mrg32k3a#

The combined multiple recursive pseudorandom number generator MRG32k3a.

Description

MRG32k3a engine is a 32-bit combined multiple recursive generator with two components of order 3 [L’Ecuyer99a]. MRG32k3a combined generator meets the requirements for modern RNGs, such as good multidimensional uniformity, or a long period ( $p \approx 2^{191}$ ).

Generation algorithm

$x_{n} = a_{11} x_{n - 1} + a_{12} x_{n - 2} + a_{13} x_{n - 3} (m o d m_{1})$

$y_{n} = a_{21} y_{n - 1} + a_{22} y_{n - 2} + a_{23} (m o d m_{2})$

$z_{n} = x_{n} - y_{n} (m o d m_{1})$

$u_{n} = z_{n} / m_{1}$

$a_{11} = 0, a_{12} = 1403580, a_{13} = - 810728, m_{1} = 2^{32} - 209$

$a_{21} = 527612, a_{22} = 0, a_{23} = - 1370589, m_{2} = 2^{32} - 22853$

class mrg32k3a#

Syntax

namespace oneapi::math::rng::device {
  template<std::int32_t VecSize = 1>
  class mrg32k3a {
  public:
    static constexpr std::uint32_t default_seed = 1;
    static constexpr std::int32_t vec_size = VecSize;

    mrg32k3a();
    mrg32k3a(std::uint32_t seed, std::uint64_t offset = 0);
    mrg32k3a(std::initializer_list<std::uint32_t> seed, std::uint64_t offset = 0);
    mrg32k3a(std::uint32_t seed, std::initializer_list<std::uint64_t> offset);
    mrg32k3a(std::initializer_list<std::uint32_t> seed, std::initializer_list<std::uint64_t> offset);
  };
}

Class Template Parameters

VecSize: Describes the size of vector which will be produced by generate function by this engine. VecSize values may be 1, 2, 3, 4, 8, 16 as sycl::vec class size. By default VecSize = 1, for this case, a single random number is returned by the generate function.

Class Members

Routine	Description
mrg32k3a()	Default constructor
mrg32k3a(std::uint32_t seed, std::uint64_t offset = 0)	Constructor for common seed initialization of the engine and common number of skipped elements
mrg32k3a(std::initializer_list<std::uint32_t> seed, std::uint64_t offset = 0)	Constructor for extended seed initialization of the engine and common number of skipped elements
mrg32k3a(std::uint32_t seed, std::initializer_list<std::uint64_t> offset)	Constructor for common seed initialization of the engine and extended number of skipped elements
mrg32k3a(std::initializer_list<std::uint32_t> seed, std::initializer_list<std::uint64_t> offset)	Constructor for extended seed initialization of the engine and extended number of skipped elements

Constructors

mrg32k3a::mrg32k3a()

mrg32k3a::mrg32k3a(std::uint32_t seed, std::uint64_t offset = 0)

Input Parameters

seed

The initial conditions of the generator state, assume if $n = 0 : x_{- 3} = x_{- 2} = x_{- 1} = y_{- 3} = y_{- 2} = y_{- 1} = 1$

if $n = 1 : x_{- 3} = s e e d [0] m o d m_{1}, x_{- 2} = x_{- 1} = y_{- 3} = y_{- 2} = y_{- 1} = 1$

if $n = 2 : x_{- 3} = s e e d [0] m o d m_{1}, x_{- 2} = s e e d [1] m o d m_{1}, x_{- 1} = y_{- 3} = y_{- 2} = y_{- 1} = 1$

if $n = 3 : x_{- 3} = s e e d [0] m o d m_{1}, x_{- 2} = s e e d [1] m o d m_{1}, x_{- 1} = s e e d [2] m o d m_{1}$

$y_{- 3} = y_{- 2} = y_{- 1} = 1$

if $n = 4 : x_{- 3} = s e e d [0] m o d m_{1}, x_{- 2} = s e e d [1] m o d m_{1}, x_{- 1} = s e e d [2] m o d m_{1}$

$y_{- 3} = s e e d [3] m o d m_{2}, y_{- 2} = y_{- 1} = 1$

if $n = 5 : x_{- 3} = s e e d [0] m o d m_{1}, x_{- 2} = s e e d [1] m o d m_{1}, x_{- 1} = s e e d [2] m o d m_{1}$

$y_{- 3} = s e e d [3] m o d m_{2}, y_{- 2} = s e e d [4] m o d m_{2}, y_{- 1} = 1$

if $n ⩾ 6 : x_{- 3} = s e e d [0] m o d m_{1}, x_{- 2} = s e e d [1] m o d m_{1}, x_{- 1} = s e e d [2] m o d m_{1}$

$y_{- 3} = s e e d [3] m o d m_{2}, y_{- 2} = s e e d [4] m o d m_{2}, y_{- 1} = s e e d [5] m o d m_{2}$

if the values prove to be $x_{- 3} = x_{- 2} = x_{- 1} = 0$ , assume $x_{- 3} = 1$

if the values prove to be $y_{- 3} = y_{- 2} = y_{- 1} = 0$ , assume $y_{- 3} = 1$ .

offset

Number of skipped elements.

mrg32k3a::mrg32k3a(std::initializer_list<std::uint32_t> seed, std::uint64_t offset = 0)

Input Parameters

seed: Initial conditions of the engine state.
offset: Number of skipped elements.

mrg32k3a::mrg32k3a(std::uint32_t seed, std::initializer_list<std::uint64_t> offset)

Input Parameters

seed

The initial conditions of the generator state, assume if $n = 0 : x_{- 3} = x_{- 2} = x_{- 1} = y_{- 3} = y_{- 2} = y_{- 1} = 1$

if $n = 1 : x_{- 3} = s e e d [0] m o d m_{1}, x_{- 2} = x_{- 1} = y_{- 3} = y_{- 2} = y_{- 1} = 1$

if $n = 2 : x_{- 3} = s e e d [0] m o d m_{1}, x_{- 2} = s e e d [1] m o d m_{1}, x_{- 1} = y_{- 3} = y_{- 2} = y_{- 1} = 1$

if $n = 3 : x_{- 3} = s e e d [0] m o d m_{1}, x_{- 2} = s e e d [1] m o d m_{1}, x_{- 1} = s e e d [2] m o d m_{1}$

$y_{- 3} = y_{- 2} = y_{- 1} = 1$

if $n = 4 : x_{- 3} = s e e d [0] m o d m_{1}, x_{- 2} = s e e d [1] m o d m_{1}, x_{- 1} = s e e d [2] m o d m_{1}$

$y_{- 3} = s e e d [3] m o d m_{2}, y_{- 2} = y_{- 1} = 1$

if $n = 5 : x_{- 3} = s e e d [0] m o d m_{1}, x_{- 2} = s e e d [1] m o d m_{1}, x_{- 1} = s e e d [2] m o d m_{1}$

$y_{- 3} = s e e d [3] m o d m_{2}, y_{- 2} = s e e d [4] m o d m_{2}, y_{- 1} = 1$

if $n ⩾ 6 : x_{- 3} = s e e d [0] m o d m_{1}, x_{- 2} = s e e d [1] m o d m_{1}, x_{- 1} = s e e d [2] m o d m_{1}$

$y_{- 3} = s e e d [3] m o d m_{2}, y_{- 2} = s e e d [4] m o d m_{2}, y_{- 1} = s e e d [5] m o d m_{2}$

if the values prove to be $x_{- 3} = x_{- 2} = x_{- 1} = 0$ , assume $x_{- 3} = 1$

if the values prove to be $y_{- 3} = y_{- 2} = y_{- 1} = 0$ , assume $y_{- 3} = 1$ .

offset

Number of skipped elements. Offset is calculated as: num_to_skip [0]+ num_to_skip [1]*2⁶⁴ + num_to_skip [2]* 2¹²⁸ + … + num_to_skip [n-1]*2⁶⁴ *(n-1).

mrg32k3a::mrg32k3a(std::initializer_list<std::uint32_t> seed, std::initializer_list<std::uint64_t> offset)

Input Parameters

seed: Initial conditions of the engine state.
offset: Number of skipped elements. Offset is calculated as: num_to_skip [0]+ num_to_skip [1]*2⁶⁴ + num_to_skip [2]* 2¹²⁸ + … + num_to_skip [n-1]*2⁶⁴ *(n-1).

Parent topic: Device Engines (Basic Random Number Generators)

mrg32k3a

Contents

mrg32k3a#

class mrg32k3a#