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  2. Lehmer random number generator - Wikipedia

    en.wikipedia.org/wiki/Lehmer_random_number_generator

    The basic reduction step divides the product into two e-bit parts, multiplies the high part by d, and adds them: (ax mod 2 e) + d ⌊ ax/2 e ⌋. This can be followed by subtracting m until the result is in range. The number of subtractions is limited to ad/m, which can be easily limited to one if d is small and a < m/d is chosen.

  3. Mersenne Twister - Wikipedia

    en.wikipedia.org/wiki/Mersenne_Twister

    The 'Extract number' section shows an example where integer 0 has already been output and the index is at integer 1. 'Generate numbers' is run when all integers have been output. For a w -bit word length, the Mersenne Twister generates integers in the range [ 0 , 2 w − 1 ] {\displaystyle [0,2^{w}-1]} .

  4. Luhn mod N algorithm - Wikipedia

    en.wikipedia.org/wiki/Luhn_mod_N_algorithm

    The mapping of characters to code-points and back can be implemented in a number of ways. The simplest approach (akin to the original Luhn algorithm) is to use ASCII code arithmetic. For example, given an input set of 0 to 9, the code-point can be calculated by subtracting the ASCII code for '0' from the ASCII code of the desired character. The ...

  5. Xorshift - Wikipedia

    en.wikipedia.org/wiki/Xorshift

    Xorshift random number generators, also called shift-register generators, are a class of pseudorandom number generators that were invented by George Marsaglia. [1] They are a subset of linear-feedback shift registers (LFSRs) which allow a particularly efficient implementation in software without the excessive use of sparse polynomials . [ 2 ]

  6. Linear congruential generator - Wikipedia

    en.wikipedia.org/wiki/Linear_congruential_generator

    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 ...

  7. Pseudorandom number generator - Wikipedia

    en.wikipedia.org/wiki/Pseudorandom_number_generator

    It can be shown that if is a pseudo-random number generator for the uniform distribution on (,) and if is the CDF of some given probability distribution , then is a pseudo-random number generator for , where : (,) is the percentile of , i.e. ():= {: ()}. Intuitively, an arbitrary distribution can be simulated from a simulation of the standard ...

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    mail.aol.com

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  9. Fisher–Yates shuffle - Wikipedia

    en.wikipedia.org/wiki/Fisher–Yates_shuffle

    Their description of the algorithm used pencil and paper; a table of random numbers provided the randomness. The basic method given for generating a random permutation of the numbers 1 through N goes as follows: Write down the numbers from 1 through N. Pick a random number k between one and the number of unstruck numbers remaining (inclusive).