
#========================================================================
#                      RGB Timing Test
#
# This test times the selected random number generator only.  It is
# generally run at the beginning of a run of -a(ll) the tests to provide
# some measure of the relative time taken up generating random numbers
# for the various generators and tests.
#                        Run Details
# Random number generator tested: mt19937_1999
# Samples per test pvalue = 1000000 (test default is 1000000)
# P-values in final KS test = 10 (test default is 10)
#========================================================================
# rgb_timing() test using the mt19937_1999 generator 
# Average time per rand = 2.720320e+01 nsec.
# Rands per second = 3.676038e+07.

#========================================================================
#                   RGB Bit Persistence Test
# This test generates 256 sequential samples of an random unsigned
# integer from the given rng.  Successive integers are logically
# processed to extract a mask with 1's whereever bits do not
# change.  Since bits will NOT change when filling e.g. unsigned
# ints with 16 bit ints, this mask logically &'d with the maximum
# random number returned by the rng.  All the remaining 1's in the
# resulting mask are therefore significant -- they represent bits
# that never change over the length of the test.  These bits are
# very likely the reason that certain rng's fail the monobit
# test -- extra persistent e.g. 1's or 0's inevitably bias the
# total bitcount.  In many cases the particular bits repeated
# appear to depend on the seed.  If the -i flag is given, the
# entire test is repeated with the rng reseeded to generate a mask
# and the extracted mask cumulated to show all the possible bit
# positions that might be repeated for different seeds.
#                        Run Details
# Random number generator tested: mt19937_1999
# Samples per test pvalue = 256 (test default is 256)
# P-values in final KS test = 1 (test default is 1)
#==================================================================
#                          Results
# Results for mt19937_1999 rng, using its 32 valid bits:
# (Cumulated mask of zero is good.)
# cumulated_mask =          0 = 00000000000000000000000000000000
# randm_mask     = 4294967295 = 11111111111111111111111111111111
# random_max     = 4294967295 = 11111111111111111111111111111111
# rgb_persist test PASSED (no bits repeat)
#==================================================================

#========================================================================
#                 RGB Bit Distribution Test
# Accumulates the frequencies of all n-tuples of bits in a list
# of random integers and compares the distribution thus generated
# with the theoretical (binomial) histogram, forming chisq and the
# associated p-value.  In this test n-tuples are selected without
# WITHOUT overlap (e.g. 01|10|10|01|11|00|01|10) so the samples
# are independent.  Every other sample is offset modulus of the
# sample index and ntuple_max.
#
#                        Run Details
# Random number generator tested: mt19937_1999
# Samples per test pvalue = 100000 (test default is 100000)
# P-values in final KS test = 100 (test default is 100)
# Testing 1-bit ntuples in 32-bit random words
#==================================================================
#                Histogram of p-values
# Counting histogram bins, binscale = 0.100000
#     20|    |    |    |    |    |    |    |    |    |    |
#       |    |    |    |    |    |    |    |    |    |    |
#     18|    |    |    |****|    |    |    |    |    |    |
#       |    |    |    |****|    |    |    |    |    |    |
#     16|    |    |    |****|    |    |    |    |    |    |
#       |    |    |    |****|    |    |    |    |    |    |
#     14|    |    |    |****|    |    |****|    |    |    |
#       |    |    |    |****|    |    |****|    |    |    |
#     12|****|    |    |****|    |    |****|    |    |    |
#       |****|****|    |****|    |    |****|    |    |    |
#     10|****|****|    |****|    |    |****|    |    |    |
#       |****|****|    |****|****|    |****|    |****|    |
#      8|****|****|****|****|****|    |****|    |****|    |
#       |****|****|****|****|****|****|****|    |****|****|
#      6|****|****|****|****|****|****|****|    |****|****|
#       |****|****|****|****|****|****|****|****|****|****|
#      4|****|****|****|****|****|****|****|****|****|****|
#       |****|****|****|****|****|****|****|****|****|****|
#      2|****|****|****|****|****|****|****|****|****|****|
#       |****|****|****|****|****|****|****|****|****|****|
#       |--------------------------------------------------
#       | 0.1| 0.2| 0.3| 0.4| 0.5| 0.6| 0.7| 0.8| 0.9| 1.0|
#==================================================================
#                          Results
Kuiper KS: p = 0.454306
Assessment: PASSED at > 5% for RGB Bit Distribution Test

#========================================================================
#                 RGB Bit Distribution Test
# Accumulates the frequencies of all n-tuples of bits in a list
# of random integers and compares the distribution thus generated
# with the theoretical (binomial) histogram, forming chisq and the
# associated p-value.  In this test n-tuples are selected without
# WITHOUT overlap (e.g. 01|10|10|01|11|00|01|10) so the samples
# are independent.  Every other sample is offset modulus of the
# sample index and ntuple_max.
#
#                        Run Details
# Random number generator tested: mt19937_1999
# Samples per test pvalue = 100000 (test default is 100000)
# P-values in final KS test = 100 (test default is 100)
# Testing 2-bit ntuples in 32-bit random words
#==================================================================
#                Histogram of p-values
# Counting histogram bins, binscale = 0.100000
#     20|    |    |    |    |    |    |    |    |    |    |
#       |    |    |    |    |    |    |    |    |    |    |
#     18|    |    |    |    |    |    |    |    |    |    |
#       |    |    |    |    |    |    |    |    |    |    |
#     16|    |    |    |    |    |    |    |    |    |    |
#       |    |    |    |    |****|    |    |    |    |    |
#     14|    |    |    |    |****|    |    |    |    |    |
#       |    |    |    |    |****|    |    |    |    |****|
#     12|****|    |    |****|****|****|    |    |    |****|
#       |****|    |    |****|****|****|    |    |    |****|
#     10|****|    |    |****|****|****|    |    |    |****|
#       |****|    |    |****|****|****|****|    |    |****|
#      8|****|    |    |****|****|****|****|****|    |****|
#       |****|    |    |****|****|****|****|****|****|****|
#      6|****|****|****|****|****|****|****|****|****|****|
#       |****|****|****|****|****|****|****|****|****|****|
#      4|****|****|****|****|****|****|****|****|****|****|
#       |****|****|****|****|****|****|****|****|****|****|
#      2|****|****|****|****|****|****|****|****|****|****|
#       |****|****|****|****|****|****|****|****|****|****|
#       |--------------------------------------------------
#       | 0.1| 0.2| 0.3| 0.4| 0.5| 0.6| 0.7| 0.8| 0.9| 1.0|
#==================================================================
#                          Results
Kuiper KS: p = 0.677257
Assessment: PASSED at > 5% for RGB Bit Distribution Test

#========================================================================
#                 RGB Bit Distribution Test
# Accumulates the frequencies of all n-tuples of bits in a list
# of random integers and compares the distribution thus generated
# with the theoretical (binomial) histogram, forming chisq and the
# associated p-value.  In this test n-tuples are selected without
# WITHOUT overlap (e.g. 01|10|10|01|11|00|01|10) so the samples
# are independent.  Every other sample is offset modulus of the
# sample index and ntuple_max.
#
#                        Run Details
# Random number generator tested: mt19937_1999
# Samples per test pvalue = 100000 (test default is 100000)
# P-values in final KS test = 100 (test default is 100)
# Testing 3-bit ntuples in 32-bit random words
#==================================================================
#                Histogram of p-values
# Counting histogram bins, binscale = 0.100000
#     20|    |    |    |    |    |    |    |    |    |    |
#       |    |    |    |    |    |    |    |    |    |    |
#     18|    |    |    |    |    |    |    |    |    |    |
#       |****|    |    |    |    |    |    |    |    |    |
#     16|****|    |    |    |    |    |    |    |    |    |
#       |****|    |    |    |    |    |    |    |    |    |
#     14|****|    |    |    |    |    |    |    |    |    |
#       |****|    |    |    |    |    |    |    |    |    |
#     12|****|    |    |    |    |****|****|    |    |****|
#       |****|    |    |    |    |****|****|    |    |****|
#     10|****|    |    |    |****|****|****|****|    |****|
#       |****|    |    |    |****|****|****|****|    |****|
#      8|****|    |    |****|****|****|****|****|    |****|
#       |****|****|    |****|****|****|****|****|****|****|
#      6|****|****|    |****|****|****|****|****|****|****|
#       |****|****|****|****|****|****|****|****|****|****|
#      4|****|****|****|****|****|****|****|****|****|****|
#       |****|****|****|****|****|****|****|****|****|****|
#      2|****|****|****|****|****|****|****|****|****|****|
#       |****|****|****|****|****|****|****|****|****|****|
#       |--------------------------------------------------
#       | 0.1| 0.2| 0.3| 0.4| 0.5| 0.6| 0.7| 0.8| 0.9| 1.0|
#==================================================================
#                          Results
Kuiper KS: p = 0.562547
Assessment: PASSED at > 5% for RGB Bit Distribution Test

#========================================================================
#                 RGB Bit Distribution Test
# Accumulates the frequencies of all n-tuples of bits in a list
# of random integers and compares the distribution thus generated
# with the theoretical (binomial) histogram, forming chisq and the
# associated p-value.  In this test n-tuples are selected without
# WITHOUT overlap (e.g. 01|10|10|01|11|00|01|10) so the samples
# are independent.  Every other sample is offset modulus of the
# sample index and ntuple_max.
#
#                        Run Details
# Random number generator tested: mt19937_1999
# Samples per test pvalue = 100000 (test default is 100000)
# P-values in final KS test = 100 (test default is 100)
# Testing 4-bit ntuples in 32-bit random words
#==================================================================
#                Histogram of p-values
# Counting histogram bins, binscale = 0.100000
#     20|    |    |    |    |    |    |    |    |    |    |
#       |    |    |    |    |    |    |    |    |    |    |
#     18|    |    |    |    |    |    |    |    |    |    |
#       |    |    |    |    |    |    |    |    |    |    |
#     16|    |    |    |    |    |    |    |    |    |    |
#       |    |    |    |    |    |    |    |    |    |    |
#     14|    |****|    |    |    |    |    |    |    |    |
#       |    |****|    |    |    |    |    |    |****|    |
#     12|    |****|    |    |****|    |****|    |****|    |
#       |    |****|    |    |****|    |****|    |****|    |
#     10|    |****|    |    |****|****|****|    |****|****|
#       |****|****|    |    |****|****|****|    |****|****|
#      8|****|****|****|    |****|****|****|    |****|****|
#       |****|****|****|    |****|****|****|****|****|****|
#      6|****|****|****|    |****|****|****|****|****|****|
#       |****|****|****|****|****|****|****|****|****|****|
#      4|****|****|****|****|****|****|****|****|****|****|
#       |****|****|****|****|****|****|****|****|****|****|
#      2|****|****|****|****|****|****|****|****|****|****|
#       |****|****|****|****|****|****|****|****|****|****|
#       |--------------------------------------------------
#       | 0.1| 0.2| 0.3| 0.4| 0.5| 0.6| 0.7| 0.8| 0.9| 1.0|
#==================================================================
#                          Results
Kuiper KS: p = 0.981092
Assessment: PASSED at > 5% for RGB Bit Distribution Test

#========================================================================
#                 RGB Bit Distribution Test
# Accumulates the frequencies of all n-tuples of bits in a list
# of random integers and compares the distribution thus generated
# with the theoretical (binomial) histogram, forming chisq and the
# associated p-value.  In this test n-tuples are selected without
# WITHOUT overlap (e.g. 01|10|10|01|11|00|01|10) so the samples
# are independent.  Every other sample is offset modulus of the
# sample index and ntuple_max.
#
#                        Run Details
# Random number generator tested: mt19937_1999
# Samples per test pvalue = 100000 (test default is 100000)
# P-values in final KS test = 100 (test default is 100)
# Testing 5-bit ntuples in 32-bit random words
#==================================================================
#                Histogram of p-values
# Counting histogram bins, binscale = 0.100000
#     20|    |    |    |    |    |    |    |    |    |    |
#       |    |    |    |    |    |    |    |    |    |    |
#     18|    |    |    |    |    |    |    |    |    |****|
#       |    |    |    |    |    |    |    |    |    |****|
#     16|    |    |    |    |    |    |    |    |    |****|
#       |    |    |    |    |    |    |    |    |    |****|
#     14|    |    |    |    |    |    |    |    |    |****|
#       |    |    |    |    |    |    |    |    |    |****|
#     12|    |    |    |****|    |    |    |    |****|****|
#       |    |    |    |****|    |    |    |    |****|****|
#     10|    |    |    |****|    |****|****|    |****|****|
#       |    |****|    |****|    |****|****|    |****|****|
#      8|    |****|****|****|    |****|****|****|****|****|
#       |    |****|****|****|****|****|****|****|****|****|
#      6|****|****|****|****|****|****|****|****|****|****|
#       |****|****|****|****|****|****|****|****|****|****|
#      4|****|****|****|****|****|****|****|****|****|****|
#       |****|****|****|****|****|****|****|****|****|****|
#      2|****|****|****|****|****|****|****|****|****|****|
#       |****|****|****|****|****|****|****|****|****|****|
#       |--------------------------------------------------
#       | 0.1| 0.2| 0.3| 0.4| 0.5| 0.6| 0.7| 0.8| 0.9| 1.0|
#==================================================================
#                          Results
Kuiper KS: p = 0.459934
Assessment: PASSED at > 5% for RGB Bit Distribution Test

#========================================================================
#                 RGB Bit Distribution Test
# Accumulates the frequencies of all n-tuples of bits in a list
# of random integers and compares the distribution thus generated
# with the theoretical (binomial) histogram, forming chisq and the
# associated p-value.  In this test n-tuples are selected without
# WITHOUT overlap (e.g. 01|10|10|01|11|00|01|10) so the samples
# are independent.  Every other sample is offset modulus of the
# sample index and ntuple_max.
#
#                        Run Details
# Random number generator tested: mt19937_1999
# Samples per test pvalue = 100000 (test default is 100000)
# P-values in final KS test = 100 (test default is 100)
# Testing 6-bit ntuples in 32-bit random words
#==================================================================
#                Histogram of p-values
# Counting histogram bins, binscale = 0.100000
#     20|    |    |    |    |    |    |    |    |    |    |
#       |    |    |    |    |    |    |    |    |    |    |
#     18|    |    |    |    |    |    |    |    |    |    |
#       |    |    |    |    |    |****|    |    |    |    |
#     16|    |    |    |    |    |****|    |    |    |    |
#       |    |    |    |    |    |****|    |    |    |    |
#     14|    |    |    |    |    |****|    |****|    |    |
#       |    |    |    |    |****|****|    |****|    |    |
#     12|    |    |    |    |****|****|    |****|    |    |
#       |    |    |    |    |****|****|****|****|    |    |
#     10|    |    |    |    |****|****|****|****|****|    |
#       |    |    |****|    |****|****|****|****|****|    |
#      8|****|    |****|    |****|****|****|****|****|    |
#       |****|    |****|****|****|****|****|****|****|    |
#      6|****|    |****|****|****|****|****|****|****|****|
#       |****|****|****|****|****|****|****|****|****|****|
#      4|****|****|****|****|****|****|****|****|****|****|
#       |****|****|****|****|****|****|****|****|****|****|
#      2|****|****|****|****|****|****|****|****|****|****|
#       |****|****|****|****|****|****|****|****|****|****|
#       |--------------------------------------------------
#       | 0.1| 0.2| 0.3| 0.4| 0.5| 0.6| 0.7| 0.8| 0.9| 1.0|
#==================================================================
#                          Results
Kuiper KS: p = 0.048979
Assessment: POSSIBLY WEAK at < 5% for RGB Bit Distribution Test
Recommendation:  Repeat test to verify failure.

#========================================================================
#                 RGB Bit Distribution Test
# Accumulates the frequencies of all n-tuples of bits in a list
# of random integers and compares the distribution thus generated
# with the theoretical (binomial) histogram, forming chisq and the
# associated p-value.  In this test n-tuples are selected without
# WITHOUT overlap (e.g. 01|10|10|01|11|00|01|10) so the samples
# are independent.  Every other sample is offset modulus of the
# sample index and ntuple_max.
#
#                        Run Details
# Random number generator tested: mt19937_1999
# Samples per test pvalue = 100000 (test default is 100000)
# P-values in final KS test = 100 (test default is 100)
# Testing 7-bit ntuples in 32-bit random words
#==================================================================
#                Histogram of p-values
# Counting histogram bins, binscale = 0.100000
#     20|    |    |    |    |    |    |    |    |    |    |
#       |    |    |    |    |    |    |    |    |    |    |
#     18|    |    |    |    |    |    |    |    |    |    |
#       |    |    |    |    |    |    |    |    |    |    |
#     16|    |    |    |    |    |    |    |    |    |    |
#       |    |    |    |    |    |    |    |    |    |    |
#     14|    |    |    |    |    |    |    |    |    |    |
#       |    |    |    |    |    |    |****|    |****|    |
#     12|    |    |    |    |    |    |****|    |****|    |
#       |****|    |    |    |****|    |****|    |****|    |
#     10|****|    |****|    |****|****|****|****|****|    |
#       |****|    |****|    |****|****|****|****|****|****|
#      8|****|    |****|****|****|****|****|****|****|****|
#       |****|    |****|****|****|****|****|****|****|****|
#      6|****|    |****|****|****|****|****|****|****|****|
#       |****|****|****|****|****|****|****|****|****|****|
#      4|****|****|****|****|****|****|****|****|****|****|
#       |****|****|****|****|****|****|****|****|****|****|
#      2|****|****|****|****|****|****|****|****|****|****|
#       |****|****|****|****|****|****|****|****|****|****|
#       |--------------------------------------------------
#       | 0.1| 0.2| 0.3| 0.4| 0.5| 0.6| 0.7| 0.8| 0.9| 1.0|
#==================================================================
#                          Results
Kuiper KS: p = 0.735182
Assessment: PASSED at > 5% for RGB Bit Distribution Test

#========================================================================
#                 RGB Bit Distribution Test
# Accumulates the frequencies of all n-tuples of bits in a list
# of random integers and compares the distribution thus generated
# with the theoretical (binomial) histogram, forming chisq and the
# associated p-value.  In this test n-tuples are selected without
# WITHOUT overlap (e.g. 01|10|10|01|11|00|01|10) so the samples
# are independent.  Every other sample is offset modulus of the
# sample index and ntuple_max.
#
#                        Run Details
# Random number generator tested: mt19937_1999
# Samples per test pvalue = 100000 (test default is 100000)
# P-values in final KS test = 100 (test default is 100)
# Testing 8-bit ntuples in 32-bit random words
#==================================================================
#                Histogram of p-values
# Counting histogram bins, binscale = 0.100000
#     20|    |    |    |    |    |    |    |    |    |    |
#       |    |    |    |    |    |    |    |    |    |    |
#     18|    |    |    |    |    |    |    |    |    |    |
#       |    |    |    |    |    |    |    |    |    |    |
#     16|    |    |    |    |    |    |****|    |    |    |
#       |    |    |    |    |****|    |****|    |    |    |
#     14|    |    |    |    |****|    |****|    |    |    |
#       |    |    |    |    |****|    |****|    |    |    |
#     12|    |    |    |    |****|    |****|    |    |    |
#       |****|    |****|    |****|    |****|    |    |    |
#     10|****|    |****|    |****|    |****|****|    |    |
#       |****|    |****|    |****|    |****|****|    |****|
#      8|****|****|****|****|****|    |****|****|    |****|
#       |****|****|****|****|****|    |****|****|    |****|
#      6|****|****|****|****|****|****|****|****|****|****|
#       |****|****|****|****|****|****|****|****|****|****|
#      4|****|****|****|****|****|****|****|****|****|****|
#       |****|****|****|****|****|****|****|****|****|****|
#      2|****|****|****|****|****|****|****|****|****|****|
#       |****|****|****|****|****|****|****|****|****|****|
#       |--------------------------------------------------
#       | 0.1| 0.2| 0.3| 0.4| 0.5| 0.6| 0.7| 0.8| 0.9| 1.0|
#==================================================================
#                          Results
Kuiper KS: p = 0.730004
Assessment: PASSED at > 5% for RGB Bit Distribution Test

#========================================================================
#                 RGB Bit Distribution Test
# Accumulates the frequencies of all n-tuples of bits in a list
# of random integers and compares the distribution thus generated
# with the theoretical (binomial) histogram, forming chisq and the
# associated p-value.  In this test n-tuples are selected without
# WITHOUT overlap (e.g. 01|10|10|01|11|00|01|10) so the samples
# are independent.  Every other sample is offset modulus of the
# sample index and ntuple_max.
#
#                        Run Details
# Random number generator tested: mt19937_1999
# Samples per test pvalue = 100000 (test default is 100000)
# P-values in final KS test = 100 (test default is 100)
# Testing 9-bit ntuples in 32-bit random words
#==================================================================
#                Histogram of p-values
# Counting histogram bins, binscale = 0.100000
#     20|    |    |    |    |    |    |    |    |    |    |
#       |    |    |    |    |    |    |    |    |    |    |
#     18|    |    |    |    |    |    |    |    |    |    |
#       |    |    |    |    |    |    |    |    |****|    |
#     16|    |****|    |    |    |    |    |    |****|    |
#       |    |****|    |    |    |    |    |    |****|    |
#     14|    |****|    |    |    |    |    |    |****|    |
#       |    |****|    |    |    |    |    |    |****|    |
#     12|    |****|****|    |    |    |    |    |****|    |
#       |    |****|****|    |    |****|    |    |****|    |
#     10|    |****|****|    |****|****|    |    |****|    |
#       |****|****|****|    |****|****|    |    |****|    |
#      8|****|****|****|    |****|****|    |****|****|    |
#       |****|****|****|    |****|****|    |****|****|    |
#      6|****|****|****|    |****|****|****|****|****|****|
#       |****|****|****|****|****|****|****|****|****|****|
#      4|****|****|****|****|****|****|****|****|****|****|
#       |****|****|****|****|****|****|****|****|****|****|
#      2|****|****|****|****|****|****|****|****|****|****|
#       |****|****|****|****|****|****|****|****|****|****|
#       |--------------------------------------------------
#       | 0.1| 0.2| 0.3| 0.4| 0.5| 0.6| 0.7| 0.8| 0.9| 1.0|
#==================================================================
#                          Results
Kuiper KS: p = 0.717035
Assessment: PASSED at > 5% for RGB Bit Distribution Test

#========================================================================
#                 RGB Bit Distribution Test
# Accumulates the frequencies of all n-tuples of bits in a list
# of random integers and compares the distribution thus generated
# with the theoretical (binomial) histogram, forming chisq and the
# associated p-value.  In this test n-tuples are selected without
# WITHOUT overlap (e.g. 01|10|10|01|11|00|01|10) so the samples
# are independent.  Every other sample is offset modulus of the
# sample index and ntuple_max.
#
#                        Run Details
# Random number generator tested: mt19937_1999
# Samples per test pvalue = 100000 (test default is 100000)
# P-values in final KS test = 100 (test default is 100)
# Testing 10-bit ntuples in 32-bit random words
#==================================================================
#                Histogram of p-values
# Counting histogram bins, binscale = 0.100000
#     20|    |    |    |    |    |    |    |    |    |    |
#       |    |    |    |    |    |    |    |    |    |    |
#     18|    |    |****|    |    |    |    |    |    |    |
#       |    |    |****|    |    |    |    |    |    |****|
#     16|    |    |****|    |    |    |    |    |    |****|
#       |    |    |****|    |    |    |    |    |    |****|
#     14|    |    |****|    |    |    |    |    |    |****|
#       |    |    |****|    |    |    |    |    |    |****|
#     12|    |    |****|    |    |    |    |    |    |****|
#       |    |    |****|    |    |    |    |    |****|****|
#     10|    |    |****|    |****|    |    |    |****|****|
#       |    |****|****|    |****|****|****|    |****|****|
#      8|    |****|****|    |****|****|****|    |****|****|
#       |****|****|****|    |****|****|****|    |****|****|
#      6|****|****|****|    |****|****|****|****|****|****|
#       |****|****|****|    |****|****|****|****|****|****|
#      4|****|****|****|****|****|****|****|****|****|****|
#       |****|****|****|****|****|****|****|****|****|****|
#      2|****|****|****|****|****|****|****|****|****|****|
#       |****|****|****|****|****|****|****|****|****|****|
#       |--------------------------------------------------
#       | 0.1| 0.2| 0.3| 0.4| 0.5| 0.6| 0.7| 0.8| 0.9| 1.0|
#==================================================================
#                          Results
Kuiper KS: p = 0.251375
Assessment: PASSED at > 5% for RGB Bit Distribution Test

#========================================================================
#                 RGB Bit Distribution Test
# Accumulates the frequencies of all n-tuples of bits in a list
# of random integers and compares the distribution thus generated
# with the theoretical (binomial) histogram, forming chisq and the
# associated p-value.  In this test n-tuples are selected without
# WITHOUT overlap (e.g. 01|10|10|01|11|00|01|10) so the samples
# are independent.  Every other sample is offset modulus of the
# sample index and ntuple_max.
#
#                        Run Details
# Random number generator tested: mt19937_1999
# Samples per test pvalue = 100000 (test default is 100000)
# P-values in final KS test = 100 (test default is 100)
# Testing 11-bit ntuples in 32-bit random words
#==================================================================
#                Histogram of p-values
# Counting histogram bins, binscale = 0.100000
#     20|    |    |    |    |    |    |    |    |    |    |
#       |    |    |    |    |    |    |    |    |    |    |
#     18|    |    |    |    |    |    |    |    |    |    |
#       |    |    |    |    |    |    |    |    |    |    |
#     16|    |    |    |    |    |    |    |    |    |    |
#       |    |    |    |    |    |    |    |    |    |    |
#     14|    |    |    |    |    |    |    |    |    |****|
#       |    |    |    |    |    |    |    |    |    |****|
#     12|****|****|    |    |    |    |    |    |    |****|
#       |****|****|    |****|    |    |    |    |    |****|
#     10|****|****|    |****|****|****|    |    |    |****|
#       |****|****|    |****|****|****|****|****|    |****|
#      8|****|****|    |****|****|****|****|****|    |****|
#       |****|****|    |****|****|****|****|****|****|****|
#      6|****|****|****|****|****|****|****|****|****|****|
#       |****|****|****|****|****|****|****|****|****|****|
#      4|****|****|****|****|****|****|****|****|****|****|
#       |****|****|****|****|****|****|****|****|****|****|
#      2|****|****|****|****|****|****|****|****|****|****|
#       |****|****|****|****|****|****|****|****|****|****|
#       |--------------------------------------------------
#       | 0.1| 0.2| 0.3| 0.4| 0.5| 0.6| 0.7| 0.8| 0.9| 1.0|
#==================================================================
#                          Results
Kuiper KS: p = 0.733350
Assessment: PASSED at > 5% for RGB Bit Distribution Test

#========================================================================
#                 RGB Bit Distribution Test
# Accumulates the frequencies of all n-tuples of bits in a list
# of random integers and compares the distribution thus generated
# with the theoretical (binomial) histogram, forming chisq and the
# associated p-value.  In this test n-tuples are selected without
# WITHOUT overlap (e.g. 01|10|10|01|11|00|01|10) so the samples
# are independent.  Every other sample is offset modulus of the
# sample index and ntuple_max.
#
#                        Run Details
# Random number generator tested: mt19937_1999
# Samples per test pvalue = 100000 (test default is 100000)
# P-values in final KS test = 100 (test default is 100)
# Testing 12-bit ntuples in 32-bit random words
#==================================================================
#                Histogram of p-values
# Counting histogram bins, binscale = 0.100000
#     20|    |    |    |    |    |    |    |    |    |    |
#       |    |    |    |    |    |    |    |    |    |    |
#     18|    |    |    |    |    |    |    |    |    |    |
#       |    |    |    |    |    |    |    |    |    |    |
#     16|    |    |    |    |    |    |    |    |    |    |
#       |    |    |    |    |    |    |    |    |    |    |
#     14|****|    |    |    |    |    |****|    |    |    |
#       |****|    |    |    |    |    |****|    |    |****|
#     12|****|    |    |    |    |    |****|    |    |****|
#       |****|    |    |    |    |    |****|    |    |****|
#     10|****|    |    |    |****|    |****|    |****|****|
#       |****|****|    |    |****|    |****|    |****|****|
#      8|****|****|    |****|****|    |****|****|****|****|
#       |****|****|****|****|****|****|****|****|****|****|
#      6|****|****|****|****|****|****|****|****|****|****|
#       |****|****|****|****|****|****|****|****|****|****|
#      4|****|****|****|****|****|****|****|****|****|****|
#       |****|****|****|****|****|****|****|****|****|****|
#      2|****|****|****|****|****|****|****|****|****|****|
#       |****|****|****|****|****|****|****|****|****|****|
#       |--------------------------------------------------
#       | 0.1| 0.2| 0.3| 0.4| 0.5| 0.6| 0.7| 0.8| 0.9| 1.0|
#==================================================================
#                          Results
Kuiper KS: p = 0.837136
Assessment: PASSED at > 5% for RGB Bit Distribution Test

#==================================================================
#                Diehard "Birthdays" test (modified).
# Each test determines the number of matching intervals from 512
# "birthdays" (by default) drawn on a 24-bit "year" (by
# default).  This is repeated 100 times (by default) and the
# results cumulated in a histogram.  Repeated intervals should be
# distributed in a Poisson distribution if the underlying generator
# is random enough, and a a chisq and p-value for the test are
# evaluated relative to this null hypothesis.
#
# It is recommended that you run this at or near the original
# 100 test samples per p-value with -t 100.
#
# Two additional parameters have been added. In diehard, nms=512
# but this CAN be varied and all Marsaglia's formulae still work.  It
# can be reset to different values with -x nmsvalue.
# Similarly, nbits "should" 24, but we can really make it anything
# we want that's less than or equal to rmax_bits = 32.  It can be
# reset to a new value with -y nbits.  Both default to diehard's
# values if no -x or -y options are used.
#==================================================================
#                        Run Details
# Random number generator tested: mt19937_1999
# Samples per test pvalue = 100 (test default is 100)
# P-values in final KS test = 100 (test default is 100)
#==================================================================
#                Histogram of p-values
# Counting histogram bins, binscale = 0.100000
#     20|    |    |    |    |    |    |    |    |    |    |
#       |    |    |    |    |    |****|    |    |    |    |
#     18|    |    |    |    |    |****|    |    |    |    |
#       |    |    |    |    |    |****|    |    |    |    |
#     16|    |    |    |    |    |****|    |    |    |    |
#       |    |    |    |    |    |****|    |    |    |    |
#     14|    |    |    |    |    |****|    |    |    |    |
#       |    |    |    |****|    |****|    |    |    |    |
#     12|    |    |****|****|    |****|    |    |    |    |
#       |    |    |****|****|    |****|****|    |****|    |
#     10|    |    |****|****|    |****|****|    |****|    |
#       |****|    |****|****|    |****|****|****|****|    |
#      8|****|    |****|****|    |****|****|****|****|    |
#       |****|    |****|****|****|****|****|****|****|    |
#      6|****|    |****|****|****|****|****|****|****|****|
#       |****|    |****|****|****|****|****|****|****|****|
#      4|****|    |****|****|****|****|****|****|****|****|
#       |****|****|****|****|****|****|****|****|****|****|
#      2|****|****|****|****|****|****|****|****|****|****|
#       |****|****|****|****|****|****|****|****|****|****|
#       |--------------------------------------------------
#       | 0.1| 0.2| 0.3| 0.4| 0.5| 0.6| 0.7| 0.8| 0.9| 1.0|
#==================================================================
#                          Results
Kuiper KS: p = 0.348172
Assessment: PASSED at > 5% for Diehard(er) Birthdays Test

#==================================================================
#          Diehard Overlapping 5-Permutations Test.
# This is the OPERM5 test.  It looks at a sequence of one mill- 
# ion 32-bit random integers.  Each set of five consecutive     
# integers can be in one of 120 states, for the 5! possible or- 
# derings of five numbers.  Thus the 5th, 6th, 7th,...numbers   
# each provide a state. As many thousands of state transitions  
# are observed,  cumulative counts are made of the number of    
# occurences of each state.  Then the quadratic form in the     
# weak inverse of the 120x120 covariance matrix yields a test   
# equivalent to the likelihood ratio test that the 120 cell     
# counts came from the specified (asymptotically) normal dis-   
# tribution with the specified 120x120 covariance matrix (with  
# rank 99).  This version uses 1,000,000 integers, twice.       
#
# Note that Dieharder runs the test 100 times, not twice, by
# default.
#
# WARNING! This test currently fails ALL RNGs including ones that
# are strongly believed to be "good" ones (that pass the other 
# dieharder tests).  DO NOT USE THIS TEST TO ASSESS RNGs!  It very
# likely contains either implementation bugs or incorrect data used
# to compute the test statistic.  rgb
#==================================================================
#                        Run Details
# Random number generator tested: mt19937_1999
# Samples per test pvalue = 1000000 (test default is 1000000)
# P-values in final KS test = 100 (test default is 100)
#==================================================================
#                Histogram of p-values
# Counting histogram bins, binscale = 0.100000
#     20|    |    |    |    |    |    |    |    |    |    |
#       |    |    |    |    |    |    |    |    |    |    |
#     18|****|    |    |    |    |    |    |    |    |    |
#       |****|    |    |    |    |    |    |    |    |    |
#     16|****|    |    |    |    |    |    |    |    |****|
#       |****|    |    |    |    |    |    |    |    |****|
#     14|****|    |    |    |    |    |    |    |    |****|
#       |****|    |    |    |    |    |    |    |    |****|
#     12|****|    |    |    |    |    |    |    |    |****|
#       |****|    |    |    |    |    |****|    |****|****|
#     10|****|    |****|    |    |    |****|****|****|****|
#       |****|    |****|    |    |    |****|****|****|****|
#      8|****|    |****|    |    |    |****|****|****|****|
#       |****|****|****|    |    |****|****|****|****|****|
#      6|****|****|****|    |****|****|****|****|****|****|
#       |****|****|****|    |****|****|****|****|****|****|
#      4|****|****|****|****|****|****|****|****|****|****|
#       |****|****|****|****|****|****|****|****|****|****|
#      2|****|****|****|****|****|****|****|****|****|****|
#       |****|****|****|****|****|****|****|****|****|****|
#       |--------------------------------------------------
#       | 0.1| 0.2| 0.3| 0.4| 0.5| 0.6| 0.7| 0.8| 0.9| 1.0|
#==================================================================
#                          Results
Kuiper KS: p = 0.004524
Assessment: POOR at < 1% for Diehard OPERM5 Test
Recommendation:  Repeat test to verify failure.

#==================================================================
#                Diehard 32x32 Binary Rank Test
# This is the BINARY RANK TEST for 31x31 matrices. The leftmost 
# 31 bits of 31 random integers from the test sequence are used 
# to form a 31x31 binary matrix over the field {0,1}. The rank  
# is determined. That rank can be from 0 to 31, but ranks< 28   
# are rare, and their counts are pooled with those for rank 28. 
# Ranks are found for (default) 40,000 such random matrices and
# a chisquare test is performed on counts for ranks 31,30,29 and
# <=28.
#
# As always, the test is repeated and a KS test applied to the
# resulting p-values to verify that they are approximately uniform.
#==================================================================
#                        Run Details
# Random number generator tested: mt19937_1999
# Samples per test pvalue = 40000 (test default is 40000)
# P-values in final KS test = 100 (test default is 100)
#==================================================================
#                Histogram of p-values
# Counting histogram bins, binscale = 0.100000
#     20|    |    |    |    |    |    |    |    |    |    |
#       |    |    |    |    |    |    |    |    |    |    |
#     18|    |    |    |    |    |    |    |    |    |    |
#       |    |    |    |    |    |    |    |    |    |    |
#     16|    |    |    |    |    |    |    |    |    |    |
#       |    |    |    |    |    |    |    |    |    |    |
#     14|    |    |    |    |    |    |    |    |    |    |
#       |    |    |    |    |    |    |    |    |    |    |
#     12|    |    |****|****|    |    |    |    |    |    |
#       |    |    |****|****|    |    |    |****|****|    |
#     10|****|    |****|****|****|****|****|****|****|    |
#       |****|    |****|****|****|****|****|****|****|    |
#      8|****|    |****|****|****|****|****|****|****|    |
#       |****|****|****|****|****|****|****|****|****|****|
#      6|****|****|****|****|****|****|****|****|****|****|
#       |****|****|****|****|****|****|****|****|****|****|
#      4|****|****|****|****|****|****|****|****|****|****|
#       |****|****|****|****|****|****|****|****|****|****|
#      2|****|****|****|****|****|****|****|****|****|****|
#       |****|****|****|****|****|****|****|****|****|****|
#       |--------------------------------------------------
#       | 0.1| 0.2| 0.3| 0.4| 0.5| 0.6| 0.7| 0.8| 0.9| 1.0|
#==================================================================
#                          Results
Kuiper KS: p = 0.967591
Assessment: PASSED at > 5% for Diehard 32x32 Binary Rank Test

#==================================================================
#              Diehard 6x8 Binary Rank Test
# This is the BINARY RANK TEST for 6x8 matrices.  From each of
# six random 32-bit integers from the generator under test, a
# specified byte is chosen, and the resulting six bytes form a
# 6x8 binary matrix whose rank is determined.  That rank can be
# from 0 to 6, but ranks 0,1,2,3 are rare; their counts are
# pooled with those for rank 4. Ranks are found for 100,000
# random matrices, and a chi-square test is performed on
# counts for ranks 6,5 and <=4.
#
# As always, the test is repeated and a KS test applied to the
# resulting p-values to verify that they are approximately uniform.
#==================================================================
#                        Run Details
# Random number generator tested: mt19937_1999
# Samples per test pvalue = 100000 (test default is 100000)
# P-values in final KS test = 100 (test default is 100)
#==================================================================
#                Histogram of p-values
# Counting histogram bins, binscale = 0.100000
#     20|    |    |    |    |    |    |    |    |    |    |
#       |    |    |    |    |    |    |    |    |    |    |
#     18|    |    |    |    |    |    |    |    |    |    |
#       |    |    |    |    |    |    |    |    |    |    |
#     16|    |    |    |    |    |    |    |    |    |    |
#       |    |    |    |    |    |    |    |    |    |    |
#     14|    |    |****|    |    |    |    |    |    |    |
#       |    |    |****|    |    |****|    |****|    |    |
#     12|    |    |****|****|****|****|****|****|    |    |
#       |    |****|****|****|****|****|****|****|    |    |
#     10|    |****|****|****|****|****|****|****|    |    |
#       |    |****|****|****|****|****|****|****|    |    |
#      8|    |****|****|****|****|****|****|****|    |    |
#       |****|****|****|****|****|****|****|****|    |    |
#      6|****|****|****|****|****|****|****|****|    |    |
#       |****|****|****|****|****|****|****|****|    |****|
#      4|****|****|****|****|****|****|****|****|    |****|
#       |****|****|****|****|****|****|****|****|    |****|
#      2|****|****|****|****|****|****|****|****|    |****|
#       |****|****|****|****|****|****|****|****|****|****|
#       |--------------------------------------------------
#       | 0.1| 0.2| 0.3| 0.4| 0.5| 0.6| 0.7| 0.8| 0.9| 1.0|
#==================================================================
#                          Results
Kuiper KS: p = 0.017107
Assessment: POSSIBLY WEAK at < 5% for Diehard 6x8 Binary Rank Test
Recommendation:  Repeat test to verify failure.

#==================================================================
#                  Diehard Bitstream Test.
# The file under test is viewed as a stream of bits. Call them  
# b1,b2,... .  Consider an alphabet with two "letters", 0 and 1 
# and think of the stream of bits as a succession of 20-letter  
# "words", overlapping.  Thus the first word is b1b2...b20, the 
# second is b2b3...b21, and so on.  The bitstream test counts   
# the number of missing 20-letter (20-bit) words in a string of 
# 2^21 overlapping 20-letter words.  There are 2^20 possible 20 
# letter words.  For a truly random string of 2^21+19 bits, the 
# number of missing words j should be (very close to) normally  
# distributed with mean 141,909 and sigma 428.  Thus            
#  (j-141909)/428 should be a standard normal variate (z score) 
# that leads to a uniform [0,1) p value.  The test is repeated  
# twenty times.                                                 
# 
# Note that of course we do not "restart file", when using gsl 
# generators, we just crank out the next random number. 
# We also do not bother to overlap the words.  rands are cheap. 
# Finally, we repeat the test (usually) more than twenty time.
#
# WARNING!  Many RNGs that "should" pass this test marginally
# fail or are weak (and can be pushed to failure with increasing
# numbers of psamples).  This suggests either an implementation bug
# or an error in the presumed target data.  The tests should not
# be used to perform an assessment of RNGs until this issue is
# resolved.   rgb
#==================================================================
#                        Run Details
# Random number generator tested: mt19937_1999
# Samples per test pvalue = 2097152 (test default is 2097152)
# P-values in final KS test = 100 (test default is 100)
#==================================================================
#                Histogram of p-values
# Counting histogram bins, binscale = 0.100000
#     20|    |    |    |    |    |    |    |    |    |    |
#       |    |    |    |    |    |    |    |    |    |    |
#     18|    |    |    |    |    |    |    |    |    |    |
#       |    |    |    |    |    |    |    |    |    |    |
#     16|    |    |****|****|    |****|    |    |    |    |
#       |    |    |****|****|    |****|    |    |    |    |
#     14|    |    |****|****|****|****|    |    |    |    |
#       |    |    |****|****|****|****|    |    |    |    |
#     12|    |    |****|****|****|****|****|    |    |    |
#       |    |    |****|****|****|****|****|    |    |    |
#     10|    |    |****|****|****|****|****|    |    |    |
#       |    |    |****|****|****|****|****|    |    |    |
#      8|    |    |****|****|****|****|****|****|****|    |
#       |    |****|****|****|****|****|****|****|****|    |
#      6|    |****|****|****|****|****|****|****|****|    |
#       |    |****|****|****|****|****|****|****|****|    |
#      4|    |****|****|****|****|****|****|****|****|    |
#       |    |****|****|****|****|****|****|****|****|    |
#      2|    |****|****|****|****|****|****|****|****|****|
#       |****|****|****|****|****|****|****|****|****|****|
#       |--------------------------------------------------
#       | 0.1| 0.2| 0.3| 0.4| 0.5| 0.6| 0.7| 0.8| 0.9| 1.0|
#==================================================================
#                          Results
Kuiper KS: p = 0.000138
Assessment: POOR at < 1% for Diehard Bitstream Test
Recommendation:  Repeat test to verify failure.

#==================================================================
#        Diehard Overlapping Pairs Sparse Occupance (OPSO)
# The OPSO test considers 2-letter words from an alphabet of    
# 1024 letters.  Each letter is determined by a specified ten   
# bits from a 32-bit integer in the sequence to be tested. OPSO 
# generates  2^21 (overlapping) 2-letter words  (from 2^21+1    
# "keystrokes")  and counts the number of missing words---that  
# is 2-letter words which do not appear in the entire sequence. 
# That count should be very close to normally distributed with  
# mean 141,909, sigma 290. Thus (missingwrds-141909)/290 should 
# be a standard normal variable. The OPSO test takes 32 bits at 
# a time from the test file and uses a designated set of ten    
# consecutive bits. It then restarts the file for the next de-  
# signated 10 bits, and so on.                                  
# 
#  Note 2^21 = 2097152, tsamples cannot be varied.
#==================================================================
#                        Run Details
# Random number generator tested: mt19937_1999
# Samples per test pvalue = 2097152 (test default is 2097152)
# P-values in final KS test = 100 (test default is 100)
#==================================================================
#                Histogram of p-values
# Counting histogram bins, binscale = 0.100000
#     20|    |    |    |    |    |    |    |    |    |    |
#       |    |    |    |    |    |    |    |    |    |    |
#     18|    |    |    |    |    |    |    |    |    |    |
#       |    |    |    |    |    |    |    |    |    |    |
#     16|    |    |    |    |    |    |    |    |    |    |
#       |****|    |    |    |    |    |    |    |    |    |
#     14|****|    |    |    |    |    |    |    |    |****|
#       |****|****|    |    |    |    |    |    |    |****|
#     12|****|****|    |****|    |    |    |    |    |****|
#       |****|****|    |****|    |    |****|****|    |****|
#     10|****|****|    |****|    |    |****|****|    |****|
#       |****|****|    |****|    |    |****|****|    |****|
#      8|****|****|    |****|    |    |****|****|****|****|
#       |****|****|    |****|    |****|****|****|****|****|
#      6|****|****|****|****|    |****|****|****|****|****|
#       |****|****|****|****|    |****|****|****|****|****|
#      4|****|****|****|****|    |****|****|****|****|****|
#       |****|****|****|****|****|****|****|****|****|****|
#      2|****|****|****|****|****|****|****|****|****|****|
#       |****|****|****|****|****|****|****|****|****|****|
#       |--------------------------------------------------
#       | 0.1| 0.2| 0.3| 0.4| 0.5| 0.6| 0.7| 0.8| 0.9| 1.0|
#==================================================================
#                          Results
Kuiper KS: p = 0.216429
Assessment: PASSED at > 5% for Diehard OPSO

#==================================================================
#   Diehard Overlapping Quadruples Sparce Occupancy (OQSO) Test
#
#  Similar, to OPSO except that it considers 4-letter 
#  words from an alphabet of 32 letters, each letter determined  
#  by a designated string of 5 consecutive bits from the test    
#  file, elements of which are assumed 32-bit random integers.   
#  The mean number of missing words in a sequence of 2^21 four-  
#  letter words,  (2^21+3 "keystrokes"), is again 141909, with   
#  sigma = 295.  The mean is based on theory; sigma comes from   
#  extensive simulation.                                         
# 
#  Note 2^21 = 2097152, tsamples cannot be varied.
#==================================================================
#                        Run Details
# Random number generator tested: mt19937_1999
# Samples per test pvalue = 2097152 (test default is 2097152)
# P-values in final KS test = 100 (test default is 100)
#==================================================================
#                Histogram of p-values
# Counting histogram bins, binscale = 0.100000
#     20|    |    |    |    |    |    |    |    |    |    |
#       |    |    |    |    |    |    |    |    |    |    |
#     18|    |    |    |    |    |    |    |    |    |    |
#       |    |    |    |    |    |    |    |    |    |    |
#     16|    |    |    |    |    |    |    |    |    |    |
#       |    |    |    |    |    |    |    |    |    |    |
#     14|    |    |    |****|    |    |    |    |    |    |
#       |    |    |    |****|    |    |****|    |    |    |
#     12|    |    |    |****|    |    |****|    |    |    |
#       |****|    |    |****|****|    |****|    |    |    |
#     10|****|    |    |****|****|****|****|    |    |    |
#       |****|    |****|****|****|****|****|****|****|****|
#      8|****|    |****|****|****|****|****|****|****|****|
#       |****|    |****|****|****|****|****|****|****|****|
#      6|****|    |****|****|****|****|****|****|****|****|
#       |****|****|****|****|****|****|****|****|****|****|
#      4|****|****|****|****|****|****|****|****|****|****|
#       |****|****|****|****|****|****|****|****|****|****|
#      2|****|****|****|****|****|****|****|****|****|****|
#       |****|****|****|****|****|****|****|****|****|****|
#       |--------------------------------------------------
#       | 0.1| 0.2| 0.3| 0.4| 0.5| 0.6| 0.7| 0.8| 0.9| 1.0|
#==================================================================
#                          Results
Kuiper KS: p = 0.560892
Assessment: PASSED at > 5% for Diehard OQSO Test

#==================================================================
#                    Diehard DNA Test.
# 
#   The DNA test considers an alphabet of 4 letters::  C,G,A,T,
# determined by two designated bits in the sequence of random   
# integers being tested.  It considers 10-letter words, so that 
# as in OPSO and OQSO, there are 2^20 possible words, and the   
# mean number of missing words from a string of 2^21  (over-    
# lapping)  10-letter  words (2^21+9 "keystrokes") is 141909.   
# The standard deviation sigma=339 was determined as for OQSO   
# by simulation.  (Sigma for OPSO, 290, is the true value (to   
# three places), not determined by simulation.                  
# 
# Note 2^21 = 2097152
# Note also that we don't bother with overlapping keystrokes 
# (and sample more rands -- rands are now cheap). 
#==================================================================
#                        Run Details
# Random number generator tested: mt19937_1999
# Samples per test pvalue = 2097152 (test default is 2097152)
# P-values in final KS test = 100 (test default is 100)
#==================================================================
#                Histogram of p-values
# Counting histogram bins, binscale = 0.100000
#     20|    |    |    |    |    |    |    |    |    |    |
#       |    |    |    |    |    |    |    |    |    |    |
#     18|    |    |    |    |    |    |    |    |    |    |
#       |    |    |****|    |    |    |    |    |    |    |
#     16|    |    |****|    |    |    |    |    |    |    |
#       |    |    |****|    |    |****|    |    |    |    |
#     14|    |    |****|    |    |****|    |    |    |    |
#       |    |    |****|    |    |****|    |    |    |    |
#     12|    |    |****|    |    |****|    |****|****|    |
#       |    |    |****|    |    |****|    |****|****|    |
#     10|    |****|****|****|    |****|    |****|****|    |
#       |    |****|****|****|    |****|    |****|****|    |
#      8|****|****|****|****|    |****|    |****|****|    |
#       |****|****|****|****|****|****|    |****|****|    |
#      6|****|****|****|****|****|****|    |****|****|    |
#       |****|****|****|****|****|****|****|****|****|    |
#      4|****|****|****|****|****|****|****|****|****|****|
#       |****|****|****|****|****|****|****|****|****|****|
#      2|****|****|****|****|****|****|****|****|****|****|
#       |****|****|****|****|****|****|****|****|****|****|
#       |--------------------------------------------------
#       | 0.1| 0.2| 0.3| 0.4| 0.5| 0.6| 0.7| 0.8| 0.9| 1.0|
#==================================================================
#                          Results
Kuiper KS: p = 0.713988
Assessment: PASSED at > 5% for Diehard DNA Test

#==================================================================
#          Diehard Count the 1s (stream) (modified) Test.
# Consider the file under test as a stream of bytes (four per   
# 32 bit integer).  Each byte can contain from 0 to 8 1's,      
# with probabilities 1,8,28,56,70,56,28,8,1 over 256.  Now let  
# the stream of bytes provide a string of overlapping  5-letter 
# words, each "letter" taking values A,B,C,D,E. The letters are 
# determined by the number of 1's in a byte::  0,1,or 2 yield A,
# 3 yields B, 4 yields C, 5 yields D and 6,7 or 8 yield E. Thus 
# we have a monkey at a typewriter hitting five keys with vari- 
# ous probabilities (37,56,70,56,37 over 256).  There are 5^5   
# possible 5-letter words, and from a string of 256,000 (over-  
# lapping) 5-letter words, counts are made on the frequencies   
# for each word.   The quadratic form in the weak inverse of    
# the covariance matrix of the cell counts provides a chisquare 
# test::  Q5-Q4, the difference of the naive Pearson sums of    
# (OBS-EXP)^2/EXP on counts for 5- and 4-letter cell counts.    
#==================================================================
#                        Run Details
# Random number generator tested: mt19937_1999
# Samples per test pvalue = 256000 (test default is 256000)
# P-values in final KS test = 100 (test default is 100)
#==================================================================
#                Histogram of p-values
# Counting histogram bins, binscale = 0.100000
#     20|    |    |    |    |    |    |    |    |    |    |
#       |    |    |    |    |    |    |    |    |    |    |
#     18|    |    |    |    |    |    |    |    |    |    |
#       |    |    |    |    |    |    |    |    |    |    |
#     16|    |    |    |    |    |    |    |    |    |    |
#       |    |    |    |    |    |    |    |    |    |    |
#     14|    |    |    |    |    |    |    |    |****|    |
#       |    |    |    |****|    |    |    |    |****|    |
#     12|    |    |    |****|    |    |****|    |****|    |
#       |    |    |    |****|    |    |****|    |****|****|
#     10|    |****|****|****|    |****|****|    |****|****|
#       |    |****|****|****|****|****|****|    |****|****|
#      8|    |****|****|****|****|****|****|    |****|****|
#       |****|****|****|****|****|****|****|    |****|****|
#      6|****|****|****|****|****|****|****|    |****|****|
#       |****|****|****|****|****|****|****|    |****|****|
#      4|****|****|****|****|****|****|****|****|****|****|
#       |****|****|****|****|****|****|****|****|****|****|
#      2|****|****|****|****|****|****|****|****|****|****|
#       |****|****|****|****|****|****|****|****|****|****|
#       |--------------------------------------------------
#       | 0.1| 0.2| 0.3| 0.4| 0.5| 0.6| 0.7| 0.8| 0.9| 1.0|
#==================================================================
#                          Results
Kuiper KS: p = 0.875724
Assessment: PASSED at > 5% for Diehard Count the 1s (stream) Test

#==================================================================
#         Diehard Count the 1s Test (byte) (modified).
#     This is the COUNT-THE-1's TEST for specific bytes.        
# Consider the file under test as a stream of 32-bit integers.  
# From each integer, a specific byte is chosen , say the left-  
# most::  bits 1 to 8. Each byte can contain from 0 to 8 1's,   
# with probabilitie 1,8,28,56,70,56,28,8,1 over 256.  Now let   
# the specified bytes from successive integers provide a string 
# of (overlapping) 5-letter words, each "letter" taking values  
# A,B,C,D,E. The letters are determined  by the number of 1's,  
# in that byte::  0,1,or 2 ---> A, 3 ---> B, 4 ---> C, 5 ---> D,
# and  6,7 or 8 ---> E.  Thus we have a monkey at a typewriter  
# hitting five keys with with various probabilities::  37,56,70,
# 56,37 over 256. There are 5^5 possible 5-letter words, and    
# from a string of 256,000 (overlapping) 5-letter words, counts 
# are made on the frequencies for each word. The quadratic form 
# in the weak inverse of the covariance matrix of the cell      
# counts provides a chisquare test::  Q5-Q4, the difference of  
# the naive Pearson  sums of (OBS-EXP)^2/EXP on counts for 5-   
# and 4-letter cell counts.                                     
# 
# Note: We actually cycle samples over all 0-31 bit offsets, so 
# that if there is a problem with any particular offset it has 
# a chance of being observed.  One can imagine problems with odd 
# offsets but not even, for example, or only with the offset 7.
# tsamples and psamples can be freely varied, but you'll likely 
# need tsamples >> 100,000 to have enough to get a reliable kstest 
# result. 
#==================================================================
#                        Run Details
# Random number generator tested: mt19937_1999
# Samples per test pvalue = 256000 (test default is 256000)
# P-values in final KS test = 100 (test default is 100)
#==================================================================
#                Histogram of p-values
# Counting histogram bins, binscale = 0.100000
#     20|    |    |    |    |    |    |    |    |    |    |
#       |    |    |    |    |    |    |    |    |    |    |
#     18|    |    |    |    |    |    |    |    |    |    |
#       |    |    |    |    |    |    |    |****|    |    |
#     16|    |    |    |    |    |    |    |****|    |    |
#       |    |****|    |    |    |    |    |****|    |    |
#     14|    |****|****|    |    |    |    |****|    |    |
#       |    |****|****|    |    |    |    |****|    |    |
#     12|    |****|****|    |    |    |    |****|    |    |
#       |    |****|****|    |    |****|    |****|    |    |
#     10|    |****|****|    |    |****|    |****|    |    |
#       |    |****|****|    |    |****|****|****|    |    |
#      8|    |****|****|    |    |****|****|****|    |    |
#       |****|****|****|****|****|****|****|****|****|    |
#      6|****|****|****|****|****|****|****|****|****|****|
#       |****|****|****|****|****|****|****|****|****|****|
#      4|****|****|****|****|****|****|****|****|****|****|
#       |****|****|****|****|****|****|****|****|****|****|
#      2|****|****|****|****|****|****|****|****|****|****|
#       |****|****|****|****|****|****|****|****|****|****|
#       |--------------------------------------------------
#       | 0.1| 0.2| 0.3| 0.4| 0.5| 0.6| 0.7| 0.8| 0.9| 1.0|
#==================================================================
#                          Results
Kuiper KS: p = 0.595865
Assessment: PASSED at > 5% for Diehard Count the 1s Test (byte)

#==================================================================
#             Diehard Parking Lot Test (modified).
# This tests the distribution of attempts to randomly park a
# square car of length 1 on a 100x100 parking lot without
# crashing.  We plot n (number of attempts) versus k (number of
# attempts that didn't "crash" because the car squares 
# overlapped and compare to the expected result from a perfectly
# random set of parking coordinates.  This is, alas, not really
# known on theoretical grounds so instead we compare to n=12,000
# where k should average 3523 with sigma 21.9 and is very close
# to normally distributed.  Thus (k-3523)/21.9 is a standard
# normal variable, which converted to a uniform p-value, provides
# input to a KS test with a default 100 samples.
#==================================================================
#                        Run Details
# Random number generator tested: mt19937_1999
# Samples per test pvalue = 0 (test default is 0)
# P-values in final KS test = 100 (test default is 100)
#==================================================================
#                Histogram of p-values
# Counting histogram bins, binscale = 0.100000
#     20|    |    |    |    |    |    |    |    |    |    |
#       |    |    |    |    |    |    |    |    |    |    |
#     18|    |    |    |    |    |    |    |    |    |    |
#       |    |    |    |    |    |    |    |    |    |    |
#     16|    |    |    |    |    |    |    |    |    |    |
#       |    |    |    |    |    |    |****|    |    |    |
#     14|    |    |    |    |****|    |****|    |****|    |
#       |    |    |    |    |****|    |****|    |****|    |
#     12|    |    |    |    |****|    |****|    |****|    |
#       |    |    |    |    |****|    |****|    |****|    |
#     10|****|    |    |    |****|    |****|****|****|    |
#       |****|    |    |    |****|****|****|****|****|****|
#      8|****|****|    |    |****|****|****|****|****|****|
#       |****|****|    |****|****|****|****|****|****|****|
#      6|****|****|    |****|****|****|****|****|****|****|
#       |****|****|    |****|****|****|****|****|****|****|
#      4|****|****|****|****|****|****|****|****|****|****|
#       |****|****|****|****|****|****|****|****|****|****|
#      2|****|****|****|****|****|****|****|****|****|****|
#       |****|****|****|****|****|****|****|****|****|****|
#       |--------------------------------------------------
#       | 0.1| 0.2| 0.3| 0.4| 0.5| 0.6| 0.7| 0.8| 0.9| 1.0|
#==================================================================
#                          Results
Kuiper KS: p = 0.172167
Assessment: PASSED at > 5% for Diehard Parking Lot Test
#==================================================================
#         Diehard Minimum Distance (2d Circle) Test 
# It does this 100 times::   choose n=8000 random points in a   
# square of side 10000.  Find d, the minimum distance between   
# the (n^2-n)/2 pairs of points.  If the points are truly inde- 
# pendent uniform, then d^2, the square of the minimum distance 
# should be (very close to) exponentially distributed with mean 
# .995 .  Thus 1-exp(-d^2/.995) should be uniform on [0,1) and  
# a KSTEST on the resulting 100 values serves as a test of uni- 
# formity for random points in the square. Test numbers=0 mod 5 
# are printed but the KSTEST is based on the full set of 100    
# random choices of 8000 points in the 10000x10000 square.      
#
# This test uses a fixed number of samples -- tsamples is ignored.
# It also uses the default value of 100 psamples in the final
# KS test, for once agreeing precisely with Diehard.
#==================================================================
#                        Run Details
# Random number generator tested: mt19937_1999
# Samples per test pvalue = 8000 (test default is 8000)
# P-values in final KS test = 100 (test default is 100)
#==================================================================
#                Histogram of p-values
# Counting histogram bins, binscale = 0.100000
#     20|    |    |    |    |    |    |    |    |    |    |
#       |    |    |    |    |    |    |    |    |    |    |
#     18|    |    |    |    |    |    |    |    |    |    |
#       |    |    |    |    |    |****|    |    |    |    |
#     16|    |    |    |    |    |****|    |    |    |    |
#       |    |    |    |    |****|****|    |    |    |    |
#     14|    |    |    |    |****|****|    |    |    |    |
#       |    |****|    |    |****|****|    |    |    |    |
#     12|    |****|    |    |****|****|    |    |    |    |
#       |    |****|    |****|****|****|    |    |    |    |
#     10|****|****|    |****|****|****|    |    |    |    |
#       |****|****|    |****|****|****|    |    |    |    |
#      8|****|****|    |****|****|****|    |    |    |    |
#       |****|****|****|****|****|****|****|****|****|    |
#      6|****|****|****|****|****|****|****|****|****|****|
#       |****|****|****|****|****|****|****|****|****|****|
#      4|****|****|****|****|****|****|****|****|****|****|
#       |****|****|****|****|****|****|****|****|****|****|
#      2|****|****|****|****|****|****|****|****|****|****|
#       |****|****|****|****|****|****|****|****|****|****|
#       |--------------------------------------------------
#       | 0.1| 0.2| 0.3| 0.4| 0.5| 0.6| 0.7| 0.8| 0.9| 1.0|
#==================================================================
#                          Results
Kuiper KS: p = 0.154149
Assessment: PASSED at > 5% for Diehard Minimum Distance (2d Circle) Test

#==================================================================
#          Diehard 3d Sphere (Minimum Distance) Test
# Choose  4000 random points in a cube of edge 1000.  At each   
# point, center a sphere large enough to reach the next closest 
# point. Then the volume of the smallest such sphere is (very   
# close to) exponentially distributed with mean 120pi/3.  Thus  
# the radius cubed is exponential with mean 30. (The mean is    
# obtained by extensive simulation).  The 3DSPHERES test gener- 
# ates 4000 such spheres 20 times.  Each min radius cubed leads 
# to a uniform variable by means of 1-exp(-r^3/30.), then a     
#  KSTEST is done on the 20 p-values.                           
#
# This test ignores tsamples, and runs the usual default 100
# psamples to use in the final KS test.
#==================================================================#                        Run Details
# Random number generator tested: mt19937_1999
# Samples per test pvalue = 4000 (test default is 4000)
# P-values in final KS test = 100 (test default is 100)
#==================================================================
#                Histogram of p-values
# Counting histogram bins, binscale = 0.100000
#     20|    |    |    |    |    |    |    |    |    |    |
#       |    |    |    |    |    |    |    |    |    |    |
#     18|    |    |    |    |    |    |    |    |    |    |
#       |    |    |    |    |    |    |    |    |    |    |
#     16|    |    |    |    |    |    |    |    |    |    |
#       |    |    |    |    |    |    |    |    |    |    |
#     14|    |    |    |****|    |    |    |    |    |    |
#       |    |****|    |****|****|    |    |    |    |    |
#     12|    |****|    |****|****|****|    |    |****|    |
#       |    |****|    |****|****|****|    |    |****|****|
#     10|    |****|    |****|****|****|    |    |****|****|
#       |    |****|    |****|****|****|    |    |****|****|
#      8|    |****|    |****|****|****|    |****|****|****|
#       |****|****|    |****|****|****|    |****|****|****|
#      6|****|****|****|****|****|****|    |****|****|****|
#       |****|****|****|****|****|****|    |****|****|****|
#      4|****|****|****|****|****|****|****|****|****|****|
#       |****|****|****|****|****|****|****|****|****|****|
#      2|****|****|****|****|****|****|****|****|****|****|
#       |****|****|****|****|****|****|****|****|****|****|
#       |--------------------------------------------------
#       | 0.1| 0.2| 0.3| 0.4| 0.5| 0.6| 0.7| 0.8| 0.9| 1.0|
#==================================================================
#                          Results
Kuiper KS: p = 0.291159
Assessment: PASSED at > 5% for Diehard 3d Sphere (Minimum Distance) Test

#==================================================================
#                  Diehard Squeeze Test.
#  Random integers are floated to get uniforms on [0,1). Start- 
#  ing with k=2^31=2147483647, the test finds j, the number of  
#  iterations necessary to reduce k to 1, using the reduction   
#  k=ceiling(k*U), with U provided by floating integers from    
#  the file being tested.  Such j's are found 100,000 times,    
#  then counts for the number of times j was <=6,7,...,47,>=48  
#  are used to provide a chi-square test for cell frequencies.  
#==================================================================
#                        Run Details
# Random number generator tested: mt19937_1999
# Samples per test pvalue = 100000 (test default is 100000)
# P-values in final KS test = 100 (test default is 100)
#==================================================================
#                Histogram of p-values
# Counting histogram bins, binscale = 0.100000
#     20|    |    |    |    |    |    |    |    |    |    |
#       |    |    |    |    |    |    |    |    |    |    |
#     18|    |    |    |    |    |    |    |    |    |    |
#       |    |    |    |    |    |    |    |    |    |    |
#     16|    |    |    |    |    |    |    |    |    |    |
#       |    |    |    |    |    |    |****|    |    |    |
#     14|    |    |    |    |    |    |****|    |    |    |
#       |    |    |    |****|    |****|****|    |    |    |
#     12|****|    |    |****|    |****|****|    |    |    |
#       |****|    |    |****|****|****|****|    |    |****|
#     10|****|    |    |****|****|****|****|    |    |****|
#       |****|    |    |****|****|****|****|    |    |****|
#      8|****|    |    |****|****|****|****|    |****|****|
#       |****|    |****|****|****|****|****|    |****|****|
#      6|****|    |****|****|****|****|****|    |****|****|
#       |****|****|****|****|****|****|****|****|****|****|
#      4|****|****|****|****|****|****|****|****|****|****|
#       |****|****|****|****|****|****|****|****|****|****|
#      2|****|****|****|****|****|****|****|****|****|****|
#       |****|****|****|****|****|****|****|****|****|****|
#       |--------------------------------------------------
#       | 0.1| 0.2| 0.3| 0.4| 0.5| 0.6| 0.7| 0.8| 0.9| 1.0|
#==================================================================
#                          Results
Kuiper KS: p = 0.592784
Assessment: PASSED at > 5% for Example Dieharder Test

#==================================================================
#                  Diehard Sums Test
# Integers are floated to get a sequence U(1),U(2),... of uni-  
# form [0,1) variables.  Then overlapping sums,                 
#   S(1)=U(1)+...+U(100), S2=U(2)+...+U(101),... are formed.    
# The S's are virtually normal with a certain covariance mat-   
# rix.  A linear transformation of the S's converts them to a   
# sequence of independent standard normals, which are converted 
# to uniform variables for a KSTEST. The  p-values from ten     
# KSTESTs are given still another KSTEST.                       
#
# Note well:  -O causes the old diehard version to be run (more or
# less).  Omitting it causes non-overlapping sums to be used and 
# directly tests the overall balance of uniform rands.
#==================================================================
#                        Run Details
# Random number generator tested: mt19937_1999
# Samples per test pvalue = 100 (test default is 100)
# P-values in final KS test = 100 (test default is 100)
#==================================================================
#                Histogram of p-values
# Counting histogram bins, binscale = 0.100000
#     20|    |    |    |    |    |    |    |    |    |    |
#       |    |    |    |    |    |    |    |    |    |****|
#     18|    |    |    |    |    |    |    |    |    |****|
#       |    |    |    |    |    |    |    |    |    |****|
#     16|    |    |    |    |    |    |    |****|    |****|
#       |    |    |    |    |    |    |    |****|    |****|
#     14|    |    |    |    |    |    |****|****|    |****|
#       |    |    |    |    |    |    |****|****|    |****|
#     12|    |    |    |    |    |    |****|****|    |****|
#       |    |    |    |    |    |    |****|****|    |****|
#     10|    |    |    |****|    |    |****|****|    |****|
#       |    |    |    |****|****|****|****|****|****|****|
#      8|    |    |    |****|****|****|****|****|****|****|
#       |    |    |    |****|****|****|****|****|****|****|
#      6|****|    |    |****|****|****|****|****|****|****|
#       |****|    |****|****|****|****|****|****|****|****|
#      4|****|    |****|****|****|****|****|****|****|****|
#       |****|****|****|****|****|****|****|****|****|****|
#      2|****|****|****|****|****|****|****|****|****|****|
#       |****|****|****|****|****|****|****|****|****|****|
#       |--------------------------------------------------
#       | 0.1| 0.2| 0.3| 0.4| 0.5| 0.6| 0.7| 0.8| 0.9| 1.0|
#==================================================================
#                          Results
Kuiper KS: p = 0.002346
Assessment: POOR at < 1% for Diehard Sums Test
Recommendation:  Repeat test to verify failure.

#==================================================================
#                    Diehard Runs Test
#  This is the RUNS test.  It counts runs up, and runs down, 
# in a sequence of uniform [0,1) variables, obtained by float-  
# ing the 32-bit integers in the specified file. This example   
# shows how runs are counted:  .123,.357,.789,.425,.224,.416,.95
# contains an up-run of length 3, a down-run of length 2 and an 
# up-run of (at least) 2, depending on the next values.  The    
# covariance matrices for the runs-up and runs-down are well    
# known, leading to chisquare tests for quadratic forms in the  
# weak inverses of the covariance matrices.  Runs are counted   
# for sequences of length 10,000.  This is done ten times. Then 
# repeated.                                                     
#
# In Dieharder sequences of length tsamples = 100000 are used by
# default, and 100 p-values thus generated are used in a final
# KS test.
#==================================================================
#                        Run Details
# Random number generator tested: mt19937_1999
# Samples per test pvalue = 100000 (test default is 100000)
# P-values in final KS test = 100 (test default is 100)
#==================================================================
#                Histogram of p-values
# Counting histogram bins, binscale = 0.100000
#     20|    |    |    |    |    |    |    |    |    |    |
#       |    |    |    |    |    |    |    |    |    |    |
#     18|    |    |    |    |    |****|    |    |    |    |
#       |    |    |    |    |    |****|    |    |    |    |
#     16|    |    |    |    |    |****|    |    |    |    |
#       |    |    |    |    |    |****|    |    |    |    |
#     14|    |    |    |    |    |****|    |    |    |    |
#       |    |    |    |    |    |****|    |    |    |    |
#     12|    |    |    |    |    |****|    |    |    |    |
#       |****|****|****|****|    |****|    |    |    |    |
#     10|****|****|****|****|    |****|    |    |****|    |
#       |****|****|****|****|    |****|    |    |****|    |
#      8|****|****|****|****|    |****|    |    |****|****|
#       |****|****|****|****|****|****|    |****|****|****|
#      6|****|****|****|****|****|****|****|****|****|****|
#       |****|****|****|****|****|****|****|****|****|****|
#      4|****|****|****|****|****|****|****|****|****|****|
#       |****|****|****|****|****|****|****|****|****|****|
#      2|****|****|****|****|****|****|****|****|****|****|
#       |****|****|****|****|****|****|****|****|****|****|
#       |--------------------------------------------------
#       | 0.1| 0.2| 0.3| 0.4| 0.5| 0.6| 0.7| 0.8| 0.9| 1.0|
#==================================================================
#                          Results
Kuiper KS: p = 0.490501
Assessment: PASSED at > 5% for Diehard Runs Test
#==================================================================
#                Histogram of p-values
# Counting histogram bins, binscale = 0.100000
#     20|    |    |    |    |    |    |    |    |    |    |
#       |    |    |    |    |    |    |    |    |    |    |
#     18|    |    |    |    |    |    |    |    |    |    |
#       |    |    |    |    |    |    |    |    |    |    |
#     16|    |    |    |****|    |    |    |    |    |    |
#       |    |    |    |****|    |    |****|    |    |    |
#     14|****|    |    |****|    |    |****|****|    |    |
#       |****|    |    |****|    |    |****|****|    |    |
#     12|****|    |    |****|    |    |****|****|    |    |
#       |****|    |    |****|    |    |****|****|    |    |
#     10|****|    |    |****|    |    |****|****|    |    |
#       |****|****|****|****|    |****|****|****|    |    |
#      8|****|****|****|****|    |****|****|****|    |    |
#       |****|****|****|****|    |****|****|****|    |****|
#      6|****|****|****|****|    |****|****|****|    |****|
#       |****|****|****|****|****|****|****|****|    |****|
#      4|****|****|****|****|****|****|****|****|    |****|
#       |****|****|****|****|****|****|****|****|    |****|
#      2|****|****|****|****|****|****|****|****|****|****|
#       |****|****|****|****|****|****|****|****|****|****|
#       |--------------------------------------------------
#       | 0.1| 0.2| 0.3| 0.4| 0.5| 0.6| 0.7| 0.8| 0.9| 1.0|
#==================================================================
#                          Results
Kuiper KS: p = 0.606576
Assessment: PASSED at > 5% for Diehard Runs Test

#==================================================================
#                   Diehard Craps Test
#  This is the CRAPS TEST. It plays 200,000 games of craps, finds  
#  the number of wins and the number of throws necessary to end    
#  each game.  The number of wins should be (very close to) a      
#  normal with mean 200000p and variance 200000p(1-p), with        
#  p=244/495.  Throws necessary to complete the game can vary      
#  from 1 to infinity, but counts for all>21 are lumped with 21.   
#  A chi-square test is made on the no.-of-throws cell counts.     
#  Each 32-bit integer from the test file provides the value for   
#  the throw of a die, by floating to [0,1), multiplying by 6      
#  and taking 1 plus the integer part of the result.               
#==================================================================
#                        Run Details
# Random number generator tested: mt19937_1999
# Samples per test pvalue = 200000 (test default is 200000)
# P-values in final KS test = 100 (test default is 100)
#==================================================================
#                Histogram of p-values
# Counting histogram bins, binscale = 0.100000
#     20|    |    |    |    |    |    |    |    |    |    |
#       |    |    |    |    |    |    |    |    |    |    |
#     18|    |    |    |    |    |****|    |    |    |    |
#       |    |    |    |    |    |****|    |    |    |    |
#     16|    |    |    |    |    |****|    |    |    |    |
#       |    |    |    |    |    |****|    |    |    |    |
#     14|    |    |****|    |    |****|    |    |    |    |
#       |    |****|****|    |    |****|    |    |    |    |
#     12|    |****|****|    |    |****|    |    |****|    |
#       |    |****|****|    |    |****|    |    |****|    |
#     10|    |****|****|    |    |****|    |    |****|    |
#       |    |****|****|    |    |****|    |****|****|    |
#      8|    |****|****|    |****|****|    |****|****|    |
#       |****|****|****|    |****|****|****|****|****|    |
#      6|****|****|****|****|****|****|****|****|****|****|
#       |****|****|****|****|****|****|****|****|****|****|
#      4|****|****|****|****|****|****|****|****|****|****|
#       |****|****|****|****|****|****|****|****|****|****|
#      2|****|****|****|****|****|****|****|****|****|****|
#       |****|****|****|****|****|****|****|****|****|****|
#       |--------------------------------------------------
#       | 0.1| 0.2| 0.3| 0.4| 0.5| 0.6| 0.7| 0.8| 0.9| 1.0|
#==================================================================
#                          Results
Kuiper KS: p = 0.324327
Assessment: PASSED at > 5% for Diehard(er) Craps Test
#==================================================================
#                Histogram of p-values
# Counting histogram bins, binscale = 0.100000
#     20|    |    |    |    |    |    |    |    |    |    |
#       |    |    |    |    |    |    |    |    |    |    |
#     18|    |    |    |    |    |    |    |    |    |    |
#       |    |    |    |    |    |    |    |    |    |    |
#     16|    |    |    |    |    |    |****|    |    |    |
#       |    |    |    |    |    |    |****|    |    |    |
#     14|    |    |    |    |****|    |****|    |    |    |
#       |    |    |    |    |****|    |****|    |    |    |
#     12|    |    |    |    |****|    |****|****|    |    |
#       |    |    |    |    |****|    |****|****|****|    |
#     10|    |    |    |    |****|    |****|****|****|    |
#       |    |****|    |****|****|****|****|****|****|    |
#      8|    |****|    |****|****|****|****|****|****|****|
#       |****|****|    |****|****|****|****|****|****|****|
#      6|****|****|    |****|****|****|****|****|****|****|
#       |****|****|****|****|****|****|****|****|****|****|
#      4|****|****|****|****|****|****|****|****|****|****|
#       |****|****|****|****|****|****|****|****|****|****|
#      2|****|****|****|****|****|****|****|****|****|****|
#       |****|****|****|****|****|****|****|****|****|****|
#       |--------------------------------------------------
#       | 0.1| 0.2| 0.3| 0.4| 0.5| 0.6| 0.7| 0.8| 0.9| 1.0|
#==================================================================
#                          Results
Kuiper KS: p = 0.212450
Assessment: PASSED at > 5% for Diehard(er) Craps Test
#==================================================================
#                     Marsaglia and Tsang GCD Test
#
# 10^7 tsamples (default) of uint rands u, v are generated and two
# statistics are generated: their greatest common divisor (GCD) (w)
# and the number of steps of Euclid's Method required to find it
# (k).  Two tables of frequencies are thus generated -- one for the
# number of times each value for k in the range 0 to 41 (with counts
# greater than this range lumped in with the endpoints).
# The other table is the frequency of occurrence of each GCD w.
# k is be distributed approximately binomially, but this is useless for
# the purposes of performing a stringent test.  Instead four "good"
# RNGs (gfsr4,mt19937_1999,rndlxs2,taus2) were used to construct a
# simulated table of high precision probabilities for k (a process that
# obviously begs the question as to whether or not THESE generators
# are "good" wrt the test).  At any rate, they produce very similar tables
# and pass the test with each other's tables (and are otherwise very
# different RNGs).  The table of probabilities for the gcd distribution is
# generated dynamically per test (it is easy to compute).  Chisq tests
# on both of these binned distributions yield two p-values per test,
# and 100 (default) p-values of each are accumulated and subjected to
# final KS tests and displayed in a histogram.
#==================================================================
#                        Run Details
# Random number generator tested: mt19937_1999
# Samples per test pvalue = 10000000 (test default is 10000000)
# P-values in final KS test = 100 (test default is 100)
#==================================================================
#                Histogram of p-values
# Counting histogram bins, binscale = 0.100000
#     20|    |    |    |    |    |    |    |    |    |    |
#       |    |    |    |    |    |    |    |    |    |    |
#     18|    |    |    |    |    |    |    |    |    |    |
#       |    |    |    |    |    |    |    |    |    |    |
#     16|    |    |    |    |    |    |    |    |    |    |
#       |    |    |    |****|    |    |    |    |    |    |
#     14|    |    |    |****|    |    |    |****|    |    |
#       |    |    |    |****|    |    |    |****|    |    |
#     12|****|    |    |****|    |    |    |****|    |****|
#       |****|    |    |****|    |    |    |****|    |****|
#     10|****|    |****|****|    |    |    |****|    |****|
#       |****|****|****|****|    |    |    |****|    |****|
#      8|****|****|****|****|    |****|    |****|    |****|
#       |****|****|****|****|****|****|    |****|****|****|
#      6|****|****|****|****|****|****|****|****|****|****|
#       |****|****|****|****|****|****|****|****|****|****|
#      4|****|****|****|****|****|****|****|****|****|****|
#       |****|****|****|****|****|****|****|****|****|****|
#      2|****|****|****|****|****|****|****|****|****|****|
#       |****|****|****|****|****|****|****|****|****|****|
#       |--------------------------------------------------
#       | 0.1| 0.2| 0.3| 0.4| 0.5| 0.6| 0.7| 0.8| 0.9| 1.0|
#==================================================================
#                          Results
Kuiper KS: p = 0.677129
Assessment: PASSED at > 5% for Marsaglia and Tsang GCD Test
#==================================================================
#                Histogram of p-values
# Counting histogram bins, binscale = 0.100000
#     20|    |    |    |    |    |    |    |    |    |    |
#       |    |    |    |    |    |    |    |    |    |    |
#     18|    |    |    |    |    |    |    |    |    |    |
#       |    |    |    |    |    |    |    |    |    |    |
#     16|    |    |    |    |    |    |    |    |    |    |
#       |    |    |    |    |    |    |    |    |    |    |
#     14|    |    |    |    |    |****|    |    |    |****|
#       |    |    |    |    |    |****|    |    |    |****|
#     12|    |    |    |    |    |****|    |    |    |****|
#       |****|****|    |    |    |****|    |****|    |****|
#     10|****|****|    |    |****|****|    |****|    |****|
#       |****|****|****|****|****|****|    |****|****|****|
#      8|****|****|****|****|****|****|    |****|****|****|
#       |****|****|****|****|****|****|    |****|****|****|
#      6|****|****|****|****|****|****|    |****|****|****|
#       |****|****|****|****|****|****|    |****|****|****|
#      4|****|****|****|****|****|****|    |****|****|****|
#       |****|****|****|****|****|****|    |****|****|****|
#      2|****|****|****|****|****|****|****|****|****|****|
#       |****|****|****|****|****|****|****|****|****|****|
#       |--------------------------------------------------
#       | 0.1| 0.2| 0.3| 0.4| 0.5| 0.6| 0.7| 0.8| 0.9| 1.0|
#==================================================================
#                          Results
Kuiper KS: p = 0.835872
Assessment: PASSED at > 5% for Marsaglia and Tsang GCD Test

#==================================================================
#                     STS Monobit Test
# Very simple.  Counts the 1 bits in a long string of random uints.
# Compares to expected number, generates a p-value directly from
# erfc().  Very effective at revealing overtly weak generators;
# Not so good at determining where stronger ones eventually fail.
#==================================================================
#                        Run Details
# Random number generator tested: mt19937_1999
# Samples per test pvalue = 100000 (test default is 100000)
# P-values in final KS test = 100 (test default is 100)
#==================================================================
#                Histogram of p-values
# Counting histogram bins, binscale = 0.100000
#     20|    |    |    |    |    |    |    |    |    |    |
#       |    |    |    |    |    |    |    |    |    |    |
#     18|    |    |    |    |    |    |    |    |    |    |
#       |    |    |    |    |    |    |    |    |    |    |
#     16|    |    |    |    |    |    |    |    |    |    |
#       |    |    |    |    |    |    |    |    |    |    |
#     14|    |    |****|    |    |    |    |    |    |    |
#       |    |    |****|    |    |    |    |    |    |    |
#     12|    |    |****|    |    |    |    |    |    |    |
#       |****|****|****|    |****|    |    |    |****|****|
#     10|****|****|****|    |****|    |    |    |****|****|
#       |****|****|****|****|****|    |    |    |****|****|
#      8|****|****|****|****|****|****|****|    |****|****|
#       |****|****|****|****|****|****|****|    |****|****|
#      6|****|****|****|****|****|****|****|****|****|****|
#       |****|****|****|****|****|****|****|****|****|****|
#      4|****|****|****|****|****|****|****|****|****|****|
#       |****|****|****|****|****|****|****|****|****|****|
#      2|****|****|****|****|****|****|****|****|****|****|
#       |****|****|****|****|****|****|****|****|****|****|
#       |--------------------------------------------------
#       | 0.1| 0.2| 0.3| 0.4| 0.5| 0.6| 0.7| 0.8| 0.9| 1.0|
#==================================================================
#                          Results
Kuiper KS: p = 0.631670
Assessment: PASSED at > 5% for STS Monobit Test

#==================================================================
#                       STS Runs Test
# Counts the total number of 0 runs + total number of 1 runs across
# a sample of bits.  Note that a 0 run must begin with 10 and end
# with 01.  Note that a 1 run must begin with 01 and end with a 10.
# This test, run on a bitstring with cyclic boundary conditions, is
# absolutely equivalent to just counting the 01 + 10 bit pairs.
# It is therefore totally redundant with but not as good as the
# rgb_bitdist() test for 2-tuples, which looks beyond the means to the
# moments, testing an entire histogram  of 00, 01, 10, and 11 counts
# to see if it is binomially distributed with p = 0.25.
#==================================================================
#                        Run Details
# Random number generator tested: mt19937_1999
# Samples per test pvalue = 100000 (test default is 100000)
# P-values in final KS test = 100 (test default is 100)
#==================================================================
#                Histogram of p-values
# Counting histogram bins, binscale = 0.100000
#     20|    |    |    |    |    |    |    |    |    |    |
#       |    |    |    |    |    |    |    |    |    |    |
#     18|****|    |    |    |    |    |    |    |    |****|
#       |****|    |    |    |    |    |    |    |    |****|
#     16|****|    |    |    |    |    |    |    |    |****|
#       |****|    |    |    |    |    |    |    |    |****|
#     14|****|    |    |    |    |    |    |    |    |****|
#       |****|    |****|    |    |    |    |    |    |****|
#     12|****|    |****|    |    |    |    |    |    |****|
#       |****|    |****|    |    |    |    |    |    |****|
#     10|****|    |****|    |    |    |    |    |    |****|
#       |****|    |****|    |    |    |    |    |****|****|
#      8|****|****|****|    |****|****|    |    |****|****|
#       |****|****|****|    |****|****|    |****|****|****|
#      6|****|****|****|****|****|****|    |****|****|****|
#       |****|****|****|****|****|****|****|****|****|****|
#      4|****|****|****|****|****|****|****|****|****|****|
#       |****|****|****|****|****|****|****|****|****|****|
#      2|****|****|****|****|****|****|****|****|****|****|
#       |****|****|****|****|****|****|****|****|****|****|
#       |--------------------------------------------------
#       | 0.1| 0.2| 0.3| 0.4| 0.5| 0.6| 0.7| 0.8| 0.9| 1.0|
#==================================================================
#                          Results
Kuiper KS: p = 0.004476
Assessment: POOR at < 1% for STS Runs Test
Recommendation:  Repeat test to verify failure.

#==================================================================
#                   Example Dieharder Test
#
#                     Lagged Sum Test
# This package contains many very lovely tests.  Very few of them,
# however, test for lagged correlations -- the possibility that
# the random number generator has a bitlevel correlation after
# some period.  Diehard tests, for example, COULD NOT test for this
# sort of thing with only a few million rands to sample from.
# The template test is therefore very simple.  It takes a user-
# specified lag (-x lag) and adds up uniform deviates sampled with
# that lag.  The mean of tsamples samples summed should be
# 0.5*tsamples.  The standard deviation should be sqrt(tsamples/12).
# The experimental values of the sum are thus converted into a
# p-value (using the erf()) and a ks-test applied to psamples of them.
#==================================================================
#                        Run Details
# Random number generator tested: mt19937_1999
# Samples per test pvalue = 100000 (test default is 100000)
# P-values in final KS test = 100 (test default is 100)
# Lag used in Example Dieharder Test test: 0
#==================================================================
#                Histogram of p-values
# Counting histogram bins, binscale = 0.100000
#     20|    |    |    |    |    |    |    |    |    |    |
#       |    |    |    |    |    |    |    |    |    |    |
#     18|    |    |    |    |    |    |    |    |    |    |
#       |    |    |    |    |    |    |    |    |    |    |
#     16|    |    |    |    |    |    |    |    |    |    |
#       |    |    |    |    |    |    |****|    |    |    |
#     14|    |    |    |    |    |    |****|    |    |    |
#       |    |****|    |    |    |    |****|    |    |    |
#     12|****|****|    |    |    |    |****|    |    |    |
#       |****|****|    |    |    |****|****|****|    |    |
#     10|****|****|    |    |    |****|****|****|    |    |
#       |****|****|    |    |    |****|****|****|    |    |
#      8|****|****|****|****|    |****|****|****|    |****|
#       |****|****|****|****|****|****|****|****|****|****|
#      6|****|****|****|****|****|****|****|****|****|****|
#       |****|****|****|****|****|****|****|****|****|****|
#      4|****|****|****|****|****|****|****|****|****|****|
#       |****|****|****|****|****|****|****|****|****|****|
#      2|****|****|****|****|****|****|****|****|****|****|
#       |****|****|****|****|****|****|****|****|****|****|
#       |--------------------------------------------------
#       | 0.1| 0.2| 0.3| 0.4| 0.5| 0.6| 0.7| 0.8| 0.9| 1.0|
#==================================================================
#                          Results
Kuiper KS: p = 0.687589
Assessment: PASSED at > 5% for Example Dieharder Test
