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DRAND48(3)                 Library Functions Manual                 DRAND48(3)

delim $$

       drand48,  erand48, lrand48, nrand48, mrand48, jrand48, srand48, seed48,
       lcong48 - generate uniformly distributed pseudo-random numbers

       double drand48()

       double erand48(xsubi)
       unsigned short xsubi[3];

       long lrand48()

       long nrand48(xsubi)
       unsigned short xsubi[3];

       long mrand48()

       long jrand48(xsubi)
       unsigned short xsubi[3];

       void srand48(seedval)
       long seedval;

       unsigned short *seed48(seed16v)
       unsigned short seed16v[3];

       void lcong48(param)
       unsigned short param[7];

       This family of functions  generates  pseudo-random  numbers  using  the
       well-known linear congruential algorithm and 48-bit integer arithmetic.

       drand48()  and erand48() return non-negative double-precision floating-
       point values uniformly distributed over the interval $[0.0,~1.0).$

       lrand48() and nrand48() return  non-negative  long  integers  uniformly
       distributed over the interval (0, ~2**31).

       mrand48()  and jrand48() return signed long integers uniformly distrib-
       uted over the interval [-2**31 ~2**31).

       srand48(), seed48(), and lcong48() are initialization entry points, one
       of  which  should  be  invoked  before  either drand48(), lrand48(), or
       mrand48() is called.  Although it is not recommended practice, constant
       default initializer values will be supplied automatically if drand48(),
       lrand48(), or mrand48() is called without a prior call to  an  initial-
       ization  entry  point.   erand48(),  nrand48(),  and  jrand48()  do not
       require an initialization entry point to be called first.

       All the routines work by generating a sequence of 48-bit  integer  val-
       ues, $X sub i ,$ according to the linear congruential formula

              X sub{n+1}~=~(aX sub n^+^c) sub{roman mod~m}~~~~~~~~n>=0.

       The  parameter  m=2**48;  hence 48-bit integer arithmetic is performed.
       Unless lcong48() has been invoked, the multiplier  value  $a$  and  the
       addend value $c$ are given by

             a~mark =~roman 5DEECE66D^sub 16~=~roman 273673163155^sub 8
             c~lineup =~roman B^sub 16~=~roman 13^sub 8 .

       The  value  returned  by  any  of  the  functions drand48(), erand48(),
       lrand48(), nrand48(), mrand48(), or jrand48() is computed by first gen-
       erating  the next 48-bit $X sub i$ in the sequence.  Then the appropri-
       ate number of bits, according to the type of data item to be  returned,
       are  copied from the high-order (leftmost) bits of $X sub i$ and trans-
       formed into the returned value.

       drand48(), lrand48(), and mrand48() store the last  48-bit  $X  sub  i$
       generated  in  an internal buffer; that is why they must be initialized
       prior to  being  invoked.   The  functions  erand48(),  nrand48(),  and
       jrand48()  require  the calling program to provide storage for the suc-
       cessive $X sub i$ values in the array specified as an argument when the
       functions  are  invoked.   That is why these routines do not have to be
       initialized; the calling program merely has to place the  desired  ini-
       tial  value of $X sub i$ into the array and pass it as an argument.  By
       using  different  arguments,  functions   erand48(),   nrand48(),   and
       jrand48() allow separate modules of a large program to generate several
       independent streams of pseudo-random numbers, that is, the sequence  of
       numbers in each stream will not depend upon how many times the routines
       have been called to generate numbers for the other streams.

       The initializer function srand48() sets the high-order 32  bits  of  $X
       sub i$ to the 32 bits contained in its argument.  The low-order 16 bits
       of $X sub i$ are set to the arbitrary value $roman 330E sub 16 .$

       The initializer function seed48() sets the value of $X sub  i$  to  the
       48-bit  value specified in the argument array.  In addition, the previ-
       ous value of $X sub i$ is copied into a 48-bit  internal  buffer,  used
       only by seed48(), and a pointer to this buffer is the value returned by
       seed48().  This returned pointer, which can  just  be  ignored  if  not
       needed, is useful if a program is to be restarted from a given point at
       some future time -- use the pointer to get at and store the last $X sub
       i$ value, and then use this value to reinitialize via seed48() when the
       program is restarted.

       The initialization function lcong48() allows the user  to  specify  the
       initial $X sub i ,$ the multiplier value $a,$ and the addend value $c.$
       Argument array elements param[0-2] specify $X sub i ,$ param[3-5] spec-
       ify  the  multiplier $a,$ and param[6] specifies the 16-bit addend $c.$
       After lcong48() has been called, a subsequent call to either  srand48()
       or  seed48()  will restore the "standard" multiplier and addend values,
       $a$ and $c,$ specified on the previous page.


                                7 February 1989                     DRAND48(3)