drand48(3C) drand48(3C)
delim $$
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
integers uniformly distributed over the interval $[0,~2 sup
31 ).$
Functions mrand48 and jrand48 return signed long integers
uniformly distributed over the interval $[-2 sup 31 ,~2 sup
31 ).$ $[-2 sup 31 ,~2 sup 31 ).$ 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
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drand48(3C) drand48(3C)
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.
All the routines work by generating a sequence of 48-bit
integer values, $X sub i ,$ according to the linear
congruential formula
X sub{n+1}~=~(aX sub n^+^c) sub{roman mod~m}~~~~~~~~n>=0.
The parameter $m^=^2 sup 48$; 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
generating the next 48-bit $X sub i$ in the sequence. Then
the appropriate 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 transformed into the
returned value.
The functions 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 successive $X sub
i$ 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 initial 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, i.e., 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 $X sub i$ 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. The
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previous value of $X sub i$ is copied into a 48-bit internal
buffer, used 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 $X sub i$ value; 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 $X sub i ,$ elements param[3-5] specify 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.
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).
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