Well equidistributed long-period linear
The Well Equidistributed Long-period Linear (WELL) is a family of pseudorandom number generators developed in 2006 by François Panneton, Pierre L'Ecuyer, and Makoto Matsumoto (松本 眞). It is a form of linear feedback shift register optimized for software implementation on a 32-bit machine.
The structure is similar to the Mersenne twister, a large state made up of previous output words (32 bits each), from which a new output word is generated using linear recurrences modulo 2 over a finite binary field . However, a more complex recurrence produces a denser generator polynomial, producing better statistical properties.
Each step of the generator reads five words of state: the oldest 32 bits (which may straddle a word boundary if the state size is not a multiple of 32), the newest 32 bits, and three other words in between. Then a series of eight single-word transformations (mostly of the form x := x ⊕ (x >> k)) and six exclusive-or operations combine those into two words, which become the newest two words of state, one of which will be the output.
Specific parameters are provided for the following generators: WELL512a, WELL521a, WELL521b, WELL607a, WELL607b, WELL800a, WELL800b, WELL1024a, WELL1024b, WELL19937a, WELL19937b, WELL19937c, WELL21701a, WELL23209a, WELL23209b, WELL44497a, WELL44497b. Numbers give the state size in bits; letter suffixes denote variants of the same size.
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