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One of the very earliest and most influential designs. Linear congruential generator (LCG) 1958 W. E. Thomson; A. Rotenberg [3] [4] A generalisation of the Lehmer generator and historically the most influential and studied generator. Lagged Fibonacci generator (LFG) 1958 G. J. Mitchell and D. P. Moore [5] Linear-feedback shift register (LFSR) 1965
For example, squaring the number "1111" yields "1234321", which can be written as "01234321", an 8-digit number being the square of a 4-digit number. This gives "2343" as the "random" number. Repeating this procedure gives "4896" as the next result, and so on. Von Neumann used 10 digit numbers, but the process was the same.
0, 1, 3, 6, 2, 7, 13, 20, 12, 21, 11, 22, 10, 23, 9, 24, 8, 25, 43, 62, ... "subtract if possible, otherwise add" : a (0) = 0; for n > 0, a ( n ) = a ( n − 1) − n if that number is positive and not already in the sequence, otherwise a ( n ) = a ( n − 1) + n , whether or not that number is already in the sequence.
Random number generation is a process by which, often by means of a random number generator (RNG), a sequence of numbers or symbols is generated that cannot be reasonably predicted better than by random chance. This means that the particular outcome sequence will contain some patterns detectable in hindsight but impossible to foresee.
= is the maximum number [4]: §3 of bits that are in the sequence. The k indicates the size of a unique word of data in the sequence. If you segment the N bits of data into every possible word of length k , you will be able to list every possible combination of 0s and 1s for a k-bit binary word, with the exception of the all-0s word.
A C version [a] of three xorshift algorithms [1]: 4,5 is given here. The first has one 32-bit word of state, and period 2 32 −1. The second has one 64-bit word of state and period 2 64 −1.
In some cases, data reveals an obvious non-random pattern, as with so-called "runs in the data" (such as expecting random 0–9 but finding "4 3 2 1 0 4 3 2 1..." and rarely going above 4). If a selected set of data fails the tests, then parameters can be changed or other randomized data can be used which does pass the tests for randomness.
See the external references. As an application, a random number generator could make one probe into the range at hand for a random number, and produce a random SP. Late in 2005, the program Fritz9 became available. It has a Fischer random chess option, but, for some unexplained reason, it assigns idns to SPs in a different way.