RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-15_17:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.73 26.6798 0.937067
2 to 25 15.76 24.4889 0.893252
3 to 26 15.95 16.3449 0.500468
4 to 27 16.02 21.5610 0.797802
5 to 28 15.82 8.5625 0.047004
6 to 29 15.79 8.9265 0.057460
7 to 30 15.56 21.9693 0.814098
8 to 31 15.67 18.9644 0.669420
9 to 32 15.57 31.1742 0.980981
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.113787
Tough bday spacings test for dh-ranFile-2018-06-15_17:31: 4096 birthdays, year=2^32 days
Table of Expected vs. Observed counts:
Duplicates 0 1 2 3 4 5 6 7 8 9 >=10
Expected 9.2 36.6 73.3 97.7 97.7 78.1 52.1 29.8 14.9 6.6 4.1
Observed 8 28 58 113 97 85 60 24 19 6 2
(O-E)^2/E 0.1 2.0 3.2 2.4 0.0 0.6 1.2 1.1 1.1 0.1 1.0
Birthday Spacings: Sum(O-E)^2/E= 12.929, p= 0.772
RESULTS OF GCD FOR dh-ranFile-2018-06-15_17:31
Euclid's algorithm:
p-value, steps to gcd: 0.827478
p-value, dist. of gcd's: 0.256877
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-15_17:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.942 0.566 0.596 0.189 0.729 0.403 0.274 0.620
Bits 8 to 15---> 0.491 0.479 0.861 0.391 0.854 0.906 0.617 0.666
Bits 16 to 23---> 0.972 0.463 0.903 0.548 0.392 0.085 0.182 0.073
Bits 24 to 31---> 0.232 0.188 0.634 0.649 0.238 0.510 0.440 0.448
KS test for the above 32 p values: 0.403
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-15_17:31,
p-values for 5 runs: 0.0124, 0.5045, 0.7982, 0.5788, 0.0135
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-15_17:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 224 211.4 0.749 0.749
r= 29 5015 5134.0 2.759 3.508
r= 30 23169 23103.0 0.188 3.696
r= 31 11592 11551.5 0.142 3.838
chi-square = 3.838 with df = 3; p-value = 0.720
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-15_17:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 227 211.4 1.148 1.148
r= 30 5031 5134.0 2.067 3.215
r= 31 23232 23103.0 0.720 3.935
r= 32 11510 11551.5 0.149 4.084
chi-square = 4.084 with df = 3; p-value = 0.747
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-15_17:31
b-rank test for bits 1 to 8, p=0.33908
b-rank test for bits 2 to 9, p=0.39624
b-rank test for bits 3 to 10, p=0.33154
b-rank test for bits 4 to 11, p=0.33069
b-rank test for bits 5 to 12, p=0.45575
b-rank test for bits 6 to 13, p=0.01624
b-rank test for bits 7 to 14, p=0.75915
b-rank test for bits 8 to 15, p=0.03397
b-rank test for bits 9 to 16, p=0.32734
b-rank test for bits 10 to 17, p=0.31819
b-rank test for bits 11 to 18, p=0.91286
b-rank test for bits 12 to 19, p=0.84772
b-rank test for bits 13 to 20, p=0.00452
b-rank test for bits 14 to 21, p=0.02565
b-rank test for bits 15 to 22, p=0.09025
b-rank test for bits 16 to 23, p=0.21311
b-rank test for bits 17 to 24, p=0.03477
b-rank test for bits 18 to 25, p=0.98139
b-rank test for bits 19 to 26, p=0.58000
b-rank test for bits 20 to 27, p=0.96694
b-rank test for bits 21 to 28, p=0.32551
b-rank test for bits 22 to 29, p=0.65122
b-rank test for bits 23 to 30, p=0.21655
b-rank test for bits 24 to 31, p=0.60643
b-rank test for bits 25 to 32, p=0.44217
TEST SUMMARY, 25 tests, each on 100,000 random 6x8 matrices
The above should be 25 uniform [0,1] random variables:
The KS test for those 25 supposed UNI's yields p = 0.081035
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-15_17:31
(20 bits/word, 2097152 words 20 bitstreams. No. missing words
should average 141909.33 with sigma=428.00.)
----------------------------------------------------------------
BITSTREAM test results.
Bitstream No. missing words z-score p-value
1 141358 -1.29 0.098846
2 141417 -1.15 0.125009
3 142237 0.77 0.778038
4 140846 -2.48 0.006488
5 141624 -0.67 0.252495
6 142322 0.96 0.832523
7 141965 0.13 0.551745
8 141909 -0.00 0.499692
9 141994 0.20 0.578410
10 141929 0.05 0.518328
11 142144 0.55 0.708255
12 141461 -1.05 0.147435
13 142040 0.31 0.619933
14 141521 -0.91 0.182121
15 142328 0.98 0.836013
16 141680 -0.54 0.296042
17 142106 0.46 0.677066
18 142058 0.35 0.635840
19 141064 -1.98 0.024130
20 142029 0.28 0.610109
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-15_17:31
Bits used No. missing words z-score p-value
23 to 32 141792 -0.4046 0.342891
22 to 31 141376 -1.8391 0.032953
21 to 30 141836 -0.2529 0.400187
20 to 29 142348 1.5127 0.934816
19 to 28 142170 0.8989 0.815637
18 to 27 142149 0.8264 0.795725
17 to 26 142006 0.3333 0.630563
16 to 25 141683 -0.7804 0.217564
15 to 24 141779 -0.4494 0.326567
14 to 23 141765 -0.4977 0.309351
13 to 22 142208 1.0299 0.848471
12 to 21 141860 -0.1701 0.432464
11 to 20 142004 0.3264 0.627957
10 to 19 142092 0.6299 0.735619
9 to 18 141877 -0.1115 0.455617
8 to 17 142088 0.6161 0.731087
7 to 16 141863 -0.1598 0.436536
6 to 15 141910 0.0023 0.500922
5 to 14 141754 -0.5356 0.296110
4 to 13 142009 0.3437 0.634460
3 to 12 142123 0.7368 0.769376
2 to 11 141879 -0.1046 0.458352
1 to 10 142411 1.7299 0.958176
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-15_17:31
Bits used No. missing words z-score p-value
28 to 32 142423 1.7413 0.959181
27 to 31 141922 0.0429 0.517129
26 to 30 141856 -0.1808 0.428270
25 to 29 141629 -0.9503 0.170987
24 to 28 141844 -0.2215 0.412368
23 to 27 141680 -0.7774 0.218464
22 to 26 141886 -0.0791 0.468483
21 to 25 142220 1.0531 0.853857
20 to 24 141558 -1.1909 0.116837
19 to 23 142065 0.5277 0.701145
18 to 22 142075 0.5616 0.712803
17 to 21 141874 -0.1198 0.452336
16 to 20 141674 -0.7977 0.212514
15 to 19 142081 0.5819 0.719694
14 to 18 141773 -0.4621 0.321992
13 to 17 142145 0.7989 0.787820
12 to 16 141738 -0.5808 0.280695
11 to 15 141452 -1.5503 0.060538
10 to 14 141510 -1.3537 0.087922
9 to 13 141718 -0.6486 0.258306
8 to 12 142098 0.6396 0.738770
7 to 11 141832 -0.2621 0.396609
6 to 10 141788 -0.4113 0.340431
5 to 9 141407 -1.7028 0.044301
4 to 8 142145 0.7989 0.787820
3 to 7 142036 0.4294 0.666180
2 to 6 141895 -0.0486 0.480629
1 to 5 141482 -1.4486 0.073728
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-15_17:31
Bits used No. missing words z-score p-value
31 to 32 141693 -0.6381 0.261691
30 to 31 142019 0.3235 0.626846
29 to 30 141799 -0.3255 0.372418
28 to 29 141656 -0.7473 0.227445
27 to 28 141573 -0.9921 0.160569
26 to 27 141576 -0.9833 0.162736
25 to 26 141881 -0.0836 0.466699
24 to 25 141701 -0.6145 0.269428
23 to 24 141463 -1.3166 0.093985
22 to 23 141178 -2.1573 0.015491
21 to 22 141733 -0.5201 0.301480
20 to 21 142131 0.6539 0.743410
19 to 20 142051 0.4179 0.661992
18 to 19 141022 -2.6175 0.004429
17 to 18 141804 -0.3107 0.378011
16 to 17 141226 -2.0157 0.021914
15 to 16 142073 0.4828 0.685382
14 to 15 142015 0.3117 0.622370
13 to 14 141556 -1.0423 0.148643
12 to 13 142722 2.3973 0.991741
11 to 12 142139 0.6775 0.750953
10 to 11 141803 -0.3137 0.376891
9 to 10 141530 -1.1190 0.131577
8 to 9 141972 0.1849 0.573333
7 to 8 142013 0.3058 0.620126
6 to 7 141585 -0.9567 0.169353
5 to 6 142031 0.3589 0.640168
4 to 5 141353 -1.6411 0.050389
3 to 4 141869 -0.1190 0.452651
2 to 3 141295 -1.8122 0.034979
1 to 2 141850 -0.1750 0.430534
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-15_17:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2498.33 -0.024 0.490592
Test results for specific bytes for dh-ranFile-2018-06-15_17:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2450.02 -0.707 0.239858
2 to 9 2510.78 0.152 0.560567
3 to 10 2568.48 0.968 0.833596
4 to 11 2458.52 -0.587 0.278720
5 to 12 2439.98 -0.849 0.197995
6 to 13 2464.99 -0.495 0.310279
7 to 14 2512.18 0.172 0.568357
8 to 15 2620.24 1.700 0.955476
9 to 16 2585.36 1.207 0.886326
10 to 17 2447.53 -0.742 0.229040
11 to 18 2560.26 0.852 0.802939
12 to 19 2575.54 1.068 0.857297
13 to 20 2393.99 -1.499 0.066909
14 to 21 2633.09 1.882 0.970092
15 to 22 2615.05 1.627 0.948131
16 to 23 2568.22 0.965 0.832682
17 to 24 2396.48 -1.464 0.071595
18 to 25 2494.64 -0.076 0.469808
19 to 26 2504.32 0.061 0.524372
20 to 27 2495.68 -0.061 0.475666
21 to 28 2558.82 0.832 0.797269
22 to 29 2467.69 -0.457 0.323849
23 to 30 2421.46 -1.111 0.133340
24 to 31 2515.45 0.219 0.586503
25 to 32 2460.54 -0.558 0.288421
CDPARK for dh-ranFile-2018-06-15_17:31: result of 10 tests
(Of 12000 tries, the average no. of successes should be
3523.0 with sigma=21.9)
No. succeses z-score p-value
3513 -0.4566 0.323972
3556 1.5068 0.934075
3534 0.5023 0.692266
3514 -0.4110 0.340551
3534 0.5023 0.692266
3522 -0.0457 0.481790
3517 -0.2740 0.392053
3524 0.0457 0.518210
3476 -2.1461 0.015932
3520 -0.1370 0.445521
Square side=100, avg. no. parked=3521.00 sample std.=19.31
p-value of the KSTEST for those 10 p-values: 0.674831
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-15_17:31
0.2075,0.4470,0.2372,0.8838,0.7492,0.3490,0.0927,0.3366,0.5429,0.0089,
The KS test for those 10 p-values: 0.377511
The 3DSPHERES test for dh-ranFile-2018-06-15_17:31
sample no r^3 equiv. uni.
1 12.664 0.344344
2 33.502 0.672654
3 18.351 0.457571
4 11.157 0.310572
5 28.218 0.609613
6 32.996 0.667081
7 15.584 0.405164
8 12.534 0.341510
9 56.787 0.849365
10 3.233 0.102152
11 26.785 0.590501
12 4.812 0.148200
13 18.707 0.463966
14 2.532 0.080937
15 13.103 0.353871
16 67.164 0.893415
17 7.067 0.209873
18 40.140 0.737628
19 3.677 0.115360
20 12.824 0.347849
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.378297
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-15_17:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.8 -1.2 0.1 -0.1 0.9 0.7
0.5 -1.0 0.5 -0.6 0.2 -0.0
-0.7 -0.5 0.6 -1.5 -0.1 1.0
-0.5 -0.9 0.0 1.2 0.5 0.9
0.3 0.3 1.5 -1.0 -1.0 -0.7
1.0 -0.1 -1.0 -1.1 1.7 1.5
1.2 -0.7 0.5 -0.1 -0.6 -1.0
-1.1
Chi-square with 42 degrees of freedom:30.915379
z-score=-1.209431, p-value=0.103579
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-15_17:31
Test no p-value
1 0.059529
2 0.142874
3 0.197175
4 0.005239
5 0.206156
6 0.072182
7 0.112672
8 0.927179
9 0.737825
10 0.918650
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.023160
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-15_17:31:
(for k>=2, the prob. of a run of length k is 2*k/(k+1)!)
Length Expected UpRuns (O-E)^2/E DownRuns (O-E)^2/E
2 66666.67 66439 0.78 66534 0.26
3 25000.00 25163 1.06 25232 2.15
4 6666.67 6713 0.32 6597 0.73
5 1388.89 1389 0.00 1377 0.10
6 238.10 256 1.35 226 0.61
7 34.72 35 0.00 25 2.72
8 4.96 4 0.19 8 1.86
p=0.28237 p=0.79276
Number of rngs required: 689139, p-value: 0.803
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-15_17:31
No. of wins: Observed Expected
98636 98585.9
z-score= 0.224, pvalue=0.58872
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66703 66666.7 0.020 0.020
2 37654 37654.3 0.000 0.020
3 26877 26954.7 0.224 0.244
4 19460 19313.5 1.112 1.356
5 13895 13851.4 0.137 1.493
6 9859 9943.5 0.719 2.212
7 7115 7145.0 0.126 2.338
8 5105 5139.1 0.226 2.564
9 3610 3699.9 2.183 4.747
10 2683 2666.3 0.105 4.851
11 1931 1923.3 0.031 4.882
12 1346 1388.7 1.315 6.197
13 1017 1003.7 0.176 6.373
14 704 726.1 0.675 7.048
15 535 525.8 0.160 7.208
16 400 381.2 0.932 8.140
17 290 276.5 0.655 8.795
18 219 200.8 1.644 10.439
19 149 146.0 0.062 10.501
20 105 106.2 0.014 10.515
21 343 287.1 10.878 21.393
Chisq= 21.39 for 20 degrees of freedom, p= 0.62568
SUMMARY of craptest
p-value for no. of wins: 0.588723
p-value for throws/game: 0.625684
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-15_17:31
No. of wins: Observed Expected
98485 98585.9
z-score=-0.451, pvalue=0.32596
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66314 66666.7 1.866 1.866
2 38083 37654.3 4.880 6.746
3 27002 26954.7 0.083 6.829
4 19167 19313.5 1.111 7.940
5 13889 13851.4 0.102 8.041
6 9987 9943.5 0.190 8.231
7 7113 7145.0 0.144 8.375
8 5067 5139.1 1.011 9.386
9 3785 3699.9 1.959 11.345
10 2666 2666.3 0.000 11.345
11 1975 1923.3 1.388 12.733
12 1346 1388.7 1.315 14.048
13 949 1003.7 2.983 17.031
14 731 726.1 0.033 17.063
15 519 525.8 0.089 17.152
16 382 381.2 0.002 17.154
17 268 276.5 0.264 17.418
18 208 200.8 0.256 17.674
19 142 146.0 0.109 17.783
20 115 106.2 0.727 18.509
21 292 287.1 0.083 18.592
Chisq= 18.59 for 20 degrees of freedom, p= 0.45155
SUMMARY of craptest
p-value for no. of wins: 0.325959
p-value for throws/game: 0.451553
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0044,0.0045,0.0052,0.0065,0.0089,0.0124,0.0135,0.0155,0.0159,0.0162,
0.0219,0.0232,0.0241,0.0256,0.0330,0.0340,0.0348,0.0350,0.0443,0.0470,
0.0504,0.0575,0.0595,0.0605,0.0669,0.0716,0.0722,0.0733,0.0737,0.0809,
0.0810,0.0848,0.0879,0.0903,0.0927,0.0940,0.0988,0.1022,0.1036,0.1127,
0.1138,0.1154,0.1168,0.1250,0.1316,0.1333,0.1429,0.1474,0.1482,0.1486,
0.1606,0.1627,0.1694,0.1710,0.1821,0.1823,0.1877,0.1893,0.1972,0.1980,
0.2062,0.2075,0.2099,0.2125,0.2131,0.2166,0.2176,0.2185,0.2274,0.2290,
0.2325,0.2372,0.2376,0.2399,0.2525,0.2569,0.2583,0.2617,0.2694,0.2739,
0.2787,0.2807,0.2824,0.2884,0.2960,0.2961,0.3015,0.3094,0.3103,0.3106,
0.3182,0.3220,0.3238,0.3240,0.3255,0.3260,0.3266,0.3273,0.3307,0.3315,
0.3366,0.3391,0.3404,0.3406,0.3415,0.3429,0.3443,0.3478,0.3490,0.3539,
0.3724,0.3769,0.3775,0.3780,0.3783,0.3907,0.3921,0.3921,0.3962,0.3966,
0.4002,0.4026,0.4033,0.4052,0.4124,0.4283,0.4305,0.4325,0.4365,0.4400,
0.4422,0.4455,0.4470,0.4476,0.4516,0.4523,0.4527,0.4556,0.4557,0.4576,
0.4584,0.4629,0.4640,0.4667,0.4685,0.4698,0.4757,0.4791,0.4806,0.4818,
0.4906,0.4911,0.4997,0.5005,0.5009,0.5045,0.5101,0.5171,0.5182,0.5183,
0.5244,0.5429,0.5476,0.5517,0.5606,0.5655,0.5684,0.5733,0.5784,0.5788,
0.5800,0.5865,0.5887,0.5905,0.5955,0.6064,0.6096,0.6101,0.6169,0.6199,
0.6201,0.6202,0.6224,0.6257,0.6268,0.6280,0.6306,0.6343,0.6345,0.6358,
0.6402,0.6485,0.6512,0.6620,0.6657,0.6662,0.6671,0.6694,0.6727,0.6748,
0.6771,0.6854,0.6923,0.6923,0.7011,0.7083,0.7128,0.7197,0.7205,0.7292,
0.7311,0.7356,0.7376,0.7378,0.7388,0.7434,0.7475,0.7492,0.7510,0.7591,
0.7694,0.7723,0.7780,0.7878,0.7878,0.7928,0.7957,0.7973,0.7978,0.7982,
0.8026,0.8029,0.8141,0.8156,0.8275,0.8325,0.8327,0.8336,0.8360,0.8477,
0.8485,0.8494,0.8538,0.8539,0.8573,0.8609,0.8838,0.8863,0.8933,0.8934,
0.9026,0.9061,0.9129,0.9187,0.9272,0.9341,0.9348,0.9371,0.9423,0.9481,
0.9555,0.9582,0.9592,0.9669,0.9701,0.9716,0.9810,0.9814,0.9917,
Overall p-value after applying KStest on 269 p-values = 0.025497
In response to requests, we have provided a list of all the p-values
produced by the tests you have chosen for this run. The individual
p-values are supposed to be uniform in [0,1), but they are not necessarily
independent. So even though we have applied a KSTEST to the accumulated
p-values, the result is not necessarily---even if your file contains truly
random bits---uniform in [0,1). But it is probably pretty close, so take
that last p-value with a grain of salt. In particular, there may be some
values so close to 0 or 1 that the tests they came from should be applied
several more times, or new, related tests should be undertaken.