Period Length
The period of a general LCG is at most m, and for some choices of a much less than that. Provided that c is nonzero, the LCG will have a full period for all seed values if and only if:
- and are relatively prime,
- is divisible by all prime factors of ,
- is a multiple of 4 if is a multiple of 4.
These three requirements are referred to as the Hull-Dobell Theorem. While LCGs are capable of producing decent pseudorandom numbers, this is extremely sensitive to the choice of the parameters c, m, and a.
Historically, poor choices had led to ineffective implementations of LCGs. A particularly illustrative example of this is RANDU which was widely used in the early 1970s and led to many results which are currently being questioned because of the use of this poor LCG.
Read more about this topic: Linear Congruential Generator
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