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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 . 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 The Mersenne Twister is a general-purpose pseudorandom number generator (PRNG) developed in 1997 by and . Its name derives from the choice of a Mersenne prime as its period length. The Mersenne Twister was created specifically to address most of ..., 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 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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pseudorandom Number Generator
A pseudorandom number generator (PRNG), also known as a deterministic random bit generator (DRBG), is an algorithm for generating a sequence of numbers whose properties approximate the properties of sequences of random number generation, random numbers. The PRNG-generated sequence is not truly random, because it is completely determined by an initial value, called the PRNG's ''random seed, seed'' (which may include truly random values). Although sequences that are closer to truly random can be generated using hardware random number generators, ''pseudorandom number generators'' are important in practice for their speed in number generation and their reproducibility. PRNGs are central in applications such as simulations (e.g. for the Monte Carlo method), electronic games (e.g. for procedural generation), and cryptography. Cryptographic applications require the output not to be predictable from earlier outputs, and more cryptographically-secure pseudorandom number generator, elabora ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
François Panneton
François () is a French masculine given name and surname, equivalent to the English name Francis. People with the given name * François Amoudruz (1926–2020), French resistance fighter * François-Marie Arouet (better known as Voltaire; 1694–1778), French Enlightenment writer, historian, and philosopher * François Beauchemin (born 1980), Canadian ice hockey player for the Anaheim Ducks * François Blanc (1806–1877), French entrepreneur and operator of casinos * François Bonlieu (1937–1973), French alpine skier * François Cevert (1944–1973), French racing driver * François Chau (born 1959), Cambodian American actor * François Clemmons (born 1945), American singer and actor * François Corbier (1944–2018), French television presenter and songwriter * François Coty (1874–1934), French perfumer * François Coulomb the Elder (1654–1717), French naval architect * François Coulomb the Younger (1691–1751), French naval architect * François Couperin (1668–17 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pierre L'Ecuyer
Pierre is a masculine given name. It is a French form of the name Peter. Pierre originally meant "rock" or "stone" in French (derived from the Greek word πέτρος (''petros'') meaning "stone, rock", via Latin "petra"). It is a translation of Aramaic כיפא (''Kefa),'' the nickname Jesus gave to apostle Simon Bar-Jona, referred in English as Saint Peter. Pierre is also found as a surname. People with the given name * Monsieur Pierre, Pierre Jean Philippe Zurcher-Margolle (c. 1890–1963), French ballroom dancer and dance teacher * Pierre (footballer), Lucas Pierre Santos Oliveira (born 1982), Brazilian footballer * Pierre, Baron of Beauvau (c. 1380–1453) * Pierre, Duke of Penthièvre (1845–1919) * Pierre, marquis de Fayet (died 1737), French naval commander and Governor General of Saint-Domingue * Prince Pierre, Duke of Valentinois (1895–1964), father of Rainier III of Monaco * Pierre Affre (1590–1669), French sculptor * Pierre Agostini, French physicist * Pie ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Linear-feedback Shift Register
In computing, a linear-feedback shift register (LFSR) is a shift register whose input bit is a Linear#Boolean functions, linear function of its previous state. The most commonly used linear function of single bits is exclusive-or (XOR). Thus, an LFSR is most often a shift register whose input bit is driven by the XOR of some bits of the overall shift register value. The initial value of the LFSR is called the seed, and because the operation of the register is deterministic, the stream of values produced by the register is completely determined by its current (or previous) state. Likewise, because the register has a finite number of possible states, it must eventually enter a repeating cycle. However, an LFSR with a Primitive polynomial (field theory), well-chosen feedback function can produce a sequence of bits that appears random and has a Maximal length sequence, very long cycle. Applications of LFSRs include generating Pseudorandomness, pseudo-random numbers, Pseudorandom n ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mersenne Twister
The Mersenne Twister is a general-purpose pseudorandom number generator (PRNG) developed in 1997 by and . Its name derives from the choice of a Mersenne prime as its period length. The Mersenne Twister was created specifically to address most of the flaws found in earlier PRNGs. The most commonly used version of the Mersenne Twister algorithm is based on the Mersenne prime 2^-1. The standard implementation of that, MT19937, uses a 32-bit word length. There is another implementation (with five variants) that uses a 64-bit word length, MT19937-64; it generates a different sequence. ''k''-distribution A pseudorandom sequence x_i of ''w''-bit integers of period ''P'' is said to be ''k-distributed'' to ''v''-bit accuracy if the following holds. : Let trunc''v''(''x'') denote the number formed by the leading ''v'' bits of ''x'', and consider ''P'' of the ''kv''-bit vectors :: (\operatorname_v(x_i), \operatorname_v(x_), \, \ldots, \operatorname_v(x_)) \quad (0\leq i. The Mersenn ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Recurrence Relation
In mathematics, a recurrence relation is an equation according to which the nth term of a sequence of numbers is equal to some combination of the previous terms. Often, only k previous terms of the sequence appear in the equation, for a parameter k that is independent of n; this number k is called the ''order'' of the relation. If the values of the first k numbers in the sequence have been given, the rest of the sequence can be calculated by repeatedly applying the equation. In ''linear recurrences'', the th term is equated to a linear function of the k previous terms. A famous example is the recurrence for the Fibonacci numbers, F_n=F_+F_ where the order k is two and the linear function merely adds the two previous terms. This example is a linear recurrence with constant coefficients, because the coefficients of the linear function (1 and 1) are constants that do not depend on n. For these recurrences, one can express the general term of the sequence as a closed-form expression o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
GF(2)
(also denoted \mathbb F_2, or \mathbb Z/2\mathbb Z) is the finite field with two elements. is the Field (mathematics), field with the smallest possible number of elements, and is unique if the additive identity and the multiplicative identity are denoted respectively and , as usual. The elements of may be identified with the two possible values of a bit and to the Boolean domain, Boolean values ''true'' and ''false''. It follows that is fundamental and ubiquitous in computer science and its mathematical logic, logical foundations. Definition GF(2) is the unique field with two elements with its additive identity, additive and multiplicative identity, multiplicative identities respectively denoted and . Its addition is defined as the usual addition of integers but modulo 2 and corresponds to the table below: If the elements of GF(2) are seen as Boolean values, then the addition is the same as that of the logical XOR operation. Since each element equals its opposite (m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
