Well equidistributed long-period linear
Introduction The '''Well Equidistributed Long-period Linear (WELL)''' is a family of pseudorandom number generators developed in 2006 by François Panneton, Pierre L'Ecuyer, and . It is a form of linear-feedback shift register optimized for software implementation on a 32-bit machine.
Operational design 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  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.
Variants 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.
Implementations *  Implementations of WELL512a, WELL1024a, WELL19937a, WELL19937c, WELL44497a, WELL44497b in C (Free for non-commercial use)*  Implementations of same algorithms in Scala*  Implementations in C++*  Implementations of WELL512, WELL1024, WELL607 in Java*  Implementations of WELL512, WELL1024 in BBC BASIC*  Modified "maximally equidistributed" implementations of WELL19937, WELL44497 in C (Free for non-commercial use)*   Implementation of WELL512 in C (Public Domain)
References
External links *   The academic paper, and related articles by François Panneton*  Pierre L'Ecuyer's publications