drand48(3C)                                           drand48(3C)



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

SYNOPSIS
     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];

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

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

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

     Functions mrand48 and jrand48 return signed long integers
                                                31   31
     uniformly distributed over the interval [-2  , 2  ).
     Functions srand48, seed48, and lcong48 are initialization
     entry points, one of which should be invoked before drand48,
     lrand48, or mrand48 is called.  (Although it is not
     recommended practice, constant default initializer values
     are supplied automatically if drand48, lrand48, or mrand48
     is called without a prior call to an initialization entry
     point.)  Functions erand48, nrand48, and jrand48 do not
     require an initialization entry point to be called first.



January 1992                                                    1

drand48(3C)                                           drand48(3C)



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

          X    = (aX  + c)          n>0
           n+1      n     mod m

                        48
     The parameter m = 2  ; 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 = 5DEECE66D   =-273673163155
                       16               8
          c = B   = 13 .
               16     8

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

     The functions drand48, lrand48, and mrand48 store the last
     48-bit X  generated in an internal buffer; that is why they
             i
     must be initialized prior to being invoked.  The functions
     erand48, nrand48, and jrand48 require the calling program to
     provide storage for the successive X  values in the array
                                         i
     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 initial
     value of X  into the array and pass it as an argument.  By
               i
     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
     does 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  to the 32 bits contained in its argument.  The low-
         i
     order 16 bits of X  are set to the arbitrary value 330E  .
                       i                                    16

     The initializer function seed48 sets the value of X  to the
                                                        i
     48-bit value specified in the argument array.  The previous
     value of X  is copied into a 48-bit internal buffer, used
               i
     only by seed48.  A pointer to this buffer is the value
     returned by seed48.  The returned pointer, which can 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 and store the last X  value; then use this
                                        i
     value to reinitialize via seed48 when the program is
     restarted.




2                                                    January 1992

drand48(3C)                                           drand48(3C)



     The initialization function lcong48 allows the user to
     specify the initial X , the multiplier value a, and the
                          i
     addend value c.  Argument array elements param[0-2] specify
     X , elements param[3-5] specify the multiplier a, and
      i
     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.

NOTES
     The routines are coded in portable C.  The source code for
     the portable version can even be used on computers which do
     not have floating-point arithmetic.  In such a situation,
     functions drand48 and erand48 do not exist; instead, they
     are replaced by the following two functions:

          long irand48 (m)
          unsigned short m;

          long krand48 (xsubi,m)
          unsigned short xsubi[3],m;

     Functions irand48 and krand48 return non-negative long
     integers uniformly distributed over the interval [0, m-1].

SEE ALSO
     rand(3C)




























January 1992                                                    3