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A randomness extractor, often simply called an "extractor", is a function, which being applied to output from a weak entropy source, together with a short, uniformly random seed, generates a highly random output that appears independent from the source and uniformly distributed. [1]
For the binary representation of integers, it suffices to replace everywhere 10 by 2. [5] The second argument of the split_at function specifies the number of digits to extract from the right: for example, split_at("12345", 3) will extract the 3 final digits, giving: high="12", low="345".
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 ...
The generator fails only the MatrixRank test of BigCrush, however if the generator is modified to return only the high 32 bits, then it passes BigCrush with zero failures. [10]: 7 In fact, a reduced version with only 40 bits of internal state passes the suite, suggesting a large safety margin.
The final digit of a Universal Product Code, International Article Number, Global Location Number or Global Trade Item Number is a check digit computed as follows: [3] [4]. Add the digits in the odd-numbered positions from the left (first, third, fifth, etc.—not including the check digit) together and multiply by three.
In Python, a generator can be thought of as an iterator that contains a frozen stack frame. Whenever next() is called on the iterator, Python resumes the frozen frame, which executes normally until the next yield statement is reached. The generator's frame is then frozen again, and the yielded value is returned to the caller.
Since the generator does not require stepping through every intermediate state, it can “jump” to any point in the sequence in constant time. This is particularly useful in applications like Monte Carlo simulations where independent streams are needed. Examples include: [15] Philox: Uses multiplication-based mixing to combine the counter and ...
It is acceptable to pad the seeds with zeros to the left in order to create an even valued n-digit number (e.g. 540 → 0540). For a generator of n-digit numbers, the period can be no longer than 8 n. If the middle n digits are all zeroes, the generator then outputs zeroes forever. If the first half of a number in the sequence is zeroes, the ...