#================================================================== # 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 = 9375 (test default is 100) # P-values in final KS test = 1 (test default is 100) #================================================================== # WARNING WARNING WARNING! This test rarely requires more than # -t 300 to make nearly any generator fail, and will take a # very long time to run even there. Consider restarting. #================================================================== #================================================================== # 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 # Single test: p = 0.456299 # Assessment: # PASSED at > 2% 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 = 9375 (test default is 1000000) # P-values in final KS test = 1 (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 # Single test: p = 0.279247 # Assessment: # PASSED at > 2% for Diehard OPERM5 Test #================================================================== # 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 = 9375 (test default is 40000) # P-values in final KS test = 1 (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 # Single test: p = 0.689986 # Assessment: # PASSED at > 2% 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 = 9375 (test default is 100000) # P-values in final KS test = 1 (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 # Single test: p = 0.428448 # Assessment: # PASSED at > 2% for Diehard 6x8 Binary Rank Test #================================================================== # 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 = 9375 (test default is 2097152) # P-values in final KS test = 1 (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 # Single test: p = 0.000000 # Assessment: FAILED at < 0.02% for Diehard Bitstream Test #================================================================== # 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 = 9375 (test default is 2097152) # P-values in final KS test = 1 (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 # Single test: p = 0.000000 # Assessment: FAILED at < 0.02% 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 = 9375 (test default is 2097152) # P-values in final KS test = 1 (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 # Single test: p = 0.000000 # Assessment: FAILED at < 0.02% 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 = 9375 (test default is 2097152) # P-values in final KS test = 1 (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 # Single test: p = 0.000000 # Assessment: FAILED at < 0.02% 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 = 9375 (test default is 256000) # P-values in final KS test = 1 (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 # Single test: p = 1.000000 # Assessment: FAILED at < 0.02% 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 = 9375 (test default is 256000) # P-values in final KS test = 1 (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 # Single test: p = 1.000000 # Assessment: FAILED at < 0.02% 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 = 9375 (test default is 0) # P-values in final KS test = 1 (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 # Single test: p = 0.975204 # Assessment: # PASSED at > 2% 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 = 9375 (test default is 8000) # P-values in final KS test = 1 (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 # Single test: p = 0.823237 # Assessment: # PASSED at > 2% 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 = 9375 (test default is 4000) # P-values in final KS test = 1 (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 # Single test: p = 0.930969 # Assessment: # PASSED at > 2% 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 = 9375 (test default is 100000) # P-values in final KS test = 1 (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 # Single test: p = 0.132413 # Assessment: # PASSED at > 2% 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 = 9375 (test default is 100) # P-values in final KS test = 1 (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 # Single test: p = 0.000001 # Assessment: FAILED at < 0.02% for Diehard Sums Test #================================================================== # 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 = 9375 (test default is 100000) # P-values in final KS test = 1 (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 # Single test: p = 0.370482 # Assessment: # PASSED at > 2% 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 # Single test: p = 0.152537 # Assessment: # PASSED at > 2% 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 = 9375 (test default is 200000) # P-values in final KS test = 1 (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 # Single test: p = 0.733726 # Assessment: # PASSED at > 2% 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 # Single test: p = 0.990397 # Assessment: POOR at < 2% for Diehard(er) Craps Test Recommendation: Repeat test to verify failure. #================================================================== # 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 = 9375 (test default is 10000000) # P-values in final KS test = 1 (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 # Single test: p = 0.974280 # Assessment: # PASSED at > 2% 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 # Single test: p = 0.834955 # Assessment: # PASSED at > 2% for Marsaglia and Tsang GCD Test #======================================================================== # 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 = 9375 (test default is 1000000) # P-values in final KS test = 1 (test default is 10) #======================================================================== # rgb_timing() test using the mt19937_1999 generator # Average time per rand = 2.485333e+01 nsec. # Rands per second = 4.023605e+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 = 9375 (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) #================================================================== Setting ntmin = 1 ntmax = 12 #======================================================================== # 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 = 9375 (test default is 100000) # P-values in final KS test = 1 (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 # Single test: p = 0.802387 # Assessment: # PASSED at > 2% 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 = 9375 (test default is 100000) # P-values in final KS test = 1 (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 # Single test: p = 0.360067 # Assessment: # PASSED at > 2% 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 = 9375 (test default is 100000) # P-values in final KS test = 1 (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 # Single test: p = 0.404426 # Assessment: # PASSED at > 2% 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 = 9375 (test default is 100000) # P-values in final KS test = 1 (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 # Single test: p = 0.715202 # Assessment: # PASSED at > 2% 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 = 9375 (test default is 100000) # P-values in final KS test = 1 (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 # Single test: p = 0.940899 # Assessment: # PASSED at > 2% 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 = 9375 (test default is 100000) # P-values in final KS test = 1 (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 # Single test: p = 0.774675 # Assessment: # PASSED at > 2% 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 = 9375 (test default is 100000) # P-values in final KS test = 1 (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 # Single test: p = 0.803763 # Assessment: # PASSED at > 2% 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 = 9375 (test default is 100000) # P-values in final KS test = 1 (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 # Single test: p = 0.426223 # Assessment: # PASSED at > 2% 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 = 9375 (test default is 100000) # P-values in final KS test = 1 (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 # Single test: p = 0.891900 # Assessment: # PASSED at > 2% 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 = 9375 (test default is 100000) # P-values in final KS test = 1 (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 # Single test: p = 0.432580 # Assessment: # PASSED at > 2% 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 = 9375 (test default is 100000) # P-values in final KS test = 1 (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 # Single test: p = 0.006577 # Assessment: POOR at < 2% 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 = 9375 (test default is 100000) # P-values in final KS test = 1 (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 # Single test: p = 0.413983 # Assessment: # PASSED at > 2% for RGB Bit Distribution Test Listing available built-in gsl-linked generators: | Id Test Name | Id Test Name | Id Test Name | ==========================================================================| 0 borosh13 | 1 cmrg | 2 coveyou | 3 fishman18 | 4 fishman20 | 5 fishman2x | 6 gfsr4 | 7 knuthran | 8 knuthran2 | 9 lecuyer21 | 10 minstd | 11 mrg | 12 mt19937 | 13 mt19937_1999 | 14 mt19937_1998 | 15 r250 | 16 ran0 | 17 ran1 | 18 ran2 | 19 ran3 | 20 rand | 21 rand48 | 22 random128-bsd | 23 random128-glibc2 | 24 random128-libc5 | 25 random256-bsd | 26 random256-glibc2 | 27 random256-libc5 | 28 random32-bsd | 29 random32-glibc2 | 30 random32-libc5 | 31 random64-bsd | 32 random64-glibc2 | 33 random64-libc5 | 34 random8-bsd | 35 random8-glibc2 | 36 random8-libc5 | 37 random-bsd | 38 random-glibc2 | 39 random-libc5 | 40 randu | 41 ranf | 42 ranlux | 43 ranlux389 | 44 ranlxd1 | 45 ranlxd2 | 46 ranlxs0 | 47 ranlxs1 | 48 ranlxs2 | 49 ranmar | 50 slatec | 51 taus | 52 taus2 | 53 taus113 | 54 transputer | 55 tt800 | 56 uni | 57 uni32 | 58 vax | 59 waterman14 | 60 zuf | Listing available non-gsl generators: | Id Test Name | Id Test Name | Id Test Name | ==========================================================================| 61 /dev/random | 62 /dev/urandom | 63 empty | 64 file_input | 65 file_input_raw | #================================================================== # 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 = 9375 (test default is 100000) # P-values in final KS test = 1 (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 # Single test: p = 0.145649 # Assessment: # PASSED at > 2% 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 = 9375 (test default is 100000) # P-values in final KS test = 1 (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 # Single test: p = 0.974076 # Assessment: # PASSED at > 2% for STS Runs Test