Previous: BSD Random, Up: Pseudo-Random Numbers

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`.

— Function: double **drand48** (`void`)

This function returns a

`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`

.

— Function: double **erand48** (`unsigned short int xsubi`[`3`])

This function returns a

`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.

— Function: long int **lrand48** (`void`)

The

`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.

— Function: long int **nrand48** (`unsigned short int xsubi`[`3`])

This function is similar to the

`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.

— Function: long int **mrand48** (`void`)

The

`mrand48`

function is similar to`lrand48`

. The only difference is that the numbers returned are in the range`-2^31`

to`2^31`

(exclusive).

— Function: long int **jrand48** (`unsigned short int xsubi`[`3`])

The

`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.

— Function: void **srand48** (`long int seedval`)

The

`srand48`

function sets the most significant 32 bits of the internal state of the random number generator to the least significant 32 bits of theseedvalparameter. 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).

— Function: unsigned short int * **seed48** (`unsigned short int seed16v`[`3`])

The

`seed48`

function initializes all 48 bits of the state of the internal random number generator from the contents of the parameterseed16v. Here the lower 16 bits of the first element ofsee16vinitialize the least significant 16 bits of the internal state, the lower 16 bits ofseed16v`[1]`

initialize the mid-order 16 bits of the state and the 16 lower bits ofseed16v`[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.

— Function: void **lcong48** (`unsigned short int param`[`7`])

The

`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

paramthe least significant 16 bits of the entriesparam`[0]`

toparam`[2]`

determine the initial state, the least significant 16 bits ofparam`[3]`

toparam`[5]`

determine the 48 bit constant`a`

andparam`[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.

— Function: int **drand48_r** (`struct drand48_data *buffer, double *result`)

This function is equivalent to the

`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 pointerbuffer. The random number is returned in the variable pointed to byresult.The return value of the function indicates whether the call succeeded. If the value is less than

`0`

an error occurred anderrnois set to indicate the problem.This function is a GNU extension and should not be used in portable programs.

— Function: int **erand48_r** (`unsigned short int xsubi`[`3`]`, struct drand48_data *buffer, double *result`)

The

`erand48_r`

function works like`erand48`

, but in addition it takes an argumentbufferwhich 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 byresult.The return value is non-negative if the call succeeded.

This function is a GNU extension and should not be used in portable programs.

— Function: int **lrand48_r** (`struct drand48_data *buffer, double *result`)

This function is similar to

`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

resultcontains the result. Otherwise an error occurred.This function is a GNU extension and should not be used in portable programs.

— Function: int **nrand48_r** (`unsigned short int xsubi`[`3`]`, struct drand48_data *buffer, long int *result`)

The

`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 bybuffer. The state is described by the values inxsubi.If the return value is non-negative the variable pointed to by

resultcontains the result.This function is a GNU extension and should not be used in portable programs.

— Function: int **mrand48_r** (`struct drand48_data *buffer, double *result`)

This function is similar to

`mrand48`

but like the other reentrant functions it uses the random number generator described by the value in the buffer pointed to bybuffer.If the return value is non-negative the variable pointed to by

resultcontains the result.This function is a GNU extension and should not be used in portable programs.

— Function: int **jrand48_r** (`unsigned short int xsubi`[`3`]`, struct drand48_data *buffer, long int *result`)

The

`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 bybuffer.If the return value is non-negative the variable pointed to by

resultcontains 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.

— Function: int **srand48_r** (`long int seedval, struct drand48_data *buffer`)

The description of the random number generator represented by the information in

bufferis initialized similarly to what the function`srand48`

does. The state is initialized from the parameterseedvaland 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.

— Function: int **seed48_r** (`unsigned short int seed16v`[`3`]`, struct drand48_data *buffer`)

This function is similar to

`srand48_r`

but like`seed48`

it initializes all 48 bits of the state from the parameterseed16v.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 bybuffer.This function is a GNU extension and should not be used in portable programs.

— Function: int **lcong48_r** (`unsigned short int param`[`7`]`, struct drand48_data *buffer`)

This function initializes all aspects of the random number generator described in

bufferwith the data inparam. Here it is especially true that the function does more than just copying the contents ofparamandbuffer. More work is required and therefore it is important to use this function rather than initializing the random number generator directly.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.