NAME
drand48, erand48,
lrand48, nrand48,
mrand48, jrand48,
srand48,
srand48_deterministic,
seed48,
seed48_deterministic,
lcong48,
lcong48_deterministic —
pseudo-random number generators and
initialization routines
SYNOPSIS
#include
<stdlib.h>
double
drand48(void);
double
erand48(unsigned
short xseed[3]);
long
lrand48(void);
long
nrand48(unsigned
short xseed[3]);
long
mrand48(void);
long
jrand48(unsigned
short xseed[3]);
void
srand48(long
seed);
void
srand48_deterministic(long
seed);
unsigned short *
seed48(unsigned
short xseed[3]);
unsigned short *
seed48_deterministic(unsigned
short xseed[3]);
void
lcong48(unsigned
short p[7]);
void
lcong48_deterministic(unsigned
short p[7]);
DESCRIPTION
To satisfy portable code,
srand48(),
seed48(),
or
lcong48()
should be called to initialize the subsystem. In
OpenBSD the seeding parameters are ignored, and
strong random number results will be provided from
arc4random(3). In other systems, the parameters prime a
simplistic deterministic algorithm.
If the standardized behavior is
required then
srand48_deterministic(),
seed48_deterministic(), and
lcong48_deterministic() can be substituted for
srand48(), seed48(), and
lcong48(). That will cause subsequent calls to
drand48(), lrand48(), and
jrand48() to return results using the deterministic
algorithm.
drand48()
and erand48() return values of type double. The full
48 bits of r(n+1) are loaded into the mantissa of the returned value, with
the exponent set such that the values produced lie in the interval [0.0,
1.0).
lrand48()
and
nrand48()
return values of type long in the range [0, 2**31-1]. The high-order (31)
bits of r(n+1) are loaded into the lower bits of the returned value, with
the topmost (sign) bit set to zero.
mrand48()
and
jrand48()
return values of type long in the range [-2**31, 2**31-1]. The high-order
(32) bits of r(n+1) are loaded into the returned value.
In the deterministic mode, the
rand48()
family of functions generates numbers using a linear congruential algorithm
working on integers 48 bits in size. The particular formula employed is
r(n+1) = (a * r(n) + c) mod m where the default values are for the
multiplicand a = 0xfdeece66d = 25214903917 and the addend c = 0xb = 11. The
modulus is always fixed at m = 2 ** 48. r(n) is called the seed of the
random number generator.
For all the six generator routines described next, the first computational step is to perform a single iteration of the algorithm.
drand48(),
lrand48(), and mrand48() use
an internal buffer to store r(n). For these functions the initial value of
r(0) = 0x1234abcd330e = 20017429951246.
On the other hand,
erand48(),
nrand48(),
and jrand48() use a user-supplied buffer to store
the seed r(n), which consists of an array of 3 shorts, where the zeroth
member holds the least significant bits.
All functions share the same multiplicand and addend.
srand48_deterministic()
is used to initialize the internal buffer r(n) of
drand48(), lrand48(), and
mrand48() such that the 32 bits of the seed value
are copied into the upper 32 bits of r(n), with the lower 16 bits of r(n)
arbitrarily being set to 0x330e. Additionally, the constant multiplicand and
addend of the algorithm are reset to the default values given above.
seed48_deterministic()
also initializes the internal buffer r(n) of
drand48(), lrand48(), and
mrand48(), but here all 48 bits of the seed can be
specified in an array of 3 shorts, where the zeroth member specifies the
lowest bits. Again, the constant multiplicand and addend of the algorithm
are reset to the default values given above.
seed48_deterministic() returns a pointer to an array
of 3 shorts which contains the old seed. This array is statically allocated,
so its contents are lost after each new call to
seed48_deterministic().
Finally,
lcong48_deterministic()
allows full control over the multiplicand and addend used in
drand48(), erand48(),
lrand48(), nrand48(),
mrand48(), and jrand48(),
and the seed used in drand48(),
lrand48(), and mrand48(). An
array of 7 shorts is passed as parameter; the first three shorts are used to
initialize the seed; the second three are used to initialize the
multiplicand; and the last short is used to initialize the addend. It is
thus not possible to use values greater than 0xffff as the addend.
Note that all three methods of seeding the random number generator always also set the multiplicand and addend for any of the six generator calls.
SEE ALSO
STANDARDS
The drand48(),
erand48(), jrand48(),
lrand48(), mrand48(), and
nrand48(), functions conform to
IEEE Std 1003.1-2008 (“POSIX.1”).
The seed48(),
srand48(), and lcong48()
function do not conform to ANSI X3.159-1989
(“ANSI C89”), intentionally.
The seed48_deterministic(),
srand48_deterministic(), and
lcong48_deterministic() functions are
OpenBSD extensions.
AUTHORS
Martin Birgmeier