The source noise can be obtained algorithmically using, for example, a congruential generator
, or physically, using a semiconductor noise generator.
Linear congruential generator
generates random numbers, which are divided by modulo m and we get bits according to formula (2).
As it is usually implemented, the algorithm is known as a Prime Modulus Multiplicative Linear Congruential Generator
As a last resort, Ferrenberg substituted different random-number generators and, to his surprise, found that he came much closer to the correct answer by using a linear congruential generator
, which has known defects.
the multiplier for a Linear Congruential Generator
or the lag for a Lagged Fibonacci Generator).
If a generator is to be adopted as an "industry standard," there is no consensus that it should be a congruential generator
and far from a consensus that it should be [X.
A good congruential generator
could be used to run the casinos in Las Vegas and Atlantic City and all the state lotteries with no one the wiser.
We have used a linear congruential generator
fish by Fishman and Moore , an explicit inversive congruential generator
[Eichenauer-Herrmann 1993], and a twisted GFSR generator (tt800 by Matsumoto and Kurita ); at last the infamous randu (again an LCG) as an example of a generator with bad lattice structure (see Park and Miller ).
Equation (1) defines a linear congruential generator
(LCG) in matrix form.
Wu  proposed a clever-looking way to select the parameters and implement a linear congruential generator
(LCG): take a Mersenne prime modulus m, i.
The BMT uses sine and cosine functions--periodic functions that, when used in conjunction with a linear congruential generator
(LCG) such as the Lehmer generator, produces statistically correlated "random" numbers.
Although R250 passed a number of statistical tests, a recent experience [Selke 1993] showed that R250 gives wrong results for a clustered Monte Carlo simulation, while the multiplicative congruential generator