The seed parameter is a 64-bit integer that initializes the starting state of a pseudorandom number generator. The same seed always produces the same sequence of results.

The offset parameter is used to skip ahead in the sequence. If offset = 100, the first random number generated will be the 100th in the sequence. This allows multiple runs of the same program to continue generating results from the same sequence without overlap. Note that the skip ahead function is not available for the CURAND_RNG_PSEUDO_MTGP32 and CURAND_RNG_PSEUDO_MT19937 generators.

The order parameter is used to choose how the results are ordered in global memory. There are three ordering choices for pseudorandom sequences: CURAND_ORDERING_PSEUDO_DEFAULT, CURAND_ORDERING_PSEUDO_BEST, and CURAND_ORDERING_PSEUDO_SEEDED. There is one ordering choice for quasirandom numbers, CURAND_ORDERING_QUASI_DEFAULT. The default ordering for pseudorandom number generators is CURAND_ORDERING_PSEUDO_DEFAULT, while the default ordering for quasirandom number generators is CURAND_ORDERING_QUASI_DEFAULT.

The two pseudorandom orderings CURAND_ORDERING_PSEUDO_DEFAULT and CURAND_ORDERING_PSEUDO_BEST produce the same output ordering for all pseudo-random generators, except MT19937 for which CURAND_ORDERING_BEST may generate different output on different models of GPUs. Future releases of cuRAND may change the ordering associated with CURAND_ORDERING_PSEUDO_BEST to improve either performance or the quality of the results. It will always be the case that the ordering obtained with CURAND_ORDERING_PSEUDO_BEST is deterministic and is the same for each run of the program. The ordering returned by CURAND_ORDERING_PSEUDO_DEFAULT is guaranteed to remain the same for all cuRAND releases. In the current release, only XORWOW and MT19937 generators have more than one ordering.

The behavior of the ordering parameters for each generator type is outlined below:

• XORWOW pseudorandom generator

  • CURAND_ORDERING_PSEUDO_BEST

    The output ordering of CURAND_ORDERING_PSEUDO_BEST is the same as CURAND_ORDERING_PSEUDO_DEFAULT in the current release.

  • CURAND_ORDERING_PSEUDO_DEFAULT

    The result at offset $\mathrm{n}$ in global memory is from position

    $(nmod4096)\cdot 2^{67}+\lfloor n/4096\rfloor$

    in the original XORWOW sequence.

  • CURAND_ORDERING_PSEUDO_SEEDED

    The result at offset $\mathrm{n}$ in global memory is from position $n/4096\rfloor$ in the XORWOW sequence seeded with a combination of the user seed and the number $nmod4096$. In other words, each of 4096 threads uses a different seed. This seeding method reduces state setup time but may result in statistical weaknesses of the pseudorandom output for some user seed values.

  MRG32k3a pseudorandom generator

  • CURAND_ORDERING_PSEUDO_BEST

    The output ordering of CURAND_ORDERING_PSEUDO_BEST is the same as CURAND_ORDERING_PSEUDO_DEFAULT in the current release.

  • CURAND_ORDERING_PSEUDO_DEFAULT

    The result at offset $\mathrm{n}$ in global memory is from position

    $(nmod4096)\cdot 2^{76}+\lfloor n/4096\rfloor$

    in the original MRG32k3a sequence. (Note that the stride between subsequent samples for MRG32k3a is not the same as for XORWOW)

  MTGP32 pseudorandom generator

  • CURAND_ORDERING_PSEUDO_BEST

    The output ordering of CURAND_ORDERING_PSEUDO_BEST is the same as CURAND_ORDERING_PSEUDO_DEFAULT in the current release.

  • CURAND_ORDERING_PSEUDO_DEFAULT

    The MTGP32 generator actually generates 64 distinct sequences based on different parameter sets for the basic algorithm. Let $S(p)$ be the sequence for parameter set $p$.

    The result at offset $\mathrm{n}$ in global memory is from position $nmod256$ from the sequence

    $S(\lfloor n/256\rfloor mod64)$

    In other words 256 samples from $S(0)$ are followed by 256 samples from $S(1)$ and so-on, up to $S(63)$. This pattern repeats, so the subsequent 256 samples are from $S(0)$, followed by 256 samples from $S(1)$, ands so on.

  MT19937 pseudorandom generator

  • CURAND_ORDERING_PSEUDO_DEFAULT

    Ordering is based heavily on the standard MT19937 CPU implementation. Output is generated by 8192 independent generators. Each generator generates consecutive subsequence of the original sequence. Length of each subsequence is $2^{1000}$. Random numbers are generated by eights thus first 8 elements come from first subsequence, next 8 elements come form second subsequence and so on. Results are permuted differently than originally to achieve higher performance. Ordering is independent of the hardware that you are using. For more information please see [18].

  • CURAND_ORDERING_PSEUDO_BEST

    The output ordering of CURAND_ORDERING_PSEUDO_BEST to achieve better performance depends on number of SMs that composed your GPU. Random numbers are generated in the same way as with CURAND_ORDERING_PSEUDO_DEFAULT but the number of generators may be different to achieve better performance. Generating seeds is much faster using this ordering.

  Philox_4x32_10 pseudorandom generator

  • CURAND_ORDERING_PSEUDO_BEST

    The output ordering of CURAND_ORDERING_PSEUDO_BEST is the same as CURAND_ORDERING_PSEUDO_DEFAULT in the current release.

  • CURAND_ORDERING_PSEUDO_DEFAULT

    Each thread in Philox_4x32_10 generator generates distinct sequences based on different parameter sets for the basic algorithm. In host API there are 8192 different sequences. Each four values from one sequence are followed by four values from next sequence.

  32 and 64 bit SOBOL and Scrambled SOBOL quasirandom generators

  • CURAND_ORDERING_QUASI_DEFAULT

    When generating $n$ results in $d$ dimensions, the output will consist of $n/d$ results from dimension 1, followed by $n/d$ results from dimension 2, and so on up to dimension $d$. Only exact multiples of the dimension size may be generated. The dimension parameter $d$ is set with curandSetQuasiRandomGeneratorDimensions() and defaults to 1.