Practical generators-Super Duper

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Practical generators-Super Duper

Most modern generators involve the combination of two or more of the elementary generators described above, an improvement both from the point of enhancing the statistical quality of the numbers and increasing the period of the generator. One such is called Super-Duper, originally written at McGill University, Canada. It combines the numbers produced by a linear congruential generator with one produced by a shift-register generator and has a period in excess of 10 $^{18}$ . The former uses equation $\nu _{i}$ =(a $\nu _{i-1}$ + c) mod m with m=2 $^{32}$ , a=69069 and c=0, with the seed $\nu _{0}\protect$ , an odd integer to produce a 32 bit integer $\nu _{i}$ . The shift register employs equation b $_{i}$ =(b $_{i-q}+b_{i-q})$ mod 2 with p=32 and q=17 to produce bits, b $_{k}\protect$ , sequences of 32 of which are combined to form an integer $\mu _{i}$ ,

$\mu _{i}=\sum ^{32}_{k=1}b_{k}2^{k-1}$

Subsections

These two integers are combined bit-wise `exclusive or' and scaled to give a variate on [0,1], as,

Amaury LATAILLADE 2002-11-04