kiss.out

diehard随机数测试套件的C程序代码

	|(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
	_____________________________________________________________