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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 ...
In modular arithmetic computation, Montgomery modular multiplication, more commonly referred to as Montgomery multiplication, is a method for performing fast modular multiplication. It was introduced in 1985 by the American mathematician Peter L. Montgomery .
Z3 supports arithmetic, fixed-size bit-vectors, extensional arrays, datatypes, uninterpreted functions, and quantifiers. Its main applications are extended static checking, test case generation, and predicate abstraction. [citation needed] Z3 was open sourced in the beginning of 2015. [3]
Hence another name is the group of primitive residue classes modulo n. In the theory of rings , a branch of abstract algebra , it is described as the group of units of the ring of integers modulo n .
In modular arithmetic, a number g is a primitive root modulo n if every number a coprime to n is congruent to a power of g modulo n. That is, g is a primitive root modulo n if for every integer a coprime to n, there is some integer k for which g k ≡ a (mod n). Such a value k is called the index or discrete logarithm of a to the base g modulo n.
ACORN is particularly simple to implement in exact integer arithmetic, in various computer languages, using only a few lines of code. [4] Integer arithmetic is preferred to the real arithmetic modulo 1 in the original presentation, as the algorithm is then reproducible, producing exactly the same sequence on any machine and in any language, [2 ...
A linear congruential generator with base b = 2 32 is implemented as + = (+) , where c is a constant. If a ≡ 1 (mod 4) and c is odd, the resulting base-2 32 congruential sequence will have period 2 32.
The multiplicative order of a number a modulo n is the order of a in the multiplicative group whose elements are the residues modulo n of the numbers coprime to n, and whose group operation is multiplication modulo n. This is the group of units of the ring Z n; it has φ(n) elements, φ being Euler's totient function, and is denoted as U(n) or ...