What is the period length of the linear congruential generator?

A linear congruential generator has full period (cycle length is m) if and only if the following conditions hold: • The only positive integer that exactly divides both m and c is 1; • If q is a prime number that divides m, then q divides a − 1; • If 4 divides m, then 4 divides a − 1.

How do you find the period of a linear congruential generator?

How can you calculate the probability distribution of the period length of a linear congruential generator? That is Xn+1=(aXn+c)modm where a is chosen uniformly at random from {1,…,m−1} and c is chosen uniformly at random from {0,…,m−1} and m is a fixed prime. Take X0 to be some arbitrary value from {0,…,m−1}.

How is LCG period calculated?

To find the period of a non full cycle LCG PRNG for a given seed you just need to count the number of iterations of the PRNG until it generates the seed value once more.

How to calculate the period length of a linear congruential generator?

How can you calculate the probability distribution of the period length of a linear congruential generator? That is X n + 1 = ( a X n + c) mod m where a is chosen uniformly at random from { 1, …, m − 1 } and c is chosen uniformly at random from { 0, …, m − 1 } and m is a fixed prime. Take X 0 to be some arbitrary value from { 0, …, m − 1 }.

How to create a linear congruential generator in Excel?

Each row shows the state evolving until it repeats. The top row shows a generator with m = 9, a = 2, c = 0, and a seed of 1, which produces a cycle of length 6. The second row is the same generator with a seed of 3, which produces a cycle of length 2. Using a = 4 and c = 1 (bottom row) gives a cycle length of 9 with any seed in [0, 8].

Which is the linear congruential generator for pseudorandom numbers?

Using a = 4 and c = 1 (bottom row) gives a cycle length of 9 with any seed in [0, 8]. A linear congruential generator ( LCG) is an algorithm that yields a sequence of pseudo-randomized numbers calculated with a discontinuous piecewise linear equation. The method represents one of the oldest and best-known pseudorandom number generator algorithms.

When do you call a generator a congruential generator?

If c = 0, the generator is often called a multiplicative congruential generator (MCG), or Lehmer RNG. If c ≠ 0, the method is called a mixed congruential generator.:4- When c ≠ 0, a mathematician would call the recurrence an affine transformation, not a linear one, but the misnomer is well-established in computer science.