TRandom1.cxx

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// @(#)root/mathcore:$Id$
// Author: Rene Brun from CLHEP & CERNLIB  04/05/2006
 
/**
 
\class TRandom1
 
The Ranlux Random number generator class
 
The algorithm for this random engine has been taken from the original
implementation in FORTRAN by Fred James as part of CLHEP.
 
The initialisation is carried out using a Multiplicative Congruential
generator using formula constants of L'Ecuyer as described in "F.James,
Comp. Phys. Comm. 60 (1990) 329-344".
 
@ingroup Random
 
*/
 
 
#include "TRandom1.h"
#include "TRandom3.h"
#include "TMath.h"
#include <cstdlib>
 
// Number of instances with automatic seed selection
int TRandom1::fgNumEngines = 0;
 
// Maximum index into the seed table
int TRandom1::fgMaxIndex = 215;
const UInt_t fgSeedTable[215][2] = {
                             {           9876, 54321    },
                             {     1299961164, 253987020 },
                             {      669708517, 2079157264 },
                             {      190904760, 417696270 },
                             {     1289741558, 1376336092 },
                             {     1803730167, 324952955   },
                             {      489854550, 582847132   },
                             {     1348037628, 1661577989   },
                             {      350557787, 1155446919   },
                             {      591502945, 634133404   },
                             {     1901084678, 862916278   },
                             {     1988640932, 1785523494   },
                             {     1873836227, 508007031   },
                             {     1146416592, 967585720   },
                             {     1837193353, 1522927634   },
                             {       38219936, 921609208   },
                             {      349152748, 112892610   },
                             {      744459040, 1735807920   },
                             {     1983990104, 728277902   },
                             {      309164507, 2126677523   },
                             {      362993787, 1897782044   },
                             {      556776976, 462072869   },
                             {     1584900822, 2019394912   },
                             {     1249892722, 791083656   },
                             {     1686600998, 1983731097   },
                             {     1127381380, 198976625   },
                             {     1999420861, 1810452455   },
                             {     1972906041, 664182577   },
                             {       84636481, 1291886301   },
                             {     1186362995, 954388413   },
                             {     2141621785, 61738584      },
                             {     1969581251, 1557880415   },
                             {     1150606439, 136325185   },
                             {       95187861, 1592224108   },
                             {      940517655, 1629971798   },
                             {      215350428, 922659102   },
                             {      786161212, 1121345074   },
                             {     1450830056, 1922787776   },
                             {     1696578057, 2025150487   },
                             {     1803414346, 1851324780   },
                             {     1017898585, 1452594263   },
                             {     1184497978, 82122239      },
                             {      633338765, 1829684974   },
                             {      430889421, 230039326   },
                             {      492544653, 76320266      },
                             {      389386975, 1314148944   },
                             {     1720322786, 709120323   },
                             {     1868768216, 1992898523   },
                             {      443210610, 811117710   },
                             {     1191938868, 1548484733   },
                             {      616890172, 159787986   },
                             {      935835339, 1231440405   },
                             {     1058009367, 1527613300   },
                             {     1463148129, 1970575097   },
                             {     1795336935, 434768675   },
                             {      274019517, 605098487   },
                             {      483689317, 217146977   },
                             {     2070804364, 340596558   },
                             {      930226308, 1602100969   },
                             {      989324440, 801809442   },
                             {      410606853, 1893139948   },
                             {     1583588576, 1219225407   },
                             {     2102034391, 1394921405   },
                             {     2005037790, 2031006861   },
                             {     1244218766, 923231061   },
                             {       49312790, 775496649   },
                             {      721012176, 321339902   },
                             {     1719909107, 1865748178   },
                             {     1156177430, 1257110891   },
                             {      307561322, 1918244397   },
                             {      906041433, 360476981   },
                             {     1591375755, 268492659   },
                             {      461522398, 227343256   },
                             {     2145930725, 2020665454   },
                             {     1938419274, 1331283701   },
                             {      174405412, 524140103   },
                             {      494343653,  18063908   },
                             {     1025534808, 181709577   },
                             {     2048959776, 1913665637   },
                             {      950636517, 794796256   },
                             {     1828843197, 1335757744   },
                             {      211109723, 983900607   },
                             {      825474095, 1046009991   },
                             {      374915657, 381856628   },
                             {     1241296328, 698149463   },
                             {     1260624655, 1024538273   },
                             {      900676210, 1628865823   },
                             {      697951025, 500570753   },
                             {     1007920268, 1708398558   },
                             {      264596520, 624727803   },
                             {     1977924811, 674673241   },
                             {     1440257718, 271184151   },
                             {     1928778847, 993535203   },
                             {     1307807366, 1801502463   },
                             {     1498732610, 300876954   },
                             {     1617712402, 1574250679   },
                             {     1261800762, 1556667280   },
                             {      949929273, 560721070   },
                             {     1766170474, 1953522912   },
                             {     1849939248, 19435166      },
                             {      887262858, 1219627824   },
                             {      483086133, 603728993   },
                             {     1330541052, 1582596025   },
                             {     1850591475, 723593133   },
                             {     1431775678, 1558439000   },
                             {      922493739, 1356554404   },
                             {     1058517206, 948567762   },
                             {      709067283, 1350890215   },
                             {     1044787723, 2144304941   },
                             {      999707003, 513837520   },
                             {     2140038663, 1850568788   },
                             {     1803100150, 127574047   },
                             {      867445693, 1149173981   },
                             {      408583729, 914837991   },
                             {     1166715497, 602315845   },
                             {      430738528, 1743308384   },
                             {     1388022681, 1760110496   },
                             {     1664028066, 654300326   },
                             {     1767741172, 1338181197   },
                             {     1625723550, 1742482745   },
                             {      464486085, 1507852127   },
                             {      754082421, 1187454014   },
                             {     1315342834, 425995190   },
                             {      960416608, 2004255418   },
                             {     1262630671, 671761697   },
                             {       59809238, 103525918   },
                             {     1205644919, 2107823293   },
                             {     1615183160, 1152411412   },
                             {     1024474681, 2118672937   },
                             {     1703877649, 1235091369   },
                             {     1821417852, 1098463802   },
                             {     1738806466, 1529062843   },
                             {      620780646, 1654833544   },
                             {     1070174101, 795158254   },
                             {      658537995, 1693620426   },
                             {     2055317555, 508053916   },
                             {     1647371686, 1282395762   },
                             {       29067379, 409683067   },
                             {     1763495989, 1917939635   },
                             {     1602690753, 810926582   },
                             {      885787576, 513818500   },
                             {     1853512561, 1195205756   },
                             {     1798585498, 1970460256   },
                             {     1819261032, 1306536501   },
                             {     1133245275, 37901      },
                             {      689459799, 1334389069   },
                             {     1730609912, 1854586207   },
                             {     1556832175, 1228729041   },
                             {      251375753, 683687209   },
                             {     2083946182, 1763106152   },
                             {     2142981854, 1365385561   },
                             {      763711891, 1735754548   },
                             {     1581256466, 173689858   },
                             {     2121337132, 1247108250   },
                             {     1004003636, 891894307   },
                             {      569816524, 358675254   },
                             {      626626425, 116062841   },
                             {      632086003, 861268491   },
                             {     1008211580, 779404957   },
                             {     1134217766, 1766838261   },
                             {     1423829292, 1706666192   },
                             {      942037869, 1549358884   },
                             {     1959429535, 480779114   },
                             {      778311037, 1940360875   },
                             {     1531372185, 2009078158   },
                             {      241935492, 1050047003   },
                             {      272453504, 1870883868   },
                             {      390441332, 1057903098   },
                             {     1230238834, 1548117688   },
                             {     1242956379, 1217296445   },
                             {      515648357, 1675011378   },
                             {      364477932, 355212934   },
                             {     2096008713, 1570161804   },
                             {     1409752526, 214033983   },
                             {     1288158292, 1760636178   },
                             {      407562666, 1265144848   },
                             {     1071056491, 1582316946   },
                             {     1014143949, 911406955   },
                             {      203080461, 809380052   },
                             {      125647866, 1705464126   },
                             {     2015685843, 599230667   },
                             {     1425476020, 668203729   },
                             {     1673735652, 567931803   },
                             {     1714199325, 181737617   },
                             {     1389137652, 678147926   },
                             {      288547803, 435433694   },
                             {      200159281, 654399753   },
                             {     1580828223, 1298308945   },
                             {     1832286107, 169991953   },
                             {      182557704, 1046541065   },
                             {     1688025575, 1248944426   },
                             {     1508287706, 1220577001   },
                             {       36721212, 1377275347   },
                             {     1968679856, 1675229747   },
                             {      279109231, 1835333261   },
                             {     1358617667, 1416978076   },
                             {      740626186, 2103913602   },
                             {     1882655908, 251341858   },
                             {      648016670, 1459615287   },
                             {      780255321, 154906988   },
                             {      857296483, 203375965   },
                             {     1631676846, 681204578   },
                             {     1906971307, 1623728832   },
                             {     1541899600, 1168449797   },
                             {     1267051693, 1020078717   },
                             {     1998673940, 1298394942   },
                             {     1914117058, 1381290704   },
                             {      426068513, 1381618498   },
                             {      139365577, 1598767734   },
                             {     2129910384, 952266588   },
                             {      661788054, 19661356      },
                             {     1104640222, 240506063   },
                             {      356133630, 1676634527   },
                             {      242242374, 1863206182   },
                             {      957935844, 1490681416   }};
 
 
////////////////////////////////////////////////////////////////////////////////
/// \brief Luxury level is set in the same way as the original FORTRAN routine.
///
///  - level 0 (p=24): equivalent to the original RCARRY of Marsaglia
///                    and Zaman, very long period, but fails many tests.
///  - level 1 (p=48): considerable improvement in quality over level 0,
///                    now passes the gap test, but still fails spectral test.
///  - level 2 (p=97): passes all known tests, but theoretically still
///                    defective.
///  - level 3 (p=223): DEFAULT VALUE. Any theoretically possible
///                     correlations have very small chance of being observed.
///  - level 4 (p=389): highest possible luxury, all 24 bits chaotic.
TRandom1::TRandom1(UInt_t seed, Int_t lux)
        : fIntModulus(0x1000000),
          fMantissaBit24( TMath::Power(0.5,24.) ),
          fMantissaBit12( TMath::Power(0.5,12.) )
{
   UInt_t seedlist[2]={0,0};
 
   fTheSeeds = &fSeed;
   fLuxury = lux;
   SetSeed2(seed, fLuxury);
   // in case seed = 0 SetSeed2 calls already SetSeeds
   if (seed != 0) {
      // setSeeds() wants a zero terminated array!
      seedlist[0]=fSeed;
      seedlist[1]=0;
      SetSeeds(seedlist, fLuxury);
   }
}
 
////////////////////////////////////////////////////////////////////////////////
/// \brief Default constructor.
TRandom1::TRandom1()
        : fIntModulus(0x1000000),
          fMantissaBit24( TMath::Power(0.5,24.) ),
          fMantissaBit12( TMath::Power(0.5,12.) )
{
   fTheSeeds = &fSeed;
   UInt_t seed;
   UInt_t seedlist[2]={0,0};
 
   fLuxury = 3;
   int cycle = abs(int(fgNumEngines/fgMaxIndex));
   int curIndex = abs(int(fgNumEngines%fgMaxIndex));
   fgNumEngines +=1;
   UInt_t mask = ((cycle & 0x007fffff) << 8);
   GetTableSeeds( seedlist, curIndex );
   seed = seedlist[0]^mask;
   SetSeed2(seed, fLuxury);
 
   // setSeeds() wants a zero terminated array!
   seedlist[0]=fSeed; //<=============
   seedlist[1]=0;
   SetSeeds(seedlist, fLuxury);
}
 
////////////////////////////////////////////////////////////////////////////////
/// \brief Constructor.
TRandom1::TRandom1(Int_t rowIndex, Int_t colIndex, Int_t lux)
        : fIntModulus(0x1000000),
          fMantissaBit24( TMath::Power(0.5,24.) ),
          fMantissaBit12( TMath::Power(0.5,12.) )
{
   fTheSeeds = &fSeed;
   UInt_t seed;
   UInt_t seedlist[2]={0,0};
 
   fLuxury = lux;
   int cycle = abs(int(rowIndex/fgMaxIndex));
   int row = abs(int(rowIndex%fgMaxIndex));
   int col = abs(int(colIndex%2));
   UInt_t mask = (( cycle & 0x000007ff ) << 20 );
   GetTableSeeds( seedlist, row );
   seed = ( seedlist[col] )^mask;
   SetSeed2(seed, fLuxury);
 
   // setSeeds() wants a zero terminated array!
   seedlist[0]=fSeed;
   seedlist[1]=0;
   SetSeeds(seedlist, fLuxury);
}
 
////////////////////////////////////////////////////////////////////////////////
/// \brief Destructor.
TRandom1::~TRandom1()
{
}
 
////////////////////////////////////////////////////////////////////////////////
/// \brief Static function returning the seeds table.
void TRandom1::GetTableSeeds(UInt_t* seeds, Int_t index)
{
   if ((index >= 0) && (index < 215)) {
      seeds[0] = fgSeedTable[index][0];
      seeds[1] = fgSeedTable[index][1];
   }
   else seeds = nullptr;
}
 
////////////////////////////////////////////////////////////////////////////////
/// \brief Returns a random number in ]0,1[
Double_t TRandom1::Rndm( )
{
   float next_random;
   float uni;
   int i;
 
   uni = fFloatSeedTable[fJlag] - fFloatSeedTable[fIlag] - fCarry;
   if(uni < 0. ) {
      uni += 1.0;
      fCarry = fMantissaBit24;
   } else {
      fCarry = 0.;
   }
 
   fFloatSeedTable[fIlag] = uni;
   fIlag --;
   fJlag --;
   if(fIlag < 0) fIlag = 23;
   if(fJlag < 0) fJlag = 23;
 
   if( uni < fMantissaBit12 ){
      uni += fMantissaBit24 * fFloatSeedTable[fJlag];
      if( uni == 0) uni = fMantissaBit24 * fMantissaBit24;
   }
   next_random = uni;
   fCount24 ++;
 
// every 24th number generation, several random numbers are generated
// and wasted depending upon the fLuxury level.
 
   if(fCount24 == 24 ) {
      fCount24 = 0;
      for( i = 0; i != fNskip ; i++) {
         uni = fFloatSeedTable[fJlag] - fFloatSeedTable[fIlag] - fCarry;
         if(uni < 0. ) {
            uni += 1.0;
            fCarry = fMantissaBit24;
         } else {
            fCarry = 0.;
         }
         fFloatSeedTable[fIlag] = uni;
         fIlag --;
         fJlag --;
         if(fIlag < 0)fIlag = 23;
         if(fJlag < 0) fJlag = 23;
      }
   }
   return static_cast<Double_t>(next_random);
}
 
////////////////////////////////////////////////////////////////////////////////
/// \brief Returns an array of random numbers in ]0,1[
void TRandom1::RndmArray(const Int_t size, Float_t *vect)
{
   for (Int_t i=0;i<size;i++) vect[i] = Rndm();
}
 
////////////////////////////////////////////////////////////////////////////////
/// \brief Returns an array of random numbers in ]0,1[
void TRandom1::RndmArray(const Int_t size, Double_t *vect)
{
   float next_random;
   float uni;
   int i;
   int index;
 
   for (index=0; index<size; ++index) {
      uni = fFloatSeedTable[fJlag] - fFloatSeedTable[fIlag] - fCarry;
      if(uni < 0. ) {
         uni += 1.0;
         fCarry = fMantissaBit24;
      } else {
         fCarry = 0.;
      }
 
      fFloatSeedTable[fIlag] = uni;
      fIlag --;
      fJlag --;
      if(fIlag < 0) fIlag = 23;
      if(fJlag < 0) fJlag = 23;
 
      if( uni < fMantissaBit12 ){
         uni += fMantissaBit24 * fFloatSeedTable[fJlag];
         if( uni == 0) uni = fMantissaBit24 * fMantissaBit24;
      }
      next_random = uni;
      vect[index] = (double)next_random;
      fCount24 ++;
 
// every 24th number generation, several random numbers are generated
// and wasted depending upon the fLuxury level.
 
      if(fCount24 == 24 ) {
         fCount24 = 0;
         for( i = 0; i != fNskip ; i++) {
            uni = fFloatSeedTable[fJlag] - fFloatSeedTable[fIlag] - fCarry;
            if(uni < 0. ) {
               uni += 1.0;
               fCarry = fMantissaBit24;
            } else {
               fCarry = 0.;
            }
            fFloatSeedTable[fIlag] = uni;
            fIlag --;
            fJlag --;
            if(fIlag < 0)fIlag = 23;
            if(fJlag < 0) fJlag = 23;
         }
      }
   }
}
 
////////////////////////////////////////////////////////////////////////////////
/// \brief Set the state of the generator providing an array of seeds.
///
/// The array of seeds can be of size 24 or less. In case of an array of n seeds with n < 24
/// the n+1 element must be equal to zero.
/// The other elements are the initialized using a Multiplicative
/// Congruential generator using formula constants of L'Ecuyer
/// as described in "A review of pseudorandom number generators"
/// (Fred James) published in Computer Physics Communications 60 (1990)
/// pages 329-344
///
///  \param[in] seeds  array of seeds (size from 1 to 24)
///  \param[in] lux    Luxury level
///
void TRandom1::SetSeeds(const UInt_t *seeds, int lux)
{
   const int ecuyer_a = 53668;
   const int ecuyer_b = 40014;
   const int ecuyer_c = 12211;
   const int ecuyer_d = 2147483563;
 
   const int lux_levels[5] = {0,24,73,199,365};
   int i;
   UInt_t int_seed_table[24];
   Long64_t k_multiple,next_seed;
   const UInt_t *seedptr;
 
   fTheSeeds = seeds;
   seedptr   = seeds;
 
   if(seeds == nullptr) {
      SetSeed2(fSeed,lux);
      fTheSeeds = &fSeed;
      return;
   }
 
   fSeed = *seeds;
 
// number of additional random numbers that need to be 'thrown away'
// every 24 numbers is set using fLuxury level variable.
 
   if( (lux > 4)||(lux < 0) ) {
      if(lux >= 24) {
         fNskip = lux - 24;
      } else {
         fNskip = lux_levels[3]; // corresponds to default fLuxury level
      }
   } else {
      fLuxury = lux;
      fNskip  = lux_levels[fLuxury];
   }
 
   for( i = 0;(i != 24)&&(*seedptr != 0);i++) {
      int_seed_table[i] = *seedptr % fIntModulus;
      seedptr++;
   }
 
   if(i != 24){
      next_seed = int_seed_table[i-1];
      for(;i != 24;i++) {
         k_multiple = next_seed / ecuyer_a;
         next_seed = ecuyer_b * (next_seed - k_multiple * ecuyer_a)
         - k_multiple * ecuyer_c ;
         if(next_seed < 0)next_seed += ecuyer_d;
         int_seed_table[i] = next_seed % fIntModulus;
      }
   }
 
   for(i = 0;i != 24;i++)
      fFloatSeedTable[i] = int_seed_table[i] * fMantissaBit24;
 
   fIlag = 23;
   fJlag = 9;
   fCarry = 0. ;
 
   if( fFloatSeedTable[23] == 0. ) fCarry = fMantissaBit24;
 
   fCount24 = 0;
}
 
////////////////////////////////////////////////////////////////////////////////
/// \brief Set the state of the generator providing a single seed value and a
/// luxury level.
///
/// The initialisation of the other state values is carried out using a Multiplicative
/// Congruential generator using formula constants of L'Ecuyer
/// as described in "A review of pseudorandom number generators"
/// (Fred James) published in Computer Physics Communications 60 (1990)
/// pages 329-344
///
/// \note When provided with seed = 0, a random and unique seed is generated.
///
///  \param[in] seed   seed value (note special case if seed=0)
///  \param[in] lux    Luxury level
///
///
void TRandom1::SetSeed2(UInt_t seed, int lux)
{
   // case of seed == 0
   // use a random seed based on TRandom3(0) which is based on the UUID
   if (seed == 0) {
      UInt_t randSeeds[25];
      TRandom3 r2(0);
      for (int j = 0; j < 24; ++j)
         randSeeds[j] = static_cast<UInt_t>(4294967296. * r2.Rndm());
      randSeeds[24] = 0;
      SetSeeds(randSeeds, lux);
      return;
   }
 
   // seed List requires a zero terminated array in case the size of the array is less that the
   // state size (24)
   UInt_t seedList[2] = {seed, 0};
   SetSeeds(seedList, lux);
}
 
////////////////////////////////////////////////////////////////////////////////
/// \brief Set the state of the generator providing a single seed value and using
/// the luxury level defined when constructing the class.
///
/// The initialisation of the other state values is carried out using a Multiplicative
/// Congruential generator.
///
/// \note When seed = 0, a random and unique seed is generated.
///
/// \param[in] seed   seed value (note special case if seed=0)
///
 
void TRandom1::SetSeed(ULong_t seed)
{
   // Set RanLux seed using the luxury level provided in the constructor
   SetSeed2(seed,fLuxury);
}