 # Linear Congruence Method

One of the early pseudo-random number generators that is still used today due to its speed and ease of implementation. Not recommended for cryptographic use as the quality'' of generated numbers is insufficient. Linear Congruence Generators (LCGs) should also be avoided in geometrical simulations where there is a need to generate random points in $N$ dimensions due to serial correlations in the pseudo-random sequence ${X}_{n}$ .

The sequence ${X}_{n}$ is constructed using the following recursive equation:

where the multiplier'' $a$ , increment'' $c$ and modulus'' $m$ are heuristic constants. The quality of pseudo-random sequences generated by LCGs depends crucially on the good choice of $a$ , $c$ and $m$ . The maximum period after which the sequence ${X}_{n}$ will start repeating itself is equal to $m$ . In order to speed up computer implementations, traditionally the value of $m$ was chosen to be a power of 2. Values ${X}_{n}$ lie in the interval [ $0,m$ ). To obtain a pseudo-random floating-point number from the range [ $0,1$ ) , values ${X}_{n}$ need to be divided by $m$ .

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