FORTRAN Computer Games

Additive Congruential Random Number (ACORN) Generator

ACORN is a family of pseudo-random number generators, invented by R. S. Wikramaratna. The following code is the reference implementation in FORTRAN 77 in double precision.

Save the following code in file acorn.f.

      DOUBLE PRECISION FUNCTION ACORN()
C
C     FORTRAN IMPLEMENTATION OF ACORN RANDOM NUMBER GENERATOR OF ORDER
C     LESS THAN OR EQUAL TO 120 (HIGHER ORDERS CAN BE OBTAINED BY
C     INCREASING THE PARAMETER VALUE MAXORD) AND MODULUS LESS THAN OR
C     EQUAL TO 2^60.
C
C     AFTER APPROPRIATE INITIALIZATION OF THE COMMON BLOCK /IACO2/ EACH
C     CALL TO ACORN GENERATES A SINGLE VARIATE DRAWN FROM A UNIFORM
C     DISTRIBUTION OVER THE UNIT INTERVAL.
C
      PARAMETER (MAXORD=120, MAXOP1=MAXORD+1)
      COMMON /IACO2/ KORDEJ, MAXJNT, IXV1(MAXOP1), IXV2(MAXOP1)

      DO 10 I = 1, KORDEJ
      IXV1(I + 1) = (IXV1(I + 1) + IXV1(I))
      IXV2(I + 1) = (IXV2(I + 1) + IXV2(I))

      IF (IXV2(I + 1) .GE. MAXJNT) THEN
        IXV2(I + 1) = IXV2(I + 1) - MAXJNT
        IXV1(I + 1) = IXV1(I + 1) + 1
      END IF
      IF (IXV1(I + 1) .GE. MAXJNT) IXV1(I + 1) = IXV1(I + 1) - MAXJNT
   10 CONTINUE

      ACORN = (DBLE(IXV1(KORDEJ + 1)) +
     &         DBLE(IXV2(KORDEJ + 1)) / MAXJNT) / MAXJNT
      END
C     ******************************************************************
      SUBROUTINE SACORN(ISEED)
C
C     INITIALISES THE ACORN GENERATOR:
C
C     KORDEJ - LESS OR EQUAL MAXORD.
C     MAXJNT - SHOULD BE 2**30.
C     IXV1   - ARRAY OF ARBITRARY ODD INTEGERS, EACH LESS THAN MAXJNT.
C     IXV2   - ARRAY OF ARBITRARY INTEGERS, EACH LESS THAN MAXJNT.
C
      PARAMETER (MAXORD=120, MAXOP1=MAXORD+1)
      COMMON /IACO2/ KORDEJ, MAXJNT, IXV1(MAXOP1), IXV2(MAXOP1)

      KORDEJ = 120
      MAXJNT = 2**30
      IFIRST = MOD(ISEED, MAXJNT)
      IF (MOD(IFIRST, 2) .EQ. 0) IFIRST = IFIRST - 1
      IXV1(1) = IFIRST
      END

The test program reads a seed value from user input, initialises the ACORN generator, and outputs random numbers to screen. Save the program to file test.f:

C     ******************************************************************
C
C     TEST PROGRAM FOR THE ACORN GENERATOR.
C
C     ******************************************************************
      PROGRAM TEST
      EXTERNAL         SACORN
      DOUBLE PRECISION ACORN

      INTEGER ISEED, I
C
C     SEED THE PRNG.
C
      PRINT 100
      READ (*, *) ISEED
      CALL SACORN(ISEED)
C
C     PRINT RANDOM NUMBERS.
C
      PRINT 200, (ACORN(), I = 1, 120)

  100 FORMAT (' ADDITIVE CONGRUENTIAL RANDOM NUMBER (ACORN) GENERATOR',
     &/,' ENTER POSITIVE INTEGER SEED: ',$)
  200 FORMAT (6(X,F8.6))
      END

We can compile the program with f2c and cc:

$ f2c test.f acorn.f
test.f:
   MAIN test:
acorn.f:
   acorn:
   aseed:
$ cc -o test test.c acorn.c -lf2c -lm

Once we have entered a seed value, the program outputs 120 random numbers:

$ ./test
 ADDITIVE CONGRUENTIAL RANDOM NUMBER (ACORN) GENERATOR
 ENTER POSITIVE INTEGER SEED: 987654321
  .298797  .226591  .290228  .997080  .926994  .466868
  .184597  .953554  .000939  .012210  .054502  .599517
  .364293  .629662  .666954  .669106  .686324  .595152
  .301378  .109643  .164744  .154260  .524311  .145869
  .646038  .473907  .691274  .082447  .044297  .221484
  .111101  .027728  .219465  .582285  .578690  .174322
  .009961  .515100  .407715  .630861  .257771  .994261
  .350338  .396714  .787953  .843483  .805566  .819482
  .724334  .662736  .457410  .282202  .241905  .001693
  .369023  .016929  .631515  .938099  .320673  .962020
  .411894  .338141  .791742  .401258  .526657  .938761
  .172363  .064770  .525239  .568505  .613865  .636974
  .478574  .660045  .316117  .920511  .640789  .395848
  .819922  .049805  .530998  .112946  .830457  .731110
  .292677  .840599  .344874  .996975  .296268  .691292
  .064425  .322370  .835106  .050135  .692410  .807923
  .013601  .683316  .996426  .392138  .630321  .313052
  .736025  .277592  .166268  .222421  .453175  .623368
  .612398  .462287  .935029  .222560  .096076  .934051
  .778278  .997186  .327632  .881157  .988206  .976412

Depending on the seed value, it may be necessary to throw away the first random numbers.

References

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