// @(#)root/base:$Name:  $:$Id: TRandom.cxx,v 1.3 2000/06/23 15:15:42 brun Exp $
// Author: Rene Brun   15/12/95

/*************************************************************************
 * Copyright (C) 1995-2000, Rene Brun and Fons Rademakers.               *
 * All rights reserved.                                                  *
 *                                                                       *
 * For the licensing terms see $ROOTSYS/LICENSE.                         *
 * For the list of contributors see $ROOTSYS/README/CREDITS.             *
 *************************************************************************/

//////////////////////////////////////////////////////////////////////////
//
// TRandom
//
// basic Random number generator class (periodicity = 10**8).
//
// The following basic Random generators are provided:
// ===================================================
//   -Exp(tau)
//   -Integer(imax)
//   -Gaus(mean,sigma)
//   -Rndm()
//   -Uniform(x1)
//   -Landau(mean,sigma)
//   -Poisson(mean)
//   -Binomial(ntot,prob)
//
// Random numbers distributed according to 1-d, 2-d or 3-d distributions
// =====================================================================
// contained in TF1, TF2 or TF3 objects.
// For example, to get a random number distributed following abs(sin(x)/x)*sqrt(x)
// you can do:
//   TF1 *f1 = new TF1("f1","abs(sin(x)/x)*sqrt(x)",0,10);
//   float r = f1->GetRandom();
// The technique of using a TF1,2 or 3 function is very powerful.
// It is also more precise than using the basic functions (except Rndm).
// With a TF1 function, for example, the real integral of the function
// is correctly calculated in the specified range of the function.
// Getting a number from a TF1 function is also very fast.
// The following table shows some timings (in microsecons/call)
// for basic functions and TF1 functions.
// The left column is with the compiler, the right column with CINT.
// Numbers have been obtained on a Pentium 233Mhz running Linux.
//
//                          g++        CINT
//   Rndm..............    0.330       4.15
//   Gaus..............    2.220       6.77
//   Landau............   21.590      46.82
//   Binomial(5,0.5)...    0.890       5.34
//   Binomial(15,0.5)..    0.920       5.36
//   Poisson(3)........    2.170       5.93
//   Poisson(10).......    4.160       7.95
//   Poisson(70).......   21.510      25.27
//   Poisson(100)......    2.910       6.72
//   GausTF1...........    2.070       4.73
//   LandauTF1.........    2.100       4.73
//
//  Note that the time to generate a number from an arbitrary TF1 function
//  is independent of the complexity of the function.
//  For Landau distribution, it is recommended to use the TF1 technique.
//
//  TH1::FillRandom(TH1 *) or TH1::FillRandom(const char *tf1name)
//  ==============================================================
//  can be used to fill an histogram (1-d, 2-d, 3-d from an existing histogram
//  or from an existing function.
//
//  Note this interesting feature when working with objects
//  =======================================================
//  You can use several TRandom objects, each with their "independent"
//  random sequence. For example, one can imagine
//     TRandom *eventGenerator = new TRandom();
//     TRandom *tracking       = new TRandom();
//  eventGenerator can be used to generate the event kinematics.
//  tracking can be used to track the generated particles with random numbers
//  independent from eventGenerator.
//  This very interesting feature gives the possibility to work with simple
//  and very fast random number generators without worrying about
//  random number periodicity as it was the case with Fortran.
//  One can use TRandom::SetSeed to modify the seed of one generator.
//
//  a TRandom object may be written to a Root file
//  ==============================================
//    -as part of another object
//    -or with its own key (example gRandom->Write("Random");
//
//  The small program below has been used to get the values in the table above.
//   #ifndef __CINT__
//      #include "TROOT.h"
//   #include "TF1.h"
//   #include "TRandom.h"
//   #include "TStopwatch.h"
//   void rand();
//
//   //______________________________________________________________________________
//   int main()
//   {
//     TROOT simple("simple","Test of random numbers");
//
//     rand();
//   }
//   #endif
//   void rand() {
//     int i, N = 1000000;
//     float cpn = 1000000./N;
//     float x;
//     TStopwatch sw;
//     sw.Start();
//     for (i=0;i<N;i++) {
//        x = gRandom->Rndm(i);
//     }
//     printf("Rndm.............. %8.3f microseconds/calln",sw.CpuTime()*cpn);
//     sw.Start();
//     for (i=0;i<N;i++) {
//        x = gRandom->Gaus(0,1);
//     }
//     printf("Gaus.............. %8.3fn",sw.CpuTime()*cpn);
//     sw.Start();
//     for (i=0;i<N;i++) {
//        x = gRandom->Landau(0,1);
//     }
//     printf("Landau............ %8.3fn",sw.CpuTime()*cpn);
//     sw.Start();
//     for (i=0;i<N;i++) {
//        x = gRandom->Binomial(5,0.5);
//     }
//     printf("Binomial(5,0.5)... %8.3fn",sw.CpuTime()*cpn);
//     sw.Start();
//     for (i=0;i<N;i++) {
//        x = gRandom->Binomial(15,0.5);
//     }
//     printf("Binomial(15,0.5).. %8.3fn",sw.CpuTime()*cpn);
//     sw.Start();
//     for (i=0;i<N;i++) {
//        x = gRandom->Poisson(3);
//     }
//     printf("Poisson(3)........ %8.3fn",sw.CpuTime()*cpn);
//     sw.Start();
//     for (i=0;i<N;i++) {
//        x = gRandom->Poisson(10);
//     }
//     printf("Poisson(10)....... %8.3fn",sw.CpuTime()*cpn);
//     sw.Start();
//     for (i=0;i<N;i++) {
//        x = gRandom->Poisson(70);
//     }
//     printf("Poisson(70)....... %8.3fn",sw.CpuTime()*cpn);
//     sw.Start();
//     for (i=0;i<N;i++) {
//        x = gRandom->Poisson(100);
//     }
//     printf("Poisson(100)...... %8.3fn",sw.CpuTime()*cpn);
//
//     TF1 *f1 = new TF1("f1","gaus",-4,4);
//     f1->SetParameters(1,0,1);
//     sw.Start();
//     for (i=0;i<N;i++) {
//        x = f1->GetRandom();
//     }
//     printf("GausTF1........... %8.3fn",sw.CpuTime()*cpn);
//
//     TF1 *f2 = new TF1("f2","landau",-5,15);
//     f2->SetParameters(1,0,1);
//     sw.Start();
//     for (i=0;i<N;i++) {
//        x = f2->GetRandom();
//     }
//     printf("LandauTF1......... %8.3fn",sw.CpuTime()*cpn);
//
//   }
//////////////////////////////////////////////////////////////////////////

#include "TMath.h"
#include "TRandom.h"
#include <time.h>

ClassImp(TRandom)

//______________________________________________________________________________
 TRandom::TRandom(UInt_t seed): TNamed("Random","Default Random number generator")
{
//*-*-*-*-*-*-*-*-*-*-*default constructor*-*-*-*-*-*-*-*-*-*-*-*-*-*-*
//*-*                  ===================

   SetSeed(seed);

}

//______________________________________________________________________________
 TRandom::~TRandom()
{
//*-*-*-*-*-*-*-*-*-*-*default destructor*-*-*-*-*-*-*-*-*-*-*-*-*-*-*
//*-*                  ==================

}

//______________________________________________________________________________
 Int_t TRandom::Binomial(Int_t ntot, Float_t prob)
{
// Generates a random integer N according to the binomial law
// Coded from Los Alamos report LA-5061-MS
//
// N is binomially distributed between 0 and ntot inclusive
// with mean prob*ntot.
// prob is between 0 and 1.
//
// Note: This function should not be used when ntot is large (say >100).
// The normal approximation is then recommended instead
// (with mean =*ntot+0.5 and standard deviation sqrt(ntot*prob*(1-prob)).

   if (prob < 0 || prob > 1) return 0;
   Int_t N = 0;
   for (Int_t i=0;i<ntot;i++) {
      if (Rndm(N) > prob) continue;
      N++;
   }
   return N;
}

//______________________________________________________________________________
 Double_t TRandom::Exp(Double_t tau)
{
// returns an exponential deviate.
//
//          exp( -t/tau )

   Double_t x = Uniform();              // uniform on ( 0, 1 ]
   Double_t t = -tau * TMath::Log( x ); // convert to exponential distribution
   return t;
}

//______________________________________________________________________________
 Double_t TRandom::Gaus(Float_t mean, Float_t sigma)
{
//      Return a number distributed following a gaussian with mean and sigma

   // Local variables
   Float_t x, y, z, result;

   y = Rndm();
   if (!y) y = Rndm();
   z = Rndm();
   x = z * 6.283185;
   result = mean + sigma*TMath::Sin(x)*TMath::Sqrt(-2*TMath::Log(y));
   return result;
}

//______________________________________________________________________________
 UInt_t TRandom::Integer(UInt_t imax)
{
//  returns a random integer on [ 0, imax-1 ].

   UInt_t ui;
   ui = (UInt_t)(imax*Rndm());
   return ui;
}

//______________________________________________________________________________
 Double_t TRandom::Landau(Float_t mean, Float_t sigma)
{
//  Generate a random number following a Landau distribution
//  with average value mean and rms
//  Converted by Rene Brun from CERNLIB routine ranlan(G110)

   Double_t f[982] = {
       0       , 0       , 0       ,0        ,0        ,-2.244733,
      -2.204365,-2.168163,-2.135219,-2.104898,-2.076740,-2.050397,
      -2.025605,-2.002150,-1.979866,-1.958612,-1.938275,-1.918760,
      -1.899984,-1.881879,-1.864385,-1.847451,-1.831030,-1.815083,
      -1.799574,-1.784473,-1.769751,-1.755383,-1.741346,-1.727620,
      -1.714187,-1.701029,-1.688130,-1.675477,-1.663057,-1.650858,
      -1.638868,-1.627078,-1.615477,-1.604058,-1.592811,-1.581729,
      -1.570806,-1.560034,-1.549407,-1.538919,-1.528565,-1.518339,
      -1.508237,-1.498254,-1.488386,-1.478628,-1.468976,-1.459428,
      -1.449979,-1.440626,-1.431365,-1.422195,-1.413111,-1.404112,
      -1.395194,-1.386356,-1.377594,-1.368906,-1.360291,-1.351746,
      -1.343269,-1.334859,-1.326512,-1.318229,-1.310006,-1.301843,
      -1.293737,-1.285688,-1.277693,-1.269752,-1.261863,-1.254024,
      -1.246235,-1.238494,-1.230800,-1.223153,-1.215550,-1.207990,
      -1.200474,-1.192999,-1.185566,-1.178172,-1.170817,-1.163500,
      -1.156220,-1.148977,-1.141770,-1.134598,-1.127459,-1.120354,
      -1.113282,-1.106242,-1.099233,-1.092255,
      -1.085306,-1.078388,-1.071498,-1.064636,-1.057802,-1.050996,
      -1.044215,-1.037461,-1.030733,-1.024029,-1.017350,-1.010695,
      -1.004064, -.997456, -.990871, -.984308, -.977767, -.971247,
       -.964749, -.958271, -.951813, -.945375, -.938957, -.932558,
       -.926178, -.919816, -.913472, -.907146, -.900838, -.894547,
       -.888272, -.882014, -.875773, -.869547, -.863337, -.857142,
       -.850963, -.844798, -.838648, -.832512, -.826390, -.820282,
       -.814187, -.808106, -.802038, -.795982, -.789940, -.783909,
       -.777891, -.771884, -.765889, -.759906, -.753934, -.747973,
       -.742023, -.736084, -.730155, -.724237, -.718328, -.712429,
       -.706541, -.700661, -.694791, -.688931, -.683079, -.677236,
       -.671402, -.665576, -.659759, -.653950, -.648149, -.642356,
       -.636570, -.630793, -.625022, -.619259, -.613503, -.607754,
       -.602012, -.596276, -.590548, -.584825, -.579109, -.573399,
       -.567695, -.561997, -.556305, -.550618, -.544937, -.539262,
       -.533592, -.527926, -.522266, -.516611, -.510961, -.505315,
       -.499674, -.494037, -.488405, -.482777,
       -.477153, -.471533, -.465917, -.460305, -.454697, -.449092,
       -.443491, -.437893, -.432299, -.426707, -.421119, -.415534,
       -.409951, -.404372, -.398795, -.393221, -.387649, -.382080,
       -.376513, -.370949, -.365387, -.359826, -.354268, -.348712,
       -.343157, -.337604, -.332053, -.326503, -.320955, -.315408,
       -.309863, -.304318, -.298775, -.293233, -.287692, -.282152,
       -.276613, -.271074, -.265536, -.259999, -.254462, -.248926,
       -.243389, -.237854, -.232318, -.226783, -.221247, -.215712,
       -.210176, -.204641, -.199105, -.193568, -.188032, -.182495,
       -.176957, -.171419, -.165880, -.160341, -.154800, -.149259,
       -.143717, -.138173, -.132629, -.127083, -.121537, -.115989,
       -.110439, -.104889, -.099336, -.093782, -.088227, -.082670,
       -.077111, -.071550, -.065987, -.060423, -.054856, -.049288,
       -.043717, -.038144, -.032569, -.026991, -.021411, -.015828,
       -.010243, -.004656,  .000934,  .006527,  .012123,  .017722,
        .023323,  .028928,  .034535,  .040146,  .045759,  .051376,
        .056997,  .062620,  .068247,  .073877,
        .079511,  .085149,  .090790,  .096435,  .102083,  .107736,
        .113392,  .119052,  .124716,  .130385,  .136057,  .141734,
        .147414,  .153100,  .158789,  .164483,  .170181,  .175884,
        .181592,  .187304,  .193021,  .198743,  .204469,  .210201,
        .215937,  .221678,  .227425,  .233177,  .238933,  .244696,
        .250463,  .256236,  .262014,  .267798,  .273587,  .279382,
        .285183,  .290989,  .296801,  .302619,  .308443,  .314273,
        .320109,  .325951,  .331799,  .337654,  .343515,  .349382,
        .355255,  .361135,  .367022,  .372915,  .378815,  .384721,
        .390634,  .396554,  .402481,  .408415,  .414356,  .420304,
        .426260,  .432222,  .438192,  .444169,  .450153,  .456145,
        .462144,  .468151,  .474166,  .480188,  .486218,  .492256,
        .498302,  .504356,  .510418,  .516488,  .522566,  .528653,
        .534747,  .540850,  .546962,  .553082,  .559210,  .565347,
        .571493,  .577648,  .583811,  .589983,  .596164,  .602355,
        .608554,  .614762,  .620980,  .627207,  .633444,  .639689,
        .645945,  .652210,  .658484,  .664768,
        .671062,  .677366,  .683680,  .690004,  .696338,  .702682,
        .709036,  .715400,  .721775,  .728160,  .734556,  .740963,
        .747379,  .753807,  .760246,  .766695,  .773155,  .779627,
        .786109,  .792603,  .799107,  .805624,  .812151,  .818690,
        .825241,  .831803,  .838377,  .844962,  .851560,  .858170,
        .864791,  .871425,  .878071,  .884729,  .891399,  .898082,
        .904778,  .911486,  .918206,  .924940,  .931686,  .938446,
        .945218,  .952003,  .958802,  .965614,  .972439,  .979278,
        .986130,  .992996,  .999875, 1.006769, 1.013676, 1.020597,
       1.027533, 1.034482, 1.041446, 1.048424, 1.055417, 1.062424,
       1.069446, 1.076482, 1.083534, 1.090600, 1.097681, 1.104778,
       1.111889, 1.119016, 1.126159, 1.133316, 1.140490, 1.147679,
       1.154884, 1.162105, 1.169342, 1.176595, 1.183864, 1.191149,
       1.198451, 1.205770, 1.213105, 1.220457, 1.227826, 1.235211,
       1.242614, 1.250034, 1.257471, 1.264926, 1.272398, 1.279888,
       1.287395, 1.294921, 1.302464, 1.310026, 1.317605, 1.325203,
       1.332819, 1.340454, 1.348108, 1.355780,
       1.363472, 1.371182, 1.378912, 1.386660, 1.394429, 1.402216,
       1.410024, 1.417851, 1.425698, 1.433565, 1.441453, 1.449360,
       1.457288, 1.465237, 1.473206, 1.481196, 1.489208, 1.497240,
       1.505293, 1.513368, 1.521465, 1.529583, 1.537723, 1.545885,
       1.554068, 1.562275, 1.570503, 1.578754, 1.587028, 1.595325,
       1.603644, 1.611987, 1.620353, 1.628743, 1.637156, 1.645593,
       1.654053, 1.662538, 1.671047, 1.679581, 1.688139, 1.696721,
       1.705329, 1.713961, 1.722619, 1.731303, 1.740011, 1.748746,
       1.757506, 1.766293, 1.775106, 1.783945, 1.792810, 1.801703,
       1.810623, 1.819569, 1.828543, 1.837545, 1.846574, 1.855631,
       1.864717, 1.873830, 1.882972, 1.892143, 1.901343, 1.910572,
       1.919830, 1.929117, 1.938434, 1.947781, 1.957158, 1.966566,
       1.976004, 1.985473, 1.994972, 2.004503, 2.014065, 2.023659,
       2.033285, 2.042943, 2.052633, 2.062355, 2.072110, 2.081899,
       2.091720, 2.101575, 2.111464, 2.121386, 2.131343, 2.141334,
       2.151360, 2.161421, 2.171517, 2.181648, 2.191815, 2.202018,
       2.212257, 2.222533, 2.232845, 2.243195,
       2.253582, 2.264006, 2.274468, 2.284968, 2.295507, 2.306084,
       2.316701, 2.327356, 2.338051, 2.348786, 2.359562, 2.370377,
       2.381234, 2.392131, 2.403070, 2.414051, 2.425073, 2.436138,
       2.447246, 2.458397, 2.469591, 2.480828, 2.492110, 2.503436,
       2.514807, 2.526222, 2.537684, 2.549190, 2.560743, 2.572343,
       2.583989, 2.595682, 2.607423, 2.619212, 2.631050, 2.642936,
       2.654871, 2.666855, 2.678890, 2.690975, 2.703110, 2.715297,
       2.727535, 2.739825, 2.752168, 2.764563, 2.777012, 2.789514,
       2.802070, 2.814681, 2.827347, 2.840069, 2.852846, 2.865680,
       2.878570, 2.891518, 2.904524, 2.917588, 2.930712, 2.943894,
       2.957136, 2.970439, 2.983802, 2.997227, 3.010714, 3.024263,
       3.037875, 3.051551, 3.065290, 3.079095, 3.092965, 3.106900,
       3.120902, 3.134971, 3.149107, 3.163312, 3.177585, 3.191928,
       3.206340, 3.220824, 3.235378, 3.250005, 3.264704, 3.279477,
       3.294323, 3.309244, 3.324240, 3.339312, 3.354461, 3.369687,
       3.384992, 3.400375, 3.415838, 3.431381, 3.447005, 3.462711,
       3.478500, 3.494372, 3.510328, 3.526370,
       3.542497, 3.558711, 3.575012, 3.591402, 3.607881, 3.624450,
       3.641111, 3.657863, 3.674708, 3.691646, 3.708680, 3.725809,
       3.743034, 3.760357, 3.777779, 3.795300, 3.812921, 3.830645,
       3.848470, 3.866400, 3.884434, 3.902574, 3.920821, 3.939176,
       3.957640, 3.976215, 3.994901, 4.013699, 4.032612, 4.051639,
       4.070783, 4.090045, 4.109425, 4.128925, 4.148547, 4.168292,
       4.188160, 4.208154, 4.228275, 4.248524, 4.268903, 4.289413,
       4.310056, 4.330832, 4.351745, 4.372794, 4.393982, 4.415310,
       4.436781, 4.458395, 4.480154, 4.502060, 4.524114, 4.546319,
       4.568676, 4.591187, 4.613854, 4.636678, 4.659662, 4.682807,
       4.706116, 4.729590, 4.753231, 4.777041, 4.801024, 4.825179,
       4.849511, 4.874020, 4.898710, 4.923582, 4.948639, 4.973883,
       4.999316, 5.024942, 5.050761, 5.076778, 5.102993, 5.129411,
       5.156034, 5.182864, 5.209903, 5.237156, 5.264625, 5.292312,
       5.320220, 5.348354, 5.376714, 5.405306, 5.434131, 5.463193,
       5.492496, 5.522042, 5.551836, 5.581880, 5.612178, 5.642734,
       5.673552, 5.704634, 5.735986, 5.767610,
       5.799512, 5.831694, 5.864161, 5.896918, 5.929968, 5.963316,
       5.996967, 6.030925, 6.065194, 6.099780, 6.134687, 6.169921,
       6.205486, 6.241387, 6.277630, 6.314220, 6.351163, 6.388465,
       6.426130, 6.464166, 6.502578, 6.541371, 6.580553, 6.620130,
       6.660109, 6.700495, 6.741297, 6.782520, 6.824173, 6.866262,
       6.908795, 6.951780, 6.995225, 7.039137, 7.083525, 7.128398,
       7.173764, 7.219632, 7.266011, 7.312910, 7.360339, 7.408308,
       7.456827, 7.505905, 7.555554, 7.605785, 7.656608, 7.708035,
       7.760077, 7.812747, 7.866057, 7.920019, 7.974647, 8.029953,
       8.085952, 8.142657, 8.200083, 8.258245, 8.317158, 8.376837,
       8.437300, 8.498562, 8.560641, 8.623554, 8.687319, 8.751955,
       8.817481, 8.883916, 8.951282, 9.019600, 9.088889, 9.159174,
       9.230477, 9.302822, 9.376233, 9.450735, 9.526355, 9.603118,
       9.681054, 9.760191, 9.840558, 9.922186,10.005107,10.089353,
      10.174959,10.261958,10.350389,10.440287,10.531693,10.624646,
      10.719188,10.815362,10.913214,11.012789,11.114137,11.217307,
      11.322352,11.429325,11.538283,11.649285,
      11.762390,11.877664,11.995170,12.114979,12.237161,12.361791,
      12.488946,12.618708,12.751161,12.886394,13.024498,13.165570,
      13.309711,13.457026,13.607625,13.761625,13.919145,14.080314,
      14.245263,14.414134,14.587072,14.764233,14.945778,15.131877,
      15.322712,15.518470,15.719353,15.925570,16.137345,16.354912,
      16.578520,16.808433,17.044929,17.288305,17.538873,17.796967,
      18.062943,18.337176,18.620068,18.912049,19.213574,19.525133,
      19.847249,20.180480,20.525429,20.882738,21.253102,21.637266,
      22.036036,22.450278,22.880933,23.329017,23.795634,24.281981,
      24.789364,25.319207,25.873062,26.452634,27.059789,27.696581,
      28.365274,29.068370,29.808638,30.589157,31.413354,32.285060,
      33.208568,34.188705,35.230920,36.341388,37.527131,38.796172,
      40.157721,41.622399,43.202525,44.912465,46.769077,48.792279,
      51.005773,53.437996,56.123356,59.103894 };

   if (sigma <= 0) return 0;
   Double_t ranlan, x, u, v;
   x = Rndm();
   u = 1000*x;
   Int_t i = Int_t(u);
   u -= i;
   if (i >= 70 && i < 800) {
       ranlan = f[i-1] + u*(f[i] - f[i-1]);
   } else if (i >= 7 && i <= 980) {
       ranlan =  f[i-1] + u*(f[i]-f[i-1]-0.25*(1-u)*(f[i+1]-f[i]-f[i-1]+f[i-2]));
   } else if (i < 7) {
       v = TMath::Log(x);
       u = 1/v;
       ranlan = ((0.99858950+(3.45213058E1+1.70854528E1*u)*u)/
                 (1         +(3.41760202E1+4.01244582  *u)*u))*
                 (-TMath::Log(-0.91893853-v)-1);
   } else {
       u = 1-x;
       v = u*u;
       if (x <= 0.999) {
        ranlan = (1.00060006+2.63991156E2*u+4.37320068E3*v)/
                ((1         +2.57368075E2*u+3.41448018E3*v)*u);
       } else {
        ranlan = (1.00001538+6.07514119E3*u+7.34266409E5*v)/
                ((1         +6.06511919E3*u+6.94021044E5*v)*u);
       }
   }
   Double_t res = mean + sigma*ranlan;
   return res;
}

//______________________________________________________________________________
 Int_t TRandom::Poisson(Float_t mean)
{
// Generates a random integer N according to a Poisson law.
// Coded from Los Alamos report LA-5061-MS
// Prob(N) = exp(-mean)*mean^N/Factorial(N)
//
   Int_t N;
   if (mean <= 0) return 0;
     // use a gaussian approximation for large values of mean
   if (mean > 88) {
      N = Int_t(Gaus(0,1)*TMath::Sqrt(mean) + mean +0.5);
      return N;
   }
   Float_t expmean = TMath::Exp(-mean);
   Float_t pir = 1;
   N = -1;
   while(1) {
      N++;
      pir *= Rndm(N);
      if (pir <= expmean) break;
   }
   return N;
}

//______________________________________________________________________________
 void TRandom::Rannor(Float_t &a, Float_t &b)
{
//      Return 2 numbers distributed following a gaussian with mean=0 and sigma=1

   // Local variables
   Float_t r, x, y, z;

   y = Rndm();
   if (!y) y = Rndm();
   z = Rndm();
   x = z * 6.283185;
   r = TMath::Sqrt(-2*TMath::Log(y));
   a = r * TMath::Sin(x);
   b = r * TMath::Cos(x);
}

//______________________________________________________________________________
 Float_t TRandom::Rndm(Int_t)
{
//  Machine independent random number generator.
//  Produces uniformly-distributed floating points between 0 and 1.
//  Identical sequence on all machines of >= 32 bits.
//  Periodicity = 10**8
//  Universal version (Fred james 1985).
//  generates a number in [0,1]

   const Float_t kCONS = 4.6566128730774E-10;
   const Int_t kMASK31 = 2147483647;

   fSeed *= 69069;
      // keep only lower 31 bits
   fSeed &= kMASK31;
      // Set lower 8 bits to zero to assure exact float
   Int_t jy = (fSeed/256)*256;
   Float_t random = kCONS*jy;
   return random;
}

//______________________________________________________________________________
 void TRandom::SetSeed(UInt_t seed)
{
//  Set the random generator seed
//  if seed is zero, the seed is set to the current  machine clock
//  Note that the machine clock is returned with a precision of 1 second.
//  If one calls SetSeed(0) within a loop and the loop time is less than 1s, 
//  all generated numbers will be identical!
   
  if( seed==0 ) {
    time_t curtime;      // Set 'random' seed number  if seed=0
    time(&curtime);      // Get current time in fSeed.
    fSeed = (UInt_t)curtime;
  } else {
    fSeed = seed;
  }
}

//______________________________________________________________________________
 Double_t TRandom::Uniform(Double_t x1)
{
// returns a uniform deviate on the interval ( 0, x1 ].

   Double_t ans;
   do { ans = Rndm(); } while( ans==0 );
   return x1*ans;
}