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Implementation of algorithms for IMPpolynomials
, 1994
"... Parallel Monte Carlo methods require pseudorandom number generators with long periods and stable statistical properties, in particular in the MIMD case. The type of the compound inversive congruential generator (cICG) satisfies these two important requirements. To implement cICG, we have to know sp ..."
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Parallel Monte Carlo methods require pseudorandom number generators with long periods and stable statistical properties, in particular in the MIMD case. The type of the compound inversive congruential generator (cICG) satisfies these two important requirements. To implement cICG, we have to know specific parameters. The latter are given by the coefficients of IMP polynomials. This new class of polynomials contains the class of primitive polynomials. It has been introduced by Flahive and Niederreiter[14]. Recently, Chou[4] has presented a very effective algorithm to find IMP polynomials over a given finite field F q . In this report we discuss Chou's algorithm and present the results of a first production run for tables of IMP polynomials that use our implementation of this algorithm. Further, we have implemented and studied the resulting ICG and cICG. A first series of numerical tests has shown that the theoretical results on the statistical independence properties of this type of gen...
EMPIRICAL PSEUDORANDOM NUMBER GENERATORS
"... The most common pseudorandom number generator or PRNG, the linear congruential generator or LCG, belongs to a whole class of rational congruential generators. These generators work by multiplicative congruential method for integers, which implements a ”growandcut procedure”. We extend this concept ..."
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The most common pseudorandom number generator or PRNG, the linear congruential generator or LCG, belongs to a whole class of rational congruential generators. These generators work by multiplicative congruential method for integers, which implements a ”growandcut procedure”. We extend this concept to real numbers and call this the real congruence, which produces another class of random number generators called real congruential generators or RCG. The method in RCG inherits the procedure in LCG. Let m be a positive integer and I the interval (0,1). Consider a mapping fm:I → [m, m] and generate a sequence (xn) as follows: (1) Let x0ɛI be the seed; (2) For every positive integer n, xn+1 = [[fm (xn)]], where [[x]] = x [x], [ ] is the greatest integer function. In this paper, we investigate the sequence generated by fm (x) = msin(πx). It turns out that the finite nature of computer numbers contributes to the ”randomness ” of the sequence. Simple applications and empirical testing were implemented. 1