KS Q ISO 28640-2011 Random variate generation methods《随机变量生成方法》.pdf

1、 KSKSKSKSKSKSKSK KSKSKS KSKSK KSKS KSK KS KS Q ISO 28640 KS Q ISO 28640:2011 2011 12 30 http:/www.kats.go.krKS Q ISO 28640:2011 : ( ) ( ) ( ) : (http:/www.standard.go.kr) ： ：2011 12 30 2011-0729 ： ： ( 02-509-7274) (http:/www.kats.go.kr). 10 5 , . KS Q ISO 28640:2011 i ii 1 1 2 1 3 .1 4 .2 4.1 .2 4.2

2、 .2 5 .3 5.1 .3 5.2 M- 3 5.3 5 GFSR .3 5.4 (Tausworthe) .4 5.5 .5 6 5 6.1 .5 6.2 6 6.3 .6 6.4 8 6.5 .8 6.6 8 6.7 9 6.8 10 6.9 10 6.10 .11 6.11 .11 6.12 12 6.13 13 6.14 .13 A( ) .15 A.1 .15 A.2 16 B( ) 17 B.1 3 GFSR .17 B.2 5 GFSR .21 B.3 .27 B.4 .29 B.5 34 B.6 43 45 KS Q ISO 28640:2011 ii 2010 1 ISO

3、 28640, Random variate generation methods . KS Q ISO 28640:2011 Random variate generation methods 1 . . . , SQC , 2 . . ( ) . KS Q ISO 3534 1, 1： KS Q ISO 3534 2, 1： ISO/IEC 2382 1, Information technology Vocabulary Part 1： Fundamental terms 3 ISO/IEC 2382 1, KS Q ISO 3534 1, KS Q ISO 3534 2 . 3.1 ,

4、 (random variate, random number) 1 “ ” . 2 “ ” . 3.2 (pseudo-random number) , (3.1) “ ” . KS Q ISO 28640:2011 2 3.3 (physical random number) (3.1) 3.4 (binary random number sequence) 0 1 (3.1) 3.5 (seed) 4 4.1 ISO/IEC 2382 1, KS Q ISO 3534 1, KS Q ISO 3534 2 . , . . X U Z n 4.2 . mod(m; k) m k m k m

5、 k 1 1 1 0 0 1 1 1 0 1 0 0 0 1010 1100 0110 m k m k 2 1 1 1 0 1 0 1 0 0 0 0 0 1010 1100 1000 m : k m k m k m k KS Q ISO 28640:2011 3 m 1 (X 0 ) XA (X 1) a (X 1 ) X w 0-1 . p 2pw r 1 , GFSR . w r Xn . y： Xny： y (yu) y： y (yl) b, c w r . (p, q, r, w, a, u, s, t, l, b, c) . X2, ., Xq 1 X1 w r . y . 6 6

6、.1 KS Q ISO 28640:2011 6 X Y . F(y) . f(y) , p(y) . 6.2 6.2.1 6.2.1.1 =,010,1)(yyf 6.2.1.2 X m 1 , . mXU = 5.2 5.5 w- , m 2 . 1 X U . 2 U 1, 0 . U X = 0 0.0 . M- . 3 U1, U2, . . . 6.2.2 6.2.2.1 +=,0,/1)(bayabyf b 0. 6.2.2.2 U 6.2.1.2 , . Y bU a 6.3 6.3.1 KS Q ISO 28640:2011 7 =,010,),()1()(11ydcByyy

7、fdc B(c, d)1011)1( dxxxdc c d 0 . 6.3.2 Jhnk U1 U2 6.2.1 , Y . dcUUY/12/11+= 1 YUYc/11= . . 6.3.3 Cheng U1 U2 6.2.1 , Y . a) +0. 6.4.2 U1 U2 6.2.1 , Y Y a b(U1 U2 1) . 6.5 6.5.1 1/3 a) rqsprrrtrscr 3),3/(1),ln(,3,3/1 = . b) Z . c) Z 1/2 Cheng a) 12,4ln += ccrcq . b) U1 U2 . c) WrVqRUUZUcWUUcV += ,),

8、exp(,1ln221111 . d) R4.5Z (1 ln4.5) Y a bW , . e) RlnZ , Y a bW , . f) b) . )5.4ln1()(5.411ln124ln,12/12211111+= UUUUcUUprqccrcqcpppUUbcaY+=1116.8 6.8.1 0. 6.13.2 U1, U2, . , Y n . ln(1 U1)(1 U2)(1 Un) n n . 6 n . 6.12.2.4 . p(y) . ( 10 100) . 6.14 M N , 5.1 r . N M 1 2r . a) k . 2k 1 1N M 12k 1 k l

9、og2(N M 1) . 1 N M 1 100 k 7 . 26 1 65 100 27 128 . b) k 1 , . 2 k Z1Z2Z3Z4. Zk 2k-1Z1 2k-2Z2 2k-3Z3 2k-4Z4 . Zk . 2 7 1 011 001 64 16 8 1 89 , 89 . c) N , M 1 . 3 N M 1 2r , 1 . 4 k r . KS Q ISO 28640:2011 14 N M 1 k k , k 20 5.2 . . d) 5.2 k . e) d) N . . KS Q ISO 28640:2011 15 A ( ) A.1 . A.1 , .

10、 A.1 1 93 90 60 02 17 25 89 42 27 41 64 45 08 02 70 42 49 41 55 982 34 19 39 65 54 32 14 02 06 84 43 65 97 97 65 05 40 55 65 063 27 88 28 07 16 05 18 96 81 69 53 34 79 84 83 44 07 12 00 384 95 16 61 89 77 47 14 14 40 87 12 40 15 18 54 89 72 88 59 675 50 45 95 10 48 25 29 74 63 48 44 06 18 67 19 90 5

11、2 44 05 856 11 72 79 70 41 08 85 77 03 32 46 28 83 22 48 61 93 19 98 607 19 31 85 29 48 89 59 53 99 46 72 29 49 06 58 65 69 06 87 098 14 58 90 27 73 67 17 08 43 78 71 32 21 97 02 25 27 22 81 749 28 04 62 77 82 73 00 73 83 17 27 79 37 13 76 29 90 07 36 4710 37 43 04 36 86 72 63 43 21 06 10 35 13 61 0

12、1 98 23 67 45 2111 74 47 22 71 36 15 67 41 77 67 40 00 67 24 00 08 98 27 98 5612 48 85 81 89 45 27 98 41 77 78 24 26 98 03 14 25 73 84 48 2813 55 81 09 70 17 78 18 54 62 06 50 64 90 30 15 78 60 63 54 5614 22 18 73 19 32 54 05 18 36 45 87 23 42 43 91 63 50 95 69 0915 78 29 64 22 97 95 94 54 64 28 34

13、34 88 98 14 21 38 45 37 8716 97 51 38 62 95 83 45 12 72 28 70 23 67 04 28 55 20 20 96 5717 42 91 81 16 52 44 71 99 68 55 16 32 83 27 03 44 93 81 69 5818 07 84 27 76 18 24 95 78 67 33 45 68 38 56 64 51 10 79 15 4619 60 31 55 42 68 53 27 82 67 68 73 09 98 45 72 02 87 79 32 8420 47 10 36 20 10 48 09 72

14、 35 94 12 94 78 29 14 80 77 27 05 6721 73 63 78 70 96 12 40 36 80 49 23 29 26 69 01 13 39 71 33 1722 70 65 19 86 11 30 16 23 21 55 04 72 30 01 22 53 24 13 40 6323 86 37 79 75 97 29 19 00 30 01 22 89 11 84 55 08 40 91 26 6124 28 00 93 29 59 54 71 77 75 24 10 65 69 15 66 90 47 90 48 8025 40 74 69 14 0

15、1 78 36 13 06 30 79 04 03 28 87 59 85 93 25 73KS Q ISO 28640:2011 16 A.2 A.1 . . , . . Noiseco NC24011) . , 1 GHz . 160 mVrms . . a) / . b) , . c) . , / Keithley Instruments, Inc. DAS-4102 2) . 64 MHz 8 . 1 MHz . 3.91 mV/digit , . / . 2 . , (0, 1) (Rn) 0 (1, 0) (Rn) 1 (0, 0), (1, 1) A.1 . (0, 1) (1,

16、 0) , . 1 ms , . (0, 1) (1, 0) . . 32 , 5.5 Mersenne Twister( genrand) . Mersenne Twister init_genrand(s), s 19660809 . Mersenne Twister . A.1 32 4 . 0 9 . 10 . 1) NC2401 Noisecom . ISO . 2) DAS-4102 Keithley Instruments, Inc. . ISO . KS Q ISO 28640:2011 17 B ( ) B.1 3 GFSR C KS X ISO/IEC 9899 (p, q

17、, w) (1 279, 418, 32) (21 279 1) . gfsr( ) 0 (232 1) . gfsr( ) gfsr_31( ) , init_gfsr(s) . init_gfsr(s) 32 0 (232 1) . 39 . , 32 39- (39 ) , 0 21 274 . init_gfsr(s) s . p, q, w . w 2 . w , 32 64 . 64 w 64 gfsr( ) 0 (264 1) , gfsr_31( ) 0 (2631) . “ ” 32 . /* C code : Trinomial GFSR */ #define P 1279

18、 #define Q 418 #define W 32 /* W should be a power of 2 */ static unsigned long state P ; static int state_i ; void init_gfsr (unsigned long s) int i, j, k; static unsigned long x P ; s for (i=0 ; i31 ; s = 1664525UL * s + 1UL ; s for (k=0, i=0 ; i= P) state_i = 0 ; p0 = state ; p1 = state + Q ; for

19、 (i=0 ; i1) ; 3 GFSR Full Basic . REM /* REM BASIC code : Trinomial GFSR REM */ OPTION BASE 0 REM /*/ DECLARE NUMERIC P KS Q ISO 28640:2011 19 LET P=1279 !#define P 1279 DECLARE NUMERIC Q LET Q=418 !#define Q 418 DECLARE NUMERIC W LET W=32 !#define W 32 /* W should be power OF 2 */ DIM state(P) !sta

20、tic unsigned long stateP; DECLARE NUMERIC state_i !static INT state_i; REM /*/ FUNCTION init_gfsr(s) !void init_gfsr(unsigned long s) DECLARE NUMERIC i,j,k ! int i, j, k; DIM x(P) ! static unsigned long xP; LET s = And32(s , MskF_f) ! s FOR i = 0 TO P -1 ! for (i=0; i31; LET s = Mul32U(1664525 , s)

21、+ 1 ! s = 1664525UL * s + 1UL; LET s = And32(s, MskF_f) ! s NEXT I ! LET k=0 FOR i = 0 TO P -1 ! for (k=0,i=0; i= P THEN ! if (state_i = P) LET state_i = 0 ! state_i = 0; LET p0 = 0 ! p0 = state; LET p1 = Q ! p1 = state + Q; FOR i=0 TO P-Q-1 ! for (i=0; i1); END FUNCTION ! B.2 5 GFSR (521, 86, 197,

22、447, 32) 2521 1 . gfsr5( ) 0 (232 1) . gfsr5_31( ) 0 (231 1) . init_gfsr5(s) 32 0 (232 1) . gfsr5( ) gfsr5_31( ) , init_gfsr5(s) . 32 16- (16 ) , 0 2516 . , init_gfsr5(s) . P xP state_i . 1 p, q1, q2, q3 . /* C code : Pentanominal GFSR */ #define P 521 /* Q1 31 ; s = 1664525UL * s + 1UL ; KS Q ISO 2

23、8640:2011 22 s for (k=0, i=0 ; i= P) state_i = 0 ; p0 = state ; p1 = state + Q1 ; p2 = state + Q2 ; p3 = state + Q3 ; for (i=0 ; i1); 5 GFSR Full Basic . REM /* KS Q ISO 28640:2011 23 REM BASIC code : Pentanomial GFSR REM */ OPTION BASE 0 REM /*/ DECLARE NUMERIC P LET P = 521 !#define P 512 REM /* Q

24、1 31; LET s = Mul32U(1664525 , s) + 1 ! s = 1664525UL * s + 1UL; LET s = And32(s , MskF_f) ! s NEXT I ! LET k=0 FOR i=0 TO P-1 ! for (k=0,i=0; i= P THEN ! if (state_i = P) LET state_i = 0 ! state_i = 0; LET p0 = 0 ! p0 = state; LET p1 = Q1 ! p1 = state + Q1; LET p2 = Q2 ! p2 = state + Q2; LET p3 = Q3 ! p3 = state + Q3; FOR i=0 TO P-Q3-1 ! FOR (i=0; i1); END FUNCTION !