RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-17_12:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 16.05 21.7414 0.805129
2 to 25 15.72 11.7552 0.185274
3 to 26 15.79 26.5975 0.935758
4 to 27 15.97 8.8239 0.054374
5 to 28 15.76 22.1984 0.822790
6 to 29 16.01 9.1663 0.065102
7 to 30 15.74 23.8135 0.875409
8 to 31 15.72 9.7838 0.087567
9 to 32 15.69 16.4240 0.505999
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.351017
Tough bday spacings test for dh-ranFile-2018-06-17_12:31: 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 9 33 79 101 92 76 60 24 13 9 4
(O-E)^2/E 0.0 0.4 0.4 0.1 0.3 0.1 1.2 1.1 0.2 0.9 0.0
Birthday Spacings: Sum(O-E)^2/E= 4.730, p= 0.092
RESULTS OF GCD FOR dh-ranFile-2018-06-17_12:31
Euclid's algorithm:
p-value, steps to gcd: 0.530978
p-value, dist. of gcd's: 0.712599
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-17_12:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.522 0.763 0.746 0.179 0.846 0.182 0.017 0.452
Bits 8 to 15---> 0.772 0.724 0.745 0.698 0.760 0.908 0.181 0.931
Bits 16 to 23---> 0.053 0.885 0.209 0.670 0.686 0.202 0.516 0.240
Bits 24 to 31---> 0.417 0.575 0.840 0.119 0.056 0.831 0.318 0.565
KS test for the above 32 p values: 0.330
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-17_12:31,
p-values for 5 runs: 0.6716, 0.1148, 0.4017, 0.8374, 0.2384
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-17_12:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 203 211.4 0.335 0.335
r= 29 5152 5134.0 0.063 0.398
r= 30 23012 23103.0 0.359 0.757
r= 31 11633 11551.5 0.575 1.332
chi-square = 1.332 with df = 3; p-value = 0.278
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-17_12:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 214 211.4 0.032 0.032
r= 30 5136 5134.0 0.001 0.032
r= 31 22952 23103.0 0.988 1.020
r= 32 11698 11551.5 1.857 2.877
chi-square = 2.877 with df = 3; p-value = 0.589
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-17_12:31
b-rank test for bits 1 to 8, p=0.51995
b-rank test for bits 2 to 9, p=0.77296
b-rank test for bits 3 to 10, p=0.72937
b-rank test for bits 4 to 11, p=0.21016
b-rank test for bits 5 to 12, p=0.75559
b-rank test for bits 6 to 13, p=0.42948
b-rank test for bits 7 to 14, p=0.87433
b-rank test for bits 8 to 15, p=0.99676
b-rank test for bits 9 to 16, p=0.98166
b-rank test for bits 10 to 17, p=0.36902
b-rank test for bits 11 to 18, p=0.40914
b-rank test for bits 12 to 19, p=0.94726
b-rank test for bits 13 to 20, p=0.84564
b-rank test for bits 14 to 21, p=0.14181
b-rank test for bits 15 to 22, p=0.05080
b-rank test for bits 16 to 23, p=0.42854
b-rank test for bits 17 to 24, p=0.12694
b-rank test for bits 18 to 25, p=0.25364
b-rank test for bits 19 to 26, p=0.80770
b-rank test for bits 20 to 27, p=0.36846
b-rank test for bits 21 to 28, p=0.35263
b-rank test for bits 22 to 29, p=0.87452
b-rank test for bits 23 to 30, p=0.01467
b-rank test for bits 24 to 31, p=0.30891
b-rank test for bits 25 to 32, p=0.06969
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 = 0.722496
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-17_12:31
(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 141238 -1.57 0.058379
2 142108 0.46 0.678741
3 141902 -0.02 0.493168
4 141780 -0.30 0.381260
5 142314 0.95 0.827796
6 142366 1.07 0.857011
7 141698 -0.49 0.310737
8 141657 -0.59 0.277744
9 141189 -1.68 0.046186
10 142226 0.74 0.770315
11 142647 1.72 0.957603
12 141860 -0.12 0.454121
13 141960 0.12 0.547120
14 141456 -1.06 0.144758
15 141331 -1.35 0.088310
16 142145 0.55 0.709057
17 141240 -1.56 0.058926
18 142341 1.01 0.843411
19 140909 -2.34 0.009714
20 141537 -0.87 0.192169
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-17_12:31
Bits used No. missing words z-score p-value
23 to 32 141820 -0.3080 0.379028
22 to 31 141690 -0.7563 0.224732
21 to 30 141840 -0.2391 0.405526
20 to 29 141948 0.1333 0.553040
19 to 28 141736 -0.5977 0.275024
18 to 27 141398 -1.7632 0.038933
17 to 26 141699 -0.7253 0.234141
16 to 25 141709 -0.6908 0.244848
15 to 24 142485 1.9851 0.976432
14 to 23 142157 0.8540 0.803457
13 to 22 141619 -1.0011 0.158380
12 to 21 141917 0.0264 0.510550
11 to 20 141663 -0.8494 0.197826
10 to 19 141274 -2.1908 0.014233
9 to 18 142001 0.3161 0.624038
8 to 17 142368 1.5816 0.943132
7 to 16 141963 0.1851 0.573413
6 to 15 142022 0.3885 0.651183
5 to 14 142036 0.4368 0.668869
4 to 13 142600 2.3816 0.991382
3 to 12 141840 -0.2391 0.405526
2 to 11 141974 0.2230 0.588232
1 to 10 141805 -0.3598 0.359514
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-17_12:31
Bits used No. missing words z-score p-value
28 to 32 142271 1.2260 0.889901
27 to 31 141914 0.0158 0.506315
26 to 30 141928 0.0633 0.525232
25 to 29 142015 0.3582 0.639905
24 to 28 141442 -1.5842 0.056578
23 to 27 142510 2.0362 0.979133
22 to 26 142078 0.5718 0.716259
21 to 25 142049 0.4735 0.682057
20 to 24 141876 -0.1130 0.455022
19 to 23 141613 -1.0045 0.157567
18 to 22 141972 0.2124 0.584118
17 to 21 142405 1.6802 0.953544
16 to 20 141587 -1.0926 0.137275
15 to 19 141520 -1.3198 0.093457
14 to 18 142235 1.1040 0.865196
13 to 17 142557 2.1955 0.985936
12 to 16 141872 -0.1265 0.449651
11 to 15 142162 0.8565 0.804142
10 to 14 142074 0.5582 0.711647
9 to 13 141698 -0.7164 0.236881
8 to 12 141804 -0.3571 0.360527
7 to 11 141541 -1.2486 0.105910
6 to 10 141846 -0.2147 0.415009
5 to 9 141535 -1.2689 0.102236
4 to 8 142158 0.8429 0.800372
3 to 7 142196 0.9718 0.834416
2 to 6 141945 0.1209 0.548121
1 to 5 141771 -0.4689 0.319565
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-17_12:31
Bits used No. missing words z-score p-value
31 to 32 141690 -0.6470 0.258819
30 to 31 141882 -0.0806 0.467872
29 to 30 141743 -0.4906 0.311837
28 to 29 141989 0.2350 0.592901
27 to 28 141550 -1.0600 0.144579
26 to 27 141949 0.1170 0.546578
25 to 26 141825 -0.2488 0.401773
24 to 25 141645 -0.7797 0.217774
23 to 24 142167 0.7601 0.776399
22 to 23 141824 -0.2517 0.400632
21 to 22 141961 0.1524 0.560572
20 to 21 142236 0.9636 0.832384
19 to 20 141627 -0.8328 0.202470
18 to 19 141910 0.0020 0.500789
17 to 18 142106 0.5801 0.719092
16 to 17 142034 0.3678 0.643473
15 to 16 142135 0.6657 0.747196
14 to 15 141676 -0.6883 0.245635
13 to 14 142690 2.3029 0.989357
12 to 13 141527 -1.1278 0.129699
11 to 12 142175 0.7837 0.783388
10 to 11 141812 -0.2871 0.387014
9 to 10 141671 -0.7030 0.241016
8 to 9 141809 -0.2960 0.383631
7 to 8 141817 -0.2724 0.392673
6 to 7 142505 1.7571 0.960553
5 to 6 141369 -1.5939 0.055480
4 to 5 142422 1.5123 0.934771
3 to 4 142132 0.6568 0.744359
2 to 3 142009 0.2940 0.615626
1 to 2 141643 -0.7856 0.216041
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-17_12:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2562.01 0.877 0.809758
Test results for specific bytes for dh-ranFile-2018-06-17_12:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2281.47 -3.091 0.000999
2 to 9 2457.29 -0.604 0.272897
3 to 10 2547.38 0.670 0.748571
4 to 11 2463.38 -0.518 0.302280
5 to 12 2431.54 -0.968 0.166484
6 to 13 2513.72 0.194 0.576914
7 to 14 2577.08 1.090 0.862167
8 to 15 2488.18 -0.167 0.433621
9 to 16 2511.88 0.168 0.566713
10 to 17 2427.10 -1.031 0.151263
11 to 18 2532.75 0.463 0.678381
12 to 19 2493.20 -0.096 0.461692
13 to 20 2483.62 -0.232 0.408429
14 to 21 2494.52 -0.077 0.469119
15 to 22 2485.25 -0.209 0.417397
16 to 23 2606.36 1.504 0.933729
17 to 24 2417.18 -1.171 0.120746
18 to 25 2501.60 0.023 0.509034
19 to 26 2524.51 0.347 0.635559
20 to 27 2478.29 -0.307 0.379433
21 to 28 2438.93 -0.864 0.193888
22 to 29 2485.63 -0.203 0.419471
23 to 30 2515.93 0.225 0.589120
24 to 31 2427.62 -1.024 0.153007
25 to 32 2564.98 0.919 0.820942
CDPARK for dh-ranFile-2018-06-17_12:31: 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
3515 -0.3653 0.357445
3517 -0.2740 0.392053
3492 -1.4155 0.078457
3525 0.0913 0.536383
3530 0.3196 0.625377
3511 -0.5479 0.291865
3544 0.9589 0.831196
3512 -0.5023 0.307734
3561 1.7352 0.958644
3513 -0.4566 0.323972
Square side=100, avg. no. parked=3522.00 sample std.=18.31
p-value of the KSTEST for those 10 p-values: 0.762310
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-17_12:31
0.0478,0.9539,0.3209,0.6580,0.8655,0.4660,0.8859,0.9019,0.6922,0.8327,
The KS test for those 10 p-values: 0.094783
The 3DSPHERES test for dh-ranFile-2018-06-17_12:31
sample no r^3 equiv. uni.
1 153.305 0.993965
2 29.849 0.630265
3 20.614 0.496987
4 23.200 0.538533
5 6.513 0.195145
6 83.921 0.939030
7 23.360 0.540984
8 11.482 0.318004
9 24.050 0.551421
10 5.684 0.172607
11 11.195 0.311447
12 1.377 0.044847
13 79.419 0.929159
14 0.058 0.001941
15 76.769 0.922615
16 22.364 0.525482
17 13.906 0.370945
18 13.490 0.362158
19 7.858 0.230428
20 47.802 0.796769
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.745641
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-17_12:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
0.6 -0.3 -0.4 1.5 0.9 0.3
2.2 -0.1 0.4 -0.2 -1.0 -0.2
-1.6 -1.2 -0.3 1.0 0.2 1.8
0.2 -0.2 0.8 1.2 -1.3 -0.7
-0.6 -1.1 0.1 0.9 -0.9 0.2
0.7 0.1 -0.4 0.4 -0.6 -0.8
-0.5 0.2 -1.2 -0.7 0.9 -1.0
0.8
Chi-square with 42 degrees of freedom:31.939699
z-score=-1.097669, p-value=0.130152
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-17_12:31
Test no p-value
1 0.041498
2 0.791099
3 0.094248
4 0.109849
5 0.310492
6 0.006386
7 0.327924
8 0.057691
9 0.755305
10 0.011431
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.001612
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-17_12:31:
(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 66613 0.04 66629 0.02
3 25000.00 24983 0.01 25076 0.23
4 6666.67 6799 2.63 6536 2.56
5 1388.89 1348 1.20 1447 2.43
6 238.10 225 0.72 269 4.01
7 34.72 28 1.30 39 0.53
8 4.96 3 0.77 3 0.77
p=0.64861 p=0.89698
Number of rngs required: 690235, p-value: 0.985
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-17_12:31
No. of wins: Observed Expected
98202 98585.9
z-score=-1.717, pvalue=0.04300
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66979 66666.7 1.463 1.463
2 37752 37654.3 0.253 1.717
3 26978 26954.7 0.020 1.737
4 19189 19313.5 0.802 2.539
5 13595 13851.4 4.747 7.286
6 10041 9943.5 0.955 8.241
7 7033 7145.0 1.756 9.997
8 5206 5139.1 0.872 10.869
9 3688 3699.9 0.038 10.907
10 2612 2666.3 1.106 12.013
11 1935 1923.3 0.071 12.084
12 1342 1388.7 1.573 13.657
13 1020 1003.7 0.264 13.921
14 708 726.1 0.453 14.374
15 529 525.8 0.019 14.393
16 404 381.2 1.370 15.763
17 286 276.5 0.324 16.087
18 191 200.8 0.481 16.568
19 148 146.0 0.028 16.596
20 96 106.2 0.982 17.578
21 268 287.1 1.272 18.850
Chisq= 18.85 for 20 degrees of freedom, p= 0.46843
SUMMARY of craptest
p-value for no. of wins: 0.043004
p-value for throws/game: 0.468435
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-17_12:31
No. of wins: Observed Expected
98444 98585.9
z-score=-0.634, pvalue=0.26289
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66338 66666.7 1.620 1.620
2 37599 37654.3 0.081 1.702
3 27145 26954.7 1.343 3.045
4 19562 19313.5 3.198 6.243
5 13939 13851.4 0.554 6.797
6 9903 9943.5 0.165 6.962
7 7258 7145.0 1.786 8.748
8 5071 5139.1 0.902 9.650
9 3645 3699.9 0.814 10.464
10 2627 2666.3 0.579 11.043
11 1900 1923.3 0.283 11.326
12 1371 1388.7 0.227 11.552
13 1025 1003.7 0.451 12.004
14 738 726.1 0.194 12.197
15 528 525.8 0.009 12.206
16 349 381.2 2.712 14.918
17 294 276.5 1.102 16.021
18 184 200.8 1.410 17.431
19 141 146.0 0.170 17.601
20 105 106.2 0.014 17.615
21 278 287.1 0.289 17.905
Chisq= 17.90 for 20 degrees of freedom, p= 0.40630
SUMMARY of craptest
p-value for no. of wins: 0.262886
p-value for throws/game: 0.406304
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0010,0.0016,0.0019,0.0064,0.0097,0.0114,0.0142,0.0147,0.0172,0.0389,
0.0415,0.0430,0.0448,0.0462,0.0478,0.0508,0.0534,0.0544,0.0555,0.0565,
0.0566,0.0577,0.0584,0.0589,0.0651,0.0697,0.0785,0.0876,0.0883,0.0916,
0.0935,0.0942,0.0948,0.1022,0.1059,0.1098,0.1148,0.1187,0.1207,0.1269,
0.1297,0.1302,0.1373,0.1418,0.1446,0.1448,0.1513,0.1530,0.1576,0.1584,
0.1665,0.1726,0.1789,0.1808,0.1816,0.1853,0.1922,0.1939,0.1951,0.1978,
0.2023,0.2025,0.2089,0.2102,0.2160,0.2178,0.2247,0.2304,0.2341,0.2369,
0.2384,0.2397,0.2410,0.2448,0.2456,0.2536,0.2588,0.2629,0.2729,0.2750,
0.2777,0.2784,0.2919,0.3023,0.3077,0.3089,0.3105,0.3107,0.3114,0.3118,
0.3176,0.3180,0.3196,0.3209,0.3240,0.3279,0.3299,0.3510,0.3526,0.3574,
0.3595,0.3605,0.3622,0.3685,0.3690,0.3709,0.3790,0.3794,0.3813,0.3836,
0.3870,0.3921,0.3927,0.4006,0.4017,0.4018,0.4055,0.4055,0.4063,0.4084,
0.4091,0.4150,0.4169,0.4174,0.4195,0.4285,0.4295,0.4336,0.4497,0.4524,
0.4541,0.4550,0.4617,0.4660,0.4679,0.4684,0.4691,0.4932,0.4970,0.5008,
0.5060,0.5063,0.5090,0.5106,0.5164,0.5200,0.5220,0.5252,0.5255,0.5310,
0.5364,0.5385,0.5410,0.5466,0.5471,0.5481,0.5514,0.5530,0.5606,0.5649,
0.5667,0.5734,0.5752,0.5769,0.5841,0.5882,0.5891,0.5891,0.5929,0.6156,
0.6240,0.6254,0.6303,0.6356,0.6399,0.6435,0.6486,0.6512,0.6580,0.6689,
0.6699,0.6716,0.6784,0.6787,0.6821,0.6856,0.6922,0.6981,0.7091,0.7116,
0.7126,0.7163,0.7191,0.7225,0.7245,0.7294,0.7444,0.7447,0.7456,0.7457,
0.7472,0.7486,0.7553,0.7556,0.7604,0.7623,0.7634,0.7703,0.7715,0.7730,
0.7764,0.7834,0.7911,0.7968,0.8004,0.8035,0.8041,0.8051,0.8077,0.8098,
0.8209,0.8228,0.8278,0.8307,0.8312,0.8324,0.8327,0.8344,0.8374,0.8405,
0.8434,0.8456,0.8461,0.8570,0.8622,0.8652,0.8655,0.8743,0.8745,0.8754,
0.8845,0.8859,0.8899,0.8970,0.9019,0.9081,0.9226,0.9292,0.9313,0.9337,
0.9348,0.9358,0.9390,0.9431,0.9473,0.9535,0.9539,0.9576,0.9586,0.9606,
0.9764,0.9791,0.9817,0.9850,0.9859,0.9894,0.9914,0.9940,0.9968,
Overall p-value after applying KStest on 269 p-values = 0.614088
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.