| // Copyright 2014 Google Inc. All rights reserved. |
| // |
| // Licensed under the Apache License, Version 2.0 (the "License"); |
| // you may not use this file except in compliance with the License. |
| // You may obtain a copy of the License at |
| // |
| // http://www.apache.org/licenses/LICENSE-2.0 |
| // |
| // Unless required by applicable law or agreed to in writing, software |
| // distributed under the License is distributed on an "AS IS" BASIS, |
| // WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. |
| // See the License for the specific language governing permissions and |
| // limitations under the License. |
| |
| package fountain |
| |
| import ( |
| "math" |
| "math/big" |
| "math/rand" |
| "reflect" |
| "testing" |
| ) |
| |
| func NewTwister(seed int64) *MersenneTwister { |
| t := &MersenneTwister{} |
| t.Seed(seed) |
| |
| return t |
| } |
| |
| func TestMersenne(t *testing.T) { |
| var mt MersenneTwister |
| |
| mt.Uint32() |
| if !mt.initialized { |
| t.Error("MersenneTwister should be initialized after Uint32 call.") |
| } |
| |
| var mt2 MersenneTwister |
| mt2.Int63() |
| if !mt2.initialized { |
| t.Error("MersenneTwister should be initialized after Int63 call.") |
| } |
| |
| var mt3 MersenneTwister |
| mt3.Seed(1) |
| if !mt3.initialized { |
| t.Error("MersenneTwister should be initialized after Seed call.") |
| } |
| |
| } |
| |
| func TestMersenneGen(t *testing.T) { |
| mt := NewTwister(1) |
| |
| // See implementation at github.com/cslarsen/mersenne-twister |
| seed1Expected := []uint32{ |
| 1791095845, 4282876139, 3093770124, 4005303368, 491263, |
| 550290313, 1298508491, 4290846341, 630311759, 1013994432, |
| 396591248, 1703301249, 799981516, 1666063943, 1484172013, |
| 2876537340, 1704103302, 4018109721, 2314200242, 3634877716, |
| 1800426750, 1345499493, 2942995346, 2252917204, 878115723, |
| 1904615676, 3771485674, 986026652, 117628829, 2295290254, |
| 2879636018, 3925436996, 1792310487, 1963679703, 2399554537, |
| 1849836273, 602957303, 4033523166, 850839392, 3343156310, |
| 3439171725, 3075069929, 4158651785, 3447817223, 1346146623, |
| 398576445, 2973502998, 2225448249, 3764062721, 3715233664, |
| 3842306364, 3561158865, 365262088, 3563119320, 167739021, |
| 1172740723, 729416111, 254447594, 3771593337, 2879896008, |
| 422396446, 2547196999, 1808643459, 2884732358, 4114104213, |
| 1768615473, 2289927481, 848474627, 2971589572, 1243949848, |
| 1355129329, 610401323, 2948499020, 3364310042, 3584689972, |
| 1771840848, 78547565, 146764659, 3221845289, 2680188370, |
| 4247126031, 2837408832, 3213347012, 1282027545, 1204497775, |
| 1916133090, 3389928919, 954017671, 443352346, 315096729, |
| 1923688040, 2015364118, 3902387977, 413056707, 1261063143, |
| 3879945342, 1235985687, 513207677, 558468452, 2253996187, |
| 83180453, 359158073, 2915576403, 3937889446, 908935816, |
| 3910346016, 1140514210, 1283895050, 2111290647, 2509932175, |
| 229190383, 2430573655, 2465816345, 2636844999, 630194419, |
| 4108289372, 2531048010, 1120896190, 3005439278, 992203680, |
| 439523032, 2291143831, 1778356919, 4079953217, 2982425969, |
| 2117674829, 1778886403, 2321861504, 214548472, 3287733501, |
| 2301657549, 194758406, 2850976308, 601149909, 2211431878, |
| 3403347458, 4057003596, 127995867, 2519234709, 3792995019, |
| 3880081671, 2322667597, 590449352, 1924060235, 598187340, |
| 3831694379, 3467719188, 1621712414, 1708008996, 2312516455, |
| 710190855, 2801602349, 3983619012, 1551604281, 1493642992, |
| 2452463100, 3224713426, 2739486816, 3118137613, 542518282, |
| 3793770775, 2964406140, 2678651729, 2782062471, 3225273209, |
| 1520156824, 1498506954, 3278061020, 1159331476, 1531292064, |
| 3847801996, 3233201345, 1838637662, 3785334332, 4143956457, |
| 50118808, 2849459538, 2139362163, 2670162785, 316934274, |
| 492830188, 3379930844, 4078025319, 275167074, 1932357898, |
| 1526046390, 2484164448, 4045158889, 1752934226, 1631242710, |
| 1018023110, 3276716738, 3879985479, 3313975271, 2463934640, |
| 1294333494, 12327951, 3318889349, 2650617233, 656828586} |
| |
| got := make([]uint32, len(seed1Expected)) |
| |
| for i := range got { |
| got[i] = mt.Uint32() |
| } |
| |
| if !reflect.DeepEqual(got, seed1Expected) { |
| t.Errorf("Got bad sequence for seed=1. Got %v, want %v", got, seed1Expected) |
| } |
| |
| mt = NewTwister(1) |
| |
| u := mt.Uint32() |
| if u != 1791095845 { |
| t.Errorf("Seed=1 value is %d, should be 1791095845", u) |
| } |
| } |
| |
| func countBits(v uint32) int { |
| c := 0 |
| for i := 0; i < 32; i++ { |
| if v&0x1 == 0x1 { |
| c++ |
| } |
| v >>= 1 |
| } |
| return c |
| } |
| |
| func TestMersenneDifference(t *testing.T) { |
| // Checks that very similar seeds produce different outputs. |
| mt1 := NewTwister(123456) |
| mt2 := NewTwister(123457) |
| v1 := mt1.Uint32() |
| v2 := mt2.Uint32() |
| if math.Abs(float64(v1-v2)) < 0xF000 { |
| t.Errorf("PRNG values unseemly close for two close initial seeds. Got %d, %d", v1, v2) |
| } |
| if countBits(v1^v2) != 16 { |
| t.Errorf("Got common bits %d between random values from two close seeds. Want 16.", countBits(v1^v2)) |
| } |
| } |
| |
| // calculateBitStatistics performs about the simplest DieHard randomness test -- |
| // checks the bit count statistics of random numbers to make sure they match |
| // a binomial distribution. |
| // Returns the sum-squared-difference metric of the observed distribution and the |
| // binomial distribution, normalized to the number of trials. |
| func calculateBitStatistics(mt *MersenneTwister, trials int) float64 { |
| var bitsSet [33]int64 |
| for i := 0; i < trials; i++ { |
| bitsSet[countBits(mt.Uint32())]++ |
| } |
| |
| // bitsSet should follow a binomial distribution pretty closely |
| var ssd int64 |
| sum := 4294967296 // Sum of the binomial distribution from 0-32. |
| for i := 0; i < 33; i++ { |
| z := big.Int{} |
| binomial := int64(z.Binomial(32, int64(i)).Uint64()) * int64(trials) / int64(sum) |
| ssd += (bitsSet[i] - binomial) * (bitsSet[i] - binomial) |
| } |
| return math.Sqrt(float64(ssd)) / float64(trials) |
| } |
| |
| func TestMersenneStatistics(t *testing.T) { |
| mt := NewTwister(892349823) |
| for i := 0; i < 25; i++ { |
| seed := mt.Uint32() |
| mt = NewTwister(int64(seed)) |
| if calculateBitStatistics(mt, 10000) > 0.03 { |
| t.Errorf("Trial bits-set distribution not binomial within 3%% for seed %d", seed) |
| } |
| } |
| } |
| |
| func TestMersenneSource(t *testing.T) { |
| r := rand.New(NewMersenneTwister(8189023)) |
| count := 0 |
| for i := 0; i < 100; i++ { |
| if r.Intn(2) == 1 { |
| count++ |
| } |
| } |
| if math.Abs(float64(count)-50) > 3 { |
| t.Errorf("Expect coin toss about 50-50, was %d", count) |
| } |
| } |
| |
| // Initial run on x86 hardware: 17.8ns/op |
| func BenchmarkMersenne(b *testing.B) { |
| mt := NewTwister(903490345) |
| b.ResetTimer() |
| for i := 0; i < b.N; i++ { |
| mt.Uint32() |
| } |
| } |
| |
| func NewTwister64(seed uint64) *MersenneTwister64 { |
| t := &MersenneTwister64{} |
| t.initialize(seed) |
| |
| return t |
| } |
| |
| func TestMersenne64(t *testing.T) { |
| mt := &MersenneTwister64{} |
| seed := []uint64{0x12345, 0x23456, 0x34567, 0x45678} |
| mt.SeedSlice(seed) |
| if !mt.initialized { |
| t.Errorf("Twister should be initialized after SeedSlice") |
| } |
| r := mt.Uint64() |
| if r != 7266447313870364031 { |
| t.Errorf("MersenneTwister64(initialized with %v).Uint64() = %d, want %d", |
| seed, r, 7266447313870364031) |
| } |
| } |
| |
| func TestMersenne64Gen(t *testing.T) { |
| // See http://www.math.sci.hiroshima-u.ac.jp/~m-mat/MT/emt64.html |
| var expected64 = []uint64{ |
| 7266447313870364031, 4946485549665804864, 16945909448695747420, |
| 16394063075524226720, 4873882236456199058, 14877448043947020171, |
| 6740343660852211943, 13857871200353263164, 5249110015610582907, |
| 10205081126064480383, 1235879089597390050, 17320312680810499042, |
| 16489141110565194782, 8942268601720066061, 13520575722002588570, |
| 14226945236717732373, 9383926873555417063, 15690281668532552105, |
| 11510704754157191257, 15864264574919463609, 6489677788245343319, |
| 5112602299894754389, 10828930062652518694, 15942305434158995996, |
| 15445717675088218264, 4764500002345775851, 14673753115101942098, |
| 236502320419669032, 13670483975188204088, 14931360615268175698, |
| 8904234204977263924, 12836915408046564963, 12120302420213647524, |
| 15755110976537356441, 5405758943702519480, 10951858968426898805, |
| 17251681303478610375, 4144140664012008120, 18286145806977825275, |
| 13075804672185204371, 10831805955733617705, 6172975950399619139, |
| 12837097014497293886, 12903857913610213846, 560691676108914154, |
| 1074659097419704618, 14266121283820281686, 11696403736022963346, |
| 13383246710985227247, 7132746073714321322, 10608108217231874211, |
| 9027884570906061560, 12893913769120703138, 15675160838921962454, |
| 2511068401785704737, 14483183001716371453, 3774730664208216065, |
| 5083371700846102796, 9583498264570933637, 17119870085051257224, |
| 5217910858257235075, 10612176809475689857, 1924700483125896976, |
| 7171619684536160599, 10949279256701751503, 15596196964072664893, |
| 14097948002655599357, 615821766635933047, 5636498760852923045, |
| 17618792803942051220, 580805356741162327, 425267967796817241, |
| 8381470634608387938, 13212228678420887626, 16993060308636741960, |
| 957923366004347591, 6210242862396777185, 1012818702180800310, |
| 15299383925974515757, 17501832009465945633, 17453794942891241229, |
| 15807805462076484491, 8407189590930420827, 974125122787311712, |
| 1861591264068118966, 997568339582634050, 18046771844467391493, |
| 17981867688435687790, 3809841506498447207, 9460108917638135678, |
| 16172980638639374310, 958022432077424298, 4393365126459778813, |
| 13408683141069553686, 13900005529547645957, 15773550354402817866, |
| 16475327524349230602, 6260298154874769264, 12224576659776460914, |
| 6405294864092763507, 7585484664713203306, 5187641382818981381, |
| 12435998400285353380, 13554353441017344755, 646091557254529188, |
| 11393747116974949255, 16797249248413342857, 15713519023537495495, |
| 12823504709579858843, 4738086532119935073, 4429068783387643752, |
| 585582692562183870, 1048280754023674130, 6788940719869959076, |
| 11670856244972073775, 2488756775360218862, 2061695363573180185, |
| 6884655301895085032, 3566345954323888697, 12784319933059041817, |
| 4772468691551857254, 6864898938209826895, 7198730565322227090, |
| 2452224231472687253, 13424792606032445807, 10827695224855383989, |
| 11016608897122070904, 14683280565151378358, 7077866519618824360, |
| 17487079941198422333, 3956319990205097495, 5804870313319323478, |
| 8017203611194497730, 3310931575584983808, 5009341981771541845, |
| 6930001938490791874, 14415278059151389495, 11001114762641844083, |
| 6715939435439735925, 411419160297131328, 4522402260441335284, |
| 3381955501804126859, 15935778656111987797, 4345051260540166684, |
| 13978444093099579683, 9219789505504949817, 9245142924137529075, |
| 11628184459157386459, 7242398879359936370, 8511401943157540109, |
| 11948130810477009827, 6865450671488705049, 13965005347172621081, |
| 15956599226522058336, 7737868921014130584, 2107342503741411693, |
| 15818996300425101108, 16399939197527488760, 13971145494081508107, |
| 3910681448359868691, 4249175367970221090, 9735751321242454020, |
| 12418107929362160460, 241792245481991138, 5806488997649497146, |
| 10724207982663648949, 1121862814449214435, 1326996977123564236, |
| 4902706567834759475, 12782714623891689967, 7306216312942796257, |
| 15681656478863766664, 957364844878149318, 5651946387216554503, |
| 8197027112357634782, 6302075516351125977, 13454588464089597862, |
| 15638309200463515550, 10116604639722073476, 12052913535387714920, |
| 2889379661594013754, 15383926144832314187, 7841953313015471731, |
| 17310575136995821873, 9820021961316981626, 15319619724109527290, |
| 15349724127275899898, 10511508162402504492, 6289553862380300393, |
| 15046218882019267110, 11772020174577005930, 3537640779967351792, |
| 6801855569284252424, 17687268231192623388, 12968358613633237218, |
| 1429775571144180123, 10427377732172208413, 12155566091986788996, |
| 16465954421598296115, 12710429690464359999, 9547226351541565595, |
| 12156624891403410342, 2985938688676214686, 18066917785985010959, |
| 5975570403614438776, 11541343163022500560, 11115388652389704592, |
| 9499328389494710074, 9247163036769651820, 3688303938005101774, |
| 2210483654336887556, 15458161910089693228, 6558785204455557683, |
| 1288373156735958118, 18433986059948829624, 3435082195390932486, |
| 16822351800343061990, 3120532877336962310, 16681785111062885568, |
| 7835551710041302304, 2612798015018627203, 15083279177152657491, |
| 6591467229462292195, 10592706450534565444, 7438147750787157163, |
| 323186165595851698, 7444710627467609883, 8473714411329896576, |
| 2782675857700189492, 3383567662400128329, 3200233909833521327, |
| 12897601280285604448, 3612068790453735040, 8324209243736219497, |
| 15789570356497723463, 1083312926512215996, 4797349136059339390, |
| 5556729349871544986, 18266943104929747076, 1620389818516182276, |
| 172225355691600141, 3034352936522087096, 1266779576738385285, |
| 3906668377244742888, 6961783143042492788, 17159706887321247572, |
| 4676208075243319061, 10315634697142985816, 13435140047933251189, |
| 716076639492622016, 13847954035438697558, 7195811275139178570, |
| 10815312636510328870, 6214164734784158515, 16412194511839921544, |
| 3862249798930641332, 1005482699535576005, 4644542796609371301, |
| 17600091057367987283, 4209958422564632034, 5419285945389823940, |
| 11453701547564354601, 9951588026679380114, 7425168333159839689, |
| 8436306210125134906, 11216615872596820107, 3681345096403933680, |
| 5770016989916553752, 11102855936150871733, 11187980892339693935, |
| 396336430216428875, 6384853777489155236, 7551613839184151117, |
| 16527062023276943109, 13429850429024956898, 9901753960477271766, |
| 9731501992702612259, 5217575797614661659, 10311708346636548706, |
| 15111747519735330483, 4353415295139137513, 1845293119018433391, |
| 11952006873430493561, 3531972641585683893, 16852246477648409827, |
| 15956854822143321380, 12314609993579474774, 16763911684844598963, |
| 16392145690385382634, 1545507136970403756, 17771199061862790062, |
| 12121348462972638971, 12613068545148305776, 954203144844315208, |
| 1257976447679270605, 3664184785462160180, 2747964788443845091, |
| 15895917007470512307, 15552935765724302120, 16366915862261682626, |
| 8385468783684865323, 10745343827145102946, 2485742734157099909, |
| 916246281077683950, 15214206653637466707, 12895483149474345798, |
| 1079510114301747843, 10718876134480663664, 1259990987526807294, |
| 8326303777037206221, 14104661172014248293, 15531278677382192198, |
| 3874303698666230242, 3611366553819264523, 1358753803061653874, |
| 1552102816982246938, 14492630642488100979, 15001394966632908727, |
| 2273140352787320862, 17843678642369606172, 2903980458593894032, |
| 16971437123015263604, 12969653681729206264, 3593636458822318001, |
| 9719758956915223015, 7437601263394568346, 3327758049015164431, |
| 17851524109089292731, 14769614194455139039, 8017093497335662337, |
| 12026985381690317404, 739616144640253634, 15535375191850690266, |
| 2418267053891303448, 15314073759564095878, 10333316143274529509, |
| 16565481511572123421, 16317667579273275294, 13991958187675987741, |
| 3753596784796798785, 9078249094693663275, 8459506356724650587, |
| 12579909555010529099, 7827737296967050903, 5489801927693999341, |
| 10995988997350541459, 14721747867313883304, 7915884580303296560, |
| 4105766302083365910, 12455549072515054554, 13602111324515032467, |
| 5205971628932290989, 5034622965420036444, 9134927878875794005, |
| 11319873529597990213, 14815445109496752058, 2266601052460299470, |
| 5696993487088103383, 6540200741841280242, 6631495948031875490, |
| 5328340585170897740, 17897267040961463930, 9030000260502624168, |
| 14285709137129830926, 12854071997824681544, 15408328651008978682, |
| 1063314403033437073, 13765209628446252802, 242013711116865605, |
| 4772374239432528212, 2515855479965038648, 5872624715703151235, |
| 14237704570091006662, 678604024776645862, 12329607334079533339, |
| 17570877682732917020, 2695443415284373666, 4312672841405514468, |
| 6454343485137106900, 8425658828390111343, 16335501385875554899, |
| 5551095603809016713, 11781094401885925035, 9395557946368382509, |
| 9765123360948816956, 18107191819981188154, 16049267500594757404, |
| 16349966108299794199, 1040405303135858246, 2366386386131378192, |
| 223761048139910454, 15375217587047847934, 15231693398695187454, |
| 12916726640254571028, 8878036960829635584, 1626201782473074365, |
| 5758998126998248293, 18077917959300292758, 10585588923088536745, |
| 15072345664541731497, 3559348759319842667, 12744591691872202375, |
| 2388494115860283059, 6414691845696331748, 3069528498807764495, |
| 8737958486926519702, 18059264986425101074, 3139684427605102737, |
| 12378931902986734693, 410666675039477949, 12139894855769838924, |
| 5780722552400398675, 7039346665375142557, 3020733445712569008, |
| 2612305843503943561, 13651771214166527665, 16478681918975800939, |
| 566088527565499576, 4715785502295754870, 6957318344287196220, |
| 11645756868405128885, 13139951104358618000, 17650948583490040612, |
| 18168787973649736637, 5486282999836125542, 6122201977153895166, |
| 17324241605502052782, 10063523107521105867, 17537430712468011382, |
| 10828407533637104262, 10294139354198325113, 12557151830240236401, |
| 16673044307512640231, 10918020421896090419, 11077531235278014145, |
| 5499571814940871256, 2334252435740638702, 18177461912527387031, |
| 2000007376901262542, 7968425560071444214, 1472650787501520648, |
| 3115849849651526279, 7980970700139577536, 12153253535907642097, |
| 8109716914843248719, 3154976533165008908, 5553369513523832559, |
| 10345792701798576501, 3677445364544507875, 10637177623943913351, |
| 7380255087060498096, 14479400372337014801, 15381362583330700960, |
| 204531043189704802, 13699106540959723942, 3817903465872254783, |
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| 8628445623963160889, 4298916726468199239, 12773165416305557280, |
| 5240726258301567487, 4975412836403427561, 1842172398579595303, |
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| 5364843095234852245, 218335432181198977, 4891472444796201742, |
| 4564628942836375772, 15500501278323817088, 4913946328556108657, |
| 2684786251736694229, 12090498456116310122, 5310885782157038567, |
| 5032788439854011923, 12627401038822728242, 11869662610126430929, |
| 17650156853043540226, 12126672500118808436, 10437658933435653256, |
| 13133995470637873311, 4601324715591152820, 1874350460376708372, |
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| 900692047897995877, 14723287313048560400, 6132094372965340305, |
| 7572797575350925726, 12725160700431903514, 380860122911632449, |
| 1900504978569024571, 8423729759529914138, 7305587201606052334, |
| 12446871355267313320, 4615812356515386206, 3361817115406652303, |
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| 16029152738918251363, 14444848757576686696, 12941757045272633696, |
| 10900480525147953314, 12547307449905859302, 16001571796892398181, |
| 407942194622690676, 13873235372903944444, 18071603799493008777, |
| 1015646077646778622, 9387605808959554815, 11566702442022019410, |
| 7061722181092883183, 2629032108249254109, 5271820053177594520, |
| 12640880742139693547, 10098688629735675775, 5716304472850923064, |
| 3312674502353063071, 7295926377425759633, 833281439103466115, |
| 16316743519466861667, 9912050326606348167, 11651133878100804242, |
| 18026798122431692459, 6157758321723692663, 4856021830695749349, |
| 7074321707293278978, 10748097797809573561, 2949954440753264783, |
| 9813922580940661152, 9949237950172138336, 15643982711269455885, |
| 16078663425810239127, 12508044395364228880, 12920301578340189344, |
| 15368071871011048915, 1610400750626363239, 11994736084146033126, |
| 6042574085746186088, 4154587549267685807, 15915752367312946034, |
| 1191196620621769193, 467437822242538360, 2836463788873877488, |
| 10476401302029164984, 1716169985450737419, 5327734953288310341, |
| 3994170067185955262, 884431883768190063, 11019001754831208284, |
| 14322807384384895215, 161011537360955545, 1466223959660131656, |
| 5227048585229497539, 12410731857504225031, 2142243279080761103, |
| 17682826799106851430, 1792612570704179953, 14727410295243056025, |
| 1459567192481221274, 5669760721687603135, 17507918443756456845, |
| 10354471145847018200, 10362475129248202288, 13143844410150939443, |
| 6861184673150072028, 18396524361124732580, 543906666394301875, |
| 12476817828199026728, 11853496871128122868, 12747674713108891748, |
| 7986179867749890282, 9158195177777627533, 2217320706811118570, |
| 8631389005200569973, 5538133061362648855, 3369942850878700758, |
| 7813559982698427184, 509051590411815948, 10197035660403006684, |
| 13004818533162292132, 9831652587047067687, 7619315254749630976, |
| 994412663058993407} |
| |
| mt := &MersenneTwister64{} |
| mt.SeedSlice([]uint64{0x12345, 0x23456, 0x34567, 0x45678}) |
| out := []uint64{} |
| for _ = range expected64 { |
| out = append(out, mt.Uint64()) |
| } |
| |
| if !reflect.DeepEqual(out, expected64) { |
| t.Errorf("Mersenne Twister 64-bit expected output incorrect") |
| for i := range out { |
| if out[i] != expected64[i] { |
| t.Errorf("Bad at %d: Got %d, want %d", i, out[i], expected64[i]) |
| } |
| } |
| } |
| } |
| |
| func TestMersenne64Source(t *testing.T) { |
| r := rand.New(NewMersenneTwister64(8189023)) |
| count := 0 |
| for i := 0; i < 100; i++ { |
| if r.Intn(2) == 1 { |
| count++ |
| } |
| } |
| if math.Abs(float64(count)-50) > 3 { |
| t.Errorf("Expect coin toss about 50-50, was %d", count) |
| } |
| } |
| |
| // Initial run on x86 hardware: 16ns/op |
| func BenchmarkMersenne64(b *testing.B) { |
| mt := &MersenneTwister64{} |
| mt.SeedSlice([]uint64{0x12345, 0x23456, 0x34567, 0x45678}) |
| b.ResetTimer() |
| |
| for i := 0; i < b.N; i++ { |
| mt.Uint64() |
| } |
| } |
