Random Number Generators

Preamble

This is obviously a work in-progress. The Section from Random Number Generators to The Process, the Steps, are next. was posted by DAL on Aug 1,18. The Section following The Process, the Steps, are next. is taken from the Kokkos public repo Wiki page in the API Content:Algorithms, Random Number section and inserted here; the API section is not complete and has been removed from there until it is completed. The two Sections outlined here should be combined/merged/integrated someway prior to calling the Random Number Section "done."

Random Number Generators

The basis for the Kokkos Random Number Generators and their usage is outlined here.

Description of Generators

The implementation of random number generators in Kokkos is based on two primary references (Marsaglia¹, 2003; Vigna², 2014). Marsaglia's paper introduces Xorshift (bit-shifts with exclusive ors) pseudorandom number generators and tests some non-linear transformations to improve their performance on standard test suites. In spite of less than desirable performance numbers statistically, he showed that these generators are very fast and can generate hundreds of millions of random numbers in very few clock cycles. Using the same 64-bit state as Marsaglia, Vigna made improved parameter selections than Marsaglia but still achieve "poor" results. Applying an invertible multiplication step (hinted at by Marsaglia and called a "scramble" by Vigna) and correcting/adding to Marsaglia's xorshift64 algorithms, much improved behavior on test suites and higher statistical quality was achieved. Vigna describes tests on 1024 and 4096-bit versions of these generators later in his experimental process.

Kokkos implements a 64-bit and 1024-bit (high-dimensional) version of the scrambled xorshift generators. Please refer to the above references for details of the algorithms.

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¹ George Marsaglia. 2003. XorshiftRNGs. Journal of Statistical Software 8, 14 (2003), 1-6.

² Vigna, Sebastiano (2014). "An experimental exploration of Marsaglia's xorshift generators, scrambled“ ( http://arxiv.org/abs/1402.6246)

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Implementation of Random Number Generators for Applications

The Process, the Steps, are next.

The following Sections have been removed from the Kokkos/Wiki/API section and placed here until such time as it is completed.

Start here:

Kokkos::Generator

Header Files: Kokkos_core.hpp Kokkos_Complex.hpp

Synopsis

Kokkos_Random provides the structure necessary for pseudorandom number generators. These generators are based on Vigna, Sebastiano (2014). ["An experimental exploration of Marsaglia's xorshift generators, scrambled." See: http://arxiv.org/abs/1402.6246] .

The Random number generators themselves have two components: a state-pool and the actual generator. A state-pool manages a number of generators so that each active thread is able to grab its own. This allows the generation of random numbers which are independent between threads. Note that in contrast to CuRAND, none of the functions of the pool (or the generator) are collectives, i.e. all functions can be called inside conditionals.

 template<class Device>
 class Pool {
   public:
   typedef Device Device_Type;
   typedef Generator<Device> Generator_Type;
 
   Pool();
   Pool(RanNum_type seed);

   void init(RanNum_type seed, int num_states);
   Generator_Type get_state();
   void free_state(Generator_Type Gen);
 }

A Pool of Generators are intialized using a starting seed and establishing a pool_size of num_states. The Random_XorShift64 generator is used in serial to initialize all states making the intialization process platform independent and deterministic. Requesting a generator locks it's state guaranteeing that each thread has a private (independent) generator. (Note, getting a state on a Cuda device involves atomics, making it non-deterministic!) Upon completion, a generator is returned to the state pool, unlocking it, and upon updating of it's status, once again becomes available within the pool.

Given a pool and selection of a generator from within that pool, the next step is development of a functor that will draw random numbers, of the desired type, using the generator.

    template<class Device>
    class Generator {
     public:

    typedef DeviceType device_type;

    //Max return values of respective [X]rand[S]() functions (XorShift).
    enum {MAX_URAND = 0xffffffffU};
    enum {MAX_URAND64 = 0xffffffffffffffffULL-1};
    enum {MAX_RAND = static_cast<int>(0xffffffffU/2)};
    enum {MAX_RAND64 = static_cast<int64_t>(0xffffffffffffffffULL/2-1)};

    //Init with a state and the idx with respect to pool. Note: in serial the
    //Generator can be used by just giving it the necessary state arguments
    KOKKOS_INLINE_FUNCTION
    Generator (STATE_ARGUMENTS, int state_idx = 0);

    //Draw a equidistributed uint32_t in the range [0,MAX_URAND)
    KOKKOS_INLINE_FUNCTION
    uint32_t urand();

    //Draw a equidistributed uint32_t in the range [0,range)
    KOKKOS_INLINE_FUNCTION
    uint32_t urand(const uint32_t& range);

    //Draw a equidistributed uint32_t in the range [start,end)
    KOKKOS_INLINE_FUNCTION
    uint32_t urand(const uint32_t& start, const uint32_t& end );
    }

For the selected 32-bit unsigned integer type, three range options are shown: [0,MAX_URAND), [0,range) and [start,end). The first, and default, option selects unsigned integers over max possible range for that data type. The defined value of MAX_URAND is shown above as an enum. (And also shown is maX_URAND for a 64-bit unsigned integer.) The latter two options cover a user-defined range of integers.

More for other data types: Scalar, uint64_t, int, int32_t, int64_t, float, double; also normal distribution and a View-fill option for the [0, range) and [start, end) options.