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ru.algorithms
- RU.ALGORITHMS ----------------------------------------------------------------
From : Serhiy Savychenko 2:5020/400 21 Sep 2001 11:23:06
To : Artur Kamilyanov
Subject : Re: Генерирование случайных чисел
--------------------------------------------------------------------------------
Приветствую, "Artur Kamilyanov"
<Artur.Kamilyanov@p31.f105.n5011.z2.fidonet.org>! Вы сообщили:
> DP> Слышал в кратце про метод вычетов, который использует рекуррентное
> DP> соотношение x[i]=b*x[i-1]%M, где % - остаток от деления, а b и M
некоторые
> DP> константы.
> это не совсем случайная последовательность. Так как каждый следующее число
> зависит от предыдущего. Она есть у Кнута во 2-м томе.
В новом издании есть и новые методы, типа x[i]=(b*x[i-33]-x[i-97])%M
или что-то в этом роде. Причем весь смысл именно в этих цифрах 13 и 53.
>
> DP> Так как сие чудо реализовать? Или есть другой несложный способ?
> В talks.asm обсуждали что-то про генерацию с использованием времени. Кто
> подскажет как это делается?
Этот метод хорош для игрушек, или других программ с использованием ввода
оператора. Для метода Монте-Карло например он не подходит.
Hиже привожу код на фортране, тут более понятен алогоритм, кроме того читай
комментарии вначале о качестве метода. Кнут, кстати, хвалит этот алгоритм.
Есть реализация на асме, но немного старая. Я проводил года три назад тесты,
остался доволен.
=========================================================================
C This random number generator originally appeared in "Toward a Universal
C Random Number Generator" by George Marsaglia and Arif Zaman.
C Florida State University Report: FSU-SCRI-87-50 (1987)
C
C It was later modified by F. James and published in "A Review of Pseudo-
C random Number Generators"
C
C THIS IS THE BEST KNOWN RANDOM NUMBER GENERATOR AVAILABLE.
C (However, a newly discovered technique can yield
C a period of 10^600. But that is still in the development stage.)
C
C It passes ALL of the tests for random number generators and has a period
C of 2^144, is completely portable (gives bit identical results on all
C machines with at least 24-bit mantissas in the floating point
C representation).
C
C The algorithm is a combination of a Fibonacci sequence (with lags of 97
C and 33, and operation "subtraction plus one, modulo one") and an
C "arithmetic sequence" (using subtraction).
C
C On a Vax 11/780, this random number generator can produce a number in
C 13 microseconds.
C========================================================================
PROGRAM TstRAN
REAL temp(100)
INTEGER IJ, KL, len
C These are the seeds needed to produce the test case results
IJ = 1802
KL = 9373
C Do the initialization
call rmarin(ij,kl)
C Generate 20000 random numbers
len = 100
do 10 i = 1, 200
call RANMAR(temp, len)
10 continue
C If the random number generator is working properly, the next six random
C numbers should be:
C 6533892.0 14220222.0 7275067.0
C 6172232.0 8354498.0 10633180.0
len = 6
call RANMAR(temp, len)
write(*,*)' If the random number generator is working properly
*, the next six random'
write(*,*)' numbers should be:'
write(*,*)' 6533892.0 14220222.0 7275067.0'
write(*,*)' 6172232.0 8354498.0 10633180.0'
write(*,*)
write(*,20) (4096.0*4096.0*temp(I), I=1,6)
20 format (3f12.1)
end
subroutine RMARIN(IJ,KL)
C This is the initialization routine for the random number generator
RANMAR()
C NOTE: The seed variables can have values between: 0 <= IJ <= 31328
C 0 <= KL <= 30081
C The random number sequences created by these two seeds are of sufficient
C length to complete an entire calculation with. For example, if sveral
C different groups are working on different parts of the same calculation,
C each group could be assigned its own IJ seed. This would leave each group
C with 30000 choices for the second seed. That is to say, this random
C number generator can create 900 million different subsequences -- with
C each subsequence having a length of approximately 10^30.
C
C Use IJ = 1802 & KL = 9373 to test the random number generator. The
C subroutine RANMAR should be used to generate 20000 random numbers.
C Then display the next six random numbers generated multiplied by 4096*4096
C If the random number generator is working properly, the random numbers
C should be:
C 6533892.0 14220222.0 7275067.0
C 6172232.0 8354498.0 10633180.0
real U(97), C, CD, CM
integer I97, J97
logical TEST
common /raset1/ U, C, CD, CM, I97, J97, TEST
TEST=.FALSE.
if( IJ .lt. 0 .or. IJ .gt. 31328 .or.
* KL .lt. 0 .or. KL .gt. 30081 ) then
write(*,*)' The first random number seed must have a value
*between 0 and 31328'
write(*,*)' The second seed must have a value between 0 and
*30081'
stop
endif
i = mod(IJ/177, 177) + 2
j = mod(IJ , 177) + 2
k = mod(KL/169, 178) + 1
l = mod(KL, 169)
do 2 ii = 1, 97
s = 0.0
t = 0.5
do 3 jj = 1, 24
m = mod(mod(i*j, 179)*k, 179)
i = j
j = k
k = m
l = mod(53*l+1, 169)
if (mod(l*m, 64) .ge. 32) then
s = s + t
endif
t = 0.5 * t
3 continue
U(ii) = s
2 continue
C = 362436.0 / 16777216.0
CD = 7654321.0 / 16777216.0
CM = 16777213.0 /16777216.0
I97 = 97
J97 = 33
TEST = .TRUE.
return
end
subroutine ranmar(RVEC, LEN)
C This is the random number generator proposed by George Marsaglia in
C Florida State University Report: FSU-SCRI-87-50
C It was slightly modified by F. James to produce an array of pseudorandom
C numbers.
REAL RVEC(*)
real U(97), C, CD, CM
integer I97, J97
logical TEST
common /raset1/ U, C, CD, CM, I97, J97, TEST
integer ivec
if( .NOT. TEST ) then
write(*,*)' Call the init routine (RMARIN) before calling RAN
*MAR'
stop
endif
do 100 ivec = 1, LEN
uni = U(I97) - U(J97)
if( uni .lt. 0.0 ) uni = uni + 1.0
U(I97) = uni
I97 = I97 - 1
if(I97 .eq. 0) I97 = 97
J97 = J97 - 1
if(J97 .eq. 0) J97 = 97
C = C - CD
if( C .lt. 0.0 ) C = C + CM
uni = uni - C
if( uni .lt. 0.0 ) uni = uni + 1.0
RVEC(ivec) = uni
100 continue
return
end
=========================================================================
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