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The Lehmer random number generator [1] (named after D. H. Lehmer), sometimes also referred to as the Park–Miller random number generator (after Stephen K. Park and Keith W. Miller), is a type of linear congruential generator (LCG) that operates in multiplicative group of integers modulo n. The general formula is
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For Monte Carlo simulations, an LCG must use a modulus greater and preferably much greater than the cube of the number of random samples which are required. This means, for example, that a (good) 32-bit LCG can be used to obtain about a thousand random numbers; a 64-bit LCG is good for about 2 21 random samples (a little over two million), etc.
Random Cycle Bit Generator (RCB) 2016 R. Cookman [33] RCB is described as a bit pattern generator made to overcome some of the shortcomings with Mersenne Twister and short periods/bit length restriction of shift/modulo generators. Middle-Square Weyl Sequence RNG (see also middle-square method) 2017 B. Widynski [34] [35]
When the divisor is a power of two, taking the remainder essentially means throwing away the high-order bits, such that one ends up with a significantly less random value. Different rules apply if the LCG has prime modulo, but such generators are uncommon. This is an example of the general rule that a poor-quality RNG or PRNG will produce poor ...
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The maximum possible period for the modulus q is q itself, i.e. the sequence includes every value from 0 to q − 1 before repeating. A sufficient condition for the sequence to have the maximum possible period is to choose a and c such that the polynomial f ( x ) = x 2 − c x − a ∈ F q [ x ] {\displaystyle f(x)=x^{2}-cx-a\in \mathbb {F ...
RS: A random (input-dependent) shift, for cases where rotates are more expensive. Again, the output is half the size of the input. Beginning with a 2 b -bit input word, the top b −3 bits are used for a shift amount, which is applied to the next-most-significant 2 b −1 +2 b −3 −1 bits, and the least significant 2 b −1 bits of the ...