Editing Pseudorandom number generator (section)

== Counter-based RNGs ==
{{Main|Counter-based random number generator}}
A counter-based random number generation (CBRNG, also known as a counter-based pseudo-random number generator, or CBPRNG) is a kind of PRNG that uses only an integer counter as its internal state:

<math display="block">\text { output }=f(n, \text { key })</math>

They are generally used for generating pseudorandom numbers for large parallel computations, such as over GPU or CPU clusters.<ref name="salmon-desres">{{Cite conference |last1=Salmon |first1=John |last2=Moraes |first2=Mark |last3=Dror |first3=Ron |last4=Shaw |first4=David |date=2011 |title=Parallel random numbers: as easy as 1, 2, 3 |doi=10.1145/2063384.2063405 |book-title=Proceedings of 2011 International Conference for High Performance Computing, Networking, Storage and Analysis, Article No. 16}}</ref> They have certain advantages:

* The only “state” needed is the counter value and the key. For a given counter and key, the output is always the same. This property makes CBRNGs reproducible.
* Because each random number is computed independently of any previous outputs, they can be generated in parallel. For example, in a massively parallel application, each thread or GPU core can be assigned a range of counter values and compute random numbers without synchronization or shared state.
* Since the generator does not require stepping through every intermediate state, it can “jump” to any point in the sequence in constant time. This is particularly useful in applications like [[Monte Carlo method|Monte Carlo simulations]] where independent streams are needed.

Examples include:<ref name="salmon-desres" />

* Philox: Uses multiplication-based mixing to combine the counter and key.
* Threefry: Based on a reduced-strength version of the [[Threefish]] block cipher.