# Programmer’s guide#

## Generator types#

There are two main classes of generator in rocRAND: Pseudo-Random Number Generators (PRNGs), and Quasi-Random Number Generators (QRNGs). The following pseudo-random number generators are available:

XORWOW.

MRG32K3A.

MTGP32.

Philox 4x32-10.

MRG31K3P.

LFSR113.

MT19937.

ThreeFry 2x32-20, 4x32-30, 2x64-20 and 4x64-20.

Additionally, the following quasi-random number generators are available:

Sobol32.

Sobol64.

Scrambled Sobol32.

Scrambled Sobol64.

## Ordering#

rocRAND generators can be configured to change how results are ordered in global memory. These parameters can be used to, for example, tune the performance versus the reproducibility of rocRAND generators. The following ordering types are available:

ROCRAND_ORDERING_PSEUDO_BEST

ROCRAND_ORDERING_PSEUDO_DEFAULT

ROCRAND_ORDERING_PSEUDO_SEEDED

ROCRAND_ORDERING_PSEUDO_LEGACY

ROCRAND_ORDERING_PSEUDO_DYNAMIC

ROCRAND_ORDERING_QUASI_DEFAULT

ROCRAND_ORDERING_PSEUDO_DEFAULT and ROCRAND_ORDERING_QUASI_DEFAULT` are the default ordering for pseudo- and quasi-random number generators respectively. ROCRAND_ORDERING_PSEUDO_DEFAULT is currently the same as ROCRAND_ORDERING_PSEUDO_BEST and ROCRAND_ORDERING_PSEUDO_LEGACY.

ROCRAND_ORDERING_PSEUDO_DYNAMIC indicates that rocRAND may change the output ordering such that the best performance is obtained for a particular generator on a particular GPU. Currently, this is not yet implemented, and is the same as ROCRAND_ORDERING_PSEUDO_LEGACY.

ROCRAND_ORDERING_PSEUDO_LEGACY indicates that rocRAND should generate values in a way that is backward compatible. Using this ordering, the outputs are generated as follows:

- XORWOW
There are \(131072\) generators in total, each of which are separated by \(2^{67}\) values. The results are generated in an interleaved fashion. The result at offset \(n\) in memory is generated from offset \((n\;\mathrm{mod}\; 131072) \cdot 2^{67} + \lfloor n / 131072 \rfloor\) in the XORWOW sequence for a particular seed.

- MRG32K3A
There are \(131072\) generators in total, each of which are separated by \(2^{76}\) values. The results are generated in an interleaved fashion. The result at offset \(n\) in memory is generated from offset \((n\;\mathrm{mod}\; 131072) \cdot 2^{76} + \lfloor n / 131072 \rfloor\) in the MRG32K3A sequence for a particular seed.

- MTGP32
There are \(512\) generators in total, each of which generates \(256\) values per iteration. Blocks of \(256\) elements from generators are concatenated to form the output. The result at offset \(n\) in memory is generated from generator \(\lfloor n / 256\rfloor\;\mathrm{mod}\; 512\).

- Philox 4x32-10
There is only one Philox generator, and the result at offset \(n\) is simply the \(n\)-th value from this generator.

- MT19937
The Mersenne Twister sequence is generated from \(8192\) generators in total, and each of these are separated by \(2^{1000}\) values. Each generator generates \(8\) elements per iteration. The result at offset \(n\) is generated from generator \((\lfloor n / 8\rfloor\;\mathrm{mod}\; 8192) \cdot 2^{1000} + \lfloor n / (8 \cdot 8192) \rfloor + \lfloor n / 8 \rfloor\).

- MRG31K3P
There are \(131072\) generators in total, each of which are separated by \(2^{72}\) values. The results are generated in an interleaved fashion. The result at offset \(n\) in memory is generated from offset \((n\;\mathrm{mod}\; 131072) \cdot 2^{72} + \lfloor n / 131072 \rfloor\) in the MRG31K3P sequence for a particular seed.

- LFSR113
There are \(131072\) generators in total, each of which are separated by \(2^{55}\) values. The results are generated in an interleaved fashion. The result at offset \(n\) in memory is generated from offset \((n\;\mathrm{mod}\; 131072) \cdot 2^{55} + \lfloor n / 131072 \rfloor\) in the LFSR113 sequence for a particular seed.

- ThreeFry
There is only one ThreeFry generator, and the results at offset \(n\) is simply the \(n\)-th value from this generator.

- Sobol
The (scrambled) 32- and 64-bit sobol quasi-random number generators generated the result from \(d\) dimensions by flattening them into the output. The result at offset \(n\) in memory is generated from offset \(n\;\mathrm{mod}\; d\) in dimension \(\lfloor n / d \rfloor\), where \(d\) is the generator’s number of dimensions.