7750560848702540400, 7596648026010355826, 118 -3132152619100351065, 7834161864828164065, 7103445518877254909, 4390861237357459201, 119 -4780718172614204074, -319889632007444440, 622261699494173647, -3186110786557562560, 120 -8718967088789066690, -1948156510637662747, -8212195255998774408, -7028621931231314745, 121 2623071828615234808, -4066058308780939700, -5484966924888173764, -6683604512778046238, 122 -6756087640505506466, 5256026990536851868, 7841086888628396109, 6640857538655893162, 123 -8021284697816458310, -7109857044414059830, -1689021141511844405, -4298087301956291063, 124 -4077748265377282003, -998231156719803476, 2719520354384050532, 9132346697815513771, 125 4332154495710163773, -2085582442760428892, 6994721091344268833, -2556143461985726874, 126 -8567931991128098309, 59934747298466858, -3098398008776739403, -265597256199410390, 127 2332206071942466437, -7522315324568406181, 3154897383618636503, -7585605855467168281, 128 -6762850759087199275, 197309393502684135, -8579694182469508493, 2543179307861934850, 129 4350769010207485119, -4468719947444108136, -7207776534213261296, -1224312577878317200, 130 4287946071480840813, 8362686366770308971, 6486469209321732151, -5605644191012979782, 131 -1669018511020473564, 4450022655153542367, -7618176296641240059, -3896357471549267421, 132 -4596796223304447488, -6531150016257070659, -8982326463137525940, -4125325062227681798, 133 -1306489741394045544, -8338554946557245229, 5329160409530630596, 7790979528857726136, 134 4955070238059373407, -4304834761432101506, -6215295852904371179, 3007769226071157901, 135 -6753025801236972788, 8928702772696731736, 7856187920214445904, -4748497451462800923, 136 7900176660600710914, -7082800908938549136, -6797926979589575837, -6737316883512927978, 137 4186670094382025798, 1883939007446035042, -414705992779907823, 3734134241178479257, 138 4065968871360089196, 6953124200385847784, -7917685222115876751, -7585632937840318161, 139 -5567246375906782599, -5256612402221608788, 3106378204088556331, -2894472214076325998, 140 4565385105440252958, 1979884289539493806, -6891578849933910383, 3783206694208922581, 141 8464961209802336085, 2843963751609577687, 3030678195484896323, -4429654462759003204, 142 4459239494808162889, 402587895800087237, 8057891408711167515, 4541888170938985079, 143 1042662272908816815, -3666068979732206850, 2647678726283249984, 2144477441549833761, 144 -3417019821499388721, -2105601033380872185, 5916597177708541638, -8760774321402454447, 145 8833658097025758785, 5970273481425315300, 563813119381731307, -6455022486202078793, 146 1598828206250873866, -4016978389451217698, -2988328551145513985, -6071154634840136312, 147 8469693267274066490, 125672920241807416, -3912292412830714870, -2559617104544284221, 148 -486523741806024092, -4735332261862713930, 5923302823487327109, -9082480245771672572, 149 -1808429243461201518, 7990420780896957397, 4317817392807076702, 3625184369705367340, 150 -6482649271566653105, -3480272027152017464, -3225473396345736649, -368878695502291645, 151 -3981164001421868007, -8522033136963788610, 7609280429197514109, 3020985755112334161, 152 -2572049329799262942, 2635195723621160615, 5144520864246028816, -8188285521126945980, 153 1567242097116389047, 8172389260191636581, -2885551685425483535, -7060359469858316883, 154 -6480181133964513127, -7317004403633452381, 6011544915663598137, 5932255307352610768, 155 2241128460406315459, -8327867140638080220, 3094483003111372717, 4583857460292963101, 156 9079887171656594975, -384082854924064405, -3460631649611717935, 4225072055348026230, 157 -7385151438465742745, 3801620336801580414, -399845416774701952, -7446754431269675473, 158 7899055018877642622, 5421679761463003041, 5521102963086275121, -4975092593295409910, 159 8735487530905098534, -7462844945281082830, -2080886987197029914, -1000715163927557685, 160 -4253840471931071485, -5828896094657903328, 6424174453260338141, 359248545074932887, 161 -5949720754023045210, -2426265837057637212, 3030918217665093212, -9077771202237461772, 162 -3186796180789149575, 740416251634527158, -2142944401404840226, 6951781370868335478, 163 399922722363687927, -8928469722407522623, -1378421100515597285, -8343051178220066766, 164 -3030716356046100229, -8811767350470065420, 9026808440365124461, 6440783557497587732, 165 4615674634722404292, 539897290441580544, 2096238225866883852, 8751955639408182687, 166 -7316147128802486205, 7381039757301768559, 6157238513393239656, -1473377804940618233, 167 8629571604380892756, 5280433031239081479, 7101611890139813254, 2479018537985767835, 168 7169176924412769570, -1281305539061572506, -7865612307799218120, 2278447439451174845, 169 3625338785743880657, 6477479539006708521, 8976185375579272206, -3712000482142939688, 170 1326024180520890843, 7537449876596048829, 5464680203499696154, 3189671183162196045, 171 6346751753565857109, -8982212049534145501, -6127578587196093755, -245039190118465649, 172 -6320577374581628592, 7208698530190629697, 7276901792339343736, -7490986807540332668, 173 4133292154170828382, 2918308698224194548, -7703910638917631350, -3929437324238184044, 174 -4300543082831323144, -6344160503358350167, 5896236396443472108, -758328221503023383, 175 -1894351639983151068, -307900319840287220, -6278469401177312761, -2171292963361310674, 176 8382142935188824023, 9103922860780351547, 4152330101494654406, 177 } 178) 179 180type rngSource struct { 181 tap int // index into vec 182 feed int // index into vec 183 vec [rngLen]int64 // current feedback register 184} 185 186// seed rng x[n+1] = 48271 * x[n] mod (2**31 - 1) 187func seedrand(x int32) int32 { 188 const ( 189 A = 48271 190 Q = 44488 191 R = 3399 192 ) 193 194 hi := x / Q 195 lo := x % Q 196 x = A*lo - R*hi 197 if x < 0 { 198 x += int32max 199 } 200 return x 201} 202 203// Seed uses the provided seed value to initialize the generator to a deterministic state. 204func (rng *rngSource) Seed(seed int64) { 205 rng.tap = 0 206 rng.feed = rngLen - rngTap 207 208 seed = seed % int32max 209 if seed < 0 { 210 seed += int32max 211 } 212 if seed == 0 { 213 seed = 89482311 214 } 215 216 x := int32(seed) 217 for i := -20; i < rngLen; i++ { 218 x = seedrand(x) 219 if i >= 0 { 220 var u int64 221 u = int64(x) << 40 222 x = seedrand(x) 223 u ^= int64(x) << 20 224 x = seedrand(x) 225 u ^= int64(x) 226 u ^= rngCooked[i] 227 rng.vec[i] = u 228 } 229 } 230} 231 232// Int63 returns a non-negative pseudo-random 63-bit integer as an int64. 233func (rng *rngSource) Int63() int64 { 234 return int64(rng.Uint64() & rngMask) 235} 236 237// Uint64 returns a non-negative pseudo-random 64-bit integer as an uint64. 238func (rng *rngSource) Uint64() uint64 { 239 rng.tap-- 240 if rng.tap < 0 { 241 rng.tap += rngLen 242 } 243 244 rng.feed-- 245 if rng.feed < 0 { 246 rng.feed += rngLen 247 } 248 249 x := rng.vec[rng.feed] + rng.vec[rng.tap] 250 rng.vec[rng.feed] = x 251 return uint64(x) 252} 253