Implementation status: to be implemented

Synopsis

#include <stdlib.h>

double drand48(void);
double erand48(unsigned short xsubi[3]);
long jrand48(unsigned short xsubi[3]);
void lcong48(unsigned short param[7]);
long lrand48(void);
long mrand48(void);
long nrand48(unsigned short xsubi[3]);
unsigned short *seed48(unsigned short seed16v[3]);
void srand48(long seedval);

Description

The functions generate uniformly distributed pseudo-random numbers using a linear congruential algorithm and 48-bit integer arithmetic.

Arguments:

xsubi - a work vector used in generating the pseudo-random numbers.

param - parameter values for the 48 bit pseudo-random number generation routines.

seed16v - a 48-bit number that is used as the seed for pseudo-random number generation. Each element of seed16v contains 16 bits of the number.

seedval - a beginning value for the pseudo-random number sequence. For the same seed the same sequence of numbers is generated.

The initializer function srand48() sets the high-order 32 bits of Xi to the low-order 32 bits contained in its argument. The low-order 16 bits of Xi are set to the arbitrary value 330E16.

The initializer function seed48() sets the value of Xi to the 48-bit value specified in the argument array. The low-order 16 bits of Xi are set to the low-order 16 bits of seed16v[0]. The mid-order 16 bits of Xi are set to the low-order 16 bits of seed16v[1]. The high-order 16 bits of Xi are set to the low-order 16 bits of seed16v[2]. In addition, the previous value of Xi is copied into a 48-bit internal buffer, used only by seed48(), and a pointer to this buffer is the value returned by seed48(). This returned pointer, which can just 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 at and store the last Xi value, and then use this value to reinitialize via seed48() when the program is restarted.

The initializer function lcong48() allows the user to specify the initial Xi, the multiplier value a, and the added value c. Argument array elements:

  • param[0-2] specify Xi,
  • param[3-5] specify the multiplier a,
  • param[6] specifies the 16-bit added value c.

After lcong48() is called, a subsequent call to either srand48() or seed48() restores the standard multiplier and addend values, a and c, specified above.

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

The lrand48() and nrand48() functions return non-negative, long integers, uniformly distributed over the interval [0,231).

The mrand48() and jrand48() functions return signed long integers uniformly distributed over the interval [-231,231).

The srand48(), seed48(), and lcong48() functions are initialization entry points, one of which should be invoked before either 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.) The erand48(), nrand48(), and jrand48() functions do not require an initialization entry point to be called first.

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

Xn+1 = (aXn + c)mod m , where n>= 0

The parameter m = 248; hence 48-bit integer arithmetic is performed. Unless lcong48() is invoked, the multiplier value a and the addend value c are given by:

a = 5DEECE66D16 = 2736731631558

c = B16 = 138

The value returned by any of the drand48(), erand48(), jrand48(), lrand48(), mrand48(), or nrand48() functions is computed by first generating the next 48-bit Xi 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 Xi and transformed into the returned value.

The drand48(), lrand48() and mrand48() functions store the last 48-bit Xi generated in an internal buffer; that is why the application ensures that these are initialized prior to being invoked. The erand48(), nrand48(), and jrand48() functions require the calling program to provide storage for the successive Xi 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 Xi into the array and pass it as an argument. By using different arguments, 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 are called to generate numbers for the other streams.

The drand48(), lrand48() and mrand48() functions are not thread-safe.

Return value

As described above.

Errors

No errors are defined.

Examples

None.

Implementation tasks

  • Implement lcong48(),
  • Implement seed48(),
  • Implement srand48(),
  • Implement drand48(),
  • Implement erand48(),
  • Implement jrand48(),
  • Implement lrand48(),
  • Implement mrand48(),
  • Implement nrand48().