RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-29_19:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.89 13.0418 0.266616
2 to 25 15.77 24.9582 0.904351
3 to 26 16.03 16.2934 0.496860
4 to 27 15.99 15.6682 0.452530
5 to 28 15.93 33.7435 0.990940
6 to 29 15.76 18.4405 0.638424
7 to 30 15.58 13.7417 0.314707
8 to 31 15.57 16.9847 0.544599
9 to 32 15.76 8.7304 0.051659
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.875922
Tough bday spacings test for dh-ranFile-2018-06-29_19:31: 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 7 42 69 97 92 69 62 37 14 5 6
(O-E)^2/E 0.5 0.8 0.2 0.0 0.3 1.1 1.9 1.8 0.1 0.4 0.9
Birthday Spacings: Sum(O-E)^2/E= 7.954, p= 0.367
RESULTS OF GCD FOR dh-ranFile-2018-06-29_19:31
Euclid's algorithm:
p-value, steps to gcd: 0.713189
p-value, dist. of gcd's: 0.775609
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-29_19:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.172 0.510 0.555 0.712 0.987 0.163 0.876 0.458
Bits 8 to 15---> 0.676 0.064 0.173 0.754 0.910 0.872 0.955 0.089
Bits 16 to 23---> 0.593 0.978 0.925 0.529 0.225 0.386 0.811 0.429
Bits 24 to 31---> 0.292 0.281 0.571 0.837 0.012 0.158 0.606 0.029
KS test for the above 32 p values: 0.139
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-29_19:31,
p-values for 5 runs: 0.8861, 0.8391, 0.9371, 0.1520, 0.6148
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-29_19:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 228 211.4 1.301 1.301
r= 29 5235 5134.0 1.987 3.287
r= 30 23100 23103.0 0.000 3.287
r= 31 11437 11551.5 1.135 4.423
chi-square = 4.423 with df = 3; p-value = 0.781
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-29_19:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 211 211.4 0.001 0.001
r= 30 5283 5134.0 4.324 4.325
r= 31 23182 23103.0 0.270 4.594
r= 32 11324 11551.5 4.481 9.076
chi-square = 9.076 with df = 3; p-value = 0.972
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-29_19:31
b-rank test for bits 1 to 8, p=0.99340
b-rank test for bits 2 to 9, p=0.01493
b-rank test for bits 3 to 10, p=0.38980
b-rank test for bits 4 to 11, p=0.35739
b-rank test for bits 5 to 12, p=0.68382
b-rank test for bits 6 to 13, p=0.40281
b-rank test for bits 7 to 14, p=0.46575
b-rank test for bits 8 to 15, p=0.99120
b-rank test for bits 9 to 16, p=0.19132
b-rank test for bits 10 to 17, p=0.69987
b-rank test for bits 11 to 18, p=0.46465
b-rank test for bits 12 to 19, p=0.09300
b-rank test for bits 13 to 20, p=0.73311
b-rank test for bits 14 to 21, p=0.73562
b-rank test for bits 15 to 22, p=0.25996
b-rank test for bits 16 to 23, p=0.18833
b-rank test for bits 17 to 24, p=0.19420
b-rank test for bits 18 to 25, p=0.81723
b-rank test for bits 19 to 26, p=0.56781
b-rank test for bits 20 to 27, p=0.89002
b-rank test for bits 21 to 28, p=0.73058
b-rank test for bits 22 to 29, p=0.85485
b-rank test for bits 23 to 30, p=0.32334
b-rank test for bits 24 to 31, p=0.46706
b-rank test for bits 25 to 32, p=0.75056
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 = 0.784223
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-29_19:31
(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 141822 -0.20 0.419160
2 141996 0.20 0.580237
3 142306 0.93 0.822985
4 141998 0.21 0.582063
5 141965 0.13 0.551745
6 142261 0.82 0.794364
7 141368 -1.26 0.102973
8 141667 -0.57 0.285632
9 141516 -0.92 0.179049
10 142341 1.01 0.843411
11 142022 0.26 0.603820
12 141739 -0.40 0.345327
13 142072 0.38 0.648053
14 142115 0.48 0.684577
15 141295 -1.44 0.075594
16 141555 -0.83 0.203871
17 142262 0.82 0.795029
18 142004 0.22 0.587528
19 142141 0.54 0.705844
20 141703 -0.48 0.314875
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-29_19:31
Bits used No. missing words z-score p-value
23 to 32 142137 0.7851 0.783793
22 to 31 142299 1.3437 0.910476
21 to 30 142039 0.4471 0.672612
20 to 29 141861 -0.1667 0.433821
19 to 28 142220 1.0713 0.857977
18 to 27 141713 -0.6770 0.249203
17 to 26 142229 1.1023 0.864837
16 to 25 142131 0.7644 0.777679
15 to 24 142262 1.2161 0.888027
14 to 23 141771 -0.4770 0.316681
13 to 22 142590 2.3471 0.990541
12 to 21 142425 1.7782 0.962312
11 to 20 142207 1.0264 0.847660
10 to 19 141823 -0.2977 0.382970
9 to 18 142044 0.4644 0.678812
8 to 17 141751 -0.5460 0.292545
7 to 16 142107 0.6816 0.752261
6 to 15 141711 -0.6839 0.247020
5 to 14 141821 -0.3046 0.380341
4 to 13 141495 -1.4287 0.076542
3 to 12 142237 1.1299 0.870740
2 to 11 141990 0.2782 0.609560
1 to 10 142174 0.9127 0.819288
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-29_19:31
Bits used No. missing words z-score p-value
28 to 32 142121 0.7175 0.763475
27 to 31 141864 -0.1537 0.438939
26 to 30 141840 -0.2350 0.407098
25 to 29 141796 -0.3842 0.350426
24 to 28 141962 0.1785 0.570852
23 to 27 142280 1.2565 0.895534
22 to 26 142432 1.7718 0.961783
21 to 25 142036 0.4294 0.666180
20 to 24 142046 0.4633 0.678421
19 to 23 141686 -0.7571 0.224510
18 to 22 141566 -1.1638 0.122246
17 to 21 142024 0.3887 0.651255
16 to 20 141537 -1.2621 0.103450
15 to 19 142073 0.5548 0.710489
14 to 18 141854 -0.1876 0.425611
13 to 17 142180 0.9175 0.820566
12 to 16 141565 -1.1672 0.121561
11 to 15 141869 -0.1367 0.445629
10 to 14 141855 -0.1842 0.426940
9 to 13 142191 0.9548 0.830164
8 to 12 141740 -0.5740 0.282984
7 to 11 141952 0.1446 0.557504
6 to 10 141776 -0.4520 0.325647
5 to 9 141709 -0.6791 0.248542
4 to 8 141503 -1.3774 0.084196
3 to 7 141767 -0.4825 0.314734
2 to 6 141476 -1.4689 0.070928
1 to 5 142246 1.1413 0.873118
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-29_19:31
Bits used No. missing words z-score p-value
31 to 32 141518 -1.1544 0.124175
30 to 31 142381 1.3914 0.917941
29 to 30 142491 1.7158 0.956904
28 to 29 141587 -0.9508 0.170846
27 to 28 142048 0.4091 0.658751
26 to 27 141819 -0.2665 0.394942
25 to 26 141376 -1.5732 0.057831
24 to 25 141866 -0.1278 0.449147
23 to 24 141774 -0.3992 0.344872
22 to 23 142068 0.4681 0.680127
21 to 22 141544 -1.0777 0.140591
20 to 21 141485 -1.2517 0.105338
19 to 20 142281 1.0964 0.863542
18 to 19 142418 1.5005 0.933258
17 to 18 142392 1.4238 0.922749
16 to 17 141715 -0.5732 0.283240
15 to 16 141122 -2.3225 0.010103
14 to 15 141765 -0.4258 0.335144
13 to 14 141811 -0.2901 0.385886
12 to 13 142042 0.3914 0.652233
11 to 12 142334 1.2527 0.894845
10 to 11 142150 0.7099 0.761130
9 to 10 141357 -1.6293 0.051626
8 to 9 142343 1.2793 0.899598
7 to 8 142119 0.6185 0.731876
6 to 7 141943 0.0993 0.539559
5 to 6 141994 0.2498 0.598615
4 to 5 141637 -0.8033 0.210891
3 to 4 141676 -0.6883 0.245635
2 to 3 141556 -1.0423 0.148643
1 to 2 142115 0.6067 0.727974
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-29_19:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2509.54 0.135 0.553670
Test results for specific bytes for dh-ranFile-2018-06-29_19:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2591.85 1.299 0.903009
2 to 9 2430.91 -0.977 0.164276
3 to 10 2412.21 -1.242 0.107203
4 to 11 2511.62 0.164 0.565264
5 to 12 2507.74 0.109 0.543581
6 to 13 2481.68 -0.259 0.397775
7 to 14 2519.88 0.281 0.610696
8 to 15 2471.02 -0.410 0.340939
9 to 16 2447.77 -0.739 0.230041
10 to 17 2397.33 -1.452 0.073253
11 to 18 2484.58 -0.218 0.413661
12 to 19 2457.83 -0.596 0.275448
13 to 20 2636.04 1.924 0.972813
14 to 21 2544.40 0.628 0.734963
15 to 22 2569.64 0.985 0.837645
16 to 23 2439.63 -0.854 0.196633
17 to 24 2507.86 0.111 0.544274
18 to 25 2468.79 -0.441 0.329478
19 to 26 2407.54 -1.308 0.095513
20 to 27 2523.60 0.334 0.630740
21 to 28 2658.97 2.248 0.987717
22 to 29 2422.98 -1.089 0.138031
23 to 30 2598.49 1.393 0.918167
24 to 31 2400.26 -1.410 0.079200
25 to 32 2436.79 -0.894 0.185674
CDPARK for dh-ranFile-2018-06-29_19:31: 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
3572 2.2374 0.987371
3487 -1.6438 0.050105
3516 -0.3196 0.374623
3518 -0.2283 0.409702
3482 -1.8721 0.030593
3515 -0.3653 0.357445
3536 0.5936 0.723613
3515 -0.3653 0.357445
3518 -0.2283 0.409702
3541 0.8219 0.794438
Square side=100, avg. no. parked=3520.00 sample std.=24.51
p-value of the KSTEST for those 10 p-values: 0.553334
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-29_19:31
0.0406,0.7150,0.1846,0.0098,0.4270,0.1477,0.7853,0.7154,0.4322,0.8924,
The KS test for those 10 p-values: 0.538385
The 3DSPHERES test for dh-ranFile-2018-06-29_19:31
sample no r^3 equiv. uni.
1 3.446 0.108524
2 9.203 0.264185
3 8.002 0.234114
4 57.827 0.854496
5 15.204 0.397573
6 36.168 0.700486
7 1.230 0.040168
8 28.934 0.618818
9 173.859 0.996958
10 0.462 0.015287
11 3.694 0.115849
12 10.119 0.286307
13 2.410 0.077202
14 77.282 0.923928
15 20.498 0.495037
16 16.930 0.431267
17 19.100 0.470953
18 5.841 0.176925
19 6.115 0.184411
20 83.196 0.937537
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.219418
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-29_19:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.8 -1.2 -0.8 -0.7 2.1 -1.0
-0.9 -0.6 0.8 -1.3 -0.3 -0.3
-0.5 1.0 0.0 1.0 -0.2 -1.0
-1.7 0.8 1.9 0.9 0.3 0.3
0.5 -0.6 -0.9 -1.3 -0.8 0.4
1.4 -0.9 -0.7 -1.5 1.0 -1.4
0.0 1.1 -1.6 0.4 -0.6 1.0
0.8
Chi-square with 42 degrees of freedom:42.572324
z-score=0.062446, p-value=0.553656
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-29_19:31
Test no p-value
1 0.923529
2 0.042969
3 0.748146
4 0.006456
5 0.404069
6 0.334651
7 0.133278
8 0.022836
9 0.009931
10 0.047749
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.001101
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-29_19:31:
(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 66993 1.60 66769 0.16
3 25000.00 24654 4.79 24908 0.34
4 6666.67 6648 0.05 6680 0.03
5 1388.89 1431 1.28 1394 0.02
6 238.10 236 0.02 216 2.05
7 34.72 32 0.21 25 2.72
8 4.96 5 0.00 7 0.84
p=0.75798 p=0.59359
Number of rngs required: 688310, p-value: 0.457
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-29_19:31
No. of wins: Observed Expected
98317 98585.9
z-score=-1.202, pvalue=0.11459
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66355 66666.7 1.457 1.457
2 37932 37654.3 2.048 3.505
3 26772 26954.7 1.239 4.744
4 19423 19313.5 0.621 5.365
5 13892 13851.4 0.119 5.484
6 10022 9943.5 0.619 6.103
7 7136 7145.0 0.011 6.114
8 5055 5139.1 1.375 7.490
9 3708 3699.9 0.018 7.507
10 2674 2666.3 0.022 7.530
11 1986 1923.3 2.042 9.572
12 1399 1388.7 0.076 9.648
13 1007 1003.7 0.011 9.658
14 720 726.1 0.052 9.710
15 534 525.8 0.127 9.837
16 385 381.2 0.039 9.876
17 248 276.5 2.945 12.821
18 171 200.8 4.431 17.252
19 154 146.0 0.440 17.692
20 107 106.2 0.006 17.698
21 320 287.1 3.767 21.465
Chisq= 21.46 for 20 degrees of freedom, p= 0.62975
SUMMARY of craptest
p-value for no. of wins: 0.114586
p-value for throws/game: 0.629745
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-29_19:31
No. of wins: Observed Expected
98157 98585.9
z-score=-1.918, pvalue=0.02755
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66521 66666.7 0.318 0.318
2 37622 37654.3 0.028 0.346
3 27096 26954.7 0.740 1.086
4 19319 19313.5 0.002 1.088
5 13826 13851.4 0.047 1.135
6 10065 9943.5 1.484 2.618
7 7083 7145.0 0.538 3.157
8 5162 5139.1 0.102 3.259
9 3787 3699.9 2.052 5.311
10 2599 2666.3 1.699 7.010
11 1898 1923.3 0.334 7.343
12 1408 1388.7 0.267 7.610
13 993 1003.7 0.114 7.725
14 731 726.1 0.033 7.757
15 525 525.8 0.001 7.759
16 380 381.2 0.003 7.762
17 287 276.5 0.396 8.158
18 179 200.8 2.373 10.531
19 159 146.0 1.160 11.691
20 97 106.2 0.800 12.491
21 263 287.1 2.025 14.516
Chisq= 14.52 for 20 degrees of freedom, p= 0.19659
SUMMARY of craptest
p-value for no. of wins: 0.027549
p-value for throws/game: 0.196588
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0011,0.0065,0.0098,0.0099,0.0101,0.0117,0.0149,0.0153,0.0228,0.0275,
0.0288,0.0306,0.0402,0.0406,0.0430,0.0477,0.0501,0.0516,0.0517,0.0578,
0.0643,0.0709,0.0733,0.0756,0.0765,0.0772,0.0792,0.0842,0.0889,0.0930,
0.0955,0.1030,0.1035,0.1053,0.1072,0.1085,0.1146,0.1158,0.1216,0.1222,
0.1242,0.1333,0.1380,0.1392,0.1406,0.1477,0.1486,0.1520,0.1579,0.1632,
0.1643,0.1708,0.1716,0.1733,0.1769,0.1790,0.1844,0.1846,0.1857,0.1883,
0.1913,0.1942,0.1966,0.1966,0.2039,0.2109,0.2194,0.2245,0.2251,0.2300,
0.2341,0.2456,0.2470,0.2485,0.2492,0.2600,0.2642,0.2666,0.2754,0.2809,
0.2830,0.2832,0.2856,0.2863,0.2921,0.2925,0.3147,0.3147,0.3149,0.3167,
0.3233,0.3256,0.3295,0.3347,0.3351,0.3409,0.3449,0.3453,0.3504,0.3574,
0.3574,0.3574,0.3667,0.3746,0.3803,0.3830,0.3859,0.3863,0.3898,0.3949,
0.3976,0.3978,0.4028,0.4041,0.4071,0.4097,0.4097,0.4137,0.4192,0.4256,
0.4269,0.4270,0.4285,0.4313,0.4322,0.4338,0.4389,0.4456,0.4491,0.4525,
0.4574,0.4582,0.4647,0.4657,0.4671,0.4710,0.4950,0.4969,0.5096,0.5292,
0.5384,0.5396,0.5436,0.5443,0.5446,0.5517,0.5533,0.5537,0.5537,0.5554,
0.5575,0.5653,0.5678,0.5708,0.5709,0.5802,0.5821,0.5875,0.5935,0.5936,
0.5986,0.6038,0.6057,0.6096,0.6107,0.6148,0.6188,0.6297,0.6307,0.6384,
0.6481,0.6513,0.6522,0.6588,0.6662,0.6726,0.6764,0.6784,0.6788,0.6801,
0.6838,0.6846,0.6999,0.7005,0.7058,0.7105,0.7117,0.7132,0.7150,0.7154,
0.7236,0.7280,0.7306,0.7319,0.7331,0.7350,0.7356,0.7481,0.7506,0.7523,
0.7545,0.7580,0.7611,0.7635,0.7756,0.7777,0.7807,0.7838,0.7842,0.7853,
0.7944,0.7944,0.7950,0.8107,0.8172,0.8193,0.8206,0.8230,0.8302,0.8365,
0.8376,0.8391,0.8434,0.8477,0.8545,0.8549,0.8580,0.8635,0.8648,0.8707,
0.8717,0.8731,0.8759,0.8765,0.8861,0.8880,0.8900,0.8924,0.8948,0.8955,
0.8996,0.9030,0.9044,0.9096,0.9105,0.9179,0.9182,0.9227,0.9235,0.9239,
0.9247,0.9333,0.9371,0.9375,0.9555,0.9569,0.9618,0.9623,0.9717,0.9728,
0.9778,0.9866,0.9874,0.9877,0.9905,0.9909,0.9912,0.9934,0.9970,
Overall p-value after applying KStest on 269 p-values = 0.686317
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.