ms_24_55.die

				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 numbers
	(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)

	Bits used	mean		chisqr		p-value
	 1 to 24	15.82		15.4556		0.562701
	 2 to 25	15.90		14.8476		0.606459
	 3 to 26	15.57		16.2743		0.504479
	 4 to 27	15.71		15.5996		0.552376
	 5 to 28	15.60		23.0795		0.146679
	 6 to 29	15.99		14.2868		0.646709
	 7 to 30	15.84		12.8771		0.744372
	 8 to 31	15.76		13.0737		0.731237
	 9 to 32	16.08		20.6900		0.240464

			degree of freedoms is: 17
	---------------------------------------------------------------
		p-value for KStest on those 9 p-values: 0.414178


	|-------------------------------------------------------------|
	|           THE OVERLAPPING 5-PERMUTATION TEST                |
	|This is the OPERM5 test.  It looks at a sequence of one mill-|
	|ion 32-bit random integers.  Each set of five consecutive    |
	|integers can be in one of 120 states, for the 5! possible or-|
	|derings of five numbers.  Thus the 5th, 6th, 7th,...numbers  |
	|each provide a state. As many thousands of state transitions |
	|are observed,  cumulative counts are made of the number of   |
	|occurences of each state.  Then the quadratic form in the    |
	|weak inverse of the 120x120 covariance matrix yields a test  |
	|equivalent to the likelihood ratio test that the 120 cell    |
	|counts came from the specified (asymptotically) normal dis-  |
	|tribution with the specified 120x120 covariance matrix (with |
	|rank 99).  This version uses 1,000,000 integers, twice.      |
	|-------------------------------------------------------------|

			OPERM5 test for file 
		  (For samples of 1,000,000 consecutive 5-tuples)

			  sample 1 
	chisquare=-2280052090810.440918 with df=99; p-value= nan
	_______________________________________________________________

			  sample 2 
	chisquare=1693761347444.962402 with df=99; p-value= nan
	_______________________________________________________________


	|-------------------------------------------------------------|
	|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 numbers

	RANK	OBSERVED	EXPECTED	(O-E)^2/E	SUM

	r<=28	208         	211.4       	0.055       	0.055       
	r=29	5156        	5134.0      	0.094       	0.149       
	r=30	23019       	23103.0     	0.306       	0.455       
	r=31	11617       	11551.5     	0.371       	0.826       

		chi-square = 0.826 with df = 3;  p-value = 0.843
	--------------------------------------------------------------

	|-------------------------------------------------------------|
	|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 numbers

	RANK	OBSERVED	EXPECTED	(O-E)^2/E	SUM

	r<=29	220         	211.4       	0.348       	0.348       
	r=30	5024        	5134.0      	2.357       	2.706       
	r=31	23122       	23103.0     	0.016       	2.721       
	r=32	11634       	11551.5     	0.589       	3.310       

		chi-square = 3.310 with df = 3;  p-value = 0.346
	--------------------------------------------------------------

	|-------------------------------------------------------------|
	|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 numbers

			      bits  1 to  8

	RANK	OBSERVED	EXPECTED	(O-E)^2/E	SUM

	r<=4	963         	944.3       	0.370       	0.370       
	r=5	21773       	21743.9     	0.039       	0.409       
	r=6	77264       	77311.8     	0.030       	0.439       

		chi-square = 0.439 with df = 2;  p-value = 0.803
	--------------------------------------------------------------

			      bits  2 to  9

	RANK	OBSERVED	EXPECTED	(O-E)^2/E	SUM

	r<=4	974         	944.3       	0.934       	0.934       
	r=5	21617       	21743.9     	0.741       	1.675       
	r=6	77409       	77311.8     	0.122       	1.797       

		chi-square = 1.797 with df = 2;  p-value = 0.407
	--------------------------------------------------------------

			      bits  3 to 10

	RANK	OBSERVED	EXPECTED	(O-E)^2/E	SUM

	r<=4	955         	944.3       	0.121       	0.121       
	r=5	21823       	21743.9     	0.288       	0.409       
	r=6	77222       	77311.8     	0.104       	0.513       

		chi-square = 0.513 with df = 2;  p-value = 0.774
	--------------------------------------------------------------

			      bits  4 to 11

	RANK	OBSERVED	EXPECTED	(O-E)^2/E	SUM

	r<=4	920         	944.3       	0.625       	0.625       
	r=5	21735       	21743.9     	0.004       	0.629       
	r=6	77345       	77311.8     	0.014       	0.643       

		chi-square = 0.643 with df = 2;  p-value = 0.725
	--------------------------------------------------------------

			      bits  5 to 12

	RANK	OBSERVED	EXPECTED	(O-E)^2/E	SUM

	r<=4	913         	944.3       	1.037       	1.037       
	r=5	21818       	21743.9     	0.253       	1.290       
	r=6	77269       	77311.8     	0.024       	1.314       

		chi-square = 1.314 with df = 2;  p-value = 0.518
	--------------------------------------------------------------

			      bits  6 to 13

	RANK	OBSERVED	EXPECTED	(O-E)^2/E	SUM

	r<=4	877         	944.3       	4.796       	4.796       
	r=5	21931       	21743.9     	1.610       	6.406       
	r=6	77192       	77311.8     	0.186       	6.592       

		chi-square = 6.592 with df = 2;  p-value = 0.037
	--------------------------------------------------------------

			      bits  7 to 14

	RANK	OBSERVED	EXPECTED	(O-E)^2/E	SUM

	r<=4	911         	944.3       	1.174       	1.174       
	r=5	21659       	21743.9     	0.331       	1.506       
	r=6	77430       	77311.8     	0.181       	1.687       

		chi-square = 1.687 with df = 2;  p-value = 0.430
	--------------------------------------------------------------

			      bits  8 to 15

	RANK	OBSERVED	EXPECTED	(O-E)^2/E	SUM

	r<=4	942         	944.3       	0.006       	0.006       
	r=5	21902       	21743.9     	1.150       	1.155       
	r=6	77156       	77311.8     	0.314       	1.469       

		chi-square = 1.469 with df = 2;  p-value = 0.480
	--------------------------------------------------------------

			      bits  9 to 16

	RANK	OBSERVED	EXPECTED	(O-E)^2/E	SUM

	r<=4	961         	944.3       	0.295       	0.295       
	r=5	21740       	21743.9     	0.001       	0.296       
	r=6	77299       	77311.8     	0.002       	0.298       

		chi-square = 0.298 with df = 2;  p-value = 0.862
	--------------------------------------------------------------

			      bits 10 to 17

	RANK	OBSERVED	EXPECTED	(O-E)^2/E	SUM

	r<=4	908         	944.3       	1.395       	1.395       
	r=5	21804       	21743.9     	0.166       	1.562       
	r=6	77288       	77311.8     	0.007       	1.569       

		chi-square = 1.569 with df = 2;  p-value = 0.456
	--------------------------------------------------------------

			      bits 11 to 18

	RANK	OBSERVED	EXPECTED	(O-E)^2/E	SUM

	r<=4	958         	944.3       	0.199       	0.199       
	r=5	21677       	21743.9     	0.206       	0.405       
	r=6	77365       	77311.8     	0.037       	0.441       

		chi-square = 0.441 with df = 2;  p-value = 0.802
	--------------------------------------------------------------

			      bits 12 to 19

	RANK	OBSERVED	EXPECTED	(O-E)^2/E	SUM

	r<=4	1002        	944.3       	3.526       	3.526       
	r=5	21861       	21743.9     	0.631       	4.156       
	r=6	77137       	77311.8     	0.395       	4.552       

		chi-square = 4.552 with df = 2;  p-value = 0.103
	--------------------------------------------------------------

			      bits 13 to 20

	RANK	OBSERVED	EXPECTED	(O-E)^2/E	SUM

	r<=4	954         	944.3       	0.100       	0.100       
	r=5	21919       	21743.9     	1.410       	1.510       
	r=6	77127       	77311.8     	0.442       	1.951       

		chi-square = 1.951 with df = 2;  p-value = 0.377
	--------------------------------------------------------------

			      bits 14 to 21

	RANK	OBSERVED	EXPECTED	(O-E)^2/E	SUM

	r<=4	932         	944.3       	0.160       	0.160       
	r=5	21767       	21743.9     	0.025       	0.185       
	r=6	77301       	77311.8     	0.002       	0.186       

		chi-square = 0.186 with df = 2;  p-value = 0.911
	--------------------------------------------------------------

			      bits 15 to 22

	RANK	OBSERVED	EXPECTED	(O-E)^2/E	SUM

	r<=4	996         	944.3       	2.831       	2.831       
	r=5	21530       	21743.9     	2.104       	4.935       
	r=6	77474       	77311.8     	0.340       	5.275       

		chi-square = 5.275 with df = 2;  p-value = 0.072
	--------------------------------------------------------------

			      bits 16 to 23

	RANK	OBSERVED	EXPECTED	(O-E)^2/E	SUM

	r<=4	950         	944.3       	0.034       	0.034       
	r=5	21538       	21743.9     	1.950       	1.984       
	r=6	77512       	77311.8     	0.518       	2.503       

		chi-square = 2.503 with df = 2;  p-value = 0.286
	--------------------------------------------------------------

			      bits 17 to 24

	RANK	OBSERVED	EXPECTED	(O-E)^2/E	SUM

	r<=4	952         	944.3       	0.063       	0.063       
	r=5	21650       	21743.9     	0.406       	0.468       
	r=6	77398       	77311.8     	0.096       	0.564       

		chi-square = 0.564 with df = 2;  p-value = 0.754
	--------------------------------------------------------------

			      bits 18 to 25

	RANK	OBSERVED	EXPECTED	(O-E)^2/E	SUM

	r<=4	917         	944.3       	0.789       	0.789       
	r=5	21706       	21743.9     	0.066       	0.855       
	r=6	77377       	77311.8     	0.055       	0.910       

		chi-square = 0.910 with df = 2;  p-value = 0.634
	--------------------------------------------------------------

			      bits 19 to 26

	RANK	OBSERVED	EXPECTED	(O-E)^2/E	SUM

	r<=4	938         	944.3       	0.042       	0.042       
	r=5	21854       	21743.9     	0.557       	0.600       
	r=6	77208       	77311.8     	0.139       	0.739       

		chi-square = 0.739 with df = 2;  p-value = 0.691
	--------------------------------------------------------------

			      bits 20 to 27

	RANK	OBSERVED	EXPECTED	(O-E)^2/E	SUM

	r<=4	971         	944.3       	0.755       	0.755       
	r=5	21562       	21743.9     	1.522       	2.277       
	r=6	77467       	77311.8     	0.312       	2.588       

		chi-square = 2.588 with df = 2;  p-value = 0.274
	--------------------------------------------------------------

			      bits 21 to 28

	RANK	OBSERVED	EXPECTED	(O-E)^2/E	SUM

	r<=4	988         	944.3       	2.022       	2.022       
	r=5	21420       	21743.9     	4.825       	6.847       
	r=6	77592       	77311.8     	1.016       	7.863       

		chi-square = 7.863 with df = 2;  p-value = 0.020
	--------------------------------------------------------------

			      bits 22 to 29

	RANK	OBSERVED	EXPECTED	(O-E)^2/E	SUM

	r<=4	953         	944.3       	0.080       	0.080       
	r=5	21645       	21743.9     	0.450       	0.530       
	r=6	77402       	77311.8     	0.105       	0.635       

		chi-square = 0.635 with df = 2;  p-value = 0.728
	--------------------------------------------------------------

			      bits 23 to 30

	RANK	OBSERVED	EXPECTED	(O-E)^2/E	SUM

	r<=4	911         	944.3       	1.174       	1.174       
	r=5	21648       	21743.9     	0.423       	1.597       
	r=6	77441       	77311.8     	0.216       	1.813       

		chi-square = 1.813 with df = 2;  p-value = 0.404
	--------------------------------------------------------------

			      bits 24 to 31

	RANK	OBSERVED	EXPECTED	(O-E)^2/E	SUM

	r<=4	896         	944.3       	2.470       	2.470       
	r=5	21813       	21743.9     	0.220       	2.690       
	r=6	77291       	77311.8     	0.006       	2.696       

		chi-square = 2.696 with df = 2;  p-value = 0.260
	--------------------------------------------------------------

			      bits 25 to 32

	RANK	OBSERVED	EXPECTED	(O-E)^2/E	SUM

	r<=4	942         	944.3       	0.006       	0.006       
	r=5	21759       	21743.9     	0.010       	0.016       
	r=6	77299       	77311.8     	0.002       	0.018       

		chi-square = 0.018 with df = 2;  p-value = 0.991
	--------------------------------------------------------------
	    TEST SUMMARY, 25 tests on 100,000 random 6x8 matrices
	    These should be 25 uniform [0,1] random variates:
 
	0.802994    	0.407195    	0.773639    	0.724981    	0.518484     
	0.037030    	0.430308    	0.479717    	0.861501    	0.456380     
	0.802037    	0.102719    	0.376924    	0.911074    	0.071539     
	0.286138    	0.754123    	0.634354    	0.691120    	0.274145     
	0.019617    	0.727884    	0.403901    	0.259800    	0.990938    
		The KS test for those 25 supposed UNI's yields
			KS p-value = 0.938803

	|-------------------------------------------------------------|
	|                  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 numbers
	 (20 bits/word, 2097152 words 20 bitstreams. No. missing words 
	  should average 141909.33 with sigma=428.00.)
	----------------------------------------------------------------
		   BITSTREAM test results for numbers.

	Bitstream	No. missing words	z-score		p-value
	   1		141360 			-1.28		0.900338
	   2		142209 			 0.70		0.241913
	   3		141731 			-0.42		0.661536
	   4		142032 			 0.29		0.387205
	   5		141710 			-0.47		0.679294
	   6		141390 			-1.21		0.887509
	   7		141061 			-1.98		0.976265
	   8		142724 			 1.90		0.028492
	   9		141691 			-0.51		0.695015
	   10		141456 			-1.06		0.855242
	   11		140706 			-2.81		0.997535
	   12		141876 			-0.08		0.531036
	   13		141942 			 0.08		0.469578
	   14		141323 			-1.37		0.914646
	   15		142585 			 1.58		0.057206
	   16		141597 			-0.73		0.767226
	   17		141640 			-0.63		0.735416
	   18		142088 			 0.42		0.338173
	   19		141554 			-0.83		0.796790
	   20		141999 			 0.21		0.417025
	----------------------------------------------------------------

	|-------------------------------------------------------------|
	|        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 numbers

	Bits used	No. missing words	z-score		p-value
	23 to 32  		141598 		-1.0736		0.858488
	22 to 31  		141614 		-1.0184		0.845751
	21 to 30  		142010 		 0.3471		0.364244
	20 to 29  		142258 		 1.2023		0.114622
	19 to 28  		142030 		 0.4161		0.338667
	18 to 27  		141933 		 0.0816		0.467474
	17 to 26  		142027 		 0.4058		0.342460
	16 to 25  		141541 		-1.2701		0.897976
	15 to 24  		141649 		-0.8977		0.815324
	14 to 23  		141666 		-0.8391		0.799285
	13 to 22  		142010 		 0.3471		0.364244
	12 to 21  		141783 		-0.4356		0.668444
	11 to 20  		141532 		-1.3011		0.903394
	10 to 19  		141630 		-0.9632		0.832278
	9 to 18  		141843 		-0.2287		0.590458
	8 to 17  		142266 		 1.2299		0.109368
	7 to 16  		141487 		-1.4563		0.927347
	6 to 15  		142123 		 0.7368		0.230624
	5 to 14  		141887 		-0.0770		0.530688
	4 to 13  		142151 		 0.8333		0.202325
	3 to 12  		141989 		 0.2747		0.391764
	2 to 11  		141705 		-0.7046		0.759466
	1 to 10  		141561 		-1.2011		0.885151
	-----------------------------------------------------------------

	|------------------------------------------------------------ |
	|    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 numbers

	Bits used	No. missing words	z-score		p-value
	28 to 32  		141794 		-0.3909		0.652083
	27 to 31  		142364 		 1.5413		0.061627
	26 to 30  		141568 		-1.1571		0.876374
	25 to 29  		141657 		-0.8554		0.803823
	24 to 28  		142118 		 0.7074		0.239673
	23 to 27  		141420 		-1.6587		0.951416
	22 to 26  		142049 		 0.4735		0.317943
	21 to 25  		142212 		 1.0260		0.152446
	20 to 24  		141854 		-0.1876		0.574389
	19 to 23  		142197 		 0.9752		0.164742
	18 to 22  		142099 		 0.6429		0.260128
	17 to 21  		142318 		 1.3853		0.082977
	16 to 20  		141788 		-0.4113		0.659569
	15 to 19  		141727 		-0.6181		0.731735
	14 to 18  		141887 		-0.0757		0.530169
	13 to 17  		141624 		-0.9672		0.833283
	12 to 16  		142099 		 0.6429		0.260128
	11 to 15  		142359 		 1.5243		0.063716
	10 to 14  		141371 		-1.8248		0.965988
	9 to 13  		141793 		-0.3943		0.653335
	8 to 12  		142307 		 1.3480		0.088824
	7 to 11  		141993 		 0.2836		0.388348
	6 to 10  		142137 		 0.7718		0.220127
	5 to 9  		141488 		-1.4282		0.923388
	4 to 8  		142130 		 0.7480		0.227220
	3 to 7  		141747 		-0.5503		0.708933
	2 to 6  		141420 		-1.6587		0.951416
	1 to 5  		141858 		-0.1740		0.569067
	-----------------------------------------------------------------

	|------------------------------------------------------------ |
	|    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 numbers

	Bits used	No. missing words	z-score		p-value
	31 to 32  		141647 		-0.7738		0.780486
	30 to 31  		141072 		-2.4700		0.993244
	29 to 30  		141964 		 0.1613		0.435941
	28 to 29  		142072 		 0.4799		0.315666
	27 to 28  		141256 		-1.9272		0.973024
	26 to 27  		141648 		-0.7709		0.779612
	25 to 26  		141628 		-0.8299		0.796697
	24 to 25  		142150 		 0.7099		0.238870
	23 to 24  		142005 		 0.2822		0.388890
	22 to 23  		141720 		-0.5585		0.711747
	21 to 22  		141670 		-0.7060		0.759902
	20 to 21  		142001 		 0.2704		0.393421
	19 to 20  		142053 		 0.4238		0.335854
	18 to 19  		141889 		-0.0600		0.523910
	17 to 18  		141910 		 0.0020		0.499211
	16 to 17  		141124 		-2.3166		0.989737
	15 to 16  		141564 		-1.0187		0.845821
	14 to 15  		141350 		-1.6499		0.950522
	13 to 14  		142103 		 0.5713		0.283899
	12 to 13  		141997 		 0.2586		0.397967
	11 to 12  		141577 		-0.9803		0.836537
	10 to 11  		141737 		-0.5083		0.694395
	9 to 10  		142056 		 0.4327		0.332633
	8 to 9  		142059 		 0.4415		0.329424
	7 to 8  		141746 		-0.4818		0.685026
	6 to 7  		142149 		 0.7070		0.239786
	5 to 6  		141480 		-1.2665		0.897326
	4 to 5  		142167 		 0.7601		0.223601
	3 to 4  		142008 		 0.2911		0.385502
	2 to 3  		142192 		 0.8338		0.202187
	1 to 2  		142096 		 0.5506		0.290937
	-----------------------------------------------------------------

	|-------------------------------------------------------------|
	|    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 numbers
	  (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)

			chisquare	z-score		p-value
			2604.57		 1.479		0.069599

	|-------------------------------------------------------------|
	|    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 numbers
	  (Degrees of freedom: 5^4-5^3=2500; sample size: 256000)

	bits used	chisquare	z-score		p-value
	1 to 8  	2483.97		-0.227		0.589655
	2 to 9  	2473.65		-0.373		0.645282
	3 to 10  	2590.08		 1.274		0.101334
	4 to 11  	2575.18		 1.063		0.143830
	5 to 12  	2404.88		-1.345		0.910714
	6 to 13  	2430.61		-0.981		0.836797
	7 to 14  	2518.82		 0.266		0.395079
	8 to 15  	2515.82		 0.224		0.411471
	9 to 16  	2507.17		 0.101		0.459629
	10 to 17  	2473.20		-0.379		0.647662
	11 to 18  	2381.84		-1.671		0.952640
	12 to 19  	2625.74		 1.778		0.037685
	13 to 20  	2545.57		 0.645		0.259618
	14 to 21  	2532.68		 0.462		0.321968
	15 to 22  	2541.58		 0.588		0.278248
	16 to 23  	2536.08		 0.510		0.304926
	17 to 24  	2423.56		-1.081		0.860146
	18 to 25  	2412.92		-1.232		0.890940
	19 to 26  	2477.31		-0.321		0.625863
	20 to 27  	2535.17		 0.497		0.309478
	21 to 28  	2491.05		-0.127		0.550377
	22 to 29  	2571.05		 1.005		0.157489
	23 to 30  	2520.18		 0.285		0.387658
	24 to 31  	2505.13		 0.073		0.471100
	25 to 32  	2530.67		 0.434		0.332231
	|-------------------------------------------------------------|
	|              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 numbers
	  (Of 12000 tries, the average no. of successes should be 
	   3523.0 with sigma=21.9)

	   No. succeses		z-score		p-value
		3501		-1.0046		0.842447
		3503		-0.9132		0.819442
		3533		 0.4566		0.323972
		3510		-0.5936		0.723613
		3544		 0.9589		0.168804
		3499		-1.0959		0.863437
		3507		-0.7306		0.767486
		3525		 0.0913		0.463617
		3511		-0.5479		0.708135
		3502		-0.9589		0.831196
	  Square side=100, avg. no. parked=3513.50 sample std.=14.53
	     p-value of the KSTEST for those 10 p-values: 0.097388


	|-------------------------------------------------------------|
	|              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 numbers

	Sample no.	 d^2		 mean		equiv uni
	   5		1.3103		1.2023		0.732022
	   10		1.2397		1.1722		0.712318
	   15		3.2444		1.1611		0.961639
	   20		1.1568		1.1653		0.687337
	   25		0.1967		0.9891		0.179366
	   30		0.2448		1.1181		0.218134
	   35		0.5320		1.1321		0.414168
	   40		1.1456		1.1219		0.683799
	   45		0.1940		1.0849		0.177179
	   50		0.1109		1.0601		0.105462
	   55		1.3854		1.0858		0.751518
	   60		0.2429		1.0349		0.216589
	   65		1.8075		1.0053		0.837416
	   70		0.6129		1.0242		0.459897
	   75		1.3461		1.0316		0.741492
	   80		0.3975		1.0215		0.329319
	   85		0.4999		1.0242		0.394948
	   90		0.9722		1.0138		0.623600
	   95		1.6094		1.0183		0.801612
	   100		1.4731		1.0364		0.772486
	--------------------------------------------------------------
	Result of KS test on 100 transformed mindist^2's: p-value=0.516049


	|-------------------------------------------------------------|
	|             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 numbers

		sample no	r^3		equiv. uni.
		   1		12.256		0.335373
		   2		20.103		0.488339
		   3		133.784		0.988431
		   4		27.804		0.604184
		   5		91.882		0.953241
		   6		53.079		0.829546
		   7		12.446		0.339571
		   8		13.799		0.368693
		   9		3.348		0.105589
		   10		7.891		0.231277
		   11		33.534		0.673006
		   12		1.998		0.064425
		   13		58.197		0.856280
		   14		27.237		0.596627
		   15		8.625		0.249863
		   16		3.968		0.123902
		   17		33.942		0.677422
		   18		23.049		0.536198
		   19		72.076		0.909510
		   20		83.672		0.938521
	--------------------------------------------------------------
		p-value for KS test on those 20 p-values: 0.786671


	|-------------------------------------------------------------|
	|                 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 numbers

		    Table of standardized frequency counts
		(obs-exp)^2/exp  for j=(1,..,6), 7,...,47,(48,...)
		 1.3  	-0.7  	 0.1  	 0.5  	-0.9  	-0.1  
		 0.8  	-0.0  	 2.7  	 1.3  	 1.4  	-0.1  
		 1.6  	-0.5  	-1.2  	-0.5  	-0.8  	 0.9  
		-0.2  	 0.4  	 0.3  	-1.4  	-0.3  	-0.0  
		 0.6  	-0.0  	-1.5  	-1.4  	 0.4  	-0.2  
		-1.9  	 0.8  	-0.1  	 0.3  	-1.2  	-0.1  
		-0.5  	-0.7  	 1.3  	-1.3  	 2.4  	 2.0  
		 1.8  
		Chi-square with 42 degrees of freedom:50.567180
		z-score=0.934756, p-value=0.171185
	_____________________________________________________________


	|-------------------------------------------------------------|
	|            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 numbers

			Test no			p-value
			  1 			0.753349
			  2 			0.082006
			  3 			0.124644
			  4 			0.032086
			  5 			0.018259
			  6 			0.709832
			  7 			0.008609
			  8 			0.879114
			  9 			0.344850
			  10 			0.738011
	_____________________________________________________________

		p-value for 10 kstests on 100 kstests:0.037998

	|-------------------------------------------------------------|
	|    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 numbers
		(Up and down runs in a sequence of 10000 numbers)
				Set 1
		 runs up; ks test for 10 p's: 0.519032
		 runs down; ks test for 10 p's: 0.045036
				Set 2
		 runs up; ks test for 10 p's: 0.341957
		 runs down; ks test for 10 p's: 0.330510

	|-------------------------------------------------------------|
	|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 numbers 
	No. of wins:  Observed	Expected
	                 98330        98585.858586
		z-score=-1.144, pvalue=0.87376

	Analysis of Throws-per-Game:

	Throws	Observed	Expected	Chisq	 Sum of (O-E)^2/E
	1	66924		66666.7		0.993		0.993
	2	37465		37654.3		0.952		1.945
	3	27155		26954.7		1.488		3.433
	4	19331		19313.5		0.016		3.449
	5	13706		13851.4		1.527		4.976
	6	10003		9943.5		0.356		5.331
	7	7143		7145.0		0.001		5.332
	8	5108		5139.1		0.188		5.520
	9	3621		3699.9		1.681		7.201
	10	2643		2666.3		0.204		7.404
	11	1907		1923.3		0.139		7.543
	12	1340		1388.7		1.711		9.254
	13	977		1003.7		0.711		9.965
	14	775		726.1		3.288		13.252
	15	491		525.8		2.308		15.560
	16	385		381.2		0.039		15.599
	17	267		276.5		0.329		15.928
	18	195		200.8		0.169		16.097
	19	138		146.0		0.437		16.534
	20	116		106.2		0.901		17.435
	21	310		287.1		1.824		19.260

	Chisq=  19.26 for 20 degrees of freedom, p= 0.50501

		SUMMARY of craptest on numbers
	 p-value for no. of wins: 0.873760
	 p-value for throws/game: 0.505015
	_____________________________________________________________