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
Famous quotes containing the words period and/or length:
“Colonial system, public debts, heavy taxes, protection, commercial wars, etc., these offshoots of the period of manufacture swell to gigantic proportions during the period of infancy of large-scale industry. The birth of the latter is celebrated by a vast, Herod-like slaughter of the innocents.”
—Karl Marx (18181883)
“Baltimore lay very near the immense protein factory of Chesapeake Bay, and out of the bay it ate divinely. I well recall the time when prime hard crabs of the channel species, blue in color, at least eight inches in length along the shell, and with snow-white meat almost as firm as soap, were hawked in Hollins Street of Summer mornings at ten cents a dozen.”
—H.L. (Henry Lewis)