Included in Java Development Kit 8 and above. PuzyninaĪperiodic pseudorandom number generators based on infinite words technique.īased upon the final mixing function of MurmurHash3. ShawĪ simplified version of the AES block cipher, leading to very fast performance on systems supporting the AES-NI.Ī simplified version of the Threefish block cipher, suitable for GPU implementations.Ī simplification and modification of the block cipher Threefish with the addition of an S-box. MatsumotoĪ LFSR closely related with Mersenne Twister, aiming at remedying some of its shortcomings. Well equidistributed long-period linear (WELL)į. The xorwow generator is the default generator in the CURAND library of the nVidia CUDA application programming interface for graphics processing units.

Marsaglia also suggested as an improvement the xorwow generator, in which the output of a xorshift generator is added with a Weyl sequence. It is a very fast sub-type of LFSR generators. Default generator in R and the Python language starting from version 2.3. In its MT19937 implementation is probably the most commonly used modern PRNG. Prototypical example of a combination generator.Ĭlosely related with LFSRs. for particle physics simulations.Ī method with roots in number theory, although never used in practical applications. A SWB generator is the basis for the RANLUX generator, widely used e.g. The rationale behind the MIXMAX family of generators relies on results from ergodic theory and classical mechanics.Ī modification of Lagged-Fibonacci generators.Ī modification of Lagged-Fibonacci generators. It is a member of the class of matrix linear congruential generator, a generalisation of LCG. Easy to extend for arbitrary period length and improved statistical performance over higher dimensions and with higher precision. With appropriate initialisations, passes all current empirical test suites, and is formally proven to converge. Simple to implement, fast, but not widely known. The Additive Congruential Random Number generator. Its base is based on prime numbers.Ī specific implementation of a Lehmer generator, widely used because it is included in C++ as the function minstd_rand0 from C++11 onwards. īlum-Blum-Shub is a PRNG algorithm that is considered cryptographically secure. it is used in Excel 2003 and later versions for the Excel function RAND and it was the default generator in the language Python up to version 2.2. Also called Tausworthe generators.Ī combination of three small LCGs, suited to 16-bit CPUs. One of the very earliest and most influential designs.Ī generalisation of the Lehmer generator and historically the most influential and studied generator.Ī hugely influential design. In its original form, it is of poor quality and of historical interest only. The following algorithms are pseudorandom number generators. Whenever using a pseudorandom number generator, keep in mind John von Neumann's dictum 'Anyone who considers arithmetical methods of producing random digits is, of course, in a state of sin.'

This list includes many common types, regardless of quality or applicability to a given use case. Random number generators are important in many kinds of technical applications, including physics, engineering or mathematical computer studies (e.g., Monte Carlo simulations), cryptography and gambling (on game servers).

Random number generation