-
Notifications
You must be signed in to change notification settings - Fork 4
/
kiss.out
937 lines (767 loc) · 37.1 KB
/
kiss.out
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
758
759
760
761
762
763
764
765
766
767
768
769
770
771
772
773
774
775
776
777
778
779
780
781
782
783
784
785
786
787
788
789
790
791
792
793
794
795
796
797
798
799
800
801
802
803
804
805
806
807
808
809
810
811
812
813
814
815
816
817
818
819
820
821
822
823
824
825
826
827
828
829
830
831
832
833
834
835
836
837
838
839
840
841
842
843
844
845
846
847
848
849
850
851
852
853
854
855
856
857
858
859
860
861
862
863
864
865
866
867
868
869
870
871
872
873
874
875
876
877
878
879
880
881
882
883
884
885
886
887
888
889
890
891
892
893
894
895
896
897
898
899
900
901
902
903
904
905
906
907
908
909
910
911
912
913
914
915
916
917
918
919
920
921
922
923
924
925
926
927
928
929
930
931
932
933
934
935
936
NOTE
Most of the tests in DIEHARD return a p-value, which
should be uniform on [0,1) if the input file contains truly
independent random bits. Those p-values are obtained by
p=1-F(X), where F is the assumed distribution of the sample
random variable X---often normal. But that assumed F is often just
an asymptotic approximation, for which the fit will be worst
in the tails. Thus you should not be surprised with occasion-
al p-values near 0 or 1, such as .0012 or .9983. When a bit
stream really FAILS BIG, you will get p`s of 0 or 1 to six
or more places. By all means, do not, as a Statistician
might, think that a p < .025 or p> .975 means that the RNG
has "failed the test at the .05 level". Such p`s happen
among the hundreds that DIEHARD produces, even with good RNGs.
So keep in mind that "p happens"
Enter the name of the file to be tested.
This must be a form="unformatted",access="direct" binary
file of about 10-12 million bytes. Enter file name:
HERE ARE YOUR CHOICES:
1 Birthday Spacings
2 Overlapping Permutations
3 Ranks of 31x31 and 32x32 matrices
4 Ranks of 6x8 Matrices
5 Monkey Tests on 20-bit Words
6 Monkey Tests OPSO,OQSO,DNA
7 Count the 1`s in a Stream of Bytes
8 Count the 1`s in Specific Bytes
9 Parking Lot Test
10 Minimum Distance Test
11 Random Spheres Test
12 The Sqeeze Test
13 Overlapping Sums Test
14 Runs Test
15 The Craps Test
16 All of the above
To choose any particular tests, enter corresponding numbers.
Enter 16 for all tests. If you want to perform all but a few
tests, enter corresponding numbers preceded by "-" sign.
Tests are executed in the order they are entered.
Enter your choices.
|-------------------------------------------------------------|
| This is the BIRTHDAY SPACINGS TEST |
|Choose m birthdays in a "year" of n days. List the spacings |
|between the birthdays. Let j be the number of values that |
|occur more than once in that list, then j is asymptotically |
|Poisson distributed with mean m^3/(4n). Experience shows n |
|must be quite large, say n>=2^18, for comparing the results |
|to the Poisson distribution with that mean. This test uses |
|n=2^24 and m=2^10, so that the underlying distribution for j |
|is taken to be Poisson with lambda=2^30/(2^26)=16. A sample |
|of 200 j''s is taken, and a chi-square goodness of fit test |
|provides a p value. The first test uses bits 1-24 (counting |
|from the left) from integers in the specified file. Then the|
|file is closed and reopened, then bits 2-25 of the same inte-|
|gers are used to provide birthdays, and so on to bits 9-32. |
|Each set of bits provides a p-value, and the nine p-values |
|provide a sample for a KSTEST. |
|------------------------------------------------------------ |
RESULTS OF BIRTHDAY SPACINGS TEST FOR kiss.32
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.59 29.9601 0.026634
2 to 25 15.79 17.3824 0.428760
3 to 26 15.72 20.1714 0.265557
4 to 27 15.58 14.1076 0.659469
5 to 28 15.86 21.2774 0.214128
6 to 29 15.74 18.5951 0.352263
7 to 30 15.65 18.1323 0.380544
8 to 31 15.46 29.2788 0.032041
9 to 32 15.45 16.3663 0.498032
degree of freedoms is: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.077945
|-------------------------------------------------------------|
|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 40,000 such random matrices and a chisqu-|
|are test is performed on counts for ranks 31,30,28 and <=28. |
|-------------------------------------------------------------|
Rank test for binary matrices (31x31) from kiss.32
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 233 211.4 2.203 2.203
r=29 5108 5134.0 0.132 2.335
r=30 23234 23103.0 0.742 3.077
r=31 11425 11551.5 1.386 4.463
chi-square = 4.463 with df = 3; p-value = 0.216
--------------------------------------------------------------
|-------------------------------------------------------------|
|This is the BINARY RANK TEST for 32x32 matrices. A random 32x|
|32 binary matrix is formed, each row a 32-bit random integer.|
|The rank is determined. That rank can be from 0 to 32, ranks |
|less than 29 are rare, and their counts are pooled with those|
|for rank 29. Ranks are found for 40,000 such random matrices|
|and a chisquare test is performed on counts for ranks 32,31,|
|30 and <=29. |
|-------------------------------------------------------------|
Rank test for binary matrices (32x32) from kiss.32
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 191 211.4 1.972 1.972
r=30 5062 5134.0 1.010 2.982
r=31 23092 23103.0 0.005 2.987
r=32 11655 11551.5 0.927 3.914
chi-square = 3.914 with df = 3; p-value = 0.271
--------------------------------------------------------------
|-------------------------------------------------------------|
|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 (0,...,4) (pooled together). |
|-------------------------------------------------------------|
Rank test for binary matrices (6x8) from kiss.32
bits 1 to 8
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=4 1009 944.3 4.433 4.433
r=5 21688 21743.9 0.144 4.577
r=6 77303 77311.8 0.001 4.578
chi-square = 4.578 with df = 2; p-value = 0.101
--------------------------------------------------------------
bits 2 to 9
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=4 1027 944.3 7.243 7.243
r=5 21587 21743.9 1.132 8.375
r=6 77386 77311.8 0.071 8.446
chi-square = 8.446 with df = 2; p-value = 0.015
--------------------------------------------------------------
bits 3 to 10
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=4 964 944.3 0.411 0.411
r=5 21581 21743.9 1.220 1.631
r=6 77455 77311.8 0.265 1.897
chi-square = 1.897 with df = 2; p-value = 0.387
--------------------------------------------------------------
bits 4 to 11
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=4 936 944.3 0.073 0.073
r=5 21456 21743.9 3.812 3.885
r=6 77608 77311.8 1.135 5.020
chi-square = 5.020 with df = 2; p-value = 0.081
--------------------------------------------------------------
bits 5 to 12
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=4 922 944.3 0.527 0.527
r=5 21616 21743.9 0.752 1.279
r=6 77462 77311.8 0.292 1.571
chi-square = 1.571 with df = 2; p-value = 0.456
--------------------------------------------------------------
bits 6 to 13
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=4 966 944.3 0.499 0.499
r=5 21782 21743.9 0.067 0.565
r=6 77252 77311.8 0.046 0.612
chi-square = 0.612 with df = 2; p-value = 0.737
--------------------------------------------------------------
bits 7 to 14
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=4 919 944.3 0.678 0.678
r=5 21661 21743.9 0.316 0.994
r=6 77420 77311.8 0.151 1.145
chi-square = 1.145 with df = 2; p-value = 0.564
--------------------------------------------------------------
bits 8 to 15
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=4 940 944.3 0.020 0.020
r=5 21627 21743.9 0.628 0.648
r=6 77433 77311.8 0.190 0.838
chi-square = 0.838 with df = 2; p-value = 0.658
--------------------------------------------------------------
bits 9 to 16
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=4 909 944.3 1.320 1.320
r=5 21710 21743.9 0.053 1.372
r=6 77381 77311.8 0.062 1.434
chi-square = 1.434 with df = 2; p-value = 0.488
--------------------------------------------------------------
bits 10 to 17
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=4 952 944.3 0.063 0.063
r=5 21721 21743.9 0.024 0.087
r=6 77327 77311.8 0.003 0.090
chi-square = 0.090 with df = 2; p-value = 0.956
--------------------------------------------------------------
bits 11 to 18
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=4 938 944.3 0.042 0.042
r=5 21754 21743.9 0.005 0.047
r=6 77308 77311.8 0.000 0.047
chi-square = 0.047 with df = 2; p-value = 0.977
--------------------------------------------------------------
bits 12 to 19
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=4 910 944.3 1.246 1.246
r=5 21982 21743.9 2.607 3.853
r=6 77108 77311.8 0.537 4.390
chi-square = 4.390 with df = 2; p-value = 0.111
--------------------------------------------------------------
bits 13 to 20
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=4 900 944.3 2.078 2.078
r=5 21874 21743.9 0.778 2.857
r=6 77226 77311.8 0.095 2.952
chi-square = 2.952 with df = 2; p-value = 0.229
--------------------------------------------------------------
bits 14 to 21
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=4 969 944.3 0.646 0.646
r=5 21666 21743.9 0.279 0.925
r=6 77365 77311.8 0.037 0.962
chi-square = 0.962 with df = 2; p-value = 0.618
--------------------------------------------------------------
bits 15 to 22
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=4 963 944.3 0.370 0.370
r=5 21622 21743.9 0.683 1.054
r=6 77415 77311.8 0.138 1.191
chi-square = 1.191 with df = 2; p-value = 0.551
--------------------------------------------------------------
bits 16 to 23
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=4 931 944.3 0.187 0.187
r=5 22021 21743.9 3.531 3.719
r=6 77048 77311.8 0.900 4.619
chi-square = 4.619 with df = 2; p-value = 0.099
--------------------------------------------------------------
bits 17 to 24
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=4 910 944.3 1.246 1.246
r=5 21817 21743.9 0.246 1.492
r=6 77273 77311.8 0.019 1.511
chi-square = 1.511 with df = 2; p-value = 0.470
--------------------------------------------------------------
bits 18 to 25
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=4 964 944.3 0.411 0.411
r=5 21683 21743.9 0.171 0.582
r=6 77353 77311.8 0.022 0.604
chi-square = 0.604 with df = 2; p-value = 0.740
--------------------------------------------------------------
bits 19 to 26
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=4 923 944.3 0.480 0.480
r=5 21521 21743.9 2.285 2.765
r=6 77556 77311.8 0.771 3.537
chi-square = 3.537 with df = 2; p-value = 0.171
--------------------------------------------------------------
bits 20 to 27
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=4 960 944.3 0.261 0.261
r=5 21616 21743.9 0.752 1.013
r=6 77424 77311.8 0.163 1.176
chi-square = 1.176 with df = 2; p-value = 0.555
--------------------------------------------------------------
bits 21 to 28
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=4 947 944.3 0.008 0.008
r=5 21665 21743.9 0.286 0.294
r=6 77388 77311.8 0.075 0.369
chi-square = 0.369 with df = 2; p-value = 0.831
--------------------------------------------------------------
bits 22 to 29
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=4 921 944.3 0.575 0.575
r=5 21678 21743.9 0.200 0.775
r=6 77401 77311.8 0.103 0.878
chi-square = 0.878 with df = 2; p-value = 0.645
--------------------------------------------------------------
bits 23 to 30
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=4 906 944.3 1.553 1.553
r=5 21807 21743.9 0.183 1.737
r=6 77287 77311.8 0.008 1.744
chi-square = 1.744 with df = 2; p-value = 0.418
--------------------------------------------------------------
bits 24 to 31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=4 875 944.3 5.086 5.086
r=5 21445 21743.9 4.109 9.195
r=6 77680 77311.8 1.754 10.948
chi-square = 10.948 with df = 2; p-value = 0.004
--------------------------------------------------------------
bits 25 to 32
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=4 905 944.3 1.636 1.636
r=5 21645 21743.9 0.450 2.085
r=6 77450 77311.8 0.247 2.332
chi-square = 2.332 with df = 2; p-value = 0.312
--------------------------------------------------------------
TEST SUMMARY, 25 tests on 100,000 random 6x8 matrices
These should be 25 uniform [0,1] random variates:
0.101382 0.014654 0.387393 0.081280 0.455949
0.736504 0.564019 0.657683 0.488121 0.956049
0.976818 0.111338 0.228562 0.618236 0.551158
0.099323 0.469750 0.739521 0.170608 0.555386
0.831470 0.644824 0.418013 0.004194 0.311537
The KS test for those 25 supposed UNI's yields
KS p-value = 0.489549
|-------------------------------------------------------------|
| THE 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. |
|-------------------------------------------------------------|
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for kiss.32
(20 bits/word, 2097152 words 20 bitstreams. No. missing words
should average 141909.33 with sigma=428.00.)
----------------------------------------------------------------
BITSTREAM test results for kiss.32.
Bitstream No. missing words z-score p-value
1 142021 0.26 0.397080
2 141511 -0.93 0.823990
3 141928 0.04 0.482603
4 142357 1.05 0.147790
5 141199 -1.66 0.951508
6 141894 -0.04 0.514286
7 142279 0.86 0.193872
8 141488 -0.98 0.837544
9 141864 -0.11 0.542174
10 141879 -0.07 0.528247
11 142351 1.03 0.151050
12 141600 -0.72 0.765078
13 142388 1.12 0.131701
14 142755 1.98 0.024085
15 141585 -0.76 0.775709
16 142181 0.63 0.262798
17 141703 -0.48 0.685125
18 141505 -0.94 0.827593
19 141867 -0.10 0.539392
20 141233 -1.58 0.942971
----------------------------------------------------------------
|-------------------------------------------------------------|
| OPSO means Overlapping-Pairs-Sparse-Occupancy |
|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. |
|------------------------------------------------------------ |
OPSO test for file kiss.32
Bits used No. missing words z-score p-value
23 to 32 142347 1.5092 0.065623
22 to 31 142167 0.8885 0.187131
21 to 30 142216 1.0575 0.145146
20 to 29 141554 -1.2253 0.889764
19 to 28 141714 -0.6736 0.749702
18 to 27 141849 -0.2080 0.582399
17 to 26 141945 0.1230 0.451053
16 to 25 141561 -1.2011 0.885151
15 to 24 141540 -1.2736 0.898589
14 to 23 142495 2.0196 0.021715
13 to 22 142211 1.0402 0.149114
12 to 21 141891 -0.0632 0.525199
11 to 20 142050 0.4851 0.313814
10 to 19 142234 1.1196 0.131452
9 to 18 142198 0.9954 0.159767
8 to 17 142386 1.6437 0.050120
7 to 16 141407 -1.7322 0.958379
6 to 15 141815 -0.3253 0.627514
5 to 14 141349 -1.9322 0.973331
4 to 13 142062 0.5264 0.299288
3 to 12 141779 -0.4494 0.673433
2 to 11 142258 1.2023 0.114622
1 to 10 141886 -0.0804 0.532060
-----------------------------------------------------------------
|------------------------------------------------------------ |
| OQSO means Overlapping-Quadruples-Sparse-Occupancy |
| The test OQSO is similar, 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. |
|------------------------------------------------------------ |
OQSO test for file kiss.32
Bits used No. missing words z-score p-value
28 to 32 142130 0.7480 0.227220
27 to 31 141728 -0.6147 0.730616
26 to 30 142201 0.9887 0.161402
25 to 29 141944 0.1175 0.453222
24 to 28 142036 0.4294 0.333820
23 to 27 142191 0.9548 0.169836
22 to 26 142269 1.2192 0.111380
21 to 25 142139 0.7785 0.218125
20 to 24 141985 0.2565 0.398779
19 to 23 141656 -0.8587 0.804760
18 to 22 142345 1.4768 0.069858
17 to 21 141705 -0.6926 0.755733
16 to 20 142035 0.4260 0.335054
15 to 19 141747 -0.5503 0.708933
14 to 18 141801 -0.3672 0.643273
13 to 17 142143 0.7921 0.214151
12 to 16 141632 -0.9401 0.826417
11 to 15 142222 1.0599 0.144595
10 to 14 141931 0.0735 0.470721
9 to 13 141655 -0.8621 0.805694
8 to 12 142335 1.4429 0.074517
7 to 11 142287 1.2802 0.100231
6 to 10 141418 -1.6655 0.952096
5 to 9 141776 -0.4520 0.674353
4 to 8 142705 2.6972 0.003496
3 to 7 142123 0.7243 0.234439
2 to 6 141943 0.1141 0.454565
1 to 5 141793 -0.3943 0.653335
-----------------------------------------------------------------
|------------------------------------------------------------ |
| 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. |
|------------------------------------------------------------ |
DNA test for file kiss.32
Bits used No. missing words z-score p-value
31 to 32 141360 -1.6204 0.947431
30 to 31 141725 -0.5437 0.706692
29 to 30 142363 1.3383 0.090406
28 to 29 142059 0.4415 0.329424
27 to 28 141591 -0.9390 0.826141
26 to 27 141979 0.2055 0.418584
25 to 26 141941 0.0934 0.462784
24 to 25 142561 1.9223 0.027282
23 to 24 142089 0.5300 0.298056
22 to 23 141811 -0.2901 0.614114
21 to 22 141635 -0.8092 0.790809
20 to 21 141844 -0.1927 0.576408
19 to 20 141838 -0.2104 0.583327
18 to 19 142043 0.3943 0.346677
17 to 18 141965 0.1642 0.434780
16 to 17 142265 1.0492 0.147049
15 to 16 142192 0.8338 0.202187
14 to 15 141683 -0.6676 0.747818
13 to 14 142092 0.5388 0.294995
12 to 13 142582 1.9843 0.023612
11 to 12 142434 1.5477 0.060847
10 to 11 141887 -0.0659 0.526259
9 to 10 141593 -0.9331 0.824623
8 to 9 141763 -0.4317 0.667003
7 to 8 141691 -0.6440 0.740226
6 to 7 141992 0.2439 0.403668
5 to 6 142153 0.7188 0.236135
4 to 5 141575 -0.9862 0.837988
3 to 4 142069 0.4710 0.318819
2 to 3 142127 0.6421 0.260406
1 to 2 142371 1.3619 0.086621
-----------------------------------------------------------------
|-------------------------------------------------------------|
| This is the COUNT-THE-1''s TEST on a stream of bytes. |
|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. |
|-------------------------------------------------------------|
Test result for the byte stream from kiss.32
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2569.63 0.985 0.162389
|-------------------------------------------------------------|
| 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. |
|-------------------------------------------------------------|
Test results for specific bytes from kiss.32
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2534.09 0.482 0.314881
2 to 9 2579.59 1.126 0.130163
3 to 10 2454.72 -0.640 0.739022
4 to 11 2421.58 -1.109 0.866290
5 to 12 2388.23 -1.581 0.943023
6 to 13 2392.09 -1.526 0.936499
7 to 14 2658.54 2.242 0.012476
8 to 15 2475.71 -0.344 0.634403
9 to 16 2389.81 -1.558 0.940419
10 to 17 2626.24 1.785 0.037108
11 to 18 2448.12 -0.734 0.768427
12 to 19 2478.40 -0.305 0.620006
13 to 20 2409.81 -1.276 0.898937
14 to 21 2526.94 0.381 0.351593
15 to 22 2519.69 0.278 0.390349
16 to 23 2495.75 -0.060 0.523965
17 to 24 2698.18 2.803 0.002534
18 to 25 2562.83 0.889 0.187107
19 to 26 2472.54 -0.388 0.651141
20 to 27 2450.04 -0.706 0.760057
21 to 28 2511.11 0.157 0.437590
22 to 29 2430.02 -0.990 0.838847
23 to 30 2678.79 2.529 0.005727
24 to 31 2422.40 -1.097 0.863774
25 to 32 2558.90 0.833 0.202414
|-------------------------------------------------------------|
| THIS IS A PARKING LOT TEST |
|In a square of side 100, randomly "park" a car---a circle of |
|radius 1. Then try to park a 2nd, a 3rd, and so on, each |
|time parking "by ear". That is, if an attempt to park a car |
|causes a crash with one already parked, try again at a new |
|random location. (To avoid path problems, consider parking |
|helicopters rather than cars.) Each attempt leads to either|
|a crash or a success, the latter followed by an increment to |
|the list of cars already parked. If we plot n: the number of |
|attempts, versus k: the number successfully parked, we get a |
|curve that should be similar to those provided by a perfect |
|random number generator. Theory for the behavior of such a |
|random curve seems beyond reach, and as graphics displays are|
|not available for this battery of tests, a simple characteriz|
|ation of the random experiment is used: k, the number of cars|
|successfully parked after n=12,000 attempts. Simulation shows|
|that k should average 3523 with sigma 21.9 and is very close |
|to normally distributed. Thus (k-3523)/21.9 should be a st- |
|andard normal variable, which, converted to a uniform varia- |
|ble, provides input to a KSTEST based on a sample of 10. |
|-------------------------------------------------------------|
CDPARK: result of 10 tests on file kiss.32
(Of 12000 tries, the average no. of successes should be
3523.0 with sigma=21.9)
No. succeses z-score p-value
3522 -0.0457 0.518210
3523 0.0000 0.500000
3528 0.2283 0.409702
3552 1.3242 0.092718
3495 -1.2785 0.899470
3497 -1.1872 0.882429
3517 -0.2740 0.607947
3524 0.0457 0.481790
3518 -0.2283 0.590298
3558 1.5982 0.055002
Square side=100, avg. no. parked=3523.40 sample std.=19.01
p-value of the KSTEST for those 10 p-values: 0.791810
|-------------------------------------------------------------|
| THE MINIMUM DISTANCE 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 is the MINIMUM DISTANCE test for file kiss.32
Sample no. d^2 mean equiv uni
5 0.2407 0.6853 0.214846
10 0.2691 1.3127 0.236941
15 0.5289 1.0430 0.412292
20 2.6530 1.2501 0.930494
25 1.1462 1.1289 0.683971
30 0.5493 1.1258 0.424251
35 1.0378 1.1293 0.647593
40 1.3810 1.0513 0.750398
45 0.0568 0.9854 0.055528
50 0.2866 0.9918 0.250301
55 1.4535 0.9500 0.767949
60 0.3224 0.9427 0.276778
65 0.2098 0.9488 0.190091
70 1.2683 0.9188 0.720464
75 0.4661 0.8860 0.374017
80 0.1541 0.8685 0.143476
85 2.1244 0.9002 0.881767
90 0.5448 0.8727 0.421622
95 0.8266 0.8758 0.564282
100 0.9794 0.8981 0.626309
--------------------------------------------------------------
Result of KS test on 100 transformed mindist^2's: p-value=0.339825
|-------------------------------------------------------------|
| THE 3DSPHERES 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. |
|-------------------------------------------------------------|
The 3DSPHERES test for file kiss.32
sample no r^3 equiv. uni.
1 13.084 0.353465
2 36.078 0.699590
3 13.449 0.361279
4 2.501 0.079978
5 8.187 0.238822
6 31.268 0.647350
7 7.178 0.212801
8 1.237 0.040411
9 8.990 0.258923
10 22.029 0.520155
11 0.985 0.032315
12 29.327 0.623777
13 25.061 0.566286
14 18.910 0.467589
15 6.227 0.187435
16 34.239 0.680600
17 3.653 0.114642
18 25.439 0.571711
19 4.945 0.151976
20 9.214 0.264445
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.033280
|-------------------------------------------------------------|
| This is the 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. |
|-------------------------------------------------------------|
RESULTS OF SQUEEZE TEST FOR kiss.32
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-1.5 -0.7 0.6 -0.3 -0.7 1.6
1.4 1.0 -0.7 0.9 0.3 -0.3
1.3 1.5 2.0 -1.1 -0.7 -0.9
-0.6 -1.1 -0.9 0.1 0.4 -0.2
-0.9 -0.8 0.7 -0.1 0.3 -1.1
-0.3 0.6 0.7 2.0 -0.2 1.0
-0.2 1.1 1.7 1.0 0.9 -1.0
0.8
Chi-square with 42 degrees of freedom:40.358142
z-score=-0.179141, p-value=0.543189
_____________________________________________________________
|-------------------------------------------------------------|
| The OVERLAPPING 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. |
|-------------------------------------------------------------|
Results of the OSUM test for kiss.32
Test no p-value
1 0.360690
2 0.206068
3 0.290307
4 0.769668
5 0.445720
6 0.279731
7 0.729134
8 0.948065
9 0.169536
10 0.538107
_____________________________________________________________
p-value for 10 kstests on 100 kstests:0.825647
|-------------------------------------------------------------|
| 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|
|another three sets of ten. |
|-------------------------------------------------------------|
The RUNS test for file kiss.32
(Up and down runs in a sequence of 10000 numbers)
Set 1
runs up; ks test for 10 p's: 0.067228
runs down; ks test for 10 p's: 0.333222
Set 2
runs up; ks test for 10 p's: 0.581523
runs down; ks test for 10 p's: 0.217533
|-------------------------------------------------------------|
|This the CRAPS TEST. It plays 200,000 games of craps, counts|
|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), and |
|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. |
|-------------------------------------------------------------|
RESULTS OF CRAPS TEST FOR kiss.32
No. of wins: Observed Expected
98760 98585.858586
z-score= 0.779, pvalue=0.21803
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66445 66666.7 0.737 0.737
2 37506 37654.3 0.584 1.321
3 27179 26954.7 1.866 3.187
4 19499 19313.5 1.782 4.970
5 13788 13851.4 0.290 5.260
6 9821 9943.5 1.510 6.770
7 7173 7145.0 0.110 6.880
8 5329 5139.1 7.019 13.899
9 3686 3699.9 0.052 13.951
10 2690 2666.3 0.211 14.162
11 1887 1923.3 0.686 14.848
12 1370 1388.7 0.253 15.101
13 982 1003.7 0.470 15.571
14 751 726.1 0.851 16.422
15 523 525.8 0.015 16.437
16 368 381.2 0.454 16.891
17 273 276.5 0.045 16.936
18 175 200.8 3.322 20.258
19 143 146.0 0.061 20.319
20 138 106.2 9.512 29.831
21 274 287.1 0.599 30.430
Chisq= 30.43 for 20 degrees of freedom, p= 0.06318
SUMMARY of craptest on kiss.32
p-value for no. of wins: 0.218031
p-value for throws/game: 0.063185
_____________________________________________________________