Pi10K Pseudo-Random Number Generator Algorithm Test.
   by William Donnelly

Additional information, description, and explanation below-bottom.

This page was coded for Firefox 3.x+, but should work on any modern browser.

Pi 10K PRNG

   var gnPiLength = gsPiDigits.length;    // see below-bottom for gsPiDigits string
   var gnPiOffset = 0;

   function Pi10K()
   {
      var sNumber = "";
      var nLength = parseInt (gsPiDigits[gnPiOffset++]);

      if (gnPiOffset >= gnPiLength)
         gnPiOffset = 0;

      for (var ii = 0;  ii < nLength;  ++ii) {

         sNumber += gsPiDigits[gnPiOffset++];

         if (gnPiOffset >= gnPiLength)
            gnPiOffset = 0;

      } // for

      return parseInt (sNumber) & 0xFF;
   } // Pi10K

More information, description and explanation.

Test of a PRNG created from choosing digit-values from the first 10,000 digits of the Pi constant.

You can see by the reported results that this a VERY poor PRNG algorithm.

Min Times a Rand# was Chosen = 35
Max Times a Rand# was Chosen = 8828
Average Times a Rand# was Chosen = 256
Average Distance between Rand# Chosen Again = 439.70993631558287
Min Average Distance = 6.422632532850023
Max Average Distance = 1852.857142857143
Min Distance = 0
Max Distance = 1853

Min and Max Times a Rand# was Chosen should be near 256 (+/- 50?), as should be Min and Max Average Distance, as should be Average Distance between Rand# Chosen Again. The rough Plot clearly shows weird, extreme anomalies. (and is "blown out" with the very high values of some number chosen counts because it is expected that each number will be chosen about 256 times and not more or less than about half (+/-) that value)

   var gsPiDigits = "3" +
      "14159265358979323846264338327950288419716939937510" +
      "58209749445923078164062862089986280348253421170679" +
      "82148086513282306647093844609550582231725359408128" +
      "48111745028410270193852110555964462294895493038196" +
      "44288109756659334461284756482337867831652712019091" +
      "45648566923460348610454326648213393607260249141273" +
      "72458700660631558817488152092096282925409171536436" +
      "78925903600113305305488204665213841469519415116094" +
      "33057270365759591953092186117381932611793105118548" +
      "07446237996274956735188575272489122793818301194912" +
      "98336733624406566430860213949463952247371907021798" +
      "60943702770539217176293176752384674818467669405132" +
      "00056812714526356082778577134275778960917363717872" +
      "14684409012249534301465495853710507922796892589235" +
      "42019956112129021960864034418159813629774771309960" +
      "51870721134999999837297804995105973173281609631859" +
      "50244594553469083026425223082533446850352619311881" +
      "71010003137838752886587533208381420617177669147303" +
      "59825349042875546873115956286388235378759375195778" +
      "18577805321712268066130019278766111959092164201989" +
      "38095257201065485863278865936153381827968230301952" +
      "03530185296899577362259941389124972177528347913151" +
      "55748572424541506959508295331168617278558890750983" +
      "81754637464939319255060400927701671139009848824012" +
      "85836160356370766010471018194295559619894676783744" +
      "94482553797747268471040475346462080466842590694912" +
      "93313677028989152104752162056966024058038150193511" +
      "25338243003558764024749647326391419927260426992279" +
      "67823547816360093417216412199245863150302861829745" +
      "55706749838505494588586926995690927210797509302955" +
      "32116534498720275596023648066549911988183479775356" +
      "63698074265425278625518184175746728909777727938000" +
      "81647060016145249192173217214772350141441973568548" +
      "16136115735255213347574184946843852332390739414333" +
      "45477624168625189835694855620992192221842725502542" +
      "56887671790494601653466804988627232791786085784383" +
      "82796797668145410095388378636095068006422512520511" +
      "73929848960841284886269456042419652850222106611863" +
      "06744278622039194945047123713786960956364371917287" +
      "46776465757396241389086583264599581339047802759009" +
      "94657640789512694683983525957098258226205224894077" +
      "26719478268482601476990902640136394437455305068203" +
      "49625245174939965143142980919065925093722169646151" +
      "57098583874105978859597729754989301617539284681382" +
      "68683868942774155991855925245953959431049972524680" +
      "84598727364469584865383673622262609912460805124388" +
      "43904512441365497627807977156914359977001296160894" +
      "41694868555848406353422072225828488648158456028506" +
      "01684273945226746767889525213852254995466672782398" +
      "64565961163548862305774564980355936345681743241125" +
      "15076069479451096596094025228879710893145669136867" +
      "22874894056010150330861792868092087476091782493858" +
      "90097149096759852613655497818931297848216829989487" +
      "22658804857564014270477555132379641451523746234364" +
      "54285844479526586782105114135473573952311342716610" +
      "21359695362314429524849371871101457654035902799344" +
      "03742007310578539062198387447808478489683321445713" +
      "86875194350643021845319104848100537061468067491927" +
      "81911979399520614196634287544406437451237181921799" +
      "98391015919561814675142691239748940907186494231961" +
      "56794520809514655022523160388193014209376213785595" +
      "66389377870830390697920773467221825625996615014215" +
      "03068038447734549202605414665925201497442850732518" +
      "66600213243408819071048633173464965145390579626856" +
      "10055081066587969981635747363840525714591028970641" +
      "40110971206280439039759515677157700420337869936007" +
      "23055876317635942187312514712053292819182618612586" +
      "73215791984148488291644706095752706957220917567116" +
      "72291098169091528017350671274858322287183520935396" +
      "57251210835791513698820914442100675103346711031412" +
      "67111369908658516398315019701651511685171437657618" +
      "35155650884909989859982387345528331635507647918535" +
      "89322618548963213293308985706420467525907091548141" +
      "65498594616371802709819943099244889575712828905923" +
      "23326097299712084433573265489382391193259746366730" +
      "58360414281388303203824903758985243744170291327656" +
      "18093773444030707469211201913020330380197621101100" +
      "44929321516084244485963766983895228684783123552658" +
      "21314495768572624334418930396864262434107732269780" +
      "28073189154411010446823252716201052652272111660396" +
      "66557309254711055785376346682065310989652691862056" +
      "47693125705863566201855810072936065987648611791045" +
      "33488503461136576867532494416680396265797877185560" +
      "84552965412665408530614344431858676975145661406800" +
      "70023787765913440171274947042056223053899456131407" +
      "11270004078547332699390814546646458807972708266830" +
      "63432858785698305235808933065757406795457163775254" +
      "20211495576158140025012622859413021647155097925923" +
      "09907965473761255176567513575178296664547791745011" +
      "29961489030463994713296210734043751895735961458901" +
      "93897131117904297828564750320319869151402870808599" +
      "04801094121472213179476477726224142548545403321571" +
      "85306142288137585043063321751829798662237172159160" +
      "77166925474873898665494945011465406284336639379003" +
      "97692656721463853067360965712091807638327166416274" +
      "88880078692560290228472104031721186082041900042296" +
      "61711963779213375751149595015660496318629472654736" +
      "42523081770367515906735023507283540567040386743513" +
      "62222477158915049530984448933309634087807693259939" +
      "78054193414473774418426312986080998886874132604721" +
      "56951623965864573021631598193195167353812974167729" +
      "47867242292465436680098067692823828068996400482435" +
      "40370141631496589794092432378969070697794223625082" +
      "21688957383798623001593776471651228935786015881617" +
      "55782973523344604281512627203734314653197777416031" +
      "99066554187639792933441952154134189948544473456738" +
      "31624993419131814809277771038638773431772075456545" +
      "32207770921201905166096280490926360197598828161332" +
      "31666365286193266863360627356763035447762803504507" +
      "77235547105859548702790814356240145171806246436267" +
      "94561275318134078330336254232783944975382437205835" +
      "31147711992606381334677687969597030983391307710987" +
      "04085913374641442822772634659470474587847787201927" +
      "71528073176790770715721344473060570073349243693113" +
      "83504931631284042512192565179806941135280131470130" +
      "47816437885185290928545201165839341965621349143415" +
      "95625865865570552690496520985803385072242648293972" +
      "85847831630577775606888764462482468579260395352773" +
      "48030480290058760758251047470916439613626760449256" +
      "27420420832085661190625454337213153595845068772460" +
      "29016187667952406163425225771954291629919306455377" +
      "99140373404328752628889639958794757291746426357455" +
      "25407909145135711136941091193932519107602082520261" +
      "87985318877058429725916778131496990090192116971737" +
      "27847684726860849003377024242916513005005168323364" +
      "35038951702989392233451722013812806965011784408745" +
      "19601212285993716231301711444846409038906449544400" +
      "61986907548516026327505298349187407866808818338510" +
      "22833450850486082503930213321971551843063545500766" +
      "82829493041377655279397517546139539846833936383047" +
      "46119966538581538420568533862186725233402830871123" +
      "28278921250771262946322956398989893582116745627010" +
      "21835646220134967151881909730381198004973407239610" +
      "36854066431939509790190699639552453005450580685501" +
      "95673022921913933918568034490398205955100226353536" +
      "19204199474553859381023439554495977837790237421617" +
      "27111723643435439478221818528624085140066604433258" +
      "88569867054315470696574745855033232334210730154594" +
      "05165537906866273337995851156257843229882737231989" +
      "87571415957811196358330059408730681216028764962867" +
      "44604774649159950549737425626901049037781986835938" +
      "14657412680492564879855614537234786733039046883834" +
      "36346553794986419270563872931748723320837601123029" +
      "91136793862708943879936201629515413371424892830722" +
      "01269014754668476535761647737946752004907571555278" +
      "19653621323926406160136358155907422020203187277605" +
      "27721900556148425551879253034351398442532234157623" +
      "36106425063904975008656271095359194658975141310348" +
      "22769306247435363256916078154781811528436679570611" +
      "08615331504452127473924544945423682886061340841486" +
      "37767009612071512491404302725386076482363414334623" +
      "51897576645216413767969031495019108575984423919862" +
      "91642193994907236234646844117394032659184044378051" +
      "33389452574239950829659122850855582157250310712570" +
      "12668302402929525220118726767562204154205161841634" +
      "84756516999811614101002996078386909291603028840026" +
      "91041407928862150784245167090870006992821206604183" +
      "71806535567252532567532861291042487761825829765157" +
      "95984703562226293486003415872298053498965022629174" +
      "87882027342092222453398562647669149055628425039127" +
      "57710284027998066365825488926488025456610172967026" +
      "64076559042909945681506526530537182941270336931378" +
      "51786090407086671149655834343476933857817113864558" +
      "73678123014587687126603489139095620099393610310291" +
      "61615288138437909904231747336394804575931493140529" +
      "76347574811935670911013775172100803155902485309066" +
      "92037671922033229094334676851422144773793937517034" +
      "43661991040337511173547191855046449026365512816228" +
      "82446257591633303910722538374218214088350865739177" +
      "15096828874782656995995744906617583441375223970968" +
      "34080053559849175417381883999446974867626551658276" +
      "58483588453142775687900290951702835297163445621296" +
      "40435231176006651012412006597558512761785838292041" +
      "97484423608007193045761893234922927965019875187212" +
      "72675079812554709589045563579212210333466974992356" +
      "30254947802490114195212382815309114079073860251522" +
      "74299581807247162591668545133312394804947079119153" +
      "26734302824418604142636395480004480026704962482017" +
      "92896476697583183271314251702969234889627668440323" +
      "26092752496035799646925650493681836090032380929345" +
      "95889706953653494060340216654437558900456328822505" +
      "45255640564482465151875471196218443965825337543885" +
      "69094113031509526179378002974120766514793942590298" +
      "96959469955657612186561967337862362561252163208628" +
      "69222103274889218654364802296780705765615144632046" +
      "92790682120738837781423356282360896320806822246801" +
      "22482611771858963814091839036736722208883215137556" +
      "00372798394004152970028783076670944474560134556417" +
      "25437090697939612257142989467154357846878861444581" +
      "23145935719849225284716050492212424701412147805734" +
      "55105008019086996033027634787081081754501193071412" +
      "23390866393833952942578690507643100638351983438934" +
      "15961318543475464955697810382930971646514384070070" +
      "73604112373599843452251610507027056235266012764848" +
      "30840761183013052793205427462865403603674532865105" +
      "70658748822569815793678976697422057505968344086973" +
      "50201410206723585020072452256326513410559240190274" +
      "21624843914035998953539459094407046912091409387001" +
      "26456001623742880210927645793106579229552498872758" +
      "4610126483699989225695968815920560010165525637568";

 
# END #

E-mail the author / creator / programmer: Contact William Donnelly