“Finally, we give you Knuth's suggestion for a portable routine, which we have translated to the present conventions as RAN3. This is not based on the linear congruential method at all, but rather on a subtractive method. One might hope that its weaknesses, if any, are therefore of a highly different character from the weaknesses, if any, of RAN1 above [not given]. If you ever suspect trouble with one routine, it is a good idea to try the other in the same application. RAN3 has one nice feature: if your machine is poor on integer arithmetic, (i.e. is limited to 16-bit integers), substitution of the two "commented" lines for the one directly following them will render the routine entirely floating point.”

      FUNCTION RAN3(IDUM)
Returns a uniform random deviate between 0.0 and 1.0. Set IDUM to any negative value
to initialize or reinitialize the sequence.
C         IMPLICIT REAL*4(M)
C         PARAMETER (MBIG=4000000.,MSEED=1618033.,MZ=0.,FAC=2.5E-7)
      PARAMETER (MBIG=1000000000,MSEED=161803398,MZ=0,FAC=1.E-9)
According to Knuth, any large MBIG, and any smaller (but still large) MSEED can be
substituted for the above values.
      DIMENSION MA(55)                  Save MA. This value is special and should not be modified; see Knuth
      DATA IFF /0/
      IF(IDUM.LT.0.OR.IFF.EQ.0)THEN     Initialization
        IFF=1
        MJ=MSEED-IABS(IDUM)             Initialize MA(55) using the seed IDUM and the large number MSEED.
        MJ=MOD(MJ,MBIG)
        MA(55)=MJ
        MK=1
        DO 11 I=1,54                    Now initialize the rest of the table
          II=MOD(21*I,55)               in a slightly random order
          MA(II)=MK                     with numbers that are not especially random
          MK=MJ-MK
          IF(MK.LT.MZ)MK=MK+MBIG
          MJ=MA(II)
11      CONTINUE
        DO 13 K=1,4                     We randomize them by "warming up the generator"
          DO 12 I=1,55
            MA(I)=MA(I)-MA(1+MOD(I+30,55))
            IF(MA(I).LT.MZ)MA(I)=MA(I)+MBIG
12        CONTINUE
13      CONTINUE
        INEXT=0                         Prepare indices for our first generated number
        INEXTP=31                       The constant 31 is special; see Knuth
        IDUM=1
      ENDIF
      INEXT=INEXT+1                     Here is where we start, except on initialization. Increment INEXT,
      IF(INEXT.EQ.56)INEXT=1             wrapping around 56 to 1.
      INEXTP=INEXTP+1                   Ditto for INEXTP
      IF(INEXTP.EQ.56)INEXTP=1
      MJ=MA(INEXT)-MA(INEXTP)           Now generate a new random number subtractively
      IF(MJ.LT.MZ)MJ=MJ+MBIG            Be sure that it is in range
      MA(INEXT)=MJ                      and output the derived uniform deviate
      RAN3=MJ*FAC
      RETURN
      END

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