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The generator computes an odd 128-bit value and returns its upper 64 bits. This generator passes BigCrush from TestU01, but fails the TMFn test from PractRand. That test has been designed to catch exactly the defect of this type of generator: since the modulus is a power of 2, the period of the lowest bit in the output is only 2 62, rather than ...
Sudoku can be solved using stochastic (random-based) algorithms. [11] [12] An example of this method is to: Randomly assign numbers to the blank cells in the grid. Calculate the number of errors. "Shuffle" the inserted numbers until the number of mistakes is reduced to zero. A solution to the puzzle is then found.
Example of a Killer Sudoku problem Solution to the example above The same example problem, as it would be printed in black and white. Killer sudoku (also killer su doku, sumdoku, sum doku, sumoku, addoku, or samunanpure サムナンプレ sum-num(ber) pla(ce)) is a puzzle that combines elements of sudoku and kakuro.
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.
In the asymptotic setting, a family of deterministic polynomial time computable functions : {,} {,} for some polynomial p, is a pseudorandom number generator (PRNG, or PRG in some references), if it stretches the length of its input (() > for any k), and if its output is computationally indistinguishable from true randomness, i.e. for any probabilistic polynomial time algorithm A, which ...
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Given a 2 b-bit input word, the b−1 most significant bits bits are used for the rotate amount, the next-most-significant 2 b−1 bits are rotated right and used as the output, and the low 2 b−1 +1−b bits are discarded. RS: A random (input-dependent) shift, for cases where rotates are more expensive. Again, the output is half the size of ...
[10]: 19 A similar generator suggested in Numerical Recipes [11] as RanQ1 also fails the BirthdaySpacings test. Vigna [9] suggests the following xorshift1024* generator with 1024 bits of state and a maximal period of 2 1024 −1; however, it does not always pass BigCrush. [5] xoshiro256** is therefore a much better option.