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The C library on SVID systems contains yet another kind of random number generator functions. They use a state of 48 bits of data. The user can choose among a collection of functions which return the random bits in different forms.
Generally there are two kinds of function. The first uses a state of the random number generator which is shared among several functions and by all threads of the process. The second requires the user to handle the state.
All functions have in common that they use the same congruential formula with the same constants. The formula is
Y = (a * X + c) mod m |
where X is the state of the generator at the beginning and
Y the state at the end. a
and c
are constants
determining the way the generator works. By default they are
a = 0x5DEECE66D = 25214903917 c = 0xb = 11 |
but they can also be changed by the user. m
is of course 2^48
since the state consists of a 48-bit array.
The prototypes for these functions are in `stdlib.h'.
double
value in the range of 0.0
to 1.0
(exclusive). The random bits are determined by the global
state of the random number generator in the C library.
Since the double
type according to IEEE 754 has a 52-bit
mantissa this means 4 bits are not initialized by the random number
generator. These are (of course) chosen to be the least significant
bits and they are initialized to 0
.
double
value in the range of 0.0
to 1.0
(exclusive), similarly to drand48
. The argument is
an array describing the state of the random number generator.
This function can be called subsequently since it updates the array to guarantee random numbers. The array should have been initialized before initial use to obtain reproducible results.
lrand48
function returns an integer value in the range of
0
to 2^31
(exclusive). Even if the size of the long
int
type can take more than 32 bits, no higher numbers are returned.
The random bits are determined by the global state of the random number
generator in the C library.
lrand48
function in that it
returns a number in the range of 0
to 2^31
(exclusive) but
the state of the random number generator used to produce the random bits
is determined by the array provided as the parameter to the function.
The numbers in the array are updated afterwards so that subsequent calls to this function yield different results (as is expected of a random number generator). The array should have been initialized before the first call to obtain reproducible results.
mrand48
function is similar to lrand48
. The only
difference is that the numbers returned are in the range -2^31
to
2^31
(exclusive).
jrand48
function is similar to nrand48
. The only
difference is that the numbers returned are in the range -2^31
to
2^31
(exclusive). For the xsubi
parameter the same
requirements are necessary.
The internal state of the random number generator can be initialized in several ways. The methods differ in the completeness of the information provided.
srand48
function sets the most significant 32 bits of the
internal state of the random number generator to the least
significant 32 bits of the seedval parameter. The lower 16 bits
are initialized to the value 0x330E
. Even if the long
int
type contains more than 32 bits only the lower 32 bits are used.
Owing to this limitation, initialization of the state of this
function is not very useful. But it makes it easy to use a construct
like srand48 (time (0))
.
A side-effect of this function is that the values a
and c
from the internal state, which are used in the congruential formula,
are reset to the default values given above. This is of importance once
the user has called the lcong48
function (see below).
seed48
function initializes all 48 bits of the state of the
internal random number generator from the contents of the parameter
seed16v. Here the lower 16 bits of the first element of
see16v initialize the least significant 16 bits of the internal
state, the lower 16 bits of seed16v[1]
initialize the mid-order
16 bits of the state and the 16 lower bits of seed16v[2]
initialize the most significant 16 bits of the state.
Unlike srand48
this function lets the user initialize all 48 bits
of the state.
The value returned by seed48
is a pointer to an array containing
the values of the internal state before the change. This might be
useful to restart the random number generator at a certain state.
Otherwise the value can simply be ignored.
As for srand48
, the values a
and c
from the
congruential formula are reset to the default values.
There is one more function to initialize the random number generator which enables you to specify even more information by allowing you to change the parameters in the congruential formula.
lcong48
function allows the user to change the complete state
of the random number generator. Unlike srand48
and
seed48
, this function also changes the constants in the
congruential formula.
From the seven elements in the array param the least significant
16 bits of the entries param[0]
to param[2]
determine the initial state, the least significant 16 bits of
param[3]
to param[5]
determine the 48 bit
constant a
and param[6]
determines the 16-bit value
c
.
All the above functions have in common that they use the global parameters for the congruential formula. In multi-threaded programs it might sometimes be useful to have different parameters in different threads. For this reason all the above functions have a counterpart which works on a description of the random number generator in the user-supplied buffer instead of the global state.
Please note that it is no problem if several threads use the global state if all threads use the functions which take a pointer to an array containing the state. The random numbers are computed following the same loop but if the state in the array is different all threads will obtain an individual random number generator.
The user-supplied buffer must be of type struct drand48_data
.
This type should be regarded as opaque and not manipulated directly.
drand48
function with the
difference that it does not modify the global random number generator
parameters but instead the parameters in the buffer supplied through the
pointer buffer. The random number is returned in the variable
pointed to by result.
The return value of the function indicates whether the call succeeded.
If the value is less than 0
an error occurred and errno is
set to indicate the problem.
This function is a GNU extension and should not be used in portable programs.
erand48_r
function works like erand48
, but in addition
it takes an argument buffer which describes the random number
generator. The state of the random number generator is taken from the
xsubi
array, the parameters for the congruential formula from the
global random number generator data. The random number is returned in
the variable pointed to by result.
The return value is non-negative if the call succeeded.
This function is a GNU extension and should not be used in portable programs.
lrand48
, but in addition it takes a
pointer to a buffer describing the state of the random number generator
just like drand48
.
If the return value of the function is non-negative the variable pointed to by result contains the result. Otherwise an error occurred.
This function is a GNU extension and should not be used in portable programs.
nrand48_r
function works like nrand48
in that it
produces a random number in the range 0
to 2^31
. But instead
of using the global parameters for the congruential formula it uses the
information from the buffer pointed to by buffer. The state is
described by the values in xsubi.
If the return value is non-negative the variable pointed to by result contains the result.
This function is a GNU extension and should not be used in portable programs.
mrand48
but like the other reentrant
functions it uses the random number generator described by the value in
the buffer pointed to by buffer.
If the return value is non-negative the variable pointed to by result contains the result.
This function is a GNU extension and should not be used in portable programs.
jrand48_r
function is similar to jrand48
. Like the
other reentrant functions of this function family it uses the
congruential formula parameters from the buffer pointed to by
buffer.
If the return value is non-negative the variable pointed to by result contains the result.
This function is a GNU extension and should not be used in portable programs.
Before any of the above functions are used the buffer of type
struct drand48_data
should be initialized. The easiest way to do
this is to fill the whole buffer with null bytes, e.g. by
memset (buffer, '\0', sizeof (struct drand48_data)); |
Using any of the reentrant functions of this family now will automatically initialize the random number generator to the default values for the state and the parameters of the congruential formula.
The other possibility is to use any of the functions which explicitly initialize the buffer. Though it might be obvious how to initialize the buffer from looking at the parameter to the function, it is highly recommended to use these functions since the result might not always be what you expect.
srand48
does. The state is initialized from the parameter
seedval and the parameters for the congruential formula are
initialized to their default values.
If the return value is non-negative the function call succeeded.
This function is a GNU extension and should not be used in portable programs.
srand48_r
but like seed48
it
initializes all 48 bits of the state from the parameter seed16v.
If the return value is non-negative the function call succeeded. It
does not return a pointer to the previous state of the random number
generator like the seed48
function does. If the user wants to
preserve the state for a later re-run s/he can copy the whole buffer
pointed to by buffer.
This function is a GNU extension and should not be used in portable programs.
If the return value is non-negative the function call succeeded.
This function is a GNU extension and should not be used in portable programs.
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