RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-07-08_13:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.96 17.1343 0.554699
2 to 25 15.61 21.4492 0.793160
3 to 26 15.46 20.4772 0.749448
4 to 27 15.51 23.4059 0.863502
5 to 28 15.72 17.0437 0.548593
6 to 29 15.56 15.2279 0.420933
7 to 30 15.42 21.0890 0.777664
8 to 31 15.68 14.3907 0.360723
9 to 32 15.53 22.8681 0.846407
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.111381
Tough bday spacings test for dh-ranFile-2018-07-08_13:31: 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 11 34 72 105 110 68 46 35 12 5 2
(O-E)^2/E 0.4 0.2 0.0 0.5 1.6 1.3 0.7 0.9 0.6 0.4 1.0
Birthday Spacings: Sum(O-E)^2/E= 7.636, p= 0.336
RESULTS OF GCD FOR dh-ranFile-2018-07-08_13:31
Euclid's algorithm:
p-value, steps to gcd: 0.418587
p-value, dist. of gcd's: 0.916040
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-07-08_13:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.467 0.824 0.349 0.982 0.525 0.364 0.062 0.166
Bits 8 to 15---> 0.204 0.819 0.128 0.322 0.815 0.378 0.611 0.356
Bits 16 to 23---> 0.365 0.737 0.040 0.433 0.357 0.101 0.840 0.136
Bits 24 to 31---> 0.242 0.293 0.835 0.444 0.646 0.635 0.922 0.275
KS test for the above 32 p values: 0.449
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-07-08_13:31,
p-values for 5 runs: 0.5685, 0.5924, 0.7008, 0.7566, 0.2133
Rank test for binary matrices (31x31) for dh-ranFile-2018-07-08_13:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 230 211.4 1.633 1.633
r= 29 5182 5134.0 0.449 2.082
r= 30 23115 23103.0 0.006 2.088
r= 31 11473 11551.5 0.534 2.622
chi-square = 2.622 with df = 3; p-value = 0.546
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-07-08_13:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 225 211.4 0.873 0.873
r= 30 5159 5134.0 0.122 0.994
r= 31 22930 23103.0 1.296 2.290
r= 32 11686 11551.5 1.565 3.856
chi-square = 3.856 with df = 3; p-value = 0.723
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-07-08_13:31
b-rank test for bits 1 to 8, p=0.45389
b-rank test for bits 2 to 9, p=0.46062
b-rank test for bits 3 to 10, p=0.12927
b-rank test for bits 4 to 11, p=0.93416
b-rank test for bits 5 to 12, p=0.34480
b-rank test for bits 6 to 13, p=0.90476
b-rank test for bits 7 to 14, p=0.86907
b-rank test for bits 8 to 15, p=0.36650
b-rank test for bits 9 to 16, p=0.95198
b-rank test for bits 10 to 17, p=0.30883
b-rank test for bits 11 to 18, p=0.82103
b-rank test for bits 12 to 19, p=0.23525
b-rank test for bits 13 to 20, p=0.23517
b-rank test for bits 14 to 21, p=0.60064
b-rank test for bits 15 to 22, p=0.24901
b-rank test for bits 16 to 23, p=0.37525
b-rank test for bits 17 to 24, p=0.10210
b-rank test for bits 18 to 25, p=0.23103
b-rank test for bits 19 to 26, p=0.40405
b-rank test for bits 20 to 27, p=0.43831
b-rank test for bits 21 to 28, p=0.06670
b-rank test for bits 22 to 29, p=0.32167
b-rank test for bits 23 to 30, p=0.23167
b-rank test for bits 24 to 31, p=0.31105
b-rank test for bits 25 to 32, p=0.61531
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 = 0.199872
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-07-08_13:31
(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 141276 -1.48 0.069471
2 143000 2.55 0.994587
3 141850 -0.14 0.444875
4 141856 -0.12 0.450419
5 141370 -1.26 0.103814
6 140739 -2.73 0.003125
7 141845 -0.15 0.440263
8 141489 -0.98 0.163030
9 141609 -0.70 0.241431
10 142606 1.63 0.948209
11 141699 -0.49 0.311563
12 141640 -0.63 0.264584
13 141383 -1.23 0.109397
14 141613 -0.69 0.244356
15 142510 1.40 0.919756
16 142026 0.27 0.607417
17 141769 -0.33 0.371504
18 142435 1.23 0.890314
19 142048 0.32 0.627029
20 142783 2.04 0.979389
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-07-08_13:31
Bits used No. missing words z-score p-value
23 to 32 142402 1.6989 0.955327
22 to 31 141903 -0.0218 0.491293
21 to 30 141975 0.2264 0.589574
20 to 29 141711 -0.6839 0.247020
19 to 28 141611 -1.0287 0.151805
18 to 27 142223 1.0816 0.860289
17 to 26 142294 1.3264 0.907654
16 to 25 142294 1.3264 0.907654
15 to 24 142254 1.1885 0.882685
14 to 23 142024 0.3954 0.653731
13 to 22 142233 1.1161 0.867811
12 to 21 141885 -0.0839 0.466569
11 to 20 141605 -1.0494 0.146994
10 to 19 141778 -0.4529 0.325324
9 to 18 142032 0.4230 0.663852
8 to 17 142490 2.0023 0.977374
7 to 16 141883 -0.0908 0.463829
6 to 15 141882 -0.0942 0.462459
5 to 14 141595 -1.0839 0.139205
4 to 13 141833 -0.2632 0.396196
3 to 12 141403 -1.7460 0.040408
2 to 11 141904 -0.0184 0.492668
1 to 10 142029 0.4127 0.660070
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-07-08_13:31
Bits used No. missing words z-score p-value
28 to 32 141714 -0.6621 0.253942
27 to 31 141918 0.0294 0.511723
26 to 30 142063 0.5209 0.698787
25 to 29 141403 -1.7164 0.043047
24 to 28 142122 0.7209 0.764519
23 to 27 141541 -1.2486 0.105910
22 to 26 141554 -1.2045 0.114197
21 to 25 141910 0.0023 0.500906
20 to 24 142301 1.3277 0.907861
19 to 23 142181 0.9209 0.821453
18 to 22 141744 -0.5604 0.287589
17 to 21 141787 -0.4147 0.339189
16 to 20 141999 0.3040 0.619423
15 to 19 142120 0.7141 0.762428
14 to 18 142247 1.1446 0.873822
13 to 17 141721 -0.6384 0.261605
12 to 16 142008 0.3345 0.630989
11 to 15 141939 0.1006 0.540057
10 to 14 142099 0.6429 0.739872
9 to 13 141379 -1.7977 0.036110
8 to 12 141605 -1.0316 0.151123
7 to 11 142338 1.4531 0.926905
6 to 10 141616 -0.9943 0.160029
5 to 9 141761 -0.5028 0.307548
4 to 8 141389 -1.7638 0.038880
3 to 7 141930 0.0701 0.527930
2 to 6 142088 0.6057 0.727630
1 to 5 141720 -0.6418 0.260503
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-07-08_13:31
Bits used No. missing words z-score p-value
31 to 32 141504 -1.1957 0.115914
30 to 31 141939 0.0875 0.534872
29 to 30 141593 -0.9331 0.175377
28 to 29 141478 -1.2724 0.101623
27 to 28 142286 1.1111 0.866742
26 to 27 142380 1.3884 0.917493
25 to 26 141982 0.2144 0.584869
24 to 25 142380 1.3884 0.917493
23 to 24 142212 0.8928 0.814026
22 to 23 142297 1.1436 0.873599
21 to 22 141782 -0.3756 0.353605
20 to 21 141645 -0.7797 0.217774
19 to 20 141844 -0.1927 0.423592
18 to 19 141847 -0.1839 0.427060
17 to 18 141998 0.2616 0.603171
16 to 17 142466 1.6421 0.949715
15 to 16 141708 -0.5939 0.276292
14 to 15 141741 -0.4965 0.309754
13 to 14 141753 -0.4612 0.322345
12 to 13 141752 -0.4641 0.321288
11 to 12 141114 -2.3461 0.009485
10 to 11 141621 -0.8505 0.197515
9 to 10 141515 -1.1632 0.122371
8 to 9 142269 1.0610 0.855649
7 to 8 141739 -0.5024 0.307676
6 to 7 141925 0.0462 0.518434
5 to 6 141790 -0.3520 0.362417
4 to 5 141832 -0.2281 0.409780
3 to 4 141850 -0.1750 0.430534
2 to 3 141759 -0.4435 0.328720
1 to 2 141938 0.0846 0.533699
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-07-08_13:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2376.60 -1.745 0.040476
Test results for specific bytes for dh-ranFile-2018-07-08_13:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2513.03 0.184 0.573082
2 to 9 2474.87 -0.355 0.361144
3 to 10 2490.70 -0.132 0.447687
4 to 11 2455.22 -0.633 0.263283
5 to 12 2449.63 -0.712 0.238118
6 to 13 2438.84 -0.865 0.193531
7 to 14 2472.50 -0.389 0.348679
8 to 15 2448.86 -0.723 0.234768
9 to 16 2603.70 1.467 0.928757
10 to 17 2539.02 0.552 0.709481
11 to 18 2614.56 1.620 0.947398
12 to 19 2370.56 -1.831 0.033581
13 to 20 2470.64 -0.415 0.338999
14 to 21 2474.79 -0.356 0.360747
15 to 22 2632.16 1.869 0.969186
16 to 23 2594.84 1.341 0.910069
17 to 24 2427.01 -1.032 0.150991
18 to 25 2500.46 0.007 0.502597
19 to 26 2402.29 -1.382 0.083518
20 to 27 2540.00 0.566 0.714189
21 to 28 2576.98 1.089 0.861859
22 to 29 2413.04 -1.230 0.109394
23 to 30 2417.82 -1.162 0.122580
24 to 31 2534.52 0.488 0.687305
25 to 32 2464.98 -0.495 0.310222
CDPARK for dh-ranFile-2018-07-08_13:31: 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
3503 -0.9132 0.180558
3544 0.9589 0.831196
3558 1.5982 0.944998
3583 2.7397 0.996925
3532 0.4110 0.659449
3542 0.8676 0.807188
3511 -0.5479 0.291865
3568 2.0548 0.980051
3523 0.0000 0.500000
3517 -0.2740 0.392053
Square side=100, avg. no. parked=3538.10 sample std.=24.56
p-value of the KSTEST for those 10 p-values: 0.071784
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-07-08_13:31
0.4879,0.6048,0.8178,0.8036,0.0305,0.1997,0.4240,0.9171,0.5848,0.8247,
The KS test for those 10 p-values: 0.669893
The 3DSPHERES test for dh-ranFile-2018-07-08_13:31
sample no r^3 equiv. uni.
1 19.303 0.474509
2 2.927 0.092944
3 125.165 0.984581
4 47.257 0.793043
5 44.157 0.770509
6 44.696 0.774598
7 12.495 0.340648
8 148.287 0.992866
9 15.020 0.393864
10 14.146 0.375961
11 108.465 0.973097
12 15.265 0.398806
13 63.932 0.881289
14 70.956 0.906068
15 13.154 0.354979
16 6.819 0.203330
17 0.833 0.027397
18 98.353 0.962313
19 42.081 0.754066
20 0.107 0.003555
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.108965
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-07-08_13:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.8 -0.3 -0.8 0.3 -0.4 -0.3
-0.6 -1.0 1.1 -0.1 -0.4 0.2
-0.9 1.5 0.7 0.4 -0.1 0.4
-1.3 0.4 -1.0 -0.1 -1.1 0.5
-0.6 -1.4 0.8 0.4 1.0 0.4
1.1 2.0 1.0 -1.1 -0.1 1.7
1.7 -0.1 1.7 -1.8 -1.3 -1.0
0.8
Chi-square with 42 degrees of freedom:39.571653
z-score=-0.264954, p-value=0.421889
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-07-08_13:31
Test no p-value
1 0.626160
2 0.630649
3 0.685758
4 0.658082
5 0.483509
6 0.013731
7 0.658989
8 0.467502
9 0.071106
10 0.372326
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.344897
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-07-08_13:31:
(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 66556 0.18 66532 0.27
3 25000.00 25119 0.57 25190 1.44
4 6666.67 6632 0.18 6638 0.12
5 1388.89 1418 0.61 1401 0.11
6 238.10 230 0.28 199 6.42
7 34.72 34 0.01 33 0.09
8 4.96 10 5.12 6 0.22
p=0.67469 p=0.80685
Number of rngs required: 689134, p-value: 0.801
RESULTS OF CRAPS TEST for dh-ranFile-2018-07-08_13:31
No. of wins: Observed Expected
98657 98585.9
z-score= 0.318, pvalue=0.62483
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66677 66666.7 0.002 0.002
2 37550 37654.3 0.289 0.291
3 26977 26954.7 0.018 0.309
4 19360 19313.5 0.112 0.421
5 13755 13851.4 0.671 1.092
6 10058 9943.5 1.317 2.410
7 7066 7145.0 0.874 3.284
8 5106 5139.1 0.213 3.497
9 3696 3699.9 0.004 3.501
10 2703 2666.3 0.505 4.006
11 1922 1923.3 0.001 4.007
12 1389 1388.7 0.000 4.007
13 1035 1003.7 0.975 4.982
14 713 726.1 0.238 5.220
15 531 525.8 0.051 5.271
16 415 381.2 3.006 8.277
17 298 276.5 1.665 9.942
18 182 200.8 1.765 11.708
19 135 146.0 0.827 12.534
20 100 106.2 0.364 12.898
21 332 287.1 7.017 19.915
Chisq= 19.92 for 20 degrees of freedom, p= 0.53674
SUMMARY of craptest
p-value for no. of wins: 0.624828
p-value for throws/game: 0.536744
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-07-08_13:31
No. of wins: Observed Expected
98795 98585.9
z-score= 0.935, pvalue=0.82521
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66632 66666.7 0.018 0.018
2 37619 37654.3 0.033 0.051
3 27097 26954.7 0.751 0.802
4 19428 19313.5 0.679 1.481
5 13737 13851.4 0.945 2.426
6 9868 9943.5 0.574 3.000
7 7104 7145.0 0.236 3.236
8 5209 5139.1 0.952 4.187
9 3620 3699.9 1.724 5.911
10 2730 2666.3 1.522 7.433
11 1949 1923.3 0.343 7.776
12 1328 1388.7 2.657 10.433
13 993 1003.7 0.114 10.547
14 758 726.1 1.398 11.945
15 523 525.8 0.015 11.960
16 393 381.2 0.368 12.329
17 284 276.5 0.201 12.530
18 202 200.8 0.007 12.537
19 139 146.0 0.334 12.871
20 118 106.2 1.308 14.178
21 269 287.1 1.143 15.321
Chisq= 15.32 for 20 degrees of freedom, p= 0.24225
SUMMARY of craptest
p-value for no. of wins: 0.825210
p-value for throws/game: 0.242255
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0031,0.0036,0.0095,0.0137,0.0274,0.0305,0.0336,0.0361,0.0389,0.0400,
0.0404,0.0405,0.0430,0.0623,0.0667,0.0695,0.0711,0.0718,0.0835,0.0929,
0.1005,0.1016,0.1021,0.1038,0.1059,0.1090,0.1094,0.1094,0.1114,0.1142,
0.1159,0.1224,0.1226,0.1279,0.1293,0.1359,0.1392,0.1470,0.1510,0.1511,
0.1518,0.1600,0.1630,0.1664,0.1754,0.1806,0.1935,0.1975,0.1997,0.1999,
0.2033,0.2038,0.2133,0.2178,0.2310,0.2317,0.2348,0.2352,0.2352,0.2381,
0.2414,0.2418,0.2423,0.2444,0.2470,0.2490,0.2539,0.2605,0.2616,0.2633,
0.2646,0.2755,0.2763,0.2876,0.2919,0.2932,0.3075,0.3077,0.3088,0.3098,
0.3102,0.3110,0.3116,0.3213,0.3216,0.3217,0.3223,0.3253,0.3287,0.3356,
0.3390,0.3392,0.3406,0.3448,0.3449,0.3487,0.3492,0.3536,0.3550,0.3558,
0.3569,0.3607,0.3607,0.3611,0.3624,0.3640,0.3650,0.3665,0.3715,0.3723,
0.3752,0.3760,0.3780,0.3921,0.3939,0.3962,0.3988,0.4040,0.4098,0.4186,
0.4209,0.4219,0.4236,0.4240,0.4271,0.4305,0.4332,0.4383,0.4403,0.4437,
0.4449,0.4477,0.4485,0.4504,0.4539,0.4606,0.4625,0.4638,0.4666,0.4674,
0.4675,0.4745,0.4835,0.4879,0.4913,0.4927,0.5000,0.5009,0.5026,0.5117,
0.5184,0.5251,0.5279,0.5337,0.5349,0.5367,0.5401,0.5463,0.5486,0.5547,
0.5685,0.5731,0.5848,0.5849,0.5896,0.5924,0.6006,0.6032,0.6048,0.6074,
0.6108,0.6153,0.6194,0.6248,0.6262,0.6270,0.6306,0.6310,0.6350,0.6460,
0.6537,0.6581,0.6590,0.6594,0.6601,0.6639,0.6699,0.6747,0.6858,0.6873,
0.6988,0.7008,0.7095,0.7142,0.7225,0.7276,0.7373,0.7399,0.7494,0.7541,
0.7566,0.7624,0.7645,0.7705,0.7746,0.7777,0.7930,0.7932,0.8010,0.8036,
0.8068,0.8072,0.8140,0.8155,0.8178,0.8194,0.8210,0.8215,0.8243,0.8247,
0.8252,0.8312,0.8353,0.8404,0.8464,0.8556,0.8603,0.8619,0.8635,0.8667,
0.8678,0.8691,0.8736,0.8738,0.8813,0.8827,0.8903,0.9048,0.9061,0.9077,
0.9077,0.9079,0.9101,0.9160,0.9171,0.9175,0.9175,0.9198,0.9220,0.9269,
0.9288,0.9342,0.9450,0.9474,0.9482,0.9497,0.9520,0.9553,0.9623,0.9692,
0.9731,0.9774,0.9794,0.9801,0.9820,0.9846,0.9929,0.9946,0.9969,
Overall p-value after applying KStest on 269 p-values = 0.605200
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.