61-bit Prime Modulus Linear Congruential Generator

This algorithm is slower than the generators using a power of two modulus, but produces a random number sequence free of short period patterns in the low order bits. A pattern does occur for this generator, however, and is described in [5]. The next value for the random state x[n] is determined from the current value x[n - 1] by:

x[n] = a x[n - 1]   (modp) (6)

Where the multiplier, a = 437799614237992725, is hardwired into the algorithm and p is a Mersenne prime; that is, a prime that is of the form p = 2^m - 1 where m is also a prime. For this generator m = 61, which is the largest value of m less than 64 for which 2^m - 1 and m are primes. The multiplier was again chosen to obtain maximal period of the generator, 2⁶¹ -2 $\approx$ 2.3 x 10¹⁸, for this algorithm. This generator is the same as the default one-stream SPRNG pmlcg generator and was checked to insure that it satisfies the requirements for maximal period. The interface routines for this generator are declared as: Rng_Type RngP61Seed( Rng_UInt32 i, Rng_UInt32 j );

Rng_Type RngP61Spawn( Rng_Type *x );

int iRngP61( Rng_Type *x );

double dRngP61( Rng_Type *x );

float fRngP61( Rng_Type *x );