drand48(3)
NAME
drand48, erand48, lrand48, nrand48, mrand48, jrand48, srand48, seed48, lcong48 − generate uniformly distributed pseudo-random numbers
SYNTAX
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
These subroutines generate pseudo-random numbers using the well-known linear congruential algorithm and 48-bit integer arithmetic.
The drand48 and erand48 subroutines return non-negative double-precision floating-point values uniformly distributed over the interval[0.0, 1.0). The lrand48 and nrand48 subroutines return non-negative long integers uniformly distributed over the interval [0, 231). The mrand48 and jrand48 subroutines return signed long integers uniformly distributed over the interval [−231, 231).
The srand48, seed48 and lcong48 subroutines 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 will be supplied automatically if drand48, lrand48 or mrand48 is called without a prior call to an initialization entry point.) The erand48, nrand48 and jrand48 subroutines 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 n≥0.
The parameterm = 248; hence 48-bit integer arithmetic is performed. Unless lcong48 has been invoked, the multiplier valuea and the addend valuec are given by:
a = 5DEECE66D 16 = 273673163155 8c = B 16 = 13 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 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 ofXi and transformed into the returned value.
The drand48, lrand48 and mrand48 subroutines store the last 48-bitXi generated in an internal buffer. That is why they must be initialized prior to being invoked. The erand48, nrand48 and jrand48 subroutines require the calling program to provide storage for the successiveXi 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 ofXi 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 will not depend upon how many times the routines have been called to generate numbers for the other streams.
The initializer srand48 sets the high-order 32 bits ofXi to the 32 bits contained in its argument. The low-order 16 bits ofXi are set to the arbitrary value 330E16.
The initializer seed48 sets the value ofXi to the 48-bit value specified in the argument array. In addition, the previous value ofXi 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 lastXi value, and then use this value to reinitialize with seed48 when the program is restarted.
The lcong48 initialization subroutine allows the user to specify the initialXi, the multiplier value a, and the addend valuec. Argument array elements param[0-2] specifyXi, param[3-5] specify the multipliera, and param[6] specifies the 16-bit addendc. After lcong48 has been called, a subsequent call to either srand48 or seed48 will restore the “standard” multiplier and addend values,a andc, specified on the previous page.
NOTES
These routines are coded in assembly language for maximum speed. It requires approximately 130 μsec on a PDP-11/70 to generate one pseudo-random number.