Well equidistributed long-period linear

hideThis article has multiple issues. Please help or discuss these issues on the talk page. (Learn how and when to remove these template messages) This article relies largely or entirely on a single source. Relevant discussion may be found on the talk page. Please help by introducing citations to additional sources. Find sources:  –  ·  ·  · scholar · JSTOR (November 2017) This article's use of external links may not follow Wikipedia's policies or guidelines. Please by removing excessive or inappropriate external links, and converting useful links where appropriate into footnote references. (November 2017) (Learn how and when to remove this template message) (Learn how and when to remove this template message)

The Well Equidistributed Long-period Linear (WELL) is a family of pseudorandom number generators developed in 2006 by , , and  [ja] (松本 眞).^[1] 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 ${\displaystyle F_{2}}$. 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.

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