RANDU

RANDU is a linear congruential pseudorandom number generator (LCG) of the Park–Miller type, which was used primarily in the 1960s and 1970s. It is defined by the recurrence

: $V\_\{j+1\}\; =\; 65539\; \backslash cdot\; V\_j\; \backslash bmod\; 2^\{31\}$

with the initial seed number $V\_0$ as an odd number. It generates pseudorandom integers $V\_j$ which are uniformly distributed in the interval , but in practical applications are often mapped into pseudorandom rationals $X\_j$ in the interval , by the formula : $X\_j\; =\; \backslash frac\{V\_j\}\{2^\{31\}\}.$

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, as shown below.

The reason for choosing these particular values for the multiplier and modulus had been that with a 32-bit-integer word size, the arithmetic of mod 2³¹ and $65539\; =\; 2^\{16\}\; +\; 3$ calculations could be done quickly, using bitwise operators in hardware, but the values were chosen for computational convenience, not statistical quality. Provided by Wikipedia