TRandom3 - randomness test

ROOT
1

Hello,
I’m taking an exam about statistical analysis and I have to generate random number and then submit them to a randomness test. I’m generating pseudo-random number with the TRandom3 generator, since I read that is a robust generator with a very large period. As concerns the randomness test I’m using the testing suite dieharder. In the following the source code for the generation of pseudo-random numbers.

// c++ -o die_trandom3 die_trandom3.cpp `root-config --libs --glibs --cflags`
#include "TRandom3.h"
#include <climits>
#include <iostream>

int main(int argc, char** argv){

    TRandom3* r = new TRandom3();

    unsigned long long int rnd_num = r->Uniform(-ULONG_MAX,ULONG_MAX);

    std::cout.write(reinterpret_cast<char*>(&rnd_num), sizeof rnd_num);

    while(1){

    rnd_num = r->Uniform(-ULONG_MAX,ULONG_MAX);
    //std::cout << rnd_num << std::endl;
    std::cout.write(reinterpret_cast<char*>(&rnd_num), sizeof rnd_num);

    }
    return 0;
}

And then I’m passing the random numbers into the dieharder suite using the piping, in this way:

>./die_trandom3 |dieharder -a -g 200
Where the arguments -a -g run all the tests with standard/default options to create a
user-controllable report. While the argument 200 stands for the type of input passed to dieharder, in this case a raw binary input.
Looking at the results, the TRandom3 generator fails almost every test, as described in the following output:

#=============================================================================#
#            dieharder version 3.31.1 Copyright 2003 Robert G. Brown          #
#=============================================================================#
   rng_name    |rands/second|   Seed   |
stdin_input_raw|  2.06e+07  | 261925433|
#=============================================================================#
        test_name   |ntup| tsamples |psamples|  p-value |Assessment
#=============================================================================#
   diehard_birthdays|   0|       100|     100|0.00000000|  FAILED  
      diehard_operm5|   0|   1000000|     100|0.00000000|  FAILED  
  diehard_rank_32x32|   0|     40000|     100|0.00000000|  FAILED  
    diehard_rank_6x8|   0|    100000|     100|0.00000000|  FAILED  
   diehard_bitstream|   0|   2097152|     100|0.00000000|  FAILED  
        diehard_opso|   0|   2097152|     100|0.00000000|  FAILED  
        diehard_oqso|   0|   2097152|     100|0.00000000|  FAILED  
         diehard_dna|   0|   2097152|     100|0.00000000|  FAILED  
diehard_count_1s_str|   0|    256000|     100|0.00000000|  FAILED  
diehard_count_1s_byt|   0|    256000|     100|0.00000000|  FAILED  
 diehard_parking_lot|   0|     12000|     100|0.00000000|  FAILED  
    diehard_2dsphere|   2|      8000|     100|0.00000000|  FAILED  
    diehard_3dsphere|   3|      4000|     100|0.88784058|  PASSED  
     diehard_squeeze|   0|    100000|     100|0.00000000|  FAILED  
        diehard_sums|   0|       100|     100|0.00000000|  FAILED  
        diehard_runs|   0|    100000|     100|0.00000000|  FAILED  
        diehard_runs|   0|    100000|     100|0.00000000|  FAILED  
       diehard_craps|   0|    200000|     100|0.00000000|  FAILED  
       diehard_craps|   0|    200000|     100|0.00000000|  FAILED  
 marsaglia_tsang_gcd|   0|  10000000|     100|0.00000000|  FAILED  
 marsaglia_tsang_gcd|   0|  10000000|     100|0.04028199|  PASSED  
         sts_monobit|   1|    100000|     100|0.00000000|  FAILED  
            sts_runs|   2|    100000|     100|0.00000000|  FAILED  
          sts_serial|   1|    100000|     100|0.00000000|  FAILED  
          sts_serial|   2|    100000|     100|0.00000000|  FAILED  
          sts_serial|   3|    100000|     100|0.00000000|  FAILED  
          sts_serial|   3|    100000|     100|0.00000000|  FAILED  
          sts_serial|   4|    100000|     100|0.00000000|  FAILED  
          sts_serial|   4|    100000|     100|0.00000000|  FAILED  
          sts_serial|   5|    100000|     100|0.00000000|  FAILED  
          sts_serial|   5|    100000|     100|0.00000000|  FAILED  
          sts_serial|   6|    100000|     100|0.00000000|  FAILED  
          sts_serial|   6|    100000|     100|0.00000000|  FAILED  
          sts_serial|   7|    100000|     100|0.00000000|  FAILED  
          sts_serial|   7|    100000|     100|0.00000000|  FAILED  
          sts_serial|   8|    100000|     100|0.00000000|  FAILED  
          sts_serial|   8|    100000|     100|0.00000000|  FAILED  
          sts_serial|   9|    100000|     100|0.00000000|  FAILED  
          sts_serial|   9|    100000|     100|0.00000000|  FAILED  
          sts_serial|  10|    100000|     100|0.00000000|  FAILED  
          sts_serial|  10|    100000|     100|0.00000000|  FAILED  
          sts_serial|  11|    100000|     100|0.00000000|  FAILED  
          sts_serial|  11|    100000|     100|0.00000000|  FAILED  
          sts_serial|  12|    100000|     100|0.00000000|  FAILED  
          sts_serial|  12|    100000|     100|0.00000000|  FAILED  
          sts_serial|  13|    100000|     100|0.00000000|  FAILED  
          sts_serial|  13|    100000|     100|0.00000000|  FAILED  
          sts_serial|  14|    100000|     100|0.00000000|  FAILED  
          sts_serial|  14|    100000|     100|0.00000000|  FAILED  
          sts_serial|  15|    100000|     100|0.00000000|  FAILED  
          sts_serial|  15|    100000|     100|0.00000000|  FAILED  
          sts_serial|  16|    100000|     100|0.00000000|  FAILED  
          sts_serial|  16|    100000|     100|0.00000000|  FAILED  
         rgb_bitdist|   1|    100000|     100|0.00000000|  FAILED  
         rgb_bitdist|   2|    100000|     100|0.00000000|  FAILED  
         rgb_bitdist|   3|    100000|     100|0.00000000|  FAILED  
         rgb_bitdist|   4|    100000|     100|0.00000000|  FAILED  
         rgb_bitdist|   5|    100000|     100|0.00000000|  FAILED  
         rgb_bitdist|   6|    100000|     100|0.00000000|  FAILED  
         rgb_bitdist|   7|    100000|     100|0.00000000|  FAILED  
         rgb_bitdist|   8|    100000|     100|0.00000000|  FAILED  
         rgb_bitdist|   9|    100000|     100|0.00000000|  FAILED  
         rgb_bitdist|  10|    100000|     100|0.00000000|  FAILED  
         rgb_bitdist|  11|    100000|     100|0.00000000|  FAILED  
         rgb_bitdist|  12|    100000|     100|0.00000000|  FAILED  
rgb_minimum_distance|   2|     10000|    1000|0.00000000|  FAILED  
rgb_minimum_distance|   3|     10000|    1000|0.03558598|  PASSED  
rgb_minimum_distance|   4|     10000|    1000|0.82921211|  PASSED  
rgb_minimum_distance|   5|     10000|    1000|0.04670306|  PASSED  
    rgb_permutations|   2|    100000|     100|0.00000000|  FAILED  
    rgb_permutations|   3|    100000|     100|0.00000000|  FAILED  
    rgb_permutations|   4|    100000|     100|0.00000000|  FAILED  
    rgb_permutations|   5|    100000|     100|0.00000000|  FAILED  
      rgb_lagged_sum|   0|   1000000|     100|0.00000000|  FAILED  
      rgb_lagged_sum|   1|   1000000|     100|0.95060370|  PASSED  
      rgb_lagged_sum|   2|   1000000|     100|0.00000000|  FAILED  
      rgb_lagged_sum|   3|   1000000|     100|0.49842990|  PASSED  
      rgb_lagged_sum|   4|   1000000|     100|0.00000000|  FAILED  
      rgb_lagged_sum|   5|   1000000|     100|0.44218592|  PASSED  
      rgb_lagged_sum|   6|   1000000|     100|0.00000000|  FAILED  
      rgb_lagged_sum|   7|   1000000|     100|0.65994037|  PASSED  
      rgb_lagged_sum|   8|   1000000|     100|0.00000000|  FAILED  
      rgb_lagged_sum|   9|   1000000|     100|0.59490720|  PASSED  
      rgb_lagged_sum|  10|   1000000|     100|0.00000000|  FAILED  
      rgb_lagged_sum|  11|   1000000|     100|0.99763782|   WEAK   
      rgb_lagged_sum|  12|   1000000|     100|0.00000000|  FAILED  
      rgb_lagged_sum|  13|   1000000|     100|0.02174411|  PASSED  
      rgb_lagged_sum|  14|   1000000|     100|0.00000000|  FAILED  
      rgb_lagged_sum|  15|   1000000|     100|0.79885105|  PASSED  
      rgb_lagged_sum|  16|   1000000|     100|0.00000000|  FAILED  
      rgb_lagged_sum|  17|   1000000|     100|0.96606420|  PASSED  
      rgb_lagged_sum|  18|   1000000|     100|0.00000000|  FAILED  
      rgb_lagged_sum|  19|   1000000|     100|0.19696643|  PASSED  
      rgb_lagged_sum|  20|   1000000|     100|0.00000000|  FAILED  
      rgb_lagged_sum|  21|   1000000|     100|0.46770216|  PASSED  
      rgb_lagged_sum|  22|   1000000|     100|0.00000000|  FAILED  
      rgb_lagged_sum|  23|   1000000|     100|0.28057671|  PASSED  
      rgb_lagged_sum|  24|   1000000|     100|0.00000000|  FAILED  
      rgb_lagged_sum|  25|   1000000|     100|0.84512112|  PASSED  
      rgb_lagged_sum|  26|   1000000|     100|0.00000000|  FAILED  
      rgb_lagged_sum|  27|   1000000|     100|0.97932394|  PASSED

Then my question is: am I doing something wrong, or is it normal? Has anyone tried testing this generator?

Thank you,

Wahid

2

Hi,
Wahid, welcome to the ROOT forum and thank you for the interesting feedback!
The right person to address your question is @moneta, who is currently travelling and will be back in a couple of weeks. If you don’t receive an answer by then, feel free to ping us again.

In the meanwhile, looking at the docs I see that some issues with randomness tests are known for TRandom3 and TRandomMixMax is recommended as an alternative.

Cheers,
Enrico

3

Hi Enrico,

thank you for the quick answer!
In the meanwhile I will try the TRandomMixMax generator.
And just for feedback, the Marsenne Twister homepage linked in the docs you sent me is no more reachable.

Thanks again,
Wahid

4

Hi,

I think you have some issues in the way you are passing the random numbers to diehard. TRandom3 it might fail one test, but not all of them. I am not sure abouyt diehard, but I know that it fails a couple of tests of the TestU01 big crush test suite.

Looking at your code I spot immediately a problem. You are doing :

 r->Uniform(-ULONG_MAX,ULONG_MAX);

but TRandom3 is not a 64 bit generator but a 32 bit one. So you can have randomly uniform distributed integers only between [0,UINT_MAX]

Instead if you use MixMax in that case the range is [0, 2^61-1] since Mixmax is a 61 bit generator.

Lorenzo

2 Likes
5

I missed that TRandom3 is a 32-bit generator. This time it worked, TRandom3 passes almost all tests! In the following the results:

#=============================================================================#
#            dieharder version 3.31.1 Copyright 2003 Robert G. Brown          #
#=============================================================================#
   rng_name    |rands/second|   Seed   |
stdin_input_raw|  1.70e+07  |2242555673|
#=============================================================================#
        test_name   |ntup| tsamples |psamples|  p-value |Assessment
#=============================================================================#
   diehard_birthdays|   0|       100|     100|0.40629140|  PASSED  
      diehard_operm5|   0|   1000000|     100|0.53152825|  PASSED  
  diehard_rank_32x32|   0|     40000|     100|0.38403041|  PASSED  
    diehard_rank_6x8|   0|    100000|     100|0.74866932|  PASSED  
   diehard_bitstream|   0|   2097152|     100|0.40544717|  PASSED  
        diehard_opso|   0|   2097152|     100|0.43282000|  PASSED  
        diehard_oqso|   0|   2097152|     100|0.59129887|  PASSED  
         diehard_dna|   0|   2097152|     100|0.38517388|  PASSED  
diehard_count_1s_str|   0|    256000|     100|0.66433769|  PASSED  
diehard_count_1s_byt|   0|    256000|     100|0.97169353|  PASSED  
 diehard_parking_lot|   0|     12000|     100|0.70977074|  PASSED  
    diehard_2dsphere|   2|      8000|     100|0.29409879|  PASSED  
    diehard_3dsphere|   3|      4000|     100|0.03110855|  PASSED  
     diehard_squeeze|   0|    100000|     100|0.47118828|  PASSED  
        diehard_sums|   0|       100|     100|0.03917410|  PASSED  
        diehard_runs|   0|    100000|     100|0.96282371|  PASSED  
        diehard_runs|   0|    100000|     100|0.67148326|  PASSED  
       diehard_craps|   0|    200000|     100|0.06023367|  PASSED  
       diehard_craps|   0|    200000|     100|0.01702184|  PASSED  
 marsaglia_tsang_gcd|   0|  10000000|     100|0.12151743|  PASSED  
 marsaglia_tsang_gcd|   0|  10000000|     100|0.12230227|  PASSED  
         sts_monobit|   1|    100000|     100|0.49222693|  PASSED  
            sts_runs|   2|    100000|     100|0.22623199|  PASSED  
          sts_serial|   1|    100000|     100|0.04809104|  PASSED  
          sts_serial|   2|    100000|     100|0.21095563|  PASSED  
          sts_serial|   3|    100000|     100|0.63221253|  PASSED  
          sts_serial|   3|    100000|     100|0.63557234|  PASSED  
          sts_serial|   4|    100000|     100|0.78614170|  PASSED  
          sts_serial|   4|    100000|     100|0.89113756|  PASSED  
          sts_serial|   5|    100000|     100|0.97619918|  PASSED  
          sts_serial|   5|    100000|     100|0.98746903|  PASSED  
          sts_serial|   6|    100000|     100|0.50921995|  PASSED  
          sts_serial|   6|    100000|     100|0.83262655|  PASSED  
          sts_serial|   7|    100000|     100|0.48401391|  PASSED  
          sts_serial|   7|    100000|     100|0.78771052|  PASSED  
          sts_serial|   8|    100000|     100|0.84599025|  PASSED  
          sts_serial|   8|    100000|     100|0.67507288|  PASSED  
          sts_serial|   9|    100000|     100|0.35272463|  PASSED  
          sts_serial|   9|    100000|     100|0.24302299|  PASSED  
          sts_serial|  10|    100000|     100|0.19595265|  PASSED  
          sts_serial|  10|    100000|     100|0.14073411|  PASSED  
          sts_serial|  11|    100000|     100|0.07435980|  PASSED  
          sts_serial|  11|    100000|     100|0.03476741|  PASSED  
          sts_serial|  12|    100000|     100|0.14378596|  PASSED  
          sts_serial|  12|    100000|     100|0.11385618|  PASSED  
          sts_serial|  13|    100000|     100|0.88688573|  PASSED  
          sts_serial|  13|    100000|     100|0.24539239|  PASSED  
          sts_serial|  14|    100000|     100|0.60422387|  PASSED  
          sts_serial|  14|    100000|     100|0.34563908|  PASSED  
          sts_serial|  15|    100000|     100|0.87991159|  PASSED  
          sts_serial|  15|    100000|     100|0.25650886|  PASSED  
          sts_serial|  16|    100000|     100|0.98470992|  PASSED  
          sts_serial|  16|    100000|     100|0.87874630|  PASSED  
         rgb_bitdist|   1|    100000|     100|0.85641515|  PASSED  
         rgb_bitdist|   2|    100000|     100|0.92933162|  PASSED  
         rgb_bitdist|   3|    100000|     100|0.51244987|  PASSED  
         rgb_bitdist|   4|    100000|     100|0.84728393|  PASSED  
         rgb_bitdist|   5|    100000|     100|0.82310855|  PASSED  
         rgb_bitdist|   6|    100000|     100|0.54247080|  PASSED  
         rgb_bitdist|   7|    100000|     100|0.80333970|  PASSED  
         rgb_bitdist|   8|    100000|     100|0.00265040|   WEAK   
         rgb_bitdist|   9|    100000|     100|0.86695148|  PASSED  
         rgb_bitdist|  10|    100000|     100|0.94960922|  PASSED  
         rgb_bitdist|  11|    100000|     100|0.29025528|  PASSED  
         rgb_bitdist|  12|    100000|     100|0.53652740|  PASSED  
rgb_minimum_distance|   2|     10000|    1000|0.83730423|  PASSED  
rgb_minimum_distance|   3|     10000|    1000|0.59392927|  PASSED  
rgb_minimum_distance|   4|     10000|    1000|0.23724007|  PASSED  
rgb_minimum_distance|   5|     10000|    1000|0.00471703|   WEAK   
    rgb_permutations|   2|    100000|     100|0.96829968|  PASSED  
    rgb_permutations|   3|    100000|     100|0.79394494|  PASSED  
    rgb_permutations|   4|    100000|     100|0.49703395|  PASSED  
    rgb_permutations|   5|    100000|     100|0.47887377|  PASSED  
      rgb_lagged_sum|   0|   1000000|     100|0.32939114|  PASSED  
      rgb_lagged_sum|   1|   1000000|     100|0.62681040|  PASSED  
      rgb_lagged_sum|   2|   1000000|     100|0.68381487|  PASSED  
      rgb_lagged_sum|   3|   1000000|     100|0.25702647|  PASSED  
      rgb_lagged_sum|   4|   1000000|     100|0.54036495|  PASSED  
      rgb_lagged_sum|   5|   1000000|     100|0.02650876|  PASSED  
      rgb_lagged_sum|   6|   1000000|     100|0.37242251|  PASSED  
      rgb_lagged_sum|   7|   1000000|     100|0.77416385|  PASSED  
      rgb_lagged_sum|   8|   1000000|     100|0.05550322|  PASSED  
      rgb_lagged_sum|   9|   1000000|     100|0.25380434|  PASSED  
      rgb_lagged_sum|  10|   1000000|     100|0.16766434|  PASSED  
      rgb_lagged_sum|  11|   1000000|     100|0.07145531|  PASSED
      rgb_lagged_sum|  12|   1000000|     100|0.48163452|  PASSED  
      rgb_lagged_sum|  13|   1000000|     100|0.97923940|  PASSED  
      rgb_lagged_sum|  14|   1000000|     100|0.19260145|  PASSED  
      rgb_lagged_sum|  15|   1000000|     100|0.49309873|  PASSED  
      rgb_lagged_sum|  16|   1000000|     100|0.03533053|  PASSED  
      rgb_lagged_sum|  17|   1000000|     100|0.70601600|  PASSED  
      rgb_lagged_sum|  18|   1000000|     100|0.93404284|  PASSED  
      rgb_lagged_sum|  19|   1000000|     100|0.99404305|  PASSED  
      rgb_lagged_sum|  20|   1000000|     100|0.04990219|  PASSED  
      rgb_lagged_sum|  21|   1000000|     100|0.85254511|  PASSED  
      rgb_lagged_sum|  22|   1000000|     100|0.78350112|  PASSED  
      rgb_lagged_sum|  23|   1000000|     100|0.26719186|  PASSED  
      rgb_lagged_sum|  24|   1000000|     100|0.86354832|  PASSED  
      rgb_lagged_sum|  25|   1000000|     100|0.74678400|  PASSED 
      rgb_lagged_sum|  26|   1000000|     100|0.85100016|  PASSED
      rgb_lagged_sum|  27   1000000|     100|0.83412301|  PASSED

Thank you!

Wahid

6

Hi,
If you need a 64 bit generator you can use TRandomMT64, an implementation of Mersenne-Twister (as in TRandom3) but for 64 bits

Lorenzo

7

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