RANDU

RANDU is a linear congruential pseudorandom number generator (LCG) of the Park–Miller type, which has been used since the 1960s. It is defined by the recurrence: RANDU is a linear congruential pseudorandom number generator (LCG) of the Park–Miller type, which has been used since the 1960s. It is defined by the recurrence: with the initial seed number, V 0 {displaystyle scriptstyle V_{0}} as an odd number. It generates pseudorandom integers V j {displaystyle scriptstyle V_{j}} which are uniformly distributed in the interval , but in practical applications are often mapped into pseudorandom rationals X j {displaystyle scriptstyle X_{j}} in the interval (0, 1), by the formula: IBM's RANDU is widely considered to be one of the most ill-conceived random number generators ever designed, and was described as 'truly horrible' by Donald Knuth. It fails the spectral test badly for dimensions greater than 2, and every integer result is odd. However, at least eight low-order bits are dropped when converted to single-precision (32 bit, 24 bit mantissa) floating-point. The reason for choosing these particular values is that with a 32-bit-integer word size, the arithmetic of mod 231 and 65539 {displaystyle 65539} ( i.e.,  2 16 + 3 ) {displaystyle ({ ext{i.e., }}2^{16}+3)} calculations could be done quickly, using special features of some computer hardware. In general, when an LCG with modulus 231 is used to produce points (xk, xk+1, xk+2) in 3-dimensional space, the points fall into no more than 2,344 parallel planes, a result which indicates an LCG is unsuitable for Monte Carlo simulation. Choice of multiplier determines the number of planes. To show the problem with the values of multiplier 65539 and modulus 231 chosen for RANDU, consider the following calculation where every term should be taken mod 231. Start by writing the recursive relation as: